“Probably the worst theoretical prediction in all of physicsis an infamous line from a text book on general relativity published in 2006. It describes the perilous situation physicists find themselves in when trying to calculate the energy density of a vacuum.

Their thinking goes like this. According to quantum field theory, a vacuum is filled with particles that jump in and out of existence in a foam of quantum activity.

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

This results in a huge number, something on the order of 10^117 eV. This is equivalent to the relatively strong gravitational effect that appears as a strong curvature of the universe.

## cosmic constant

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

This is about 120 orders of magnitude smaller than the expected value, hence the infamous line about the worst prediction.

All of this is evidence that something is wrong with the way physicists think about the universe. He suggests that the problem must lie either with quantum field theory, which describes very young physics and happens to be one of the most successful and accurate theories of all time.

Or it must lie in general relativity, which describes the physics of the massive including the cosmological constant. It is also one of the most successful theories of physics. Maybe they are both wrong.

What might help, of course, is a way to measure the gravitational effect of zero point energy on a much smaller-than-cosmic scale.

Now Suman Kondo and colleagues at Syracuse University in New York state have developed just that – A method for measuring the gravitational effect of zero point energy on the atomic scale. They say their measurements significantly constrain the effect and set important boundaries for how gravity and quantum field theory can finally be unified.

The team’s technology exploits exotic atoms, called Rydberg atoms, which behave like hydrogen atoms but on a much larger scale. These bodies begin their life as an ordinary atom, like rubidium, but are then excited so that the outer electron is forced to orbit the nucleus at a great distance.

In these conditions, the innermost electrons furthest from the electric field of the nucleus are shielded. So the outer electron spins as if it were alone, just like the electron around a hydrogen atom.

The result is an atom similar to hydrogen on an enormous scale. The hydrogen atom is only a few micrometres wide while the outermost electron in the Rydberg atom can orbit at distances measured in micrometres – millions of times larger.

Rydberg atoms are believed to have enormous potential in fields as diverse as quantum computing and the chemistry of fundamental physics. They’re also powerful sensors, and that’s where Kondo and his cohorts come into this story.

They concluded that the electron in the Rydberg atom must be affected by the gravity associated with the zero-point field and that this effect must be detectable at the orbitals occupied by the electron and the energy levels between them.

Measuring these energy levels should reveal the magnitude of any gravitational disturbance. “The achievable precision and the relatively large size of the excited Rydberg atoms enable us to measure the gravitational properties of a vacuum,” Kondo and colleagues say.

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

## force field

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

This is not close to the magnitude that naive theory predicts (ie 10^117 eV). But there is another reason why it is so important. “This is interesting because it cancels out most of the putative contributions from particle physics that are at least 100 gigaelectronvolts in scale,” Kondo and colleagues say. “This has interesting implications for cosmology and emerging theories of quantum gravity.”

Kondo and his colleagues left it to other physicists to determine exactly what these effects would be. But it does bring the measurements closer to the value that cosmologists measure in the form of a cosmological constant. “We find it fascinating that an atom in an Earth-based lab can teach us something about cosmology,” the researchers inspire.

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

But these seemingly simple cracks soon turned into yawning gaps 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 effect of zero point energy can be solved within the framework of quantum field theory, perhaps in quantum gravity theory. Probably!

But what Kondo and his colleagues have shown is that this rift in our understanding of the universe shows no sign of getting smaller.

Reference: Is Void Attractive? Rydberg Atoms says “Probably not!” : arxiv.org/abs/2208.14192