Gravity is the weakest of the fundamental forces, but it's the only force that operates over very long distances. Hence, planets orbit stars, stars form galaxies, and galaxies cluster. Gravity also operates at the tiniest of scales, too, but its weakness makes it very hard to detect its influence. It's worth trying, though, as violations of the laws of gravity at very small scales would be good evidence for New Physics™. So physicists have been looking, though without much luck so far.

Searching for flaws in gravity

The force due to gravity reduces with the square of the distance. If you double the distance, the force is not halved but reduced to a quarter of its original value. This law, called an inverse-square law, is based purely on geometry: we live in three spatial dimensions, and therefore the inverse-square law holds. However, if the universe has more than three spatial dimensions, the inverse-square law would break.

We know that over long distances—the Earth to the Moon, and the distances between stars—the inverse-square law appears to be correct. At galactic and cosmological scales, the inverse-square law also holds, with the caveat that dark matter and dark energy are required. You might think that what we call dark matter or dark energy would be potential evidence of extra dimensions, but it isn’t quite that simple. At these scales, the hidden dimension would have to be both large and unable to influence anything else, like photons. Since we also require consistency, and large hidden dimensions don’t appear to offer it at the moment, we are restricted to tiny hidden dimensions and changes to gravity at very small scales.

At very small scales—in the laboratory—verifying that gravity obeys the inverse-square law is much more challenging. The force of gravity is so weak that stray electric fields (from the electrical lines in the wall, for instance) will overwhelm any signal.

Quietly spinning in the corner

To make small-scale gravity measurements, researchers rely on conceptually simple experiments: measure the changes in rotational speed of an oscillating disc that is subject to a periodically changing gravitational force. The periodic force is supplied by a spinning disc. Both discs have wedges cut out so that the force due to gravity varies as the gaps spin past each other. The two discs are arranged right on top of each other. One is attached to a thin cable and is set in motion by twisting the cable, while the other rotates at a constant rotational speed.

As the oscillating disc changes its direction of rotation, it is still subject to a periodic torque from the rotating disc. These torque changes are highly periodic and can be measured very accurately. The wedged disc design gives a set of three rotational frequencies, so the instrumentation errors can be filtered out by examining changes that are common to all three frequencies.

The researchers have gone through several iterations to slowly improve their sensitivity over the last decade. Their experiment eliminates—so far as possible—all forces due to electrical and magnetic fields. The researchers have a set of three test masses that sit on top of the experiment to allow them to calibrate their analysis against a larger signal.

The major improvement, however, was in the analysis. To extract the force due to gravity, careful modeling is required. The researchers changed the design of the pattern cut out of the test mass so that analytical solutions to the model were obtainable for the torques involved. This eliminated many of the uncertainties due to computer modeling.

This and many other experimental refinements have allowed them to measure gravitational attraction down to a distance of just 52µm. Once they add additional stabilization against vibration, they will be able to measure at even smaller separations. In the meantime, they have verified that the inverse-square law holds for distances shorter than 50µm, and therefore we have no New Physics™.

Physical Review Letters, 2020, DOI: 10.1103/PhysRevLett.124.101101 (About DOIs)