NOVA | Teachers | Elegant Universe, The | The Science of Superstrings

Back to Teachers Home

The Science of Superstrings

Today's physicists are struggling with a quandary. They have accepted two separate theories that explain how the universe works: Albert Einstein's general theory of relativity, which describes the universe on a very large scale, and quantum mechanics, which describes the universe on a very small scale. Both of these theories have been supported overwhelmingly by experimental evidence.

Unfortunately, these theories don't complement one another. General relativity, which describes how gravity works, implies a smooth and flowing universe of warps and curves in the fabric of spacetime. Quantum mechanics—with its uncertainty principle—implies that on an infinitesimally small scale, the universe is a turbulent, chaotic place where events can only be predicted with probabilities. In two cases where the competing theories must both be applied—to describe the big bang and the depths of black holes—the equations break down.

Most physicists have a hard time accepting that the universe operates according to two separate (and sometimes contradictory) theories. They think it is more likely that the universe is governed by a single theory that explains all observations and data.

The Hunt for One Theory

For that reason, physicists are on the hunt for a unified theory. Such a theory would bring together under one umbrella all four forces of nature: gravity, the weakest of the four, as explained by general relativity; and electromagnetism and the strong and weak forces, as explained by quantum field theory. Einstein pursued a unified theory by trying to unite electromagnetism and gravity.

Superstring theory, also called string theory, is the current formulation of this ongoing quest. String theory attempts to unify all four forces, and in so doing, unify general relativity and quantum mechanics. At its core is a fairly simple idea—all particles are made of tiny vibrating strands of energy. (String theory gets its name from the string-like appearance of these energy strands.) Unlike everyday strings, these strings have length (averaging about 10^-33 centimeters) but no thickness. String theory implies that the particles that comprise all the matter that you see in the universe—and all the forces that allow matter to interact—are made of tiny vibrating strands of energy.

The currently accepted and experimentally verified theory of how the universe works on subatomic scales holds that all matter is composed of—and interacts through—point particles. Known as the Standard Model, this theory describes the elementary particles and three of the four fundamental forces that serve as the building blocks for our world (see the Elementary Particles chart and the Fundamental Force Particles chart for a listing of these particles). This theory does not include gravity.

In string theory, each type of elementary matter particle—and each type of fundamental force carrier particle that mediates interactions between matter particles—corresponds to a unique string vibrational pattern, somewhat as different notes played by a violin correspond to unique string vibrations. How a string vibrates determines the properties—such as charge, mass, and spin—of the particle it is. The equations of string theory could give rise to elementary particles like those currently known (electrons, quarks, photons, etc.), but because detailed numerical predictions cannot yet be made, it is difficult to know whether the assortment of possible vibrational patterns correctly accounts for all known matter and force carrier particles. Strings can either be open-ended or closed to form a loop. Whether a string is open or closed determines the type of interactions it can undergo.

It is the nature of strings that unifies general relativity and quantum mechanics. Under quantum field theory, particles interact over zero distance in spacetime. Under the general theory of relativity, the theorized force carrier particle for gravity, the graviton, cannot operate at zero distance. Strings help solve this dilemma. Because they are one-dimensional and have length, they "smear" interactions over small distances. This smearing smooths out spacetime enough for the graviton to interact with other quantum field particles, thus unifying the two sets of laws.

A Hefty Price Tag

But string theory, for all its elegance, comes with a price. For the theory to be consistent, the universe must have more than three spatial dimensions. In fact, string theory predicts a universe with nine spatial and one time dimension, for a total of 10 dimensions. (The most current version of string theory predicts 11 dimensions.) The nine spatial dimensions consist of the three extended dimensions that we experience in everyday life, plus six theorized tiny, curled-up dimensions that can't be seen with existing technologies. These extra six dimensions occur at every point in the familiar three-dimensional world. The existence of more than three spatial dimensions is such a difficult concept to grasp that even string theorists cannot visualize it. They often use analogies to help picture these abstractions.

For example, picture a piece of paper with a two-dimensional, flat surface. If you roll up this surface, it will form a tube, and one dimension will become curled. Now imagine that you continue rolling the surface until it is rolled so tightly that the interior curled-up dimension seems to disappear and the tube simply looks like a line. In a similar manner, the extra dimensions predicted by string theory are so tightly curled that they seem to disappear in everyday experience.

These curled-up dimensions may take on certain complex configurations known as Calabi-Yau shapes. Unfortunately, tens of thousands of variations of these shapes exist, and it is difficult to know which ones might correctly represent the extra dimensions of our universe. It is important to know which ones are correct because it is the shape of these extra dimensions that determines the patterns of the string vibrations. These patterns, in turn, represent all the components that allow the known universe to exist.

These extra dimensions might be as small as 10^-35 meters or as big as a tenth of a millimeter. Alternatively, the extra dimensions could be as large or larger than our own universe. If that's the case, some physicists believe gravity might be leaking across these extra dimensions, which could help explain why gravity is so weak compared to the other three forces.

It's a Match

String theory also calls for every known matter particle to have an as-yet-undiscovered corresponding "super" force carrier particle and every known force carrier particle to have an as-yet-undiscovered corresponding "super" matter particle. This idea, known as supersymmetry, helps establish a relationship between matter particles and force carrier particles. Called superpartners (see "Particles and Sparticles" below), these theorized particles are thought to be more massive than their known counterparts, which may be why they have not yet been observed with current particle accelerators and detectors.

* The graviton and the Higgs boson have not yet been experimentally confirmed. Find a full listing of particles and their proposed superpartners in "Elementary Particles" at www.pbs.org/nova/elegant/.

The potential for what string theory could help explain is huge. It could reveal what happened at the moment the universe began. The big bang theory only describes what happened after the first extremely small fraction of a second. Under conventional theories, prior to that the universe shrank to zero size—an impossibility. Under the auspices of string theory, the universe may never have shrunk to a point at which it disappeared but rather may have begun at a miniscule size—the size of a single string.

String theory could also help reveal the nature of black holes, which, while predicted by general relativity, have never been fully explained at the quantum level. Using one type of string theory, physicists have mathematically described miniature massless black holes that—after undergoing changes in the geometry of string theory's extra dimensions—reappear as elementary particles with mass and charge. Some theorists now think that black holes and fundamental particles are identical and that their perceived differences reflect something akin to phase transitions, like liquid water transitioning into ice.

String theory also opens the door to different hypotheses about the evolution and nature of space and time, such as how the universe might have looked before the big bang or the ability of space to tear and repair itself or to undergo topological changes.

When It All Started

String theory is not entirely new. It has been evolving since the late 1960s. At one point, there were five variations of the theory. Then, in the mid-1990s a theory known as M-theory emerged that unified the five theories. M-theory is considered the latest step in string theory evolution (see "M-theory, Magic, Mystery, Mother?" at right).

Diagram of m-theory unifying five theories

The latest incarnation of string theory—M theory—revealed that five earlier versions of string theory were just five different aspects of one theory.

No part of string theory has been experimentally confirmed. This is in part because theoreticians do not yet understand the theory well enough to make definitive testable predictions. In addition, strings are thought to be so small—less than a billionth of a billionth of the size of an atom—that technologies such as current accelerators and detectors aren't powerful enough to detect them (see "Seeking the Fundamental" below). While string theory can't yet be experimentally verified, physicists hope that some of its facets can be supported by circumstantial evidence, such as demonstrating the existence of:

extra dimensions. Physicists hope that current or future particle accelerators will be able to help indicate the existence of extra dimensions. Detectors might measure the missing energy that would have leaked from our dimensions into those extra dimensions, possibly providing evidence that these dimensions exist.
superpartner particles. Researchers will use current and next-generation particle accelerators to search for the superpartner particles predicted by string theory.
fluctuations in background radiation. The universe is permeated by uniform radiation of the very low temperature of 2.7 degrees Kelvin. This is believed to be left over from the original very high temperature of the big bang. Comparing the temperatures from different locations in the sky only about 1 degree apart, extremely small differences in temperature have been found (on the order of one hundred thousandth of a degree Kelvin). Scientists are looking for even smaller differences in temperature of a specific form that may be left over from the earliest moments of the big bang, when the energies needed to create strings may have been attained.

Seeking the Fundamental

Diagram of fundamental particles along the energy (GeV) scale

While physicists using colliders have found evidence for most of the matter and force particles that comprise the Standard Model, they are still seeking a theorized force carrier particle called the Higgs boson. This graphic shows the energies at which some particles and force unifications have been found or theorized (solid circles) and indicates the energies that can be probed with current or planned colliders (empty circles). Physicists hope that CERN's Large Hadron Collider in Switzerland and France—scheduled to go online in 2007—might reveal evidence of the Higgs boson, as well as indications of the theorized graviton and the elusive superpartner particles. Unifying the strong and electroweak forces or finding theorized strings appears to require probing energies far beyond what current technologies offer. Some theorists, however, believe that the string energy may be closer to current or planned accelerator energies.

What Does "Fundamental" Mean?
Particle physicists sometimes use the word fundamental, or elementary, to describe the particles and forces found in the Standard Model. They are using this word to describe what they currently know are the most indivisible particles and the most basic forces in nature. But are these particles and forces really the most fundamental? The answer is that no one really knows.

In ancient times, people believed that nature's most fundamental elements were earth, water, air, and fire. In about 400 b.c. the Greek philospher Democritus conceived that matter was composed of little individual pieces, called atomos, which is Greek for uncuttable. Early in the 20th century, it was believed that neutrons and protons were the basic indivisible constituents of an atom's nucleus. Now it is thought that quarks and leptons are the most basic units possible. But if string theory is verified, strings will become the most fundamental units. Discovering the building blocks of nature is an evolutionary process. What was fundamental in the past no longer is, and what is considered fundamental today might not be tomorrow.

So when we say particles are fundamental, or elementary, throughout this text, we mean that these are the most indivisible building blocks of nature that we currently know of.

If rolled up tightly enough and seen from a distance, a two-dimensional piece of paper can apear as a one-dimensional line, with the second—curled up—dimension hidden from view.

What a String Looks Like (Mathematically, That Is)
Think of a string as a curve in space. Open strings have two ends like an ordinary piece of string, while closed strings have no ends, like a rubber band. Both kinds of strings are important in string theory. Open strings were proposed first and are the strings described here. Mathematically, a string is defined, or parameterized, by a parameter called σ, which varies from 0 to 1. The point σ = 0 labels one end of the string, and the point σ = 1 labels the other end. The point σ = 1/2 is the point halfway between the ends, and so forth.

To know how a string is positioned in space you have to know the spatial coordinates of each point on the string. For example, the X coordinate of the point σ is called X (σ). Now the string can wiggle and move in space. This means that the coordinates of points on the string can change with time. In other words, X is really a function of both σ and time τ, X (σ, τ). The way a string moves through space is described by an equation that involves the partial derivatives of X with respect to σ and τ as follows:

There is an equation like the one above for each coordinate of the string. These equations describe the complicated wiggling and vibrating motions that a string can have.

Courtesy of Leonard Susskind, Stanford University, California.

M-theory: Magic, Mystery, Mother?
M-theory is the latest incarnation of string theory. By adding another spatial dimension to the mix—thus creating a theory with 11 dimensions—M-theory reveals that the five different string theories are just different aspects of the same theory. But M-theory adds a new layer to the theory—it says that strings may not be the only fundamental elements in nature. There may also exist things called membranes (or "branes" for short), which are just as fundamental. The difference between membranes and strings is that membranes are higher-dimensional objects than strings (strings are one-dimensional). Some theorists think that we live in a "three-brane" universe that is moving through higher-dimensional spacetime. Physicist Edward Witten, who first proposed the theory and named it, has never stated exactly what the M stands for; some conjectures have included "magic," "mystery," "membrane," "matrix," or "mother."