Go to Horizon

Go to Interact

A Short Course in String Theory (With No Equations)

The goal of basic science is to understand how the natural world works. For some physicists, this means trying to understand what the world is made of at the most fundamental level.

In the 19th century, scientists established that all matter was composed of tiny particles called atoms. They understood that, while the everyday world was made of thousands of different kinds of things--rock, water, wood, feathers and so forth--all of these were composed of different combinations of just a few dozen kinds of atoms.

They began to learn that atoms were made of even smaller objects. Today, we know there are just three major kinds of subatomic particles--protons and neutrons in the nucleus at the center of the atom, plus electrons whizzing around the nucleus. All atoms are combinations of these three particles.

Then physicists discovered in the mid-20th century that protons and neutrons were made of still tinier particles, which they named quarks. Each proton and each neutron is made of three quarks. There are different kinds of quarks, and the exact combination determines whether the result is a proton or a neutron. Electrons, it has turned out, are not made of anything smaller.

But that was not the end of the quest. Are quarks and electrons made of yet smaller particles? All evidence so far says no. But in the last 25 years, some physicists have devised a new and, they hope, improved way to think about these so-called fundamental particles.

They believe that this new way to think, called string theory or, more formally, superstring theory, may be history's greatest scientific theory, embracing and uniting the two reigning but partly contradictory theories of physics--general relativity and quantum mechanics.

If they are correct, string theory could be the one, grand theory that explains how every bit of matter and every pulse of energy in the universe came into being and why each has the properties it has.

The new, as yet unproven, theory starts with one major departure from the way physicists used to think. Until now, physics treated everything, from a quark to a star, as a point--an infinitesimal, dimensionless dot. In calculating Earth's orbit around the sun from Isaac Newton's 17th century theories, for example, physicists treat both as if their entire mass were concentrated within a point at the center of each body.

For all practical purposes, that works fine, as long as rocket scientists remember that a spacecraft returning to Earth must land about 3,900 miles above the center of the mass used to calculate the flight path.

String theory, by contrast, says the smallest particles are not like points but like strings. A point has no dimensions, but a string, like a line, has one dimension. Strings are so much smaller than the smallest subatomic particle that, to our instruments, they look like points.

Actually, according to the theory, they are very small strands, just 10 -33 centimeters long. Written the long way, that would be a decimal point followed by 32 zeroes and then a 1. The length of a string has the same ratio to the diameter of a proton as the proton has to the diameter of the solar system.

Moreover, physicists say these short strings vibrate at different frequencies. Each quark is a string. So is each electron. And so are the very different particles that are not part of matter but instead give us energy.

These particles carry forces. For example, the photons that we often think of as particles of light carry the electromagnetic force. And just as vibrating guitar or violin strings produce various tones, so the differing vibrations of subatomic strings--including overtones like those in music--show up in scientific instruments as protons, neutrons, electrons, photons and so on. Much as the sound of the note ąC' is what we perceive from a guitar string vibrating in a certain way, so the attributes that we call "proton" are what we perceive from a string, or superstring, vibrating in a certain combination of ways.

"Strings can sing," says Jim Gates, a physicist who specializes in string theory at the University of Maryland. "So you can think of the world around us as a symphony of strings vibrating in different frequencies."

A proton can be thought of as three vibrating strings, one for each quark. Together, their many vibrations play a chord analogous to a musical chord--a combination of notes played together to make a new sound. Instead of producing music, the chord of subatomic strings shows up in scientific instruments as having all the standard properties of a proton--a positive charge, a certain mass and a certain value of a third property called spin. Likewise with the other particles.

So, too, an atom is a combination of chords. A molecule, being a combination of atoms, is an even more complex piece of music. And the world as a whole is, as Gates puts it, a symphony.

But that's not what has physicists so excited about string theory. As explained so far, strings are little more than a different set of metaphors for what we already knew. What elates many scientists is that string theory looks like a possible solution to an embarrassing puzzle that has bedeviled the world's greatest physicists for the last 80 years. If the puzzle can be solved, physicists say they will have achieved a virtually complete understanding of the nature of existence.

The puzzle is that the two greatest theories of modern physics--general relativity and quantum mechanics--give what seem to be conflicting explanations of gravity. This would not be such a problem if the two theories were mere hypotheses, but both are theories in the grand sense in which science uses that term.

A scientific theory is a broad, coherent explanation of natural phenomena that has withstood many experimental tests. Take atomic theory, for example. It explains the structure and behavior of atoms and has been verified in countless experiments.

The same is true of the theory of general relativity, Albert Einstein's great creation of 1916, and of quantum mechanical theory, which began with Einstein earlier in the century and was developed further by many others through the 1920s. Both are embodied by mathematical formulas that can be used to predict natural phenomena just as the simpler formulas in Newton's laws of motion can be used to predict the path of a thrown ball or a satellite in space. The puzzle is embarrassing because both relativity and quantum theory have been proven true in thousands of experiments.

"In fact," Gates says, "every experiment ever done to test relativity has given positive results. The theory correctly predicts what happens in the real world. And the same is true of quantum theory. They're both firmly established. They work, and there's no way to escape that fact."

Relativity and quantum mechanics are, all physicists agree, the grandest established advances in human understanding of the fundamental nature of matter and energy. But their seemingly contradictory statements about gravity show that something is lacking in science's understanding.

Quantum theory says gravity is one of the four fundamental forces in nature. The other three are electromagnetism, the strong force and the weak force. Within the everyday world, the only obvious ones are gravity and electromagnetism, which binds electrons to atomic nuclei and thus is responsible for all chemical reactions. Electromagnetism also makes electrons jump from atom to atom in a wire, accounting for electricity. The force is carried by photons moving through space.

The other two forces operate inside the atom's nucleus. The weak force is involved in radioactivity and carried by W-bosons. The other, called the strong force and carried by gluons, binds protons in the nucleus and is the source of the sun's energy and that of thermonuclear explosions.

Physicists believe that all four forces are present-day remnants of one original force that existed at the beginning of the universe, when the Big Bang was less than a second old and immensely hot. As the universe expanded and cooled, that primordial force changed into the four different forms. Just as matter can change form with cooling (gases turn into liquids and then into solids), the one original force changed in steps, splitting again and again to yield the four known forces of today.

In recent decades, physicists have unified electromagnetism and the weak force. In other words, they have mathematically described a process in the early universe through which one force--not the original single force but a supposed intermediate--could have broken down to yield these two forces.

That success, called the electroweak theory, won Nobel Prizes for its discoverers and whetted appetites for the next step--unifying the electroweak force with the strong force. When accomplished, that would be called the Grand Unified Theory, omitting only the force of gravity. The holiest grail in physics is to unify gravity with the other three.

Quantum theory says gravity must be like the other forces in being transmitted by special force-carrying particles that move back and forth between particles of matter. In the electromagnetic force, photons play this role. Particles with opposite electrical charges exchange photons and thus are drawn toward one another. This is what makes opposite charges attract.

The simplest prediction of quantum theory is that the gravitational force must be carried by particles, called gravitons. Nobody has ever found a graviton, but scientists have devoted entire careers and considerable grant money to searching for them on the strength of mathematical predictions that they must exist. Because the equations are rock solid in all other respects, physicists have faith that gravitons exist.

Here is the conflict: The theory of general relativity also describes gravity, not as a force but as a kind of illusion created by the curvature of space. This in itself is a weird statement because most people think of space as the absence of anything or as a volume that may be empty or filled with matter.

How can a void have internal structure? Unfortunately, this is one place where ordinary thinking processes fail. Only if you understand the language of math can you follow the argument completely.

Weirdness, incidentally, is not a sin in physics. Earlier this century, Niels Bohr, a founder of atomic theory, was in an audience listening to Wolfgang Pauli, a pioneer in quantum theory, explain his early attempt at reconciling relativity and quantum mechanics. Afterward, Bohr stood up and said, "We are all agreed that your theory is absolutely crazy. But what divides us is whether your theory is crazy enough."

The physicists' best explanation to nonmathematicians about the curvature of space is this metaphor:

Imagine a large rubber sheet supported on all edges; then place a bowling ball in the middle. The rubber is space. The mass of the ball curves the rubber. Now roll a billiard ball straight across the sheet. Its path will curve toward the bowling ball just as if the ball were pulling on it with the force of gravity.

If the billiard ball goes fast enough, it will approach the bowling ball and then climb out of the gravity well and escape. If it goes slow enough, it will spiral ever closer to the bowling ball and hit it. The billiard ball does not behave this way because the mass of the bowling ball is pulling on it. It does so because the bowling ball has curved the the rubber sheet.

This is clear enough for the one surface of the rubber sheet. But what about three-dimensional space? This is the hard part in the metaphor. Imagine that the bowling ball is lying on an infinite number of rubber sheets oriented in all possible planes and simultaneously curving each of them. This is the curvature of space, a phenomenon that reaches in all directions from anything that has mass. It's weird, but the math of relativity theory that passes every test in the real world says this must be what gravity is.

The two sets of mathematical equations (relativity and quantum theory) that work so well in predicting so many things about the real world are diametrically opposed when it comes to gravity. That's what's so embarrassing.

"Like drunks coming out of a bar," Gates says, "physicists have been stumbling about, looking for explanations of this embarrassing failure. The stumbling, of course, has been in the form of many abortive ideas."

Physicists see this as a problem because they have learned to have faith in mathematics. The universe, they have discovered, is unfailingly mathematical. If you have an equation that reliably predicts phenomena in the real world, you may manipulate the terms of that equation in any mathematically permissible way, and the result of solving the reworked equation, however counterintuitive, has always proven true when tested by an experiment in the real world.

For example, when Newton was developing his laws of motion, he believed that the planets were responding to gravity and moving in ways that could not be predicted by the known mathematics of his time. So Newton invented a new kind of math, now called calculus. When he used calculus with his laws of motion, he could predict the orbital paths of planets and moons precisely. Nature, in a sense, already knew calculus.

So, why not simply say the non-gravity parts of relativity and quantum theory are okay and discard the gravity parts? That ignores the fact that gravity does exist in our world. Because gravity is real, it should be possible to find a mathematical description consistent with both theories. The only way to reconcile the two theories, physicists say, is to find some overarching theory, some new way of describing the fundamental nature of matter and energy such that both relativity's gravity and quantum theory's gravity can be derived from it.

That is what string theory does. In a nutshell, you simply declare that fundamental particles are not dimensionless points but one-dimensional lines. In beginning lectures on string theory, Gates calls them spaghetti strands. Give each type of string a characteristic way to vibrate, calculate the properties of those vibrations with the same formulas developed in the 19th century to describe vibrations of strings in musical instruments and, Gates says, string theory will give you good mathematical descriptions of all known fundamental particles of matter and energy. Even better, it gives you gravitons.

This is what has grabbed the attention of so many scientists. If you were to hand superstring equations to a mathematician who knew nothing about the particles that make up matter and energy, that person could, amazingly, predict the existence and properties of every single member of the great particle zoo that has been discovered so painstakingly through theory and experiment over the last century.

Moreover, superstring theory also accomplishes not only unification of the electroweak force with the strong nuclear force but also unifies them with gravity. Thus, scientists such as Gates argue, it is the "super-unified theory" of all physics that Einstein and generations of others sought. Einstein called it a "unified field theory."

So, does this make string theory true?

No, not yet. Scientists don't consider a theory valid or believable until it has produced predictions that can be tested, yielding results that agree with what the theory predicted. Quark theory was shown true in experiments with large atom smashers. Collisions of subatomic particles produce such high energies in a concentrated space, briefly recreating the energy density of a moment early in the Big Bang, that some of the energy cools and condenses into recognizable quarks and other subatomic particles that can be detected before they fly away or turn into more ordinary things.

In principle, vastly more powerful particle accelerators could test string theory, but a machine powerful enough would have to have been a million billion times more powerful than the 53-miles-around Superconducting Super Collider (SSC) that was to have been built in Texas before Congress killed its funding.

Still, the SSC could have tested parts of string theory. It might have demonstrated the reality of supersymmetry, the broader theory linking superstrings and the observed world of particles and forces. Now physicists are looking to a new accelerator being built in Europe, the Large Hadron Collider. Gates says experiments on this machine, not likely to begin for several years, might show that nature obeys principles of supersymmetry. Still, a direct test of string theory seems impossible and, as a result, some physicists say the equations do not deserve the lofty term "theory" in the scientific sense. They regard string theory as mere speculation. Also, there's another complication.

String theory makes mathematical sense only if the universe has 26 dimensions. At first glance, that is a ridiculous statement since today's world obviously has just the three dimensions of space plus one dimension of time. Most physicists can't imagine a world with more than four dimensions of space-time.

But when an early version of string theory emerged in the 1970s, it didn't meld properly with the other theories unless you assumed that the world had 26 dimensions. Mathematically, it is trivial to add dimensions to equations, but the only plausible way to claim 26 dimensions is to assert that 22 of them are somehow hidden from our perception.

"Well, when this came out, a lot of people just couldn't swallow a 26-dimension world," Gates says. "It just seemed too much to have to explain away, and most physicists stopped working on string theory. It didn't look like it was going to be the answer."

Then in 1984, four Princeton University physicists found a way to make string theory work in a 10-dimensional world, the other 16 supposed dimensions having concealed themselves--"curled up," as physicists put it--and no longer playing parts in the everyday world. It is mathematically permissible to say such things, and string theory reemerged as a contender for the long-sought unified field theory.

More recently, some scientists, including Gates, have found a way to roll up all 22 "extra" dimensions, thus making string theory work to produce a world with just the four garden-variety dimensions. This has not, however, met with universal acceptance. Some physicists feel that the math of a 10-dimensional world and superstring theory is more acceptable.

"We may never find out for sure what is the correct theory," Gates says. "But I hope we do. To me, this is the most intellectually exciting thing to think about--and the most fun."