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Helping ‘big G’ get back on track

03 Aug 2001

New measurements of the gravitational constant confirm that the official value needs to be increased and, as John Moore reports, could explain what went wrong in a previous experiment.

Gee whizz

Ever since Henry Cavendish first measured Newton’s gravitational constant in 1798, the value of “big G” has remained the least accurate of all the fundamental physical constants. Indeed, when the most recent list of recommended values for the fundamental constants was published in 1998, the uncertainty in G had increased by a factor of 10 from the previous list.

Last year, however, two US physicists reported the most accurate measurement ever, and now a team of researchers from the Bureau International des Poids et Mesures (BIPM) in France and Birmingham University in the UK has reported the results of another experimental tour de force. Moreover, they claim to have discovered the reasons for the errant measurement that led to the factor of 10 increase in the uncertainty surrounding the constant.

Big G is difficult to measure because gravity is by far the weakest of the four fundamental forces and because it is impossible to shield experiments from the gravitational influences of their environment. Today the official value is G = 6.673 x 10-11 in units of metres cubed per kilogram per second squared, with a relative uncertainty of 1500 parts per million (ppm). By contrast, the mass of the electron is known with an accuracy of 0.08 ppm.

In 1994, when Winfried Michaelis and co-workers at the German standards lab, the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig, began an experiment to measure G, the accepted value was 6.672 59 x 10-11 with an uncertainty of 128 ppm. The PTB result shocked the big G community because it was more than 5000 ppm larger than the accepted value at the time, placing it well outside the experimental error bars (Metrologia 1995/6 32 267). Metrologists have been puzzling over the PTB results ever since.

Back to basics

In a traditional Cavendish “torsion balance” experiment, test masses are suspended on a wire that rotates in response to a gravitational torque created by source masses placed nearby. This rotation is opposed by the torsion of the wire. By measuring the amount of the twist in the wire, which is proportional to the gravitational attraction between the masses, the value of G can then be determined.

Last year Jens Gundlach and Stephen Merkowitz of the University of Washington in Seattle used a highly modified version of Cavendish’s torsion balance in which both the source and test masses rotated on turntables. The key feature of their set-up was that the torsion fibre did not twist, which, according to Gundlach, enabled them “to avoid most of the systematic uncertainties”. Last year Gundlach and Merkowitz reported a value of 6.674 215 x 10-11 with an uncertainty of just 14 ppm, surpassing all previous measurements in accuracy and setting a whole new standard for measuring G (Phys. Rev. Lett. 2000 85 2869).

The BIPM-Birmingham experiment also uses a modified Cavendish set-up, which rests on a marble block that is bonded to the local bedrock in a temperature-controlled laboratory. The four 1.2 kg test masses are mounted on a disk, which is suspended from a copper-beryllium ribbon in a vacuum chamber. There are four 12 kg source masses outside the chamber, resting on a carousel that is driven by a stepping motor. When the source masses are radially aligned with the test masses, there is no gravitational torque on the balance. When the source masses are rotated by 18.7° in either direction, the torque is at a maximum.

“A unique feature of our experiment,” says Terry Quinn of the BIPM, “is that we can carry out both a Cavendish experiment and a servo-controlled experiment with the same apparatus.” Using the servo-controlled method, the gravitational torque generated by the source masses is balanced by an electrostatic torque that acts directly on the test masses. This electrostatic torque is generated by applying an AC voltage between the test masses and a pair of thin copper electrodes near each mass. G can be calculated by measuring the electrostatic torque needed to balance the gravitational torque due to the source masses.

Following some 38 Cavendish experiments lasting four hours each and 25 servo experiments, all 10 hours long, the BIPM team arrived at a value of G = 6.675 59 x 10-11, with an uncertainty of 41 ppm. “The close agreement of the results from the two methods is evidence for the absence of many of the systematic errors to which a G measurement is subject,” says Quinn. “Our result is close to, but not exactly equal to, the value of Gundlach and Merkowitz.”

Indeed, the BIPM and Seattle results differ by more than four times their combined uncertainty. “The difference is likely to be due to systematic errors, at the level of one or two parts in 104, hidden in one or both of the measurements,” the BIPM team writes in a paper accepted by Physical Review Letters.

PTB or not PTB

The BIPM team also believes it knows the reason for the PTB discrepancy. “It is very subtle,” says Quinn, explaining that the problem is related to the frequency dependencies of various capacitances in the experiment and the use of AC and DC servo-control systems. Put simply, Quinn claims that the PTB team calibrated its apparatus at one frequency and made its measurements at another. The BIPM team encountered similar problems in the early days of its experiments when it was using a DC servo system. “The problems were eliminated when we started using an AC servo working at the same frequency,” says Quinn.

However, Winfried Michaelis has visited the BIPM experiment and does not believe that Quinn’s theory can explain the errant PTB measurement. “The BIPM experiment has a relatively open arrangement of electrostatic components with insulating materials in it,” he says, “whereas we had a nearly closed electrometer box without any insulators.” Nonetheless, the PTB team will soon be performing a new experiment together with specialists in the measurement of capacitance.

The big G community now awaits the results of other experiments. In July a task group from CODATA, the international body that controls the values of the fundamental constants, decided not to change either the value of G or the uncertainty given in the 1998 recommended values.

“What is most likely to happen when other results come out,” says Quinn, “is that the value of G may be changed towards where we are now, and the uncertainty is going to be reduced, probably by a factor of 10.”

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