It is a wonderful feeling to realize the unity of a complex of phenomena which, to immediate sensory perception, appear to be totally separate things.

In the fictional world of Dr. Seuss, small is beautiful. “A person’s a person, no matter how small,” he wrote in Horton Hears a Who. But except for Olympic gymnasts, small gets no respect in real life. And sometimes not even in science. Which is why superstrings are often treated like the scientific equivalent of Rodney Dangerfield.

If they exist, superstrings are small in the extreme. A superstring would be smaller than a virus in the same proportion that a marble is smaller than the whole universe. To the critics, superstrings are superstitions. There’s no evidence that they exist, and even if they did,

they’d be so small that they could never be detected, and they are therefore meaningless figments of mathematical imagination.

Nevertheless, among many pretty smart scientists, superstrings are the most popular undiscovered objects in the history of theoretical physics. These supertiny loops might just be the ultimate stuff of all of nature’s basic particles. Each species of particle might be a different mode of vibration of the fundamental superstring. That would explain the great diversity of particles in nature as merely separate manifestations of one primordial object. And so all the matter in the universe, everything from stars and atoms to green eggs and ham, might be made of string.

Best of all, superstrings offer a natural way to combine the math of gravity with quantum mechanics, paving the way to the unified theory of nature’s forces and particles that Einstein dreamed of but failed to find.

Unification is a powerful motivation for physicists because they have seen such grand examples of its power. It’s as though their motto is “one theory is better than two.” By unification, physicists mean finding one explanation for different things, or finding one theory that incorporates others into a single unified mathematical package.

Newton, for example, established a whole new scientific world-view by unifying the physics of the heavens with the physics of Earth. Einstein superseded Newton by unifying space and time, matter and energy, and gravity and geometry with the theories of special and general relativity. And in between Newton and Einstein came another famous unification—the merger of electricity, magnetism, and light by the Scottish physicist James Clerk Maxwell.

Born in 1831, Maxwell was the son of a Scottish laird who enjoyed keeping up with the latest science and technology news, and

had the resources to give his son a good education. Young James turned out to be fairly precocious. As a small child, on encountering a new mechanical device he would always ask “What’s the go of that?” And when he received an oversimplified answer designed to satisfy a small child, he’d say. “But what’s the particular go of that?”¹ Later he became a mathematical whiz kid, writing papers while still in his teens that were read before the Royal Society of Edinburgh. (He was too young to be allowed to read them himself.) He entered the University of Edinburgh in 1847, and after graduating went on to Cambridge, the alma mater of Newton, the greatest physicist of the seventeenth century. Maxwell became the greatest physicist of the nineteenth century.

Despite his unfortunately short life (he died at age 48), Maxwell was prolific. He mastered electricity and magnetism with a depth that enabled his equations to survive some of the assaults of twentieth-century physics that Newton’s laws did not. Maxwell also developed the math for describing the molecular motion in gases, explained the rings of Saturn, and figured out the physics of color vision, inventing color photography on the side. It was his work on electricity and magnetism, though, which earned Maxwell his eternal reputation. He lived at just the right time to pull together the pieces of an electromagnetic picture that began to form in the early decades of the nineteenth century.

In 1820, Hans Christian Oersted in Denmark showed that an electric current could deflect a magnetic compass needle, an inescapable sign of a connection between electricity and magnetism. In 1831, the year of Maxwell’s birth, Michael Faraday announced the discovery of electromagnetic induction—he could create an electric current by moving a magnet in the vicinity of a wire. Clearly electricity and magnetism shared not only some common features but also a deep and meaningful relationship.

From then on Faraday struggled to explain the nature of electric-

ity and magnetism. Not much of a mathematician, he tried to understand electromagnetic relationships conceptually. He envisioned magnetic and electric lines of force that could extend through space in a way that would explain his experiments. Faraday created the first crude pictures of what nowadays is known as the electromagnetic field.

Along the way it became clear that light itself might get mingled into the new electromagnetic picture. In 1845 Faraday showed that a magnetic field can twist the orientation of a light wave. So the understanding of electromagnetism became entangled with old arguments about the nature of light extending back to Newton’s time.

Actually, arguments about light had gone on far longer. But especially from Newton’s time on, physicists had debated whether light was a wave or made of particles; nineteenth-century experiments weighed in heavily on the wave side. By mid-century no reasonable doubt remained; even Newton, champion of the particle picture, would have dropped his final appeal. He would have won a consolation prize, though, for the wave nature of light implied the existence of something else that Newton had suggested—the existence of an ether. If light was a wave, it needed a medium to wave in. You cannot, after all, have an ocean wave without water. And nobody could imagine a light wave without some “luminiferous” medium for light to vibrate in. It seemed natural enough to identify that medium with the old idea of an ether, some mysterious, invisible substance permeating all of space.

Of course, if there were an ether for light to wave through, there might be other ethers, too—perhaps one for electricity and magnetism. Faraday himself was skeptical of the ether idea, though. He thought his lines of force could exist on their own. Maxwell, however, sought to produce a thorough mathematical description of Faraday’s ideas, and couldn’t figure out how to do it without some space-filling medium.

So Maxwell tried to describe such a medium in a series of papers called “On Physical Lines of Force,” published in 1861 and 1862. In the first paper he described the magnetic medium as a fluid of some sort consisting of magnetic whirlpools or “vortex tubes” arranged to correspond with Faraday’s idea of magnetic lines of force. Maxwell developed the math to describe the stresses involved in the motion of the vortex tubes in a way that successfully delineated magnetic forces.

Working electricity into this picture was a little more difficult. In subsequent installments in his series of papers, Maxwell adopted a more elaborate model of his ether. He pictured the magnetic tubes as something like cylindrical cells separated by layers of particles, sort of like the steel balls used in bearings, to permit easier rotation. And a string of these cylindrical cells, surrounded by the bearing-particles, would then correspond to a magnetic field line.

More mathematical analysis showed Maxwell that if the cylinders spun at equal rates (corresponding to a constant magnetic field), the bearing-particles would spin but stay put. When nearby cylinders rotated differently—corresponding to a changing magnetic field— the bearing-particles would have to move through the medium. The math describing the particle motion in this model looked to Maxwell suspiciously similar to André Ampère’s equations from the early nineteenth century relating electric currents to magnetic fields.

“It appears therefore, that according to our hypothesis, an electric current is represented by the transference of the movable particles interposed between the neighboring vortices,” Maxwell wrote.²

There were further problems to resolve—such as how to represent static electrical charges—which Maxwell tackled later. Ultimately he succeeded, and “Maxwell’s equations” describing electricity and magnetism remain among the most cherished creations in physical science.

Maxwell’s success in turning Faraday’s pictures into equations would surely have earned a Nobel Prize, if there had been Nobel

Prizes in those days. In any event, the mathematical unification of electricity and magnetism marked an enormous achievement in physics. But best of all, it came with a bonus—one of the greatest prediscoveries ever. For Maxwell had, in effect, anticipated radio waves. In fact, he essentially prediscovered the electromagnetic spectrum.

His original intent had been to show how the stresses in a medium—described mathematically—could account for electric and magnetic forces. In the process, he discovered that he could also account for the nature of light. For he realized that in his model of an electromagnetic medium, the charges and forces involved could produce disturbances, or waves, that propagated through the medium. It was simple enough to calculate how fast those waves would travel, based on the relative strengths of electric and magnetic forces. The answer came out to about 310 million meters per second.

Maxwell must have been pleased. For that number was almost exactly the speed of light. A famous 1849 experiment by Fizeau had measured light’s velocity in air as 314,858,000 meters per second. In 1862, a new, more accurate experiment was conducted by Foucault, who reported 298 million meters per second. In either case, Maxwell’s number was too close to be coincidence. (Nowadays, the speed of light is known to be just slightly less than 300 million meters per second.)

“We can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena,” Maxwell declared.³

A couple of years later, Maxwell pursued the electromagnetic-light connection more deeply. He was not really happy with his mechanical model of the ether—the bearing-particles struck him as a little too artificial. In any case, he saw advantages in developing the math of his theory without depending on any detailed physical model. Rather than relying on the ether, Maxwell began to talk about

the “electromagnetic field,” and wrote in 1864 a paper called “A Dynamical Theory of the Electromagnetic Field,” explaining that electrical bodies, “matter in motion,” produced electromagnetic phenomena in the space around them.

This approach enabled Maxwell to describe light more specifically as a combination of electric and magnetic waves vibrating at right angles to each other. And it did not escape Maxwell’s attention that such electromagnetic radiation might come in other forms. In one brief passage, he alluded to a source of many future discoveries: “. . . it seems we have strong reason to conclude that light itself (including radiant heat, and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws.”⁴

Nowadays we know that these “other radiations” do not require an ether, as Maxwell believed. But his belief in the ether wasn’t critical to his conclusion. Although he seemed to believe in the ether, Maxwell didn’t think you needed to know the details of the ether to describe electromagnetic phenomena successfully. Even so, I think it’s significant that he arrived at his math by studying the relationships in a physical model to begin with. It reminds me of Alexander Friedmann, grasping the nature of the cosmos after learning to relate his squiggles on paper to the way the atmosphere behaved. Maxwell mastered the math of electromagnetism after working out the equations for describing rotating cylinders and balls. In both cases, finding math that represented physical relationships led to the pre-discovery of things not present in the physical models that produced the math.

Maxwell realized that nature did not have to use the same model as his to guide electromagnetic phenomena. But nature did appear to use a model that preserved the mathematical relationships that Maxwell had expressed. And those real relationships required the existence of previously unknown things: forms of radiation that nobody before Maxwell had imagined.

Once Maxwell clued others in to the possibility, though, the search was on. A few years after Maxwell’s death in 1879, the German physicist Heinrich Hertz embarked on a series of experiments designed to test Maxwell’s theory. By 1887 Hertz had detected hints of “electric waves” (nowadays we’d say radio waves) traveling through the air in his laboratory, and in 1888 he demonstrated their existence conclusively—confirming Maxwell’s intuition and the power of his math to reveal previously hidden features of the physical world.

Wrapping electricity, magnetism, and light into one neat mathematical package, Maxwell not only set the stage for radio and television, he inspired physicists who followed him with the notion that unifying nature’s forces is a great way to make great discoveries. And nobody was better at playing the unification game than Albert Einstein.

Einstein was a simple man. He dressed simply, spoke simply, lived simply. There’s a great story about Einstein using the same soap for shaving as for bathing. Discovering this, a visitor asked why he didn’t use shaving soap. “Two soaps?” Einstein replied. “That is too complicated!”⁵

In physics, Einstein sought simplicity through the strategy of unification. “The real goal of my research has always been the simplification and unification of the system of theoretical physics,” he wrote in his later years.⁶

His great early papers achieved unifications of enormous consequence for the future of physics. His special theory of relativity paved the way to merging space and time into a unified “spacetime.” Another consequence of special relativity was that mass and energy are two sides of a unified coin.

Later, in his general theory of relativity, Einstein declared the equivalence of gravitation and accelerated motion and deduced that the geometry of space and gravitational force were also one and

the same. His success with such unifications led him to seek the grandest unification imaginable at the time, the melding of gravity with the previous century’s great unified theory, electromagnetism.

In pursuing that dream for the last three or four decades of his life, Einstein drew further and further away from the rest of physics. Yet even though he failed, Einstein’s quest served an important purpose—as an inspiration for generations of physicists to follow. Einstein’s followers soon realized that his failure reflected a deep schism between the twentieth century’s greatest theoretical achievements—general relativity and quantum mechanics. Einstein’s goal became reshaped. The grand challenge to grand unification, it seemed, would be reconciling general relativity with quantum theory. Only then, most experts reasoned, would it be possible to merge electromagnetism with gravity—and with nature’s other forces.

For by mid-century, gravity and electromagnetism were not the only forces around to unify. By then the atomic nucleus had begun to liberate not only nuclear energy, but also some fundamental secrets of physics about where that energy came from. While Einstein’s equation E = mc² could be used to calculate the release of energy from the nucleus, it didn’t really explain it. The energy was available because particles within the nucleus are held so tightly together. Splitting a nucleus lessens some of the need for energy to do that binding, so energy can be released. But while they could figure out how to make a bomb by splitting a nucleus, physicists only dimly grasped the nature of the force that held the nucleus together.

Somewhat more progress had been made in understanding a second nuclear force—a force that causes some nuclei to decay radioactively and governs certain other features of nuclear behavior. This is the weak nuclear force—weak in comparison to the strong force that holds the particles together. (The weak force is responsible for the production of neutrinos, Pauli’s prediscovery discussed in Chapter 4.) Part of Einstein’s problem was his neglect of the nuclear forces. He believed they weren’t so important and that if he succeeded in unify-

ing gravity and electromagnetism, everything else would fall into place.

As it turns out, the first real progress came with the nuclear forces. In the 1960s, the weak force was shown to be very similar to electromagnetism. Proof came in 1983, when physicists at CERN found the W and Z bosons, the particles predicted by the math unifying electromagnetism and the weak force (remember Chapter 3). The strong force worked its way into the picture in the 1970s, as physicists developed the theory of quantum chromodynamics. By the mid-1970s physicists were fairly satisfied with their Standard Model incorporating the particles of matter and three of nature’s forces.

But gravity resisted. Nobody could figure out a way to combine gravity with the other forces. Everything else fit together nicely, with quantum mechanics as the overarching framework. But gravity remained aloof, described exquisitely well by general relativity but sharing no common ground with quantum mechanics.

Meanwhile, a handful of theorists were in the process of pioneering an entirely new idea to explain the strong nuclear force. The new view envisioned the nuclear particles held together as though connected by a string.

At first, the physicists working on the problem of strongly interacting particles didn’t realize they were dealing with strings. The math came before the idea. In particular Gabriele Veneziano, in 1968, found some interesting equations that described some strong-particle processes quite well. Other theorists developed further mathematical descriptions of the strong force at work.

According to John Schwarz of Caltech, one of the superstring pioneers, the early work had the look of “just a bunch of phenomenological formulas.”⁷ When it became clear that something substantial was emerging from the math, “it was natural to ask for a

physical interpretation.” As nearly as Schwarz can sort through the historical haze, three different physicists independently identified the physical idea at work: a one-dimensional object, or string.

One was Yoichiro Nambu, who mentioned the string idea at an obscure conference in 1969. Another was Leonard Susskind, who expressed the string concept in papers published in 1969 and 1970. In 1970, Holger Nielsen submitted a paper that also included the string idea to a conference in the Soviet Union. Then, in 1971, Pierre Ramond, André Neveu, and Schwarz developed a string theory variant that incorporated what turned out to be supersymmetry (which is why “string” theory eventually became known as “superstring” theory).

By 1974, though, string enthusiasm had diminished considerably. Quantum chromodynamics, string theory’s rival for explaining the strong force, had made spectacular progress. Almost everybody came to believe then (and still does) that it is the “right” theory of the strong force. It fit in fine with the Standard Model. String theory, on the other hand, seemed, to be heading to a dead end.

Fortunately, John Schwarz was stubborn.

Schwarz had dabbled in string theory as an assistant professor at Princeton, and his work had impressed Murray Gell-Mann, the inventor of quarks. So Gell-Mann induced Schwarz to come to Caltech in 1972. “I didn’t know what string theory was going to be good for.” Gell-Mann told me. “I knew it was going to be good for something.”⁸

So just as everyone else decided to cut all ties to string theory, Schwarz invited Joël Scherk to visit Caltech and work on strings. Scherk, a French physicist, had worked with Schwarz at Princeton. During the first half of 1974, they renewed their collaboration, exploring various aspects of string math, eventually focusing on a peculiar particle that kept popping up in the string equations. It was a particle without mass and with two units of spin, utterly unlike anything involved in the strong force. But Schwarz and Scherk realized

that it did fit the description of one theoretical particle—the graviton, responsible for transmitting the force of gravity.

Soon Scherk and Schwarz were able to show that the stringy spin-2 particle would in fact behave exactly like the graviton. In other words, string theory contained gravity! Scherk and Schwarz had stumbled onto a quantum theory that was not only compatible with general relativity, it demanded general relativity. “Once we had digested the fact that string theory inevitably contains gravity we were very excited,” Schwarz recalled. “Evidently, the way to make a consistent quantum theory of gravity is to posit that the fundamental entities are strings rather than point particles.”⁹

And that wasn’t all. Other features of the string equations looked just like the math used in the Standard Model for describing other forces. In other words, string theory turned out not to be a theory of the strong force but a theory of all the forces, and all the particles to boot. “This means that one is dealing with a unified quantum theory—an explicit realization of Einstein’s dream,” Schwarz explained.¹⁰ So string theory might be the grandest of all unified theories—the “theory of everything” (a phrase, incidentally, that is detested by many physicists, including Schwarz and Gell-Mann).¹¹

True, they had not actually devised a theory of everything, but Schwarz and Scherk had good reasons for supposing that string theory was the best foundation on which to build such a theory. And it seems to me like that should have been big news. But it wasn’t, not even in the world of physics. Only a handful of physicists besides Scherk and Schwarz took strings seriously, and Scherk died in 1980. Most physicists still thought of strings as a theory of the strong force, and a better theory for that had come along. String theory also had another aesthetic problem, which we’ll get to later. So for a decade, hardly anyone paid any attention to what Schwarz and Scherk had accomplished. But Schwarz stuck to his strings.

In 1979, he began collaborating with Michael Green of Queen Mary College in London. They explored the role of supersymmetry

in the theory and made some progress, although slowly. Then in 1984, Schwarz and Green fired the shot heard ’round the superstring world, launching what later became known as the first superstring revolution. They produced a major breakthrough in the math, showing, in essence, how certain inconsistencies could be avoided. In particular, mixing quantum theory with gravity had always caused problems called “anomalies,” in which symmetries related to conservation laws might be violated. And violating conservation laws is a bad sign. Schwarz and Green showed how in particular versions of superstring math, the anomalies would disappear.

For some reason, physicists took notice this time, perhaps because it seemed for the first time (to many of them) that superstrings might actually describe the real world.

All of a sudden string theory became the hottest candidate for theory-of-everything status. As news of Green and Schwarz’s paper spread, other prominent physicists began to discuss the new results in seminars and colloquia. But word had not yet leaked out to the rest of the world. That was the situation until the spring of 1985. On May 7, a story appeared in the New York Times by the famous science writer Walter Sullivan. He began by writing:

This was big news to the general public, except for careful readers of the Dallas Morning News. For on April 22, two weeks earlier, I had written:

In those days, I still had other duties at the Morning News besides science, and I couldn’t keep up with every development as it happened. But I’d recently gone to a public lecture in Dallas by the famous physicist Steven Weinberg, of the University of Texas at Austin. Weinberg had won a Nobel Prize for his part in framing the unification of electromagnetism with the weak nuclear force, prediscovering the W and Z bosons found at CERN in 1983. He was widely regarded as one of the intellectual leaders in all of theoretical physics, the sort of guy that everybody took very seriously, as they do Edward Witten today. (Weinberg is still taken seriously too, by the way.)

As Weinberg talked, I realized he was describing a whole new twist on the frontiers of theoretical physics, a development that hadn’t made it into the popular press yet. In fact, that is what caught my attention—Weinberg mentioned specifically that nothing had appeared yet in the news media about this development. Those are the words that every reporter wants to hear.

So I listened closely as Weinberg described the new idea: nature’s particles aren’t points, but strings. By string, he did not mean twine, but simply that particles should be construed as one-dimensional objects, like the line segments of Euclidean geometry.

Traditionally, I knew, physicists regarded particles as geometrical points—objects with no dimension at all. That was a necessary assumption, it seemed, because the math for describing particles did not work very well if you assumed them to be little marbles or something. In the quantum realm where subatomic particles roam, it is unwise to try to grasp things visually, anyway. It just turned out that for the purpose of calculating the properties of particles and describing their behavior, they acted like zero-dimensional objects, or points.

But the new developments, Weinberg said, showed that it was possible to describe particles as one-dimensional objects. And in fact,

that approach offered some interesting advantages. He recounted the recent advance by Green and Schwarz and described how string math inherently included the graviton. That seemed to Weinberg to be a clear sign pointing the way toward the unification of gravity and quantum mechanics. String theory, Weinberg suggested, could be a “major breakthrough, possibly leading to another really great period in physics.”¹³

It really did sound like an elegant idea. Weinberg discussed how the strings, small as they were, could be responsible for all the known particles of nature. By vibrating at different frequencies, or “notes,” a string could mimic any elementary particle. The higher the frequency of vibration, the greater the mass of the particle, Weinberg explained.

And then he made an interesting point about the ultimate reality of the whole picture. “You can regard this as a mathematical artifice,” he said, “or you can regard the string as having a real physical reality moving through spacetime. I’d like to downplay the reality of the strings.”

So when I began working on a story on strings, I called John Schwarz at Caltech and raised just that point. “I know these strings can just be thought of as mathematical conveniences,” I said, echoing Weinberg. “Oh no!” Schwarz exclaimed. “They’re intended to be real, not just mathematical.”

Over the next few years, more and more reporters wrote about strings, and more and more physicists jumped on the string bandwagon. And as more people worked on it, the theory got more complicated. Soon string theory split into five distinct versions, known as Type I, Type IIA, Type IIB, E8XE8 (also known as heterotic, or HE for short), and SO(32) (another heterotic version, known as HO for short). Each theory had its own mathematical peculiarities. Type I

differed from the others in allowing two kinds of strings, “closed” and “open.” Closed strings are like little loops, sort of like supertiny rubber bands. Open strings have unconnected ends, like a rubber band that has broken. While strings could be either open or closed in Type I theory, strings in the other four version are always closed loops.

String theory’s five flavors cast suspicion over any claims that it was the obvious theory of everything. It seemed to many physicists that one theory of everything should be sufficient. The existence of five string theories provided further ammunition to the critics who didn’t like the idea to begin with.

But the main reason superstrings got so little respect was their size, implying the impossibility of ever seeing them. Basic calculations showed that the natural size for the strings was so small as to be almost unimaginable. I’ve tried to express it different ways. It would take a trillion trillion of them to cross the smallest atom, for example. Or enlarging a superstring to the size of a real string is comparable to making a virus bigger than the entire Milky Way galaxy. If you want to know more specifically, the size of a superstring is something like 10^-31 centimeters.¹⁴

On the one hand, the small size is good, because it explains why ordinary quantum theories, which treat particles as points, are so accurate. Experiments in the most powerful atom smashers might be able to probe sizes down to 10^-16 centimeters. Particles (or strings) smaller than that would seem to behave like points, since the probe would not be able to reveal finer features. On the other hand, the small size is bad. An atom smasher with enough energy to probe down to the string size is beyond comprehension. With current technology, such a machine would have to be bigger than the solar system. So the tiny size of superstrings rendered it inconceivable that any microscope could ever “see” them. And thus critics broadcast the claim that it’s meaningless to talk about superstrings to begin with.

Murray Gell-Mann does not agree. Sure, he says, the energy scale

of superstring theories is too high to observe. “That doesn’t mean that the theories have no consequences that are observable,” he pointed out to me. The energy scale where phenomena related to the theory can be observed may be much lower than the energy scale where all the forces are unified.

“It’s a really stupid mistake to mix those two things up,” he said.¹⁵

Still, to some scientists, the impossibility of ever observing something makes it unscientific. But I think that point of view is overly simplistic, and reflects a fundamental misunderstanding of what science is and does. Sure, if you define what is real as what you can see, then you can reject a lot of things as meaningless. But if you regard science as a way of finding out what is real, and how the world works, then you may very well encounter aspects of reality that imply the existence of things you can’t see. As Martin Rees argued about other universes, being unable to see them does not mean we cannot infer their existence from things we do see.

With superstrings, I think the case for their existence could be made even stronger than that for other universes. Because their small size implies only that strings would be very, very difficult to “see.” That’s a lot different from being impossible to detect in principle. When you argue that superstrings aren’t real because no imaginable technology can detect them, you’re basically saying that their unobservability is a practical problem, not that they’re impossible to observe in principle.

I think this point is worth exploring a little because it gets to the heart of the relationship between math and reality. The math of Heisenberg’s uncertainty principle, for instance, reveals something about nature. It shows that a particle can’t have both a precise position and precise momentum at the same time. It is not merely that you can’t measure them at the same time in practice—an electron does not possess these properties simultaneously, in principle. The theory does not allow it. With superstrings, the theory requires the existence

of the strings. They are very hard to observe, but it’s not impossible, in principle, to observe them, or their effects.

To me, the superstring critics sound suspiciously similar to the nineteenth century critics of atoms. The atomic theory became a central part of science in the nineteenth century, even though atoms could not be observed and some physicists contended that their “reality” was illusory. Even by the century’s end, Ernst Mach, the physicist-philosopher who so greatly influenced the young Einstein, still denied the reality of atoms. Mach maintained to his death that atoms were mathematical fictions, unobservable and therefore not real. “Have you ever seen one?” he asked of anyone who disagreed.

To be fair, Mach was a truly deep thinker, and his analysis of the history of mechanics is one of the most insightful books about the nature of science ever written. Born in 1838, Mach began his scientific career only a few decades after the invention of modern atomic theory. While he was still a young professor, he developed a view of science as what he called “economy of thought.” The world was a complicated place, with a lot going on. Nature presents all sorts of different phenomena. Science offers a way to categorize those phenomena and describe them simply and concisely. If you can boil down what goes on in nature to a few simple rules (call them “physical laws”), then you don’t have to reevaluate every new situation you encounter in order to describe it or to predict what will happen next. That’s economy of thought.

Atoms seemed at first glance to advance the economy-of-thought principle. It was possible to describe much of what happens in the world by assuming stuff is made up of tiny particles. But from his reading of scientific history, Mach concluded that all knowledge of nature was ultimately rooted in experience through the senses. So the proper province of science, he insisted, was understanding sensations. The primary features of the world to understand were colors, pressures, tones, and other sounds, the things that presented

themselves to the senses directly. Atoms, of course, didn’t do that. So for Mach, explaining phenomena in terms of atoms was just an analogy. To say the universe behaved in a mechanical way like a clock did not mean the universe was really a clock, Mach would have said. And to describe the world as made of atoms in motion did not mean that such invisibly small objects really existed.

“The mental artifice atom . . . is a product especially devised for the purpose in view,” Mach wrote. “Atoms cannot be perceived by the senses . . . ; they are things of thought.”¹⁶ Someday, he believed, the “economy of thought” that science pursued would be possible without such fictional crutches; atoms were merely a temporary stopping place in the development of physical science. It would never be possible to detect them. “Atoms and molecules . . .,” Mach wrote, “from their very nature can never be made the objects of sensuous contemplation.”¹⁷

It took Einstein to find the flaw in Mach’s approach. You did not need to make atoms accessible to “sensuous” contemplation to prove that they exist. In 1905, the same year that Einstein published his first paper on relativity theory, he found a way to show that atoms really do exist, beyond any reasonable doubt, even if it was still impossible to actually see one. The trick he used was to show how the visible motion of relatively large particles could prove the existence of invisibly small molecules.

The clue to Einstein’s insight had been visible for decades, waiting around for someone to notice. When suspended in a liquid, particles large enough to be seen through an ordinary microscope bounce around like the Ping-Pong balls in a Lotto tank. That “Brownian motion” (first observed in 1828 by the biologist Robert Brown) could be explained only as the result of bombardment of the floating particles by molecules of the liquid, Einstein demonstrated mathematically. (In principle, there is no difference in this case between molecules and atoms.)

Although most scientists soon recognized that Einstein was right, Mach refused to yield. Until his death in 1916, he maintained his disbelief. Others might be willing to accept the indirect proof from Einstein’s mathematics, but not Mach. He was sure that the existence of atoms could never be known, that atoms were forever out of the reach of the senses.

But he was wrong again, failing to foresee the possibilities of modern microscope technology. By the mid-1950s, a device called the field ion microscope succeeded in making pictures showing individual atoms (appearing as rather fuzzy dots of light, of course, but as it turns out, atoms are in fact rather fuzzy things). In 1990, IBM scientists, using an even fancier device called a scanning tunneling microscope, actually moved single atoms one by one to spell out IBM for a picture on the cover of the British scientific journal Nature. Mach would surely not have objected to using instruments to enhance the power of the senses. (He used special cameras, after all, to record the paths of bullets through fluids—research that led to the concept of Mach number for measuring the speed of sound.) So perhaps today even Mach would agree that the reality of atoms is well enough established to count as real science.

The story with superstrings may turn out to be similar. It might not be necessary to detect them directly—superstring theory could predict consequences accessible to smaller accelerators or other instruments. In fact, scientists today have already figured out ways that the existence of superstrings might be confirmed.

One possibility would exploit almost precisely the same trick that Einstein used to prove the existence of atoms. Physicists Ian Percival and Walter Strunz of the University of London have suggested that events on the atomic scale could be influenced by processes on the much smaller scale where superstrings operate, just as atoms and molecules bounce bigger particles around via Brownian motion. Since atoms behave like waves, devices could be built to measure

interference patterns where individual atomic waves reinforce or cancel each other out. This process could detect properties of space and time on the scale of superstrings in just the way Brownian motion revealed to Einstein the properties of atoms and molecules.

In another approach, Massimo Galluccio, of the Astronomical Observatory in Rome, and his colleagues have studied the properties of gravity waves that may have been propagating through space since the earliest moments of the universe. Patterns in these waves could reveal signs of superstrings from the era when the universe itself was so small that the string size was significant. Gravity wave detectors now in place on the ground may not be able to detect such signals. But those effects might lie within the range accessible to a second generation of gravity wave detectors or perhaps orbiting gravity wave detectors (a project called LISA) that physicists have proposed.

So I think superstrings ought to be regarded as a prime candidate for prediscovery. Prospects for detecting them may very well be slim, but no slimmer than the prospects for detecting Pauli’s neutrino.

In fact, the parallel between the neutrino and the superstring is intriguing in this regard. John Horgan’s book The End of Science dismisses superstrings by noting it would take an accelerator 1,000 light-years around to provide evidence of their existence. That’s ironically similar to the supposed need for a 1,000 light-year liquid hydrogen tank to detect neutrinos. The flaw in Horgan’s reasoning, of course, is that there might be a way to detect superstrings other than by using an atom smasher. Just as the neutrino pessimists of the 1930s did not foresee nuclear reactors, today’s superstring critics cannot know what invention of the future may offer a way, at least in principle, of testing the predictions of superstring theory.

On the other hand, there is one further objection to superstring theory that I haven’t yet mentioned, another case where the mathematics implies an aspect of reality that many people find hard to swallow. For superstring math does not work unless space is a lot

more complicated than almost anyone can imagine. Specifically, superstring math says space has more than 3 dimensions—maybe 9 or 10. The implication is obvious. Superstring theory implies that Rod Serling prediscovered The Twilight Zone.