Thank you to 80,000 Hours, a project of
Effective Ventures, for supporting PBS 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? — 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. Thank you to 80,000 Hours, a project of Effective
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