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Neutrons probe gravity’s inverse square law

04 Jan 2018
Photograph of the neutron area of the J-PARC facility
Gravitating toward Newton’s law: the J-PARC neutron facility

A spallation neutron source has been used by physicists in Japan to search for possible violations of the inverse square law of gravity. By scattering neutrons off noble-gas nuclei, the researchers found no evidence of any deviation from the tried and tested formula. However, they could slightly reduce the wiggle room for any non-conventional interactions at distances of less than 0.1 nm, and are confident they can boost the sensitivity of their experiment over the next few months.

According to Newton’s law of universal gravitation, the gravitational force between two objects is proportional to each of their masses and inversely proportional to the square of the distance between them. This relationship can also be derived using general relativity, when the field involved is fairly weak and objects are travelling significantly slower than the speed of light. However, there are many speculative theories – some designed to provide a quantum description of gravity – that predict that the relationship breaks down at small distances.

Physicists have done a wide range of different experiments to look for such a deviation. These include torsion balances, which measure the tiny gravitational attraction between two masses suspended on a fibre and two fixed masses. However, this approach is limited by environmental noise such as seismic vibrations and even the effects of dust particles. As a result such experiments cannot probe gravity at very short distances, with the current limit being about 0.01 mm.

Scattered in all directions

Neutrons, on the other hand, can get down to the nanoscale and beyond. The idea is to fire a beam of neutrons at a gas and record how the neutrons are scattered by the constituent nuclei. In the absence of any new forces modifying gravity at short scales, the neutrons and nuclei essentially only interact via the strong force (neutrons being electrically neutral). But the strong force acts over extremely short distances – roughly the size of the nucleus, about 10–14 m – while the neutrons have a de Broglie wavelength of around 1 nm. The neutrons therefore perceive the nuclei as point sources and as such are scattered equally in all directions.

Any new force, however, would likely extend beyond the nucleus. If its range were comparable to the neutrons’ wavelength then those neutrons would be scattered more frequently in a forward direction than at other angles. Evidence of such a force, should it exist, can therefore be sought by firing in large numbers of neutrons and measuring the distribution of their scattering angles.

In 2008, Valery Nesvizhevsky of the Institut Laue-Langevin in France and colleagues looked for evidence of such forward scattering in data from previous neutron experiments. They ended up empty handed but could place new upper limits on the strength of any new forces, improving on the existing constraints for scales between 1 pm and 5 nm by several orders of magnitude. Those limits were then pushed back by about another order of magnitude two years ago, when Sachio Komamiya at the University of Tokyo and team scattered neutrons off atomic xenon at the HANARO research reactor at the Korean Atomic Energy Research Institute in South Korea.

Time of flight

In the new research, Tamaki Yoshioka of Kyushu University in Japan and colleagues use neutrons from a spallation source at the Japan Proton Accelerator Research Complex (J-PARC) in Tokai, which they fire at samples of xenon and helium. Because the J-PARC neutrons come in pulses, the researchers can easily measure their time of flight, and, from that, work out their velocity and hence their wavelength.

Armed with this information, the team can establish whether any forward scattering is due to a new force or simply caused by neutrons bouncing off larger objects in the gas, such as trace amounts of atmospheric gases. At any given wavelength, both types of scattering would be skewed in the forward direction and so would be indistinguishable from one another. But across a range of wavelengths different patterns would emerge. For atmospheric gases, the scattering angle would simply be proportional to the neutrons’ wavelength. In the case of a new force, on the other hand, the relationship would be more complex because the effective size of the nucleus would itself vary with neutron wavelength.

Reactors can also be used to generate pulses, by “chopping” a neutron beam. But that process severely limits the beam’s intensity. Taking advantage of the superior statistics at J-PARC, Yoshioka and colleagues were able to reduce the upper limit on any new forces below 0.1 nm by about an order of magnitude over the HANARO results – showing that their inherent strength can at most be 1024 times that of gravity’s (gravity being an exceptionally weak force).

Cost-effective search

That is still nowhere near the sensitivity of torsion balance searches at bigger scales – which can get down to the strength of gravity itself. As Nesvizhevsky points out, torsion balances use macroscopic masses with “Avogadro numbers” (1023) of atoms, whereas neutron scattering experiments involve at most a few tens of millions of neutrons. Nevertheless, he believes that the new line of research is well worth pursuing, pointing out that many theories positing additional gravity-like forces “predict forces in this range of observations”. Such experiments, he argues, represent “an extremely cost-effective way of looking for a new fundamental force” when compared to searches carried out in high-energy physics.

Spurred on by the prospect of discovery, Yoshioka and colleagues are currently taking more data. The lead author of a preprint on arXiv describing the latest research, Christopher Haddock of Nagoya University, says that they hope to have new results by the summer. A series of improvements to the experiment, including less scattering from the beam stop, he says, could boost sensitivity to new forces in the sub-nanometre range by up to a further order of magnitude and should also improve existing limits at distances of up to 10 nm.

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