For 10 years, physicist Stephan Schlamminger pursued one of the most stubborn figures in science. Now, after a decade of experiments, corrections, and painstaking analysis, the answer was in a sealed envelope. He wasn’t 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 the 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 decipher 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 to form galaxies, and plays a central role in shaping the enormous cosmic network of galaxy clusters that spans the universe. However, scientists still do not know its fundamental force with the precision they have achieved for other basic forces of nature. That force is represented by the big G. Scientists have been trying to measure the big G for more than 225 years, about a century after Isaac Newton introduced his law of universal gravitation. Despite generations of increasingly sophisticated experiments, the gravitational constant remains less understood than comparable constants associated with the other three fundamental forces of nature: electromagnetism and the strong and weak nuclear forces. Part of the problem is surprisingly simple. Gravity is extraordinarily weak. A small magnet can demonstrate the problem. A magnet about the size of the head of a pin can lift a paper clip against the gravitational pull of the entire Earth. In that simple competition, the electromagnetic force produced by the magnet easily defeats gravity. The challenge becomes even greater in the laboratory. Scientists can’t move planets to conduct controlled experiments, so they have to measure the gravitational attraction between much smaller objects that can be precisely weighed and positioned. Those experimental masses are approximately 500 billion trillion times smaller than Earth. As a result, the gravitational forces that researchers are trying to detect are incredibly weak. Measurements That Refuse to Match Modern instruments have become extraordinarily sensitive, but big-G measurements still produce slightly different responses. The disagreements are small, about one part in 10,000. However, they are still larger than what 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 was missed. But there’s also a much more intriguing possibility: Maybe 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 simple. If an independent team at the NIST campus in Gaithersburg, Maryland, could reproduce the French measurement using essentially the same approach, it could help resolve the disagreement over the big G. But Schlamminger was worried about another source of error: himself. Scientists can unintentionally influence how they interpret or analyze measurements when they know what response they expect. Schlamminger wanted to eliminate that possibility as much as possible. So he asked his colleague Patrick Abbott to mask the experiment by encoding part of the data. Abbott subtracted a secret number from the carefully measured weights of some of the masses used in the experiment. Since only Abbott knew that number, Schlamminger was able to analyze the experiment without knowing the true value of the large 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 a single envelope Schlamminger was close to opening the envelope in 2022. However, at the last moment he realized that the team had not fully taken into account a subtle effect related to air pressure. Since even the smallest perturbations can matter in such a sensitive experiment, he postponed the revelation and returned to the analysis. Two years later, the time finally came. At 3 p.m. on July 11, 2024, Schlamminger was scheduled to present the results at the annual Precision Electromagnetic Measurements Conference in Aurora, Colorado. He was so anxious that he skipped the morning sessions. Instead, he mentally reviewed the many things that could have distorted the measurement, including small variations in temperature and pressure. By then, he believed the team had realized everything it could reasonably do. “I had really dotted all the i’s and crossed all the t’s of the experiment,” he said. During his evening presentation, Schlamminger finally revealed the hidden number. He immediately felt relieved. For the experiment to produce the result he expected, Abbott’s secret correction had to be relatively large and negative. Was. At first, that seemed like good news. But as the day progressed, Schlamminger realized there was a problem. The correction was too big. Once the blinded data was restored, the NIST measurement did not agree with the French result. A small difference with big implications After another two years of detailed analysis, Schlamminger and his collaborators published their measurement in Metrologia. Its value for G was 6.67387 × 10-11 meters3/kilogram/second2. This result is 0.0235% lower than the value obtained in the French experiment. In ordinary life, such a small difference would be meaningless. It will not noticeably change the reading on a bathroom scale and will not affect the amount of peanut butter required to produce a 16-ounce container. However, for fundamental physics the discrepancy is significant. Other fundamental constants of nature are known to six or more significant digits. The Big G remains stubbornly less accurate. History also gives physicists a reason to pay attention to small discrepancies. On several occasions, small mismatches between measurements and expectations have ultimately revealed that scientists were missing something important about how nature works. That doesn’t mean that the disagreement over the big G points to new physics. Experimental error remains the most 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 the BIPM and NIST teams has a history dating back more than two centuries. Their experiments were based 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 back to a famous experiment conducted 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 placed two much heavier masses nearby. The heavier masses gravitationally attracted the smaller lead balls, causing the suspended beam to rotate. As the beam spun, the cable twisted until its resistance balanced the gravitational pull. By measuring the small motion of the beam with a mirror and a light pointer, Cavendish was able to determine the gravitational interaction between the masses and obtain information corresponding to the value of the large G. More than 200 years later, the same basic principle is still useful, although the equipment has become much more sophisticated. Measuring a force almost too small to see The BIPM and NIST experiments used eight cylindrical metal masses. Four larger cylinders were placed on a rotating carousel in a configuration that resembled four candelabras from an antique chandelier. Four smaller masses were located inside the carousel on a disk suspended from a copper-beryllium ribbon the thickness of 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 were able to calculate a 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 a single method. In another series of measurements, the scientists placed electrodes next to the internal masses and applied electrical voltage to them. The resulting electrostatic force produced a torque in the opposite direction to the gravitational torque. The researchers then adjusted the voltage until the electrostatic effect exactly balanced the gravitational effect, preventing the torsion balance from spinning. Because the amount of voltage needed to achieve that balance could be measured with exceptional precision, it provided another way to calculate the big G. Copper and sapphire give the same answer Schlamminger’s team introduced an additional test. They wanted to know if the material used for the experimental masses could in any way influence the result. The researchers first made the measurements using copper masses. They then repeated the experiment using sapphire. The result was essentially the same with both materials. That result eliminated a 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’ ongoing effort to determine the true value of the big G. “Every measurement matters, because the truth matters,” Schlamminger said. “For me, making an accurate measurement is a way to put order in the universe, regardless of whether the number matches the expected value or not,” he added. After spending years on the problem, Schlamminger says he’s ready to hand the challenge to others. “I will let the younger generations of scientists work on the problem,” he added. “We must move forward.” Big G is not the same as small g Big G is not the only letter g associated with gravity. Physicists also use small g, but the two quantities describe very different things. The small g refers to the acceleration an object experiences due to the gravitational pull of a nearby large body, such as the Earth. Unlike the big G, the small g changes depending on where you are. Near the Earth’s surface, the small g measures 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 a weaker gravitational acceleration. The Big G, on the other hand, is considered universal. As far as scientists know, it has the same value everywhere in the cosmos. Determine the gravitational force between any two objects, whether they are two laboratory masses, a person and the Earth, or two astronomical bodies separated by enormous distances. Newton’s law of gravitation uses the big G to connect mass, distance, and gravitational force. For two masses, m1 and m2, scientists multiply the masses, divide the result by the square of the distance r between them, and then multiply by large 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 hardest numbers to pin down in physics.
