Universal Gravitational Constant Gets a 10-Year Recheck

Physicists have been trying to measure the fundamental gravitational constant for well over two centuries. The current accepted value of big G, as it’s known, is 6.67430 × 10-11 cubic meters per kilogram per square second. It also has an uncertainty of ±0.00015 × 10^-11 m³/(kg s²). As far as constants of the universe go, that’s very uncertain.

Stephan Schlamminger recently completed a 10-year effort at the U.S. National Institute of Standards and Technology to replicate an earlier measurement of big G from the International Bureau of Weights and Measures, or BIPM (located near Paris) that’s notably higher than most measurements. He spoke with IEEE Spectrum about why it took so long to get a number—6.67387 x 10^-11 m³/(kg s²)—and why it’s notably lower than the BIPM result, to the tune of 0.0235 percent.

Why is it so difficult to measure big G?

Stephan Schlamminger: Gravity is very weak. When you were a kid, you probably played with fridge magnets, and it was a force you could feel. But if you have two coffee cups, you can try all you want—you can’t feel the force between them. It is there, but it’s so, so weak.

How did you attempt to measure big G?

NIST used a torsion balance with a fourfold geometry. This animation shows an exaggerated version of how the outer green masses gravitationally attract the inner blue masses.S. Kelley/NIST

Schlamminger: We used what’s called a torsion balance. The key idea in the torsion balance is that it decouples vertical gravity that you have from Earth from horizontal gravity, and that makes it sensitive to masses that are around the torsion balance but not the Earth below.

Ours had a fourfold geometry. It has a very thin torsion strip, then four cylinders in a “plus sign” arrangement. All of this is inside a vacuum. Outside, we have four larger cylinders that gravitationally attract the four smaller masses to them. If I move the outer masses just a tiny little bit, the plus sign will rotate, and we measure that angle that it moves. That angle is proportional to the gravitational torque.

Why try to replicate the BIPM value?

Schlamminger: We could move the field forward. The measurements have been plagued with inconsistencies, so by redoing an experiment, we hoped to shed light on the inconsistencies.

We did not find a smoking gun, so there’s no single reason why it’s different—our value versus their value. It’s still a big question mark.

What was it like spending 10 years on this?

Schlamminger: It’s a bit like herding cats. I’ve measured other fundamental constants, like Planck’s constant, and for most experiments, they have some sort of self-calibration built in. But with the gravitational constant, you have to keep track of every single mass that moves—where they are, how big they are, and weigh them.

How does your result compare to the rest?

Schlamminger: Our result is a little bit below the standard accepted literature value. I was disappointed because it doesn’t agree with the BIPM value, nor with the literature value. If there’s something wrong with the BIPM experiment, then the literature value—which includes that result—probably ought to come down a bit. But that is not for me to say. I think somebody else, independent, should figure out what the new mean value ought to be.