Why is spacetime distorted

Like a ladybug bends space-time

Four fundamental forces keep the world moving: gravity, electromagnetism, weak interaction, and strong interaction. At least that was the general consensus in the professional community until a few decades ago. In the meantime this picture has got cracks. Today's standard model of elementary particle physics has already been able to trace the electromagnetic and weak interaction back to a common origin. Of course, this particularly pleases those researchers who are after the "holy grail" of physics, the theoretical union of all these basic forces with quantum theory - also often referred to as the "world formula".

At the moment one still seems a long way from this. The strong interaction in the current standard model of elementary particle physics still stands around unconnected, and the weakest of the four fundamental forces, gravitational force, generally reluctantly struggles in many directions, especially when it comes to quantum physics.

Unruly gravitation

In classical physics, it is calculated as a force acting directly and without loss of time, Albert Einstein's general theory of relativity, on the other hand, sees gravity less as a force and more as a consequence of the mass that distorts four-dimensional space-time. The strength of gravity is also determined by the distance to the center. On the moon, which is about 80 times lighter and almost four times smaller than the earth, all objects fall six times more slowly per second.

And on a planet the size of a ladybug? That too would of course bend space-time, but the acceleration due to gravity there would be 30 billion times less than on Earth. What sounds like a number game here could in truth help to reconcile gravity with quantum physics. A team led by Markus Aspelmeyer from the Faculty of Physics at the University of Vienna had an interesting idea of ​​how this could work.

Paradoxical phenomena

The problem on very small scales is that the general theory of relativity can be used to describe the phenomena of gravitation, but the quantum phenomena, which sometimes appear paradoxical, are incompatible with it. For example, in quantum physics experiments, one could let quanta occupy two or more contradicting states at the same time - physicists call this "superposition". "It is unclear, however, whether the gravitational field of such a mass is also in a superposition," says Aspelmeyer, who also works at the Institute for Quantum Optics and Quantum Information (IQOQI) of the OeAW.

But the physicist sees an experimental way to clarify whether gravity needs a quantum description. Of course, the researchers are only at the very beginning, we are still far from a mass that is large enough to be able to measure its gravitational field and at the same time small enough to be able to bring it into superposition. "But I believe that it is possible in principle," said Aspelmeyer, who, together with Tobias Westphal, took a step in this direction.

Measurement record based on a historical model

Ultimately, the problem came down to the question: How small is the smallest mass whose gravitational force can still be measured beyond doubt? So the researchers first researched the smallest gravitational force measured so far and found that most of the experiments were carried out with balls weighing several kilograms. US colleagues try to measure gravity over very small distances, but they too use objects with a weight in the gram range.

The Viennese researchers have succeeded in undercutting this mass by a factor of ten with their gold balls around two millimeters in size and only around 90 milligrams in weight. When setting up their experiment, they resorted to the famous experiment of the British naturalist Henry Cavendish (1731–1810). In 1797 he was able to measure the gravitational force with the help of a so-called rotary balance, which is generated by a 30 centimeter large and 160 kilogram lead ball and acts on a much smaller ball. For the first time, Cavendish was able to use Newton's law of gravity to determine the earth's mass and thus its mean density.

Filigree structure

Aspelmeyer and Westphal have built a miniature version of this experiment. A gold ball weighing 90 milligrams and measuring two millimeters in diameter serves as the gravitational mass (the so-called "swelling mass"). As with Cavendish, its effect was determined using a so-called torsion pendulum. For this purpose, two gold spheres of the same size as the swelling compound were attached to the ends of a four centimeter long and half a millimeter thin glass rod, and this "dumbbell" was suspended from a glass fiber that was only a few thousandths of a millimeter thick. The researchers use gold "because its density is large and homogeneously distributed and so the center of gravity is close to the center of the sphere," says Aspelmeyer. This means that distances between the centers of mass can be measured very precisely.

If the swelling mass is now moved back and forth on the torsion pendulum near a ball, the force of attraction on this ball changes and the torsion pendulum begins to oscillate accordingly. This movement of just a few millionths of a millimeter can be measured with the help of a laser, and from this one can deduce the gravitational force of the gold ball.

Fight against the disturbance variables

It was not easy for the physicists to keep other influences on the torsion pendulum as small as possible, such as seismic vibrations that are generated by pedestrians and the traffic around the laboratory in Vienna-Alsergrund. The gravitational field of the tram, which passes the laboratory around 70 meters away, also had to be taken into account: "The tram's gravitational force is about as great as that of our source mass," said Aspelmeyer.

For this reason, the scientists used a torsion pendulum and measured mostly at night and during the Christmas holidays when there was little traffic. Other effects such as electrostatic attractive forces also had to be shielded. But the effort was worth it: For the first time, it made it possible to determine the gravity field of such a small object, as the researchers write in the journal "Nature". "So what we are actually measuring here is how a ladybug bends space-time," says Westphal.

On towards Planck-Masse

Even if one is still a long way from the interface between quantum physics and gravitation, the possibility of measuring gravitational fields of small masses and at small distances opens up new possibilities for researching gravitational physics. "There are unanswered questions everywhere you look," says Aspelmeyer.

As a next step, the physicists want to further miniaturize their experiment and "go in the direction of the Planck mass and see whether we can measure the gravitational field of an object in the microgram range. That would be a factor of 1,000 smaller than the mass of our gold globule. " (red, APA, March 11, 2021)