By George Johnson, New York Times
September 22, 1998

Related Article
New Dimension in Dance: Thinking Man's Macarena

Diagram
So Are We Quarks, Strings, Branes or What?

When many science fans last tuned in, physicists in search of the universe's deepest secrets were pinning their hopes on a dazzlingly beautiful and bewildering invention called superstring theory. The ultimate explanation of nature would finally come together, it was promised, if one thought of the hundreds of subatomic particles as musical notes produced by incredibly tiny strings vibrating in a realm made of 10 dimensions. Never mind that the universe seems to be made of only four dimensions (counting time). The other six were said to be conveniently curled up into vanishingly tiny balls, out of sight and mind.

	Brian Payne for The New York Times
	A workshop on M theory and black holes was held this summer at the Aspen Center for Physics in Colorado.

Since its quiet beginnings in the 1960's, the idea has flared and faded through a first "superstring revolution" in the mid-1980's and a second revolution a decade later. In recent months, a new wave of discoveries is fomenting what some physicists are excitedly hailing as a third revolution, leading toward a day when all the laws of creation may fit into a single, elegant frame.

But the subject of the latest enthusiasm is not called superstring theory anymore. Along the way, the name has changed to M theory, with the M standing for "magic," "mystery," "mother" (as in mother of all theories) or, more prosaically, "meta," "matrix" or "membrane." For the wiggling superstrings, which were at least vaguely possible to visualize, have been joined (and possibly supplanted) by even more abstract entities: membranes, or "branes," which come in as many as nine dimensions.

All of creation, according to some recent speculation, may be concocted from these barely imaginable objects: God's Tinkertoys. If this realization is correct, then physics may be closer than ever to writing down the elusive theory of quantum gravity, a feat that would unify quantum mechanics and general relativity -- the two hitherto irreconcilable pillars of modern physics -- and explain all the forces of nature in the same terms.

"People are going to look back on this as one of the most important periods in 20th century physics, as significant as the development of quantum mechanics and relativity," predicted Dr. John Schwarz, a physicist at the California Institute of Technology and an early pioneer of string theory.

Enthusiastic pronouncements from the string theorists themselves are nothing new. But the excitement is also leaking into other domains, like cosmology.

A theory of quantum gravity would unify all the forces of nature.

Dr. Andrew Strominger, a Harvard University physicist who recently used M theory to leap across disciplines and solve a problem involving black holes, said: "We were once considered semi-crackpots working on some bizarre idea. While that may still be true, at least we're no longer perceived that way."

One evening this past summer at the annual superstring fiesta, Strings '98, in Santa Barbara, Calif., some 200 physicists heralded the latest developments by dancing the Macarena, or, rather, a new version called the Maldacena, named after a young Argentine theorist, Dr. Juan Maldacena (pronounced mal-dah-SAY-nah) of Harvard University, whose new theory is the source of the latest excitement:

You start with the brane
and the brane is B.P.S.
Then you go near the brane
and the space is A.D.S.
Who knows what it means
I don't, I confess
Ehhhh! Maldacena!

As Dr. Jeffrey Harvey, a University of Chicago theorist, rapped out the lyrics, one esoteric verse piling on top of another, the physicists worked their way through the 14 steps of the dance.

What the message came down to was this: Physicists have a very successful framework called quantum field theory that describes three of the four forces. The strong force holds the atomic nucleus together; the weak force governs radioactive processes, and electromagnetism combines electrical and magnetic effects. All three can be portrayed as fields transmitted by particles called quanta. For electromagnetism the carriers are photons, for the strong force gluons, and for the weak force W and Z particles. But no one has been able to fit gravity into the picture. It is assumed that the force must be carried by particles called gravitons, but getting these to obey the laws of quantum field theory has proved impossible.

Gravity can be described, however, by superstring theory, or M theory, using the completely different vocabulary of strings and branes. Maldacena's conjecture, elaborated in an explosion of more than a hundred recent papers by superstring theorists, suggests the possibility of a deep, hidden connection between quantum field theory and string theory, these two seemingly immiscible worldviews.

"This is a very dramatic claim," said Dr. Nathan Seiberg, a theorist at the Institute for Advanced Study in Princeton, N.J. In addition to bringing gravity and the other forces closer together, the tentative links Maldacena has found may provide a powerful new calculational tool for solving difficult problems in particle physics.

The Origin
New Vision for a Quandary

String theory first arose in the late 1960's and early 70's as an ill-fated attempt to understand the strong force. Parsing the world in terms of particles and fields had already led to a spectacularly successful theory of electromagnetism, and the weak nuclear force was on the verge of succumbing to a similar explanation.

But the strong force seemed, at the time, stubbornly resistant. Some physicists were taking this as a sign that field theory needed to be scrapped and replaced with a whole new vision. What emerged was the possibility that particles were really different notes produced by vibrating strings.

The potential payoffs seemed immense. One big problem of dealing with the infinitesimally small particles of quantum field theory was that they caused mathematical absurdities to pop up in the equations, the equivalent of trying to divide a number by zero. The result was infinite terms that rendered the calculations nonsensical. The problem, which had been solved for electromagnetism, crippled attempts to explain the strong force. If sizeless particles were replaced by little strings, the mavericks proposed, maybe the cancerous infinities would go away.

But there were many problems to overcome. If one could believe the equations, the strings would have to be vibrating in a space of 25 dimensions (with a 26th representing time). Where were the extra 22? The equations also kept coughing up a weird massless particle whose spin (a quantum mechanical analogue of rotation) was 2. The only such particle anyone knew about was the purely hypothetical graviton. If physicists ever succeeded in devising a quantum field theory of gravity, the graviton would be the carrier. But what was it doing in a theory of the strong force?

In any event, physicists soon succeeded in explaining the strong force with a field theory called quantum chromodynamics, or Q.C.D., and most theorists turned their backs on strings.

According to Q.C.D., elemental building blocks called quarks come in three "colors" (somewhat analogous to electrical charge). The quarks are bound together by gluons, the carriers of the strong force, to form protons, neutrons and their subatomic kin. By the end of the 70's, Q.C.D. had been incorporated into the Standard Model, an amalgam of quantum field theories describing the strong force, the weak force and electromagnetism. The most daring theorists were trying for a "grand unified theory" in which all three forces were shown to be manifestations of a single superforce. But gravity remained far out of the game.

The Revolution
Tying in Gravity With Superstrings

But not everyone gave up on strings. In the mid-1970's, two physicists, Dr. Schwarz and Dr. Jöel Scherk, tried to turn one of string theory's flaws into a virtue: maybe the persistent appearance of the graviton in the equations was no accident. Maybe what they were looking at was not a model of the strong force, but a model of gravity -- a new way to formulate Einstein's general theory of relativity. And if gravity could be described by string theory, then maybe the other forces could also be reformulated this way. All would then be unified into the same package.

Around this time, string theorists found they could pare the 26 space-time dimensions required by the original theory to a mere 10. Along the way, the theory came to be called superstrings when it was endowed with a hypothetical quality called supersymmetry, in which the force-carrying particles like gluons and the matter-making particles like quarks are closely knit together.

Ten dimensions were still a lot to swallow. And, in an embarrassment of riches, it appeared that one could potentially construct an infinite number of different 10-dimensional string theories. How would physicists ever know which one described this universe? A breakthrough came in the mid-1980's when, in the first revolution, it was shown that of all possible string theories, only five were mathematically sturdy; the rest would come crashing down because of various inconsistencies. But this was still four theories too many. Even worse, there were still tens of thousands of different ways to roll up the six extraneous dimensions to get the theories to describe a four-dimensional world.

A small band of die-hards remained optimistic. Dr. Edward Witten, a rising young star of string theory, romantically described it as "a piece of 21st century physics that fell by chance into the 20th century."

They kept quietly toiling away until the second revolution of the mid-90's. The many ways to hide the extra dimensions were found to be closely related. And the five 10-dimensional theories turned out to be just different views of a single underlying 11-dimensional theory. All could be connected by "dualities," mathematical lenses through which the seemingly different turn out to be the same.

"It reminds me of the story of the blind people examining the elephant," said Seiberg, the theorist at Princeton. "We used to look at different pieces and did not see the big picture."

In funneling the plenitude of theories into one, physicists realized that their equations spoke of a world made not just from strings but also from membranous things called p-branes, with the p standing for the number of dimensions. What is normally thought of as a membrane is a two-dimensional surface, like a bedsheet, stretching across a three-dimensional space. This is now called a 2-brane. A point is a 0-brane, and a line is a 1-brane. Extending the idea in the other direction, one can have 3-branes, 4-branes, 5-branes, all the way up to 9-branes: nine-dimensional surfaces flapping inside a 10-dimensional world.

Especially important to M theory is a special type called a D-brane, named for the 19th century mathematician Peter Dirichlet. In 1995, Dr. Joseph Polchinsky of the University of California at Santa Barbara showed that D-branes, which also come in as many as nine dimensions, described surfaces on which strings can end. But these surfaces are more than mere boundaries: D-branes are now seen as entities at least as fundamental as strings. According to a controversial version of M theory called Matrix theory, D-branes may be the fundamental objects from which strings and everything else is made.

Before long, physicists like Dr. Strominger of Harvard were finding that some of the puzzles about black holes could be better understood if they were thought of as being made from D-branes. In fact, D-branes themselves could be conceived of as extremely tiny black holes. A string came to an end because the rest of it was sucked down one of these infinitesimal wells. A closed string, shaped like a loop, became an open, two-ended string when a chunk of it was bitten off by a D-brane.

And D-branes are an essential part of the choreography of the mathematical dance called the Maldacena, in which string theory and field theory pirouette on the same floor. Dr. Maldacena used D-branes to construct a quantum field theory similar to Q.C.D., in the ordinary four dimensions.

He also used D-branes to build a 10-dimensional string theory (with 5 of the dimensions curled up and hidden away). By their nature string theories include gravity. Thus the excitement when Maldacena showed that the two theories were intimately related. The unification of all four forces may now be a step closer to realization.

The Universe
Linking Inner Space to Outer Space

But the finding is still just a conjecture, lingering in the netherworld between hunches and fully developed theories. To get his model to work, Maldacena had to pull some clever theoretical tricks. In Q.C.D., quarks come in three "colors." Drawing on an idea from the Dutch physicist Gerard 't Hooft, he simplified the calculations by using a toy theory with many more colors.

And so far, the connection Maldacena found only works in something called anti-de Sitter space (after the Dutch astronomer Willem de Sitter). An anti-de Sitter universe would be "curved" in such a manner that the expansion from the big bang would gradually decelerate and collapse into a big crunch.

Recent evidence hints that in our own universe the expansion may be eternally accelerating. But that is far from certain.

Taking into account these qualifications, the bottom line of the Maldacena conjecture is this: The curvature of the space-time described by the string theory is equivalent to the number of colors in the field theory; more colors mean less curvature. An unexpected bridge may have been found between two different theoretical worlds.

Physicists are now trying to extend the work so it applies to more realistic situations. Dr. Strominger, for one, is betting that the relationship will be found to hold across the board, showing that "string theory and quantum field theory are just two sides of the same coin."

"We're not at the bottom of it yet," he said. "We're all in a good mood because we think there is a lot more to be learned."

Maldacena's work also supports a hot new theory that the universe is holographic. In laser holography, a three-dimensional object is projected onto a two-dimensional plane, retaining the richness of the original image. In the Maldacena model, the four-dimensional field theory can be thought of as a holographic projection of the five-dimensional string theory (remember that the other five dimensions are rolled up and tucked away). In a holographic universe, the information about everything in a volume of space would be displayed somehow on its surface. The bizarre implications of this notion are only beginning to unfold.

The Meaning
Just Fancy Math, or Real Science?

Maldacena concedes that his conjecture is burdened with the criticism that applies to all of M theory: that it cannot yet be tested by experiment.

"Up to now, all that has been done is mostly from the conceptual point of view," he said. "There are no experimental predictions so far, but hopefully there will be in the future. We don't know whether that will happen soon or not. How far you can extend a new method is a question that is always hard to answer."

Some physicists still maintain that for all the conceptual revolutions in string theory, there is little to show but a lot of beautiful mathematics.

"No observable physical phenomena have been explained," said Dr.'t Hooft. "So it is tempting to be sarcastic about these developments."

And even M theory's enthusiasts are baffled by what it all really means.

"Before the second superstring revolution, life was simple," said Dr. Steven Giddings, a theorist at the University of California at Santa Barbara. "We believed that everything in the universe, quarks, photons, gravitons, electrons, and the rest, were all made out of strings. The recent upheaval has shattered that view, and we've yet to find a convincing logical structure to replace it."

Giddings continued: "We no longer know what the fundamental constituents of the theory are. Strings and D-branes appear equally fundamental, and it's not clear whether either one of them is made out of the other.

Perhaps they're all made from something even more fundamental. It's like climbing a mountain to reach the top and discovering that it's just a foothill to a more distant range. We've made an enormous amount of progress in the past few years, but now realize the greater depth of our ignorance."

He was leaving that day, for a peak in the Sierras, to do something he considered easy: climbing a thousand-foot wall of vertical ice.

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