Our universe has three spatial dimensions – or rather, three that our human senses can actively perceive. Some theories suggest there could be many more dimensions that we're unaware of, mostly because they're imperceptibly tiny. Now, Japanese researchers have taken the search for extra dimensions down to the nanoscale, using a neutron beam to study the gravitational force more precisely than ever before.

According to the Standard Model of particle physics, the world is governed by four fundamental forces: gravity, electromagnetism, and the weak and strong nuclear forces. Although things act a bit "spooky" down on the quantum level, science has managed to generally describe all of these forces at both the macro and quantum scales – except gravity.

Newton's law of universal gravitation says that the gravitational force between two objects gets stronger as objects get more massive, and weaker the further apart those objects get. But it's only really been shown experimentally down to the submillimeter scale, which is still "macro". According to some theories of quantum gravity, on smaller levels that law might break down.

Gravity is the weakest of the fundamental forces, and it's been suggested that this is because some gravitons – the hypothetical particles that carry the gravitational force – tend to escape into extra dimensions. While we're not sure there are any more than the three spatial dimensions we're used to, M-theory (one of the current leading candidates for a theory of everything) takes place across 11 dimensions.

If it's hard to picture where these other dimensions are hiding, Professor Matt Strassler uses the excellent analogy of vessels on a canal. A submarine could move through the canal in three dimensions, but a small boat on the surface is restricted to two – it can't move up and down. Meanwhile a large ship would experience the canal as one-dimensional, since it can only move forwards or backwards. In this analogy, we humans are that ship – we're simply too big to travel through or even notice these other dimensions.

So, to study whether these extra dimensions are lurking in extremely tiny spaces, the researchers from Osaka, Kyushu and Nagoya Universities set out to test gravity on the subnanometer scale. To do so, they used the world's highest intensity neutron beam, which is housed at the Japan Proton Accelerator Research Complex (J-PARC).

The experiments involved firing pulses of neutrons into a chamber filled with either xenon or helium gas, and monitoring how long the neutrons took to move through the chamber, as well as their scattering angles. Because the neutrons have no charge, they're not affected by the electromagnetic background that may interfere with similar experiments.

The team found that the results matched predictions based on the known laws of physics, which indicates that Newton's law still applies as expected down to a scale of less than 0.1 nanometers. No unexplained force – ie, another dimension – is acting on these particles at this scale.

That doesn't mean those extra dimensions aren't there, just that they may be hiding at even smaller scales still. The researchers are currently working to further improve the sensitivity of the equipment, which might help them probe those tiny spaces.

"As the performance of the world's most powerful beamlines improves, we are able to significantly enhance our knowledge and understanding in step," says Tamaki Yoshioka, corresponding author of the study. "Such iterative improvements can be very revealing. In the case of gravitational interactions we have made substantial steps towards understanding the dimensions of the space around us."

The research was published in the journal Physical Review D.

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