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relativity superseded.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.