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FORGET Flatland, the two-dimensional world imagined in the 1884 novella by Edwin Abbott. On tiny scales, 3D space may give way to mere lines.

So say researchers working on theories of quantum gravity, which aim to unite quantum mechanics with general relativity. They have recently noticed that several different quantum gravity theories all predict the same strange behaviour at small scales: fields and particles start to behave as if space is one-dimensional.

The observation could help unite these disparate ideas. “There are some strange coincidences here that might be pointing toward something important,” says Steven Carlip at the University of California, Davis.

He has noted that the theories yield similar results and has come up with an explanation for how dimensions might vanish (). “The hope is that we could use that to figure out what quantum gravity really is,” he says.

Disappearing dimensions first came to light in 2005 in computer simulations by Renate Loll of Utrecht University in the Netherlands, and colleagues. They have been pursuing a quantum gravity idea known as causal dynamical triangulation.

In their simulations, they focus on a parameter called the spectral dimension, which describes how particles or fields gradually move away from a given point – a process similar to diffusion. To their surprise, Loll found this process happens much faster at scales of 10^-35 metres, equivalent to the “Planck length”, the distance at which quantum gravity effects become significant.

This can be explained if the particles are effectively moving in just one spatial dimension. That’s because the fewer dimensions that are available, the fewer directions in which a particle can move, and so the less time it will take to wander away from its original position.

It was hard to make sense of such a strange result at first. Now, as Carlip notes, it seems that a reduction in dimensions pops up in many theories of quantum gravity (see “Different theories, same ingredient”). A technique called renormalisation group analysis suggests the same sort of reduction in spectral dimension might occur at tiny scales, says Carlip, as does a theory that radically alters the rules of general relativity, published last year by of the University of California, Berkeley.

Finding that very different approaches have something in common is exciting, as it suggests we may have stumbled upon an underlying property of quantum gravity, says Leonardo Modesto of the Perimeter Institute for Theoretical Physics in Waterloo, Canada. “People have emerged from quite different corners of the community and started saying, ‘let’s understand this result’,” adds Loll.

“People have emerged from quite different corners of the community, saying ‘let’s understand this’”

But how can dimensions simply vanish? Carlip suggests we could explain this by turning to the idea of “quantum foam”, proposed by John Wheeler in the 1950s. Wheeler suggested that quantum fluctuations alter the geometry of space-time, rendering it choppy and inhomogeneous at small scales. “But that was a qualitative picture,” Loll says. “No one had any sense of what it actually looks like.”

Carlip suggests that this foam behaves similarly to the space-time close to a singularity, the object at the centre of a black hole. According to general relativity, gravity is so strong near a singularity that space-time becomes distorted. Under these conditions, light is so strongly bent that it can take an infinitely long time to travel between nearby points. This means neighbouring patches of space-time become effectively disconnected from one another, allowing them to expand and contract independently.

Carlip suggests that at the tiny length scales of quantum gravity, the same sort of disconnection happens between different regions of space. This in turn allows space at different points to expand or contract faster in one dimension than in the others.

“The dimensions of space may become disconnected at the tiny length scales of quantum gravity”

As a result, over very short distances and timescales, the motion of a particle is dominated by one dimension, though this favoured dimension keeps changing randomly. This means that if you wait long enough or look at larger distance scales, space becomes effectively three-dimensional.

“It’s a potentially fruitful idea,” Loll says. “But there are still some hard questions you can ask.” Carlip agrees: “We have a very long way to go before we can claim that it describes the real world.”

One big question is how quantum foam can focus light so strongly that nearby regions become effectively disconnected from one another. Modesto says a possible explanation is that the foam can be treated as being made up of minuscule black holes.

For experimental evidence of space-time’s fundamental structure, light from distant galaxies might hold clues. Last year, NASA’s orbiting Fermi gamma-ray telescope found no evidence that the speed of light might vary with its frequency, an effect that would be evidence for a quantum foam. However, more precise measurements are needed to exclude the possibility. These might even allow different models for the foam, including some with fewer dimensions, to be tested, Carlip says.

In the meantime, some physicists continue to be delighted that multiple teams are homing in on the same idea. “I think it is one of the most interesting things to happen in quantum gravity for quite some time,” says Loll.