Gravitation is formative for our universe – and yet it is elusive. Because it only has a very weak effect, especially in the area of small masses. Now, for the first time, researchers have succeeded in measuring the tiny gravitational force between gold spheres that are just two millimeters in size and a good 90 milligrams in weight. It is the smallest gravitational force ever measured. The result confirms that Newton’s law of gravity, but also Einstein’s theories, are valid even with small masses. At the same time, the experiment opens up new opportunities to penetrate even smaller measuring ranges in the future.
Gravitational force is the weakest of all known basic forces, yet it is present everywhere in our everyday life. Every ball we throw, every coin we drop – all objects are attracted to the earth’s gravity. But despite its ubiquity, gravity is the basic force that has so far eluded any classification in the standard model of physics. While the mediator particles of the other forces are known, a corresponding transmitter for gravity is missing up to now. Albert Einstein also gave it a special status by describing it as the curvature of space-time – and thus as a property of the basic matrix of our universe. But even the great physicist failed in his attempt to bring gravity with the remaining basic forces into a unified theory.
To make matters worse, the gravitational force between masses decreases rapidly with their mass. Measuring the subtle attraction between very small objects is therefore extremely difficult and prone to failure. “Although the test masses in such experiments cover the whole range of macroscopic objects down to quantum systems, their counterparts are typically either the earth or masses in the kilogram range and larger,” explain Tobias Westphal from the Institute for Quantum Optics and Quantum Information in Vienna and Markus Aspelmeyer from the university Vienna and her colleagues.
Historical experiment in miniature format
In contrast, measuring the gravitational force between two masses in the gram range has so far only been successful in isolated cases; even smaller masses have so far eluded measurement. This has changed now. For their experiment, the researchers resorted to a famous Henry Cavendish experiment from the end of the 18th century. In 1797 he had constructed a pendulum device with which he could measure the gravitational effect of a lead ball around 30 centimeters in size and 160 kilograms. The core of the apparatus was a torsion pendulum – a thin, horizontally suspended rod with weights at both ends. If one of these weights came into the sphere of influence of the lead ball, it was tightened slightly and this movement was transferred to the other weight via the rod. Its deflection could be measured.
Westphal and his colleagues took up this principle and developed a miniature version of the Cavendish experiment. A gold ball two millimeters in size and weighing 90 milligrams served as a gravitational mass. The torsion pendulum consists of a four centimeter long and half a millimeter thick glass rod that is suspended from a fiberglass with a diameter of a few thousandths of a millimeter. Similar sized gold balls are attached to the ends of the rod. For the actual measurement, the gravitational mass is moved towards one of the two end spheres of the pendulum and then removed again. “We move the gold ball back and forth, creating a gravitational field that changes over time,” explains co-author Jeremias Pfaff from the University of Vienna. “As a result, the torsion pendulum then also oscillates with this particular excitation frequency.” This movement of just a few millionths of a millimeter can be read out with the aid of a laser and the gravitational force between the balls can be determined from it.
“Gravitational effect of a ladybug”
Because the gravitational force between such small masses is extremely weak, all interference must be kept away as much as possible – otherwise the measured value will be drowned out in the noise. Therefore, the entire experiment took place in a vacuum chamber, and the set-up stood on soft rubber feet that largely dampened external vibrations. “The largest non-gravitational effect in our experiment comes from seismic vibrations that are generated by pedestrians and tram traffic around our laboratory in Vienna,” says co-author Hans Hepach. “We therefore received the best measurement data at night and during the Christmas holidays, when there was little traffic.” The researchers suppressed other effects such as the electrostatic attraction between the gold spheres by means of a conductive shield between the gold masses.
With this experimental setup, the team was able for the first time to determine the gravitational field of an object that has only the mass of a ladybug. The measurements gave a value of 6.04 x 10-11 Cubic meters per kilogram and square second. This value is close to the official reference value for Newton’s constant of 6.67 x 10-11 m3 kg-1 s-2as the physicists report. The deviation is less than ten percent. “Our results show that we can isolate and measure the gravity of a single, small swelling mass by reducing interference to below ten percent,” said Westphal and his colleagues. The experiment opens up new possibilities for checking the laws of gravity on previously unattainable small scales. “According to Einstein, the gravitational force is a result of the fact that masses bend space-time in which other masses move,” says Westphal. “So what we are actually measuring here is how a ladybug bends space-time.”
Such measurements are particularly exciting because there are some unanswered questions in physics, the answers of which could be expressed in tiny deviations in the gravitational force on the smallest scale. In the behavior of gravity, for example, there could be indications of the nature of dark matter and dark energy, which significantly shape our universe.
Source: Tobias Westphal (Institute for Quantum Optics and Quantum Information, Vienna) et al., Nature, doi: 10.1038 / s41586-021-03250-7