“We have taken an important step towards carrying out an exciting experiment on this topic. We want to measure the gravitational interaction of muons,” says physics professor Souter.

The familiar matter that makes up humans, planets, and almost everything around us consists of protons, neutrons, and electrons. Physicists classify these particles as members of the first generation of matter.

Nature also contains two additional generations made up of heavier particles. One of these particles is the muon, a second-generation and much heavier relative of the electron.

Researchers at PSI can use powerful particle accelerators to produce muons and their antiparticles. When a positively charged antimuon combines with a negatively charged electron, the pair forms a neutral atom called muonium.

Why scientists want to test gravity with muons

The Standard Model of particle physics describes the different generations of matter, but it does not explain why multiple generations exist in the first place.

“But we physicists still don’t understand why these additional generations exist in the first place,” Souter says. “So why are there three in total?”

This mystery raises another fundamental question: Do the heavier particles of the second and third generations respond to gravity in exactly the same way as the lighter particles of the first generation?

Testing Einstein’s equivalence principle

For ordinary matter, objects at the same position in a gravitational field fall at the same speed. Galileo Galilei and Isaac Newton recognized this universality of free fall centuries ago. It later became central to Albert Einstein’s theory of gravity through the equivalence principle, which connects gravitational mass and inertial mass.

So far, researchers have demonstrated this principle only with ordinary matter or first-generation antimatter. Measuring how muonium behaves under gravity could provide the first test involving second-generation particles.

“Muonium is a neutral atom, so it’s very suitable for this. After all, you need something neutral to make something fall,” Souter explains.

Gravity is extremely weak compared with electromagnetism, making electrical neutrality essential. In experiments with charged particles, stray electromagnetic fields can overwhelm the gravitational effects scientists are trying to measure.

Muonium presents another major challenge. Muons exist for only about 2.2 microseconds before decaying. Earlier production methods also created muonium atoms traveling at different speeds and in different directions, making them unsuitable for highly precise gravity measurements.

Superfluid helium creates a controlled muonium beam

PSI researchers have now developed a method that could overcome these challenges.

“We were able to create muonium atoms in a ‘cold’ state, which is what made gravity experiments possible in the first place,” Souter says. “In this case, ‘cold’ means that the atoms propagate nearly parallel to each other and at similar speeds.”

The team’s method uses superfluid helium cooled to nearly absolute zero—approximately minus 273 degrees Celsius.

“Superfluid helium is known as a quantum fluid and does not allow individual helium atoms to lose their identity and contain impurities within them,” explains Jesse Zhang, lead author of the study.

The process begins by directing antimuons from PSI’s accelerator into a thin layer of superfluid helium. The particles slow down in the helium. When an antimuon encounters a free electron, the two form a muonium atom with a positive chemical potential.

That chemical potential effectively pushes the newly formed atoms out of the liquid. Once the atoms reach the surface, the chemical potential is converted into kinetic energy, giving them a boost and sending them vertically upward.

“So we’re using the chemical potential as an atomic cannon,” Zhang explains.

The muonium atoms must pass through the quantum liquid at a predictable speed without colliding. Because they have such a short lifespan, any significant delay could prevent them from reaching the surface before they decay.

“Our experiments also utilize PSI’s particle accelerator, which produces the most powerful continuous muon beam in the world,” Souter says. “Thanks to this high-quality source, we are able to produce very large numbers of muonium atoms.”

Using atomic interference to measure gravity

The researchers are building an instrument called an interferometer to measure how Earth’s gravity affects the muonium beam.

An interferometer uses the wave properties of atoms to create interference patterns. Earth’s gravitational pull should cause extremely small changes in those patterns. By measuring the displacement, scientists can determine how gravity acts on the muon.

“We hope to be able to test this method using an atomic beam for the first time this year. If all goes well, real gravity experiments should follow in the next two or three years,” Souter says.

The new muonium beam could also enable more precise laser spectroscopy experiments. These measurements could improve scientists’ understanding of the muon’s mass and other fundamental physical constants, which is another long-term goal of the research group.

Could the experiment reveal a fifth force?

If muonium responds to gravity differently from ordinary matter, the implications could be significant.

“It is certainly surprising and could point to the existence of a fifth force, in addition to other theories,” Souter says.

Modern physics recognizes four fundamental interactions: gravity, electromagnetism, the strong interaction, and the weak interaction. Scientists have repeatedly proposed the possibility of an additional fifth force, but no such force has been confirmed.

Discovering a fifth force is not the main purpose of Souter’s experiment. The immediate goal is more fundamental: to determine whether one of Einstein’s central principles applies to different generations of particles.

“I’m completely open-minded,” she says. “I simply want to measure for the first time whether the equivalence of gravitational mass and inertial mass also applies to second-generation particles. This alone is very exciting research.”

This study was supported by the National Center of Competence in Research Muoniverse.