NEWS FEATURE

The curious case of the gravitational constantMore than 200 years after it was first measured, this fundamental property of our universe

continues to confound

Adam Mann, Science Writer

In 1763, surveyors Charles Mason and Jeremiah Dixonset off from Philadelphia to demarcate the borderbetween Pennsylvania and Maryland. On the otherside of the Atlantic, British scientist Henry Cavendishworried about the effect of the Allegheny Mountainson Mason’s and Dixon’s measurements, which wouldeventually establish the famous Mason–Dixon line.Cavendish reasoned that the gravitational attractionof the mountains would pull at the theodolite plumb-bob that Mason and Dixon were using, enough to throwoff their measurements of local latitudes by as much as200 meters (1).

Such analysis set Cavendish down a path to perform-ing one of the first high-precision experiments in physics.Using a newly designed device called a torsion balance,Cavendish measured the almost-infinitesimal gravita-tional attraction between two spheres of lead. Hisexperiment allowed physicists to calculate a value forthe gravitational constant—often called Big G to dif-ferentiate it from little g, the acceleration due to gravity—for the first time since IsaacNewtonwrote down his law ofgravity approximately a century earlier.

Cavendish’s brilliant insights are more obvious inlight of modern experiments. More than 200 years and350 experiments later, scientists know the gravita-tional constant to a precision only about 1,000-timesbetter than could be calculated from Cavendish’sdata. “For any other experiment in physics, this wouldbe a real surprise or shame,” says physicist GuglielmoTino of the University of Florence in Italy.

That’s because the majority of physical constantsare known with extreme precision—often out to 9, 10,or even 12 digits. But G stops at five digits. Worse, manyof the measurements disagree with one another. It’s nowonder that physicists are continuing to develop newtechniques to accurately measure this fundamental con-stant. “In some sense gravity is the most basic force thathumans experience, and yet it’s the hardest to mea-sure,” says physicist Holger Müller of the University ofCalifornia, Berkeley. “As a physicist it makes me uncom-fortable that we can’t measure it better.”

Does our inability to pin down the gravitationalconstant result from subpar means of measurement,or might it actually signal something deeper about thenature of reality? There’s the possibility that new phys-ics waits to be uncovered, perhaps a variable gravita-tional constant, hidden extra dimensions, or even the

long sought after unification of Einstein’s general rel-ativity with quantum mechanics.

High PrecisionCavendish would have hardly suspected the implica-tions when he did his experiment in 1798. His devicewas deceptively simple. He attached two small leadballs to the ends of a beam and suspended the beamhorizontally using a thin wire. In the same horizontalplane, near each of the two small balls, he placed alarge, spherical 158-kilogram lead weight. The smalllead balls were attracted to the heavy lead weights,causing the wire to twist. (See Fig. 3.) “As the force withwhich the balls are attracted by these weights is ex-cessively minute, not more than 1/50,000,000 of theirweight, it is plain, that a very minute disturbing force

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

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will be sufficient to destroy the success of the experi-ment,” he wrote (2).

Seeking to minimize interference, Cavendish keptthe entire apparatus sitting inside a dark closed roomand watched the experiment through a window usinga telescope. The meticulous effort paid off. Cavendishhad built the device to calculate the density of Earth,but decades later physicists recast the measure-ments in terms of G and came up with a value of6.74 × 10−11 m3·kg−1·s−2, only about 1% off fromthe modern accepted value.

Most measurements since then have used someversion of Cavendish’s torsion balance. “It’s one of thesimplest systems you can imagine and yet there’s a lotof detail you have to take into account,” says physicistStephan Schlamminger of the National Institute ofStandards and Technology in Gaithersburg, Maryland.

That’s because for everyday objects, gravity is anexceedingly weak force (you can easily pick up a pencilfrom the floor, overcoming the pull of our entire planeton it). And unlike electromagnetism, gravity can’t beshielded against, meaning the gravitational attractionof any nearby objects—such as someone walking by—will affect the experiment. As will tidal forces of the sunand the moon, not to mention the physical propertiesof the wire whose twist is being measured. And thenthere are the irregularities in the density of the weightsbeing used in the experiment.

Still, technological and experimental improvementsmeant that by the early 1980s, researchers had de-termined the gravitational constant about 100-timesbetter than the value obtained from Cavendish’s in-strument (3). But then an experiment in 1995, shock-ingly, came up with a value for G that differed from theaccepted value by 0.7%, in addition to causing a 12-foldincrease 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 theUniversity of Washington in Seattle, placed a torsionbalance on a computer-controlled turntable. “Wemadethe turntable go a little faster and slower at exactly theright rate so the torsion wire wasn’t twisted anymore,”says Gundlach. This meant that the material propertiesof the wire weren’t influencing the results. Using thisdevice, the team calculated the most precise value forG to date, with an uncertainty of only 0.0014% (5).

Not Quite ConstantFor the next decade, researchers steadily improvedon their techniques and even invented some newones. In 2006, Schlamminger—then at the Universityof Zurich—worked with a team that measured G usingtwo small test masses connected to a balance, weighingthem as two steel containers filled with 6.5 tons ofmercury moved up and down around them and pulledon them gravitationally (6).

Despite such progress, the discrepancies didn’tdisappear. In 2010, Harold Parks of the Joint Institutefor Lab Astrophysics (JILA) in Boulder, Colorado,and James Faller of Sandia National Laboratories inAlbuquerque, NewMexico, produced one of the lowestgravitational constant measurements yet, about 0.025%below the accepted international value (7). Then in2013, a team at the International Bureau of Weights andMeasures in France found G to be 0.024% higher (8).These two divergences seem small, but in the field ofhigh-precision metrology they are indeed significant.

“An outside observer would say the two outliersare wrong, those are just experimental errors,” saysphysicist Terry Quinn, who led the International Bureauof Weights and Measures effort. “But then there’s aniggling doubt. If there was one outlier, we would saymaybe. But we did our experiment twice and gotthe same answer, and JILA used a completely differentapparatus and is a lab that people greatly respect.”

To try and settle the issue, researchers have re-cently tried to create completely different methods ofmeasurement, relying on different physical propertiesof materials. For example, in 2014, Tino and his co-workers calculated G using what’s known as an atomicfountain (9). In it, a laser splits rubidium atoms intosuperposition of two quantum states and acceleratesthem vertically, allowing them to rise and fall in thepresence of 516 kilograms of tungsten. One state riseshigher and experiences a different gravitational pullfrom the tungsten than the other state. When the twostates are recombined, they produce an interferencepattern that can be used to calculate G.

Although the experiment revealed a value of Gthat was lower than the accepted standard and whichhad a relatively high uncertainty, the technique wasthe first to use quantum effects to measure the grav-itational constant. Tino thinks that replacing the tung-sten with crystalline silicon weights that containfewer irregularities, as well as replacing the rubidiumwith strontium atoms that are immune to magneticinterference, would improve the precision of the mea-surement by a couple of orders-of-magnitude. Otherlaboratories around the world are now performing

Fig. 2. Despite improvements in techniques, there arestill significant measurement discrepancies for Big Gamong different research groups. Image courtesy ofDave Cutler.

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similar atomic fountain experiments that could yieldconsistent results in the coming years.

“One of the wonderful things about this field is thatthere’s no attempt to sweep the discrepancies underthe rug,” says Müller. “Quite on the contrary, they’rehighlighting this problem.”

Physicists are doing everything they can to mea-sure G more accurately. Efforts are currently underwayin some laboratories to repeat previous experimentsdone by different teams to tease out systematic errors.A Chinese group is rebuilding Gundlach’s ultrahigh-precision instrument in incredible detail and Quinnand his colleague have handed over their equipmentto National Institute of Standards and Technology re-searchers to see if they get a similar result.

This July, the National Science Foundation heldan Ideas Lab in Gaithersburg, Maryland, that broughttogether 15 researchers working in both gravitationalconstant experiments and other fields, such as con-densed matter physics, atomic physics, and evenastrophysics.

Physicist Pedro Marronetti, who spearheaded theeffort, called it “a grueling week of physics discussions.”He and other participants hope the gathering spurs newexperiments that “could potentially increase the pre-cision to which G is known by an order of magnitude.”

Exotic PossibilitiesPractically speaking, even if physicists do succeed inmeasuring G with the same precision as other funda-mental constants, nothing will shift in our basic un-derstanding of the foundations of physics. Measurementsof G are a textbook example of pure science: experi-ments done for their own sake and nothing else. “It’s al-most like an art,” says Gundlach. “You want to do anexperiment to figure out something as well as you can.”

But because the field has been working at thisproblem for so long with no resolution, there remainsthe small but real possibility of more exotic explana-tions for the discrepancies in the measured values of G.“We can measure much more complicated things, sowhy can’t we measure this?” asks Quinn. “Is it becausewe’re trying to measure forces that are extremely smallor because there’s some hidden physics?”

One possible—if rather far-fetched—explanation isthat the gravitational constant changes slightly withtime, a case that several theoreticians have tried tomakeafter looking at the ever-changing G measurements.“In particle physics, if you have an anomaly in your signalthat’s five times the error bars, or five-sigma as they sayin statistics, then you can claim discovery of a new ef-fect,” says Müller. “The disagreement in the measure-ments of Big G passes that threshold.”

Another intriguing idea is that the universe hasmore dimensions than the four we normally experi-ence (three in space and one in time). Theoreticianshave dreamed up scenarios in which these extra di-mensions are so small that we wouldn’t notice them,but they would influence reality at microscopic scales.Perhaps gravity is weak because it is leaking into theseother dimensions, and at extremely short distancesit departs from Newton’s inverse square law (whichsays that gravity’s strength falls as the square of the

“One of thewonderful things about this field is that there’sno attempt to sweep the discrepancies under the rug.”

—Holger Müller

distance). The differing G results might be hinting atthe presence of extradimensional distortions.

However, no theory or experiment so far has offereda compelling reason to abandon our current under-standing of gravity. If G noticeably varied, it would havean influence on everything from the formation of starsand galaxies to the movements of planets. Whateverthe potential variation, it must be small enough to notperturb the workings of the universe as we know it.

Still, our model of gravity is incomplete. As de-scribed by Einstein’s general relativity, gravity isthe only force that has resisted quantization, unlikethe other three fundamental forces of nature, whichcome under the purview of quantum mechanics.Perhaps one day, a new theory will combine thesetwo pillars of physics and predict the value of G. Ifso, the ongoing efforts to measure G ever moreaccurately would be well-placed to verify suchpredictions.

Knowing why G has the value it does could haveother implications. With the Laser InterferometerGravitational-Wave Observatory now detecting grav-itational waves and with other more advanced ob-servatories on the horizon, experimental gravitationalphysics is maturing as a field. Perhaps a better de-termination of G could provide insight into gravita-tional waves. It may even have something to say aboutthe two other long-standing mysteries in cosmology:the nature of dark matter (the universe’s unseen massthat we know is there because of its gravitational pullon normal matter) and dark energy (thought to makeup three-quarters of the matter and energy in theuniverse), both of which are intimately connectedto gravity.

Schlamminger also points out that in 2018 theInternational Committee for Weights and Measures

Fig. 3. In 1798, Henry Cavendish used this torsionbalance to measure Big G. With the help of a pulley,large balls hung from a frame were rotated into positionnext to the small balls. Reproduced from ref. 2.

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plans to redefine the International System of Units(SI)—in particular the kilogram—wholly in terms ofphysical constants, such as the Planck constant,Boltzmann constant, and Avogadro’s number. Al-though the gravitational constant won’t be part ofthe reclassification, it could become important asresearchers refine their definitions of smaller masses.“I think if we want to understand the milligram

better, we will need to understand Big G better,”he says.

In the meantime, the search for greater precisionwill likely continue to tug on physicists. “Why dopeople climb Mount Everest? Because it’s there,”says Schlamminger. “A fundamental constant that’sdifficult to measure—just the challenge itself is a callfor some people.”

1 Falconer I (1999) Henry Cavendish: The man and the measurement. Meas Sci Technol 10(6):470–477.2 Cavendish H (1798) Experiments to determine the density of the earth. Phil Trans R Soc 88:469–526.3 Luther G, Towler W (1982) Redetermination of the Newtonian gravitational constant G. Phys Rev Lett 48(3):121–123.4 Michaelis W, et al. (1995) A new precise determination of Newton’s gravitational constant. Metrologia 32(4):267–276.5 Gundlach JH, Merkowitz SM (2000) Measurement of Newton’s constant using a torsion balance with angular acceleration feedback.Phys Rev Lett 85(14):2869–2872.

6 Schlamminger S (2006)Measurement ofNewton’s gravitational constant. Phys Rev D Part Fields Gravit Cosmol 74(8):082001-1–082001-25.7 Parks HV, Faller JE (2010) Simple pendulum determination of the gravitational constant. Phys Rev Lett 105(11):110801.8 Quinn T, Parks H, Speake C, Davis R (2013) Improved determination of G using two methods. Phys Rev Lett 111(10):101102.9 Rosi G, Sorrentino F, Cacciapuoti L, Prevedelli M, Tino GM (2014) Precision measurement of the Newtonian gravitational constantusing cold atoms. Nature 510(7506):518–521.

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