Daniel and Jorge Explain the UniverseDaniel and Jorge talk about what it means for space to be curved, how we measure it and why the answer is a puzzle.
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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.
I guess it could go either way. You know, nobody likes their soda flat or they 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 it sphericle, 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 Hojorhey mc, cartoonist 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 metaphorical, but also literally and physiologically, I have flat feet. So yeah, I wear inserts.
Does that have to make you taller? 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 life 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 it.
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, 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 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, 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? Or 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 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 its size, its 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 one questions to ask about why the universe looks this particular way, especially about the curvature of space.
To be 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.
M 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 got to send 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 a space more complicated twisting and curving on a global sense, we're talking here 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 is being kind of like flat, right, not weirder in curve.
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 counter into what is actually happening. Are we gonna 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 two questions at Danielandjorge dot 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 shot out from the Big Bang in every direction in equal measure, and therefore it stayed flat to this day.
I think that we're not one hundred percent 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 dimension on the plant has to do with two D.
I think the flat space is somehow stable equilibrium points, so the space will eventually evolve into the flat version.
I was 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 multi dimensional. I don't know what really is meant by that maybe like stuff forms discs, 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 discs 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 implies 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.
M Yeah. If somebody like bakes your 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 two dimensional cake would be pretty oh calorie.
I don't think the calorie 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.
As if a truck runs over it, 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 roads smootheners they have in cartoons all the time. That's crushing wily 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 flatted 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.
But 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 there's sort of two different concepts of there, 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 it 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, 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 curve space makes me think of like a road. Like a road is curved, and so anything that tries to follow a stradeline on that road is going to follow the same path. But maybe in real life it would kind of depend. Right, I don't know how fast you're going or what your mass is, or right, isn't it.
Yeah, curve 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 curve road of space, and space moves your car forward. You sort of like guides it along the curvature of space and fundamensional 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 like if I throw a bowling ball at a low speed and a high speed, and I threw a feather at a low speed and as high speed, 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, right, So it definitely depends on the velocity of the object as it moves through curve space. So that's all inertial motion, that's motion under no forces, just the curvature of space.
So 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, space like 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, 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. Like if you enter a pipe and 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, 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 doue 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 three D 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 this 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 it's all equations in general relativity, not me. They can only solve those in certain situations, in situations where the who like the universe is empty or the universe is filled with matter, but that matter is perfectly smooth, like, nobody can solve the general relativit 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 this 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.
Mmm, 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.
Well, 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 this and looks pretty flat. But actually if you sort of keep going or you're 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 try to measure the curvature of the Earth. Imagine you lived on like a truly flat part of the 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 of space sort of is kind of about how mass spans space, and how the Moon goes around the Earth and the Earth goes around the Sun through curve 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 three D. So we do this thing where we talk about two dimensional versions. Sometimes that's helpful and 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 three D space. And 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 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 one hundred and eighty 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 one hundred and eighty. 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 one eighty. So those are two D examples of curved surfaces. Then you have to extrapolate those two three D space, and it's very similar to a lot of the ideas carry over.
I feel like this is getting a little bit technical, So when't we stretch these thoughts out and try to get them down flat and talk about what it actually means for three D universal space to be flat. But first, let's take a quick break.
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All Right, we're asking the question why is space so flat? And I guess the preceding question is is space flat? And the preceding preceding question is what does it mean for this for space to be flat? Because I guess base sort of seems flat to us. You know, it doesn't seem curve or bent to us, at least our immediate surroundings. But we know that if you expand your your surroundings a little bit, you see that space time is flat. That's how gravity works, and that what makes the Moon go around the Earth and the Earth around go 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 two D space to sort of bootstrap our way to understand the curvature of three D 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 xyz they will never meet. In flat space, the extension of flat space from two D three D is pretty straightforward.
I wonder if, like we even have to go to a two D analogy. Why can't we just talk about the curvature space in three D?
Yeah, I think three D flat space is pretty straightforward, but it can help us understand the curved space to starting two D, or at least let's give it a shot. In two dimensional curve 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 in the north pole, bill cross when they hit the north pole, right.
What I think this is why it's confusing, And I wonder if you can just stick with three D, like three D flat space. If I shoot two lasers out in space, they're never going to meet. These two laser beams, they're never gonna meet. Right now, let's talk about curve three D 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 curveness 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 curving, 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 being drips down. What does what would that mean?
Isn't that the same as bending away from each other?
I guess if I just turn my head sideways, 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 can doesn't even have to be totally connected. So a laser beam can 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 they go past a large massive objects in space, like the Sun, they're gonna curve, And if they're maybe on opposite or different sides of the Sun, they're gonna curve in a different way. And as they go through a galaxy, they're gonna 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.
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 life. And we sort of got our minds around a little bit. The general reativity 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 with 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 to 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 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 bend y. 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 imagine this scenario where the whole universe is filled with the same gas or evenly distributed star. If I shoot a laser beam, which way does it curve? If the universe is positively curve, so curve up, down, left to 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.
What it 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 maybe it might loop around a few times before it hits me in the back of the head.
Any point on a sphere is the same, so it doesn't really matter where you are which direction you shoot it. You always get the same results.
From that point of view, I feel like then now it's getting a little bit into this idea of the how space is connected to itself, which is at the case is a curvature of space necessarily the same as how space is connected to itself, whether 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 three D sphere can be finite but unbounded because it has positive curvature. So these two ideas are definitely connected. The 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 three D 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 to hit each other.
They will eventually cross. Yeah.
Mmm.
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.
M all right. I think that gives us as good of an explanation of what the curvature space is in the universe, right.
M hm.
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 energy of 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, 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. All 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 that 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 measure the density of stuff. But I guess we never covered why the density of 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 curve?
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. 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 in 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 curve 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're less than that, you get negative curvature. So a flat universe is sort of balanced on a knife's edge. You have to have like 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 choose laser beams, they would diverge. Isn't that weird because shouldn't space be like neutral or totally empty.
Well, 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 mess 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 the universe has positive curvature can collapse on itself, making itself more and more positively curved, or 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 the universe has positively curves and end up with the universe that's negative the.
Curved, unless maybe the density of energy and matter decreases enough. Isn't that possible. No, As like you 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 negatively curve space. That would correspond to like changing from a finite universe to an infinite universe, which you can't do, right. You can't take the service of a sphere and snap it out to an infinite plane.
You can pop a balloon, you can flat that birthday cake.
That's one of the confusing things about these two D analogies, right, is that you're imagining it in a three D space. You're thinking about really a two D service on a three D sphere. But in those analogies, the two D 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, and then let's ask the big question why is the universe flat? But first, let's take another quick break.
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All right, we're asking the question, why is space flat or I guess why space so flat because it's maybe flatter than what you expected.
Yeah, when we go out to measure the curvage 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 three hundred thousand years after the Big Bang, where the universe was very hot and dense with its bright plasma, and 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. Doesn't depend on how the universe formed or what came before. It just depends on 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 it by looking at the acceleration of the universe, like looking at supernova seeing how fast they're moving away from us, or looking at cephids. This expansion rate of the universe also helps us measure these various components. So the components of the energy density of the universe are the dark energy, the normal matter, and the dark matter and the super KNOVEA 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 one's or combinations of each one, to help us in down exactly what those contributions are. Dark energy is of like seventy percent of the critical density, matters like thirty percent of the critical density, where most of that is dark matter, and they add up to basically this critical density.
This is from this CMB measurement or from all measurements.
The CMB 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 buryon 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 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 write 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 one percent.
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 the part, they're not going to hit me in the back of the head. Those two laser beings are just gonna 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 and a little bit below and then you very quickly veer away from it. So 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 in 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 have 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 to Like, if you measure the density of the universe and it's a little bit 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 lessen 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 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 of the universe, 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 couragere 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, and then the 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 do the universe have to start to the critical density to end up at one percent. The answer is we had to be within the critical density to within ten to the minus sixty two. 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, it seems too neat. Physicists like a reason for these numbers to line 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 ten to the thirty in like ten to the negative thirty seconds. And this kind of accelerating expansion tends to push the universe towards 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.
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 happened to live in a universe that was that close to flat that we ended up in the universe that didn't overexpand or didn't collapse on itself. But inflation makes it less sensitive. Inflation says, you know, you could have 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 the 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 somebody expands it rapidly by a factor of ten to the thirty. Then now you're standing on the surface of a huge sphere. It looks flat, right, So a bigger sphere looks flatter, and then 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 mood inflation have somehow adjusted or slowed 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 it 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.
But 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 in a radiation dominated time when the universe is then driven by this critical density and it continues to expand that 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 in the universe pushes you back towards zero curvature.
Mmm.
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 theoretic 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 that the universe is. And to us, the math and the measurements look like it could have 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.
Well, unless the universe sort of like prevents the matter and energy to be anything else, Chase makes 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 us and be like, hah, 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 relatio they 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 tam 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.
At least we think we're smart enough. Might just be falling flat on our facebooks.
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 iHeartRadio. For more podcasts from iHeartRadio, visit the iHeartRadio app. Apple podcasts or wherever you listen to your favorite shows. When you pop a piece of cheese into your mouth, you're probably not thinking about the environmental impact. But the people in the dairy industry are. That's why they're working hard every day to find new ways to reduce waste, conserve natural resources, and drive down green house gas emissions. House US dairy tackling greenhouse gases. Many farms use anaerobic digestors to turn the methane from manure into renewable energy that can power farms, towns, and electric cars. Visit you as dairy dot COM's Last Sustainability to learn more.
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