Without regularities embodied in the laws of physics we would be unable to make sense of physical events; without regularities in the laws of nature we would be unable to discover the laws themselves.

Emmy Noether is hardly a household name.

She’ll probably never be an answer on Who Wants to Be a Millionaire? or a question on Jeopardy. She rarely comes up in conversation, even conversations where people talk about Einstein or Feynman or Marie Curie. Yet Emmy Noether was one of the great mathematicians of the twentieth century, regarded at the time of her death in 1935 as perhaps the greatest woman mathematician in history.

During her career in Germany and the last one and a half years of her life at Bryn Mawr College in Pennsylvania, she made major contributions to various fields of mathematics, particularly in advanced

forms of algebra. She also showed that some of physics’ most sacred laws are not accidents of nature, but rather are strict requirements— imposed by fundamental symmetries in space and time.

Take the law of conservation of energy, for example. It was discovered in the middle of the nineteenth century after a considerable amount of toil and trouble. No theorist prediscovered it. It seemed to be simply a lesson taught by observation—energy could be neither created nor destroyed. However much energy you started with, you ended with. Energy, in physics lingo, is “conserved.”

In 1918, though, Emmy Noether showed that conservation of energy, and other important conservation laws, could have been deduced from purely mathematical considerations—assuming that moving through space and time did not change the laws of nature. In other words, she proved that the universe has something deep in common with snowflakes.

Snowflakes are exquisite examples of symmetry. You don’t need to be a scientist to see it. Each snowflake exhibits six elaborately designed yet identical arms. Turn the flake by 60 degrees once, then again, then again. From each angle the appearance of the snowflake remains the same. And that is the essence of symmetry—change without change. A circle is symmetric because it looks the same upside down or flipped over. A baseball park is symmetric if the distances to the left-field wall are equal to the corresponding distances to right field; switching left with right leaves the distances to the fences the same. A symmetric face looks the same when viewed in a mirror.

To the artist, the architect, or the biologist, symmetry shines through the messy aspects of reality to illuminate an underlying beauty. Mathematicians regard symmetry with similar awe. And to physicists, symmetry is at the very heart of using mathematics to understand nature.

“In modern physics,” write Leon Lederman and fellow Fermilab physicist Chris Hill, “symmetry may be the most crucial concept of

all. . . . All of the fundamental forces in nature are unified under one elegant symmetry principle. . . . Symmetry controls physics in a most profound way, and this was the ultimate lesson of the twentieth century.”¹

Indeed, symmetry is often the critical consideration in instances of prediscovery. Dirac’s prediscovery of antimatter relied on the symmetry between positive and negative energy. The possibility of mirror matter hinges on nature’s respecting, at some level, the symmetry between left and right. Symmetry’s success at revealing nature’s secrets in the past has led many physicists to believe that it will also map the way to the future.

Specifically, many scientists foresee that the future will bring proof of a special type of symmetry that they consider to possess uncommon beauty. They call it SUSY, for the Greek goddess of beautiful symmetry. (Just kidding. SUSY stands for supersymmetry. The beauty is not in a marble sculpture but in mathematical equations.)

Supersymmetry comprises a mathematical framework that may spell out the secrets of nature’s particles and forces. If SUSY proves true, the universe could be full of a strange form of matter so far never encountered. Exploiting the possibilities latent in SUSY, physicists have identified numerous potential prediscoveries that might resolve the dark matter mystery while solving other problems as well (or perhaps creating new ones).

So far, the evidence for SUSY is slim. The situation is much as it was in June 1999, when I encountered Neal Lane, President Clinton’s science adviser, during a supersymmetry conference at Fermilab. I had just heard a presentation by Jianming Qian on the latest experimental search for SUSY at Fermilab, and Lane asked me what his conclusions had been.

“There is no experimental evidence for supersymmetry,” I told Lane. And he scowled. “However,” I added, “he also said there is no experimental evidence against supersymmetry, either.” And Lane smiled. “That means we need to do more research,” he said.²

A few hints have been interpreted as signs of SUSY’s existence. In the early 1990s, experiments at CERN (the acronym for the European Organization for Nuclear Research, located outside of Geneva, Switzerland) indicated that the strengths of the various fundamental forces, extrapolated to what they would be at very high energies, did not seem to meet at a common point where expected. Corrections for the existence of SUSY would explain the discrepancy. Early in 2001, scientists at Brookhaven National Laboratory reported new measurements on the behavior of muons in magnetic fields. Those results also suggested support for SUSY, although later analyses called that conclusion into question.

In the absence of strong evidence either way, physicists’ faith in SUSY may seem somewhat surprising. But the time and money that have been poured into SUSY searches simply reflect the incredible successes achieved in the twentieth century by following the path of symmetry. Two people stand out among the pioneers of that path— the mathematician Noether, and one of the century’s premier physicists, Eugene Wigner.

Emmy Noether came first, but she’s by far less well known than Wigner. In part that’s because most of her career was devoted to pure mathematics, with little application to physics. Yet no doubt part of her obscurity reflects the difficulty women had pursuing academic careers in those days. She was born in 1882 in Erlangen, a small town in Bavaria. Her father taught math at the university there, but women were not allowed to enroll. It was possible to audit classes, with the

assent of the professor, and Emmy obtained permission from some of her father’s friends.

She had planned to be a teacher of foreign languages—French and English—but after auditing some math classes she changed her mind. And then Erlangen changed its policies, permitting women to earn degrees, so in 1904 Emmy enrolled as a math student and graduated with honors in 1907.

From then until 1915 she worked at the university without pay, often filling in for her father as failing health impaired his ability to lecture. During that time Emmy met David Hilbert, considered by many to be the outstanding mathematician of his day. He asked her to come to the university at Göttingen to serve as his assistant.

Soon it was clear that Emmy deserved a faculty position, and she had the support of the math department. But faculty members from other disciplines objected. If you put her on the faculty, they argued, she might then someday become a professor and therefore a member of the university senate, where women were not allowed.

Hilbert was annoyed. “I do not see that the sex of the candidate is an argument against her admission,” he declared. “After all, the senate is not a public bathhouse.”³

Noether was initially denied faculty status, but through a compromise she was allowed to lecture, in courses offered under Hilbert’s name. And without pay, of course. Only after World War I did the German authorities loosen up enough to allow Noether to lecture officially. In any event, Noether’s presence at Göttingen was a great help to Hilbert. In particular, he called on her to work on a problem he had encountered with Einstein’s theory of general relativity, the theory that explained gravity.

Noether had arrived at Göttingen shortly before Einstein visited in the summer of 1915 to deliver a series of lectures on his new theory. (It wasn’t quite finished at the time; not until November did Einstein add the final touches and figure out the proper form of the key equa-

tions.) So Noether was sufficiently familiar with Einstein’s theory that Hilbert sought her input on a tricky question involving the conservation of energy.

Einstein’s 1905 theory of special relativity posed no problem for energy conservation. In fact, it was easy to show that if you monitored any specific volume of space, the amount of energy flowing outward across that volume’s boundary would exactly equal the loss of energy inside the volume. To physicists, that fact said that energy was “conserved locally.”

But in Einstein’s general theory of relativity, which incorporated gravity, the proof of local energy conservation no longer worked. This deeply concerned Hilbert. Violating energy conservation was considered a pretty serious crime. So he asked Noether to investigate the mathematics of general relativity to try to figure out what was going on.

Noether succeeded. She showed that while energy was not conserved locally, it was conserved globally—in other words, if you considered a big enough region of space, everything was fine. Energy conservation held. It was just that in smaller regions, looked at from different points of view, the measurement of energy content could differ depending on that point of view.⁴

Noether’s solution came with a bonus. In working out the math she found that the key to energy conservation was an important symmetry in nature. And in fact, she found, any conservation law owes its power to a symmetry principle.⁵ Thus she delivered to the physics world a deep insight into what symmetry really means. Many laws of nature are not merely arbitrary conditions imposed on how things must work, but reflections of profound properties of the universe captured in the symmetries of space and time.

One such symmetry ensures that funny things don’t happen merely by a change of direction, a fact expressed by the law of conservation of angular momentum. Angular momentum is basically a

measure of the quantity of spin, based on how much mass is spinning, how rapidly, over what distance. The textbook example of angular momentum conservation is the spinning ice skater. By pulling both arms in, the skater brings some mass closer to the center of the spinning. As the distance from the center is reduced, the skater’s spinning speed must increase to keep the quantity of spin the same.

Besides promoting higher scores in figure skating, this law figures prominently in everything from the properties of subatomic particles to the behavior of pulsars in outer space. And it’s all a consequence of spatial symmetry with respect to direction—in other words, space doesn’t care which way you point.

Think back to the days before laser pointers and imagine one of those long sticks that teachers used to use to point at the blackboard. (Let’s make it a wooden one, not the collapsible metallic kind.) You can be pretty sure that no matter which direction in space the teacher aimed the pointer, the stick stayed the same length. To the pointer, or anything else, it doesn’t matter what direction in space you’re pointing. Space is the same in all directions. The technical way to say it is that space is symmetric with respect to rotation. Noether showed that rotation symmetry guarantees that the law of conservation of angular momentum will hold true.

Noether also proved that ordinary (linear) momentum is also conserved by virtue of another symmetry of space, symmetry with respect to displacement—that is, movement from one point in space to another. In other words, any one point in space is just the same as any other point. It doesn’t matter where on Earth, or in the universe, you do your experiment; the laws of nature will look the same.

In a similar way, if time is symmetric—one point in time is intrinsically no different from another—then energy must be conserved. So not only does it make no difference where you do your experiment, it makes no difference when you do your experiment. Thus, decades after experimenters discovered the law of conservation of

energy, Emmy Noether showed that the experiments wouldn’t have been necessary if those men had known more math. Conservation of energy wasn’t prediscovered, but it could have been.

Physicists may have been behind the mathematicians in appreciating symmetry, but soon learned to take advantage of what the math revealed. One of the first to realize the importance of exploiting symmetry for physics was the Hungarian genius Eugene Wigner.

Born in Budapest in 1902, Wigner went to secondary school there with the slightly younger John von Neumann, who was destined to become one of the twentieth century’s great mathematicians. Wigner also enjoyed math—and physics—but his father insisted on a practical education, so Eugene attended a technical school in Berlin to learn chemical engineering. While in Berlin, though, Wigner found time to sit in on many physics seminars at the university. In 1925, he went home to Budapest to work in his father’s leather factory. But soon the offer of a physics research job came from Berlin, so Wigner seized the opportunity to become a scientist.

Back in Berlin, Wigner threw himself into understanding the mathematics of symmetry. On the advice of von Neumann, he mastered what mathematicians call group theory—the math on which much of modern physics has been built.

Group theory is the sort of topic that makes me stop reading physics books. It seems so abstract, so obscure, and so complex that it always seemed to me impossible to simplify. Ultimately, though, I decided it was unavoidable. And guess what—it turns out not to be so bad after all. In fact, the basics of group theory are pretty simple. You just need

to know a very short list of rules of what makes a group. It’s not much more elaborate than having a vocalist, drummer, and guitarist.

First of all, you need to know that a group is just a set of things, which is pretty much in line with its common definition. In a mathematical group, the “things” might be objects, or numbers, or operations—like rotations. The key feature of a group is that its members are governed by rules that relate the members to one another in specific ways. Here they are:

Rule 1: You can combine two members of the group to produce another member of the group. (Example: 2 and 3 are members of the group; they can be combined by a procedure called multiplication that yields 6, and 6 is also a member of the group.)

Rule 2: When combining three members, you can combine the first two and then the third, or combine the second two first. (In other words, combining 2, 3, and 5 by multiplication gives the same answer if you first multiply 2 times 3—to get 6—and then multiply by 5, or if you first multiply 3 times 5—to get 15—and then multiply by 2. The answer is 30 either way.)

Rule 3: You can do something that changes nothing. (In multiplication, you can multiply any member of the group by 1, and the answer is the same member you started with. This is called the identity rule.)

Rule 4: You can undo whatever you’ve done. (This is called the inverse rule. You can undo the multiplication of 3 by 5 (15) if you multiply again by the inverse of 5, 1 over 5—or one-fifth. One-fifth of 15 is 3, the original member.)

Remember, groups can involve things other than numbers. Operations such as rotating geometrical figures work the same way, and in such cases the groups are referred to as symmetry groups.

Symmetry groups can get pretty complicated mathematically,

but the basic idea is the same as the symmetry of snowflakes. Remember, you can rotate a snowflake by 60 degrees and it looks the same. Rotating it by 120 degrees also leaves it looking the same. So does rotating it by 180 degrees. So you can see that these rotations make up part of a group—a combination of 60 and 120 degree rotations, both members of the symmetry group, produce a 180 degree rotation, also a member of the group (Rule 1). And you can easily check to see that you could combine the rotations in different ways to satisfy Rule 2.

You can also rotate by 360 degrees, which not only leaves the snowflake looking the same, but also returns all the arms to the original positions. In other words, rotating by 360 degrees is the same as doing nothing (Rule 3). Finally, you can undo what you’ve done just by rotating a negative number of degrees (counterclockwise instead of clockwise) to satisfy rule 4.

Of course, not everything in nature is a snowflake. Different objects possess different kinds of symmetries, and therefore manipulations of those objects are governed by different symmetry groups.

Wigner found that a major key to making progress in physics was figuring out which symmetry groups describe nature. He was able to show how the properties of matter’s basic particles could be related to certain sets of symmetry operations. Symmetry groups, he determined, captured patterns in the laws of nature that described how elementary particles and forces interact. Instead of symmetries of rotations, elementary particles obeyed symmetries of interactions. Those interactions are governed by forces that can be described mathematically by symmetry groups.

Wigner’s work made it clear that symmetry groups captured something profound about the construction of nature. The laws of nature are useful because they express regularities in the events and processes in the universe—processes that seem irregular and complex because the laws act on diverse initial conditions. And then when

you look at all the laws, you see regularities in them, too. While laws summarized the regularities in natural processes, Wigner emphasized, symmetry principles summarized the regularities within the laws.

With this insight, Wigner anticipated the principles that laid the foundation for progress in understanding particles and forces. Over the decades that progress produced the Standard Model of particle physics, the symmetry-based equations that describe all the matter particles and force-transmitting particles in nature.

By the 1970s, the essential components of the Standard Model were in place. It grouped all matter into two main types of particles:

quarks, which make up the particles of the atomic nucleus; and leptons, which include electrons and their subatomic cousins. Forces are transmitted by particles called bosons.

As it turns out, the Standard Model is based on a peculiar type of symmetry, known as gauge symmetry. Gauge symmetry is even harder to explain than groups. It has to do with how to reconcile different ways of measuring (gauging) nature. Fortunately, you don’t need to learn the intricacies of gauge symmetry to get the basic idea. Remember, symmetry means that when something is changed, something else remains the same. In gauge symmetries, what changes is the gauge, or the system of measurement.

Gauge symmetry is a little like exchanging money when you vacation in Europe; you have to change the way of measuring money but presumably you get equal value in the exchange (corresponding to the laws of nature staying the same when you convert from feet and inches to meters and centimeters.) But it turns out that preserving gauge symmetries requires a mechanism for managing the conversion—something needs to tell the bankers what the exchange rate is. Nature’s way of doing this is what’s commonly called “force.” The forces in the Standard Model are nature’s way of enforcing gauge symmetry—so the laws stay the same no matter what you are doing or what units of measurement you are using.⁶

Einstein’s general theory of relativity, it turns out, is a gauge theory, and the force it requires is gravity. Its essential feature is the ability to describe the laws of nature in the same way for any observer in motion. Another way of saying it is that the laws must look the same no matter what kind of a map you set up to specify the location of moving objects and observers. Such maps are known as coordinate systems, kind of like the system of latitude and longitude

used for locating positions on the surface of Earth. In general relativity, the coordinate system describes locations throughout all of space and time.

There is no reason, of course, why any two observers should use the same system of coordinates. My sister might want to use a coordinate system centered on Avon, Ohio. An astronomer might choose the sun. Some gaseous-cloud life form orbiting Proxima Centauri might prefer to use the center of the Milky Way galaxy. If these beings wanted to communicate, they would have to transform measurements from one coordinate system to another. General relativity guarantees that such a change in gauge leaves the laws of nature the same—that is, it encompasses a gauge symmetry.

As Edward Witten has explained to me, this feature of general relativity essentially answers the question of why gravity exists. For the laws of nature to remain the same no matter how you’re moving and what coordinate system you adopt, some force must be at work to convey the connection between one viewpoint and another. In general relativity, gravity is that force. Other gauge-symmetric forces govern the fundamental particles of nature. For the laws describing the fundamental particles to remain the same for everybody, forces must exist.

The first major work to apply gauge principles to particles was a historic paper published in 1954 by Robert Mills and Chen Ning Yang (the same Yang who collaborated with Lee on parity violation two years later). Following the gauge trail blazed by Yang and Mills, physicists produced the Standard Model of particle physics by the mid-1970s. By far the biggest breakthrough during that time was the use of symmetry principles to unify the math describing electromagnetism and the weak nuclear force (responsible for some forms of radioactivity)—and in the process prediscovering some unknown subatomic particles.

During the 1960s, symmetry principles were theorists’ chief guide

to the proliferation of subatomic particles discovered in the 1950s. “If you knew that the laws of nature looked the same from different points of view, you could make predictions that could be tested,” Steven Weinberg, of the University of Texas, remarked in a 1997 interview. “Even if you didn’t understand the forces involved, you didn’t know where the particles came from, you could make predictions. And sometimes they would be right.”

When the predictions went wrong, theorists could try out new symmetry principles to see which ones nature obeyed. “We learned a lot about what symmetry principles governed the laws of nature,” Weinberg recalled.

But symmetry was not simple enough to reveal all the answers instantly. Many of nature’s symmetries were not quite exact. It seemed that nature liked perfect symmetry in principle, but imperfect symmetry in practice. In the language of the physicists, symmetries were broken.

“A great breakthrough was the idea of broken symmetry,” Weinberg told me. The concept originated in studies of solid-state physics, describing such phenomena as magnetism and superconductivity. The underlying idea is simple enough—something happens in the course of events to mask the underlying sameness that symmetry preserves. Remember, your face in a mirror looks pretty much like you look to other people. But if you part your hair on one side or the other, the images become distinguishable—the symmetry is broken. Something similar happens to a perfectly symmetric cloud of steam as it cools. Water droplets begin to form and then sooner or later you’ll also get some ice—three forms of the same substance, breaking the symmetry of the original steam cloud.

It’s the same with a magnet. Heat a magnet up, and at some temperature it will lose its magnetism. In other words, at high temperatures the magnet possesses a symmetry; particles within it are oriented in no special direction. But cool the magnet down again and

the particles will line up along an axis, pointing through the magnet’s poles. The magnet now singles out one direction as special—it’s no longer perfectly symmetric. The symmetry has been broken.

Weinberg, in his Nobel Prize lecture, said he “fell in love” with the idea of broken symmetry. He soon figured out how to apply it to the problem of subatomic particles. “The idea was that you could have a physical system that is governed by laws that have a high degree of symmetry, and yet the symmetry won’t be apparent in the phenomena, the particles,” Weinberg explained to me. “To put it a little bit more mathematically, the equations have a symmetry, the solutions of the equations don’t have that symmetry.”⁷

In 1967, Weinberg saw that the weak nuclear force could be described mathematically the same way as electromagnetism. In other words, an underlying symmetry united the two forces, a symmetry that is broken under current conditions in the universe.

Working out the math, Weinberg found solutions corresponding to four force-carrying particles. One was massless and seemed obviously to be the photon, the particle that transmits electromagnetic force. But the other three particles were unknown at the time. Those particles turned out to be the carrier particles for the weak nuclear force. One should have a negative charge, one a positive charge, and one no charge at all. The charged ones were called W bosons and the neutral one became known as the Z boson, or Z-zero. Exactly those three particles were discovered at CERN in 1983, once again establishing the power of mathematics to produce prediscoveries. (Weinberg had already won the Nobel Prize by then, thanks to indirect evidence persuading everyone that the particles had to exist. He shared the 1979 Nobel with Abdus Salam, who had published similar conclusions at about the same time as Weinberg, and Sheldon Glashow, another contributor to the physics of the Standard Model.)

So in the Standard Model, electromagnetic forces become just one form of a more fundamental “electroweak” force. The massless

photon transmits electromagnetism. But the particles transmitting the weak force, the W and the Z, are very massive. At some point in the history of the universe, the W and Z and photon all weighed the same, but then that symmetry was broken. Even earlier, scientists surmise, all the forces were equal in strength, and the particles transmitting them were all equal in mass. But as the universe cooled, the symmetries were broken to produce the four different-strength forces in the universe today, much in the way cooling steam produces three different versions of H₂O.

By the mid-1970s the Standard Model had been pretty much pieced together, with the strong nuclear force joining the electroweak. Then came the job of testing the model, a process requiring another 20 years or so. By the end of the twentieth century, the experimental evidence favoring the Standard Model was overwhelming. Frank Wilczek, a physicist at MIT, proclaimed that the name should be changed. Henceforth, he proclaimed, the “Standard Model” should be known as the “Theory of Matter.”⁸

To be sure, one piece of the puzzle remained missing. The symmetries of the Standard Model could explain the existence of many subatomic particles, but not why they had mass. During the 1960s, several physicists noticed that some unknown field permeating space might solve that problem. Particles interacting with that field would seem to acquire mass, in much the way a marble trying to pass through molasses seems to acquire additional inertia. Various species of particle would acquire different masses depending on how strongly they interacted with this invisible field.

One of the physicists who figured this out, Peter Higgs of the University of Edinburgh, realized that if such a field existed, you should be able to make particles out of it. Such a particle, now known as the Higgs boson, is widely (if tritely) regarded by many as the Holy Grail of modern physics. It is a potential prediscovery that most physicists fervently, almost desperately, believe will happen. Near

the end of 2000, experimenters at CERN reported a hint of the Higgs—just before the particle accelerator there was shut down to make way for a new, more powerful accelerator. So the race for the Higgs is now under a yellow flag, possibly providing an opportunity for SUSY to be found first.

At the same time the theory of matter was being developed, another approach rooted in notions of symmetry had been following a parallel path. That path’s destination, many physicists hoped, would be the supersymmetric world beyond the Standard Model, the place with answers to the questions that the Standard Model couldn’t answer.

Edward Witten, one of the world’s top SUSY experts, explains supersymmetry as the quantum version of Einstein’s relativity. “I’ve often thought about how supersymmetry can be explained to the public,” Witten told me during one of my visits to Princeton. “Maybe there would be more enthusiasm from the public for particle physics if we could make supersymmetry sound as exciting as it is. Supersymmetry is really the modern version of relativity.”

Einstein’s theories of relativity seized on the realization that moving through space also means moving through time, and the secret to finding the underlying symmetry is considering space and time combined into “spacetime.” It was the mathematician Hermann Minkowski who showed, soon after Einstein’s original relativity papers were published, that the theory revealed important symmetries in time and space. A few years later Einstein himself showed how the special theory, limited to uniform motion, could be “generalized” to incorporate accelerated motion. And since falling in a gravitational field is, in fact, accelerated motion, Einstein’s general theory of rela-

tivity was able to explain gravity as the result of the way that matter distorted spacetime.

But relativity is a classical theory. It doesn’t include (and has resisted the incorporation of) the quantum features of reality that rule the realm of the atom. Nowadays, physicists realize that spacetime must have its quantum aspects, and supersymmetry may explain them. As Witten put it, “Supersymmetry is the beginning of the quantum story of spacetime. . . . It’s a new symmetry involving new dimensions where you can’t explain either the dimensions or the symmetry unless you know about quantum mechanics.”⁹

Supersymmetry’s new dimensions are utterly unlike the ordinary dimensions of space that you can move around in. It’s not even that SUSY’s dimensions are just very small so that you could only move around in them if you were a subatomic-sized flea. SUSY’s “quantum dimensions” are smaller than small—they have no size at all. You couldn’t move around in them no matter how small you were.

But SUSY’s strange new dimensions bring with them one tangible physical effect—a new subatomic partner for every kind of particle now known. Because “supersymmetric partner particle” is a mouthful, most physicists call them superpartners. Or sparticles. I like to call them supermatter.

In Einstein’s relativity, the world is still the same when you interchange space and time. In supersymmetry, the world is still the same when you interchange matter with force. It’s this deep symmetry between matter and force that gives SUSY the power to create new particles beyond those found in the Standard Model.

Basically, the Standard Model describes two kinds of fundamental particles—roughly, particles of matter and particles that transmit forces. An electron is a matter particle; a photon is a force particle,

responsible for electromagnetic interactions. Fundamental matter particles are called fermions; fundamental force particles are called bosons. The defining feature of a boson or fermion is its spin; some composite matter particles are actually bosons. To the ordinary (bosonic) dimensions of space and time, SUSY adds “fermionic,” or what Witten likes to call “quantum,” dimensions.

SUSY’s assertion of force-matter symmetry suggests that in some way, force and matter are just two aspects of the same thing. If so, then it ought to be possible to devise a mathematical framework describing a partner force particle for every matter particle, and vice versa. It’s pretty much the same reasoning that gives every particle an antiparticle and every particle a mirror partner. And that’s just what the pioneers of SUSY did. They worked out the math for a universe containing supersymmetric partner particles for every matter and force particle.

It’s interesting that the early investigators had begun to develop SUSY math even before physicists had put the pieces of the Standard Model together. SUSY was born around 1970, a few years before the Standard Model really took shape. The first SUSY steps came in Russia (in those days, the Soviet Union). Evgeny Likhtman, working with Yuri Golfand at the Lebedev Physical Institute, produced the first mathematical expression for force-matter symmetry and speculated whether the equations might correspond to new particles in nature. At about the same time, Pierre Ramond (now at the University of Florida) uncovered some mathematical insights creating a stream of thought that merged with later SUSY theories.¹¹

Then came an important paper in 1973 from Julius Wess and Bruno Zumino, in which the idea of superpartner particles first clearly appeared. The term supersymmetry itself apparently first showed up in a 1974 paper by Abdus Salam and John Strathdee.¹⁰ But the full implications appeared in sharper detail in 1981, when Savas Dimopoulos and Howard Georgi produced a paper laying out the SUSY version

of the Standard Model, with the whole shebang of superparticles. SUSY had been unveiled, with the shocking implication that perhaps physicists had been playing around with only half the particles that nature possessed.

Dimopoulos, now at Stanford, is one of the most exuberant of theoretical physicists, a fast and animated talker, clearly passionate about every sentence he utters. It’s not hard to get him going. At dinner one evening, during a conference where he had been presenting newer work, I asked him about the original proposal of the SUSY world.

“People ask me how did you dare propose the supersymmetric standard model when it doubled the number of particles in the universe? It predicted particles for which we have no evidence,” he said. “But I didn’t find it that revolutionary.”

The reason, he explained, was his familiarity with the history of prediscovery. “I knew that twice in history this had happened before,” he said. “First with Dirac, predicting antimatter. Then with Pauli, predicting spin.”¹² Indeed, Dirac’s prediscovery of antimatter was no less ambitious than that of supersymmetry—for every known particle there would be an antiparticle, another case of doubling the census count in the subatomic universe. Pauli’s accomplishment was similar, if not quite as dramatic. Electrons had previously been considered all identical; Pauli identified a distinction—some spin in one direction, others spin the opposite direction. In a sense, they could be thought of as different particles, too.

There was one big difference, Dimopoulos acknowledged. The symmetries exploited by Pauli and Dirac were exact. The mass of an antiparticle, for example, would be precisely the same as that of the ordinary particle. But superpartners could not be identical in mass. They had to be much more massive; otherwise, they would have been discovered already.

Thus Dimopoulos and Georgi had to propose that SUSY was not

perfect after all, but—at least as it appeared in nature—had to be a “broken” symmetry, like the symmetry describing the electroweak force discovered by Weinberg and Salam. Applying the idea of symmetry breaking to SUSY explained why the supermatter partners had not yet been discovered. They must be much more massive than their partners, and so it would take very high energy to produce them, beyond the power of the best atom smashers available.

For the last two decades, mathematicians and physicists have spent countless hours developing variations of SUSY mathematics, seeking insights that would lead to explanations for known phenomena and solutions to subatomic and cosmological problems. In fact, working out the intricacies of SUSY math seems to occupy every waking moment of dozens of physicists around the world. Out of all that effort come numerous surmises about things the world might possess if SUSY turns out to be true. In other words, SUSY is a fertile field for cultivating prediscoveries.

The most likely SUSY discovery, of course, would be one of the superpartner particles. SUSY scientists are well prepared for this discovery, as names for the new particles have already been devised. For matter particles, the naming rules are simple—put an s in front of the name. Thus the superpartner of the electron would be called a selectron; quarks’ partners would be squarks. For force particles (bosons), add -ino to the basic name—the photon’s superpartner goes by photino, for example.

Naming the particles was the easy part. Finding them will be harder. Not only must the superparticles be much more massive than their ordinary counterparts, and therefore hard to make, they would also be difficult to detect. Despite their mass, supermatter particles would be very reluctant to interact with ordinary matter, entering

only into reactions where the weak nuclear force is involved. These timid, weakly interacting massive particles are known as WIMPs.

SUSY says WIMPs of all sorts should exist—one type of WIMP for every known type of particle. Right after the big bang, WIMPs should have been abundant. But they would also almost all be unstable, decaying into lighter particles, so most of the WIMPs in the universe would be long gone by now. But one of them has to be the lightest of all, and it should still be around, in massive quantities, if SUSY is true.

Sometimes physicists call it the lightest supersymmetric particle, or LSP. Since it would certainly have no electrical charge, some theorists think it is probably the photon’s superpartner, the photino. On the other hand, some physicists prefer to refer to the LSP as the neutralino, because it might actually be a quantum mixture of different neutral superparticles. (In quantum physics, you cannot specify a particle’s identity with absolute certainty. The equations allow a given particle in flight to possess properties of different related species simultaneously. When you capture it, it adopts one identity.)

In any event, WIMPs may very well be abundant in the universe, flying freely through space, a few passing through the very room you’re sitting in at the moment. Since they interact weakly, though, you are in no danger—although physicists seeking a sign of the WIMPs might be willing to risk a little danger to improve the chances of finding one.

Actually, some searchers think they have already succeeded.

You might remember from Chapter 2 (this is only Chapter 3, after all) that astronomers infer the existence of a lot of mass in the outer regions, or halos, of galaxies. Some of it seems to be in the form of massive compact halo objects, known as MACHOs. But not all of it. Most experts believe that at least some of the dark matter comes in the form of WIMPs.

In fact, at the Texas Symposium for Relativistic Astrophysics in

Paris in 1998, it seemed that the WIMPs were about to kick the H out of the MACHOs. At that meeting Katherine Freese, of the University of Michigan, suggested that the sightings of MACHOs between Earth and the Large Magellanic Cloud may have been misleading. It’s possible, she said, that the MACHOs were not in the halo after all, but in the Large Magellanic Cloud itself. Another MACHO candidate, seen toward the Small Magellanic Cloud, was almost certainly in the cloud, not the Milky Way halo, she said. If so, maybe the dark matter was mostly WIMPs, and MACHO should be rewritten as MACO. Which doesn’t have quite the same ring to it as MACHO.

Freese suggested that as much as 90 percent of the galactic dark matter is WIMP matter. And at the same meeting, a team from the DAMA (for dark matter) experiment in the underground Gran Sasso laboratory in Italy reported a strong hint of a particle that matched a WIMP’s expected properties.

If WIMPs lurk throughout the galaxy, the DAMA team reasoned, the Earth should be running into them all the time. After all, the whole solar system speeds around the galaxy at 140 miles per second. And if WIMPs really are the dark matter, there ought to be maybe one WIMP particle out there in every cubic centimeter of space. With that many WIMPs, it ought to be possible to detect some of them, even if most escape notice. So the DAMA experimenters constructed detectors containing chunks of sodium iodide that give off a flash of light when a WIMP strikes.

Even though the detectors are deep underground, to screen out other kinds of particles that might fool the detectors, it’s impossible to know whether any given flash really represents a WIMP encounter. There might be radioactive rocks somewhere giving off particles of some sort as well, for example. Presumably, though, any other particles that strike should do so all year round, with no preference for summer over winter. WIMPs, on the other hand, would strike

more often in the summer, when the Earth is moving through the galaxy in the same direction that the sun is—into the WIMP wind, so to speak. In the winter, the Earth is revolving away from the WIMP wind. Therefore, if the detector flashes more in June than in December, the extra flashes may be signals of WIMPs.

And that’s just what the DAMA team reported in Paris. In 1997, Pierluigi Belli of the DAMA team reported, the detectors saw a hint of the excess in June. In 1998, he said, the team found an even stronger signal. Belli said the team’s analysis favored a WIMP weighing in at about 59 billion electron volts, or roughly 60 times the mass of a proton.

In the question period following his talk, however, other scientists sharply criticized the DAMA team’s data analysis. Similar disputes arose a year later during a conference in California. The DAMA team once again proclaimed their belief that WIMPs had been detected. This time, though, a rival team disputed their analysis. Experiments at Stanford, using a different WIMP-searching method altogether, had also recorded some flashes in their detectors. But those flashes were not caused by WIMPs, the experimenters concluded, but by neutrons.

By the end of the year 2000, the controversy had not cooled. In December, the Texas Symposium on Relativistic Astrophysics was actually held in Texas for a change—in Austin, where the WIMP debate continued. Rita Bernabei, leader of the DAMA team, delivered a spirited and contentious defense of her group’s findings. After four years of tests, she proclaimed, the June-December mismatch in detections remained clear.

“Where you expect the maximum you get the maximum,” she said. “Where you expect the minimum you get the minimum.” Possible confusion from other particles, say, radioactive emissions from underground radon, could be excluded, she said. “We have the presence of a modulation with the proper features for WIMPs.”¹³

Blas Cabrera, of the coalition performing the WIMP search at Stanford, was not impressed. He remained calm, but clearly rejected Bernabei’s claim. “Our conclusions,” he said, “are in disagreement with those of the Rome group.”¹⁴

Rather than comparing June and December, he explained, the Stanford experiment tried to trap WIMPs in small detectors made of silicon or germanium, maintained at ultracold temperatures. Both are semiconducting elements used in electronic devices, and both are sensitive to the impact of WIMP particles. In the case of silicon, sensors are tuned to faint vibrations caused by a WIMP impact. With germanium, the sensors measure the tiny rise in temperature caused when a WIMP deposits its energy.

The Stanford experiment was set up only 35 feet underground— shielded from most problems, but not deep enough to escape an occasional cosmic ray. Cosmic ray particles called muons could, without too much trouble, smash into rocks outside the experimental chamber and eject neutrons that would trigger the germanium or silicon sensors. There would be no obvious way to tell if any given impact had been caused by a neutron rather than a WIMP.

However, the germanium detectors are very much more sensitive to WIMPS than silicon is, while silicon is only a tiny bit more sensitive to neutrons than germanium is. Consequently, if both types of detector record hits at about the same rate, they must be seeing neutrons, not WIMPs.

And that’s just what the results seemed to indicate—both detector types recorded something like one or two hits a month. If the hits were from WIMPs, germanium should have been recording ten times as many hits as silicon.

“Our conclusion is it’s a better fit with a neutron background than a WIMP signal,” Cabrera said. But if the June-December effect seen by DAMA really revealed the presence of WIMPs, he said, the Stanford experiment should have seen some, too. Cabrera attempted

to remain diplomatic and noncommittal in his statements, but the clear implication was that the DAMA team might have committed some errors in its analysis.

Fortunately, further WIMP searches are in the works. The Stanford group plans to move more sensitive equipment to a mine in Minnesota, where greater depth below the surface will reduce contamination from cosmic rays, and any WIMP signal should emerge more clearly. Atom smashers continue to probe higher ranges of mass where WIMPs might be found. WIMPs may even turn up in collision debris at Fermilab, the Illinois atom smasher, any day now. An even better bet, most scientists think, is the Large Hadron Collider, now under construction at CERN, expected to begin smashing in 2006 or so.

If SUSY particles don’t show up by then, many scientists will be disappointed, and even surprised. Physicists have long known that all the dark matter in the universe cannot be made of MACHOs. Some dark matter must be something other than the ordinary stuff from which MACHOs presumably are made.

So if WIMPs are not found, many physicists will be frightened. For that would raise the likelihood of a different potential prediscovery: the idea that dark matter might actually be the terrifying particles known as WIMPZILLAS.