In
general relativity, matter and energy curve spacetime, which we
experience as gravity. Why can't there be an "antigravity"
force?
In
Newton's gravity, all masses attracted one another; there is no
"negative mass" to repel. In Einstein's general
relativity, matter and energy curves spacetime, and curved spacetime
is experienced as gravity.
If
there were negative mass, or even some sort of negative energy, you
might imagine that spacetime could "curve" in the opposite
fashion, resulting in antigravity. But this doesn't describe our
Universe.
This
is a profound fact, and makes gravitation very different from other
forces, like electromagnetism, that have both attractive and
repulsive features. So why can't there be any "antigravitation"
in our Universe?
Although
there are four known fundamental forces to the Universe, there’s
only one that matters on the largest cosmic scales of all:
gravitation. The other three fundamental forces:
the
strong nuclear force, which holds protons and neutrons together,
the
weak nuclear force, responsible for radioactive decays and any
“species change” among quarks and leptons,
and
the electromagnetic force, which causes neutral atoms to form,
are
all largely irrelevant on cosmic scales. The reason why is simple:
the other forces, when you gather large sets of particles together,
all balance out at large distances. Matter, under those three forces,
appears “neutral” at large scales, and no net force exists.
But
not so with gravitation. In fact, gravitation is unique in this
sense. With gravitation, there are only “positive” charges:
things with positive amounts of mass and/or energy. Between those
things, the gravitational force is only attractive, and so
cumulatively, it can really add up. But why is it this way, and not
any other? That’s what Alex Gebethner wants to know, writing in to
ask:
“The
common model used to explain spacetime to laymen like me is the
bowling ball on a bedsheet. The weight of the ball deforms the flat
sheet and draws in smaller objects nearby. But it seems logical that
the bedsheet could be deformed in the other direction (upward, to
continue with the bedsheet analogy) by a very similar object, pushing
objects away from the point of deformation. However, we never observe
this occurring. Why? Why does spacetime only bend in one direction
(that of gravity)?”
It’s
a profound question, and one that deserves a quality answer.
The
gravitational behavior of the Earth around the Sun is not due to an
invisible gravitational pull, but is better described by the Earth
falling freely through curved space dominated by the Sun. The
shortest distance between two points isn’t a straight line, but
rather a geodesic: a curved line that’s defined by the
gravitational deformation of spacetime. The notion of “distance”
and “time” is unique for every observer, but under Einstein’s
description, all frames of reference are equally valid, and the
“spacetime interval” remains an invariant quantity.
The
“classic” illustration of general relativity is the notion that
space (and spacetime) is simply a fabric, and that all objects —
including both massless and massive objects — exist within this
fabric. The more mass (and/or energy) you have in one place, the more
space is curved by the presence of that mass/energy, and so the
greater the amount that the fabric is deformed. For any object that
moves through this region of space, the curvature of that space
(i.e., the amount and direction that the fabric is distorted)
determines how all entities, both massive and massless, will move
through it.
Now, a
great many people will object to this picture, because it:
depicts
space as two-dimensional, instead of three-dimensional,
shows
the deformation (or curvature) of space as being in the “down”
direction, as though gravitation were causing this deformation (like
a bowling ball on a bed), and
makes
it seem like, far away from even a large mass, space is no longer
bent at all.
None
of these things are true, and so for those of you who have those
objections, I’ll encourage you to instead visualize space as a
three-dimensional grid. Only, instead of a “Cartesian” grid,
where all the lines are mutually perpendicular in all three
dimensions, think of it as a grid where lines get “sucked” inward
by the presence of masses, as though someone grabbed a bunch of
strings from a Cartesian grid and pulled them all in toward a single
point.
An
animated look at how spacetime responds as a mass moves through it
helps showcase exactly how, qualitatively, it isn’t merely a sheet
of fabric. Instead, all of 3D space itself gets curved by the
presence and properties of the matter and energy within the Universe.
Multiple masses in orbit around one another will cause the emission
of gravitational waves, while any light passing through a region that
contains this distorted spacetime will be bent, distorted, and
possibly magnified by the effects of curved space.
The
big question that we need to consider is why gravity can’t work in
a repulsive fashion as well: things only gravitate; they don’t seem
to anti-gravitate. It’s as though space can only “curve” in one
direction: the direction that makes things attractive, not repulsive.
In the “2D bedsheet” analogy, matter and energy only ever cause
space to curve “down,” never “up,” and so there’s only
attraction, not repulsion. In the “3D grid” analogy, matter and
energy only ever cause those lines to be drawn “inward,” never
“outward,” and again, there’s only attraction, not repulsion.
There’s
a profound and important reason for this that gets straight to the
heart of what makes gravitation not only remarkable, but unique,
among the four fundamental forces: there’s only one “sign” for
the type of gravitational “charge” in the Universe: a positive
one.
Think
about that for a minute, because it’s not typically the way we
conceive of gravitation. We don’t talk about gravitational charges;
we talk about things like “mass” and “energy” when it comes
to gravity. But of all the physical entities, both macroscopic and
down on a quantum level, that have been demonstrated to exist,
there’s no such thing as “negative mass” or “negative energy”
that’s ever been discovered. Mass and energy, overall, must always
be positive.
Newton’s
law of universal gravitation and Coulomb’s law for electrostatics
have almost identical forms, but the fundamental difference of one
type vs. two types of charge open up a world of new possibilities for
electromagnetism. In both instances, however, only one force-carrying
particle, the graviton or the photon, respectively, is required.
Compare
this up against a force like electromagnetism, and you’ll
immediately see the difference. When it comes to a phenomenon like
electric charge, you don’t just have “one type” of charge; you
have two: positive (+) and negative (-). Under the rules of
electromagnetism:
positive
and positive charges repel,
positive
and negative charges attract,
negative
and negative charges repel, and
negative
and positive charges attract.
In
other words, the sign of the electromagnetic force — which
direction the net force on each particle points — is dependent on
whether the charges are alike (in which case they repel) or opposite
(in which case they attract).
The
electromagnetic force, as it turns out, is much stronger
than the gravitational force: if you put two (positively charged)
protons close together and measured the (repulsive) electric force
and compared it to the (attractive) gravitational force, you’d find
that repulsion wins… by a factor of about ~1036, or, written out,
1,000,000,000,000,000,000,000,000,000,000,000,000.
So why
doesn’t the electric force dominate the Universe, instead of the
gravitational force?
Magnetic
field lines are imprinted by the galaxy on the cosmic dust in the
interstellar medium, as revealed by the Planck CMB experiment. These
field lines are of microgauss strength and can be coherent over
hundreds or even thousands of light-years. On large cosmic scales,
the electromagnetic force is no match for gravity, despite being
fundamentally many orders of magnitude stronger.
The
answer is that the Universe is electrically neutral, where the amount
of positive charge and the amount of negative charge balance out.
Atoms are electrically neutral, with the positive electric charge of
the nucleus exactly balanced by the negative electric charge of the
electrons that orbit it. Planets, stars, and galaxies are
predominantly made of atoms as well, and are electrically neutral
overall. The reason the gravitational force is so important —
arguably, the only important force on extremely large cosmic scales —
is because even though it’s so tiny, it’s cumulative. There’s
only one type of gravitational charge, and it adds up over time.
The
other two (nuclear) forces are also prohibited from affecting large
scales. For the weak nuclear force, it’s the fact that the force is
mediated by extremely massive particles: the W-and-Z bosons. Because
these particles are so much more massive than the particles that
experience the weak interaction, these interactions are suppressed
very strongly. It’s only through the process of quantum tunneling,
from an (unstable) initial state to a (more stable) final state, that
the weak interactions can typically proceed. At greater distances,
the suppression is greater, and so on scales greater than a subatomic
particle, the weak interaction plays no role at all.
The
decays of the positively and negatively charged pions, shown here,
occur in two stages. First, the quark/antiquark combination exchanges
a W boson, producing a muon (or antimuon) and a mu-neutrino (or
antineutrino), and then the muon (or antimuon) decays through a
W-boson again, producing a neutrino, an antineutrino, and either an
electron or positron at the end. This is the key step in making the
neutrinos for a neutrino beamline, and requires two separate decays
through the weak interaction: first of the pion into a muon, and then
of a muon into an electron. The weak interaction is incredibly
short-range, owing to the massiveness of the bosons (W and Z) that
govern it.
For
the strong nuclear force, the situation is a little more complicated.
The strong force is mediated by gluons, and gluons are massless, like
photons (which mediate the electromagnetic force). Unlike the
gravitational force (which has one type of charge) or the
electromagnetic force (which has two types of charge), the strong
nuclear force actually has three types of charges that are all
interrelated. We typically use a color analogy when it comes to the
strong force, where:
red,
green, and blue are the three colors,
cyan,
magenta, and yellow are the three anti-colors,
that
a color plus its anticolor (red and cyan, green and magenta, blue
and yellow) is colorless,
and
where three colors combined (red+green+blue) or three anticolors
combined (cyan+magenta+yellow) also makes a colorless combination.
Only
quarks and gluons have color among the fundamental particles, and the
only states that quarks and antiquarks can exist in are colorless
states: baryons (three quarks), anti-baryons (three antiquarks),
mesons (quark-antiquark combinations), and more complex,
shorter-lived states such as tetraquarks (two quarks and two
antiquarks) and pentaquarks (four quarks and one antiquark or four
antiquarks and one quark).
Because
only bound, colorless states of quarks exist in nature, the force
between any of these bound states must also occur through a colorless
combination that conserves baryon number: therefore, the mesons.
Because all mesons are massive, this “residual strong force,” as
it’s known, is also short-range, just like the weak nuclear force.
Individual
protons and neutrons are colorless entities: the only type of quark
state admissible in the Universe today. Although the strong force is
mediated by massless (gluon) particles, the only force that exists
between individual bound states are due to mesons, which themselves
are all quite massive, limiting the strong force’s range severely.
On
cosmic scales, that just leaves us with gravity. All masses are
positive, all energies are positive, and since it’s the mass/energy
in space, at all locations, that determines spatial curvature, and
spatial curvature determines gravity, the gravitational force must
always be attractive.
Now,
that’s with the Universe that we (apparently) have: the Universe as
we know it. But we could have imagined a very different Universe: one
where either negative mass or negative energy states could exist.
Unlike the electromagnetic force, where like charges repel and
opposite charges attract, gravitation would be flipped:
positive
mass/energy states would attract positive mass/energy states,
positive
mass/energy states would repel negative mass/energy states,
negative
mass/energy states would attract negative mass/energy states, and
negative
mass/energy states would attract positive mass/energy states.
Were
negative mass/energy states a part of our reality, we’d be able to
manipulate them in some very clever, important ways. We could move
negative states around in such a way that they could “shield” us
from the gravitational force, allowing us to experience
weightlessness without needing to be in free-fall.
Here
on Earth, in the gravitational field of our planet, there is no way
to “shield” ourselves from the gravitational influence of Earth,
as there are no gravitationally negative charges/masses/forms of
energy. The only way to experience weightlessness is to be in
free-fall, as the late Stephen Hawking experienced in 2007.
We
could create spacecrafts where the floors were made of positive
energy states, in space, and atop them, the ceilings could be made of
negative energy states, enabling us to create a uniform “artificial
gravity” field in the same way that an electromagnetic capacitor
creates a uniform electric field inside of it.
And,
perhaps most remarkably, with large enough amounts of positive and
negative energy states at our disposal, we could use these dual
negative energy and positive energy states to create a warp field:
where
the
space in front of a spacecraft is positively curved, and contracted,
the
space behind the spacecraft is negatively curved, and
expanded/rarified,
and
the space where the spacecraft is located is flat, preventing it
from being destroyed/damaged by gravitational tidal forces.
This
is the big idea behind the Alcubierre drive: the solution within
general relativity that allows for a realistic warp drive, contingent
on the existence of negative mass/energy states. One great hope for a
realistic warp drive was the possibility that antimatter, even though
it has positive mass from Einstein’s E = mc², would behave as
though it had a negative gravitational mass. When put to the test in
a gravitational field, however, it was shown that was not the case,
crushing our greatest hope for a realistic warp drive without needing
to invoke new physics.
The
way to make a realistic warp drive involves manipulating the energy
field and the spacetime curvature of the region around a spacecraft.
By compressing the space in front of you at the expense of rarifying
the space behind you, it’s possible to shorten the distance between
the point of origin and your destination.
Credit:
Trekky0623/Wikimedia Commons
Is
there any circumstance that doesn’t require “new physics” where
we could actually observe or test the effects of gravitational
repulsion? Are there any configurations we can imagine or create,
under which the gravitational force can be effectively negative,
instead of positive?
Yes,
you can design one. Instead of starting with empty space, imagine
that space is uniformly filled with matter: like a massive, perfect
fluid. Now, imagine that within this fluid, you have two types of
“particle” to put down:
a
positive mass particle, whose density is greater than the density of
the fluid (e.g., a lead particle in a fluid like water),
and
(effectively) a negative mass particle, whose density is lower than
the density of the fluid (e.g., a solid-walled balloon, or an
impermeable aerogel, in a fluid like water).
Under
these circumstances, we can actually observe what’s gravitationally
attractive and what’s repulsive. As you might expect:
two
positive mass particles attract one another,
two
negative mass particles attract one another,
but
one positive mass and one negative mass particle repel one another.
There
isn’t a “fundamental” repulsion, but if you fill your Universe
with mass/energy and have a stable region that has less of it, that
region behaves as though it possesses negative mass/energy, with the
precise consequences described above.
If you
have a uniform-mass/energy fluid, a positive mass within it will
behave in a gravitationally attractive fashion, but a lower-density,
lower-mass/energy region will behave as though it has negative
mass/energy, and will be gravitationally repulsed: but only
relatively, not absolutely.
However,
on a fundamental level, there are no negative mass/energy states to
speak of. As determined by measuring the cosmological constant (i.e.,
the effects of dark energy), the total amount of energy inherent to
empty space is positive — small, but greater than zero — and that
there’s nothing you can remove or take away from space to drive
that energy to a less-than-zero (i.e., negative) value. Sure, you can
manipulate space to create lower energy states in one region than
another, and you can leverage that phenomenon to create an
effectively negative (relative to the average mass/energy state)
energy region, but it’s still a region where the gravitational
force is attractive. It’s just “less attractive” than the
surrounding regions.
If you
have a helium balloon floating in your car and slam on the brakes,
all the passengers will jerk forward, but the balloon will float to
the back. It isn’t because the balloon violates Newton’s law of
“an object in motion remaining in motion,” but because the
(denser, heavier) air in the car “remains in motion” more
strongly than the (less dense, lighter) helium balloon. That is the
only sense in which we have antigravity, where something with less
mass/energy than average can behave like a negative source of
gravity: negative compared to something that’s “more positive.”
Unless, or until, some sort of new physics is discovered that shows
that negative mass or negative energy states can exist, antigravity,
at least at a fundamental level, will remain a mere mathematical
curiosity.
by
Ethan Siegel at bigthink.com on December 1, 2023
