New Measurements of G
Riley D. Newman
Lay Language Paper related to my talk in session B5, spring 1996 APS meeting
in Indianapolis.
Newton's constant G, which relates the gravitational force between two objects to their mass and separation, has long been the least well known of the fundamental constants of nature. In 1986 the international Committee on Data for Science and Technology (CODATA) assessed the fractional uncertainty in G to be about 128 ppm -- in stark contrast to the much smaller uncertainties the CODATA report attributed for example to the electrical charge of an electron (0.3 ppm), the mass of the proton (0.6 ppm), Planck's constant (0.6 ppm), and the fine structure constant (0.045 ppm).
But now the uncertainty in G looks far greater. At the Spring meeting of the APS last year three groups reported measurements of G which were dramatically inconsistent with one another and with the previous "best" value. Most disturbing was the value reported by the Physikalisch- Technische Bundesanstalt (PTB), the German equivalent of the U.S. National Institute of Standards and Technology (NIST). The PTB result for G, the product of many years of carefully repeated measurements, was a stunning 6400 ppm (more than half a percent) greater than the accepted CODATA value. A good article on this disturbing situation appeared in the March 1996 issue of Discover Magazine.
These results have stimulated a number of new measurements of G. Unfortunately, the PTB group will not be continuing its G measurements. The other two laboratories whose results were reported last year are continuing to refine their measurements. One of these, at Wuppertal University in Germany, uses a novel technique: two large suspended masses form the two mirrored walls of a microwave cavity. A large source mass brought near to one of the suspended masses pulls it away from the other; measuring the resultant change in the resonant frequency of the cavity determines the strength of the pull and hence the value of G. The Wuppertal group is improving their ability to measure their source mass position, and plans to move their apparatus to another site where temperature and noise level control will be better, aiming for accuracy well below 100 ppm.
The other continuing group, at the New Zealand Institute of Industrial Research, uses a method which measures the electrostatic force required to exactly balance a gravitational force acting on a stationary torsion balance. The electrostatic force source is calibrated by measuring the angular acceleration it produces when acting alone on the balance.
Gabriel Luther at Los Alamos National Laboratory is making G measurements using an improved version of the apparatus used in the 1982 measurement on which the current CODATA G value is based. That measurement used the so-called "dynamic" method, in which the change in natural oscillation frequency of a torsional pendulum is measured when the positions of source masses near the pendulum are changed.
A Japanese physicist, Kazuaki Kuroda, has pointed out a previously unnoticed source of systematic error in this dynamic method: the restoring forces produced by the supporting fiber of the pendulum tend to relax with time, so that the fiber is effectively less stiff when the pendulum is forced to oscillate at lower frequencies. This effect contributes to the frequency change when the source masses are moved, and if ignored results in an apparent G value which is too large (see editorial in Nature, October 19, 1995 p573). Kuroda showed that the fractional error is likely to be 1/(pi Q), where the "Q" of a pendulum is the number of oscillation cycles required for its amplitude to die down to about 4.3% of its original value. We have been able to show that the error can be no more than 1/(2Q) in the model Kuroda considered. This is much too small to account for the discrepancy between the CODATA G and the PTB G value. However, Luther is studying these effects in his system.
Several completely new G measurements are underway or planned. At Zurich University an experiment will determine G by measuring the change in apparent weight of 1 kilogram masses when steel tanks filled with seven tons of mercury are positioned alternately above and below them. This experiment, which is nearly ready to run, aims for 10 ppm accuracy or better.
Wei-Tou Ni in Taiwan is developing a method similar in principle to the Wuppertal experiment: suspended masses will form an optical resonant cavity in Ni's experiment, and the suspension uses a clever scheme developed by Kuroda which makes its effective length much greater than its actual length. Ni hopes for an eventual G accuracy of about 1 ppm.
At UC Irvine we are preparing a G measurement which will use the "dynamic" method with several novel features. The torsion pendulum will be a thin fused quartz plate suspended vertically, and the gravity source masses will be a pair of copper rings (see figure). The pendulum will oscillate freely in a torsional mode (rotating around the fiber axis. G is determined by measuring the change in oscillation frequency when the ring pair is rotated by 90 degrees around the vertical axis (for example, from a north-south alignment to an east-west alignment). The ring source mass geometry produces a specially shaped gravity field (an extremely uniform field gradient) which interacts with the thin pendulum in such a way that the measured value of G is extremely insensitive to errors in the mass distribution and position of the pendulum. A unique feature of the experiment is that the pendulum will operate in a cryogenic environment at a temperature of 4K or below, to reduce thermal noise sources and to increase the oscillation "Q" to a level such that Kuroda's effect will not disturb the measurement by more than 1 ppm. The experiment will operate in a former Nike missile bunker at the Hanford site in eastern Washington, near the LIGO gravitational wave detector site. We aim for a G measurement with 10 ppm accuracy. If the copper rings are replaced with fused silica rings (whose mass distribution may be mapped optically) our accuracy might eventually be improved to about 2 ppm.
At the University of Washington, Jens Gundlach plans a G measurement which, like the Irvine experiment, involves a suspended fused quartz plate and a source mass system which produces a specially shaped gravity field (instead of rings, Gundlach's source masses will be a set of eight specially located spherical masses). A key feature of Gundlach's system is that the pendulum will be mounted on a platform rotating at about 1 revolution per hour. As the platform rotates with respect to the source masses their gravity field will exert forces on the pendulum which make it try to speed ahead or fall behind the platform's rotation. The clever trick of Gundlach's scheme is that a "feedback" mechanism will control the platform rotation speed so that it speeds up or slows in such a way that the pendulum always remains fixed relative to the platform. The measured angular acceleration of the platform accurately then reflects the acceleration the pendulum would have if it were experiencing only forces due to the source masses, and thus may be used to determine G. In this scheme the suspension fiber never twists significantly, so that concerns related to Kuroda's effect are elegantly avoided. Gundlach has experimentally demonstrated that this scheme should be capable of a 10 ppm G measurement.