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.
The title gave me serious crank vibes. Then I watched the video and it was pretty legitimate and actually pretty good!
Great fan of the show and physics/science enthusiast here, I was a bit confused by the part at the very end when he says conservation of energy breaks down within a GR framework and that's what allows the increase of dark energy from thin air.
It was my understanding that conservation of energy was an absolute, even at the universe's scale. I also kind of understand the "breakdown" for GR is at large scale because of how you can express conservation of energy in either differential or integral form; the equivalence between these two forms being broken in GR because space-time is locally "flat" (differential) but curved at large scales (integral).
Can someone more enlightened than I am weigh in on this and eventually correct me as I'm probably wrong somewhere?
This show continually raises the bar.
Bloody awesome.
it was a great video. great channel, as others said, "legit". been watching each one.
BUT, the ending, starting here https://www.youtube.com/watch?v=UwYSWAlAewc&feature=youtu.be&t=667
left me, like, /arrgghhghghhgh/ - assertions without explanation. how can energy come from nowhere? seriously, this is a huge possibility that flies in the face of all established Newtonian physics.
seriously, can someone explain this idea better?