Physicists measure smallest gravitational field yet

Physicists in Austria have measured the gravitational field from the smallest ever object: a gold sphere with a diameter of just 2 mm. Carried out using a miniature torsion balance, the measurement paves the way to even more sensitive gravitational probes that could reveal gravity’s quantum nature.

For years, Einstein’s general theory of relativity and Newton’s universal law of gravitation have been subjected to ever more stringent tests. These tests have involved both astronomical observations and laboratory experiments. Usually, the masses that provide the gravitational field in the latter are large objects of several kilograms or more, such is the need to compensate for gravity’s inherent weakness.

The latest work, in contrast, uses a gold sphere with a mass of just 92 mg as its source. Markus Aspelmeyer and Tobias Westphal of the Institute for Quantum Optics and Quantum Information in Vienna and colleagues positioned this mass a few millimetres away from another tiny gold sphere with about the same mass located at one end of a 4 cm-long glass rod. The rod was suspended at its centre via a silica fibre, while a third sphere at the far end of the rod acted as a counterbalance.

Such “torsion balances” have been used for more than 200 years to make precise measurements of gravity. The idea is that the source mass pulls the near end of the bar towards itself, causing the suspending fibre or wire to rotate. By measuring this rotation and balancing it against the stiffness of the wire, the strength of the gravitational interaction can be calculated. The fact that the bar moves horizontally means it is less exposed to the far larger gravitational field of the Earth.

Noise-reduction strategies

A major challenge with such experiments is screening out noise. Aspelmeyer and colleagues did this by placing the balance in a vacuum to limit acoustic and thermal interference, while also grounding the source mass and placing a Faraday shield between it and the test mass to reduce electromagnetic interactions. In addition, they mainly collected data at night to minimize ambient sources of gravity. This is important because the gravitational attraction of the source mass is equivalent to the pull of a person standing 2.5 m from the experiment or a Vienna tram 50 m away.

To generate signals above the remaining noise, the researchers used a bending piezoelectric device to cyclically move the source towards and away from the test mass. Doing this at a fixed frequency (12.7 mHz) allowed them to look for a corresponding variation in the rotation of the balance – which they measured by bouncing a laser beam off a mirror below the silica fibre.

After repeating this process hundreds of times over a 13.5-hour period and then converting the time-series data into a frequency spectrum, Aspelmeyer and colleagues identified two clear signals above the background. These were the principle oscillation at 12.7 mHz and, at 25.4 mHz, the second harmonic generated by the gravitational field’s nonlinear variation in space. As the researchers point out, both harmonics were well above the resonant frequency of the oscillating balance and below the frequencies of readout noise.

A Newtonian result – for now

By using a camera to record the changing distance between source and test mass, the physicists also plotted how the gravitational force varied in space. They say that their data – a smooth curve dropping off as the square of the distance – provide unambiguous evidence of Newtonian gravity. What’s more, they also calculated their own value for the gravitational constant, G. This quantity remains a headache for metrologists, given the very precise but mutually inconsistent measurements of it made by different groups. The group’s result – a weighted mean based on 29 measurements during the seismically-quiet Christmas period in 2019 – is unlikely to resolve those disputes, being around 9.5% smaller than the official CODATA value of 6.674×10−11m3kg−1s−2. However, the researchers note that that this margin is within the roughly 10% uncertainty they obtain by totting up all the known sources of systematic error in their experiment.

Looking ahead, Aspelmeyer and colleagues argue that their experimental approach could in principle be extended to still smaller source masses. In particular, they say it should be possible to significantly reduce thermal noise by increasing the fibre’s quality factor. Raising the current value of about 5 to more than 20,000 could allow for source masses below the Planck mass of 22 μg – thereby raising the prospect of probing quantum gravity.

Getting to that point will, they caution, require mitigating other sources of noise. However, they reckon that these problems are solvable. Low-frequency noise from human sources, for example, could be reduced by transferring the experiment to a suitably remote location. Casimir forces, meanwhile, could be limited through electromagnetic shielding and signal modulation.

Andrew Geraci of Northwestern University in the US agrees that the work could lead to quantum-based investigations. He explains that placing very small objects into a quantum superposition would allow scientists to determine whether gravity plays a role in the entanglement of quantum systems. “While there is still a long way to go before this can be achieved,” he says, “I consider the work to be exciting progress in this direction.”

The research is published in Nature.