BIG "G": Researchers at the International Bureau of Weights and Measures (BIPM) in Sévres, France used a torsion balance apparatus (pictured) to calculate the gravitational constant, "big G,"—a fundamental constant that has proven difficult to measure. The latest calculation, the result of a 10-year experiment, just adds to the confusion. Image: Terry Quinn
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Gravity, one of the constants of life, not to mention physics, is less than constant when it comes to being measured. Various experiments over the years have come up with perplexingly different values for the strength of the force of gravity, and the latest calculation just adds to the confusion.
The results of a painstaking 10-year experiment to calculate the value of “big G,” the universal gravitational constant, were published this month—and they’re incompatible with the official value of G, which itself comes from a weighted average of various other measurements that are mostly mutually incompatible and diverge by more than 10 times their estimated uncertainties.
The gravitational constant “is one of these things we should know,” says Terry Quinn at the International Bureau of Weights and Measures (BIPM) in Sévres, France, who led the team behind the latest calculation. “It’s embarrassing to have a fundamental constant that we cannot measure how strong it is.”
In fact, the discrepancy is such a problem that Quinn is organizing a meeting in February at the Royal Society in London to come up with a game plan for resolving the impasse. The meeting’s title—“The Newtonian constant of gravitation, a constant too difficult to measure?”—reveals the general consternation.
Although gravity seems like one of the most salient of nature’s forces in our daily lives, it’s actually by far the weakest, making attempts to calculate its strength an uphill battle. “Two one-kilogram masses that are one meter apart attract each other with a force equivalent to the weight of a few human cells,” says University of Washington physicist Jens Gundlach, who worked on a separate 2000 measurement of big G. “Measuring such small forces on kg-objects to 10-4 or 10-5 precision is just not easy. There are a many effects that could overwhelm gravitational effects, and all of these have to be properly understood and taken into account.”
This inherent difficulty has caused big G to become the only fundamental constant of physics for which the uncertainty of the standard value has risen over time as more and more measurements are made. “Though the measurements are very tough, because G is so much weaker than other laboratory forces, we still, as a community, ought to do better,” says University of Colorado at Boulder physicist James Faller, who conducted a 2010 experiment to calculate big G using pendulums.
The first big G measurement was made in 1798 by British physicist Henry Cavendish using an apparatus called a torsion balance. In this setup, a bar with lead balls at either end was suspended from its middle by a wire. When other lead balls were placed alongside this bar, it rotated according to the strength of the gravitational attraction between the balls, allowing Cavendish to measure the gravitational constant.
Quinn and his colleagues’ experiment was essentially a rehash of Cavendish’s setup using more advanced methods, such as replacing the wire with a wide, thin strip of copper beryllium, which allowed their torsion balance to hold more weight. The team also took the further step of adding a second, independent way of measuring the gravitational attraction: In addition to observing how much the bar twisted, the researchers also conducted experiments with electrodes placed inside the torsion balance that prevented it from twisting. The strength of the voltage needed to prevent the rotation was directly related to the pull of gravity. “A strong point of Quinn’s experiment is the fact that they use two different methods to measure G,” says Stephan Schlamminger of the U.S. National Institute of Standards and Technology in Gaithersburg, Md., who led a separate attempt in 2006 to calculate big G using a beam balance setup. “It is difficult to see how the two methods can produce two numbers that are wrong, but yet agree with each other.”
Through these dual experiments, Quinn’s team arrived at a value of 6.67545 X 10-11 m3 kg-1 s-2. That’s 241 parts per million above the standard value of 6.67384(80) X 10-11 m3 kg-1 s-2, which was arrived at by a special task force of the International Council for Science’s Committee on Data for Science and Technology (CODATA) (pdf) in 2010 by calculating a weighted average of all the various experimental values. These values differ from one another by as much as 450 ppm of the constant, even though most of them have estimated uncertainties of only about 40 ppm. “Clearly, many of them or most of them are subject either to serious significant errors or grossly underestimated uncertainties,” Quinn says. Making matters even more complex is the fact that the new measurement is strikingly close to a calculation of big G made by Quinn and his colleagues more than 10 years ago, published in 2001, that used similar methods but a completely separate laboratory setup.
Most scientists think all these discrepancies reflect human sources of error, rather than a true inconstancy of big G. We know the strength of gravity hasn’t been fluctuating over the past 200 years, for example, because if so, the orbits of the planets around the sun would have changed, Quinn says. Still, it’s possible that the incompatible measurements are pointing to unknown subtleties of gravity—perhaps its strength varies depending on how it’s measured or where on Earth the measurements are being made?
“Either something is wrong with the experiments, or there is a flaw in our understanding of gravity,” says Mark Kasevich, a Stanford University physicist who conducted an unrelated measurement of big G in 2007 using atom interferometry. “Further work is required to clarify the situation.”
If the true value of big G turns out to be closer to the Quinn team’s measurement than the CODATA value, then calculations that depend on G will have to be revised. For example, the estimated masses of the solar system’s planets, including Earth, would change slightly. Such a revision, however, wouldn’t alter any fundamental laws of physics, and would have very little practical effect on anyone’s life, Quinn says. But getting to the bottom of the issue is more a matter of principle to the scientists. “It’s not a thing one likes to leave unresolved,” he adds. “We should be able to measure gravity.”
Quinn and his team from the BIPM and the University of Birmingham in England published their results Sept. 5 in Physical Review Letters.