May-June 2003 > Right Now

Extra-Dimensional Perception

Gravity's Riddle

by Craig Lambert

Ever since the fabled apple fell before Isaac Newton, gravity has posed enigmas. Along with electromagnetism and the strong and weak forces that bind atomic nuclei together, it is one of the four fundamental forces of physics. Gravity behaves idiosyncratically. While other forces cancel each other out (positive and negative charges, for example), gravity just keeps adding up: the bigger the mass, the more its gravitational attraction. “Gravity is definitely the weirdest of all these forces,” says professor of physics Nima Arkani-Hamed. “It was the first force discovered, and it’s still the most mysterious.”

In physics, deep problems often arise from simple questions, like this one: Why is gravity so weak? Consider that a refrigerator magnet easily picks up a paper clip from the kitchen tabletop; its magnetic force defeats the gravitational power of the entire Earth, a ball 8,000 miles in diameter. Even at the subatomic level, the electrical forces binding two protons together are 10⁴⁰ times stronger than the gravitational attraction between them.

Theoretical physicist Arkani-Hamed explores scenarios that take place beyond the "standard model" of particle physics. That model has remained intact for the past 30 years, consistently validated by experimental results. "There are no chinks in the armor — the standard model describes nature very well, from astronomical scales down to a distance that is 1/100 the diameter of a proton, or 10^-16 centimeters," says Arkani-Hamed. "But there are strong reasons, rooted in quantum theory, to think that there is something deeply wrong with it — not some detail, but a big piece of the picture missing. And we know the distance scale — the ‘electroweak’ scale — where the ‘normal’ relationship of mass and gravity should break down: 10^-17 centimeters, or 1/1000 of a proton’s diameter." (For comparison, the well-known nanoscale is a relatively gigantic 10^-8 centimeters.)

Gravity, so feeble in the larger world, might be an important force at such close quarters. Recall that gravity diminishes as the inverse square of distance. How small would that distance have to be before gravity “catches up” and becomes, well, a force to be reckoned with? Newtonian physics predicts this would not happen until reaching the minuscule Planck scale, 10^-33 centimeters — far, far smaller than the electroweak scale and well beyond the reach of even the largest particle accelerators, such as those at Fermilab in Batavia, Illinois, and CERN (founded by the Conseil Européen pour la Recherche Nucléaire) in Geneva. However, the Planck scale convergence is purely hypothetical, since gravity has never been measured at distances smaller than one millimeter, a vast 10³² times larger than the Planck scale. In the past few years, Arkani-Hamed and his colleagues have taken a new theoretical tack on the gravity conundrum in publications ranging from physics journals to Scientific American. They propose that gravity may reach parity with the other forces not at the Planck scale, but at the electroweak scale of 10^-17 centimeters.

Particle accelerators to date have explored energy at scales as small as 10^-16 centimeters. The electroweak scale should be within reach soon. The Large Hadron Collider at CERN, a new particle accelerator capable of investigating the electroweak scale and even smaller scales of 10^-18 centimeters and beyond, is expected to come online in 2008. “For the first time in 30 years, we’ll have really new data,” says Arkani-Hamed. “It’s such an exciting field right now.”

Arkani-Hamed and other theoretical physicists (including professor of physics Lisa Randall) have been investigating the remarkable possibility that what could come into play at these tiny scales — or even at the scale of a millimeter — are extra dimensions of space. Perhaps "Gravity is actually way stronger than observed,” he says. “But it looks weak at the distances where we have measured it." He postulates that gravity’s strength may actually reside in other dimensions — fifth and sixth dimensions, say — that don’t show up in our three- and four-dimensional models and measurements: "Gravity only looks weak because it is spread out in other dimensions. Only gravity goes into these dimensions; the other forces are stuck to a three-dimensional subworld of this higher-dimensional universe."

Drawing an analogy to Edwin A. Abbott’s famous 1884 book Flatland, about a two-dimensional world, Arkani-Hamed says, “From far away, a straw looks like a line, but nearby it has diameter.” In other words, at different distances, different dimensions become observable. “It may be that the fifth and sixth dimensions only appear at certain scales,” he says.

Radical as it sounds, the theory has a Copernican quality of recasting our world as a sliver within something much larger. It opens up paradoxical possibilities like parallel universes. “Our three-dimensional world is floating in a higher-dimensional space,” Arkani-Hamed says. “In fact, maybe the dimensions, and even space itself, are not fundamental concepts. We don’t expect the idea of space to survive in any deeper description of reality. Space almost certainly emerges from something more fundamental. I strongly suspect that even time is an emergent thing.”

 

Nima Arkani-Hamed e-mail address: arkani-hamed[at]physics [dot] harvard [dot] edu