“Probably the worst theoretical prediction in all of physics” is an infamous line from a general relativity textbook published in 2006. It describes the predicament physicists find themselves in when trying to calculate the energy density of the vacuum.

Their thinking is like this. According to quantum field theory, the vacuum is filled with particles that bounce in and out of existence in a bubbling froth of quantum activity.

All this activity must be financed by some kind of energy budget, which physicists call zero-point energy. And since energy is equivalent to mass, it must exert a gravitational force on things around it. To figure out how much gravity is involved, all you have to do is add up all the quantum activity that contributes to it.

This produces a number that is huge, something on the order of 10^117 eV. And this equates to a relatively powerful gravitational effect that would manifest itself as a strong distortion of the universe.

## Cosmological constant

But there is another way to deal with this problem. In recent years, cosmologists have been able to measure the curvature of the universe, given by a number called the cosmological constant. This number also represents the energy density of the vacuum and its measured value is about 0.002 eV.

This is about 120 orders of magnitude less than the predicted value, hence the infamous worst-prediction line.

All of this is a clue that there is something wrong with the way physicists think about the universe. This suggests that the problem must lie either in quantum field theory, which describes the physics of the very small and turns out to be one of the most successful and accurate theories of all time.

Or that it must be consistent with general relativity, which describes the physics of the very large, including the cosmological constant. It is also one of the most successful theories of physics. Maybe they are both wrong.

What would help, of course, is a way to measure the gravitational influence of zero-point energy on a scale significantly smaller than the cosmological one.

Now, Suman Kundu and colleagues at Syracuse University in New York state have developed just that — a way to measure the gravitational effect of zero-point energy on the atomic scale. They say their measurements significantly constrain the effect and place important constraints on how gravity and quantum field theory can finally be unified.

The team’s technique uses exotic atoms called Rydberg atoms, which behave like hydrogen atoms but on a much larger scale. These objects begin life as an ordinary atom, such as rubidium, but then become excited so that the outermost electron is forced to orbit the nucleus over a great distance.

Under these circumstances, the inner electrons shield the outermost from the nucleus’s electric field. So the outermost electron goes around as if it were alone, just like an electron around a hydrogen atom.

The result is a hydrogen-like atom on a massive scale. A hydrogen atom is only a few picometers in diameter, while the outermost electron in a Rydberg atom can travel distances measured in micrometers—that’s millions of times larger.

Rydberg atoms are believed to have enormous potential in fields as diverse as quantum computing and fundamental physical chemistry. They are also powerful sensors, which is where Kundu and co come into this story.

They reasoned that the electron in the Rydberg atom should be affected by the gravity associated with the zero-point field, and that this influence should be noticeable in the orbits the electron occupies and the energy levels between them.

Measuring these energy levels should reveal the size of any gravitational perturbation. “The exceptional achievable precision and relatively large size of the excited Rydberg atoms allows us to measure the gravitational properties of the vacuum,” say Kundu and co.

And that’s exactly what they did. “The Rydberg atom experiments are now able to excite atoms to energy levels on the order of n = 100, while measuring the energy levels with an accuracy of 10^−10 eV,” they say.

## A force field

The results make for thought-provoking reading. Kundu and co say that as far as they can tell, Rydberg atoms experience no gravitational effect from the zero-point energy. This does not mean that there is no effect, but that it must be smaller than about 7 GeV.

This is nowhere near the size that naive theory predicts (ie 10^117 eV). But there is another reason why it is significant. “This is interesting because it eliminates most of the suspected contributions from particle physics that have a scale of at least 100 GeV,” say Kundu and company. “This has interesting implications for cosmology and emerging theories of quantum gravity.”

Exactly what those consequences will be, Kundu and co leave it to other physicists to determine. But this brings the measurements closer to the value that cosmologists measure in the form of the cosmological constant. “We find it remarkable that an atom in an Earth laboratory can teach us something about cosmology,” the researchers muses.

At the end of the 19th century, many scientists believed that most of the unsolved problems in physics were close to being solved. These included Ludwig Boltzmann’s discovery in 1877 that the energy systems of some systems could be discrete, Heinrich Hertz’s discovery in 1887 of the photoelectric effect, and the long-standing observation that Mercury’s orbit was precessing around the Sun faster than predicted. But the point was that physicists would find clear solutions to these problems in time.

But these seemingly minor cracks soon became gaping chasms that gave birth to the two greatest theories of the 20th century – quantum mechanics and relativity.

Many physicists hope that the problem of the gravitational influence of zero-point energy can be solved within the framework of quantum field theory, possibly in quantum gravity theory. Perhaps!

But what Kundu and co show is that this rift in our understanding of the universe shows no signs of abating.

Reference: Does the vacuum gravitate? Rydberg Atoms Say “Probably Not!” : arxiv.org/abs/2208.14192