More than 200 years after it was first measured, this fundamental property of our universe continues to confound

In 1763, surveyors Charles Mason and Jeremiah Dixon set off from Philadelphia to demarcate the border between Pennsylvania and Maryland. On the other side of the Atlantic, British scientist Henry Cavendish worried about the effect of the Allegheny Mountains on Mason’s and Dixon’s measurements, which would eventually establish the famous Mason–Dixon line. Cavendish reasoned that the gravitational attraction of the mountains would pull at the theodolite plumb-bob that Mason and Dixon were using, enough to throw off their measurements of local latitudes by as much as 200 meters (1).

Fig. 1. Physicists have had a surprisingly difficult time calculating the gravitational constant, Big G, one of the most fundamental measures in all of physics. Image courtesy of Dave Cutler.

Such analysis set Cavendish down a path to performing one of the first high-precision experiments in physics. Using a newly designed device called a torsion balance, Cavendish measured the almost-infinitesimal gravitational attraction between two spheres of lead. His experiment allowed physicists to calculate a value for the gravitational constant—often called Big G to differentiate it from little g, the acceleration due to gravity—for the first time since Isaac Newton wrote down his law of gravity approximately a century earlier.

Cavendish’s brilliant insights are more obvious in light of modern experiments. More than 200 years and 350 experiments later, scientists know the gravitational constant to a precision only about 1,000-times better than could be calculated from Cavendish’s data. “For any other experiment in physics, this would be a real surprise or shame,” says physicist Guglielmo Tino of the University of Florence in Italy.

That’s because the majority of physical constants are known with extreme precision—often out to 9, 10, or even 12 digits. But G stops at five digits. Worse, many of the measurements disagree with one another. It’s no wonder that physicists are continuing to develop new techniques to accurately measure this fundamental constant. “In some sense gravity is the most basic force that humans experience, and yet it’s the hardest to measure,” says physicist Holger Müller of the University of California, Berkeley. “As a physicist it makes me uncomfortable that we can’t measure it better.”

Does our inability to pin down the gravitational constant result from subpar means of measurement, or might it actually signal something deeper about the nature of reality? There’s the possibility that new physics waits to be uncovered, perhaps a variable gravitational constant, hidden extra dimensions, or even the long sought after unification of Einstein’s general relativity with quantum mechanics.

High Precision Cavendish would have hardly suspected the implications when he did his experiment in 1798. His device was deceptively simple. He attached two small lead balls to the ends of a beam and suspended the beam horizontally using a thin wire. In the same horizontal plane, near each of the two small balls, he placed a large, spherical 158-kilogram lead weight. The small lead balls were attracted to the heavy lead weights, causing the wire to twist. (See Fig. 3.) “As the force with which the balls are attracted by these weights is excessively minute, not more than 1/50,000,000 of their weight, it is plain, that a very minute disturbing force will be sufficient to destroy the success of the experiment,” he wrote (2). Seeking to minimize interference, Cavendish kept the entire apparatus sitting inside a dark closed room and watched the experiment through a window using a telescope. The meticulous effort paid off. Cavendish had built the device to calculate the density of Earth, but decades later physicists recast the measurements in terms of G and came up with a value of 6.74 × 10−11 m3⋅kg−1⋅s−2, only about 1% off from the modern accepted value. Most measurements since then have used some version of Cavendish’s torsion balance. “It’s one of the simplest systems you can imagine and yet there’s a lot of detail you have to take into account,” says physicist Stephan Schlamminger of the National Institute of Standards and Technology in Gaithersburg, Maryland. That’s because for everyday objects, gravity is an exceedingly weak force (you can easily pick up a pencil from the floor, overcoming the pull of our entire planet on it). And unlike electromagnetism, gravity can’t be shielded against, meaning the gravitational attraction of any nearby objects—such as someone walking by—will affect the experiment. As will tidal forces of the sun and the moon, not to mention the physical properties of the wire whose twist is being measured. And then there are the irregularities in the density of the weights being used in the experiment. Still, technological and experimental improvements meant that by the early 1980s, researchers had determined the gravitational constant about 100-times better than the value obtained from Cavendish’s instrument (3). But then an experiment in 1995, shockingly, came up with a value for G that differed from the accepted value by 0.7%, in addition to causing a 12-fold increase in its uncertainty (4). Although the measurement turned out to be flawed, it pushed physicists to perform new experiments. In 2000, Jens Gundlach and Stephen Merkowitz, of the University of Washington in Seattle, placed a torsion balance on a computer-controlled turntable. “We made the turntable go a little faster and slower at exactly the right rate so the torsion wire wasn’t twisted anymore,” says Gundlach. This meant that the material properties of the wire weren’t influencing the results. Using this device, the team calculated the most precise value for G to date, with an uncertainty of only 0.0014% (5). Fig. 2. Despite improvements in techniques, there are still significant measurement discrepancies for Big G among different research groups. Image courtesy of Dave Cutler.

Not Quite Constant For the next decade, researchers steadily improved on their techniques and even invented some new ones. In 2006, Schlamminger—then at the University of Zurich—worked with a team that measured G using two small test masses connected to a balance, weighing them as two steel containers filled with 6.5 tons of mercury moved up and down around them and pulled on them gravitationally (6). Despite such progress, the discrepancies didn’t disappear. In 2010, Harold Parks of the Joint Institute for Lab Astrophysics (JILA) in Boulder, Colorado, and James Faller of Sandia National Laboratories in Albuquerque, New Mexico, produced one of the lowest gravitational constant measurements yet, about 0.025% below the accepted international value (7). Then in 2013, a team at the International Bureau of Weights and Measures in France found G to be 0.024% higher (8). These two divergences seem small, but in the field of high-precision metrology they are indeed significant. “An outside observer would say the two outliers are wrong, those are just experimental errors,” says physicist Terry Quinn, who led the International Bureau of Weights and Measures effort. “But then there’s a niggling doubt. If there was one outlier, we would say maybe. But we did our experiment twice and got the same answer, and JILA used a completely different apparatus and is a lab that people greatly respect.” To try and settle the issue, researchers have recently tried to create completely different methods of measurement, relying on different physical properties of materials. For example, in 2014, Tino and his coworkers calculated G using what’s known as an atomic fountain (9). In it, a laser splits rubidium atoms into superposition of two quantum states and accelerates them vertically, allowing them to rise and fall in the presence of 516 kilograms of tungsten. One state rises higher and experiences a different gravitational pull from the tungsten than the other state. When the two states are recombined, they produce an interference pattern that can be used to calculate G. Although the experiment revealed a value of G that was lower than the accepted standard and which had a relatively high uncertainty, the technique was the first to use quantum effects to measure the gravitational constant. Tino thinks that replacing the tungsten with crystalline silicon weights that contain fewer irregularities, as well as replacing the rubidium with strontium atoms that are immune to magnetic interference, would improve the precision of the measurement by a couple of orders-of-magnitude. Other laboratories around the world are now performing similar atomic fountain experiments that could yield consistent results in the coming years. “One of the wonderful things about this field is that there’s no attempt to sweep the discrepancies under the rug,” says Müller. “Quite on the contrary, they’re highlighting this problem.” Physicists are doing everything they can to measure G more accurately. Efforts are currently underway in some laboratories to repeat previous experiments done by different teams to tease out systematic errors. A Chinese group is rebuilding Gundlach’s ultrahigh-precision instrument in incredible detail and Quinn and his colleague have handed over their equipment to National Institute of Standards and Technology researchers to see if they get a similar result. This July, the National Science Foundation held an Ideas Lab in Gaithersburg, Maryland, that brought together 15 researchers working in both gravitational constant experiments and other fields, such as condensed matter physics, atomic physics, and even astrophysics. Physicist Pedro Marronetti, who spearheaded the effort, called it “a grueling week of physics discussions.” He and other participants hope the gathering spurs new experiments that “could potentially increase the precision to which G is known by an order of magnitude.” Fig. 3. In 1798, Henry Cavendish used this torsion balance to measure Big G. With the help of a pulley, large balls hung from a frame were rotated into position next to the small balls. Reproduced from ref. 2.