Plato considered it first.
What if everything we hold dear is but a thin slice of some larger, unreachable reality, like a flickering shadow cast on the craggy wall of a cave? What if the moon and stars, your home, your thoughts, your cat, are but projections on this wall -- mere suggestions of unfathomable realms beyond?
In the last few years, a mathematically rigorous version of Plato's 2,000-year-old thought experiment has been refashioning the way physicists think about everything from subatomic particles to the Big Bang. The universe we see, according to this scenario, is stuck on a thin membrane of space-time embedded in a much larger cosmos. And our membrane may be only one of many, all of which may warp, wiggle, connect and collide with one another in as many as 10 dimensions. Physicists call this new frontier the "brane world."
The idea could help solve a long list of outstanding mysteries. Among them: What is the "dark matter" that seems to make up 90% of the universe? And why is gravity trillions of times weaker than electromagnetism?
The revolution was set off in the mid-1990s when UC Santa Barbara physicist Joe Polchinski determined through mathematics that branes were a surface to which things attach, like hair to skin -- except the "things" in this case were the minuscule "strings" that may well be the fundamental ingredients of the universe.
"I was just fiddling around with mathematics.... Within a week or two [other physicists] had done things with it I hadn't envisioned. It was like taking the stopper out of the dam. Things poured through."
Alan Guth of the Massachusetts Institute of Technology, creator of the currently accepted version of the Big Bang, said recently he felt a little like Rip Van Winkle -- picking up his head from a long sleep only to notice that the landscape of physics he thought he knew had suddenly, drastically, changed.
Stephen Hawking of the University of Cambridge, among others, envisions brane worlds bubbling up out of the void, giving rise to whole new universes. He ends his latest book, "The Universe in a Nutshell," with a call to explore this "brane new world."
One might well wonder why such a seemingly bizarre concept has attracted so many well-established physicists. The short answer is: desperation.
The laws of nature that describe the large-scale universe to an astonishing degree of precision (Einstein's general relativity) are incompatible with the laws that describe the small-scale universe with the same astonishing exactness (quantum theory). This means either that one of these well-tested theories is wrong (all but inconceivable) or that there is some larger, more encompassing theory that somehow accommodates both.
To date, the only theory that comes close to marrying the two is "string theory" -- a mathematically elegant set of ideas that has swept the world of physics over the last few decades. According to string theory, the basic ingredients of the universe are not point-like particles, but tiny strings vibrating in 10-dimensional space. Although still untested, string theory has scored a spectacular series of theoretical successes, earning it an ever-widening circle of admirers.
And yet string theory remains a realm apart from day-to-day physics -- lovely to behold but innately aloof.
For one thing, the strings are so small that it would take a particle accelerator larger than the solar system to create the energies needed to "see" them. This means, in effect, that strings can never be detected.
For another, the complex mathematics required to deal with the tortured 10-dimensional landscape is beyond the reach of most physicists.
Brane models change all that. Unlike in string theory, the extra dimensions in brane worlds can be big, infinitely big. "It led to a whole new bunch of possibilities that could be experimentally tested," said physicist Jim Cline of McGill University in Montreal.
What's more, branes don't require the full range of mathematical tools required for string theory, opening the door to new groups of scientists. "You can use methods that are part and parcel of more traditional physics," said Columbia University physicist Brian Greene. "So a person who's not a string theorist can jump into the field and make contributions."
This sense of promise was palpable last summer at the Aspen Center for Physics, where string theorists and cosmologists -- the scientists who study the origin and structure of the universe -- gathered for a workshop to explore links between the smallest scales in the universe and the largest. Brane scenarios popped up everywhere, enveloped in the thick fog of uncertainty that clouds the birth of new worlds.
The setting was strangely church-like. The faithful sat in rows under spires of white-barked aspens, their round leaves fluttering in the wind.
In front, a maestro in sneakers tapped out symbols on a blackboard, chalk flying like fairy dust, black jeans covered in white handprints. There was lots of talk about the infinite; lots of recitation and response. Everyone strained to channel some larger reality through equations.
"Your bulk could contain many 3-branes," one physicist said.
"The 9-branes could still annihilate."
This was not your grandmother's physics. There were no objects in the usual sense. No matter, no particles. Not even numbers. Only "instantons," "alpha vacua" and multidimensional membranes wrapping around one another, traveling down throats of black holes and bouncing back, transformed.
Even to physicists, much of this seems unbearably strange. But in physics, strangeness comes with the territory. "When I first learned about quantum physics as an undergraduate, it just about destroyed my mind," said Stanford post-doctoral fellow Stephon Alexander. "And now, 12 years later, it's just a tool."
There's actually nothing particularly new about the idea that space may extend into unseen dimensions, or even that the world we know is somehow trapped on a membrane.
Extra dimensions were such a hot topic in the 19th century that Victorian schoolmaster Edwin Abbott wrote a famous science fiction novel, "Flatland," based on the notion that our limited perceptions prevented us from seeing worlds existing right in front of our three-dimensional noses. Albert Einstein made extra dimensions an integral part of physics when he used a fourth dimension, time, in his theory of relativity in 1905. Ten years later, he showed that this interwoven fabric of space-time could warp under the influence of massive objects -- "causing" the force we know as gravity.
Extra-dimensional membranes were kicking around in string theory since at least the mid-1980s, but no one took them very seriously. One of the first suggestions that the world we know might be stuck to such a membrane appeared in a 1985 paper that was a parody of string theory titled "The Super G-String" by V. Gates, et al., from the University of Cauliflower (actually, physicist Warren Siegel of State University of New York, Stony Brook). "It was based on a serious paper that was totally overlooked because it was before its time," Polchinski said.
The branes playing such a large role in physics today are richer and more mathematically rigorous than early versions.
Essentially, a brane is a discontinuity in space-time, a boundary where things meet, like the surface of a pond where the water meets the sky.
"It's a defect in the quantum fabric," said Ruth Gregory of the University of Durham in Britain. On one side of the defect would be the vacuum of empty space. A vacuum with somewhat different properties might exist on the other side.
Imagine our brane as pond scum -- a thin film that divides the air above from a deep (perhaps infinitely deep) body of water below. Most of what we experience is trapped in the scum. But beyond is a whole other world of currents swirling beneath the surface. Their motion might tug on our scum. We'd feel it as nothing but a gentle disturbance, never dreaming of what lurks below.
A brane doesn't always divide one thing from another. It may just be a condensation of stuff, "a localized lump of energy and curvature that likes to hang together," Stanford University physicist Steve Shenker said.
Either way, it's a place where things get stuck -- like the scum on the pond. "That was the revolution," said Harvard University physicist Lisa Randall. "To realize that branes were honest-to-goodness objects."
Randall played a pivotal role in the revolution when she and Johns Hopkins University physicist Raman Sundrum realized that branes could be infinitely large and yet remain invisible.
The reason: We can't see anything outside our brane, because light can't escape or enter it. We can't hear anything outside, because sound travels through matter, and matter is stuck to our brane. We can't use radioactivity to sense what's beyond, or even break through with nuclear bombs, because nuclear forces are also firmly nailed to our brane. There could be a big blue elephant sitting not a millimeter away in another dimension, but we wouldn't know it's there because everything we use to "see" is stuck to our brane.
Only gravity can't be glued to a particular brane. Gravity, as Einstein revealed, is the curving of space-time itself, so it wanders willy-nilly where it will, leaking off our brane into what physicists call "the bulk" -- the rest of space-time.
Brane scenarios offer an elegant explanation for why gravity is such a weakling: Maybe it's not any weaker than the other forces. Maybe it's just concentrated somewhere else in the bulk, or on another brane.
Explaining the wimpiness of gravity is but a taste of what this Brane New World might do.
Consider another embarrassing problem that has stumped astronomers for decades. At least 90% of the matter in the universe is AWOL. Or more precisely, it is known to exist because of its gravitational pull (without it, galaxies wouldn't hold together) but can't be detected by any other means. The standard approach has been to populate the universe with exotic new forms of matter, too elusive to be readily seen.
If our brane is but a small slice of a much larger cosmos, however, the "dark matter" might be nothing but ordinary matter trapped on another brane.
Such a shadow world, Hawking speculates, might contain "shadow human beings wondering about the mass that seems to be missing from their world."
Or take the mystery of why elementary particles always appear in triplets, each set heavier than the next.
One possibility is that each triplet is the same particle repeating itself on three layers of branes. They would have different masses on our brane for the same reason as shadows on a wall can be different sizes depending on the distance of the object that casts them.
"One of the neat things about the whole extra-dimensional idea," Polchinski said, "is that all the physics that we see -- all the kinds of particles and their detailed properties -- are reflections of some inner geometry."
As in real estate, value depends on location, location, location.
The physicists most entranced with brane worlds are cosmologists. Over the last decade, a new array of telescopes and satellites has provided them with sophisticated tools for taking the measure of the universe. What was once little more than navel gazing is fast becoming a data-drenched science.
But cosmologists need string theory to understand the origin of the universe, because laws of physics break down at the tiny distances and immense gravity at play in the Big Bang. For now, cosmologists can see back in time only so far, and no farther.
Consider the Big Bang. According to current theory, the universe sprang from an infinitely small speck of space-time known as a "singularity" -- a paradox in the accepted laws of physics, which hold that nothing can be infinitely small.
"A singularity is a euphemism for: 'Things have gone haywire.... Things make no sense,' " said Greene, one of the coordinators of the Aspen workshop. "The Big Bang singularity is an 'It doesn't make sense' on the most important problem -- namely, how did it all begin."
Branes can enclose the Big Bang singularity like a sheet of cellophane -- avoiding the problem of the infinitely small by giving the singularity some dimension.
Not surprisingly, the string-cosmology connection that brane worlds brought about is also producing something of a culture clash. Until recently, string theorists have remained skeptical of the grand theories of cosmologists. String theory is mathematically rigorous. Cosmologists are a wilder bunch, willing to try out almost any model of the universe and see where it leads.
"We know how branes work," said string theorist Nathan Seiberg of the Institute for Advanced Study in Princeton, N.J. "We know what are properties of branes, and what are not properties of branes. [Cosmologists] violate all the rules. Is this good or bad? I'm not sure. Because if they come up with something which violates the rules of string theory but does all sorts of other wonderful things, then maybe we in string theory will have a motivation to look into it."
Branes already have brought a whole new zoo of exotic species into the world of physics. There are skinny branes and fat branes; empty branes and full; active and still.
"A brane which is wiggling a lot would translate to a brane that has excitations on it, particles on it," said McGill's Cline. That would be a brane with atoms, forces, us. "But I could also have a cold brane," he said. "That would be like a cold, empty universe. The brane still has some energy density, but there's no particles living there."
And while the term brane derives from membrane -- a two-dimensional surface -- branes could also exist in every possible dimension. A string is a "1-brane," for one-dimensional object. Brane worlds (like the one we might live in) must by necessity be "3 plus 1" branes -- three dimensions of space plus one of time. But you can just as easily have a pair of 10-dimensional branes bounding an 11-dimensional universe.
For now, no one knows whether the building blocks of the ultimate theory will be strings or branes. "You can't really say," Polchinski said. "It's kind of Zen-like, but in a very precise way."
Ultimately, brane worlds will stand or fall, like all science, on the twin tests of consistency and experiment. Whatever bizarre brane worlds may exist in some larger dimensional landscape, they can't change what we perceive. The stars can't slip off into hyperspace. The cat can't be disturbed from the couch. Physics has to answer to nature as we know it.
Experimental evidence could come in the next decade from two very different realms. A new particle collider under construction in Europe could reach high-enough energies to produce, say, a five-dimensional "particle" of gravity -- a telltale sign of brane worlds beyond. This particle might be detected as energy missing from a collision because it "leaks" into an extra dimension.
At the same time, cosmologists are figuring out ways to read the signature of extra dimensions in the microwaves that pervade space as the afterglow of the Big Bang; the effects would be subtle but detectable, with a new generation of satellites.
"We just have to keep hoping that nature will be kind," Cline said.
In the end, there's always the chance that all these ideas will turn out to be too, well, off-the-wall. "Who knows?" said University of Chicago physicist Sean Carroll. But even if brane worlds aren't real, Carroll said, "they will have taught us a useful lesson that we should have known all along, which is that we don't have a clue to what's going on."
Polchinski, for one, believes that branes are probably real, even though he isn't sure where the idea will lead. "It's possible that nature doesn't work that way," he said. "But it's so rich with possibilities, if it's not good for this, it's probably good for something else."