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Testing String Theory

Advocates say vibrating strings underlie every particle and every force in the universe. But will anyone ever be able to prove that?

By Michio Kaku
Aug 30, 2005 5:00 AMJun 27, 2023 7:20 PM


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In his classic book The Dragons of Eden, astronomer Carl Sagan tidily summarized the central challenge scientists face when they try to formulate grand new theories: “Remarkable claims require remarkable proof.” One of the most remarkable claims made in modern times comes from string theory, which holds that everything in the universe is composed of tiny vibrating strings of energy. In this view, every particle in your body, every speck of light that lets you read these words, and every packet of gravity that pushes you into your chair is just a variant of this one fundamental entity. Over the past three decades, string theory has increasingly captured the imagination of physicists. Hundreds of researchers around the world now hammer away at its equations every day, trying to make the different parts of the theory hang together. They, like me, consider it the greatest step forward in science since Albert Einstein and Max Planck introduced the key ideas of relativity and quantum mechanics about a century ago.

Yet string theory, like all scientific theories, eventually must face the harsh test Sagan described. So far, it cannot stand up. To be brutally honest, there is no proof whatsoever that string theory is correct.

How, then, can its advocates persist? Part of the answer lies in the theory’s breathtaking premise. The natural world abounds with a baffling variety of particles smaller than atoms and four seemingly independent forces: gravity, electromagnetism, and the strong and weak nuclear forces. By describing subatomic particles as vibrating strings, somewhat like taut rubber bands, string theory ties all these disparate parts into a single framework. Every type of particle—including the electrons that form part of ordinary matter and the photons that transmit the electromagnetic force—simply corresponds to a specific frequency of vibration of the string. Much as pulling on a rubber band changes its vibration frequency, altering a string’s mode of vibration transforms an electron into a neutrino, a quark, or another particle.

Strings have another enticing, even more esoteric property. As they vibrate, they force space and time to curl around them, giving rise to gravity in exactly the manner that Einstein described in his theory of relativity. String theory thus promises to merge the equations describing the action of the tiny world we cannot see—that of subatomic particles—with the equations describing gravity and the large-scale world we experience every day. Einstein spent the final three decades of his life searching for such a merger, which he likened to “reading the mind of God.” String theory may achieve what Einstein could not, a unified theory that explains how the universe works.

Throughout modern history, the discovery of each new unifying principle in physics has sparked stunning new practical insights. Isaac Newton’s laws of mechanics paved the way for steam engines and the industrial revolution. Michael Faraday and James Clerk Maxwell’s insight that electricity and magnetism are two aspects of the same force, electromagnetism, ultimately unleashed the age of electronics. Einstein’s realization that energy and matter are interchangeable helped usher in the nuclear age. We can only guess at the discoveries that might follow the confirmation of string theory.

Finally, the math behind string theory is extremely sophisticated and beautiful, and the equations have survived every mathematical challenge. People who have worked on string theory often walk away with a powerful, if unquantifiable, feeling that it smells like truth.

But any theory, no matter how grand, must be reproducible, and that is where testing string theory gets a little crazy. Each of the theory’s solutions represents an entire universe, so to test the theory fully, one would have to create a baby universe in a laboratory. State-of-the-art technology barely lets us escape the planet, never mind re-create another cosmos. So skeptics, who often admit the loveliness of the math, have long dismissed string theory as an untestable fantasy.

That could change soon. An array of new devices—including new atom smashers, gravity detectors, spaceborne satellites, and buried detectors—could provide significant evidence that would support string theory. The rub is that all this new evidence, no matter how compelling, will still provide only indirect proof.

Gravity-wave test The strings in string theory are so tiny—about a billionth of a billionth the size of a proton—they can be conjured up only in our imagination. The smallness of the strings means we should look for evidence of them shortly after the Big Bang, when the entire universe was extremely small. The vibration of strings in that early era should have created ripples in gravity, or gravitational waves, that resonated across the universe at the speed of light. String theory predicts the frequencies of such waves. If we observe gravity waves and find that their frequency does not match what string theory predicts, the whole idea would be thrown into doubt.

Nobody has yet detected a gravitational wave, but not for a lack of trying. The new Laser Interferometer Gravitational Wave Observatory, housed in two sprawling facilities in Louisiana and Washington State, went online in 2002. Scientists are still calibrating the equipment and increasing its sensitivity; they are hopeful that, in the coming years, the observatory will detect gravitational waves for the first time.

In about eight years, NASA and the European Space Agency plan to launch the Laser Interferometer Space Antenna, called LISA. It consists of three satellites orbiting the sun. They will be linked by three laser beams, forming a triangle of light whose sides are each 3 million miles long. The satellites are designed to detect a change in their spacing as small as one-tenth the diameter of a single atom. In theory, a gravity wave passing by would change the contours of space between the satellites, altering how the laser beams combine with each other in a measurable way.

Gravity waves should be generated by many sources, including colliding black holes and exploding stars, but LISA should also be able to detect waves created immediately after the birth of the cosmos. Earlier satellites such as the Wilkinson Microwave Anisotropy Probe detected microwave energy left over from the Big Bang, showing what the infant universe looked like when it was roughly 300,000 years old. LISA should be able to peer back in time much earlier—to one-trillionth of a second after the Big Bang.

Results from LISA might allow physicists to distinguish between different theories about what happened immediately after, and even before, the moment when the universe went bang. A leading cosmological model, known as inflation, predicts that our universe is just one part of a greater multiverse and that our Big Bang may have been one of many. In this model, our universe expanded extremely rapidly during the first fraction of a second of its existence. Another theory, rooted in string theory, envisions a scenario in which the Big Bang occurred as a result of the collision between two parallel universes floating in higher-dimensional space.

These theories may seem fantastic, but they each predict a specific pattern of gravity waves emitted from the Big Bang. LISA might be able to distinguish between some of them, offering an empirical test of conditions that existed when the universe began 13.7 billion years ago. Even if LISA is not sensitive enough to perform this test, then the betting among physicists is that its successors will be. If the signals LISA and its successors pick up are those expected by string theorists, they will verify that some version of string theory is the correct quantum theory of gravity.

Particle-accelerator test

Impatient physicists may not have to wait for LISA to find out whether string theorists are on the right track. In just two years, the world’s most powerful particle accelerator, the Large Hadron Collider, will begin operation outside Geneva. It will smash high-energy protons into one another in a scenario somewhat analogous to shooting two watches out of cannons at each other to find out what they are made of. By sorting through the debris momentarily created by the colliding protons, string theorists hope to find massive particles that have never been seen before.

According to string theory, familiar particles such as protons, neutrons, and electrons represent the lowest vibration mode of a string—the lowest octave, in a sense. Other, higher-pitched vibration modes should produce related but substantially more massive families of particles, dubbed superparticles, or sparticles. String theory predicts that all subatomic particles have such partners. For example, the electron should have a superpartner dubbed the selectron, while each quark has a superpartner called a squark. No one has yet detected a sparticle, perhaps because existing particle accelerators are too feeble.

Some physicists expect the Large Hadron Collider to be powerful enough to reveal sparticles. The heart of the collider is a 17-mile-long circular tunnel straddling the border of France and Switzerland. There, two beams of protons will circulate in opposite directions. When engineers flip a switch in 2007, a 12,000-ampere pulse of electrical power will slam down huge coils of electromagnets, creating fields 100,000 times more powerful than Earth’s. The magnets will bend particles along a circular path as they accelerate to 99.999999 percent the speed of light and attain energies approaching 14 trillion electron volts, trillions of times more powerful than the energy released by dynamite.

Before the Large Hadron Collider goes hunting for sparticles, it will first test the boundaries of the standard model of particle physics, the reigning theory of how subatomic particles behave (see “Catch Me if You Can” by Karen Wright, Discover, July 2005). The standard model is perhaps the most successful quantum theory, explaining every subatomic interaction witnessed so far, but it merely whets the appetite of string theorists. They believe the standard model is contrived, ugly, and incomplete because it contains at least 19 adjustable parameters, three near-identical copies of subatomic particles, and no description of gravity.

Superstring theory holds that the standard model describes only the lowest vibration modes of the strings. In this view, the standard model does a good job describing the world we know, yet it is unfinished. Nevertheless, the standard model has worked as a viable theory for decades. The discovery of sparticles would mark its first failure to adequately explain the tiny quantum world and would unleash an avalanche of new tests by experimental particle physicists, who sometimes deride string theory as too abstract. Sparticles would not, however, seal the deal on string theory. Some physics theories explain the existence of sparticle-like particles without resorting to strings.

The Large Hadron Collider could support string theory in other ways. For instance, it might create miniature black holes predicted by one version of the theory; these in turn would produce telltale showers of subatomic particles as they disintegrated. (Physicists say the black holes are so small they pose no danger of swallowing up Switzerland and the rest of Earth.) The collider may also be powerful enough to test one of the most bizarre predictions of string theory—that there are many dimensions out there. Recent versions of string theory predict there are actually seven spatial dimensions beyond the three that we can sense. Collisions at the Large Hadron Collider might be able to knock subatomic particles into one of the other dimensions, batting them right out of our three-dimensional ballpark. The missing mass and energy, or the decay products of the higher-dimension particles themselves, could then be detected by the Large Hadron Collider’s sensors.

Laboratory gravity tests

There is a surprisingly simple way to detect the higher dimensions predicted by string theory: Look for deviations in Newton’s law of gravity. Newton deduced that gravity falls off with the square of distance. Double your distance from Earth, for example, and its gravitational pull feels one-fourth as strong. Gravity spreads out through all of empty space, so its properties are sensitive to the number of dimensions it is spreading through. If the additional dimensions predicted by string theory exist, some gravity should leak away into those dimensions as well. We would observe this leakage as slight deviations from the inverse-square pattern that Newton described.

Newton’s theory has been tested with exquisite accuracy in our solar system and beyond. It is so precise we can tell a space probe like Cassini how to weave its way through the rings of Saturn, a billion miles away. But according to string theory, at small scales like a millimeter (1/25 of an inch), gravity might hop across higher dimensions and perhaps into other, parallel universes, growing diluted in the process.

Six years ago, physicist John Price and his colleagues at the University of Colorado at Boulder conducted the first experiment to detect a higher dimension via gravity. The team constructed an ingenious device consisting of two parallel tungsten reeds. One of the reeds vibrated 1,000 times per second, creating a small gravitational disturbance that ought to tug subtly on the other reed. The motion of the second strip should then indicate how gravity traveled between the two.

Price’s device was so responsive it could measure a disturbance a billionth the weight of a single grain of sand, but the researchers could find no deviation from Newton’s laws of gravity with the reeds separated by a distance of only 0.108 millimeter (1/250 of an inch). A half dozen other groups have developed tests to probe the behavior of gravity over similar distances. So far there is no sign of other universes. (Or perhaps the experiment just showed that there are no parallel universes in Colorado.)

Perhaps the additional dimensions would show up only on smaller scales—string theory is still somewhat vague about this prediction. Other experimentalists are therefore trying to test Newton’s law of gravity over distances as small as the size of an atom. Umar Mohideen of the University of California at Riverside is attempting to measure the attraction between a minuscule gold-coated polystyrene sphere and a gold-coated sapphire plate. The attraction is due not just to gravity but also to an esoteric quantum phenomenon called the Casimir effect, caused by the latent energy present even in empty space. Mohideen has started by trying to measure gravity over distances of a few hundred nanometers, a thousand times the diameter of an atom.

A team led by Ricardo Decca of Indiana University–Purdue University has developed an alternative approach that would cancel out the Casimir effect and thus measure the gravitational interaction directly. He has recently completed a nanoscale experiment that compares the attractive force between a gold-coated sphere and test samples of gold and germanium coated with a shared layer of gold. A comparison of the forces acting on the gold and on the germanium makes it possible to subtract the role of the Casimir effect and expose any previously unseen aspects of gravity, which could provide evidence of string theory’s extra dimensions. In the future Decca and his colleagues plan to run an analogous experiment using closely spaced plates made of nickel-58 and nickel-64, isotopic forms that have identical chemical properties but differ in mass by about 10 percent. To date, Decca’s group has yet to find any sign of higher dimensions, but improved versions of the tests will soon be under way.

Dark-matter searches

Like the search for extra dimensions, the hunt for particles may not require city-size, multibillion-dollar accelerators. Astronomical studies show that about 23 percent of the mass and energy of the universe consists of dark matter, particles that emit no light and that barely interact with ordinary matter except through gravitational pull. This unseen material surrounds galaxies and typically weighs several times as much as the galaxy itself. No one knows what it is made of, but string theory predicts the abundant existence of sparticles that are invisible and massive—precisely the characteristics of dark matter.

Dark matter seems to permeate our own galaxy, the Milky Way. If it consists of sparticles, they should be everywhere. As Earth orbits through the Milky Way, our planet should move continually through an unseen wind of dark-matter particles that pass right through the planet and everything on it: your neighborhood, your living room, your body.

Several teams in Italy, France, the United Kingdom, Japan, and the United States are racing to capture dark-matter particles. Many of them rely on high-purity materials such as liquid xenon and germanium crystals, cooled to low temperatures and placed in deep mines to shield the devices from the continuous spray of ordinary particles that strike Earth’s atmosphere. Most of the time, passing dark-matter particles would fly right through the material without hitting anything and thus becoming detectable. (At the quantum level of scale, atoms overwhelmingly consist of empty space.) But on rare occasions a dark particle might collide with an atom. The sudden recoil of the atom’s nucleus would trigger a shower of electrically charged particles and atoms as well as light and heat, which can be picked up by a sensor.

This approach is simple in principle but tricky in practice because many other events can mimic a dark-matter particle. In 1999 a group at the University of Rome announced that they had found dark matter in their detector, but other teams questioned their result when they could not duplicate it. The Cryogenic Dark Matter Search, located within the Soudan Mine in Minnesota, is currently about 10 times as sensitive as the University of Rome detector was, and yet it sees no sign of the urgently sought particles.

Once particles of dark matter are identified in the laboratory, their properties can be analyzed and compared with the predictions of string theory. A leading candidate for dark matter is the neutralino, the sparticle partner of force-carrying bosons. String theory predicts that neutralinos may have been created and immediately annihilated in tremendous numbers right after the Big Bang. As the universe cooled, a slight departure from equilibrium caused more neutralinos to be created than destroyed, leaving an excess that persists today. The latest calculations indicate that neutralinos may be 10 times as plentiful as atoms. That abundance roughly matches the inferred quantity of dark matter in the universe.

Most physicists are confident that the particles we refer to as dark matter will be found, whether or not they are the specific particles predicted by string theory. But what if, contrary to all predictions, nobody ever manages to identify a dark-matter particle? For cosmologists and physicists alike, that would trigger an intellectual crisis. Yet string theory has another, even odder explanation to offer. Perhaps the dark stuff does not consist of unknown particles in our universe. Perhaps it consists of particles residing outside our universe—hovering just above us in a parallel dimension.

That may seem like an explanation from a science fiction novel (and it does in fact resemble the principle of invisibility set out in H. G. Wells’s The Invisible Man), but it emerges naturally in the higher-dimensional mathematics of string theory. Imagine for a moment that our universe is two dimensional, like a piece of paper. Now envision another, separate paper-sheet universe lying parallel to ours. We would be oblivious to that other universe even if it were just a fraction of an inch away. We would not be able to see it because there is no way of sensing or pointing to the higher-dimensional direction that leads to the other universe.

If another, three-dimensional universe were separated from us by a higher dimension, we similarly would not be able to see it directly even if it were right next to us. A few physicists, such as Joe Lykken of the Fermi National Laboratory and Lisa Randall of Harvard University, speculate that our situation in the real universe is just like that. Einstein’s general relativity predicts that gravity from matter in the other universe would leak into ours. We would thus feel the tug of matter that we cannot see—another possible explanation of dark matter. This unseen pull could be a sign of the higher-dimensional universe predicted by string theory.

Astronomers have noted that invisible matter seems to cluster around galaxies, forming a spherical halo stretching up to 10 times the diameter of the visible galaxy. Perhaps this occurs because huge clumps of shadow matter in a parallel universe pull on matter in our universe, causing our galaxies to form in mirror-image locations.

There are no convincing proposals of how to test this idea, but scientists could be forced to take it seriously if all the searches for dark matter located within our universe come up empty.

Pure mathematics

Despite new ideas and experimental activity, it is possible that none of these tests will find any support for string theory. Perhaps the evidence emerges only at energies much greater than are possible with today’s technologies. Perhaps the only way to study strings directly is to run experiments at the so-called Planck energy, a level not seen since the first 10–43 second after the Big Bang.

For those of us who want to know the answers before we die, this is a discouraging possibility. In our impatience for results, however, we tend to forget that many of the greatest ideas in science have waited centuries for even indirect confirmation. In 1783 astronomer John Michell predicted the existence of a star so massive that even light could not escape its enormous gravity. His prediction was difficult to accept because the object would be impossible to observe. Two hundred years later the Hubble Space Telescope has amassed stunning evidence that black holes are real and common—not by seeing the black holes themselves but by detecting disks of hot gas spinning around them.

Atomic theory offers another example of delayed confirmation. The Greek philosopher Democritus predicted that matter is composed of atoms in the fourth century B.C. In 1906, more than two millennia later, physicist Ludwig Boltzmann committed suicide in part because he was mercilessly ridiculed for believing in atoms, for which there was no direct proof. Our ability to directly observe and manipulate atoms is less than 20 years old.

Some theorists, myself among them, believe that the final verdict on string theory will not come from experiments at all. Rather, the answer may come from pure mathematics. The principal reason predictions of string theory are not well defined is that the theory is not finished. The underlying mathematics of string theory was accidentally discovered by two physics postdocs, Gabriele Veneziano of Italy and Mahiko Suzuki of Japan, working independently in 1968. The theory has evolved in fits and starts ever since. Even its greatest proponents agree that the final version has not yet been determined. When it is, we may be able to put it to a mathematical test.

If string theory is sound, it should allow us, mathematically, to compute basic properties of the universe from first principles. For instance, it should explain all the properties of familiar subatomic particles, including their charges, mass, and other quantum properties. The periodic table of elements that students learn in chemistry class should emerge from the theory, with all the properties of the elements precisely correct. If the computed properties do not fit the known features of the universe, string theory will immediately become a theory of nothing. But if the predictions accurately match reality, that would represent the most significant discovery in the history of science.

Einstein once said that “the creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.” If so, some enterprising physicist could vindicate string theory as early as tomorrow. The remarkable proof of the theory might not cost years of effort and billions of dollars. It might come instead from the most basic tools of science: paper, pencil, and a human brain.

Who's pushing string theory

In its 37-year history, string theory has already experienced two major revolutions. The first showed that strings describe gravity and particles and are free of mathematical inconsistencies. The second unified the various versions of string theory by adding an 11th dimension. These are just a few of the many key researchers who have guided the theory’s development and continue to push it forward.

John Schwarz of Caltech showed that string theory could describe quantum gravity, launching the first superstring revolution in 1984.

Michael Green of Cambridge worked closely with Schwarz, establishing the viability of string theory as a theory of everything.

David Gross of U.C. Santa Barbara helped develop “heterotic string theory” in the mid-1980s. He shared the Nobel Prize in Physics in 2004.

Joseph Polchinski of U.C. Santa Barbara showed that multidimensional membranes can describe large objects as groups of open strings.

Edward Witten of Princeton was the driving force behind M-theory, which sparked the second superstring revolution, in the mid-1990s.

Paul Townsend of Cambridge, along with Witten, developed M-theory, an 11-dimensional model that unified various forms of string theory.

Cumrun Vafa of Harvard put string theory on firmer theoretical ground in 1996 when he helped use it to calculate the entropy of black holes.

Juan Maldacena of Princeton found a link between string theory and field theory in 1997, bridging two branches of quantum physics.

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