## Measuring gravity at nanometer range

-- This work is published in Physical Review D ; preprint available at arXiv.org --

Newton’s law of gravitation is one of the most fundamental laws of physics. Its validity has been tested in various experiments and up to date it seems that the famous inverse square law holds from the millimeter range to intergalactic distances for nonreleativistic cases. Christopher Haddock from Nagoya University and coauthors succeeded in designing an experimental setup measuring the gravitational force at the nanometer range thus taking the short range limit of the measurements even closer.

There are four types of fundamental force exist in the universe on which we build the theory of physics. Gravitational force as being one of them got its final description from Albert Einstein’s general theory of relativity (lecture notes by S. Carroll). Before this remarkable theory, for centuries, Newton’s law of gravitation (as remarkable as the former) had been capable of describing the motion of bodies particularly planets on which the gravitational pull is empirically eminent. We had not required a more comprehensive theory of gravity until several observations showed slight differences from the results of Newton’s law, so that the general relativity superseded. Newton’s law of gravitation is still being used in most of the applications as relativity is required only when there is a need for extreme precision, or when dealing with strong gravitational fields (vicinity of a massive object or a black hole). On the other hand, today theoretical physicists are still searching for a universal theory capable of describing all four interactions. The standard model of particle physics built on quantum field theory has been the most successful combining the three fundamental forces other than the gravity. Taking gravitational interaction into this frame requires a quantum theory accounting the quanta of gravitational field called graviton. However, since general relativity is a classical theory, description of the gravitational fields in quantum field theory leads non-renormalizable results. Formulation of a theory of quantum gravity is the most fundamental and no doubt that improvements in measuring the gravitational force at the quantum scale shine light on the matter.

C. Haddock and colleagues in their work rely on the interpretation that the possible inverse square law violation produces a Yukawa-like exponential falloff ($$\small\alpha\exp{-r/\lambda}$$) in the gravitational potential energy function. They designed an experimental setup using neutron-noble gas scattering that is sensitive to the Yukawa like dependence. Neutron scattering experiments have an important place in physics because with this technique one can thoroughly explore the atomic structure as a result of electrically neutral neutrons can travel closer to nuclei without feeling electric charges of the nuclei and electrons. The team measured scattering angles and travel time of the neutrons: The scattering amplitude as a function of the momentum transferred from the neutron to the gas atoms, considered in four terms one of which is the possible exotic Yukawa-like interaction. The single neutron-noble gas atom scattering results extracted from the kinetic Monte Carlo simulations based on the total measured gas scattering intensity. At the end, the scattering results seem to fit well with the predictions of known physics, therefore within the sensitivity of the experiment the inverse square law holds at the nanometer range. A final note however, would be that this experiment improves the upper bound to the strength of an unexplained gravitational interaction but the precision still needs improvement, which is as promised by the team to be achieved by an order of magnitude higher sensitivity in the near future —currently found upper bound imposes that at around 3 nm separation, the exotic interaction cannot be more than a percent of gravitation.