June 19, 2000

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How much of the universe can you pinch between your thumb and finger? Maybe a lot more than you think. Far reaches of the cosmos may lie less than a millimeter away. Whole other universes may be within your grasp. Even if you cannot see these distant places and other worlds, you may be in communication with them through that most familiar of forces, gravity.


In just two years this seemingly preposterous proposal has become one of the hottest theories in physics. The Los Angeles Times and New Scientist have already written it up for the public, the BBC and Discover magazine have stories in the works, and this summer Scientific American will feature an article by its originators, Nima Arkani-Hamed of Berkeley Lab's Physics Division and the University of California at Berkeley, Savas Dimopoulos of Stanford University, and Gia Dvali of New York University.

Arkani-Hamed and his colleagues came up with the theory (which is still awaiting a catchy name) to explain why the Standard Model of particle physics can give a common explanation for all the forces of nature -- except gravity. Many other attempts to explain this failure have been made, but the new theory has an enormous advantage over them all: it can easily be tested in giant particle accelerators already under construction and in tabletop experiments already underway.

One facet of the puzzle is the huge disparity between the apparent strength of gravity and that of electromagnetism and the nuclear forces. Although we think of gravity as strong -- we can get hurt if we fall down -- compared to electromagnetism, gravity is astonishingly weak. It takes the whole mass of the Earth to hold a pin on a tabletop; a toy magnet can lift it easily.

This weakness makes it difficult to study gravity's relationship to the other forces. For example, the Large Hadron Collider at CERN, scheduled to begin operating in 2005, will probe an energy region where electromagnetism and the nuclear forces show themselves to be aspects of a unified force. To incorporate feeble gravity in this picture would require energies so vast they have not existed since the first moments of the Big Bang.

Yet what if gravity only seems weak? What if, unlike electromagnetism and the nuclear forces, gravity is not confined to our everyday world of three spatial dimensions and one time dimension? If gravity is acting in two or three or several other dimensions as well as the familiar four, we may be experiencing only part of its effects.

Mathematics has no trouble describing multidimensional spaces, but human brains aren't built to visualize more than three spatial dimensions. Imagine instead that our world is reduced to a single spatial dimension, an arbitrarily thin strand of fiber-optic cable.

Photons, the quantum particles of electromagnetism, easily move back and forth along our fiber, but they are trapped here. There may be other fiber-worlds, some right next to ours, but because our photons can't move sideways and reflect objects outside, they can't bring us the news.

Gravitons, the quantum particles of gravity, have no such limitation. Indeed, in a universe with extra dimensions, we might feel the pull of mass in those other dimensions even though they are invisible.

Not long after Isaac Newton saw the apple fall in 1665, he devised the gravitational constant, G, needed to calculate the attractive force between masses at different distances. Scientists have long assumed that G is fundamental and unchanging.

But, asks Arkani-Hamed, "What reason do we have for assuming that G is fundamental? It has only been measured down to about a millimeter. What if gravity is actually as strong as the other forces at distances we haven't measured yet?"

To measure the gravitational attraction between two masses requires that the masses be smaller than the distance between them -- easy to calculate with apples falling toward the Earth, but much more difficult with weights smaller than a millimeter in diameter.

And, says Arkani-Hamed, "As the test masses get smaller, residual electromagnetic effects come into play and swamp gravitation. Nobody knows what the real force of gravity is at short distances."

In a world of three spatial dimensions, gravity obeys an inverse square law: if you halve the distance between masses, the gravitational attraction between them quadruples; cut the distance to a third, and the force increases nine times. In four spatial dimensions, however, gravitational force is proportional to the inverse cube of the distance. With each additional dimension, the power of the inverse law increases.

These extra dimensions would have to be limited in extent, unlike the three endless dimensions we're accustomed to, or else we would have seen their effects already. Consider a performer on a high wire. To her, the wire might as well be a single dimension, along which she can travel only forward or back. But a flea on the wire sees a second dimension, the wire's circumference -- a "rolled-up" dimension that brings a flea traveling along it right back where he started.


Illustration by Flavio Robles

For gravity to be strong enough to unite with the other forces at energies accelerators can reach, our world would need only two extra dimensions, extending about a millimeter. More than two extra dimensions would be smaller still.

Objects close enough to lie within them would experience phenomenally greater gravitational attraction. This leads to specific predictions that can soon be put to the test of experiment.

One class of experiments will take place in accelerators, where high-energy collisions could create ripples in the higher-dimensional space, in the form of gravitons escaping into the extra dimensions. Collisions of this kind would appear to violate the first law of thermodynamics, the conservation of mass and energy.

Even more startling to contemplate, accelerators may be able to create black holes, regions smaller than the radius of the extra dimensions where gravity is so strong that nothing can escape. Small black holes quickly evaporate by Hawking radiation -- consisting of orphaned members of pairs of virtual particles whose partners are swallowed by the hole, and which carry off some of the hole's mass -- and this low-energy radiation from a high-energy collision in an accelerator would be an unmistakable signal that a black hole had been formed.

Another class of experiments will take place on the tabletop, where increasingly sophisticated systems of moving masses are directly measuring the force of gravity at ever closer distances. With one such experiment, Jens Gundlach of the University of Washington recently measured G more accurately than ever before, at distances under a millimeter. So far, Gundlach has seen no sudden wild increases in gravitational attraction, but there's still a big gap to close.

Implications for String Theory and Dark Matter

Although the theory of gravity in extra dimensions is not string theory, which characterizes fundamental particles as bits of "string" vibrating in numerous, incredibly compact extra dimensions, Arkani-Hamed and his colleagues have shown that their theory is in fact compatible with string theory.

Imagine, rather than a single-dimensional optic fiber or a high wire, that the photons and other bosons that carry electromagnetism and the nuclear forces are confined to a two-dimensional "wall" in a multidimensional "bulk." Only gravitons are free to move off the wall. In string theory, such walls are called "D-branes."

The picture suggests possible solutions to many outstanding questions in physics and astrophysics. If there are other 'branes in the bulk -- real worlds less than a millimeter from our own, stacked up like sheets of paper -- invisible masses confined to these parallel worlds could be the universe's mysterious dark matter, whose gravitation we feel even though its source is invisible.

"Or instead of invoking parallel universes, we might live on a folded universe," Arkani-Hamed suggests. "In this view, 'dark matter' might be just ordinary matter, because the light from a star on a fold only one millimeter away might have to travel billions of light years along the wall to reach us. Although we feel its gravity, we haven't seen it yet."

Arkani-Hamed says that "all the old mysteries of the Standard Model can be addressed in this theory," and that, indeed, "the most extraordinary thing about the theory is that it didn't die an immediate death. It explains a lot and raises a lot of possibilities, yet it contradicts no experimental results." He adds, "If we do the experiments, we have a good chance of seeing evidence for or against these ideas in the next 10 years."

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