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.

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, a  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 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 gravitatio nal field OR the sign of tche   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 behaving this way?

An antim  atter 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 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.

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 0.13 times that  of regular hydrogen atoms, meaning it might   fall slower.

That actually sounds like a big  difference, but it’s less than a 3 sigma result,   so could be a fluke.

Indeed the authors of the  ALPHA-g paper do claim that the gravitational   acceleration of antimatter is consistent  with it being the same as for 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’ll 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   … 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.