In the very smallest measured units of space and time in the Universe, not a lot is going on. In a new search for quantum fluctuations of space-time on Planck scales, physicists have found that everything is smooth.

This means that - for now at least - we still can't find a way to resolve general relativity with quantum mechanics.

It's one of the most vexing problems in our understanding of the Universe.

General relativity is the theory of gravitation that describes gravitational interactions in the large-scale physical Universe. It can be used to make predictions about the Universe; general relativity predicted gravitational waves, for instance, and some behaviours of black holes.

Space-time under relativity follows what we call the principle of locality - that is, objects are only directly influenced by their immediate surroundings in space and time.

In the quantum realm - atomic and subatomic scales - general relativity breaks down, and quantum mechanics takes over. Nothing in the quantum realm happens at a specific place or time until it is measured, and parts of a quantum system separated by space or time can still interact with each other, a phenomenon known as nonlocality.

Somehow, in spite of their differences, general relativity and quantum mechanics exist and interact. But so far, resolving the differences between the two has proven extremely difficult.

This is where the Holometer at Fermilab comes into play - a project headed by astronomer and physicist Craig Hogan from the University of Chicago. This is an instrument designed to detect quantum fluctuations of space-time at the smallest possible units - a Planck length, 10-33 centimetres, and Planck time, how long it takes light to travel a Planck length.

It consists of two identical 40-metre (131-foot) interferometers that intersect at a beam splitter. A laser is fired at the splitter and sent down two arms to two mirrors, to be reflected back to the beam splitter to recombine. Any Planck-scale fluctuations will mean the beam that returns is different from the beam that was emitted.

A few years ago, the Holometer made a null detection of back-and-forth quantum jitters in space-time. This suggested that space-time itself as we can currently measure it is not quantised; that is, could be broken down into discrete, indivisible units, or quanta.

Because the interferometer arms were straight, it could not detect other kinds of fluctuating motion, such as if the fluctuations were rotational. And this could matter a great deal.

"In general relativity, rotating matter drags space-time along with it. In the presence of a rotating mass, the local nonrotating frame, as measured by a gyroscope, rotates relative to the distant Universe, as measured by distant stars," Hogan wrote on the Fermilab website.

"It could well be that quantum space-time has a Planck-scale uncertainty of the local frame, which would lead to random rotational fluctuations or twists that we would not have detected in our first experiment, and much too small to detect in any normal gyroscope."

So, the team redesigned the instrument. They added additional mirrors so that they would be able to detect any rotational quantum motion. The result was an incredibly sensitive gyroscope that can detect Planck-scale rotational twists that change direction a million times per second.

In five observing runs between April 2017 and August 2019, the team collected 1,098 hours of dual interferometer time series data. In all that time, there was not a single jiggle. As far as we know, space-time is still a continuum.

But that doesn't mean the Holometer, as has been suggested by some scientists, is a waste of time. There's no other instrument like it in the world. The results it returns - null or not - will shape future efforts to probe the intersection of relativity and quantum mechanics at Planck scales.

"We may never understand how quantum space-time works without some measurement to guide theory," Hogan said. "The Holometer program is exploratory. Our experiment started with only rough theories to guide its design, and we still do not have a unique way to interpret our null results, since there is no rigorous theory of what we are looking for.

"Are the jitters just a bit smaller than we thought they might be, or do they have a symmetry that creates a pattern in space that we haven't measured? New technology will enable future experiments better than ours and possibly give us some clues to how space and time emerge from a deeper quantum system."

The research has been published on arXiv.