Only 2 years ago, the idea of extra dimensions inhabited a nebulous region somewhere between physics and science fiction.
Many physicists had already begun to see the up-and-coming string theory as the next major step for theoretical physics. In that theory, everything in the universe is composed of tiny loops, or strings, of energy vibrating in a space-time that has six or seven extra dimensions beyond the seemingly endless three standard dimensions of space and one of time.
Conveniently, however, those extra dimensions are compactified, as physicists say, crumpled up in a space so small as to be unobservable.
The idea that extra dimensions might be larger—perhaps detectable—was something that scientists mostly talked about “late at night, after a lot of wine,” says Gordon L. Kane, a theorist from the University of Michigan in Ann Arbor. Kane therefore felt he was walking on the wild side when he penned a fictional news story about experimenters discovering extra dimensions.
Kane’s story, which appeared in the May 1998 Physics Today, was one of three winners of an essay contest sponsored by that magazine. Basing his tale on some innovative theorizing published in 1990 by Ignatius Antoniadis of the École Polytechnique in Palaiseau, France, Kane wrote of peculiar sprays of particles yielding “startling data.” He set his experiments in 2011 at a European accelerator, known as the Large Hadron Collider (LHC), which is currently under construction.
The results could imply the existence of one or two extra spatial dimensions, the story stated, “a surprise to everyone.” Even by the time his article came out, however, the possibility no longer seemed quite as surprising as it had when he wrote it a few months earlier. Between the submission of Kane’s story and its publication, two theoretical studies had come out that suddenly pushed the idea of relatively large extra dimensions into the spotlight.
One study came from a team at CERN, the European Laboratory for Particle Physics in Geneva where LHC is being built. It examined the consequences of extra dimensions being 10,000 trillion times larger than the extra dimensions of string theory are typically imagined to be. At the larger size, still only about one-ten-thousandth the size of a proton, the extra dimensions might produce effects detectable by the current generation of particle accelerators or their immediate successors, such as LHC, the researchers found.
The other study argued that certain types of extra dimensions could be even larger, as grand as a millimeter. They might then be accessible not only in colliders but in small-scale, table-top experiments as well, say researchers at Stanford University and the Abdus Salam International Centre for Theoretical Physics (ICTP) in Trieste, Italy.
Today, teams of experimentalists in both the United States and Europe are searching for the signatures of extra dimensions.
The hunt for such indicators “is certainly one of the best chances of making a very spectacular discovery in the next couple of years,” says Joseph Lykken of the Fermi National Accelerator Laboratory in Batavia, Ill.
Meanwhile, the wave of novel, extradimension theory continues to roll on. In the latest splash, researchers have proposed extra dimensions of infinite size.
Imagining any of these extra dimensions isn’t easy. Depending on how many extra dimensions there are, physicists say, they might curl into a simple loop or sphere or bend into a tortuous 6-dimensional pretzel popular in string theory.
Every point in the traditional, apparently 4-dimensional universe is then a tiny, multidimensional volume. Theorists suggest that an extra dimension might be on the order of 10-35 meter.
Physicists also measure the extra dimensions in terms of the energy needed to probe them. A particle accelerated to 1 trillion electron volts (TeV) has, according to standard arguments from quantum mechanics, a wave aspect with a wavelength of about 2 x 10-19 m. It can therefore explore facets of the subatomic world on that scale. Doubling the energy means seeing features half that size, and so on. So far, the smallest length scale observable with accelerators is a little greater than 10-19 m.
The idea of extra dimensions dates back to at least the 1920s. At that time, physicist Oskar Klein, building upon work by mathematician Theodor Kaluza, added a curled-up fifth dimension to the familiar universe in an ingenious but unsuccessful attempt to unite the forces of electromagnetism and gravity.
Physicists believe that the four forces—electromagnetic, weak, strong, and gravitational—were joined as a single superforce at the time of the Big Bang. In theory, they could merge only if the forces were about the same strength under conditions of high energy. However, gravity is much weaker than the others.
As some researchers today explore extra dimensions, they are on the lookout for implications regarding unification of the four forces. Other scientists striving for models that unify the forces have found extra dimensions a useful tool.
Testing unification theories directly appears to be impossible, however, since the phenomenon would only occur at energies in the range of 1013 to 1016 TeV. The highest-energy collisions achieved in accelerators today approach only 1 TeV.
CERN theorists Keith R. Dienes, Emilian Dudas, and Tony Gherghetta wondered what would happen if they uncurled one or more of the extra dimensions in string theory to 10-19 m, the largest size that would not already have been detected. To their surprise, they discovered that the three nongravitational forces could unify in the energy range of 1 TeV. This unification could then be observed directly in LHC and indirectly in less-powerful colliders.
They posted their study on the physics archive (http://xxx.lanl.gov/abs/hep-ph9803466) maintained by Los Alamos (N.M.) National Laboratory in March 1998.
For physicists, an energy of 1 TeV was already a landmark. Both theory and experiment had established that a mixing of the electromagnetic and weak forces begins to take place a little below that energy level. Physicists have been troubled because unification of even three forces requires much higher energies. They refer to this puzzle as the hierarchy problem.
Scientists at Stanford University and ICTP used extra dimensions in their attempt to solve the hierarchy problem. They focused first on gravity and looked for a way to make it comparable in strength to the other forces at an energy of about 1 TeV.
They accomplished that feat by hypothesizing extra dimensions that affect only gravity and are as large as 1 mm. Only a yawning gap in the scientific record makes such extra dimensions feasible. While physicists have probed the other forces of nature down to nearly 10-19 m, they’ve made extensive measurements of gravity only down to about 1 centimeter.
To describe extra dimensions that would affect gravity alone, the Stanford-Trieste researchers made use of entities known as branes. Those complex, membranous objects, which can have many spatial dimensions themselves, have become a central part of string theory. In some versions of the theory, the universe itself is a brane with three spatial dimensions—a 3-brane—moving through a higher-dimensional space-time.
String theory dictates that any extra dimensions outside a brane affect only gravity. In other words, just the force-carrying particles of gravity, called gravitons, could travel in the space-time beyond the brane, leaving the other forces confined to the brane.
By contrast, extra dimensions associated with the brane influence all the forces. Therefore, even if gravity boasts an intrinsic strength similar to that of the other three forces, because it diffuses throughout the external space-time, also called the bulk, its apparent strength in the 3-brane universe is much reduced.
Any extra dimensions affecting gravity would alter Isaac Newton’s inverse-square law, which holds that objects attract each other with a force inversely proportional to the square of the distance between them. The theorists calculated that one extra dimension in the bulk would have a scale of 100 million kilometers—about the distance from Earth to the sun. That option isn’t feasible because Earth’s orbit obeys the inverse-square law.
If there were two extra dimensions, however, each would have a scale of 0.1 to 1.0 mm—large enough to be detectable but small enough not to be ruled out by tests of the inverse-square law to date. With more extra dimensions, the length scale shrinks far below the millimeter range.
Combining both approaches, “you wind up with a very compelling picture,” says Dienes, a CERN team member, now at the University of Arizona in Tucson. “These two scenarios together lower all the fundamental high-energy scales of physics.”
Inspired by these proposals, experimenters are looking for signs of extra dimensions both at accelerators and in gravitational laboratories.
Most of the accelerator searches have begun in the past year, says Kingman Cheung of the University of California, Davis. Before that, researchers had been translating the theorists’ proposals into concrete predictions. Cheung presented a summary of ongoing and proposed searches last December at the Seventh International Symposium on Particles, Strings, and Cosmology ’99 (PASCOS ’99) conference at Tahoe City, Calif.
To find extra dimensions of the type studied by the CERN group, experimenters are on the alert for what they call Kaluza-Klein towers, which are associated with carriers of the nongravitational forces, such as the photon of electromagnetism and the Z boson of the weak force.
Excitations of energy within the extra dimensions would turn each of these carriers into a family of increasingly massive clones of the original particle—analogous to the harmonics of a musical note. “I like to think of these Kaluza-Klein states as echoes off the fifth dimension,” Dienes says.
Because these towers tend to magnify the strengths of the forces, their influence might even be detected at energies below those at which the towers themselves become apparent, researchers say.
Going back through the data from an earlier run of CERN’s Large Electron-Positron Collider (LEP), researchers have found no evidence of such extradimensional influences at up to an energy of 4 TeV, Cheung told Science News. The CERN team’s extra dimensions must therefore be smaller than 0.5 x 10-19 m. The towers might become detectable in 6 or 7 years, when the completed LHC will be able to probe energies of up to 14 TeV, he says.
Gravity doesn’t lend itself to measurement in accelerators because the other forces overwhelm its tiny influence on particle interactions. “The graviton is so weakly interacting, it doesn’t enter the picture,” Cheung says.
Instead, physicists typically make precision measurements of gravity by using extremely delicate experiments, named after the 18th-century scientist Henry Cavendish, that determine the force between two suspended masses. At very small separations, however, electrostatic influences and molecular interactions known as van der Waals forces again swamp the gravitational effects.
By conducting Cavendish experiments with extremely sensitive equipment, at least two teams of scientists are testing for millimeter-scale extra dimensions. If those dimensions exist, gravity in the submillimeter range would increase not according to Newton’s inverse-square law but in inverse proportion to the fourth power of the separation.
Researchers at Stanford University led by Aharon Kapitulnik have developed a micromachined cantilever that reacts to the gravitational tug of an arm swinging back and forth 80 micrometers beneath it. A laser detects motion in the cantilever, which is chilled to 4 kelvins to reduce random thermal motion.
The experimenters intend to measure not only gravity but also van der Waals and other short-distance forces. However, because of the hubbub over extra dimensions right now, “we are neglecting all other experiments,” Kapitulnik says.
Similarly in Boulder, Colo., a tungsten strip resembling a diving board weighing a few grams sits in a vacuum over another strip of tungsten. As a motor rapidly wiggles the diving board up and down, scientists look for motion in the strip below. A next-generation instrument operating at 4 K will eventually replace the current room-temperature version, says John C. Price of the University of Colorado, who leads the effort.
Given the dearth of knowledge about gravity in the subcentimeter range, the group is looking for any kind of deviation from expectations, not just extradimensional effects, he says.
Nonetheless, the excitement about extra dimensions helps spur the group on, Price says. If the strength of gravity takes a sharp turn upward at around 1 TeV, as the Stanford-Trieste scenario implies, an opportunity opens for testing this theory also in accelerators. Collisions at such energies could produce gravitons in large numbers, and some of these particles would immediately vanish into the extra dimensions, carrying energy with them. Experimenters would look for an unusual pattern of so-called missing energy events.
This and more subtle effects of extra dimensions could show up at existing accelerators, such as LEP and the Tevatron at Fermilab, only if the dimensions have scales nearly as big as a millimeter. The powerful LHC will greatly improve the chances for detecting missing energy events and other prominent extradimension effects.
Despite his award-winning literary fling 2 years ago, Kane has soured on large extra dimensions. He remains a firm believer in six or seven extra dimensions, he says, but only at about 10-35 m. The theory is cleaner that way, he argues, with just the three familiar, very large spatial dimensions, and the rest reduced to the scale of strings themselves. “If I was trying to win a contest today, I’d write on something else,” he says.
By contrast to Kane’s insistence on small extra dimensions, one pair of researchers recently came up with an argument for extra dimensions of unlimited extent, similar in size to the familiar dimensions. These scientists noted that the 3-brane, like any other object with energy or mass, would warp space-time and thereby confine gravitons to a region just slightly larger than the brane.
The warping would also localize extra dimensions’ effects on Newton’s inverse-square law of gravity to subcentimeter distances not yet explored. Such localization allows the dimensions themselves to stretch indefinitely, argue Lisa Randall of the Massachusetts Institute of Technology and Princeton University and Raman Sundrum of Boston University. This novel idea, described in the Dec. 6, 1999 Physical Review Letters, has many implications and may suggest new indicators of extra dimensions. The work has already sparked dozens of journal and online articles.
Whether or not large extra dimensions actually show up in the laboratory, researchers are sparing no effort to push the limits of one hidden dimension on which everyone agrees: imagination.