Perfect liquids suggest theory’s math mirrors something real
Shadows live in a simple world. They glide effortlessly across any sort of surface, oblivious to the higher dimension of space in which 3-D bodies move, collide and sometimes block the paths of rays of light.
Shadows have no idea how important that third dimension is, and how objects in it endow those very shadows with their quasi-physical existence. Indeed, the laws of shadow physics all depend on the third dimension’s presence. And just as the clueless inhabitants of the shadow world require an extra dimension to explain how they exist and interact, reality for humans may also depend on an invisible dimension or dimensions unknown.
Physicists, in fact, have long pondered possible higher dimensions beyond the familiar four — three of space and one of time — that describe ordinary experience. Such extra dimensions have emerged as essential features in a sophisticated mathematical pastime known as superstring theory. Believed by some theorists to be the ultimate building blocks of all physical reality, superstrings are supposedly inaccessible to experimental study. If they exist, they would be far too small to detect directly —enlarging a superstring to the size of an amoeba would be the equivalent of making an ant as big as the visible universe. Similarly, the extra dimensions that strings require would probably be far too small to detect by available methods.
So string theory has long remained in the physics version of The Twilight Zone, disconnected from the ordinary world of sight and sound. But now the extra-dimensional math has begun to audition for Reality TV. For the first time, superstring theorists can point to a place where their formulas help other physicists understand something they can see in their experiments.
One such experiment generates matter in its most fiery form —simulating the temperatures of the Big Bang itself. Another probes matter most frigid — atoms vastly colder than even the depths of outer space. At both extremes, matter behaves surprisingly like a liquid, contrary to all expectations. More surprising still, explaining this behavior apparently requires an extra dimension of space, something that superstring theory conveniently provides. And so the scientists who study hot matter, cold matter and string matter have found themselves sharing common ground in an extra-dimensional world.
“It surprised the heck out of us two years ago when we started realizing that this was the case,” says physicist Peter Steinberg of Brookhaven National Laboratory on Long Island, N.Y. “It’s a once-in-a-generation convergence of scientific communities. None of us really saw this coming.”
Steinberg and other scientists discussed the new developments recently in Chicago at the annual meeting of the American Association for the Advancement of Science. Speakers at a session there described the surprising confluence of different physics fields as a sort of perfect storm, with the eye centered on the esoteric idea of a “perfect liquid.”
Liquids are usually the Goldilocks state of matter, the not-too-hot, not-too-cold, cohesive yet shapeless assemblages of molecules that exist only in a relatively narrow range of temperatures. Colder, and matter typically becomes solid — rigid and crystalline. Hotter, and matter turns gaseous, with molecules flying about freely and occasionally colliding. Hotter still, and a gas should become plasma, with electrons torn from atoms to form an electromagnetic mélange of charged particles, a gas with flash.
When the universe was very young, and still superhot from the aftermath of the Big Bang, plasma should have been the only state of matter around. And that’s what scientists at Brookhaven expected to see when they smashed gold ions together at 99.99 percent of the speed of light using a machine called RHIC (for Relativistic Heavy Ion Collider). RHIC physicists thought the ion collisions would melt the gold’s protons and neutrons into a hot plasma of quarks and gluons at a temperature of a trillion kelvins, replicating conditions similar to those a microsecond after the birth of the universe. But instead of a gaslike plasma, the physicists reported in 2005, RHIC served up a hot quark soup, behaving more like a liquid than a plasma or gas.
“It’s given us a certain amount of consternation about what to call this stuff,” says Barbara Jacak of the RHIC team. “It certainly shows liquidlike properties.”
An ordinary plasma’s electrically charged particles should block the path of light, for example, just as a thick fog dampens the beams of a car’s headlights. But light passes right through RHIC’s quark-gluon soup, says Jacak. And free-flying quarks would easily be able to zip through the rarefied molecules of a gas, like a bowling ball scattering any pins in its way. But even the heaviest quarks get stuck in the soup.
“That is really astounding,” Jacak says. “It’s as if these bowling pins stopped the big giant bowling ball, and the only way they could do that is if they are somehow tied together with strings.”
Soon after the RHIC experiments, string theorists realized that their strings might be tying the bowling pins together, explaining the odd liquidlike behavior of the quark-gluon plasma. That was a spectacular realization in itself. But around the same time, another branch of physics found itself dipping into a perfect liquid, this time made from cold lithium atoms.
In 2002, physicists at Duke University first created what they called a stable, strongly interacting gas of cold atoms, using the isotope lithium-6. Using laser beams to confine and cool the lithium atoms, researchers produced an atomic cloud with a temperature lower than a tenth of a millionth kelvins — barely above absolute zero.
Curiously, when researchers released the cigar-shaped cloud from its laser prison, it expanded at its sides, but not at the tips. Such an odd “elliptical flow” also described the expanding cloud of quarks and gluons produced at RHIC.
“It’s quite remarkable that we have such different systems, yet we have this common behavior,” says Duke’s John E. Thomas, who also spoke at the Chicago meeting.
Such similar flow seemed especially surprising given the wide disparity of the two systems, with a temperature difference of 19 orders of magnitude separating them. In both cases, the flow seemed to signal the features of a liquid — and a liquid with extremely low resistance to flow. Both cases constituted what physicists call a “strongly coupled” system, in which the particles exhibit collective behavior.
Strongly coupled systems are like a baseball stadium with a big crowd, where the fans can perform the wave, rather than a poorly attended game with the crowd so “weakly coupled” that nobody else notices if one fan stands up. In strongly coupled systems, string theory–based calculations suggest, there is a limit to how low the resistance to flow, or viscosity, can go. A liquid with that lowest possible viscosity earns the label “perfect,” and both the hot RHIC soup and the cold lithium cloud turn out to be nearly as close to perfect as possible.
This formula for perfection is actually a ratio of viscosity to entropy — a measure of disorder that depends on the system’s temperature. For a perfect liquid, the viscosity-entropy ratio is a very small number (about 0.08 in units derived from certain fundamental constants). For ordinary water, the ratio is 380 times higher than that theoretical minimum; liquid helium’s ratio is only 0.7, still about nine times higher than perfection. But both RHIC’s soup and the lithium atoms approach the theoretical limit even more closely. Cold lithium’s ratio is less than 0.5, and the quark-gluon soup is in the neighborhood of 0.2.
Not only does string theory predict the perfect liquid limit for the viscosity-entropy ratio, string math also offers an explanation for how the cold and hot worlds can be so similar. Both systems can be described as something like a shadow world sitting in a higher dimension. Strongly coupled particles are linked by ripples traveling through the extra dimension, says Steinberg, of Brookhaven.
String math describing such ripples stems from an idea called the holographic principle, used by string theorists to describe certain kinds of black holes. A black hole’s entropy depends on its surface area — as though all the information in its three-dimensional interior is stored on its two-dimensional surface. (The “holographic” label is an allusion to ordinary holograms, where 3-D images are coated on a 2-D surface, like an emblem on a credit card.) The holographic principle has value because in some cases the math for a complex 3-D system (neglecting time) can be too hard to solve, but the equivalent 4-D math provides simpler equations to describe the same phenomena.
“The point is that we have two different kinds of systems capturing the same kind of physics,” says string theorist Clifford Johnson of the University of Southern California in Los Angeles. “String theory provides us with a dictionary that translates between these two systems.”
One of the two systems is a realm of four spatial dimensions where the string math describes gravity and quantum theory; the other is the 3-D world of quarks and gluons. Usually the math for describing each of these systems looks very different. But string theory’s extra dimension allows the math to be transformed in ways that show the two systems to actually be equivalent — in technical terms, the systems are “dual” to each other.
“The bottom line is we can exploit all this, because we can use … easy computations in the gravity system to compute hard-to-compute things in the dual system,” Johnson said at the Chicago meeting.
So just as shadow physics is hard to explain without knowing about objects in the third dimension, quark physics makes more sense using the 4-D math. Quarks can be viewed, for instance, as the endpoints of strings that vibrate in an extra dimension, and that explains how they can be so strongly coupled. Precisely the same math can then also describe the collective behavior of the cold lithium atoms. As Johnson points out, viscosity is all about how neighboring pieces of a fluid communicate with each other. With an extra dimension, that communication can take place as disturbances in the higher dimensional space, explaining the perfect liquid behavior.
Strings strike back
In recent years it has become popular to criticize string theory as out of touch with reality. Popular books have been written by scientists, some prominent and others not so prominent, arguing that string theory makes no predictions that experiment can test, that its fundamental objects can’t be observed, that physicists have wasted their time on an enterprise that isn’t even scientific to begin with.
Such arguments leave an impression of utter unfamiliarity with the history of science. In times past, the same kinds of aspersions were cast against quarks, neutrinos, even the very existence of atoms. Superstrings are in good company. And string theory’s limit on how low viscosity can go now seems to have established that string math does indeed mirror something real in nature. “This may well be the first prediction from string theory to be validated by experiment,” Steinberg writes in a recent paper (arxiv.org/abs/0903.1474).
Superstrings’ success with perfect liquids does not, of course, establish that the whole theory is the correct description of the universe. Much work remains to figure out how much of reality string theory actually captures beyond the realm of perfect liquids. But the usefulness of superstring math in these instances argues strongly that those equations capture something true. Establishing that truth for certain will still not be easy.
It’s not surprising, of course, that such groundbreaking science should be difficult and controversial. Advances in physics today are naturally much tougher to achieve than they used to be —because the problems remaining to be solved are precisely those that have resisted solution for so long.
“A new truth always has to contend with many difficulties,” the German physicist Max Planck said decades ago. “If it were not so, it would have been discovered much sooner.”
Steinberg, P. 2007. Hotter, denser, faster, smaller...and nearly-perfect: What's the matter at RHIC? [Go to]
Steinberg, P. 2009. Soft physics from RHIC to LHC. [Go to]
Kovtun, P.K., D.T. Son, and A.O. 2005. Starinets viscosity in strongly interacting quantum field theories from Black Hole physics. Physical Review Letters 94(March 25):111601.http://arxiv.org/abs/hep-th/0405231
Turlapov, A., et al. 2007. Is a gas of strongly interacting atomic fermions a nearly perfect fluid?
RHIC News release:
View slides from the AAAS session “Quest for the Perfect Liquid”: [Go to]