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Physics

Physicists Measure the Gravitational Force between the Smallest
Masses Yet

A laboratory experiment captured the pull between two minuscule gold
spheres, paving the way for experiments that probe the quantum nature
of gravity

* By Ben Brubaker on March 10, 2021

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Physicists Measure the Gravitational Force between the Smallest
Masses Yet
Gravity is measured between two gold masses (one-millimeter radius
each) that are brought close to each other. Credit: Tobias Westphal
University of Vienna
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Physicist Markus Aspelmeyer vividly remembers the day, nearly a
decade ago, that a visitor to his lab declared the gravitational pull
of his office chair too weak to measure. Measurable or not, this
force certainly ought to exist. Ever since the work of Isaac Newton
in 1687, physicists have understood gravity to be universal: every
object exerts a gravitational force proportional to its mass on
everything around it. The visitor's comment was intended to bring an
increasingly fanciful conversation back down to Earth, but
Aspelmeyer, a professor at the University of Vienna, took it as a
challenge. "My resolution was 'Okay, I am going to not only measure
the gravitational field of this chair, but we are going to go small,
small, small!'" he recalls.

The research effort born on that day has now produced its first
result: a measurement of the gravitational force between two tiny
gold spheres, each about the size of a sesame seed and weighing as
much as four grains of rice--the smallest masses whose gravity has
been measured to date. The results, published in Nature today, bring
physicists one step closer to the distant goal of reconciling gravity
with quantum mechanics, the theory underlying all of nongravitational
physics.

Precision Gravity

It is hard to fathom just how extraordinarily weak gravity is for
such small masses. The gravitational pull of one sphere (the "source
mass") on the other (the "test mass") a few millimeters away is more
than 10 million times smaller than the force of a falling snowflake.
The central challenge facing Aspelmeyer's team was to design a
detector exquisitely sensitive to this gravitational force yet
totally insensitive to much larger background forces pushing and
pulling on the test mass from all sides.

The researchers achieved this sensitivity using a detector called a
torsion pendulum, which looks like a miniature version of a mobile
hanging above a child's crib. The test-mass sphere is fixed to one
end of a thin rod that is suspended at its midpoint by a
four-micron-thick quartz fiber. An identical sphere on the other end
of the rod acts as a counterweight. A force on the test mass causes
the torsion pendulum to rotate until it is balanced by a restoring
force from the twisting of the fiber. Such a thin fiber is extremely
compliant, so even a very weak force yields a relatively large
rotation. Critically, the torsion pendulum is very insensitive to
forces from distant objects, which tug on the test mass and
counterbalance together and thus do not induce rotation.

Precision gravity art concept. Gravity can be understood as
originating from a warping of spacetime, which is shown in this
artist's impression. Credit: Arkitek Scientific

But even this clever torsion pendulum design did not totally isolate
the test mass from the busy urban environment of daytime Vienna. "The
sweet spots are always between midnight and 5 A.M., when no people
are on the street," Aspelmeyer explains. "[But] this was not true of
Friday or Saturday."

To measure the gravitational force of the source mass, the
researchers did not simply place it near the test mass. Instead they
moved it continuously back and forth around an average separation of
a few millimeters. This technique, called modulation, is implicit in
the design of turn signals and blinking bike lights: regular,
periodic signals are much more visible against ever-present
background noise than constant ones. Sure enough, the scientists
observed an oscillating force at precisely the right frequency. They
then repeated this process many times, changing the average
separation between the masses, and measured forces as small as
10 femtonewtons at separations between 2.5 and 5.5 millimeters. The
team compared these measurements to Newton's famous inverse square
law of gravity, which describes how the gravitational force between
two objects depends on their separation: the data were consistent
with Newton's law to within 10 percent.

"[That] you can measure these really, really, really tiny forces--I
think that is pretty amazing," says Stephan Schlamminger, a physicist
at the National Institute of Standards and Technology, who studies
gravity but was not involved in the work.

But Aspelmeyer and his colleagues could not declare victory quite
yet: they still had to rule out the possibility that the source mass
modulation was generating other forces on the test mass that would
oscillate at precisely the same frequency. Periodic rocking of the
table supporting the experimental apparatus, caused by recoil from
the barely visible motion of the source mass, was just one of a host
of confounders the researchers had to carefully quantify. In the end,
they found that all known nongravitational forces would be at least
10 times smaller than the gravitational interaction.

Reaching toward Quantum Scales

Aspelmeyer believes that an improved torsion pendulum will be
sensitive to gravity from masses 5,000 times smaller still--lighter
than a single eyelash. His ultimate goal is to experimentally test
the quantum nature of gravity, a question that has perplexed
physicists for nearly a century. Quantum mechanics is one of the most
successful and precisely tested theories in all of science: it
describes everything from the behavior of subatomic particles to the
semiconductor physics that makes modern computing possible. But
attempts to develop a quantum theory of gravity have repeatedly been
stymied by contradictory and nonsensical predictions.

Particles described by quantum mechanics behave in remarkably
counterintuitive ways. One of the strangest kinds of quantum behavior
is a special form of correlation called entanglement: when two
particles become entangled, their fates become inextricably linked,
and they cannot be described separately. Entanglement and other
quantum effects are most prominent in very small and well-isolated
systems such as atoms and molecules, and they become increasingly
fragile on larger scales where gravity is relevant. Until recently,
tests of quantum gravity have seemed far beyond the reach of
laboratory-scale experiments.

But the past few years have seen remarkable experimental progress
toward discerning subtle quantum effects in ever larger systems. In
late 2017 two groups of theoretical physicists independently proposed
an ambitious but possibly realizable experiment that could make a
definitive statement about the quantum nature of gravity. The effort
would measure whether gravity can entangle two quantum particles. If
so, "there's no escape from the fact that it has to be, in some
sense, nonclassical," says Chiara Marletto, a theoretical physicist
at the University of Oxford, who co-authored one of the proposals
with her Oxford colleague Vlatko Vedral.

The observation of gravitationally induced entanglement would be
groundbreaking. But a conclusive demonstration that gravity is
quantum mechanical would require proving that the two particles
interacted only through gravity. Aspelmeyer's efforts to isolate
gravitational forces between progressively smaller masses are a
critical step toward such a definitive test. "Since quantum is going
from small to big, there's a chance for gravity and quantum to meet
somewhere in the middle," says Sougato Bose, a theoretical physicist
at University College London, who co-wrote the other proposal with
nine collaborators.

"The question of whether gravity fundamentally behaves quantum is an
experimental question," Aspelmeyer says. "We can't wait to go the
whole nine yards and see how things turn out."

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