Millimetre-sized masses: Physics boffins measure smallest known gravitational field (so far)

Tiny golden balls may help unravel mysteries of nature's weakest force at a quantum level

It might not have occured to rock lugging early humans in the Stone Age that gravity is a relatively weak force, but it is.

Throughout their evolution, humans have become accustomed to living on the surface of a ball with a mass of around 6 × 10²⁴ kg, and our planet being this size makes gravity on Earth a real visceral experience for such sentient bipeds.

Fast-forward a few millennia, and we now know gravity as the weakling of the fundamental forces, which also include weak and strong nuclear interactions and electromagnetic force. Gravity is, for example, about 36 orders of magnitude weaker than the electromagnetic force.

Measuring gravitational forces between less-than-planet-sized objects has always been tricky, and limited to a few kilograms, but research published in Nature shows it can be achieved between two gold spheres with a mass of about 90 milligrams, and a radius of 1mm. That’s about the mass of an average-sized worker bee (although its body takes up a lot more space with a length of around 15mm).

A team led by Markus Aspelmeyer, physics professor at the University of Vienna, used a torsion balance to achieve the result. The approach used the twisting action on a thread or wire to measure forces perpendicular to the Earth’s gravitational force. The technique is not new: Henry Cavendish first used it in 1798 to measure the Earth's density and it is the standard way to measure the gravitational constant, G – necessary to predict gravitational forces between objects according to Newton's laws.

Aspelmeyer’s lab used a miniaturised version of the apparatus to measure the tiny gravitational forces and in doing so the team had to block electrostatic forces using a Faraday shield, and seismic and acoustic effects by connecting one of the gold spheres to a vacuum chamber.

Meanwhile, the other sphere was moved closer and further from the grounded sphere in a regular motion. The predictability in the resulting changes in the gravitational force helped cancel out any interfering noise (see the paper for a more detailed explanation).

The experimenters succeeded in measuring a force of about 9 × 10^–14 newtons between the two spheres. This is roughly the same weight acting on a mass of 9 picograms on Earth; 9 picograms is about one-third the mass of a human red blood cell.

“This work opens the way to the unexplored frontier of microscopic source masses, which will enable studies of fundamental interactions and provide a path towards exploring the quantum nature of gravity,” the authors said.

In an accompanying news and views paper, Christian Rothleitner, a research associate at Germany’s Physikalisch-Technische Bundesanstalt, said the result was significant as a feat of experimental ingenuity and one that shows Newton’s 334-year-old law of gravity holds well at this scale.

“The experiment is... the first to show that Newton’s law of gravity holds even for source masses as small as these,” Rothleitner said.

Newton’s laws have been greatly expanded by understanding gleaned from Einstein’s general theory of relativity – a geometric theory of gravitation – in terms of explaining gravity.

But even this has its problems. Rothleitner said physicists are puzzled by relativity's failure to explain why the observed speed of stars moving around galaxies is faster than expected, prompting the idea of dark matter, a mysterious gravity-generating substance. “However, nobody really knows what this dark matter is made of,” he pointed out.

At the same time, measurements of the gravitational constant G have failed to get more accurate over time, unlike other universal constants such as the speed of light.

Meanwhile, relativity doesn’t say how gravity behaves at the tiny, sub-atomic level of quantum mechanics, which is something string theory has attempted to explain.

Rothleitner said that as the methods proposed by Aspelmeyer and his team are refined over time, it could help physicists tackle this last problem. ®