Gravity measured with record precision

The gravitational constant, G, which governs the strength of gravitational interactions, is hard to measure accurately. Two independent determinations of G have been made that have the smallest uncertainties so far.
Stephan Schlamminger is in the Fundamental Electrical Measurements Group, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA.

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Although gravity seems strong in our everyday lives, such as when lifting a heavy object, it is the weakest of the four fundamental forces. The gravitational force between two bodies is proportional to the masses of these bodies. If one of the bodies is Earth, the force can be considerable. But if the bodies are objects in a laboratory, the force can be too small to measure accurately. For example, the gravitational force between two 1-kilogram objects separated by 1 metre is equivalent to the weight of a few biological cells. For this reason, the gravitational constant, G, which quantifies the strength of this force, is one of the most poorly defined physical constants. But in a paper in Nature, Li et al.1 report high-precision measurements of G using two different techniques.

In 1798, the scientist Henry Cavendish determined G for the first time in the laboratory, using an instrument called a torsion balance2. In Cavendish’s work, the torsion balance consisted of a dumb-bell that was suspended from its centre by a thin fibre. A gravitational force was applied to the masses at the ends of the dumb-bell, acting perpendicularly to the bar of the dumb-bell and to the axis of the fibre. This force led to a rotation of the dumb-bell about this axis, causing the fibre to twist.

Eventually, the dumb-bell reached a position at which the twisting force of the fibre balanced the gravitational force. The rotation angle of the dumb-bell in this position was recorded. The gravitational force was then applied in the opposite direction and a second rotation angle was measured. The magnitude of the gravitational force was calculated from the difference between these two angles.

In torsion-balance experiments, the gravitational force is provided by a well-characterized assembly of external masses. These masses are moved between two or more different positions to change the direction and magnitude of the force. Because the dumb-bell rotates in a horizontal plane, the otherwise overwhelming effects of Earth’s gravity on the experiments are negligible. Over the years, many techniques have been developed to measure G using a torsion balance3. In 2000, a substantial improvement in the precision of these experiments was achieved by replacing the dumb-bell with a thin plate4 (also termed a plate pendulum).

Li and colleagues built two plate-containing torsion balances that are based on different measurement techniques: the time-of-swing (TOS) method5 and the angular-acceleration-feedback (AAF) method6 (see Fig. 1 of the paper1). In the TOS method, the rotation of the plate is oscillatory. G is calculated from the change in the speed of the oscillation when the external masses are in two different configurations. By contrast, in the AAF method, two turntables are used to rotate the torsion balance and the external masses individually. G is determined from the angular acceleration of the turntable associated with the torsion balance when the amount of twisting of the fibre is reduced to zero.

The authors obtained G values of 6.674184 × 10−11 and 6.674484 × 10−11 cubic metres per kilogram per square second for the TOS method and the AAF method, respectively. The relative uncertainties are the smallest reported so far: about 11.6 parts per million. By comparison, the previous record, which was achieved using the AAF method, was 13.7 parts per million4.

Li et al. carried out their experiments with great care and gave a detailed description of their work. The study is an example of excellent craftsmanship in precision measurements. However, the true value of G remains unclear. Various determinations of G that have been made over the past 40 years have a wide spread of values (Fig. 1). Although some of the individual relative uncertainties are of the order of 10 parts per million, the difference between the smallest and largest values is about 500 parts per million.

Figure 1 | Measurements of the gravitational constant. The strength of the gravitational force between two bodies is described by the gravitational constant, G, which can be expressed in units of cubic metres per kilogram per square second. The data points are high-precision measurements of G taken over the past 40 years, with uncertainties indicated by the error bars. The points marked by squares are results obtained by Li et al. in current work1 (red) and in previous work8,9 (purple). The vertical grey line denotes the value of G adopted by the Committee on Data for Science and Technology, with an uncertainty indicated by the shaded area11. (Adapted from Fig. 3 of ref. 1.)

There are at least two possible explanations for this discrepancy. One is that the technical details of one or more of the experiments were not fully understood, which could have led either to a systematic shift in the reported values of G or to uncertainties that were not included in the reported uncertainties of G. An example of the former is the effect of a fibre property, called anelasticity, that could bias the TOS method — an effect that was first pointed out7 in 1995. A second possibility is that some unknown physics could explain the scatter in the published values. Although this possibility is, of course, the more exciting, it is also the less likely. Nevertheless, it should not be dismissed lightly.

At this point, it is as important to try to understand the discrepancy between the different results as it is to make new measurements. Even Li and colleagues’ results are in disagreement: the values of G determined in the two current experiments, as well as values obtained in two previous experiments at the same laboratory8,9, are statistically inconsistent with one another. The authors speculate that fibre anelasticity might be responsible, but they do not give a definitive explanation.

Because all four of these experiments were carried out at the same institution, it should be more straightforward to compare them than it would be to compare different experiments from various groups around the globe. An excellent opportunity exists, therefore, to uncover the causes of the discrepancy and, in turn, to learn more about the true value of G. Li et al. should be encouraged to take on this challenge. In the end, if we want to understand the measurements of G, we must find the reasons for the inconsistent results10.

Nature 560, 562-563 (2018)

doi: 10.1038/d41586-018-06028-6
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