 Physics 1, Physics 1303, just in case you were wondering. Have you been in the wrong class this whole semester? Yeah, no problem. All right, let's go ahead and get started because this is going to be a very, there's going to be a lot in this lecture, okay? We have to cover a lot of topics. This short title belies a lot of things that are going on underneath the hood. There's absolutely no way that I can cover every single detail that is needed in a lecture like this in order to communicate this information. But I will cherry pick my way through the story. I will offer you highlights where, as we go forward, connecting to some introductory physics concepts as I move through this subject material and you should be taking notes because stuff on this can be fodder for the final exam multiple choice questions. So if that comes as news to you, get a notebook out right now. So here's the program for the lecture today. It's mainly in three acts. The first one is entitled The Star is Born. And then we'll move into the sort of deaths of stars and talk about a shadow where no light shines. And then finally, we'll use the lives and deaths of stars to motivate the way in which physicists and astrophysicists have come to understand how the universe itself might end. But it will also take a look at what will likely happen to the planet and to the solar system and to the galaxy. Okay. And then I'll have some comments on the end about the sort of second topic that people ranked up there which has to do with the death of the universe by means other than the ones I'll talk about in the first three acts. Okay. So let's begin with Act One, A Star is Born. And to motivate all of this, I want to get you thinking a little bit about stars themselves, right? So go out tonight or some other night when it's clear, the weather sucks this week, so maybe pick a nice night when you can go outside around 9.30, 10 o'clock. It's getting to be toward the longest day of the year in June, so you're going to have to go out later in order for it to be dark enough to see the stars in the night sky over the Metroplex. But I promise you that, you know, if you look up, you'll be treated to some pretty spectacular views. I mean, so for instance, around 10, 10.30, you go out at night, you should have a pretty clear view of the constellation Orion. So if you're facing south, just look up and a little to your right and you'll see the stars that make up Orion. And one of those stars will play a role later in this lecture. These are the Pleiades, there's many cultures on Earth that have named the stars and the constellations based on patterns that fit stories in their societies. The Greeks had a story about the Pleiades being chased by the hunter Orion, so the Pleiades are located very near the constellation Orion and they are very bright stars. These are very young stars. They formed fairly recently. They're part of a cluster that's drifting apart slowly over time and you can see around them the envelopes of gas from which they were formed. And I'll talk more about that in a bit. Okay, so they're absolutely beautiful and you can see them from Dallas even with the city lights, they are pretty bright. And cosmically speaking they're very close by. And later in the lecture I'll talk a little bit about distance scales in the universe and some of the ways that we measure them because we can't go to the Pleiades with a measuring tape and figure out how far they are. We have to use other methods to do that. And I'll talk about at least one of those today. But if we're going to understand the stars, it probably helps to start with the one that's closest to home, the sun upon which we rely for just about everything, directly or indirectly. This planet would not be as warm as it is without the star. It wouldn't be host to the rich variation in biochemistry that it's home to without this neighbor star. This is the thing that is the life-giving force in our solar system. This is a wonderful picture of the sun. It's shot with a telephoto lens. So when they were prepping to take this shot of the sun at sunset with the trees, a person and their dog accidentally walked through the shot and they decided that's our shot. So using a telephoto lens on this ridge, they were shooting from very far away. And so with the person and the dog and the hill at that scale and then the sun, which is very far away, like 90 million miles away. Nonetheless, the relative scales of this look very large. So here is the sun, okay, magnified at sunset by the Earth's atmosphere, something you'll learn about in physics too a little bit. There's a person and a dog. These are not to scale, of course. The sun is much bigger even than it looks here relative to us, okay, terrestrially sized things. What I like about this photo is you can see a little bead, a little string of smudges. And those are solar storms. Those are magnetic storms on the surface of the sun or so-called sunspots. And they are slightly cooler regions on what's called the photosphere, which is what we think of as the surface of the sun. Those smudgy things. You can see them with filters and the unaided eye. In fact, there was a spectacularly large one on the surface of the sun back in November of 2014. And under the right conditions at sunset, you could look at the sun for a few seconds and you could see the storm on the surface of the sun. It was immense. It was larger than probably 20 or 30 Earths put together. Okay, the sun is immense. So we can take a look at the sun as a laboratory for understanding other stars, although most other stars in the universe are very unlike our sun. And I'll comment a little bit on that later. All right, so let's think about the sun. Here are some basic numbers. We've had these numbers in some cases in physics problems throughout the class. All right, so for instance, we've seen the mass of the sun before. It is absolutely huge. The Earth is about 10 to the 24 kilograms or so. The sun is 10 to the 30 kilograms. If you were to take the whole solar system, which is a very large thing compared to the Earth, and weigh it, the mass of the sun is 99.999 something percent of the entire solar system. Okay, it outweighs everything else combined in the solar system by a huge amount and more. So that's a big number. Now, most of the sun is hydrogen. Hydrogen is the most common element in the universe. Hydrogen and its nearby cousin helium were primarily formed near the beginning of time within the first three minutes of the universe. That ratio, cosmically speaking, has not changed very much since then, but stars help to alter the balance a little bit. The reason that you and I are made of things like carbon and oxygen and nitrogen has nothing to do with the beginning of time. If the beginning of time was the only place that elements could have been forged, we wouldn't exist. It is the stars that allow for the creation of the heavier elements, and the only reason we exist at all in our present form is because of the life cycles of stars. So we are born from the stars, and stars can tell us something about the ultimate fate of everything, including ourselves. What are considered metals comprise less than 0.1 percent of the sun. Some of the metals in the sun got there when the sun formed, but much of the heavier elements in the sun have been forged by that star ever since it formed about 5 billion years ago. Okay, so that's a little bit about its composition. What about its temperature? Well, the photosphere, the thing we call the surface of the sun, the thing we can see with our eyes, unaided, okay, without using other wavelengths of light to look at the sun, that has a temperature of about 6,000 Kelvin. Okay, so, you know, room temperature is what, only about 273 Kelvin, something like that. This is a lot hotter than that. So there's no way you're going to just take a journey to the surface of the sun. That's not possible. Does anybody know what the closest probe we've ever gotten to the sun is? It's actually fairly recent. It's called the Parker Solar Probe. Now go take a look at that thing if you're interested, but it's a marvel in and of itself because it has to withstand the environment near the sun, but even it is not that close to the sun, okay. The closest planetary body in the solar system is Mercury. That's the one that gets closest to the sun. It's a rocky planet like ours, but much smaller. Okay, so using the above information we can begin to consider the forces that are acting on atoms in the sun, right. One of those forces we've explored a lot this semester, that's gravity, so we'll start with that. And then we're going to take a tour down into the atom to look at some of the other forces that are at play in the sun, some of which you won't really get into until Physics II and some of which you wouldn't encounter until at least Physics III if you were to continue in the subject. So let's just consider a single hydrogen atom very near the surface of the sun is our mental playground for these considerations. All right, so let's think about the gravitational force on that hydrogen atom. All right, we can use Newton's law of gravitation to calculate this. So we already have things like the mass of the sun, okay. And we can think about one hydrogen atom sitting right above the surface of the sun, the photosphere, with all the other mass of the sun pulling on it. All right, and so although gravity is fairly feeble compared to other forces we will consider, and I'll show you another one in a moment, when you have this much matter in a body like a star, gravity can be overwhelming. I mean, there's a reason we orbit the sun once a year at the distance we do is because the sun holds on to us through its gravitational force. All right, now while gravity can be overwhelming, it's also not fully in charge in a star like the sun or other stars as you'll see. But there are moments when gravity wins and when gravity wins spectacularly bad things happen to stars. So here's Newton's law of gravitation, the force on the hydrogen atom due to the rest of the sun. It's just Newton's gravitational constant, the product of the masses in the numerator, the radius of the sun squared in the denominator, and this unit vector just indicates that it points in toward the center of mass of the sun, okay, along a radial line in toward the center. All right, so here are all the numbers, radius of the sun, which I hadn't mentioned before, but I've written it here. Mass of a hydrogen atom is about 1.67 times 10 to the minus 27 kilograms. What I like about these two things is they're almost exactly polar opposites in terms of powers of 10. The mass of the sun is 10 to the 30 kilograms. The mass of a single hydrogen atom, which makes up 75% of the sun is 10 to the minus 27 kilograms, almost 30 orders of magnitude smaller than 10 to the 0. All right, and the mass of hydrogen is dominated almost completely by the proton at its center. The electron contributes about 1% half a percent of the mass of a hydrogen atom. It's not a very heavy contributor, okay? It's important for chemistry, but in terms of the mass of the hydrogen atom, it doesn't play a very important role. Okay, so if we plug all that in, put those numbers into our Newton's gravitation equation, we come up with, wow, a really tiny number, okay? The number of Newtons that the whole sun exerts on that hydrogen atom is only about 10 to the minus 28 Newtons. So, no, maybe not that impressive until you think about how little mass a hydrogen atom actually has and how much, how little force would be required to get it to do things very fast. So, if you work through Newton's second law and calculate the acceleration due to gravity at the surface of the sun, it's a whopping 300 meters per second squared, okay? The surface of the earth, it's about 10 meters per second squared. So, it is a lot stronger gravitational acceleration at the surface of the sun. Gravity is much stronger near the surface of the sun than it is near the surface of the earth. So, as a result, a hydrogen atom, if it wasn't going to bounce into other hydrogen atoms as it was pulled down toward the center of the sun, would experience an acceleration of 300 meters per second squared and you can figure out, well, how long would it take a hydrogen atom, unobstructed, to fall to the center of the sun? You could calculate things like that. You have to take into account that the gravity force gets weaker as you get closer to the center of the sun, but you could estimate. Okay, so we have one force at play in stars like the sun. We have the gravitational force, and the gravitational force relentlessly pulls matter inward toward the core of the star. But then why don't all stars merely just collapse down to as small a size as you can? If you calculate the average space between hydrogen atoms inside of this star, you'll find out it's actually pretty spacious in there. Okay, why is that? Why do stars not merely just collapse down irrevocably? Well, that's because other things are going on in stars. So, to answer this question, we briefly have to visit the atomic and nuclear realm and we have to glimpse some of the forces that are involved there. A first understanding of how stars worked was only really first glimpsed in the middle of the 20th century. After the creation of the atomic bomb, which itself was fueled by a revolution in atomic and nuclear physics, okay, which was then turned to fundamental science questions after World War II, it was only then that human beings had the ability to conceive of what would be required to power something as energy emitting as a star, okay? So, let's consider again hydrogen as our laboratory for thinking about the other forces that are at play inside of a star. And we're gonna take a look at just two of them. In total, there are four known fundamental forces in nature. One of them is gravity, it turns out to be the feeblest. One of them is electricity and magnetism or electromagnetism, which you'll study in physics too. And then there are the nuclear forces. They were discovered in the nucleus, which is why we call them that, but they don't necessarily have to only be found inside the nuclei of atoms. You can experience them without nuclei by smashing particles together at high energy. You don't need atoms to probe these forces. They just happen to be very short in range. So that limits them to things the size of the nucleus of an atom. That's no accident, that's why nuclei have the sizes that they do. So what size do they have? Well, to think about this a little bit, let's take a look at an inaccurate but helpful picture of the atom, the hydrogen atom. And this is known as the Bohr model named after the physicist Niels Bohr who conceived of it as a result of early experimentation on the atom itself in the early 1900s. So while it's technically inaccurate, it will help you to think a little bit more about what an atom really is. And so what's an atom? Fundamentally, it has a central nucleus. This can be made from one or more protons and one or more neutrons. The number of protons determines what chemical element we're talking about. One proton is hydrogen, two protons is helium, et cetera. Okay? That nucleus, however, is tiny compared to the range over which the electron or electrons can wander around the nucleus and even in a structurally stable atom. So for instance, in hydrogen, the typical size of the wandering of the one electron in electrically neutral hydrogen is about one angstrom. An angstrom is 10 to the minus 10 meters, okay? So a tenth of a nanometer, really small. To give you a sense of scale, the cell membrane is three nanometers approximately in thickness, all right? So this is another 10 times smaller than that. The nucleus is even tinier. So the electrons are wandering around the nucleus and they get pretty far from the nucleus on average. The nucleus occupies a size of about one femtometer or 10 to the minus 15 meters. And the reason for this is as we learned later, after we studied the nucleus of atoms more and more and more, is because there are new forces at play that maintain the stability of most nuclei but also destabilize nuclei on occasion to allow for things like radioactive decay. Spontaneous radioactive decay is caused by one of the nuclear forces. The stability of the nucleus in general is guaranteed by the other of the nuclear forces. So there's sort of, you know, good cop, bad cop down there in the nucleus. One of them is trying to maintain stability in the universe and the other one comes in and messes with it, periodically, okay, spontaneously. So this gives you a sense of the scale. If you think of the electron as an orbiting planet around a central star, which we would call the proton in hydrogen, you can use that as an analogy in your head, but it will fail very quickly. What's the governing force for atoms? It's electromagnetism. It is electricity and magnetism. It is the electric charge of the electron which is opposite that of the proton that binds it to the proton and overcomes most other forces that are at play that try to tear it apart, okay? So for the opposite charged things like electrons and protons, the force is attractive. But for similarly charged things, that same force is repulsive. So that's what distinguishes electromagnetism from gravity. While they both have a lot of features in common, gravity seems to only ever be attractive, whereas electromagnetism can be repulsive or attractive depending on the electric charges at play. So Coulomb's law, which is the law that governs that force and which you'll learn all about in second semester physics, looks a lot like Newton's law of gravitation and we don't really know why that is, okay? But people have tried to figure out if there's a relationship here and they've failed constantly. So it seems to be some kind of coincidence in nature that they have this feature. Just like Newton's gravitational law has a constant out in front that relates this ratio to force, there's a constant here which is the Coulomb law constant and it has a value that you have to measure. It comes out to be about nine times 10 to the nine Newton meters squared per Coulomb squared. A Coulomb is a unit of charge. All right, so it's actually a big number. Now, why doesn't the electron just spiral endlessly down into the proton? Why does it wander around one angstrom in size around this very tiny, 10,000 times smaller thing? And the answer is because protons are not particles. They're not little planets that are going around little stars that are called protons. The proton and the nucleus is a wave-like phenomenon and the electron is a wave-like phenomenon and this puts a minimum limit on how close those two things can get. This is quantum mechanics. I do not have time to cover it here but I wanted to tease this a little bit for you. The stability of the atom is guaranteed by its wave behavior. If it didn't have wave behavior, atoms could not exist in the form we observe them. The universe could simply not be the way it is. It's one of the most compelling bits of evidence for the wave nature of matter. Now I mentioned that two things with the same charge, like two protons, do not like to get near one another in electricity and magnetism. They repel each other. So you can imagine grabbing a proton and grabbing another proton and trying to bring them together and like two magnets whose north poles are aimed at each other, you can push harder and harder and harder but they resist more and more and more as you get closer and closer together. So how is it that you can have helium? How is it that you can have two protons that are less than a femtometer apart from one another when the Coulomb force between them should blow them apart? Why is the nucleus stable at all? And the answer is because there are other forces in nature. So if electromagnetism were the only fundamental force at play in the atom, besides gravity, stars could not exist. You'll see where the energy of stars come from in a moment. But there are these nuclear forces and this one we call the strong nuclear force is the one that as you get protons to within about a femtometer of each other, they can bond. So that strong force takes over and overwhelms electromagnetism and wins at short distance, okay? And the reason that neutrons form the hearts of most stable atoms is because they have no electric charge but they carry the strong nuclear force. So they come in like extra little bits of glue that can help stabilize the protons. This is why most stable nuclei have some number of neutrons in them to help the protons stick together despite their overwhelming repulsion from electromagnetism. And in the end, over a very short distance about the size of a nucleus, the strong force is way stronger than electromagnetism, okay? It's about a thousand times stronger at short distances. So this powerful short range nuclear force facilitates a process known as nuclear fusion or just fusion. And so this process is illustrated here for one of the processes that drives the sun's power output. Gravity compresses the star. As it pulls hydrogen nuclei together, some of them will get close enough to fuse. They'll spit off some radiation particles and this will result in a proton bonded to a neutron. Another pair will do that over here. Then each of these pairs will fuse again with another hydrogen nucleus, another proton. This results in the formation of helium-3. Now helium-3 is not as stable as the most stable isotope of helium, helium-4. If these get close enough together, pulled in by gravity's relentless pressure, they can fuse as well into helium-4 and spit off two protons and those protons can go off to be used in nuclear fusion for other processes. Some of these fusion processes emit radiation in the form of light, specifically gamma rays, and some of them emit an elusive little particle called the neutrino, which has almost no mass at all and is electrically neutral. The sun is extremely bright in neutrinos, but our eyes cannot see them. A single neutrino can pass through one light year of lead and never interact with a lead atom. Neutrinos really don't care about you. You barely exist to them and that's because they only operate according to the weak nuclear force. The weak nuclear force is weaker than the strong nuclear force and because they're the one particle in nature that only feels the weak nuclear force and no other forces, they can go through solid matter as if it's not even there because the only way they can talk to anything is through this really feeble force that is only very short-ranged. So they just pass on through. There are millions of neutrinos, if not billions of neutrinos passing through your body right now doing absolutely no damage whatsoever because to them you don't exist. Okay? There's a joke in physics that most of the universe can't even be bothered to interact with you which I think is a very emo way of looking at it. So anyway. So this results overall in a huge amount of energy being emitted by the core of the sun where the gravitational pressure is greatest as the outer surfaces of the star collapse down. And this radiation pressure radiates out from the core. The gamma rays will collide with other atoms, hydrogen, helium, carbon, oxygen, whatever's floating around and kick them back out. So stars are this dance, albeit a tenuous waltz between two rather large and competing forces. Gravity crushing them inward and the radiation from fusion pushing the atoms back out. And in fact, if you study stars very carefully, including our own sun, you'll find that they pulsate like a heartbeat. As gravity pulls in, fusion goes up, radiation goes up and pushes gravity back out. Fusion goes down, radiation pulls it back in, fusion goes up and so forth. It is a terrifying dance. And luckily for us, for our star, it goes on for billions of years before the end. So gravitational inward force collapses, gas to form stars, fusion begins and pushes them back out. This dance begins and you have a stable star that can last for millions or even trillions of years. This is our sun viewed in ultraviolet light. This is not a way that you and I can normally view it. But this is to illustrate that the sun is a rich laboratory for understanding the universe and other stars studied in many possible ways. You can look at the sun from the perspective of the visible light it gives up. That's the one that's most familiar to us, given the very narrow spectrum of light that we can see with our eyes. In UV, in radio, in infrared, in gamma rays, in x-rays, in neutrinos, in electrons being spewed out of the sun, the sun looks very different in all of those forms and yet it richly radiates in all of those things. This thing here is what's known as a coronal mass ejection where a magnetic field has become unstable and disconnected and reconnected somewhere else on the sun. The sun has an immense magnetic field as a result of all these heavily ionized, electrically charged particles turbulently swirling around. Heat's carried out from the core by convection, just the way the atmosphere works in our planet, although this is a much more brutal convection, so heat is distributed out from the core to the surface and radiated out. Photons take something like a million years to scatter from the core all the way out to the surface. It's busy in there. And all we can ever see from light is the surface of the sun and its surrounding corona. There's going to be a total eclipse of the sun visible to Texas in 2024 in April. You should take a look at it. It should be delightfully long and you should, for the first time, if you've never seen it before, be able to see the corona that surrounds the sun. It is not visible when the sun is blinding you, but when you cover the sun in the sky using the moon in this case, you can see the corona around it. It's a ghostly experience to realize that there's more to the sun than what you can see, okay? Now, our sun is a relatively mid-sized star. It's not the most abundant kind of star in the universe, but it's also not that uncommon. I mean, the universe, as you'll see, is a big place. And it's middle-aged. This is a middle-aged star. It formed about five billion years ago and based on everything we know about stars, it will die in about five billion years, okay? So here is one of those coronal mass ejections. And for scale, these magnetic storms that result in these things are, again, at least the size of planet Earth. The smallest one of these cold spots or hot spots is about the size of our planet. This is probably more like 10 to 20 Earths in size. So this is a fierce storm and they're gonna zoom out here. This is a NASA movie of one of these things happening. It takes tens of days for the sun to make one rotation. Okay, so you can very slowly watch these storms move over the photosphere as the sun spins. There's a lot of angular momentum. The sun is really a vast playground for all kinds of things, forces, mechanics, and so forth. Now, as I said, the sun is not typical, but it's not fully atypical either. If you imagine a primordial gas cloud that collapses under gravity and forms a star, however much mass was present in that cloud when it collapsed, whatever elements were present in that cloud when it collapsed, and it's primarily hydrogen and helium, okay, determines the fate of the star. The star's fates are determined at their birth when they join something known as the main sequence of stars. So if you go out and you look at the temperature which maps onto the color of a star and you plot it versus its brightness, how bright the star is versus what color it is, you find that there's a relationship between those things. This is what astronomers discovered a century ago. Bluer stars tend to be much hotter. Hotter temperatures are over here on the left. Redder stars tend to be much cooler and emit much less light, they're fainter. Blue stars shine bright, red stars are dim. But the joke's on the blue stars. The blue stars only get to live for about 10 million years. They live fast, they die young. They're formed from very heavy clouds of gas. They make very heavy stars as a result of that. They burn bright and blue, okay, very hot. But they die in millions of years. Our sun, which is down here, is a more yellow-y star and it's cooler, 6,000 degrees Kelvin. These blue stars are 30,000 or so Kelvin, surface temperature. Our types of stars down here near the bottom of the main sequence, they live for billions of years. And then the faintest stars, the reddest ones, the so-called red dwarfs, they can live for trillions of years because they're faint, they're cool, and they're only 3,000 Kelvin or so. They don't burn through their hydrogen as quickly and so they can live a really long life. That doesn't mean it's quiet around those stars. Proxima Centauri, who's the closest star to our own sun four light years away, is one of these red dwarfs. And it's probably not very pleasant around that star despite the fact that it's gonna be stable for trillions of years. It has storms, it has extreme magnetic fields, this causes all kinds of ejections from its surface that can threaten planets that are nearby it. So we're very lucky to live near what's called a G-type star, okay? Once a star forms it lands somewhere on the main sequence, it can't move anywhere else on the main sequence and its fate is fully determined by where it landed, as you'll see. There's only a few outcomes for stars. So we have the so-called O-class stars, the blue giants live fast, die young. Then we have the M-type stars at the other end, the so-called red dwarfs. They burn slow and they live a long time. And we're a G-type star right here, okay? So we're not very big, not compared to the giants, but we have the benefit of longevity, which is good for a planet like us and good for the formation of life. All right, so once you're on the main sequence, your fate is determined. So let's take a look at the fates of stars. In act two, we're going to visit black holes, a shadow where no light shines. But to get there, we need to understand something about the end of stars. And we can begin with our own star. Now as an analogy to the sun, okay, which is not dying right now, but will, let's take a look at a star similar to the sun that is dying and learn something from that. This is Delta Cephe. It's about four and a half times the mass of the sun. So similar in mass to our sun, roughly in the same class, okay? And unfortunately, you'll notice it's kind of a reddish orange color. It's not blue, like you, bluer than our star, like you'd expect if it were heavier and brighter, okay? It's sickly red orange. It has burned through its hydrogen in the core. And now it's currently burning helium. And that is not good. This is the equivalent of, once you've eaten all the food in the house and you can't get out of the house to get more food, you start finding things you can eat like newspaper, just in the hopes of getting some fiber or some nutritional value out of it. Helium is hard to fuse. You don't get as much energy out of it when you do it because it takes more energy in to helium to get it to fuse. And when you get to this stage, stars are getting desperate. They're just staving off the inevitable. What the inevitable is, however, determines on their mass, is determined by their mass. So this star is dying. Let's take a look at a dying star like this one. So what does that mean? Well, as I said, the main life of a star is defined by the time it spends burning that hydrogen. The hydrogen is light. It's easy to fuse, collects in the core very readily. So you fuse hydrogen, that's the good stuff. And you can fuse that for millions of years if you're a blue giant, or trillions of years if you're a red dwarf, billions for a star like ours. Now this comes at a cost. As I showed you, you fuse hydrogen into helium-4, for instance. So you've now used up a bunch of protons to make helium-4. So you now have what is known by astronomers as helium ash building up in the core. So it's not really ash. It's not like ash when you burn a log in a fireplace and you literally have ash left over. But it has similar problems to ash. If you let ash build up in your fireplace and you want to try burning the ash for warmth, you have to put a lot more energy into it to get carbon to do something new and interesting. You need a source of oxygen built into the carbon somehow to get it to burn again. That's difficult, that's expensive. Burning ash is a waste of energy. And similarly, that helium, it's not hot or heavy enough in the core of a star, a young star, to burn helium. It can't fuse it, it just sits there. It takes up space, okay? But it doesn't fuse. So the main sequence stars will burn for millions or trillions of years depending on where they started out on the main sequence. We've got about five billion years left to go in our star. But as I said, that hydrogen fusion to helium comes at a cost. And eventually, you run out of hydrogen in the core. And what happens? You have that dangerous waltz, gravity pulling in, radiation from hydrogen fusion pushing out, but now you're running out of hydrogen and you can't withstand the gravitational collapse anymore, not as much as you used to. So the radiation pressure diminishes, the star begins to shrink in size, which increases the pressure inside the core. And the first signs of stellar death is that the star's surface begins to collapse. The nuclei in the core are now pressed even closer together by gravitational forces. This ignites a flash burning of hydrogen around the core and then further ignites hydrogen fusion in the core. Things have gotten desperate at this point, okay? With sufficient compression, even the helium will begin to fuse. The star will begin to then puff out in size. Helium fusion will pump even more energy into the star, but there's not as much helium in the core to burn as there was hydrogen to start with. So you've got a limited time now. The surface of the star will puff out as the radiation pressure grows from the helium burning. You start to fuse helium into things like carbon and oxygen. Things are getting desperate. You're only making heavier elements and they're even harder to fuse. So while you're getting more energy output than during the hydrogen burning phase, giving you lots of radiation pressure which makes the star puff up even larger than its original size and cools the surface down so it becomes redder and orange-er than it was before, okay? So the fact that Delta Cephe has that red-orange color and we can see that it's very big, that's bad because it's expanded from its original main sequence, star type, and it's now desperately burning helium to stay alive. So when the sun enters its helium burning phase in about five billion years, it's expected to expand to a size beyond the radius of Venus and likely beyond even Earth and possibly even Mars. So there is a clock on getting off this planet, assuming the human beings can make it five billion years. We haven't been around that long, so time hotel, all right? We do have a situation where we need to get off this planet. We've got time, but we're not so good at using the time we're given. I mean, that's the whole of, I mean, poems and painters, poets and painters and playwrights and movie screenwriters and so forth, the right whole stories about people squandering their lives and then regretting it at the end, okay? Species-wide, it's not terribly different. So we have a clock, five billion years. Actually before that, the sun's temperature is slowly increasing over billions of years. It will keep putting out more energy during that time and it's likely it'll cook the planet even before then so it's maybe we've only got three billion years, all right? But there's definitely an end date to the Earth and that's something to keep in mind. Deep time, but in the span of the cosmos, it's not that long. So what happens at the very end is that for a star like our sun, you have the helium burning phase, you get carbon, maybe some oxygen in the core that result from this fusion process and then collapse begins again, you run out of helium. So now things have gotten really desperate. Now for a star with a mass of hours, it will never compress enough to ignite carbon and oxygen fusion. So even though you've got carbon and oxygen in there that you could burn, stars our size just can't do it. So what will happen is the star will begin to collapse, it will blow off its outer atmosphere and this results in a spectacularly beautiful phenomenon known as a planetary nebula which has nothing to do with the formation of planets. It's a misnomer left over from the history of astronomy when people didn't understand what they were looking at so they thought, oh, this must be the gas from which planets form around a star. They didn't know that this was a dead star. They didn't know this was the end of the life cycle, not the beginning. So they thought these were proto-stars and they thought this was the gas left over after their formation, it's not. It's the result of the star blowing its atmosphere off rather gently in terms of star terms as you'll see and that creates these spectacularly beautiful nebulae. But they have nothing to do with planet formation whatsoever. They're the end stages of stars. This is one of the things that will happen to our sun. It will blow off its outer atmosphere. It will illuminate that gas with its remaining light from the core and it will be pretty from a distance but you probably don't want to be near it when it happens. But by then the earth is long gone anyway. I should note by the way that while it takes 10 billion years for our sun to burn through its hydrogen, it only takes millions of years for it to burn through its helium. So that's pretty small by comparison to its original life cycle. Essentially in the cosmic time sense, this final death throw of a star like ours is rather instantaneous. So you burn through the hydrogen, maybe you spend 10 million years burning your helium and then you're dead, that's it. And what does dead mean? Well, this is an example of a pair of stars that are close to each other. One of them is very big and one of them is very small. So this is the blue star very near this thing here, this teeny tiny little star called the white dwarf. White dwarfs are the hot cores of dead stars that started out about our size. They will simply cool for the rest of time. They will eventually cool down into a black dwarf where they just can't be seen anymore because they're so cold. But they are just, all you're seeing that white dot is just the core of a dead star shining in the night, cooling down slowly for the rest of the history of the cosmos. That's how our star is supposed to end. If we can make it that far, like if we can, I don't know, move to Europa, for instance, live there, okay, terraform one of the moons of Jupiter or something like that, live there, whatever, it's gonna get nice and toasty in the outer solar system anyway when the sun expands. Maybe our species can make a go of it around a white dwarf, but life around a white dwarf is not as quiet, or it's a quiet retirement for the star, but it's kind of exciting around a white dwarf. There's lots of radiation outbursts and strong magnetic fields. It's kind of a mess down there, okay? So you don't wanna be too close to these things. That's our sun for comparison. So that roughly represents the collapsed core of a star our size, that's the core, that's the star it likely came from. Not too bad, all right? The rest of that all gets blown off into planetary nebula. That's a quiet retirement for a star. Here's a not-so-quiet retirement. So this is Orion. There's Orion's belt, outstretched arms, legs, sword, okay? The Orion nebula is absolutely gorgeous to look at with a modest telescope. You can view the Orion nebula. It's rich in oxygen and hydrogen so you get these rich reds and blues in it. It's really quite beautiful. So I recommend that if you get it. You can view that in the Metroplex, no problem. In fact, the first time I turned a telescope on the Orion nebula, I'd never seen it before. And I didn't know what I was supposed to expect to see. And when I focused on it, I actually started going, holy fuck, like it was a religious experience for me to see this beautiful cloud of hydrogen and oxygen. At that moment, a runner ran by, it was four in the morning. A runner ran by me on the side of the sidewalk while I was looking through the telescope. I can only imagine what that person thought was going on with me, that I was some kind of crazy person on the side of the sidewalk with the telescope screaming curse words into the lens, fine. But these things are tremendously beautiful. We're gonna focus on this star. If you look at Orion, you'll notice that in the upper left side of Orion, there's a very orangey red star. In the lower right side of Orion, there's a very bright, rich blue star. This is Betelgeuse, this is Rigel. Both of them are doomed. Let's take a look at Betelgeuse, okay? Betelgeuse is red orange in color, and it's 10 to 25 times the mass of the sun. So a star on the main sequence that's that heavy should be blue. But Betelgeuse ain't blue, it's red orange. That's bad, okay? So let's take a look at this. This is an image of the surface of the star, Betelgeuse. It is 600 years away if you could travel at the speed of light, so 600 light years. And this is an infrared photograph of the surface of Betelgeuse. That's how big this star is. It has expanded to an orbit beyond that equivalent of Mars in our solar system. It is far bigger than our sun, far heavier as well. If you care about this, this is an angular scale down here. This is 10,000ths of an arc second. This is big on this kind of distance scale. Those are hot spots on the surface of Betelgeuse. Now neither of them is actually hotter than the surface of our own sun. It's really puffed out, its surface is very cool overall. But it's still thousands of Kelvin, right? But neither of those hot spots is any hotter than the surface of our sun. It's energy, even though it's much more massive, its energy is really spread out over this big sphere, okay? So this is not good. This is a sign of the end for a star that's that heavy. This is a cartoon that will give you a sense again of the scale of these red super giants. This is the phase, any main sequence star will enter when it begins to die. This is a star, this is the star Arcturus here. Antares is another star like Betelgeuse in the night sky that's dying currently, and it's huge. This is the orbit of Mars for comparison, and it subsumes the orbit of Mars. That's our sun by comparison. That's our sun, that is a red giant. This is not pretty, okay? So this thing is Betelgeuse is probably currently burning through its helium. This is not good, it's only got probably tens of thousands of years left at this stage based on astronomical measurements. Stars this heavy however will collapse, burn carbon and oxygen and re-expand, collapse again, and keep burning heavier and heavier elements, fusing them until it hits the pinnacle of fusion in a star, iron 56. There are heavier elements than iron 56. Iron 56 is not the heaviest element in nature, but once you hit this, no star is big enough to ignite this into sufficient fusion to make energy to stop the collapse due to gravity. Iron fusion gives you very little energy for the input you have to make. This is the end. This is how big stars die. There's nothing left after this to stave off gravitational collapse. Now one of the things that makes a white dwarf so pretty, this is the way that our star will end, is that it collapses until the electrons in that star get so close that nature's trying to put them almost in the same places in space. And there's this thing in chemistry called the Pauli exclusion principle. You can't put two electrons in the same state. This is what allows you to arrange electrons in orbits around a central nucleus in an atom, the so-called orbitals, and the number of electrons you can pile into those orbitals. White dwarfs are supported by the pressure of the Pauli exclusion principle. That star is so compact, its electrons are so close that they stop gravitational collapse because their resistance to being in the same state of motion overcomes gravity. For a star this heavy, that's not an option. Even electron pressure will not stop the collapse of this thing, it will compress below a white dwarf stage. So let's take a look at that. This is a simulation of the ultimate collapse of a core of a star. In less than a second, a star that has burned all the way to iron 56 will completely collapse down below white dwarf stage. This is a simulation of the three dimensional turbulent flow of heat, energy, and pressure inside the core of a star as it dies. 300 milliseconds, this nightmare evolves. Two things happen. The star continues to collapse its core, but as the atmosphere collapses in, it hits this shock and is blown outward. Now we don't fully understand how that shock works, but it is spectacular when it occurs. This is a core collapse supernova. It is one of the brightest phenomena in the universe. You can see these across the universe, they are so bright. This was done with petascale computing at the Argonne National Laboratory and probably represents decades of computational and mathematical work to even get that turbulence in there that we know is necessary to cause that rebound that blows the start of pieces, at least the stuff outside the core. All of this, can you imagine something 15 times heavier than the sun collapsing down to something smaller than the size of a city in less than a second? That is terrifying, and you don't wanna be anywhere near this when it goes off. Because the first thing that happens is it sends out a blast wave of neutrinos. Remember I said neutrinos, harmless, right? Can go through a light year of lead, don't really care that the lead is there. So many neutrinos get produced in a supernova core collapse episode that the blast wave of neutrinos is so dense that even if you were standing on Jupiter when it reached you, it's capable of converting nearly every proton in your body into neutrons. So they do notice you when they pass through you in sufficient numbers to cause problems. But that's not the worst of it. So if you were to observe a core collapse supernova from some distance like Jupiter, the first thing that would happen is you'd convert to neutrons. Within a half second or a second, the radiation, the light from the explosion will reach you. It's trapped in the core and in the atmosphere until the atmosphere blows off. The neutrinos get out first, the light gets out second. So your neutron body will now be blown to pieces by gamma rays, all right? That's one of the ways a world can end around a heavy star, heavier than our sun. So what happens to the core? We'll see that in a moment. This is an example of a core collapse supernova going off in a very distant galaxy, all right? So this is the galaxy NGC4526, not very notable. This bright thing here is supernova 1994D, SN1994D. You can identify supernovas by SN, supernova, then the year in which they occurred, and then ABCDEFG, what sequence that happened in that year. So this was the fourth supernova observed in 1994. This was in a very distant galaxy. The last supernova that we know, which was recorded by human eyes seeing a bright new star appear in the sky, the last one we know about in this galaxy of ours was just before 1600, which was just before the invention of the telescope. That is frustratingly irritating because we've had the ability to really look closely at dying stars for almost 500 years, but our own galaxy has not been kind enough to give us a dead star to look at, that least a fresh one, all right? We'll take a look at the Crabnebula in a second. The Crabnebula is the result of a supernova that detonated the light reached us in 1054 AD, all right? And it's been expanding ever since then as a blast wave about 6,400 light years away. We are actually long overdue for a supernova like this. They happen in other galaxies, roughly once per century per galaxy. Milky Way is long overdue. And some of those stars I mentioned before, Betelgeuse is a good example of one that might blow sometime in the next 10,000 years, but we don't know exactly how much life it has left. So it could blow tomorrow. And there are hundreds of telescopes of many varieties already to instantly train on it. There is a whole supernova alert system. If you wanna subscribe to it, you can go and sign up for the supernova alert. You can get them emailed to you, okay? And so all these astronomers are hungrily waiting for a supernova to go off in our galaxy so they can watch it and learn. We're gonna learn so much from this. We're gonna see it in neutrinos. We're gonna see it in gamma rays. We're gonna see it in ultraviolet, visible light. A supernova in our own galaxy will shine brighter than the moon during the day. You will see it. It's brighter than Venus in the morning, okay? This is a lot of energy that's coming out of this thing. We're long overdue for one of these. So what happens at the end of a supernova? Well, if the stellar core has a mass that's about 1.4 to two times that of the sun, it will blow off its outer atmosphere. It will collapse below the electron pressure limit until it's all neutrons. And then the neutrons will stop the collapse. They cannot be put, just like electrons can't all be put in the same state. Neutrons can be packed closely, but it's very hard to put them all in the same space. So there will be one more resistance to collapse from the neutrons that are the result of the core collapse. This results in the formation of something known as a neutron star. And neutron stars are horrific. Because of the instabilities in the core when it collapses, they are birthed, spinning extremely fast. This is the crab nebula. That bright light that you see coming off the gas shroud of the nebula, that's the surface of the star that died. We first saw the light from this in 1054 AD unaided in the night sky. It just appeared, okay? This is the result of that explosion. This gas cloud has been expanding out nearly the speed of light ever since. It's moving extremely fast. In fact, we've photographed it enough that we can watch it expand. And in our astronomy class, you can measure the expansion of the crab nebula at an estimated speed. It's terrifying, okay? At the heart of this is a spinning neutron star. It's roughly the size of Dallas. It has about one and a half times the mass of the sun compressed into something the size of the city of Dallas. And it is spinning with roughly a millisecond period. It's making 1,000 revolutions per second. And it has such an immense magnetic field that it's whipping all of the ions in this cloud into a frenzy. This radiation you see from here is because the residual magnetic field of this rapidly spinning neutron star is whipping the atoms in that into a frenzy. And what magnetic fields do to charge particles? You'll learn about in physics too. This is an artist's rendition of a neutron star. Gravity will be so strong around these that it will bend light. Not as much as the next thing that can happen, which is a black hole, but appreciably bend light. So neutron stars are really interesting playgrounds for high speeds. You can think of them as one city-sized atom made almost entirely out of neutrons. So they're an elegant playground for quantum physics in that sense. If there was one near us, we could learn a lot, I think, about the interplay of gravity and quantum physics, which would be awesome. And astronomers are trying to use neutron stars to do just that, even though most of them are very far from us, including the collisions of neutron stars, which do happen. We've measured at least one of those. So where does all the intellectual power that led into predictions of these things, and then later observations of these things come from? It's a long story. I'm gonna show you two players in the story here. This is Subramanian Chandra Sekar. He was an absolutely brilliant American Indian physicist, and he estimated the minimum mass that's required such that the gravitational core collapse cannot be balanced by the electron pressure, but rather collapses all the way down to neutron pressure. He actually thought originally that he was calculating the minimum mass required to form a black hole, but this was later refined. First, you hit the neutron star state. If you're heavier than two times the mass of the sun, you can continue to collapse below the neutron pressure. He determined the limit for neutron stars to form to be 1.4 solar masses, and this is now known as the Chandra Sekar limit. Now, this is Jocelyn Bell, who as a graduate student, this is roughly the time she was in graduate school, 1967, she actually discovered these rapidly spinning neutron stars. Nobody knew that neutron stars would be rapidly spinning and have big magnetic fields and put out lots of radiation, but she was doing radio astronomy, and she noticed that there was a signal in the sky that tracked with the stars, so as the earth rotated, the signal moved like the stars move in the sky, and it was periodic, and it was assumed at the time that the only thing in the universe that could give off a regular periodic radio signal was an intelligent civilization, right? So this thing was originally dubbed Little Green Man One, as in an alien civilization that's beaming radio out like a little beacon, like, hi, we're over here, come visit us, right? But it turned out that there were more of these things and they were scattered all over the place in the sky, and so it was later determined actually to be correlated with these exploded dead stars like the Crab Nebula, and so it's actually a very common stellar phenomenon, and it's a rapidly rotating neutron star that's pulsing in radio. It's spinning so fast it's giving off radio waves, okay? So you can use some intro physics to look at some of this stuff. I'm gonna scooch through this real fast here, but the basic idea is that you can take the millisecond period of a pulsar, okay, and you can take the radius of a pulsar, a neutron star, about 10 kilometers, roughly the size of a city, and you can estimate how fast the neutrons on the surface of this stellar corpse are whirling around the axis of rotation. All right, so you do some rotational motion stuff and you find out it's 20% the speed of light. So neutron stars are spinning at what are called nearly relativistic velocities. They're moving at one-fifth the speed of light when they rotate. Now what's fascinating about neutron stars is they spin down over time, slowly, over millions of years. And the reason for this is they're warping space and time so much around them that it radiates waves in spacetime. So actually the first way we discovered these waves of spacetime, which are called gravitational waves, was by looking at the spin down of a pulsar and it exactly matched the prediction from calculations by Albert Einstein and others. That was a long time ago. We only directly observed gravitational waves by using the ripples themselves in space and time in the last three years. That's a new discovery. All right, now what's the escape velocity from a neutron star? Should we expect to see neutron stars because light can escape from their surface? If the escape velocity at the surface of a neutron star exceeds that of light, it will appear as an empty pocket of space because no light can escape it despite the fact that it's home to two solar masses of material. All right, well, you can run through the energy calculation. The initial energy equals final energy at different radii, so you start with the initial energy. You imagine firing a projectile off the surface of the neutron star off toward infinity. So you start with some kinetic energy there and then at infinity, you want the kinetic energy to come to zero and you want the gravitational potential energy to come to zero, blah, blah, blah. You get an equation like this. You solve for that initial velocity that's required to escape the neutron star. And even with physics in this class, you can very quickly solve for that and you can find out that it's actually only 77% the speed of light. All right, so we should expect to be able to see neutron stars because light can escape the surface of a neutron star. And for this calculation, I assume the mass of the pulsar, the mass of the neutron star was about twice that of the sun. So right at the limit for the next thing to occur. All right, so light should and does escape neutron stars. It does it in forms like x-ray and gamma ray, but it does escape. Now this is the way the heaviest stars die. These are one of the biggest mysteries in the universe. And with the advance in mathematics and computation and telescope instrumentation, camera instrumentation and so forth, we as a species have made tremendous strides in understanding these things, but these are the black holes. If the core of the mass of a star is bigger than twice the mass of our sun, even the neutrons cannot resist collapse. And the radius of that object will shrink, compressing the mass of that star below a certain distance, so bending space and time, creating such a strong gravitational field that the escape velocity from that object below a certain radius is in excess of the speed of light. You can never escape that object. That boundary is known as the event horizon. Beyond the event horizon, it's not like you just die. It's just that you can't get messages out anymore. If you fall below the event horizon of a black hole, the point of no return, you can probably still move around inside the event horizon, but you can never get out again. And you can't even send radio signals out. You can't tell anybody, hi, I'm trapped in a black hole, like come in here so I'm not alone. You're on your own, okay? Unless there's some other physics that takes over inside a black hole, and that may be possible. There may be new laws of physics inside of black holes. You don't know. That would be awesome, all right? Based on what we know now, you're not getting out neither is radio. And the radius below which you have to compress an object to get it to become a black hole is given by this very simple equation. And we kind of derived this as it was a challenge problem on dark stars about six lectures ago, four lectures ago, something like that, okay? This is known as the short shield radius. So what you see here is an animated GIF, okay? It's just an artist's rendition, that black circle. That's the sphere below which no light can escape. Gravity is extremely strong around this region of space and time, and it bends the light like a lens. And you can see this background object that's moved past it, gets lensed by the black hole. Black holes act like optical lenses in space that take light and bend it from directions you shouldn't have been able to see the light so that you can see it. So you see two images of this galaxy plane form and then a ring of images around it as it's exactly centered behind the black hole. It behaves just like a lens. And in fact, we've used this phenomenon to measure masses of distant objects because the amount of lensing is proportional to the amount of matter in that thing. Okay, so they're fantastic laboratories, but also fantastic instruments. Now the story of the black hole I've told you some of, they were originally conceived of as dark stars, stars from which no light can escape by a preacher, but also a philosopher and a mathematician and a physicist, polymath of all kinds, John Mitchell. He conceived of dark stars using Newton's laws. So he was definitely building on the shoulders of the giants that came before him as Newton did. But it was Albert Einstein that finally came up with the general theory of space and time finally explained what gravity is, which Newton couldn't do. Gravity is the bending of space and time by matter and energy. So matter and energy tells space and time how to bend. And the bending of space and time tells matter and energy how to move. It's a beautiful dance. Unfortunately Albert Einstein kind of derived the equations for this, but it was left to others to solve them. So you get the glory for writing the laws down, but he didn't actually solve the equations. The first solution to Einstein's equations was written down by Carl Schwarzschild of the Schwarzschild radius. And it was that first solution that predicted the existence of black holes, regions of space time with so much mass in them that light cannot escape. So this is the modern formulation of Mitchell's dark stars. But it's a much more exacting thing. Interestingly, he died a year after he wrote that solution. So he almost didn't live long enough to be the first person to solve this. This fellow over here, J. Robert Oppenheimer is most famous for being the head of the Manhattan bomb project. But before that, he was a well-regarded theoretical physicist. And he actually determined, along with two other people, Tolman and Volkov, the real limit for final collapse to a black hole. So the Chandra Sekar limit tells you the limit in mass to collapse to a neutron star. The Tov or Tolman Oppenheimer-Volkov limit, which is around two or three times the mass of the sun, tells you when you collapse to black hole inevitably. And so this is an artist's conception of a black hole with a swirling mass of gas spinning around it, slowly falling into the black hole, colliding with itself and emitting X-rays and gamma rays. And the magnetic fields due to these moving ionized atoms are so extreme, you get these giant jets of energy that belch, collimated by the magnetic fields of the swirling gas around the black hole. It's a terrifying phenomenon. We are lucky that none of these are too close to Earth because they are really radiation factories. So here's a picture of the very first black hole candidate, first very strong black hole candidate ever observed, although it took a long time to confirm that this is probably a black hole candidate. It's emitting an X-rays, it's known as Cygnus X1, it's an X-ray emitter. And what you're seeing is the light that's being emitted by the gas disk around the black hole. We cannot actually see the event horizon of the black hole itself in the center of this. It's too small, okay? But as I showed you recently, the Event Horizon Telescope used radio telescopes across the Earth to image the hot gas around a supermassive seven billion solar mass black hole at the center of a galaxy that's tens of millions of light years away from us. And that is the image that was returned by that. There is the region, the Event Horizon, the no-go zone, light doesn't return from there. This is a gravitationally warped and lensed image of the gas disk around the supermassive black hole. This is the first true photograph of a black hole. We have never seen this before this year. Although all the indirect evidence pointed that they do exist, there's tons of evidence otherwise that you can gather about black holes. So finally, let's use this information to think about how the world or the universe might actually end. And I always liked this T.S. Eliot poem. It's very famous because of the last few lines. This is the way the world ends, this is the way the world ends, this is the way the world ends, not with a bang but with a whimper. And you'll see that we think that the universe will end with the ultimate whimper. But to do this, we need to tour the whole cosmos. Let's begin with a familiar thing, home, earth, right? About 6,000 kilometers in radius seems big to us. But the universe in which earth is just a tiny bit player is much bigger. And I'm really serious about this and you're gonna see how big. The universe is a ridiculously big place. And in fact, we don't actually know how big it is. We just know how far we can observe and using all the laws of physics, we can estimate the size of the universe that we could observe, but we don't know what's outside of that, okay? Although we think it's just other visible universes to other people on other planets who are not able to see us. So this is not to scale in terms of the distances between the planets, okay? But there's the sun, Mercury, Venus, there's earth, Mars, and then the gas giants in the outer edge of the solar system, all right? To give you a sense of scale, we're gonna do everything in terms of the travel time of light. To get to the moon and back again is one light second. So when you look at the moon at night or during the day, you're not seeing the surface of the moon as it exists right now. You're seeing it as it existed one second ago when light reflected off its surface traveled to your eye and then you can see that light. The sun is eight light minutes away. You do not see the sun as it exists now. You see it as it existed eight minutes ago. If the sun explodes, it will happen in real time there, but we won't know for eight minutes because it takes eight minutes for light to get to us. We only know things when light reaches us because light is the fastest thing in the universe. The edge of the solar system, and there's arguments about exactly where that is, but roughly speaking, it's about one day at the speed of light away. It took 40 years for the Voyager probes to go that far. They're not the fastest things we've ever put into space, but they're pretty damn fast, okay? 40 years to go one, 19 light hours, not even one full light day, but about one light day, okay? But the solar system is just one system of planets around one star in the universe. This is Proxima Centauri, our neighboring star. It's a red dwarf. It's about four light years away and it's our closest neighbor. If the sun is our house, our next door neighbor is Proxima Centauri. We've gone 10 feet between buildings to get there, but this is already four light years, okay? Our solar neighborhood, like the cul-de-sac we live in, in the universe, is roughly 20 light years in size. There's a whole bunch of stars within that range. Stars like Vega and so forth, you can see them in the night sky. They're all pretty close by, all right? Now in contrast, the stars of the Big Dipper, which is a very familiar constellation, are on average about 89 years at the speed of light away. What does that mean? It means that you will not see the stars of the Big Dipper as they actually were on the day of your birth until you live to be about 89 years old. So when you're 89 years old, if you make it that far, and on average in my family, that is not going to happen to me, okay? But if you make it that far, look at the Big Dipper. You are seeing those stars as they actually were the day you were born. They're still very close by. All of this of course is contained within the Milky Way galaxy. Here's our sun, here's the center of the galaxy. This is about 10,000 light years. So it's about 30 or so thousand light years to the galactic center from where we are. This is our Metroplex. This is the city we live in. The sun is in a middle suburb of this city. 30,000 light years from the city center, okay? We see the center of the Milky Way now as it appeared about 15,000 or so light years, 15,000 light years away, so 15,000 years ago, okay? That means that we see the Milky Way center as it existed before writing and the wheel were invented. All right, we don't know what it looks like now. We know what it looks like before people started recording history. But it gets worse than that. Because the Milky Way is just one of several galaxies in our own sort of little city complex in the neighborhood. There's Andromeda, for instance, which is a big smudge in the night sky. It's hard to see in a city. You have to really go to a dark site. You have to have a good telescope and you need to expose for a long time. Andromeda is a nearby galaxy with a trillion stars in it, but they're so far away, you can barely see them. And it shows up as a moon-sized smudge in the night sky. If you could crank up the brightness of the Andromeda galaxy, it would actually be the size of the moon in the night sky. It's big, but it's really far away. By really far, I mean millions of light years. So the Milky Way is one of dozens of galaxies, each containing either 100 of billions or trillions of stars, and they form this thing called the local group. And it goes around eight million light years around the Milky Way. But it's worse than that, because the local group is part of something called the Virgo supercluster, which goes 200 million light years across. We're centered there, but you can really no longer see our galaxy. We're subsumed. This dot is the local group here. Okay, so we're somewhere in that dot. The Virgo cluster, which is where that black hole we took a picture of is located, is way over here, about 100 or so, 50 million light years away. That's still our neighborhood. This is the La Niakea supercluster. It was only discovered recently, but it is very likely a gravitationally bound cluster of clusters, of galaxies. All right, so the local group is here. All of these clusters of galaxies are part of the La Niakea supercluster. It's home to over 100,000 galaxies. It's 500 million light years in size. And each bright dot you can see there is a galaxy, each containing a half a billion to a trillion stars. You can't even begin to find us in this space. And this is still not as big as it gets. Because the visible universe of which the La Niakea supercluster is a tiny part is approximately 93 billion light years across. What do I mean by the visible universe? The universe has been expanding since its birth. There's actually been more space time added to the universe since it came into existence at the beginning of time. And it's been pulling these big clusters of galaxies along with it as it's expanded. So the stuff we see now that took 13 billion years to reach us is further away from us now, somewhere beyond our ability so far to see it. And if you run the math, you find out that the things we can see where the light has finally reached us after 13 billion years, they're 90 billion light years away by now given the expansion of the universe. So the Virgo supercluster is at the center of this sphere and this is the light sphere that we have visible to us. Nothing beyond this is visible. Doesn't mean it doesn't exist. It just means we can't ever see it. The light has not had time to reach us from distances that far yet. The Virgo supercluster is actually not even visible as a dot in this map anymore. So these are not galaxies. These are Launia KS-sized superclusters, each of these bright dots. And the only reason we're centered in this is because light travels to us equidistantly from all directions. If we were to move over 90 billion light years, we'd see a different visible universe. We'd see more of what we couldn't see before and less of what we could. So the universe is centered on us only because light travels to us from all directions. We have a false sense of being at the center of everything. So not only can most of the universe not be bothered to interact with you, most of it is actually inaccessible to you as well. So how do we measure sizes like this? Imagine having a bunch of perfectly engineered light bulbs that always, at a given distance, like one meter away, give off the same amount of light. So if you go two meters away, you know exactly how the brightness is supposed to decrease. If you go three meters away, again, you'll observe the bulb to be fainter, but you know what its original manufactured brightness was. So you can calculate. So if you see one of these bulbs downtown in Dallas and you observe how bright it seems to you and you know how bright it was according to the manufacturer, you can do some quick geometry and figure out how far away you are from the city center. Standard light bulbs would be a great tool for measuring distances. If you always know how bright they are and you know how bright they appear to you, you can calculate. This is one of the ways we measure distances, vast distances in the universe. And in fact, using certain kinds of supernovas, certain kinds of stellar explosions, we're able to do this. You need a standard light bulb, one that always gives off the same amount of brightness every time so that you can take its observed brightness and calculate distance. This is an example of one of these calibrated light bulbs. A white dwarf is paired with a red giant star. This is more common than you'd think. It slurps material off the red giant star. It builds up matter on the surface of the white dwarf. It exceeds the Chandra Sekar limit and it detonates, blows everything in that solar system to pieces. And it happens the same way at the same mass every time. These are known as Type 1A supernovas. And they are nature's little standard light bulb. So we've spent decades coming up with all the calibrations needed to use these. And using these, we've measured the distances in the cosmos. And what we found is not only is the universe expanding, which we already have known since the 20s, the 1920s, just by looking at galaxies, distant galaxies and how they're moving. We see all distant galaxies beyond the local group are all moving away from us. So the universe is pulling these groups of galaxies as it continues to expand, like bottles on the ocean just being yanked by the tides. So on these large scales, space time is dragging everything along. Down here, we can resist the pull of space time with electromagnetic forces and nearby gravitational forces. But when you get the things that are bigger than the Virgo supercluster, those clusters of galaxies are being yanked apart by space time expanding itself. But what we learned in 1998, and we have confirmed with multiple measurements since then, is that it's not that the universe is expanding and slowing down, and then eventually it's going to re-collapse. People used to think that's how the universe would end. It would expand, stop, and then gravity would reverse the expansion. In fact, what seems to be happening is that objects that have type 1a supernovas in them that are far away are farther away than we expect them to be given the expansion rate of the universe. The universe is getting bigger, faster. It's being pushed apart by something faster than it was even a few billion years ago. This is a real mystery, and there are some basic ideas about where this is coming from. But no one's really quite sure exactly what the cause of this is. More measurement is required. And if any of you go into physics, there's likely a Nobel Prize in this somewhere for you. This is Saul Perlmutter, who led one of the teams that made this discovery. And he's only notable on here not only because of the Nobel Prize, but because SMU gave him an honorary degree the year before he got the Nobel Prize. That's a pretty good foresight. We've actually had two of these now, two honorary degrees from physics where they then went on to win the Nobel Prize. So the third one we're still waiting. So how does the universe end? Right now, we think the universe ends by simply expanding forever, stretching the matter of the universe thinner and thinner, less and less dense, dropping the average temperature of the universe down below where it is now, which is about three degrees above absolute zero. And because it's expanding faster all the time, it means that things that are distant but visible now will be pulled out of our view. And over trillions of years, less and less things will be visible in the night sky as they're yanked out of view by the expansion of spacetime. We don't know if that expansion will reverse itself ultimately or not because we don't really know what's driving it. But right now, based on everything we think we know about the universe, we think that the universe will end in this way. Now I'm going to skip a bunch of stuff here just to get to the last thing here, which is the coda. One of the things that can cause the universe to expand faster and faster over time is if empty space is not empty. And what does that mean? Well, for instance, the particle that I study, the so-called Higgs boson or Higgs particle, is in a case study in a thing that exists everywhere in spacetime at all times. It has to do this because the Higgs is responsible for giving things like the electron mass. So when an electron comes into existence, it gets mass immediately because it interacts with this underlying phenomenon called the Higgs. And specifically, it's a field of force that's associated with the Higgs particle. You'll study more about these in physics, too, these fields of force, potentials and fields and the interplay of these things that result in forces. So the Higgs has a structure that underlies empty space and it's everywhere. And it's actually offset from zero energy. That's where mass comes from as all. The universe's ground state is not zero energy. It's something offset from that. And that allows mass to emerge in fundamental building blocks of nature like the electron. And we think that very early in the universe that nature started out at a zero energy in empty space but then spontaneously rolled into a different part of the Higgs structure where it's non-zero energy. And we think it's settled at a minimum in this very quickly. But all the evidence we have about the Higgs particle now, based on everything we know, suggests that actually this structure may not be very stable. And there's a possibility, if all we know now is correct, there's a possibility the universe might one day actually drop into the lowest energy state. And this will result in a huge relase of gamma rays, which will wipe all matter out of existence. And it'll restart the universe, essentially, by cooking it. This is known as the vacuum catastrophe. But there are a couple of problems with this. One, it assumes we know everything right now. That prediction is based on everything we know right now. But we know from a variety of other observations that the universe is more than what we see. So we have failed to explain it. We don't understand the expansion of the universe. We don't understand a lot of things about the universe. Maybe some of you will figure that out. The vacuum catastrophe is predicated on the hubris that humans understand everything about nature right now. And we do not. So I wouldn't lose sleep over this. Take this more as a sign that this prediction, which predicts the universe should be unstable, but it seems to be stable, is probably wrong. And as a result of that, because failures are an important teaching tool, which is how you got donuts today, that's a failure of the current understanding of nature. Go fix it. One last thing I want to do is I want to thank the teaching assistants. A professor is nothing without the people that help them teach. And one thing I want you all to take away from this is that although each of us in the teaching team here is talented, let me get this. None of us does this alone. We do this as a team. That's the message of the Avengers. No spoilers for Endgame. That's the message of the Avengers, right? As each person is strong, but they're stronger together. And so for my TAs, I have little Avenger pins, which I've been wearing the whole semester under my lapel, because you are really more than teaching assistants. You've helped to shape this class. You've shaped the lives of people in this class. You're teaching Avengers. So come on down and get one of these before you leave. Thank you very much.