For 10 years, physicist Stephan Schlamminger had been chasing one of the most stubborn numbers in science. Now, after a decade of experiments, corrections, and painstaking analysis, the answer was sitting inside a sealed envelope.
He was not entirely sure he wanted to open it.
Schlamminger, a physicist at the National Institute of Standards and Technology (NIST), had spent much of the previous decade trying to measure the universal gravitational constant. Known to physicists as big G, this fundamental number determines the strength of gravitational attraction throughout the universe.
The number hidden in the envelope was the key that would finally unscramble his experimental data and reveal what his team had measured.
Gravity’s Most Elusive Number
Gravity is one of the most familiar forces in everyday life. It keeps people anchored to Earth, guides planets around the Sun, helps gather stars into galaxies, and plays a central role in shaping the enormous cosmic web of galaxy clusters that stretches across the universe.
Yet scientists still do not know its fundamental strength with the precision they have achieved for other basic forces of nature.
That strength is represented by big G.
Scientists have been attempting to measure big G for more than 225 years, beginning roughly a century after Isaac Newton introduced his law of universal gravitation. Despite generations of increasingly sophisticated experiments, the gravitational constant remains less precisely known than comparable constants associated with nature’s other three fundamental forces: electromagnetism and the strong and weak nuclear forces.
Part of the problem is surprisingly simple. Gravity is extraordinarily weak.
A tiny magnet can demonstrate the problem. A magnet roughly the size of a pinhead can lift a paper clip against the gravitational pull of the entire Earth. In that simple contest, the electromagnetic force produced by the magnet easily overcomes gravity.
The challenge becomes even greater in the laboratory. Scientists cannot move planets around to perform controlled experiments, so they have to measure the gravitational attraction between much smaller objects that can be weighed and precisely positioned.
Those experimental masses are about 500 billion trillion times smaller than Earth. As a result, the gravitational forces researchers are trying to detect are incredibly faint.
Measurements That Refuse to Agree
Modern instruments have become extraordinarily sensitive, but measurements of big G continue to produce slightly different answers.
The disagreements are small, roughly one part in 10,000. Yet they are still larger than researchers would expect from ordinary experimental uncertainty.
That persistent mismatch has created an uncomfortable question for physicists.
The most likely explanation is that some subtle experimental effect has been overlooked. But there is also a far more intriguing possibility: Perhaps scientists are missing something about gravity itself.
Schlamminger and his colleagues hoped to clarify the problem by carefully replicating a precision experiment carried out by the International Bureau of Weights and Measures (BIPM) in Sèvres, France, in 2007.
The idea was straightforward. If an independent team at NIST’s campus in Gaithersburg, Maryland, could reproduce the French measurement using essentially the same approach, it could help resolve the disagreement surrounding big G.
But Schlamminger was concerned about another source of error: himself.
Scientists can unintentionally influence how they interpret or analyze measurements when they know what answer they expect. Schlamminger wanted to eliminate that possibility as much as possible.
So he asked colleague Patrick Abbott to blind the experiment by scrambling part of the data.
Abbott subtracted a secret number from the carefully measured weights of some of the masses used in the experiment. Because only Abbott knew that number, Schlamminger could analyze the experiment without knowing the true value of big G his team was producing.
The correction needed to recover the real answer was sealed inside an envelope.
Ten Years of Work Came Down to One Envelope
Schlamminger nearly opened the envelope in 2022.
At the last moment, however, he realized that the team had not fully accounted for a subtle effect involving air pressure. Because even tiny disturbances can matter in an experiment this sensitive, he postponed the reveal and returned to the analysis.
Two years later, the moment finally arrived.
At 3 p.m. on July 11, 2024, Schlamminger was scheduled to present the results at the annual Conference on Precision Electromagnetic Measurements in Aurora, Colorado.
He was so anxious that he skipped the morning sessions. Instead, he mentally revisited the many things that could have distorted the measurement, including small variations in temperature and pressure.
By then, he believed the team had accounted for everything it reasonably could.
“I had really dotted all the i’s and crossed all the t’s of the experiment,” he said.
During his afternoon presentation, Schlamminger finally revealed the hidden number.
He immediately felt relieved.
For the experiment to produce the result he anticipated, Abbott’s secret correction needed to be relatively large and negative.
It was.
At first, that seemed like good news.
But as the day went on, Schlamminger realized there was a problem. The correction was too large. Once the blinded data were restored, the NIST measurement did not agree with the French result.
A Tiny Difference With Big Implications
After another two years of detailed analysis, Schlamminger and his collaborators reported their measurement in Metrologia.
Their value for G was 6.67387 × 10-11 meters3/kilogram/second2.
That result is 0.0235% lower than the value obtained in the French experiment.
In ordinary life, a difference that small would be meaningless. It will not noticeably change the reading on a bathroom scale, and it would not affect how much peanut butter is required to produce a 16-ounce container.
For fundamental physics, however, the discrepancy is significant.
Other fundamental constants of nature are known to six or more significant digits. Big G remains stubbornly less precise.
History also gives physicists a reason to pay attention to tiny discrepancies. On several occasions, small mismatches between measurements and expectations have eventually revealed that scientists were missing something important about how nature works.
That does not mean the disagreement over big G points to new physics. Experimental error remains the more likely explanation. But the continued inability of precision experiments to converge on the same value keeps the mystery alive.
An Experiment With Roots in 1798
The technique used by both the BIPM and NIST teams has a history stretching back more than two centuries.
Their experiments relied on a torsion balance, an instrument capable of detecting extremely small forces by measuring how much a thin suspended fiber twists.
The basic idea dates to a famous experiment performed by English physicist Henry Cavendish in 1798.
Cavendish placed two lead balls at opposite ends of a wooden beam suspended horizontally from its center by a thin wire. He then positioned two much heavier masses nearby.
The heavier masses gravitationally attracted the smaller lead balls, causing the suspended beam to rotate. As the beam turned, the wire twisted until its resistance balanced the gravitational pull.
By measuring the tiny movement of the beam with a mirror and a light pointer, Cavendish could determine the gravitational interaction between the masses and obtain information corresponding to the value of big G.
More than 200 years later, the same basic principle remains useful, although the equipment has become vastly more sophisticated.
Measuring a Force Almost Too Small to See
The BIPM and NIST experiments used eight cylindrical metal masses.
Four larger cylinders were positioned on a rotating carousel in a configuration resembling four candlesticks on an old-fashioned chandelier. Four smaller masses were located inside the carousel on a disk suspended from a copper-beryllium ribbon about as thick as a human hair.
Gravity between the outer and inner masses caused the suspended torsion balance to rotate, twisting the thin metal ribbon.
By precisely measuring that motion and the associated gravitational torque, the researchers could calculate one value for G. Torque is simply a twisting force, similar to the force used when turning a wrench.
But the teams did not rely on only one method.
In another series of measurements, the scientists placed electrodes beside the inner masses and applied electrical voltage to them.
The resulting electrostatic force produced torque in the opposite direction from the gravitational torque.
Researchers then adjusted the voltage until the electrostatic effect exactly balanced the gravitational effect, preventing the torsion balance from turning.
Because the amount of voltage required to achieve that balance could be measured with exceptional precision, it provided another way to calculate big G.
Copper and Sapphire Give the Same Answer
Schlamminger’s team introduced an additional test.
They wanted to know whether the material used for the experimental masses could somehow influence the result.
The researchers first performed the measurements using copper masses. Then they repeated the experiment using sapphire.
The outcome was essentially the same with both materials.
That result eliminated one possible explanation for the discrepancy, but it did not solve the larger mystery.
After a decade of work, the NIST experiment has become another important data point in scientists’ continuing effort to determine the true value of big G.
“Every measurement is important, because the truth matters,” Schlamminger said. “For me, making an accurate measurement is a way of bringing order to the universe, whether or not the number agrees with the expected value,” he added.
After devoting years to the problem, Schlamminger says he is ready to hand the challenge to others.
“I’ll leave it to younger generations of scientists to work on the problem,” he added.
“We must press on.”
Big G Is Not the Same as Little g
Big G is not the only letter g associated with gravity.
Physicists also use little g, but the two quantities describe very different things.
Little g refers to the acceleration an object experiences because of the gravitational attraction of a nearby large body such as Earth.
Unlike big G, little g changes depending on where you are.
Near Earth’s surface, little g is approximately 9.8 meters per second squared. On the Moon, it is only about 1.62 meters per second squared because the Moon has much less mass and therefore produces weaker gravitational acceleration.
Big G, in contrast, is considered universal.
To the best of scientists’ knowledge, it has the same value everywhere in the cosmos. It determines the gravitational force between any two objects, whether those objects are two laboratory masses, a person and Earth, or two astronomical bodies separated by enormous distances.
Newton’s law of gravitation uses big G to connect mass, distance, and gravitational force.
For two masses, m1 and m2, scientists multiply the masses together, divide that result by the square of the distance r between them, and then multiply by big G.
Written mathematically, the relationship is:
Gm1m2/r2
More than two centuries after scientists began trying to measure it precisely, that seemingly simple constant remains one of the most difficult numbers in physics to pin down.
