Work and World

Our Ignorance About Gravity

It’s well known that gravity pulls two objects
together with a force proportional to the mass of one, times the mass of the other,
divided by the square of the distance between them. . Anyway, this equation is called Newton’s
law of universal gravitation, it’s taught to school children the world over, and it
predicts the motions of the planets and moons and asteroids in our solar system with incredible
precision. However, Newton’s law of universal gravitation
isn’t actually a universal law: first, we know that when the gravitational force in
question is really strong, Newton’s law is just wrong . And second, we know that when
the gravitational force in question is really weak , we don’t know whether it’s right
or wrong because gravity gets too weak to measure. Only in between (like, on the scale of the
solar system), do we know that the “law” of gravitation reasonably applies . Ok, but if Newton’s Law of gravitation has
been confirmed so accurately by the motions of planets and moons, how could it be wrong
at a different scale? Well, the earth looks flat when you’re relatively
close to the ground, but zoom out and it looks round, or zoom in and it looks bumpy; the
“law” describing the shape of the earth is different at different scales. Similarly, when the force of gravity is really
strong (like near a black hole), gravity is better described by the mathematics of general
relativity, and only when the forces in question get a bit weaker (for things farther apart
or with less mass) does gravity start to match up with Newton’s law of gravitation. But when you go even weaker (with objects
even farther away or even less massive ), we get to a point where we don’t know whether
Newton’s law of gravitation applies any more. And yet, even many physicists appear to be
ignorant about our ignorance about how gravity works when it’s weak – or at least, they
ignore our ignorance. It’s common to blindly apply -G m M/r^2
to decidedly non-astronomical objects, for which we haven’t tested gravitational attraction
very well at all: if you have two pieces of tape, you can calculate the gravitational
force that they in principle exert on each other according to the law of universal gravitation
– but it’s far too ridiculously ridiculously small for you to ever have the remotest chance
of noticing any effect whatsoever, let alone actually checking that the attraction between
them follows the law of universal gravitation as you move the bits of tape farther apart. In contrast, if you stick the two pieces of
tape together and then pull them apart, they’ll exchange some electric charge and then measurably
attract each other; an electrical attraction which is a million billion times stronger
than the predicted gravitational attraction , and whose strength has allowed us to confirm
Coulomb’s law of electrical attraction to a very very very high degree of accuracy . So it makes sense to apply Coulomb’s law
of electrical attraction to objects at normal human scales. But testing Newton’s law of gravitation
at these scales requires very delicate experiments, like very very sensitive oscillating pendulums
that oscillate slightly differently if there’s a heavy mass nearby (and can thus measure
the gravitational force with great precision), or incredibly finely-controlled lasers that
simultaneously levitate and measure the positions and forces on tiny little beads of glass – these
can measure ridiculously faint forces, like zeptonewtons. And so far, for objects a meter apart, we’ve
only confirmed that the gravitational attraction between them follows the law of universal
gravitation to within around one one hundredth of a percent . Which is a trillion times less
precise than our knowledge of the equivalent law for electricity. And our grasp on gravity gets worse the smaller
you go – Here’s a plot showing how our uncertainty about Newton’s gravitational law varies
across a whole range of distances – small distances on the left, big distances on the
right; and the higher the line the higher the uncertainty. Which, you will notice, is very high on the
left. Our existing experimental understanding of
short-distance gravity is so bad that gravity at the scale of the atomic nucleus could actually
be as much as a quadrillion quadrillion times stronger than Newton’s law of gravitation
predicts! That’s a HUGE range; it would be like not
knowing whether the moon pulls on us with the force of a hundred billion billion tons
of rock , or the force of a fruit fly . Or, put another way, at the scale of an atomic
nucleus, the law of gravitation could depend instead on the square of one or both masses,
or the square root, or the inverse cube of the distance, or G could be a million billion
times bigger, or a bunch of other possibilities, and we wouldn’t even know it. . The fact that there’s so much uncertainty
about gravity at short distances means that a lot of interesting truths about our universe
could be hiding under our very noses! One possibility, for example, is that there
are not just 3 dimensions of space, but an extra one that only the gravitational force
can travel through, which loops back on itself at the scale of micrometers or smaller . Just
like how the surface of a hair is technically 2-dimensional but hairs look one dimensional
from afar, this would mean that at distances much much longer than a micrometer, gravity
would act as if space had 3 dimensions and follow a roughly inverse square law (which
is what Newton’s law of gravitation is), while at distances much shorter, it would
behave as if space had 4 dimensions and follow more of an inverse cube law (which we haven’t
ruled out at particularly small scales) . However, as we’ve made increasingly precise
measurements of the gravitational attraction between small things, we haven’t yet discovered
any gravitational forces inconsistent with Newton’s law of gravitation . so it may
be that -G m M over r squared does describe the strength of gravity for very very short
distances; but our uncertainty is still very big, and it remains pretty crazy to blindly
apply Newton’s law of gravitation to things like an electron and proton in a hydrogen
atom. This video was made with the support of the
Heising-Simons Foundation, which also supports research in precision measurement of the strength
of gravity at short distances. These experiments are super cool, because
they’re small, simple, clever, and are testing our fundamental understanding of physics without
the need for giant multi-billion-dollar particle accelerators. Thanks again to the Heising-Simons Foundation
for supporting MinutePhysics, and for supporting fundamental physics research.
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