Celebrating its 340th birthday this year, the gravitational constant is the oldest fundamental constant in physics. “Big G” as it is affectionately known, was first placed at the heart of Newton’s law of universal gravitation during its formulation in 1686 and formally published a year later as an estimate yet-to-be-measured in Newton’s book Philosophiæ Naturalis Principia Mathematica. But after all these centuries, Big G is ironically still the fundamental constant with the least well-constrained value.
Scientists currently estimate a range of values arrived at for Big G, which means we can’t be totally certain if we have a good understanding of gravity or if there is something missing from our formulation. That is a situation that Stephan Schlamminger of the National Institute of Standards and Technology (NIST) has spent the last ten years trying to resolve, an endeavor that ended with the opening of an envelope containing an unknown answer, a situation more usually associated with the Oscars or some other glitzy awards ceremony than a physics experiment.
In this case, however, the drama is warranted; Big G is so ubiquitous in the equations we use to describe the universe that the uncertainty in its value is somewhat uncomfortable for scientists, especially for metrologists (nothing to do with the weather, but scientists who study measurement) like Schlamminger.
“G is gravity’s best-kept secret. It sits in this peculiar position: it is the oldest fundamental constant we know of, Newton wrote it down in 1687, and yet it remains the least precisely known of all of them,” Schlamminger told Space.com. “That strikes me as one of the great unresolved embarrassments of physics.”
Rethinking Big G
The gravitational constant was introduced as part of the equation that underpins Newton’s law of universal gravitation, which describes the force of attraction acting between every particle in the universe, and which is inversely proportional to the square of the distance separating the centers of mass of those particles. While the masses and distances used in these equations are adjustable, the value of Big G remains fixed. Therefore, this fundamental constant is key to calculating the strength of gravity everywhere in the universe.
Of course, in 1915, Newton’s theory of gravity was supplanted by Einstein’s geometric theory of gravity, general relativity, which sees this fundamental force arise from the curvature of the fabric of spacetime (the four-dimensional unification of space and time) caused by objects with mass. However, Big G survived this paradigm shift, albeit with a slightly revised role.
“Big G is a fundamental constant. As such, it is baked into our universe and has a certain value that is the same for all time through all space,” Schlamminger said. “It gives the strength of gravity in Newtonian physics. In Einstein’s theory of gravity, it determines how elastic space-time is. The smaller G, the more resistant spacetime is to being warped or deformed by massive objects like stars or planets.”
The first effort to measure Big G is credited to physicist Henry Cavendish in 1798. Cavendish was able to measure the gravitational attraction between large and small lead spheres, thereby calculating the density of Earth and arriving at the first accurate value for Big G.
However, even with the advances in scientific equipment and computing power made over the last 227 years, Big G has remained extremely difficult to measure.
“Gravity is by far the weakest of the four fundamental forces, which makes it extraordinarily difficult to isolate and measure precisely. You cannot shield against gravity the way you can shield against electric or magnetic fields,” Schlamminger said. “Everything pulls on everything else, all the time.”
Schlamminger explained that, unlike in the case of most physics experiments, in which scientists can, in his words, “crank up the signal,” researchers are instead stuck working with whatever gravity delivers.
“We now have 17 measurements of G, and they still scatter more than they should. Nobody knows why,” Schlamminger said. “We were just distraught by the large scatter in the data set. For a metrologist, it is unsatisfying having measurements that don’t converge.”
Opening the envelope
To perform their measurement of Big G, Schlamminger and a team of scientists replicated a precision experiment initially conducted by the International Bureau of Weights and Measures (BIPM) in Sèvres, France, transferring it to the NIST in Gaithersburg, Maryland, U.S. This came with its own risks, intellectual pitfalls that the researchers were careful to avoid.
“We wanted to make sure that we did not fall into the trap that’s known as ‘intellectual phase locking.’ That happens when you look at your measurement result and compare it to the literature value or the previously measured value with the same instrument,” Schlamminger said. “In this case, you may subconsciously stop when the measurement agrees with whatever expectation one has. This is not malice or intention. It happens at a subconscious level, and it is hard to guard against.”
Schlamminger came up with a fascinating idea to avoid this: having a colleague set a value or “bias” to be added to the weights used in the experiment that the team would be unaware of. That meant Schlamminger and colleagues wouldn’t know the value of Big G they had arrived at until the bias was revealed.
“We had the mass group add a bias to all the masses that they weighed for us. That bias was stored away in an envelope, and we only opened the envelope once we were happy with the self-consistency of our data,” Schlamminger said.
This envelope was opened on July 11, 2024, two years after it was initially planned to be opened in 2022. This delay occurred because Schlamminger realized he had missed a subtle but important factor related to air pressure in his calculations.
The Big G value arrived by the team was 0.000064 lower than the value currently held by the Committee on Data of the International Science Council (CODATA).
“If you had a watch that is off by 0.000064 [seconds] after one year, your watch would be off by 34 minutes,” Schlamminger explained.
This is a tiny difference, but it has interesting connotations. For instance, if the value of Big G arrived at by this team is correct, then Earth has a mass that is greater than the currently accepted value by 320,000,000,000,000,000,000 kilograms, or around 360 quadrillion tons.
“I want to be clear: the mystery is not solved. The underlying disagreement between experiments will still be there, waiting for someone to explain it,” Schlamminger said. “That is what keeps this field alive.”As for this metrologist, ten years of investigating Big G is sufficient for now.
“For now, I am stepping back from fundamental constants. These measurements take years, sometimes decades, and they take a lot out of you,” Schlamminger concluded. “As for me, I am turning my attention to precision measurements of electrical quantities, resistors, and capacitors, where I hope to cause a similar amount of trouble!”
The team’s results were published in the journal Metrologia.