The true nature of dark energy confounds even the world's
smartest astrophysicists.
It's strange anti-gravity effect is unlike anything we've
ever encountered.
Today, we get to the bottom of it.
A few episodes ago, I asked you to take a wild ride with me
into the heart of Einstein's general theory of relativity
and its description of the vaster of scales
of our universe.
Today, we get the huge payoff for our efforts.
We already have some pretty awesome insights.
One, the universe is expanding.
And it will expand forever.
There's it's just too little matter in it to recollapse.
Two, such an underdense universe should be geometrically weird,
a negatively curved hyperbolic hyperplane.
Paradoxically, our measurements points a near-perfect flatness.
This is only possible if we missed
some unknown type of energy pervading all of space.
And three, the expansion of the universe is accelerating.
We know this, because we've mapped its past expansion
history using distant supernovae.
There's an unseen influence at work.
We call it dark energy.
This dark energy is described by the cosmological constant
in the equations of general relativity.
It both flattens the universe and leads
to exponential expansion.
But this is incredible.
It means we have dark energy's number, its fingerprints
at the crime scene.
Knowing a possible theoretical form for dark energy
will unlock many of its mysteries.
Today, we're going to talk about the simplest interpretation
of dark energy, one where the cosmological constant really
is constant.
It doesn't change over time.
All of our data is completely consistent with that
being true.
A constant cosmological constant represents a nonzero energy
of empty space, a vacuum energy.
The more space you have, the more dark energy you have.
It's a constant energy density.
OK, the big, weird fact about a constant vacuum energy density
is that leads to exponential expansion.
We saw that general relativity demands
this when we looked at the first Friedmann equation.
But what physical thing about dark energy
is producing this outward push, this anti-gravity?
That's what we're going to answer today.
Now, the Friedmann equation that we've
been playing with so far just isn't going to cut it.
It only tells us that dark energy produces
an exponential change in the size of the universe, not
necessarily an exponential growth.
Looking at that question by itself,
it could just as well be an exponential shrinking.
To see why dark energy pushes outwards and accelerates
the expansion, we need to go deeper.
It's anti-gravitational effect emerges in the second Friedmann
equation.
The first Friedmann equation is all about the rate
of expansion of the universe.
The second is actually much simpler.
It's about the acceleration or deceleration of that expansion.
It describes the forces pushing or pulling on the expansion.
Here it is.
Once again, we can read this in simple English.
a is the scale factor, sort of like the size of the universe.
And a double dot is the rate at which
the expansion is changing.
It's the acceleration of the scale factor.
It depends on the density here, rho.
The more matter and energy in the universe, the harder
gravity pulls inwards, trying to stop the expansion
or speed up the collapse.
That's this negative sign here.
Positive acceleration outwards, negative inwards.
This thing is in a real way just Newton's law of gravitation
for the whole cosmos.
So if rho is density, what's this p?
That's the pressure due to fast-moving particles
and radiation.
In general relativity, energy slash mass and pressure
both curve space time.
The way pressure does this is pretty weird.
Think about a pressurized tank.
The internal gas pushes outwards as fast-moving particles
collide with the walls.
So if fast-moving particles produce an outward push
in pressure, then is this how dark energy is
causing expansion to accelerate, by causing positive pressure?
No, that can't be it.
Because pressure only produces a direct force
if there's a difference in pressure between two regions,
a pressure gradient.
In order for the pressure of fast-moving particles
to create an outward push, the region beyond them
has to be an area of lower pressure.
But on the larger scales, the universe is pretty smooth.
It's homogeneous.
And so the pressure is the same everywhere.
Instead, the overall effect of pressure
on the curvature of space time is a purely relativistic
effect.
See, high pressure from regular matter and energy
means very fast-moving particles.
And the motion of these particles
results in a combination of relativistic corrections.
The ultimate effect is that the massive
of a region of the universe is higher if its particles are
moving quickly compared to a region where the particles are
moving more slowly, even if the overall energy density
of those regions is the same
Positive pressure pulls the universe inwards.
So it looks like as long as there's
anything in the universe whatsoever, that whole right
side is negative.
So acceleration will always be inwards.
In other words, gravity is always attractive.
What goes up must come down.
Described this way, the universe is never static.
It's either expanding and slowing down or contracting
and speeding up.
This was actually Einstein's motivation
for adding the cosmological constant in the first place.
He wanted a static universe.
So he added to his field equations
that would give a positive outward acceleration
in the second Friedmann equation.
Here's what it looks like.
The plus sign here can counter the minus sign here.
The cosmological constant was designed
to work in the opposite direction
to regular matter and energy.
That's what anti-gravity looks like mathematically.
This is not just some math trick.
Dark energy is real physical stuff.
And that means its anti-gravity effect must come
from its physical properties.
The effect of the cosmological constant
is the combined effect of dark energy's own density
and pressure.
So let's describe it that way.
In our far future universe, regular matter
will have diluted away and will only
have the density and pressure due to dark energy, rho lambda
and p lamba.
Now, the energy density of dark energy
is positive, just like regular matter.
It has to be, because dark energy
helps regular matter flatten the geometry of the universe.
That means its density term also works on the side of matter
to try to slow down the universe in the regular attractive
gravity way.
So dark energy's density isn't causing expansion
to accelerate by itself.
That leaves us with pressure.
But we just discussed how positive pressure
can't cause expansion to accelerate outwards.
It turns out that dark energy does
produce an enormous pressure.
That pressure isn't a positive.
It's negative.
A negative p here cancels this minus sign
and can result in outward acceleration.
That's where dark energy's crazy anti-gravity effect comes from.
It's negative pressure.
What does negative pressure even mean?
Well, positive pressure pushes outwards,
like in our pressurized tank.
So negative pressure would pull inwards.
It will be like attaching stretched elastic bands
between the inside walls of the tank.
It's a tension.
Both have positive energy density.
But positive pressure pushes out.
Negative pressure pulls in.
And we're back to that contradiction.
Weirdly, the inward pulling pressure of dark energy
ultimately drives expansion outwards.
Again, this is due to its relativistic effect.
The direct effect of dark energy's negative pressure
doesn't do anything, because that negative pressure
is the same everywhere in the universe.
But even though the negative pressure has no direct effect,
it has its relativistic effect.
Relativistically, negative pressure
has to do the opposite of positive pressure and results
in anti-gravity, because math.
The relativistic effective of negative pressure
is actually really, really hard to describe intuitively.
And in fact, such an explanation may not be possible.
Part of the problem is that negative pressure doesn't
come from the motion of dark energy particles, whatever
they might be.
Instead, it comes directly from the fact
that the density of dark energy is constant.
Let's say I'm holding a volume of the universe that
has a constant energy density.
If I expand it, then it has more energy in it
than it did before, because it has more volume.
I would have to provide that energy, which means I'd
have to do work to expand it.
That's exactly how we define negative pressure.
A volume has negative pressure if it takes work to expand,
just like a volume with positive pressure
takes work to compress.
Negative pressure means energy is gained on expansion.
That's what happens with dark energy.
As the universe expands, more dark energy
is created because its energy density has to stay constant.
That looks like negative pressure,
and yet this abstract-sounding negative pressure
has a very real physical effect.
It's the opposite effect to positive pressure.
And it's a clear, outward-pushing anti-gravity
effect when we look at its role in the second Friedmann
equation.
In the first Friedmann equation, we
see it as an exponential change in the scale factor.
But both agree that a constant energy
density and the resulting negative pressure
leads to accelerating expansion.
OK, so it takes work to expand the volume of the universe.
And the energy turns into new dark energy.
But who's doing that work?
Where does the energy come from?
The answer is maybe nowhere.
Here's where intuition goes completely out the window.
See, the law of conservation of energy
no longer applies in an expanding universe.
This law is a property of a Newtonian universe,
in which space and time are fixed static dimensions.
In a universe governed by general relativity,
this is no longer true.
Energy can be forever lost or gained
from nothing within an expanding curved spacetime.
In a recent episode, we talked about the Breakthrough Starshot
program, LightSail to the stars.
Let's see what you had to say.
So a few people were wondering how that probe sends its signal
back to Earth.
Well, the idea is to beam the data back
with low-power lasers, or perhaps
alternatively to use the sail itself as an antenna for radio
transmission.
The signal will be weak, but we'll
know exactly where to look and can use gigantic detectors here
on Earth.
If the signal sent by laser, then the same phased array
that projects the launched laser will also
be able to spot the returning later signal.
Patrick Romo and others asked whether we
could decelerate the LightSail in the wind
from the destination star.
Well, there's actually no way to decelerate the craft.
The impulse generated by the laser
is many orders of magnitude greater
than that of the star at the other end.
No, the craft will zip through the [INAUDIBLE] system
in a few minutes, recording data as it goes.
And this is why you want to send a large number of craft.
A few of you suggested that Moore's Law is near its end.
So while it's true that there's a limit to the miniaturization
of silicon chips, Moore's Law for computing
has been roughly consistent since around 1900,
with the first mechanical tabulators followed
by solid state relay calculators,
then vacuum tube computers.
If we never move beyond silicon, then maybe we have a problem.
But there are already multiple possibilities there.
The analogies to Moore's Law for laser power, material science,
battery tech, et cetera, are also alive and well.
Aging Reversed would like to spend the entire Starshot
budget to cure cancer, rather than sending a speck of dust
into nothing.
Well, the final cost of Starshot is
expected to be several billion.
But that's similar to the annual budget of the National Cancer
Institute and a small fraction of global spending
on oncology research.
If it were possible to cure cancer
with that amount of money, well, then we
would have cured it in a year.
Advances in medical research may produce more tangible benefits,
but it's easy to underestimate the benefits
of inspiring forward-looking projects like Starshot.
They give us a sense of unity and optimism
that feeds back into all of our efforts.
Inspire enough smart kids to become
scientists instead of bankers, and it is well worth it.