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Universe's End Explained · Acedra
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Universe's End Explained
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0:02
How will this universe end? This may be the one prediction of general relativity that we never directly verify until, well, the very end. Yet the fact that Einstein's theory allows us to learn the answer to this question is incredible. Let's see how this is even possible. [THEME MUSIC] Soon after Albert Einstein proposed his general theory of relativity, industrious physicists-- and, in particular, a brilliant Russian named Alexander Friedmann-- applied the new theory to the whole universe.
0:38
Combined with observations of the redshifts of galaxies, this showed us that the fabric of space itself is expanding. Recent astronomical observations have revealed something even stranger-- the future expansion of the universe will be dominated by a mysterious influence that physicists have come to call "dark energy." In order to get a truly meaningful sense of the forces governing the fate of our universe, and especially the nature of dark energy, we're going to have to go pretty deep.
1:09
We'll need to peer into the mathematics of general relativity. Trust me, it'll be worth it for the amazing insights we'll gain. For today's episode, we're going to start by describing the universe without dark energy. Because, well-- baby steps. And the answer we get for the fate of our own universe will still be right in one very important aspect. At the heart of general relativity are the Einstein field equations, which look like this. "Equations," plural.
1:41
See, that G and T are what we call "tenses"-- multicomponent, multidimensional quantities. G is the Einstein tensor. And it defines the shape, the curvature, of spacetime. T is the stress-energy tensor. And it describes all of the energy, the pressure, the momentum, and more-- all of the stuff within that spacetime. Both have 10 independent components, giving 10 independent field equations to describe the response of the fabric of the universe to everything it contains.
2:16
John Archibald Wheeler put it more simply-- "Spacetime tells matter how to move, while matter tells spacetime how to curve." Now, before we do any general relativity, let's develop intuition a bit by thinking about gravity from a Newtonian perspective-- as a force, rather than as an Einsteinian spacetime curvature. If I throw an apple in the air, then gravity pulls it back down. The faster I release it, the further it travels before falling back.
2:45
If I throw it at 11 kilometers per second, which is the escape velocity on Earth's surface, then, by the time it almost stops moving, it will be so far away that Earth's gravitational pull will be close to zero. Now this escape velocity comes right out of Newton's universal law of gravitation, which itself can be derived from the Einstein equations. The mathematical step from Newton's gravity to escape velocity comes from thinking about energy.
3:14
As the apple rises, its kinetic energy, its energy of motion, is sapped by the gravitational field and converted into potential energy. Remember, energy is always conserved. There's a minimum kinetic energy that the apple needs in order to escape the energy-sucking gravitational-potential well of the Earth. That minimum kinetic energy tells you the escape velocity. In this Newtonian analogy-- and, remember, ignoring dark energy-- the universe also has an escape velocity that lets
3:48
distant galaxies escape each other's gravitational influence. Based on the amount of stuff in the universe, there's some current expansion speed that would allow the future expansion rate of the universe to slowly grind to a halt over infinite time. How do we calculate the escape velocity for the whole universe? By solving the Einstein field equations for the whole universe, of course. It's mind-blowing that we can actually do this and only possible because, on its largest scales,
4:19
billions of light years, all of the galaxies and galaxy clusters are very evenly dusted across all of space. When we ignore the bumps and wiggles caused by individual galaxies, the resulting smooth universe lets us reduce those 10 Einstein equations to only two relationships, called the Friedmann equations, devised by our boy Alex. The first one can be written like this. That may not look simple, but trust me, we can read this in simple English. That letter a is called the "scale factor,"
4:51
and it represents the size of the universe. Although it's more accurate to think of it as the average distance between galaxies. Now the Friedmann equation tells us how a evolves over time. That's what that a with a dot on top represents-- the speed of the expansion of the universe. Now, if you guys have taken some calculus, that's the time derivative of a. Let's stick to the left-hand side of the equation for the moment. It reflects the same balance between kinetic
5:21
and gravitational potential energy that we saw in our rising apple. In fact, this Friedmann equation is an energy equation. That first piece, the a-dot over a squared, is analogous to the kinetic energy of expansion-- how much outflowing oomph the universe has. But that oomph is resisted by the gravitational effect of all the master and energy in the universe. That's this rho thing-- the density-- how packed with stuff the universe is. So this second piece represents the capacity of the universe
5:56
to slow itself down and is analogous to the gravitational potential energy. The balance between these two energy like terms tells us the fate of the universe. So, what are the possibilities? If the kinetic energy of expansion and the potential energy of collapse are perfectly balanced, then the universe will expand to a ginormous size and grind to a near halt. Essentially, that's if the expansion is exactly equal to the escape velocity.
6:27
In that case, the left-hand side of the equation adds to zero. But if the left-hand side comes out just a little bit positive, that represents a tiny bit of extra oomph. There will be some expansion energy remaining after gravity is diluted to nothing, and the universe will expand forever, never stopping. And if the left-hand side is negative, in that case there was never a high-enough expansion rate to reach that extreme size. The universe will eventually fall back inwards,
6:59
and we'll see many of those distant galaxies up very close and personal as the universe undergoes the Big Crunch. So, what's the answer? Will the universe expand forever, or collapse? Well, we know the expansion speed. We measure it from the redshifts of galaxies as well as other independent methods. The expansion rate now is what we call the "Hubble constant." It's around 70 kilometers per second per megaparsec. For a long time-- until the late '90s--
7:29
it was believed that the answer to whether the universe would recollapse lay in measuring rho-- the density of the universe. Astronomers worked for decades to weigh up the galaxies across vast swaths of the universe, including their dark matter. But the density of the universe turns out to be too low-- only about a quarter of what is needed to reverse the expansion. The density term, the recollapsing term, falls short of the expansion term. The left side of the Friedmann equation is positive.
8:03
There's no way around it-- the universe will expand forever. In a way, we're lucky to be living in an era where we can still even see the distant galaxies. Over billions of years, they will slip beyond our cosmic horizon, leaving only darkness beyond the local region of the Milky Way. But wait-- we never got to the right side of the equation. We know that it should also be positive, because, well-- equals sign. But that right side describes something completely different to the left.
8:35
It describes the shape of the universe-- its spatial curvature. According to the first Friedmann equation, the fate of the universe-- as determined by its expansion and density-- should be intrinsically tied to its shape. After all, matter tells spacetime how to curve. We'll see in the next episode that there's a surprising mismatch between the left and the right sides of the first Friedmann equation that tells us that we're missing something crucial. That something is dark energy.
9:08
I'll show you why the Friedmann equations tell us that dark energy must exist in this universe, and what these equations can tell us about its true nature. Now, don't get your hopes up. Dark energy won't save us from infinite expansion. Quite the opposite, in fact. Dark energy accelerates the expansion. And to understand how does so will take us far beyond the capacity for Newtonian analogy. It'll shatter our intuitions about energy conservation and gravity on the largest scales of spacetime.
9:43
Hey, guys-- before we get to comments, a quick shout-out. It's webby time. PBS Digital Studios has been nominated for Best Science and Education Video/Channel. If you guys could head over there and vote, that will be really helpful. Link in the description. OK. So last week we talked about nuclear synthesis. Let's see what you had to say. Enrique Rigitano points out that there seems to be this main sequence of elements produced in the cause of dying high-mass stars
10:14
and asks how elements out of this sequence get produced. OK, that's a great question. In fact, there are many different fusion reactions occurring in the cores of those dying high-mass stars. Some of the most common involve either adding helium-- that's helium capture-- or losing helium after another fusion reaction. So, if you start with an even-atomic-number element-- like carbon, with its six protons-- this means that you end up with a much higher abundance
10:46
in even-numbered elements than odd-numbered elements. Of the 10 most abundant elements in the universe, only two have an odd number of protons-- hydrogen and nitrogen. However, there are many ways to build elements out of this sequence, in fusion reactions that just aren't quite as productive. As for fluorine, that's actually one of the more confusing ones, because it's not produced efficiently in any known reaction in high-mass stars. But recent work has suggested that it might actually
11:17
be formed in lower-mass stars like our sun after they enter the red giant phase. There's this brief period when it's possible for material near the core to be carried to the surface by convection and then blown into space as the outer layers are blown away into a planetary nebula. A lot of you were interested to know where the actual elements in our bodies came from and where the supernovae that produce those elements and their remnants are now.
11:47
So the disk of the Milky Way-- it rotates approximately once every 230 million years or so. However, stars don't all orbit at exactly the same rate. Orbits aren't perfectly circular, and stars drift apart as they move in and out of the spiral arms and above and below the galactic disc. The Sun has orbited the Milky Way around 18 times since it formed. And so, by now, it's wandered very far from the giant cloud of gas from which it formed. That cloud is long gone, anyway.
12:21
It collapsed into the Sun's sibling stars, which are also scattered across the galaxy by now. And it was blasted away by supernovae from the most massive stars it produced. The elements that form the Earth and that form you may, in part, be from those supernovae, but more will be from previous generations of stars that enriched that giant cloud before it formed stars of its own. And, last of all, thanks to you, Rod Lendaeta, for sharing this beautiful Serbian proverb.
12:55
"Be humble, for you are made of Earth. Be noble, for you are made of stars." [THEME MUSIC]
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