Gravitational Measurements Go High-Resolution

Gravity is usually observed in very low resolutions. This is for the simple reason that as a force it's most easily observed as it influences very big things: how it mediates the interactions between superclusters and black holes and dark matter—or, zooming way in, on how gravity is experienced between planets and moons. We can observe things like tidal forces, orbital decay, leaning towers, and even Earth's own gravity potato.

Those are all still pretty big things, relatively speaking, but, as described in a recent paper in Applied Physics Letters, researchers have for the first time measured and mapped the curvature of a gravitational field only a single meter across. The technique employed by researchers at the University of Florence, a team led by the physicist Guglielmo Tino, is based on observations of interacting supercooled atomic clouds.

The thing about gravity is that it's very, very, very weak. As we go about our everyday business here on Earth, gravity would seem to be our everything. Without it, we would just sail off into space; the universe would have no large-scale medium to create large-scale structures, like galaxies and stars and planets. But relative to the other fundamental forces—electromagnetism, the strong nuclear force (what holds atomic nuclei together), and the weak force (radioactive decay)—it's nothing at all.

So it's been difficult to fit gravity into quantum mechanical descriptions of reality. It would seem to be a force that only affects collections of things, rather than fundamental, individual things like particles. This is the barrier between relativistic theories of the universe—where gravity warps spacetime—and quantum mechanical theories. And it's part of why snagging a resolution as fine as a single meter across is so exciting and also illustrative of the problems with resolving the gravitational force in general.

The technique used by Tino and his team is called atom interferometry. The basic idea is that a cloud of supercooled atoms is suspended and cleaved into halves in an otherwise empty glass cylinder (as close to a perfect vacuum as possible) using laser pulses. These two halves then fall within the cylinder independently, eventually recombining at the bottom. As supercooled collections of atoms, the clouds kind of act like just single huge atoms and so exhibit the wave-like character of individual particles.

Each cloud then has its own unique wave description and, as they recombine, the two waves (the two halves) interfere with each other, leading to detectable interference patterns: light-dark-light-dark, etc. These patterns give up information about the gravitational fields influencing each of the two halves. This is a gravimeter.

The concept has been around for the better part of a decade, but Tino advances the idea here by placing three different gravimeters at different vertical positions relative to each other, allowing for extremely precise measurements of gravity as it relates to height. This variation is what we'd call gravitational curvature. The Florence team performed experiments using very large masses placed around the cylinders to ensure that the gravitational influence was indeed detectable, but they note that it could theoretically be extended to measurements of Earth's gravitational field as it varies from place to place.

"Our atom interferometer, which simultaneously probes three freely falling samples of [rubidium gas], is able to perform measurements of gravity, gravity gradient, and curvature along the vertical direction at the same time, opening new perspectives for geodesy studies and Earth monitoring applications," Tino writes. "Using this scheme, we also demonstrate a new method to measure the Newtonian constant of gravity."

That last bit is important. Gravity everywhere is mediated by the gravitational constant ("big g"), which first appeared in Newton's law of universal gravitation. This is just a number. Below is what the law of universal gravitation actually says, where F is the attractive force between objects, r is the distance between them, and the two m variables are the masses of each object. G is just g, the strength of gravity, basically.

Newton predicted big g, but it wasn't until 1798, 71 years after his death, that Henry Cavendish actually measured the thing. Cavendish's figure for g was just a hair off of the currently accepted value of 6.693(34) × 10−11 m3s2/kg, the result of atom interferometry experiments done in 2007. This is less a statement on Cavendish's measurement abilities than a statement on contemporary gravitational measurement inabilities.

Measuring g is an ongoing source of frustration. Its weakness makes it hard to measure directly, while its apparent ambivalence with regards to the other fundamental forces makes it impossible to calculate indirectly. The technique described by Tino and his team could allow for big g measurements at never before seen levels of precision.

The study can be read in preprint, open-access form at arXiv