Daniel and Kelly’s Extraordinary Universe - Why is space so flat?

Episode Date: August 24, 2023

Daniel and Jorge talk about what it means for space to be curved, how we measure it and why the answer is a puzzle.See omnystudio.com/listener for privacy information.

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to the psychology podcast on the iHeart radio app, Apple Podcasts, or wherever you get your podcasts. Do we really need another podcast with a condescending finance brof trying to tell us how to spend our own money? No, thank you. Instead, check out Brown Ambition. Each week, I, your host, Mandy Money, gives you real talk, real advice with a heavy dose of I feel uses. Like on Fridays, when I take your questions for the BAQA. Whether you're trying to invest for your future, navigate a toxic workplace, I got you. Listen to Brown Ambition on the IHeart Radio app, Apple Podcast, or wherever you get your podcast. All right. Hey, Jorge, I'm going to say a word, and I want you to tell me if you think it sounds like a positive or a negative idea. All right. Go for it. The word is flat.

Oh, I guess it could go either way. You know, nobody likes their soda phyllis. flat or there are jokes to fall flat. But I sure do like my bed to be flat. But do you like your tires to be flat? No, but I do like my roads to be flat. Does that mean you want the earth to be flat? I like a spherical, but I also like mountains, so I guess I'm anti-flat earth. Do you like falling flat from a mountain?

I like landing flat on my feet. I think this discussion has run out of air. Hi, I'm Jorge McCartunist and the author of the book, Oliver's Great Big Universe. Hi, I'm Daniel. I'm a particle physicist and a professor at UC Irvine, and I'm also flat-footed. Are you saying metaphorically or, you know, physiologically? Well, your questions often catch me flat-footed, so that's metaphor. But also literally and physiologically, I have flat feet. So, yeah, I wear inserts.

Is that to make you taller? Are you like Tom Cruise? I don't wear heels, no. I wear inserts to avoid crippling pain when running. Sounds like the solution is just not to run. Lie flat on your back. Yeah, I'm working on a floating recliner I can live in for the rest of my life and float around. There you go.

You can attach like a bicycle pedal and maybe get your workouts that way? Yeah, that's great for going upstairs. Yeah, exactly. But anyways, welcome to our podcast, Daniel and Jorge, Explain the Universe, a production of iHeartRadio. Where we take all the twists and turns and curves of this crazy universe and try to flatten it all out for you. We try to untangle all of the mysteries of the nature of matter,

the forces, the energy, the geometry of space time, the size and shape and history of the universe, and make a nice smooth story for you to understand. That's right, because it is an amazing, universe full of stuff, inflated with amazing and incredible physics and stars and galaxies and planets and particles for us to wonder at and for us to, I guess, poke at. There's so much that's amazing about the universe and sometimes you can have two amazing facts that seem to be in conflict. Like, on one hand, it's amazing that we still don't really

know so many basic things about the nature of the universe. How big is it? What is its shape? How did it all come to be? We're so ignorant. about the environment in which we live. And on the other hand, it's kind of amazing that we know anything about the universe, given that we've only lived on one tiny little dot and one random little corner of the universe and never really left. Yeah, it's amazing what we can learn just from this little corner of the universe. And as you said, how we can ask these big questions about how everything is the way it is and why it is the way it is. Like, for example, we don't know if the universe is flat-footed or not.

Does the universe even like to run or does just want to sit on the couch and eat snacks all day? Yeah, does you just sit around and spin? It has big consequences for the curvature of the universe. It is getting bigger and bigger. So, you know, maybe it could use a little bit of an exercise. It's getting wider and wider per second. I think we should be universe positive on this podcast. You know, universe, just be whatever shape you are.

We love you. Yeah, yeah, true, true, I guess. We should love the universe the way it is. It's the only universe we got. So might as well love it. Even if we don't understand it, I guess, all the time, we should, you know, take it for what it is. That's kind of what science is, right? Taking things for what they are.

Taking things for what they are, absolutely. But then always asking, why are they this way? Why couldn't they be some other way? Why do we live in this universe? Do we live in the only universe that's possible? Are there many possible universes and we just happen to be in this one? So often we look around as we try to tell the story of the universe. And we ask those kinds of questions.

Like, does this make sense? This seems weird. Is it random or is there a reason for it? Yeah, because it is pretty perplexing out there the way things are. You know, there are amazing things like black holes that seem unexplainable. And there's sort of really weird things like quantum mechanics out there that kind of keep you guessing about what the universe is going to do. And as we put together this story of physics that tells us how the universe operates, what machinery is going on behind the scenes that controls like what happens when two particles bump into each other. or how space curves and twists in the presence of mass,

we start to tell a story about the universe. We notice like, hmm, the universe seems to do this kind of thing or do that kind of thing. And sometimes the story tells is very weird. It's very surprising. It's not one that makes sense to us or seems intuitive. It makes us wonder if maybe we're missing part of the story

or if we're all just very, very lucky. Yeah. And as you said, there are big questions about the universe that we still don't know about. Like, it's size, it's shape. And what it's going to do in the future, and also a very interesting question about its curvature.

Yeah, as we develop our understanding of gravity and general relativity, and we understand that space is weird and twisted and curved, and that affects how things move. It also affects how the universe itself expands or contracts. So we have a lot of really fun questions to ask about why the universe looks this particular way, especially about the curvature of space. So today on the podcast, we'll be tackling the question.

Why is space so flat? You mean as opposed to bumpy? Like, what would be the opposite of flat? Overinflated? Under pressure, tight. Just like my arches, the opposite of flat would be curved, right? Everybody likes nice curved arches for their feet. And the opposite of flat, in the case of space or the universe, would be curved.

Well, it could also be well, bumpy. I guess bumpy is also kind of curvy. It means you have a lot of little curves. You could have bumpy feet. Yeah, exactly. That's true. You've got to sand those down a little bit. But in this case, yeah, we're talking about like the nature of space. Is space the way Euclid thought about it? You know, two parallel lines will never touch. Or is space more complicated, twisting and curving on a global sense. We're talking to hear about the curvature of the entire universe itself. Yeah. And this is, I guess, a pretty mind bending and space bending topic. Because, you know, I think we're all used to thinking of space or at least empty space as being kind of like, flat, right? Not weird and curved. It's really hard to think about this in the three dimensions of our universe. And even the word flat is kind of confusing there. It comes really from thinking about a two-dimensional version of the picture. Instead of thinking about space like

I can move in three different directions, it's easier to think about it in two different directions because then we can like draw it on a piece of paper. So if you imagine like a sheet of graph paper, that's a flat sheet of paper and two parallel lines on that piece of paper are never going to meet each other. When we talk about whether space is flat, we're asking a similar kind of question, but about three-dimensional space, though it's harder to understand like what curvature means in three dimensions than it is in two dimensions. Are you saying we're going to use a term that doesn't quite work or describe things or is counterintuitive to what is actually happening? Are we going to do that again? Yeah, that's exactly right. That's the story of

physics. Being inadequate. We think we understand the universe and then it surprises us and it sort of Outgrows even like our ideas and forces us to like generalize these concepts. Like, oh, wait, flatness can apply in three dimensions, not just two. Well, as usual, we were wondering how many people out there had thought about this question, whether space and why space is so flat. And so Daniel went out into the internet to ask people this question. Thanks very much to everybody who participates. If you'd like to hear your voice answering these questions for this segment of the podcast,

please don't be shy. Write to me to questions at Danielanhorpe.com. You'll have a good time, I promise. So think about it for a second. Why do you think space is flat? Here's what people had to say. I think space is flat because I think at the beginning, there wasn't any room for stuff to be clumpy or lumped together

or have little dips or gaps. And I assume that everything was shot out from the Big Bang in every direction in equal measure, and therefore it stayed flat to this day. I think that we are not. 100% certain that space is flat, it just seems like it's flat because space has been inflated so much from our perspective. The analogy that I've heard before is kind of like standing on the surface of the earth where the curvature of the earth is so large relative to us that it

seems like it's flat. I'm not sure. I thought it was three-dimensional and flat has to do with 2D. I think the flat space is somehow an stable equilibrium point so the space will eventually evolve into the flat version i have a sneaking suspicion it's not so flat but it just looks that way to us i know there's some bits of like string theory that posit there are dimensions we simply can't perceive and so i'm wondering if space just looks flat to us because we just don't have a capacity to see the other dimensions i don't think it is very flat i think it is pretty multidimensional i don't don't know what really is meant by that. Maybe like stuff forms disks, like the solar system or our galaxy, maybe that is meant by flat. I think that is due to that things tend to

take the shape of disks when there's rotation involved. All right. Not a lot of flat universes. Yeah, here I think you really are scoring some points because a lot of people think flat in applies two-dimensional. Yeah, that makes sense, right? Like if something, if the universe was flat, it would be the width of a sheet of paper, kind of, right? Yeah, if somebody, like, bakes you a birthday cake and then a truck drives over it and flattens it,

then you think of it as, like, thinner, right? Squeeze down to two dimensions. Two-dimensional, yeah. Although a two-dimensional cake would be pretty low calorie. I don't think the calories squeeze out of it when the truck drives over it, unless there's, like, fusion that happens. but that would be a pretty heavy truck.

Also, if a truck runs over, I don't think you want to eat it off the road. It seems like it will make you sick. I think we need to have a highly controlled experiment. One of those like road smootheners they have in cartoons all the time that's crushing Wiley Coyote, squeeze a cake and see if it still makes people fat. I'm pretty sure that if you ask YouTube, somebody out there has made a video of a cake being flaned by multiple things. Thank you, YouTube.

Sounds like the kind of thing the internet likes. If it doesn't exist on the internet before this podcast, it certainly will after. Yeah, it's an interesting question. Why is space flat? And I guess also is space flat, I guess is maybe the first question we should be asking. Or maybe the question before that should be, what does it mean for space to be flat? Yeah, it's a really fascinating question to even think about like what it means for space to be flat and to talk about how we measure it's flat and why we're surprised to find that it is flat.

But you're right. First, we should make sure we're clear about what we mean by. flat. And the sort of two different concepts, so they're, of course, connected that we need to think about. We can think about locally being flat, like is the universe bumpy? And we can think about globally, like is the universe curved on some big scale. Think about locally is a little bit easier, though, of course, still twists your brain a little bit. This is just the idea that matter bends space, that the reason things don't seem to move in straight lines, but seem to be bent by gravity is not because gravity is a force, but that space itself is curved. So, things are moving through that curved space. The sun bends the space around it, so the earth moves in that circle, which is the natural inertial motion for an object in that curved space. That's sort of local curvature. Right, right.

Although I think we always have to give the caveat that you mean space time, right? Like, space time is what's curved. Well, space is a part of space time, and the curvature of space time is a little bit different from the curvature of space, but in this case, space is also curved. But I guess I mean like curved space makes me think of, like, like a road, like a road is curved. And so anything that tries to follow a straight line on that road is going to follow the same path. But maybe in real life it would kind of depend on how fast you're going or what your mass is or right, isn't it?

Yeah, a curved road is a helpful analogy. Things that are moving through space are basically following an invisible road that we can't see. You know, space is curved, but in this way that we can't directly observe it. Like you can look at a road and say, oh, there's a curve coming up ahead. But you can't look at space and see the curvature directly. But it does affect the way things move through it. So you try to drive your car on the curved road of space. And space moves your car for you, sort of like guides it along the curvature of space.

And four-dimensional space-time, it's really fascinating because time and space bend together to make space time itself have these invariants, these things that don't actually change. But space curves and time curves due to the presence of mass. Right. But if I threw a bowling ball at a low speed and a high speed and I threw a feather at a low speed and as high speak, they would sort of curve through space or I would see them curve in a different way or would they all curve the same way? We know that because, for example, you throw a baseball at different speeds, it's going to go a different path. So it definitely depends on the velocity of the object as it moves through curved space. Though that's all inertial motion, that's motion under no forces, just the curvature of space.

I wonder if it's more accurate to say that space has curvature and not that space is curved. What's the distinction in your mind? Well, if you say that space is curved, make me think of it like a tunnel. Like if a tunnel is curved, then no matter how fast you're going or what you throw, you're going to bend the same way.

You can follow the same path, but that's not sort of how space really works, right? Like you're not everything is stuck in the same kind of path. Yeah, you're right. There aren't rigid tunnels that things have to go through. It's not like if you enter a pipe you get flushed out the bottom or something. The curvature of space does affect how you move.

So, yeah, that distinction makes sense to me. Okay, so then there's local curvature of space. What you're talking about is sort of like how things go around the sun, for example, or how the moon goes around the earth. Or how we stay on the earth, all that kind of stuff, things being gravitationally bound, even like the galaxy holding itself together. That's all local curvature. In comparison to the global curvature,

which is a question about the whole universe and its shape. So there's local and global and I guess what's the difference is just like the size of it, the scale? Like are you saying that like if I'm orbiting around the center of the galaxy, it's a different kind of curvature of due to gravity than the moon orbiting around the Earth? It's not fundamentally different. It's all described by general relativity in Einstein's equations. It's sort of like the difference between the Earth being a sphere and the Earth having mountains. Like the Earth could be flat and it could be a sphere, but it could still have mountains in either case, right? The earth could be bumpy locally.

It could have valleys and mountains, even if it's flat or even if it's a sphere. So global curvature is more about the question of like, is the earth a sphere or is the earth flat? Local curvature is about like, is the earth bumpy or is it all perfectly smooth everywhere you go? So we are asking if the universe is bumping. We're asking if the universe is sort of bent, right? Is 3D space more like the surface of a three sphere, right? Or is it flat and more an analogy to like a sheet of paper? So the global curvature of space is asking about like the big picture,

whereas the local curvature is asking about the little picture. Right, right. But I guess my question was or is, you know, where do you draw, when do you draw the distinction between local and global? Like at the galaxy level, at the galaxy cluster level, or it's only global if it's everything? It's only global if it's everything. And, you know, when we solve these equations in general relativity,

and by we, I mean, those guys who know how I saw equations in general relativity, not me, they can only solve those in. certain situations in situations where they assume like the universe is empty, or the universe is filled with matter, but that matter is perfectly smooth. Like nobody can solve the general relativity equations for our universe, which has like clumps of matter in it. So when we talk about the whole universe and its curvature, basically we're talking about a simplification of our universe where all the matter is spread out evenly. There are no lumps at all because that's all they can solve. And in that case, there's still a question of the global curvature.

Is the universe curved on some large scale and how is it curved? Is it flat? Is it open? Is it closed? These are the questions of the global curvature of space time, which are irrelevant to the little details because they still exist even if you smooth all the matter and energy out everywhere like peanut butter. But I guess, you know, if it's everything, we don't really know what everything is, right?

Like the whole entire observable universe might be just a little bump in a ginormous infinite universe. You're totally right. But the curvature around here is dependent on the energy density. Doesn't depend on what's happening out there. And then we assume that what's happening here is what's happening everywhere else. And that's an assumption. We don't know.

It could be that what we're calling global curvature is actually local on a much larger scale. That if you zoom out from the observable universe to the actual full universe that we could never see, that the curvature is different, right? And that what we were talking about the whole time is quote unquote global curvature is actually the local curvature of the observable universe. I guess it's sort of like how before we used to think that the Earth was flat because we only knew sort of the local area here around us and looks pretty flat. But actually, if you sort of keep going or are you taken to account the whole planet,

then you see that the whole planet is curved and round. Yeah, exactly. And if you lived on a part of the Earth that was literally flat, like maybe you were really precise about it and you took out a bunch of tools and you tried to measure the curvature of the Earth, imagine you lived on like a truly flat part of the Earth. Earth. And you measured it to be flat. And then you left that and you realized, oh, actually the rest of the Earth is curved. And so what I got was a misunderstanding of the bigger

picture. So you're right. We can only see the observable universe and we can measure the global curvature of this part of the universe and then assume that the rest of it is the same, but we'll never know. All right. So then a local curvature space sort of is kind of about how mass spend space and how the moon goes around the Earth and the Earth goes around the sun through curved space time. Now, when you're talking about the global picture, I guess you're not just talking about how things move, but it's more sort of a fundamental property of space about what it contains. Yeah, and it's really hard to think about it in 3D. So we do this thing where we talk about two-dimensional versions. Sometimes that's helpful. Sometimes it's misleading. So you always have

to keep in mind like how those things translate from a two-dimensional analogy that's easier for us to think about to the reality of 3D space. It's easier to think about two-dimensional analogies because we basically live on a two-dimensional surface, the surface of the earth, right? So it's easy to imagine like living on a flat sheet of paper versus living on the surface of a sphere versus living in like a hyperbola. And so those three shapes have different curvature. An infinite plane is totally flat. If you drew a triangle on the ground, the angles would add up to 180 degrees. The surface of a sphere, we say it has positive curvature. You try a triangle that follows the surface of that sphere, its angles are going to add up to more than 180.

If you live on the surface of a hyperboloid and you draw a triangle on that surface, the angles are going to add up to less than 180. So those are 2D examples of curved surfaces. Then you have to extrapolate those to 3D space. And it's very similar. A lot of the ideas carry over. I feel like this is getting a little bit technical. So why don't we stretch these thoughts out and try to get them down flat and talk about what

it actually means for 3D universal space to be flat. But first, let's take a quick break. I'm Dr. Scott Barry Kaufman, host of the psychology podcast. Here's a clip from an upcoming conversation about exploring human potential. I was going to schools to try to teach kids these skills and I get eye rolling from teachers or I get students who would be like, it's easier to punch someone in the face. When you think about emotion regulation, like you're not going to choose an adapted strategy which is more effortful to use unless you think there's a good outcome as a result of it if it's going to be beneficial to you because it's easy to say like go you go blank yourself right it's easy it's easy to just drink the extra beer it's easy to ignore to suppress seeing a colleague who's bothering you and just like walk the other way avoidance is easier ignoring is easier denial is easier drinking is easier yelling screaming is easy complex problem solving meditating, you know, takes effort. Listen to the psychology podcast on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts.

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is space flat and the preceding preceding question is what does it mean for the for space to be flat because i guess space sort of seems flat to us you know it doesn't seem curved or bent to us at least in our immediate surroundings but we know that if you expand your your surroundings a little bit you see space time is flat, that's how gravity works, and that's what makes the moon go around the Earth, and the Earth around the Sun. But we're talking now about global curvature of space, which really means universal curvature of space, which actually sort of means observable universe curvature of space, right? Yeah, and we're trying to use our understanding of 2D space to sort of bootstrap our way to understand the curvature of 3D space. So if you're like on a flat surface

and you shoot two parallel lines out, like two laser beams, then they'll never cross each other. This is Euclid's famous geometry, and that's why we call it Euclidean geometry. These two parallel lines will never meet. And you can also do that in three-dimensional space. Right now, just imagine the universe is having three directions, shoot two parallel lines, but in any direction in X, Y, Z,

they will never meet in flat space. The extension of flat space from 2D to 3D is pretty straightforward. I wonder if we even have to go to a 2D analogy. Why can we just talk about the curvature space in 3D? Yeah, I think 3D flat space is pretty straightforward, but it can help us understand the curved space to start in 2D, or at least let's give it a shot. In two-dimensional curved space,

if you fire two laser beams in the same direction, they will eventually cross. Like if you're on the surface of the earth and you fire two laser beams in the direction of the North Pole, they'll cross when they hit the North Pole, right? What? I think this is why it's confusing. And I wonder if we can just stick with 3D.

Like 3D flat space, if I shoot two lasers out in space, they're never going to meet. These two laser beams are never going to meet, right? Now, let's talk about curve 3D space. I shoot two lasers and the lasers are going to do one of two things, right? They're either going to come towards each other or bend away from each other. That's right. And whether they come towards each other and away from each other tells you the sign of the curvature. Positive curvature, they'll come towards each other, negative curvature.

They'll veer away from each other, never meet. Now, this is super weird because. what's bending the path of the lasers? Just the curviness of space? Lasers and light follow the curvature of space. They're like tracers that tell you how space is curved. So light moves in straight lines through curved space time, right? But that leads to curved motion in space.

So you're saying that space might have a property to it called curvature, which would, to us, make the light beams not go in a street line. That's right. If you assume space is flat, then light appears to be moving in a curve. If, however, space itself is curved. Those grid lines themselves are curbing. Then light is moving along those grid lines. It's just the grid lines themselves are curved.

Okay. So now, I feel like there's a third possibility. So, like, if I have a laser shooter on my right hand and a laser shooter on my left hand, and I shoot them perfectly parallel to each other, if space is flat, they're just going to keep going straight parallel forever. But if space is curved, there's some things that can. do they can bend towards each other away from each other, but I feel like they could also like bend perpendicular to each other. Like maybe my right laser beam drifts up and my left

laser beam drifts down. What does it, what would that mean? Isn't that the same as bending away from each other? I guess if I just turn my head sideways then. What if they spiral around each other? Can space be twisty? Space can have all sorts of weird combinations. I mean, in general relativity, space doesn't even have to be totally connected. why a laser beam can like disappear and appear somewhere else, right? That's basically what a wormhole would be. We're trying to talk about pretty simple constructions of space where all you have is a single overall curvature.

I guess if I shoot my laser beams and they go past a large, massive object in space like the sun, they're going to curve. And if they're maybe on opposite or different size of the sun, they're going to curve in a different way. And as they go through a galaxy, they're going to get pushed this way and that way the laser beams, but I think you're talking about like if I shoot them maybe really far apart from each other and let them go for a really, really long time on average, are they going to be moving towards each other or away from each other?

That's what you mean by global curvature, right? Yeah. And your analogy is great because it lets us make a connection between local curvature and global curvature. Local curvature, as you say, is like, is there a star there that's going to bend the path of my light? And we sort of got our minds around a little bit, the general that light is bent by masses. Even though light has no mass, it follows the curvature of space and it's bent, right? Now, instead of having a local mass, like a star, a single point of really high density, take that star and spread it out throughout the whole universe instead. So now the universe is filled with constant density of matter or energy. That creates a curvature of space

that's constant. It's not like, oh, there's a lot of curvature near that star. Let's have a little curvature everywhere instead of a lot of curvature in just one spot. And that's one way. think about the global curvature of space. Think about a universe uniformly filled with a certain matter and energy density. So like if the universe was infinite and was filled with like evenly spread out gas or an evenly spread out star, I guess what would happen to a laser beam? Would it still curve or would it go straight? It depends on the density of that stuff, right?

There's a certain critical density of energy in the universe. Below a certain level, the universe will be negatively curved. If it has exactly the right critical energy at this knife's edge, the universe will be flat. If it's more than that critical energy, the universe will be curved. So the curvature of the universe itself, of space, is connected to the energy density of stuff in the universe relative to this critical threshold. I guess that's a little counterintuitive because I would think that if the universe is filled evenly with the same energy or gas or matter or energy, then the laser beam would just go straight because it's a little counterintuitive because it's a little bit. It's being pulled the same way in all directions. Yeah, unfortunately, general relativity isn't always intuitive.

And if you add enough stuff to the universe, it curves up. It makes the universe effectively like a sphere. That's only consistent with universes that have a positive curvature. Because imagine you take every bit of space and you make it bendy. Now think about like what shapes can you build with that. If you only have curvy pieces, all you can do is build the surface of a sphere. or all you can do is build a three-dimensional version of the surface of a four-dimensional sphere

if all you have are bendy pieces. Yeah, I guess I'm still confused because I'm imagining this scenario where the whole universe is filled with the same gas or an evenly distributed star. If I shoot a laser beam, which way does it curve if the universe is positively curved? So it curve up, down, left or right? In a universe with positive curvature, if you shoot a laser beam, it looks to you like it's going straight,

but then it hits you in the back of the head. wouldn't necessarily hit me in the back of my head. In a universe that's uniformly filled with matter, that's positive curvature, it will loop back around. It's like being on the two-dimensional surface of a three-dimensional sphere. But I guess it might loop around a few times before it hits me in the back of the head. Any point in the sphere is the same. So it doesn't really matter where you are, which direction you shoot it.

You always get the same result from that point of view. I feel like now it's getting a little bit into this idea of how space is connected to itself, which is that the case? Is the curvature space necessarily the same as how space is connected to itself, whether it loops around itself? It's definitely connected, right? It's not the same, but it's definitely connected.

If space is flat, then the universe can be infinite. If space is positive curvature, then the universe can't be infinite. It can be finite, but also have no boundary. Just the way like the two-dimensional surface of a 3D sphere can be finite but unbounded because it has positive curvature. So these two ideas are definitely connected.

topology of space, the large scale shape of space and the curvature of space. The two things are definitely closely linked. The curvature of space, you can deduce from the density of matter in that space because general relativity connects those two things. Now, that was one laser beam. Now I take two laser beams and they shoot it off into 3D space and let's say that the universe has positive curvature. What's going to happen to these two laser beams? They're eventually going hit each other? They will eventually cross, yeah. And if the universe is not positively curved, if it's negatively curved, then they'll never hit each other. They won't hit each other. They'll veer apart. All right. I think that gives us as good of an explanation of what the curvature

space is in the universe, right? And all of these things together control the future of the universe, like the curvature and the topology, the matter density of the universe, that plus like the dark the universe, all these things work together to determine how fast the universe is expanding, is it expanding or is it collapsing, or is it steady state with no expansion? All of these things play a role in determining the future of the universe. Cool. Well, let's maybe talk about how you might measure the flatness of the universe in. Like, how do we know whether the universe is flat or not? So what we do is we measure this energy density. And of course, the caveat is we can only measure it in the observable universe. We can't measure outside.

And so when we say the universe here, we always really just mean the observable universe. What we can do is measure the energy density. And we can say, is there enough stuff in the universe to make it curved positively so it wraps up on itself? Is there the critical density so the space is flat? Or is there less than the critical density so the universe is open with negative curvature? So the way we do that is by measuring the amount of stuff, the energy density of stuff in the universe. Oh, I see.

You measured the density of stuff. But I guess we never covered why the density of stuff. stuff determines the curvature of space. Like, why is there a critical amount that makes it negative or positive? Like, wouldn't any amount of stuff in the universe make the universe positively curved? Yeah, that is a little counterintuitive, but a totally empty universe, one with no matter or energy in it at all, would not have flat space. It would have negatively curved space.

So you need a little bit of stuff in the universe to counteract that. Whoa, wait. So if I had an empty universe, like no stars, no planets, no galaxies in it, and I shoot to laser beams, they're going to diverge from each other? They're not just going to stay parallel to each other forever? Yeah, that's right. This is one of the situations we can actually solve in Einstein's General Relativity situation with nothing in the universe, totally empty, no matter, no energy, no dark energy.

In that case, the universe has negative curvature. So you have to add stuff to the universe to make it have no curvature or positive curvature. Oh, so even no dark energy, like this sort of necessary amount of stuff, and it is not related to the expansion of the universe either. Or do you assume the expansion of the universe or not? This does not determine the expansion of the universe. All these pieces together, the curvature, the density, the dark energy, all these things together determine whether the universe is expanding,

whether that expansion is accelerating. It's a whole complex dance. But just the curvature of the universe is determined by the matter and energy density. If you have a certain amount, then you sort of counteract the natural negative curvature of space and you get a flat universe. If you have more than that, you get a positive curvature. If you have less than that, you get negative curvature.

So a flat universe is sort of balanced on a knife's edge. You have to have exactly the right amount of stuff. And it's not a big number. Like the critical density right now is about five protons per cubic meter. I guess that's weird that space by itself has negative curvature. Like pure space, OG space, if you shoot laser beams, they would diverge. Isn't that weird? Because shouldn't space be like neutral or totally?

empty? Well, our intuitive concept of space doesn't even allow it to be bent, right? So you have to already let go of those intuitive ideas and think that space is something quite different from what we imagined as these weird properties. It's a little bit more complicated than what we've described because the amount of stuff you have to add to space to avoid this negative curvature actually changes over time. It depends also on the expansion of the universe. So there's a lot of complex moving parts here that we're trying to distill down. But I guess the main takeaway is that space by itself has negative curvature, but because we have stuff in it, matter and energy, then it's possible for space to be flat because that's what the effect of energy and mass does

to space is it makes it more positively curvy. Yeah, and we can measure the curvature of space by measuring the matter and energy density of the universe. So we go out, we measure that, and that tells us what curvature we have in our universe. The magnitude of that curvature can also change. The sign can't. If you have positively curved space, it's always going to be positively curved. But it can get more positively curved or less positively curved.

Like a universe has positive curvature can collapse on itself, making itself more and more positively curved. Or a universe that's open can expand really, really rapidly and get less and less curved. But they can't flip over. You can't start from a universe that's positively curved and end up with the universe that's negatively curved. Unless maybe the density of energy and matter decreases enough. Isn't that possible? No. As I just said, it depends on that density.

What if the density changes? The density definitely does change, right? And we'll talk a little bit about how that density is changing and how we understand how it's changing, but you can't change the curvature of the universe. You can't go from positively curved space to negative the curved space. That would correspond to like changing from a finite universe to an infinite universe, which you can't do. Or you can't take the service of a sphere and snap it out to an infinite plane. You can pop a balloon. You can flatten a birthday cake.

That's one of the confusing things about these 2D analogies, right, is that you're imagining it in a 3D space. You're thinking about really a 2D service on a 3D sphere. But in those analogies, the 2D surface is all there is. So you can't really flatten it. All right. Well, let's dig into what would happen if you change the density of matter and energy in the universe.

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See? Listen to no such thing on the Iheart radio app, Apple Podcasts, or wherever you get your podcasts. All right, we're asking the question, why is space flat? Or I guess why space is so flat? Because it's maybe flatter than what you expected? Yeah, when we go out to measure the curvature of the universe, we find something kind of surprising.

We find that it's really pretty flat. Like there's this critical density, five protons per cubic meter. And we go out to measure the amount of stuff in the universe. We add up all the mass, the stars, the galaxies, the dark matter, and also the dark energy, all of that stuff. It adds up to like very, very close to, exactly the critical density. It's within one percent, which is about our uncertainty of the critical density, which tells us that space is either flat or very, very close to flat. And that's

kind of a surprise because we don't think the universe likes to be flat. I guess before we go on, I have more questions about what you just said. Well, first of all, how do we measure the mass and energy density of the universe? And second of all, how do we know what amount you need for the universe to be flat. So how we measure it is several different ways. We can use like the cosmic microwave background radiation. This is radiation from about 300,000 years after the Big Bang, when the universe was very hot and dense with his bright plasma. Then it cooled off and formed neutral atoms and light could propagate. We can still see that light. That light was made everywhere in the universe and it's flying around everywhere. And some of it has just reached

Earth from places that used to be very, very far away. And we can use it to sort of look at what the universe looked like at that time. And there were little bumps and wiggles in it. It's not completely smooth. It's like a little bit of a frothing quantum plasma. And from the size of those wiggles, we can tell how much energy density there was in the early universe. Based on some theory that you have about how the universe formed and how these things balance out with space. Relying basically just on general relativity. I mean, we assume some model of the universe, but it's based in general relativity. It doesn't depend on how the universe formed or what came before it. It just depends on like the size of those fluctuations in the early universe and then how those propagate

through an expanding universe to us. Okay. So that's one way to measure it. So that measures the total energy density like the dark energy plus the dark matter plus the normal matter, density in the early universe. We can also measure by looking at the acceleration of the universe, like looking at supernova seeing how fast they're moving away from us. We're looking at Cephids. This expansion rate of the universe also helps us measure these various components. So the component, of the energy density of the universe are the dark energy, the normal matter, and the dark matter. And the supernova measurements, the acceleration of the universe help us measure the dark energy component minus the matter component, because that determines the expansion of the universe.

So there's like a bunch of different components here, and we have different ways to measure each ones or combinations of each one that help us pin down exactly what those contributions are. Dark energy is like 70% of the critical density, matter is like 30% of the critical density, where we're most of that is dark matter. And they add up to basically this critical density. This is from this C&B measurement or from all measurements? The C&B measurement tells us the total density. The supernova tells us the dark energy minus the matter, the difference between those two because they work against each other when controlling the expansion of the universe. There's another measurement, the baryon acoustic oscillations that tells us about like how matter was sloshing around in the early universe and made these sound waves back when the universe was super duper dense

sound traveled at nearly half the speed of light and the speed of that sound depends on the density of matter in the universe. And we can still sort of see the universe ringing from those oscillations in the early universe that separately measures just the matter portion. So we have these different pieces of the pie and they all add up to make exactly one pie. And the fascinating thing is that they didn't have to, right? It could have added up to anything. It could have added up to be twice the critical density or half the critical density, but it adds up to bang on just the critical density to within 1%. I see.

So you're saying we've measured the energy density of the universe and according to what we think is the laws of the universe, according to general relativity, we have just enough mass and density to make the universe flat, which means if I shoot two lasers

out there in space, they're not going to hit each other, they're not going to drift apart, they're not going to hit me in the back of the head. Those two laser beams are just going to keep going forever. Exactly. And this is kind of a surprise to physicists

because they think the universe doesn't like to be flat. Like the flatness of the universe is not a stable thing. If you're just above the critical density, if you're like a little bit more than the critical density, then the universe tends to collapse and become more and more dense

and you move away from the critical density. If you have less than the critical density, you're below it, then the universe is open. It tends to expand and dilute itself away from the critical density. So either you're exactly bang on the critical density in which you're stable, like a pencil balance on its tip,

or you're a little bit above or a little bit below, and then you very quickly veer away from it. So it's sort of a mystery how we're still so close to the critical density after billions of years. What do you mean it's unstable like a pencil? What does that mean? It's unstable and that if you move away from the critical density a little bit, the universe moves away even more.

It's like a pencil balance on its tip, right? It's unstable. You give it a tiny little push, a fly lands on it, air blows by it really gently. It's going to tend to fall over. Wait till like if you measure the density of the universe and it's a little bit of more than the critical amount of density you need for a flat universe, then the density is going to increase over time? Like the universe is going to get more and more denser?

Exactly. If you have more than the critical density, the universe will contract, right? And things will get denser and denser. You'll end up with like a big crunch. You mean like the expansion of the universe will reverse? Yeah, exactly. In the opposite scenario where you're less than the critical density, things expand forever and things get more and more dilute.

So the density drops, right? As the universe expands, the density of mass. matter drops. As the universe contracts, the density of matter increases. And so if you're not at the critical density, you tend to veer away from it pretty quickly. And we're like billions of years into the history and we're still super close to the critical density, which was a big question in cosmology. How can you stay so closely balanced so long? I feel like now we're tying it to the expansion. So the critical density is tied to the expansion. Like if the universe is positively curved, then the universe is going to contract eventually? The courage of the universe

definitely plays a role. The critical density and the curvature, together with the amount of dark energy, determine the expansion. You can have a universe that's positively curved and expanding if you have enough dark energy, because dark energy can overcome this critical density that you could have a universe which expands. But in the simple scenario where you take out dark energy for the moment and just have a universe with only matter and radiation, which was basically the scenario of our universe for the first nine billion years when dark energy was negligible, then a universe above the critical density will contract and increase the density. And the universe below the critical density will expand and decrease the density.

So they did this calculation. They're like, well, in that scenario, how close did the universe have to start to the critical density to end up at 1%. The answer is we had to be within the critical density to within 10 to the minus 62. If you're anything above that, then the universe would have expanded like crazy or contracted like crazy. So it seems really, really weird. that we end up with a universe so close to flat when the universe likes to veer away from flatness. Well, that's a really tight requirement for this density

that we needed at the beginning of the universe. It kind of seems like too much of a coincidence. It does seem like too much of a coincidence. And physicists don't like coincidences because the density of stuff in the universe doesn't seem to be determined by anything. It could have been anything. So for it to be like exactly close to one complete pie

of the critical density seems too neat. Physicists like a reason for these numbers to love. up and there is an explanation for it and the explanation is cosmic inflation. So you know how the universe is expanding now and that expansion is accelerating? We also think that the universe expanded very, very early on in its history, but like a huge factor. This accelerating expansion we call inflation, it's an expansion of like 10 to the 30 in like 10 to the negative 30 seconds. And this kind of accelerating expansion tends to push the universe towards flatness. flatness. It makes the universe more flat. But isn't it still sort of too much of a coincidence?

Like I wonder if maybe our theories are wrong or maybe there's some sort of mechanism that keeps the universe flat. Well, we don't know if inflation is true and it's just one of the possible scenarios and, you know, maybe it's just a coincidence and we just happen to live in a universe that was that close to flat that we ended up in a universe that didn't over expand or didn't collapse on itself. But inflation makes it less sensitive. Inflation says, you know, you could started with lots of different densities and inflation would have made your universe have the critical density early on. So you could have started with half the density or one and a half times a critical density and inflation would have made your universe super duper close to the critical

density. Meaning like you might have started with too much stuff in the universe but then some mechanism stretched out the universe enough so that you had the critical density. Exactly. The math of inflation, in fact of any accelerating expansion in the universe tends to push the universe back towards the critical density. So if you had too much, inflation would stretch out the universe in just the right way to make it have the critical density. Just like if you're standing on the surface of a tiny sphere, like a beach ball, it looks really, really curved. But then if somebody expands it rapidly by a factor of 10 to the 30, then now you're standing on the surface of a huge sphere. It looks flat, right? So a bigger sphere looks flatter than a small

sphere. In the same way, inflation pushes the universe towards less curvature. Does it also work the other way? Like if the universe had started with too little stuff in it, the density was too small, would inflation have somehow adjusted or slow down or compress the universe somehow? Would you have had deflation in order to keep the universe flat? Yeah, that's a great question. It does.

It pushes it towards critical density from either direction, which is pretty cool how the math works out. So it does do deflation. Well, they still consider inflation because you're still stretching it out. you know, imagine like a hyperbolic surface. You stretched it out. So the negative curvature goes towards zero curvature. So inflation drives you towards zero curvature from either direction.

So it's more like stackflation. Or less flation. I don't know enough economics to know if an analogy is accurate or not. Yeah, I mean it sounds like something they say in the news. And one fascinating thing about that is it means that our universe right now is driving back towards flatness. Like the brief history of the universe is you have probably inflation, which makes the universe mostly flat. And then you have a matter and radiation dominated time when the universe is then driven by this critical density. And it continues to expand, though that expansion is decelerating because of the matter-dominated nature of the universe.

And then like six billion years ago, dark energy took over, right? Because the expanding universe dilutes out the matter and radiation while dark energy grows as a fraction. So now we have an accelerating expansion again, which does the same thing. any accelerating expansion of the universe pushes you back towards zero curvature. Interesting. I guess what that makes me think

is that maybe the universe is flat. Like it's just flat. It's infinite and flat. And all these things we're seeing, all these measurements and all these theoretical concepts, they kind of have to work out to a flat universe,

and that's what we're seeing. Like maybe it's not sort of like this mystery or this universe sitting on a nice edge. It's just that's just the way the universe is. And to us, the math and the measurements

look like it could gone either way, but it could never had a chance. Yeah, it's possible, right? In the equations of general relativity, this is curvature parameter. It's either plus one, zero, or minus one. And it can't change again, right? You can't go from a negative curvature to a positive curvature. And our universe is just one of those. The interesting thing, though, is that to have K equals zero, to have zero curvature, you really have to have the critical density of matter and energy. So it sort of depends on what question you ask. Like, you could ask, well, which of the three curvatures is it? Well, maybe it's just zero, like you say.

But if you think about it in terms of the continuous spectrum of matter and energy density, then it has to have exactly the right number, which seems like one option out of an infinite number instead of one option out of three. Unless the universe sort of like prevents the matter and energy to be anything else, in which case that wouldn't make sense, right? Yeah, it's certainly possible. And these questions are really basic and also simple. And in a few hundred years, they might look back on this and be like,

ha, ha, how do they imagine they lived in a curved universe? what a bunch of idiots. What a bunch of flat-footed idiots. But these are the questions we're asking, and we don't know. And the equations of general relativity allow for all three kinds of universe, negative curvature, flat, or positive curvature. We just don't know which of those we live in and why. We've measured space to be flat.

And you're right. Either it just is flat and it started out balanced on that knife's edge and it will always be there perfectly balanced. Or it has a little bit of curvature, but then we don't understand why it's still so flat, unless you do something early on like inflation. Well, I think the idea is that maybe the universe is flat, which would mean that the pencil is not upside down,

like maybe the pencil is hanging from the tip. And that it can only sort of be that hanging down and the universe would push it down if you try to move the pencil. That's a possibility. Sounds like it's still a mystery. Why the universe is flat, we're measuring it to be flat and it seems to be staying flat, which means that the universe either is flat

or the universe is not. flat, but something is making it suspiciously flat. Those are the two options, right? Exactly. If it's not exactly flat, then something is keeping it very, very close to flat. Which would be the universe, which means the universe is flat. The universe is either exactly flat or it likes to stay very close to flat. I'm just trying to propagate flat universe theories.

And say that it's all just a conspiracy by the universe. You're curving my brain, man. All right. Well, the next time you look at Into Space, Think about what happens to those photons that you're seeing? Did they come straight at you or did they get bent by space? Are those photons curving their way through the universe, maybe even a close circular universe, or did it come straight at you from really far away?

Either way, we're grateful that photons are arriving here on Earth and that we're smart enough to figure out the messages that they send about the nature of this incredible cosmos. Or at least we think we're smart enough, might just be falling flat on our faces. We're feeling good about being smart whether or not we are. All right, we hope you enjoyed that. Thanks for joining us. See you next time. Thanks for listening.

And remember that Daniel and Jorge Explain the Universe is a production of IHeart Radio. For more podcasts from IHeart Radio, visit the IHeartRadio app, Apple Podcasts, or wherever you listen to your favorite shows. It's important that we just reassure people that they're not alone, and there is help out there. The Good Stuff podcast, Season 2, takes a deep look into One Tribe Foundation, a non-profit fighting suicide in the veteran community. September is National Suicide Prevention Month, so join host Jacob and Ashley Schick as they bring you to the front lines of One Tribe's mission. One Tribe, save my life twice. Welcome to Season 2 of The Good Stuff. Listen to the Good Stuff podcast on the Iheart Radio app, Apple Podcasts, or wherever you get your podcast.

Let's start with a quick puzzle. The answer is Ken Jennings' appearance on The Puzzler with A.J. Jacobs. The question is, what is the most entertaining listening experience in podcast land? Jeopardy Truthers believe in, I guess they would be. conspiracy theorists. That's right. They gave you the answers, and you still blew it. The Puzzler.

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