Is the universe infinite? What about the cosmological horizons, the limits to what we can see? Will we ever know for sure what’s beyond them? I discuss these questions and more in today’s Ask a Spaceman!

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EPISODE TRANSCRIPT (AUTO-GENERATED)

After a century of effort, observations spanning the breadth and width of the cosmos, theoretical insights that push humanity's vision of the universe to its utmost limits, we can finally, confidently say without a shred of doubt that the universe is infinite. or not. You see, there's a finite limit to what we can ever observe. But there's almost certainly more universe past that, we just can't see it. But we don't know for sure, and we don't know how far back it goes, and we don't know if the universe curves back on itself, or it just is. And then there's the whole multiverse thing, which is its own can of worms. It's Complicated. Insert exasperated sigh here. Let's start out with something we can say for certain. We live in an expanding universe. Every single day, the universe gets a little bit bigger than it was the day before. But right away, when we say something like, we live in an expanding universe, certain questions start to pop up.

And they're far and away one of the most common kinds of questions that I get asked. If the universe is expanding, then what is it expanding into? And what is it expanding from? Where is the edge of the universe and where is its center? I'm going to be honest with you. I dread this kind of question, especially when I give public talks. Not because I know what the answer is, but because I know how totally unsatisfying that answer feels. It's like sneaking into your kid's candy bag the night after Halloween and eating half their chocolates. Don't judge me! I know you've done it too. Feels good in the moment, but you instantly have regrets. Because here's the answer. The Big Bang has no center and it has no edge. That's it. That's the answer. No more, no less. And that doesn't really feel good because it doesn't make a lot of sense. It's easy to imagine an expanding universe, and there are plenty of analogies out there to help guide our thinking.

We can imagine drawing little galaxies on the surface of a balloon and inflating that balloon to see the galaxies getting farther apart. Or we can imagine baking a loaf of bread with raisins in it. I don't know why it's always raisins and not chocolate chips, which would be way more delicious, but that is an enduring mystery for the ages. But we can see how as the bread rises, the raisins get further apart. Yay, expanding universe! But the balloon has a center and it has an edge, and the bread has a center, it has a crust. So where's the center of the universe and where's the crust of the cosmos? This is why we can't rely on analogies too much when dealing with many concepts in fundamental physics and cosmology. In both the subatomic and cosmological realms, we're grappling with structures and concepts and physics that are as far and above what our puny human brains can imagine. That's why we have mathematics.

Mathematics is a tool that we can use to understand the universe around us even when we can't envision what's going on. That's right, kids. Imagination is important, but mathematics can be even more powerful. Let's start with the center, because that can help us understand a little bit about the edge. Where did the Big Bang start? It started right here, and right there, and right over there, and in the room next door, in the galaxy over there. The Big Bang happened everywhere all at once. The Big Bang was an event that the entire universe participated in. The Big Bang was not an explosion that happened somewhere in space. It was an explosion of space. It was when the expansion of the universe first got started. It was not a place we can point to, it was a time that we can point to. The Big Bang was a singular event that happened in the past of every single object in the universe.

If you take any particle, any bit of energy, and trace its path backwards through time, you'll end up at the Big Bang. Where that particle, that bit of energy, gets all mushed together with every other particle and every other bit of energy in the singularity. Think about it. Let's say the Big Bang happened over there. Say, I don't know, in the Andromeda Galaxy. Say, OK, that's where the universe are. You see that Andromeda galaxy? That's where the universe got started. Well, then, where were we? If that's the case, if that's true, then where were we? Right now, we're in the Milky Way galaxy. Where were we when that happened? When the universe was getting started over there, where were we? If we traveled back in time 13 and change billion years, would we be watching the Big Bang unfold from our perspective? But aren't we a part of the universe? How can we be a part of the universe but somehow outside of the event that created it? We can't. The Big Bang had to happen everywhere.

Because everywhere is, by definition, part of the universe. You can't have a universe, especially an expanding one, without a Big Bang. So, no matter where you are, your point in space had, at one time, had to participate in the Big Bang. Now what about the other side of the coin? If the universe is expanding, what is it expanding into? Where's the crust in our expanding loaf of bread? And what's the oven that we're sitting in? Go ahead, have another piece of your kid's chocolate because this is going to get weird. There is no edge. The universe has no edge. I don't even want to say something like the universe isn't expanding into anything because that still conjures up the wrong mental image. It's too tempting to imagine a wall or a boundary with galaxies and stuff on one side and nothingness on the other, with the universe expanding to fill up that nothingness with somethingness. But that's wrong. Even the vacuum of space is something.

There are still points, locations, there's still existence. There is no outside to the universe because outside implies existence, even an empty one. But the universe is, by definition, all there is. There is nothing to physical reality except the universe. Walls separate one region from another, but the universe is all the regions simultaneously. If there was an edge, you can imagine working hard enough to get outside that edge. But that's not possible. There is no outside. There is no side. There just is. Us. The universe. All there is. Like I said, this feels a little thrilling at first, but then the stomach aches kick in. So grab a bottle of Tums and prepare to explain to your kids where all their candy went, because we're just getting warmed up. I honestly don't have a decent analogy for you to explain how the universe is expanding without a center and without an edge. It just does, whether we can wrap our minds around it or not. But I can give you a way to think about it.

If I were to ask you where is the center of the Earth, you would have no problem pointing that out. It's down there in the middle of everything, you know, where the molten core is, duh. Okay, great. Now let me ask you a slightly different question. Where is the center of the surface of the Earth? Not the whole three-dimensional sphere, just the two-dimensional surface. In other words, give me the latitude and longitude coordinates of the center of the surface of the Earth. Is it the North Pole? Is it the South Pole? Is it latitude zero, longitude zero? Where is it? Point on a globe where the center of the surface of the earth is. All those coordinates are arbitrary. We decided where the line of zero longitude is by pure convention. It's the line that passes through the Greenwich Observatory in England. And we decided that the equator is the equator based on where the sun is at noon during the equinoxes.

Yes, we have good reasons for those particular definitions, but we could have just as easily picked other conventions. The equator can be wherever we want it to be. The North and South Poles could have been wherever we wanted them to be. I could, if I felt like it, define my current position right here as the center of the Earth's surface. And so could you. And so could anybody else. We all have a valid claim to being at the center, which is no claim at all. The entire universe is like the surface of the Earth. There is no center. Now imagine that the Earth is expanding. Cities getting farther apart with time. Continents and oceans growing larger. It's easy to imagine blasting off into space and looking down at the globe, seeing the Earth expanding, but that's cheating and cheating is only allowed with Patreon. That's patreon.com slash P-M-S-U-T-T-E-R. It's how you keep this show going. There is no outside perspective to the universe.

Otherwise, that perspective would be a part of the universe. There's no additional dimension that we can access to give us that outside orbital view of the expanding cosmos. We're in it and that's it. Living in the universe is like living here on the surface of the earth. We can figure out if the earth is expanding, if our earth was expanding. It would take longer to travel between points, images of distant cities would appear to be redshifted, and all that. We could confidently say that the Earth is expanding without ever leaving the surface. All we would get is an expanding two-dimensional world, and that's it. But just like living here on the Earth, there is a limit to what we can see. On our planet, the horizon is defined by the curvature. Oh yeah, curvature is going to come back in a big way in just a little bit, hold on. We can't see the entire Earth from our vantage point because it curves down and away from our view. The universe has a horizon too.

We only get to see a small portion of it. Take away the expansion of the universe for just a second. Just assume that the universe exists and it's static and it's much less complicated. If it has a finite age, if the universe is only so old, then there's a limit to what we can see. Light only travels so fast. The universe has a finite age. This means there's a bubble containing all the light that has reached us since the beginning of the universe. It's like shining a flashlight in a dark forest. There's the illuminated portion around us, surrounded by the unknown darkness beyond. Now if the universe wasn't expanding, then the radius of this bubble would simply be the age of the universe times the speed of light, which comes out to around 13.77 billion light years. And in cosmology, we give this radius a special name, the Hubble Radius or the Hubble Distance name, of course after Edwin Hubble, the guy who discovered the expansion of the universe.

It'd be awkward if it was named after James Hubble or Melinda Hubble or people who had nothing to do with cosmology. So plus that, take away the expansion of the universe for now, just imagine there's this bubble of visibility, of observability around us, plus the more distant objects appear to be younger. Light takes time to travel, so by the time light reaches us, we don't get to see what a distant galaxy is like right now. We only get to see it as it was when the light was released. We don't see the sun right now, we see the sun as it was 8 minutes ago. We see the Andromeda galaxy as it was 2.5 million years ago. and so on and so on. So the innermost portions of our observable bubble are more contemporary, more modern, more in our time. As we work our way outwards, we see images of the younger universe. The outermost shell of our observable bubble, right at the very limit of what we can see, is an image of the universe just after the Big Bang.

So the observable bubble isn't just a limit in space, representing a physical distance, it's also a limit in time. We can't see anything earlier than the Big Bang because there was no such thing as earlier, but that's a different episode. And so the maximum extent that we see in space is also the deepest we can see into the past. But like I said, different episode. So it's now 2 a.m. We've eaten most of the candy, but we can't help ourselves. I'm not sure why I picked this metaphor, but I'm not giving up on it now. An expanding universe complicates this picture that I painted just a little bit, because the universe absolutely refuses to be straightforward. Objects are still emitting light, and that light takes time to travel from over there to here. But in that intervening time, the universe grows larger. with the average distance between galaxies getting bigger. Yes, I know that sometimes galaxies can collide, but we're talking on average at big scales here.

So when we see an image of a distant galaxy and that light has traveled for billions of years to finally end up in our telescopes, we don't know how far away that galaxy is right now at the moment that we get the light. We have to turn to a cosmological model that incorporates the expansion history of the universe so we know how much the universe has grown in a given amount of time. Our current best model of the universe is called Lambda CDM, which involves both dark matter, different episode, and dark energy, different episode. We can discuss the relative merits and weaknesses of Lambda CDM, different episode, but for now let's just take it as a given. as deviations from lambda CDM don't really change the picture much. The maximum distance that we can see. which is the age of the universe, 13.77 billion years, with the cosmos expanding all that time, is about 45 billion light years away.

This distance is known as the particle horizon, the cosmological horizon, or the co-moving horizon, depending on how stylish you feel in the moment. That is the extent of our observable bubble, the maximum extent that we can see at this moment today. But wait a minute, isn't 45 greater than 13.77? Doesn't that imply that the universe is expanding faster than light? Yeah, yeah it does. This isn't a big deal. That's because the speed of light limit only applies to local observations. I'll never see a rocket ship blast by me faster than light. If you think that's some sort of cheat, it's not. It's just how special relativity is constructed. Objects at the far edge of the universe can have whatever speeds they want because they're far away. That's how it works. In fact, we can calculate the current speed of any object, and that's through redshift. If a galaxy is moving away from us, then its light will get shifted to redder parts of the electromagnetic spectrum.

This is how Edwin Hubble discovered the expansion of the universe in the first place. And in an expanding universe, more distant objects recede faster and faster because there's more space between them and us to do the work of expanding. And the turnover point where objects recede away from us faster than light is right around the Hubble distance, 13.77 billion light years away. We can still see galaxies beyond that because their light was emitted long, long ago when they were much closer to us. And if we wait long enough, we can still see some galaxies even beyond them because once again, those galaxies were at one time much closer to us. But there's a limit. It's called the cosmological event horizon, which is ever so slightly different than the black hole event horizon. It's about 17 billion light years away. Any light emitted right now, past that distance, will never reach us, no matter how long we wait.

And an accelerating universe dominated by dark energy, which is ours, makes this even worse. The cosmological event horizon, that limit to what we can see, will continue to grow in the future, but eventually it will reach a limit of around 60 billion light years. But that doesn't mean we'll be able to see everything. Light from the most distant galaxies will get redshifted to wavelengths so large they essentially become invisible. In about 100 billion years, everything outside of the local group of galaxies will disappear from view forever. So this is kind of depressing. An appropriate feeling as we've eaten almost all of our kid's candy and now we face the grim prospects of their faces the next morning. So let's get away from that and get back to Earth. The surface of the Earth is finite. We can measure it. If it was expanding, then its size would grow with time. And once again, good ol' Earth helps us understand what the universe might be doing beyond our observable horizon.

What's beyond our horizon on the Earth? Eh, more Earth. More trees. More rocks. cities, oceans, just more stuff. We just can't see it. Our best assumption of what goes on beyond the horizon of the universe is that there's just more stuff, more stars, more galaxies, more AI generated cat videos. Just like we assume that beyond a horizon on the earth, there's more earth, there's more universe beyond, you know, the universe. So how big is the whole thing? There's a limit to what we can see. There's a limit to what we can ever see. But how big is the whole enchilada? The truth is, we'll likely never know. The observable limit is just that, it's a limit. It's not just a limit to what we can see, it's a limit to what we can know. There is a total, finite amount of information contained in the universe, and a finite amount of information that we could ever hope to receive, even in the infinite future. All we can do is guess. It's totally possible that the universe is just infinite.

just goes and goes and goes and goes without end forever. But it's also possible that it's finite. But how can a finite universe still not have an edge? Well, how can the surface of the Earth be finite and not have an edge? Yes, it has an edge in the third dimension, we call it outer space, but again, that's cheating. The two-dimensional surface of the Earth is both finite and borderless. and it accomplishes that seemingly paradoxical feat by being curved. We know that the surface of the earth is curved. We can measure it without our feet ever leaving the ground. In mathematics, we can build a few tools to give us a clue as to the geometry of the earth. One tool is triangles. On a perfectly flat plane, when you draw a triangle, the interior angles add up to 180 degrees. Thanks, Euclid. But if you wanted to bust out a giant marker, pick three random cities, and draw giant lines connecting them, you would end up with a triangle with interior angles greater than 180 degrees.

That's one way. Another way is through parallel lines. On a flat plane, the parallel lines never intersect. But on curved surfaces they do. If you and me start out at the equator and follow straight lines moving north, we will eventually intersect at the north pole. Not because we turned, but because the earth curved underneath us. We can play the same games in the universe. We look at the light from the very early universe from a special event when the cosmos cooled from a hot, dense plasma and released a flood of radiation. We call this the Cosmic Microwave Background, or CMB. The physics of that plasma is actually pretty straightforward. We have a decent understanding of plasmas here on Earth. And we know from our calculations that there should be slight variations in temperature from place to place across the CMB when you know what there are. Plus, we can calculate how big those splotches, those changes in temperature and density ought to be.

If the universe is curved, then the path of light should have bent as it traveled all those billions of light years. We then compare how big they are to how big we expect them to be. If those splotches in the CMB are different sizes, then we know the universe is curved. They're exactly the size we expect them to be. And that's how we know the universe is flat. Case closed, the universe is infinite, not so fast. If we were to attempt to measure the curvature of the Earth from, I don't know, your neighborhood, we wouldn't have much success. If your triangles are too small or parallel lines too short, then you won't be able to get a sense of the overall curvature. We are limited in our measurements of the universe to our observable bubble, and within that bubble, everything seems as flat as flat can be. So maybe the universe is curved, but on much, much larger scales than our tiny little observable patch.

I know that tens of billions of light years isn't exactly tiny, but it is compared to how big the universe could be It's entirely possible that the universe curves back on itself. That would mean you could travel in one direction long enough and eventually reach your starting point, just like on the Earth. But you would have to travel beyond the horizon, which in an expanding universe is impossible. So it is only possible as a theoretical exercise. You know what's really wild? I promise this is the last piece of forbidden chocolate. The universe could be flat and still be curved. Check it out. Take a flat piece of paper and draw some triangles on it. and parallel lines on it, now bend it into a cylinder. Those triangles are still triangles, and those parallel lines are still parallel. This is the difference between geometry and topology.

The geometry of the universe appears to be flat, but one or more dimensions could be closed, meaning they wrap around while still maintaining geometric flatness. It can get weirder. A Möbius strip is just a cylinder with a rotation made before the ends connect up. A Klein bottle is just a donut with a rotation. A cylinder, a donut, a Möbius strip, and a Klein bottle are all geometrically flat. In three dimensions, there are 17 known distinct topologies that are all geometrically flat. My favorite being, of course, Hansch event space, which involves hexagonal tiling of the same pattern. We've searched for large-scale curvature, we've searched for closed topologies, we've looked for intersection points in the cosmic microwave background, or galaxies that appear on opposite sides of the sky. As far as we can tell, the universe is both flat and simple, meaning none of the dimensions wrap around on themselves. But again, there's a limit to what we can see, so we may never know for sure.

And I haven't even gotten started on the multiverse, where our universe, even beyond the observable limit, is just one bubble amongst some potential infinity of other bubbles all expanding away from each other and spawning new Big Bangs in the spaces between, but I think that's enough candy for today. Thank you to Paul M and Jonathan S for the questions that led to today's episode. Thank you for all your contributions on Patreon. That's patreon.com slash PM Sutter. Please keep sending me questions. Please keep spreading the word. Leaving reviews on your favorite podcasting platform. I truly do appreciate all of your support, and I love recording these episodes and answering your questions. Before I go, I'd like to thank my top Patreon contributors this month.

They're Justin G, Chris L, Alberto M, Duncan M, Cory D, Michael P, Nyla, Sam R, Joshua, Scott M, Louis M, John W, Alexis, Gilbert M, Rob W, Jessica M, Jules R, Jim L, David S, Scott R, Heather, Mike S, Pete H, Steve S, Lisa R, Kevin B, Eileen G, Steven W, Deb A, Michael J, Phillip L, and Stephen B. That's patreon.com slash pmsutter, and I will see you next time for more Complete Knowledge of Time and Space.

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