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From hoverboards to flying cars to cloud cities, anti-gravity is a staple of science fiction and
our dream of a less Earth-bound future. But in the real universe gravity appears to be
a purely attractive force. Feels like its main MO is keeping us stuck to the
surface of this lonely rock. But maybe if we science hard enough we can remove the fiction
from science fiction. So for the sake of our flying cars we should at least try. And for many years,
physicists have wondered whether a certain well-known exotic material may
experience gravitational repulsion from the Earth. That material is antimatter,
and physicists at CERN have just completed a very long and very difficult experiment
to answer a seemingly simple question: does antimatter fall down, or does it fall up?
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Antimatter—the evil twin of regular matter. Or is it just the misunderstood twin of regular
matter? We’ve made it in labs and seen that an antimatter particle has charge and other
quantum properties compared to its regular matter counterpart. The only thing that’s the
same is its mass. Except it may be that in at least one sense its mass may be different—even
opposite to regular matter—and that fact may give us our antigravity. Or at least teach us
profound truths about the nature of reality. The trick is going to be to think about mass
not as one property of an object, but rather as two distinct and independent properties. There’s
inertial mass—the resistance to being shoved or slowed. And there’s gravitational mass,
which determines the heft of your gravitational field, and your response to other such fields.
Now we’ve explored an aspect of this idea previously, and this is a good review episode
for the studious, or a good followup episode for the impatient. Today we’re going to focus on the
anti-matter and the flying car implications of splitting inertial and gravitational mass.
Let’s start with Isaac Newton’s description of all of this. We’ll move to Einstein’s upgrade
later. Inertial mass is the mass in Newton’s second law. It determines how much force you
need to apply to achieve a give acceleration. On the other hand gravitational mass is the mass in
Newton’s law of universal gravitation. It acts as the gravitational charge, determining the strength
of the gravitational field and the strength of response to another such field. We almost always
assume that inertial mass and gravitational mass are the same thing. This equivalence is
called the equivalence principle. We normally think of the equivalence principle as being
the epiphany that led Einstein to his general theory of relativity, but it’s older than that.
A hundred years ago, Einstein realized that there should be no experiment that could
distinguish between the feeling of weight you have when supported in a gravitational field
and the same feeling when being accelerated at the correct rate in empty space. This statement
of the equivalence principle requires that inertial mass—the mass resisting acceleration—is
the same as gravitational mass—the mass that responds to a gravitational field.
But over 300 years prior to Einstein, this guy named Galileo demonstrated the same
thing when he dropped a pair of balls off the top of the Tower of Pisa. They
had different weights but the same size so air resistance was equal. He found
that they reached the ground at the same time. We’ve now done this experiment in
the near-vacuum of the Moon’s surface with a hammer and a feather, giving the same result.
Around a century after Galileo’s Pisa-drop, Newton came along and figured out the
equations that tell us why. Let’s say that the gravitational mass in Newton’s gravity
law is the same as the inertial mass in his second law of mechanics. Then,
when we calculate the acceleration experienced by a massive object in a gravitational field,
these two masses cancel out. In other words, more massive objects feel a stronger pull but are also
harder to accelerate. Because of this, hammers and feathers fall at the same rate on the Moon.
Gravity is always attractive because gravitational charge—aka mass—is always positive. Compare to
electromagnetism, which can be attractive or repulsive due to electric charge being positive
or negative. So what happens if we allow mass to be positive OR negative. We covered the details
in our previous video, but long story short is that two positive masses behave as normal,
two negative masses repel each other, and a positive mass is repelled by a
negative mass while the negative mass is attracted to the positive. That last
part means a positive and negative mass would chase each other, accelerating at a constant
rate forever. That breaks conservation of momentum and energy and so can’t be right.
The thing that really breaks physics in this scenario is that we allowed negative inertial
mass, which will always move in the wrong direction to an applied force. But perhaps
we can fix this by separating our mass types. What if inertial mass is always positive, but
gravitational mass can be positive or negative. Then a pair of positive and negative gravitational
masses will mutually repel each other, which is just what we want for anti-gravity. But if
we say that inertial and gravitational mass are not equivalent then we’ve overturned the
equivalence principle. We should not do that lightly. After all, it’s one of the founding
axioms of general relativity, which is itself an insanely successful theory. But it turns out that
for the type of repulsive gravity we’re looking for we have to break the equivalence principle.
Speaking of general relativity, let’s see how negative masses work here. In GR gravity is
explained as mass causing the fabric of space and time to curve so that things move differently due
to that curvature. In the classic rubber sheet analogy, objects with positive mass depress the
sheet causing straight lines to deflect towards them. Hypothetical negative gravitational
masses would be depicted by pinching the sheet upwards, causing straight lines to move away.
This picture makes it somewhat intuitive why the motion of particles seems to only depend on the
shape of the gravitational field—which itself depends only on the gravitational mass of the
central object. Objects follow geodesics—the “straightest lines” in curved space regardless
of their own mass. In fact we can also think of this as the gravitational and inertial masses
canceling out, just like with Newtonian gravity. We can see that canceling in something called the
geodesic equation, which is the equation of motion for a particle in general relativity. Normally the
mass of the moving object doesn’t appear in it, just like it doesn't in the Newtonian acceleration
equation. But it’s actually hidden. If we separate inertial and gravitational mass we see it here.
And the geodesic equation also tells us how positive and negative gravitational masses
interact. We’re going to keep inertial mass positive because anything else is insane. Now,
negative gravitational masses change the sign of the gravitational field or the sign of the
mass of the interacting particle or both. If both masses are p ositive or both negative,
the minus signs get canceled and we have regular gravitational attraction. But if
only one of those masses is negative then we end up with a new minus sign
between the field and the object. The effect is gravitational repulsion.
In other words, something with a negative gravitational mass
would fall upwards in Earth’s gravitational field.
OK, great, so to make an antigravity engine we just need a negative gravitational mass.
So what’s all this about antimatter possibly having this property? An antimatter
particle has the same mass as its regular matter counterpart,
but is opposite in many quantum properties. That doesn’t sound helpful—if antimatter
has the same mass as regular matter then where’s our negative mass? Well,
remember we just broke the equivalence principle—at least in our imagination—so
maybe antimatter can have positive inertial mass but negative gravitational mass.
Two reasons we might think this is the case: First: based on its response to
the electromagnetic field we know antimatter has positive inertial mass, but we’ve never
actually measured its gravitational mass. Well, actually, just recently we finally did and I’ll
tell you the results in a bit. But we’ve had a lot of years to come up with reason two:
there are theoretical motivations for thinking that maybe antimatter has negative gravitational
mass. To understand this, we need to understand the theory behind antimatter a bit better.
Antimatter is what you get when you take regular matter and do three things to it:
flip its charge, reflect its spatial coordinates - so clockwise particles become counterclockwise,
and reverse its time axis—which is equivalent to reversing all of its motion vectors. These
transformations are called charge conjugation, parity inversion and
time reversal, and applied together we have a CPT transformation. CPT-transform regular
matter and it becomes antimatter. And of course there’s a homework episode for you on this.
Most physicists think that our universe has to be CPT symmetric—which means that,
although the laws of physics change if you perform any of these transformations separately,
if you perform all three together the laws of physics should be exactly the
same. CPT-transform the universe and you get an antimatter universe that follows
exactly the same laws of physics as our regular-matter universe.
But there’s at least one big reason to wonder if CPT-symmetry is broken,
and that’s because almost all of the matter in the universe is regular matter,
with hardly any antimatter. In a perfectly CPT-symmetric universe, matter and antimatter
probably should have been created in equal quantities soon after the big bang. If we
found out that CPT symmetry is broken, and how it breaks, we could perhaps solve this big mystery.
But I digress. We’re here to build a flying car. And understanding the CPT-symmetry can
help us here too. If this symmetry is true then all the laws of physics should look the same
under CPT transformation—so an antimatter universe should run by the same equations,
including the equations of general relativity. And indeed, if you apply a CPT transformation
to the geodesic equation you get some minus signs as you reverse the flow of time and
flip the dimensions of space, etc. But they cancel out and give you exactly
the same equation you started with. That’s equivalent to switching both of a pair of
mutually-gravitating objects to antimatter. They’d still attract each other. In fact,
we can’t even say if they both have positive or negative mass—the math looks the same as
long as they have the same sign of mass. General relativity in general seems to be CPT invariant.
But what happens if you CPT-transform only part of the equation—if you turn one of a
pair of masses into antimatter. The exact way a CPT transformation interacts with GR
is still being debated, but at least some physicists have argued that the result on
the geodesic equation is to introduce a minus sign—either to the field or to the mass in motion,
depending on which you turn into antimatter. But mathematically, that’s equivalent to changing one
of the gravitational masses negative. So, some ways of thinking about the symmetry
of general relativity gives antimatter negative gravitational mass. Remember
that this is a contested interpretation, but the result would be gravitational repulsion and hoverboards.
At the very least it's worth finding out whether anti-matter falls up or down?
Whether for the awesomeness of our vehicular future or just to see if there's any weirdness in the gravitational interaction of antimatter
that could poke holes in CPT-symmetry and help us answer some very big questions.
So, let’s get to the experiment finally. What happens when you drop an apple made of antimatter?
And to start with, why is it so hard to do this experiment? It’s because we don’t have antimatter
apples. Antimatter is extremely hard to create and keep contained. It instantly annihilates when
it encounters regular matter. At best we have antimatter atoms. The difficulty is also due to
the fact that the gravitational force is so weak compared to other fundamental forces. For example,
if we wanted to measure the effects of gravity on a free falling electron in the Earth's
gravitational field, it would be like trying to measure the force of gravity that a human
body exerts on a feather. Not that astronauts body on the dropped feather—but the force that
your body here on Earth exerts on that feather on the moon. Add the fact that any antiparticle
we analyze will be subject to vastly greater forces from ambient electromagnetic fields
and this becomes an intensely difficult experiment. But not an impossible one.
So this is a CERN experiment that has been years in the making. It starts with the antimatter
production line by the ALPHA collaboration. This team has managed to create and magnetically trap
100s of stable anti-hydrogen, consisting of a positron orbiting an anti-proton. Their sister
collaboration, ALPHA-g, then takes these atoms and drops them in freefall in a vacuum chamber. That
sounds simple, but it's an extremely delicate operation. Because of the extreme smallness
of the gravitational force on these atoms and the other effects that jostle them around, they don’t
all just tinkle downwards. Some move up, some move down, and at different rates. But by measuring the
rate and timing of anti-hydrogen atoms that reach both the top and bottom of the chamber compared to
regular hydrogen, the relative gravitational acceleration on the atoms can be calculated.
And after the first run of the ALPHA-g experiment it turns out
that acceleration is … downwards. Yup, they are almost certainly not falling
up. That likely dashes our hopes of repulsive gravity from antimatter.
However there is tentative evidence for something interesting. The gravitational
force may be slightly weaker on these anti-hydrogen atoms compared to regular
hydrogen. This fairly preliminary data suggests that the gravitational acceleration
of the anti-hydrogen 0.75 plus or minus 0.13 times that of regular hydrogen atoms, meaning it might
fall a bit slower. That actually sounds like a big difference, but it’s less than a 3 sigma result,
so could be a fluke. In fact the scientists of the ALPHA-g paper do claim that the gravitational
acceleration of antimatter is consistent with it being the same as regular matter.
That’s because misleading sub-3-sigma results happen all the time, and when it’s something
really unexpected like this, it’s much more likely to be a statistical fluke. Remember,
we’re dealing with only 100s of atoms here so random variation is going to be significant.
That said, if there is a difference in the gravitational force felt by matter versus
antimatter it would be extremely exciting. It would mean a violation of CPT symmetry.
It would mean that the universe treats antimatter differently to regular matter,
perhaps explaining why there’s this enormous imbalance between
the quantities of each. ALPHA will continue to build anti-hydrogen atoms,
and ALPHA-g will continue to drop them—and they will fall down. But whether they fall at the
same rate as regular hydrogen will be known with increasing confidence over the next few years.
So we may not have a clear path to our levitating cars
at least yet. But we do have a path to either solidifying or breaking CPT symmetry,
and so understanding what’s currently the most fundamental symmetry of space time.
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