We live in three dimensions: You can go north-south, east-west or up-down. Simple enough. If you add one more dimension for time – as Albert Einstein suggested -- that's four altogether.

That's plenty for most of us. And, until recently, it would have been enough for most physicists as well. But the past few years have brought a flurry of new ideas about the structure of the universe, and physicists are now contemplating multidimensional worlds that put our seemingly-three-dimensional surroundings to shame.

It all starts with string theory, which attempts to unify gravity with the other forces of nature. In the string picture, the most fundamental "bits" of matter are not point-like particles but rather one-dimensional loops of string. But to make the theory consistent -- to make the math work out -- string theory relies on a framework involving extra dimensions.

"String theory is the only theory we know about that consistently puts in quantum mechanics and gravity, and it necessarily has other dimensions," says Lisa Randall of Harvard University.

"It just doesn't work if the theory is fundamentally 3-plus-1 dimensional," that is, if the theory contains only three dimensions for space plus one for time.

"So if string theory really is the right theory, there are these extra dimensions. And the question isn't, 'Why are they there?' The question is, 'What happened to them?' What are their consequences? Do they do anything useful?"

The answer to that first question -- what happened to the extra dimensions -- seems to be straightforward: They're all around us, but hidden from view. That is, they're thought to be "curled up" on scales far too small to see.

As an analogy, think of a drinking straw: Seen from far away, it looks like a one-dimensional stick. Only when we see it up close does the other dimension -- the circular direction around the straw's circumference -- reveal itself.

The difference between strings and the drinking straw is merely one of scale: String theory's hidden dimensions may fold in on themselves over distances as short as 10{+-}{+3}{+3} centimetres (that's a decimal followed by 32 zeros and then a 1) -- more than a billion billion times smaller than an atomic nucleus.

However, theorists have recently suggested that the folding might happen on a larger scale, maybe approaching millimetre-size.

The original version of string theory was weird enough, but, in the 1990s,
physicists came up with a refined version known as M-theory. In the new picture, one-dimensional strings give way to higher-dimensional membranes, or "branes" for short.

As theorists investigated the properties of these branes, they found That not all of the extra dimensions needed to be curled up. Some of them, in fact, could be infinite.

That was big news for cosmologists, who had been used to thinking of a three-dimensional cosmos that started off with a big bang about 14 billion years ago. Before long, there were new models of the universe inspired by M-theory -- and they make our familiar three-dimensional cosmos seem almost dull by comparison.

These new "brane world" models offer a startling new description of the cosmos. In some of the scenarios, the entire visible universe is merely a "3-brane" -- a three-dimensional membrane -- embedded in a larger structure, called the "bulk," which has at least four space dimensions (and, as usual, one more for time).

Of course, no one can envision four dimensions, so if you want to picture
what these brane worlds are like, it's best to imagine a simpler model in which one of the dimensions is stripped away. Now, our universe becomes a two-dimensional sheet and the bulk becomes ordinary three-dimensional space.

The remarkable part of the theory is that there's no reason to presume that our universe -- our 3-brane -- is unique. There could be any number of "parallel" branes nestled alongside ours in the four-dimensional bulk. Think of a series of parallel sheets of paper suspended alongside one another.

Why don't we notice these other branes? Theorists believe that most of the known physical forces operate only within a particular brane. For example, we can't see these parallel branes because light is governed By electromagnetism; photons of light are trapped, stuck on the surface of our brane. The same goes for the nuclear forces that operate within atoms. Matter, too, is confined: We can't fly a spaceship into another brane world.

The only exception seems to be gravity: It is thought that gravity can "leak out" of the brane, perhaps allowing scientists in one brane – one universe -- to infer the presence of a parallel brane.

If the theory is right, it could explain the mystery of the "dark matter" that has puzzled astronomers for decades, the mystery of why much of the universe seems to be composed of something other than normal, luminous matter such as stars and galaxies. The missing matter, physicists speculate, could simply be ordinary matter on one of these parallel branes. Any light it emits will remain trapped in its own world, but its gravity reaches across to ours.

"The only way these branes interact is through gravity," says Paul Steinhardt of Princeton University, a pioneer in developing brane-world cosmologies. A heavy object on a parallel brane "would draw matter [from our brane] towards it -- but we couldn't touch, feel, or see it," he says. "So it would seem to us to be a kind of dark matter. In fact, maybe the dark matter is matter on this other brane."

The case is obviously still speculative, Prof. Steinhardt says, "but it seems like a natural possibility."

In 2001, he and his colleagues developed a particular brane-world picture that they called the "ekpyrotic" model of the universe. (The name comes from a Greek word meaning "cosmic fire.")

In the ekpyrotic picture, the big bang is recast in an entirely new light. Instead of a primordial explosion marking the beginning of time, it may have been a collision between our brane and a parallel brane that triggered the formation of matter in our universe. In other words, the big bang was not the beginning; it was merely a transition from one cosmic epoch to another.

Prof. Steinhardt later went a step further, suggesting that such collisions happen at regular intervals, producing a repeating cycle of "bangs" and "crunches." His "cyclic model" brings to mind oscillating-universe models of past decades -- only now the idea seems to have the support of string theory and M-theory.

"Imagine a force between these two three-dimensional worlds that would tend to draw them together, as if they were two rubber sheets being drawn together by a spring," he says. "At regular intervals, they would come together, smash together, creating a certain amount of heat -- which we would think of as radiation and matter -- and then
bounce apart."

Many prominent physicists seem intrigued, if not entirely persuaded, by brane-world scenarios such as the ekpyrotic and cyclic models. Cambridge physicist Stephen Hawking, once skeptical of extra dimensions, now routinely discusses brane worlds in his papers and at conferences (his most recent public lectures have been titled "Brane New World").

Of course, the idea of extra dimensions would be merely philosophy (with a heavy dose of mathematics thrown in) if there were no way to test it. But theorists believe that there may be at least three ways of indirectly detecting these extra dimensions.

First, because gravity seems to be intimately linked to the structure of space, they would like to examine gravitational interactions at both the very shortest and the very longest distance scales.

For example, any deviation from Isaac Newton's "inverse-square law" -- in which doubling the distance reduces the force to one-quarter -- would hint at the presence of hidden dimensions.

Physicists would also like to take a closer look at "gravitational waves," the stretching and shrinking of space produced by any massive object that is accelerating. The first gravitational-wave detectors are only now entering operation; eventually, they may reveal waves from high-energy cosmic events such as colliding black holes.

But these exotic waves may be seen indirectly by another method: It is thought that gravitational waves washed through the early universe, and they may have left their imprint on the cosmic microwave background radiation, the faint microwave "echo" of the big bang. If the background radiation can be scrutinized in close enough detail, it may reveal signatures of those ancient gravitational waves, and, perhaps, allow physicists to distinguish between brane-world and conventional big-bang scenarios.

Finally, extra dimensions may reveal themselves in experiments at particle accelerators such as the Large Hadron Collider now under construction at CERN, near Geneva. In certain kinds of collisions, some of the particles produced could seem to disappear, carrying energy off into one of the hidden dimensions.

"Extra dimensions are a compelling field now," says Joe Lykken of the Fermilab particle accelerator near Chicago.

While the idea of extra dimensions used to be on the fringes of physics, he says there might soon be hard data to support -- or refute -- such ideas. "You can actually go out and do experiments now and verify these models, or rule them out. That's what makes this an exciting field right now."

Dan Falk's book, Universe on a T-Shirt: The Quest for the Theory of Everything, was the winner of this year's Science in Society Journalism Award from the Canadian Science Writers' Association.

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Dan is the author of the award-winning new book, "Universe on a T-Shirt: The Quest for the Theory of Everything" (Viking Canada). The book, aimed at beginners, tells the story of the 2500-year-old search for nature's ultimate laws. It is the winner of this year's science journalism award from the Canadian Science Writers' Association. In 1999, he was the winner of the American Institute of Physics Prize for Science Writing in Physics and Astronomy for the non-specialist in the category of broadcast media for his documentary "From Empedocles to Einstein", which aired on the CBC radio program "Ideas". He is also featured on the Canadian Association of Physicists Careers page.