Hyperspace (26 page)

Witten is not like other physicists. Most of them begin their romance with physics at an early age (such as in junior high school or even elementary school). Witten has defied most conventions, starting out as a
history major at Brandeis University with an intense interest in linguistics. After graduating in 1971, he worked on George McGovern’s presidential campaign. McGovern even wrote him a letter of recommendation for graduate school. Witten has published articles in
The Nation
and the
New Republic. (Scientific American
, in an interview with Witten, commented, “yes, a man who is arguably the smartest person in the world is a liberal Democrat.”
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)

But once Witten decided that physics was his chosen profession, he learned physics with a vengeance. He became a graduate student at Princeton, taught at Harvard, and then rocketed a full professorship at Princeton at the age of 28. He also received the prestigious MacArthur Fellowship (sometimes dubbed the “genius” award by the press). Spinoffs from his work have also deeply affected the world of mathematics. In 1990, he was awarded the Fields Medal, which is as prestigious as the Nobel Prize in the world of mathematics.

Most of the time, however, Witten sits and stares out the window, manipulating and rearranging vast arrays of equations in his head. His wife notes, “He never does calculations except in his mind. I will fill pages with calculations before I understand what I’m doing. But Edward will sit down only to calculate a minus sign, or a factor of two.”
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Witten says, “Most people who haven’t been trained in physics probably think of what physicists do as a question of incredibly complicated calculations, but that’s not really the essence of it. The essence of it is that physics is about concepts, wanting to understand the concepts, the principles by which the world works.”
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Witten’s next project is the most ambitious and daring of his career. A new theory called superstring theory has created a sensation in the world of physics, claiming to be the theory that can unite Einstein’s theory of gravity with the quantum theory. Witten is not content, however, with the way superstring theory is currently formulated. He has set for himself the problem of finding the
origin
of superstring theory, which may prove to be a decisive development toward explaining the very instant of Creation. The key aspect of this theory, the factor that gives it its power as well as uniqueness, is its unusual geometry: Strings can vibrate self-consistently only in ten and 26 dimensions.

The essence of string theory is that it can explain the nature of both matter and space-time—that is, the nature of wood and marble. String
theory answers a series of puzzling questions about particles, such as why there are so many of them in nature. The deeper we probe into the nature of subatomic particles, the more particles we find. The current “zoo” of subatomic particles numbers several hundred, and their properties fill entire volumes. Even with the Standard Model, we are left with a bewildering number of “elementary particles.” String theory answers this question because the string, about 100 billion billion times smaller than a proton, is vibrating; each mode of vibration represents a distinct resonance or particle. The string is so incredibly tiny that, from a distance, a resonance of a string and a particle are indistinguishable. Only when we somehow magnify the particle can we see that it is not a point at all, but a mode of a vibrating string.

In this picture, each subatomic particle corresponds to a distinct resonance that vibrates only at a distinct frequency. The idea of a resonance is a familiar one from daily life. Think of the example of singing in the shower. Although our natural voice may be frail, tinny, or shaky, we know that we suddenly blossom into opera stars in the privacy of our showers. This is because our sound waves bounce rapidly back and forth between the walls of the shower. Vibrations that can fit easily within the shower walls are magnified many times, producing that resonant sound. The specific vibrations are called resonances, while other vibrations (whose waves are of an incorrect size) are canceled out.

Or think of a violin string, which can vibrate at different frequencies, creating musical notes like A, B, and C. The only modes that can survive on the string are those that vanish at the endpoint of the violin string (because it is bolted down at the ends) and undulate an integral number of times between the endpoints. In principle, the string can vibrate at any of an infinite number of different frequencies. We know that the notes themselves are not fundamental. The note A is no more fundamental than the note B. However, what is fundamental is the string itself. There is no need to study each note in isolation of the others. By understanding how a violin string vibrates, we immediately understand the properties of an infinite number of musical notes.

Likewise, the particles of the universe are not, by themselves, fundamental. An electron is no more fundamental than a neutrino. They appear to be fundamental only because our microscopes are not powerful enough to reveal their structure. According to string theory, if we could somehow magnify a point particle, we would actually see a small vibrating string. In fact, according to this theory, matter is nothing but the harmonies created by this vibrating string. Since there are an infinite number of harmonies that can be composed for the violin, there are an
infinite number of forms of matter that can be constructed out of vibrating strings. This explains the richness of the particles in nature. Likewise, the laws of physics can be compared to the laws of harmony allowed on the string. The universe itself, composed of countless vibrating strings, would then be comparable to a symphony.

String theory can explain not only the nature of particles, but that of space-time as well. As a string moves in space-time, it executes a complicated set of motions. The string can, in turn, break into smaller strings or collide with other strings to form longer strings. The key point is that all these quantum corrections or loop diagrams are finite and calculable. This is the first quantum theory of gravity in the history of physics to have finite quantum corrections. (
All
known previous theories, we recall—including Einstein’s original theory, Kaluza-Klein theory, and supergravity—failed this key criterion.)

In order to execute these complicated motions, a string must obey a large set of self-consistency conditions. These self-consistency conditions are so stringent that they place extraordinarily restrictive conditions on space-time. In other words, the string cannot self-consistently travel in any arbitrary space-time, like a point particle.

When the constraints that the string places on space-time were first calculated, physicists were shocked to find Einstein’s equations emerging from the string. This was remarkable; without assuming any of Einstein’s equations, physicists found that they emerged out of the string theory, as if by magic. Einstein’s equations were no longer found to be fundamental; they could be derived from string theory.

If correct, then string theory solves the long-standing mystery about the nature of wood and marble. Einstein conjectured that marble alone would one day explain all the properties of wood. To Einstein, wood was just a kink or vibration of space-time, nothing more or less. Quantum physicists, however, thought the opposite. They thought that marble could be turned into wood—that is, that Einstein’s metric tensor could be turned into a graviton, the discrete packet of energy that carries the gravitational force. These are two diametrically opposite points of view, and it was long thought that a compromise between them was impossible. The string, however, is precisely the “missing link” between wood and marble.

String theory can derive the particles of matter as resonances vibrating on the string. And string theory can also derive Einstein’s equations by demanding that the string move self-consistently in space-time. In this way, we have a comprehensive theory of both matter-energy and space-time.

These self-consistency constraints are surprisingly rigid. For example, they forbid the string to move in three or four dimensions. We will see that these self-consistency conditions force the string to move in a specific number of dimensions. In fact, the only “magic numbers” allowed by string theory are ten and 26 dimensions. Fortunately, a string theory defined in these dimensions has enough “room” to unify all fundamental forces.

String theory, therefore, is rich enough to explain all the fundamental laws of nature. Starting from a simple theory of a vibrating string, one can extract the theory of Einstein, Kaluza-Klein theory, supergravity, the Standard Model, and even GUT theory. It seems nothing less than a miracle that, starting from some purely geometric arguments from a string, one is able to rederive the entire progress of physics for the past 2 millennia. All the theories so far discussed in this book are automatically included in string theory.

The current interest in string theory stems from the work of John Schwarz of the California Institute of Technology and his collaborator Michael Green of Queen Mary’s College in London. Previously, it was thought that the string might possess defects that would prevent a fully self-consistent theory. Then in 1984, these two physicists proved that all self-consistency conditions on the string can be met. This, in turn, ignited the current stampede among young physicists to solve the theory and win potential recognition. By the late 1980s, a veritable “gold rush” began among physicists. (The competition among hundreds of the world’s brightest theoretical physicists to solve the theory has become quite fierce. In fact, the cover of
Discover
recently featured string theorist D. V. Nanopoulous of Texas, who openly boasted that he was hot on the trail of winning the Nobel Prize in physics. Rarely has such an abstract theory aroused such passions.)

I once had lunch with a Nobel Prize winner in physics at a Chinese restaurant in New York. While we were passing the sweet and sour pork, the subject of superstring theory came up. Without warning, he launched into a long personal discussion of why superstring theory was not the correct path for young theoretical physicists. It was a wild-goose chase, he claimed. There had never been anything like it in the history of physics, so he found it too bizarre for his tastes. It was too alien, too
orthogonal to all the previous trends in science. After a long discussion, it boiled down to one question: Why strings? Why not vibrating solids or blobs?

The physical world, he reminded me, uses the same concepts over and over again. Nature is like a work by Bach or Beethoven, often starting with a central theme and making countless variations on it that are scattered throughout the symphony. By this criterion, it appears that strings are not fundamental concepts in nature.

The concept of orbits, for example, occurs repeatedly in nature in different variations; since the work of Copernicus, orbits have provided an essential theme that is constantly repeated throughout nature in different variations, from the largest galaxy to the atom, to the smallest subatomic particle. Similarly, Faraday’s fields have proved to be one of nature’s favorite themes. Fields can describe the galaxy’s magnetism and gravitation, or they can describe the electromagnetic theory of Maxwell, the metric theory of Riemann and Einstein, and the Yang-Mills fields found in the Standard Model. Field theory, in fact, has emerged as the universal language of subatomic physics, and perhaps the universe as well. It is the single most powerful weapon in the arsenal of theoretical physics. All known forms of matter and energy have been expressed in terms of field theory. Patterns, then, like themes and variations in a symphony, are constantly repeated.

But strings? Strings do not seem to be a pattern favored by nature in designing the heavens. We do not see strings in outer space. In fact, my colleague explained to me, we do not see strings anywhere.

A moment’s thought, however, will reveal that nature has reserved the string for a special role, as a basic building block for other forms. For example, the essential feature of life on earth is the stringlike DNA molecule, which contains the complex information and coding of life itself. When building the stuff of life, as well as subatomic matter, strings seem to be the perfect answer. In both cases, we want to pack a large amount of information into a relatively simple, reproducible structure. The distinguishing feature of a string is that it is one of the most compact ways of storing vast amounts of data in a way in which information can be replicated.

For living things, nature uses the double strands of the DNA molecule, which unwind and form duplicate copies of each other. Also, our bodies contain billions upon billions of protein strings, formed of amino acid building blocks. Our bodies, in some sense, can be viewed as a vast collection of strings—protein molecules draped around our bones.

Currently, the most successful version of string theory is the one created by Princeton physicists David Gross, Emil Martinec, Jeffrey Harvey, and Ryan Rohm, who are sometimes called the Princeton string quartet. The most senior of them is David Gross. At most seminars in Princeton, Witten may ask questions in his soft voice, but Gross’s voice is unmistakable: loud, booming, and demanding. Anyone who gives a seminar at Princeton lives in fear of the sharp, rapid-fire questions that Gross will shoot at them. What is remarkable is that his questions are usually on the mark. Gross and his collaborators proposed what is called the
heterotic string
. Today, it is precisely the heterotic string, of all the various Kaluza-Klein-type theories that have been proposed in the past, that has the greatest potential of unifying all the laws of nature into one theory.

Gross believes that string theory solves the problem of turning wood into marble: “To build matter itself from geometry—that in a sense is what string theory does. It can be thought of that way, especially in a theory like the heterotic string which is inherently a theory of gravity in which the particles of matter as well as the other forces of nature emerge in the same way that gravity emerges from geometry.”
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