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A pendulum's unwavering oscillations have confirmed Newton's second law of motion to unprecedented precision.

No Twisting Out of Newton's Law

Staff Writer

The harder you push a sled across a frozen pond, the faster it accelerates. In 1687, Isaac Newton quantified this most basic bit of physics with his second law, which states that the force applied to an object equals its mass times its acceleration (F=ma). Now scientists have verified this law with unprecedented precision, challenging critics who have suggested the rule somehow bends for very small accelerations.

For almost 300 years, F=ma was the law of the land. Then some physicists began to have their doubts. About 30 years ago, astronomers noticed that stars swirl around the outer edges of galaxies so fast that they ought to fly into space. Most believe some unseen "dark matter" provides the extra gravity that keeps the fast-moving stars from escaping. But in the 1980s, a few researchers noted that the observations could be explained without dark matter if Newton's second law didn't quite hold for very small accelerations, a scheme known as Modified Newtonian Dynamics or MOND. Also, NASA's Pioneer 10 and 11 spacecraft have shown a small, unexplained acceleration toward the center of the galaxy that might also hint at a breakdown in second law.

Those possibilities seem less likely, now that physicists Jens Gundlach and Stephan Schlamminger of the University of Washington in Seattle and colleagues have tested F=ma with unprecedented accuracy. To make the test, the team employed a type of pendulum. Unlike the standard pendulum that swings back and forth, however, this torsion pendulum consisted of a small cylinder that twisted back and forth on the end of a tungsten wire one meter long and 20 micrometers thick. If Newton's second law holds, the frequency of the twisting should be the same regardless of its amplitude. Smaller twists meant smaller accelerations, and the researchers found that the frequency remained constant--verifying Newton's law--for accelerations as small as 0.00005 nanometers per second per second, as they report in a paper to be published in Physical Review Letters.

The new result doesn't quite rule out MOND because the twisting pendulum is still subject to other accelerations, such as the downward pull of gravity, which might hide any deviation because of MOND, Gundlach says. But as for the mysterious effect on the space craft, "It's not a simple violation of F=ma," Gundlach says. "That we can rule out." If Newton's law is still valid, then there must be some as-yet-unidentified force pulling on the spacecraft to create the mysterious acceleration.

"It's a very powerful, very useful result," says Riley Newman, a physicist at the University of California, Irvine. Newman has one quibble, however. The researchers simply assume that the force with which the tungsten fiber tries to unwind is exactly proportional to the amount that it twists, a relation known as Hooke's law. It's possible that this relationship is violated in some way that masks a violation of Newton's law, Newman says. Although such a conspiracy is unlikely, he says, the results "would have been more powerful if they had done this check."

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