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String Theory's Extra Dimensions Must Be Less Than Half the Width of a Human Hair

Tabletop experiment puts new limits on string theory
gravity test

If extra dimensions of space exist, they must be smaller than about half the width of a human hair, according to new measurements of the strength of gravity at short distances. Researchers found that the same law governing the gravitational pull between planets continues to work when objects are separated by as little as 56 micrometers. The finding rules out extra dimensions of 44 micrometers or larger, they report in this week's Physical Review Letters.

Discovering extra dimensions with the relatively huge size of a few micrometers would offer spectacular confirmation for string theory, the still unproved body of equations that may unify gravity with the normally incompatible realm of quantum physics. "Even though we haven't seen anything, these results put boundaries on what people can legitimately propose," says experimental physicist and study author Eric Adelberger of the University of Washington. "Testing the inverse square law [meaning Newton's law of gravity] is the bombproof way to look for extra dimensions."

"I'm a big admirer of this class of experiments; I think they're awesome," says theoretical particle physicist Raman Sundrum of Johns Hopkins University. In principle, such tests could effectively rule out theories of micrometer-size extra dimensions, he says. To study such questions researchers would normally expect to use giant particle accelerators, such as the Large Hadron Collider (LHC), set to switch on in Geneva later this year.

Sundrum says the LHC may still get its shot at large extra dimensions, because the new result leaves the idea some wiggle room. "It's not killing that scenario," he says.

With no pressing reason to check, researchers, until a few years ago, had never measured the strength of gravity when objects were separated by much less than a millimeter (roughly the width of a period on this page). But beginning in the late 1990s, some physicists proposed that string theory might cause gravity to grow stronger at such distances if the universe came with relatively big extra dimensions of micrometers in width. (To make its arithmetic come out right, string theory requires that space have extra dimensions beyond the three we can readily experience, but researchers had assumed that these dimensions are extraordinarily tiny.)

Adelberger and his colleagues on the so-called Eot-Wash experiment have led the way in checking gravity's short-distance strength. As in prior experimennts, they employed a small metal pendulum suspended above a stacked pair of fused metal disks, which exerted a gravitational tug on a metal ring on the bottom of the pendulum.

The ring and the upper disk contained a series of matching holes. If the holes lined up, gravity pulled the pendulum straight down, but if the holes were offset, the disk's gravity twisted the pendulum. As a result, the experiment was able to measure the strength of gravity at the distance between the ring and the upper disk.

The key to the experiment is the lower disk, which contains holes of a different size that are designed to cancel out the twisting caused by the upper disk when the ring and disks are in certain orientations. If that canceling does not occur, it means that the force between the ring and the upper disk has changed, either because the strength of gravity has changed or because some new force has intervened that has no effect at the slightly larger distance between the ring and the bottom disk.

In their previous experiment, the Eot-Wash team ruled out a single extra dimension larger than 160 micrometers. This time the researchers attained greater sensitivity by using more holes and covering the apparatus in gold to screen out electromagnetic forces between the ring and disks.

Adelberger says they might be able to get down to a few micrometers, but it would be very tough. "As the dimensions get smaller and smaller, the force [they cause] gets smaller much faster," he says. The payoff could be worth it, though. Sundrum says that if extra dimensions failed to turn up at that distance, it would likely prune off that branch of string theory.

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