A new experiment deepens the mystery over gravitational constant, Big G

Scientists Stephan Schlamminger (left) and Vincent Lee examine the torsion balance they used to measure the gravitational constant, Big G. (R. Eskalis/NIST via CNN Newsource)

Scientists have announced the results of a decade-long quest to measure Newton’s gravitational constant, the force that keeps our feet on the ground and holds planets in orbit.

The pursuit was more or less a bust. The most ambitious effort to date to pin down the fundamental constant, which determines the strength of the attraction between two masses anywhere in the universe, resulted in a number that disagreed with previous findings, including the results of an experiment it sought to replicate.

Stephan Schlamminger, the scientist who painstakingly conducted the latest experiment that began in 2016, called it a “life-sucking” experience. “It was really kind of walking through a dark valley,” added Schlamminger, a physicist at the National Institute of Standards and Technology in Gaithersburg, Maryland.

But he has since been able to put a positive spin on his endeavors. “Now, I’ve put it a little bit in my rearview mirror,” he said. “I think every measurement is an opportunity to learn and every measurement brings light into this darkness.”

What is the gravitational constant?

Fundamental constants of nature are key values that define the behavior of physical phenomena in the universe — and they don’t change regardless of where you are in time or space. They include the speed of light and Planck’s constant, which plays a key role in quantum physics.

These constants are “baked into the fabric of the universe,” Schlamminger said. “It’s quite beautiful, because they are the same over generations. If you ever talked to an extraterrestrial, they would have the same concept.”

For more than 225 years, scientists have tried to measure the gravitational constant, nicknamed Big G. British scientist Henry Cavendish performed the first experiment to measure it in 1798, more than a 100 years after Isaac Newton first discovered the force of gravity.

Scientists have not, however, been able to converge on a measurement with a level of precision comparable to that of constants such as the speed of light (299,792,458 metres per second) or Planck’s constant, which is known to eight decimal places.

The Committee on Data of the International Science Council, or CODATA, issues recommended values of fundamental physical constants. Its recommended numerical value for Big G is a four digit number with a measurement uncertainty of 22 points per million.

Given that other constants in nature are known to six or more significant digits and are considered exact, this value, he said, is an “embarrassment for the active metrologist,” a scientist who specializes in measurements.

“If you had a watch that runs 22 ppm late, you would measure the year 12 minutes too long,” he added.

The field of metrology — the science of measurement — is important, he noted, because it creates trust in science, the economy and trade. “It is the kind of the science that undergirds a lot of our society, and nobody notices,” he said.

“When you pay your electricity bill, you want to make sure that you pay the right amount, right? There are people who know how to measure voltages and how to measure currents and how to measure power.”

Why it’s so difficult to measure

Gravity is notoriously difficult to measure accurately for three reasons, said Christian Rothleitner, a physicist at Physikalisch-Technische Bundesanstalt, Germany’s National Metrology Institute, who was not involved in the research. First, it is a relatively weak force.

“We perceive the force of gravity as a very strong force, as we have to exert a lot of force to lift something up on the earth,” he said via email.

In reality, he said, it is much weaker than the other three fundamental forces — electromagnetic, weak nuclear and strong nuclear forces — which hold atoms and nuclei together.

“You can easily see this if you look at a magnet, which is relatively small, but nevertheless exerts a very strong force on magnetic objects.”

The other reason it’s hard to determine the gravitational constant is that in a laboratory, the masses used in the experiment must fit inside a relatively small, constrained space: “And small masses in turn only generate small gravitational forces.”

What’s more, because the gravitational force is generated by every object, it’s “extremely challenging” to make sure the force you measure in the laboratory really comes from the intended mass.

“The problem with the Big G measurements is that the values are all very scattered, so the results of the measurements are not consistent with each other,” Rothleitner said. “This leaves a lot of room for speculation about the origin of the inconsistency.”

Secret envelope

In more four decades, there have been at least 16 other attempts to measure Big G. Rather than add a new measurement to an already inconsistent dataset, Schlamminger and his colleagues sought to replicate an experiment conducted by the International Bureau of Weights and Measures in Sèvres, France.

If he could independently produce the same results, the mystery surrounding Big G’s exact value might be solved.

The experiment relied on a sensitive piece of equipment known as a torsion balance, a device that senses minute forces by measuring the twisting angle, or torsion, of metal masses suspended on a thin fiber, which must be operated in a vacuum. The twist can’t be perceived with the naked eye but can be detected with sensors, allowing the gravitational force to be inferred.

Over the course of the experiment, Schlamminger spent years calibrating the equipment and troubleshooting the physical effects of characteristics such as temperature and pressure that could confound the measurements to prove these factors weren’t affecting the results.

Given that the team was replicating a previous experiment, he also took another precaution to avoid any personal bias, conscious or unconscious, that might creep in toward the answer he thought the experiment ought to get, and to prevent him stopping the study too soon.

A colleague, who wasn’t involved in the work, added a random offset number to the masses to blind Schlamminger to the actual measurement he was taking. This number was kept in a secret envelope hidden from Schlamminger until the work was complete.

After a honeymoon research period, Schlamminger at times found the work dispiriting. “It felt to me like it was like a random number generator,” he said. “I felt like I was going to a casino every day to work.”

The envelope with the secret number was unsealed on a conference stage in July 2024, and Schlamminger and his team finally found out the real results of their work. His initial joy — the final numerical value for Big G was in the right ballpark — subsequently soured, and he said he felt a “little bit unhappy.”

The team’s measured value of Big G was 6.67387x10^-11 cubic metres per kilogram per second squared. The unit reflects distance, mass and motion: how gravity works. It is 0.0235 per cent lower than the result that the researchers had attempted to replicate and at odds with the CODATA figure.

Schlamminger said that’s a notable difference — such as measuring the height of a human and being a millimeter or two off. “It’s small in the grand scheme of things, but it’s pretty embarrassing when it comes to these fundamental concepts,” he said. A scientific paper detailing the work was published April 16 in the journal Metrologia.

Schlamminger’s endeavors may provide scientists with the tools to make precise measurements in other areas involving extremely small forces, said Ian Robinson, a fellow at the National Physical Laboratory in the United Kingdom. Robinson wasn’t involved in the research, although he attended the meeting in which Schlamminger’s data was revealed.

“Some extremely obscure problems were found, addressed and a new result was produced,” Robinson said

Unknown physics?

What might explain the inconsistency in the measurements of Big G?

It’s possible that there’s something unknown about the universe that could be preventing an accurate value. But while that unknown was an exciting possibility, Schlamminger, Robinson and Rothleitner all said that hypothesis was a stretch.

“It is highly unlikely some fundamental physics that we do not understand is causing the discrepancy in the results,” Robinson said. “It is much more likely that an undiscovered, extremely small and obscure effect, or effects, biased some results.”

Schlamminger suggested that better engineered equipment could improve the situation or perhaps there was some human error at play. Nonetheless, he said he did not consider the past 10 years wasted.

“Precision metrology is not merely about converging on a number, it is about the rigorous exposure of unknowns,” his study concluded.

Schlamminger’s passion for the field remains undiminished. His forearm is tattooed with the numbers in Planck’s constant, which was fixed in 2019 in work that he was involved in.

Schlamminger said he hoped that young researchers interested in Big G would not be discouraged from taking up the quest. But even if an exact numerical value is found, he would never tattoo Big G: “It’s too finicky of a number.”