Speaker 1: Hey, Orge, I'm going to say a word, and I
Speaker 1: want you to tell me if you think it sounds
Speaker 1: like a positive or a negative idea.
Speaker 2: All right, go for it.
Speaker 1: The word is flat.
Speaker 2: I guess it could go either way. You know, nobody
Speaker 2: likes their soda flat or they are jokes to fall flat.
Speaker 1: But I sure do like my bed to be flat.
Speaker 2: But do you like your tires to be flat?
Speaker 1: No? But I do like my roads to be flat.
Speaker 2: Does that mean you want the earth to be flat?
Speaker 1: I like it spherical, But I also like mountains, so
Speaker 1: I guess I'm anti flat earth.
Speaker 2: Do you like falling flat from a mountain?
Speaker 1: I like landing flat on my feet.
Speaker 2: I think this discussion has run out of air.
Speaker 3: Hi.
Speaker 2: I'm Hoorhey, mccartoonist and the author of the book Oliver's
Speaker 2: Great Big Universe.
Speaker 1: Hi, I'm Daniel. I'm a particle physicist and a professor
Speaker 1: at UC Irvine, and I'm also flat footed.
Speaker 2: Are you saying metaphorically or you know, physiologically?
Speaker 1: Well, your questions often catch me flat footed, so that's metaphorical,
Speaker 1: but also literally and physiologically, I have flat feet, so yeah,
Speaker 1: I wear inserts.
Speaker 2: Does that have to make you taller you like Tom Cruise,
Speaker 2: I don't wear heels.
Speaker 1: No, I wear inserts to avoid crippling pain when running.
Speaker 2: Sounds like the solution is just not to run life
Speaker 2: flat on your back.
Speaker 1: Yeah. I'm working on a floating recliner I can live
Speaker 1: in for the rest of my life and float around.
Speaker 2: There you go. You can attach like a bicycle pedal
Speaker 2: and maybe get your workouts that way.
Speaker 1: Yeah, that's great for going upstairs.
Speaker 2: Yeah exactly. But anyways, welcome to our podcast. Daniel and
Speaker 2: Jorge Explained the Universe, a productive of iHeartRadio.
Speaker 1: Where we take all the twists and turns and curves
Speaker 1: of this crazy universe and try to flatten it all
Speaker 1: out for you. We try to untangle all of the
Speaker 1: mysteries of the nature of matter, the forces, the energy,
Speaker 1: the geometry of space time, the size and shape and
Speaker 1: history of the universe and make a nice, smooth story
Speaker 1: for you to understand.
Speaker 2: That's right, because it is an amazing universe full of
Speaker 2: stuff inflated with amazing and incredible physics and stars and
Speaker 2: galaxies and planets and particles for us to wonder at
Speaker 2: and for us to I guess poke it.
Speaker 1: There's so much that's amazing about the universe. And sometimes
Speaker 1: you can have two amazing facts that seem to be
Speaker 1: in conflict, Like, on one hand, it's amazing that we
Speaker 1: still don't really know so many basic things about the
Speaker 1: nature of the universe. How big is it? What is
Speaker 1: its shape? How did it all come to be? We're
Speaker 1: so ignorant about the environment in which we live. And
Speaker 1: on the other hand, it's kind of amazing that we
Speaker 1: know anything about the universe, and then we've only lived
Speaker 1: on one tiny little dot and one random little corner
Speaker 1: of the universe and never really left.
Speaker 2: Yeah, it's amazing what we can learn just from this
Speaker 2: little corner of the universe. And as you said, how
Speaker 2: we can ask these big questions about how everything is
Speaker 2: the way it is and why it is the way
Speaker 2: it is, Like, for example, we don't know if the
Speaker 2: universe is flat footed or not.
Speaker 1: Does the universe even like to run? Or does just
Speaker 1: want to sit on the couch and eat snacks all day?
Speaker 2: Yeah, just sit around and spin.
Speaker 1: It has big consequences for the curvature of the universe.
Speaker 2: It is getting bigger and bigger, so you know, maybe
Speaker 2: it could use a little bit of exercise. It's getting
Speaker 2: wider and wider per second.
Speaker 1: I think we should be universe positive on this podcast.
Speaker 1: You know, universe just be whatever shape you are, We
Speaker 1: love you.
Speaker 2: Yeah, yeah, true, true, true. I guess we should love
Speaker 2: the universe the way it is.
Speaker 1: It's the only universe we got, so might as well
Speaker 1: love it.
Speaker 2: Even if we don't understand it. I guess all the
Speaker 2: time we should, you know, take it for what it is.
Speaker 2: That's kind of what science is, right, taking things for
Speaker 2: what they are.
Speaker 1: Taking things for what they are are, absolutely, but then
Speaker 1: always asking why are they this way? Why couldn't they
Speaker 1: be some other way? Why do we live in this universe?
Speaker 1: Do we live in the only universe that's possible? Or
Speaker 1: are there many possible universes and we just happen to
Speaker 1: be in this one. So often we look around as
Speaker 1: we try to tell the story of the universe, and
Speaker 1: we ask those kinds of questions like does this make sense?
Speaker 1: This seems weird? Is it random? Or is there a
Speaker 1: reason for it?
Speaker 2: Yeah, because it is pretty perplexing out there the way
Speaker 2: things are. You know, there are amazing things like black
Speaker 2: holes that seem unexplainable, and there's sort of really weird
Speaker 2: things like quantum mechanics out there that kind of keep
Speaker 2: you guessing about what the universe is going to do.
Speaker 1: And as we put together this story of physics that
Speaker 1: tells us how the universe operates, what machinery is going
Speaker 1: on behind the scenes, that controls like what happens when
Speaker 1: two particles bump into each other, or house space curves
Speaker 1: and twists in the presence of mass. We start to
Speaker 1: tell a story about the universe, we notice, like, hm,
Speaker 1: the universe seems to do this kind of thing or
Speaker 1: do that kind of thing. And sometimes the story tells
Speaker 1: is very weird. It's very surprising. It's not one that
Speaker 1: makes sense to us or seems intuitive. It makes us
Speaker 1: wonder if maybe we're missing part of the story or
Speaker 1: if we're all just very very lucky.
Speaker 2: Yeah, and as you said, there are big questions about
Speaker 2: the universe that we still don't know about, like its size,
Speaker 2: its shape, and what it's going to do in the future,
Speaker 2: and also a very interesting question about its curvature.
Speaker 1: Yeah. As we develop our understanding of gravity and general
Speaker 1: relativity and we understand that space is weird and twisted
Speaker 1: and curved and that affects how things move, it also
Speaker 1: affects how the universe itself expands or contracts. So we
Speaker 1: have a lot of really fun questions to ask about
Speaker 1: why the universe looks this particular way, especially about the
Speaker 1: curvature of space.
Speaker 2: So today on the podcast, we'll be tackling the question
Speaker 2: why is space so flat? You mean as opposed to bumpy? Like,
Speaker 2: what would be the opposite of flat overinflated under pressure?
Speaker 1: Just like my arches, the opposite of flat would be curved, right,
Speaker 1: everybody likes nice curved arches for their feet, and the
Speaker 1: opposite of flat in the case of space or the
Speaker 1: universe would be curved.
Speaker 2: Well, it could also be well bumpy. I guess bumpy
Speaker 2: is also kind of curvy. It means you have a
Speaker 2: lot of little curves. You could have bumpy feet.
Speaker 1: Yeah, exactly, that's true. You got to sand those down
Speaker 1: a little bit. But in this case, yeah, we're talking
Speaker 1: about like the nature of space is space the way
Speaker 1: Euclid thought about it, You know, two parallel lines will
Speaker 1: never touch, or a space more complicated twisting and curving
Speaker 1: on a global sense. We're talking here about the curvature
Speaker 1: of the entire universe itself.
Speaker 2: Yeah, and this is I guess a pretty mind bending
Speaker 2: and space bending topic, because you know, I think we're
Speaker 2: all used to thinking of space, or at least empty
Speaker 2: space is being kind of like flat, right, not weird
Speaker 2: and curved.
Speaker 1: It's really hard to think about this in the three
Speaker 1: dimensions of our universe, and even the word flat is
Speaker 1: kind of confusing there. It comes really from thinking about
Speaker 1: a two dimensional version of the picture instead of thinking
Speaker 1: about space like I can move in three different directions,
Speaker 1: it's easier to think about it in two different directions
Speaker 1: because then we can like draw it on a piece
Speaker 1: of paper. So if you imagine like a sheet of
Speaker 1: graph paper, that's a flat sheet of paper, and two
Speaker 1: parallel lines on that piece of paper are never going
Speaker 1: to meet each other. When we talk about whether space
Speaker 1: is flat, we're asking a similar kind of question, but
Speaker 1: about three dimensional space, though it's harder to understand, like
Speaker 1: what curvature means in three dimensions than it is in
Speaker 1: two dimensions.
Speaker 2: Are you saying we're going to use a term that
Speaker 2: doesn't quite work or describe things or is counterintuitive to
Speaker 2: actually what is actually happening. Are we going to do
Speaker 2: that again?
Speaker 1: Yeah, that's exactly right. That's the story of.
Speaker 2: Physics being inadequate.
Speaker 1: We think we understand the universe, and then it surprises
Speaker 1: us and it sort of outgrows even like our ideas
Speaker 1: and forces us to like generalize these concepts like, oh wait,
Speaker 1: flattness can apply in three dimensions, not just two.
Speaker 2: Well, as usual, we were wondering how many people out
Speaker 2: there had thought about this question whether space and why
Speaker 2: space is so flat, and so Daniel went out into
Speaker 2: the internet to ask people this question.
Speaker 1: Thanks very much to everybody who participates. If you'd like
Speaker 1: to hear your voice answering these questions for this segment
Speaker 1: of the podcast, please don't be shy. Write to me
Speaker 1: two questions at Danielandjorge dot com. You'll have a good time,
Speaker 1: I promise.
Speaker 2: So think about it for a second. Why do you
Speaker 2: think space is flat? Here's what people had to say.
Speaker 4: I think space is flat because I think at the
Speaker 4: beginning there wasn't any room for stuff to be clumpy
Speaker 4: or lumped together or have little dips or gaps. And
Speaker 4: I assume that everything was shot out from the big
Speaker 4: Bang in every direction in equal measure, and therefore it
Speaker 4: stayed flat to this day.
Speaker 3: I think that we're not one hundred percent certain that
Speaker 3: space is flat. It just seems like it's flat because
Speaker 3: space has been inflated so much from our perspective. The
Speaker 3: analogy that I've heard before is kind of like standing
Speaker 3: on the surface of the Earth, where the curvature of
Speaker 3: the Earth is so large relative to us that it
Speaker 3: seems like it's flat.
Speaker 1: I'm not sure. I thought it was three dimensional.
Speaker 5: Plant has to do with two D.
Speaker 6: I think the flat space is somehow stable equilibrium points,
Speaker 6: so the space will eventually evolve into the flat version.
Speaker 7: I was sneaking suspicion it's not so flat, but it
Speaker 7: just looks that way to us. I know there's some
Speaker 7: bits of like string theory that posit there are dimensions
Speaker 7: we simply can't perceive, and so I'm wondering if space
Speaker 7: just looks flat to us because we just don't have
Speaker 7: a capacity to see the other dimensions.
Speaker 5: I don't think it is very flat. I think it
Speaker 5: is pretty multi dimensional. I don't know what really is
Speaker 5: meant by that. Maybe like stuff forms discs, like the
Speaker 5: Solar System or our galaxy, maybe that is meant by flat.
Speaker 5: I think that is due to so that things tend
Speaker 5: to take the shape of discs when there's rotation.
Speaker 2: Involved, all right, and not a lot of flat universes.
Speaker 1: Yeah. Here, I think you really are scoring some points
Speaker 1: because a lot of people think flat implies two dimensional.
Speaker 2: Yeah, that makes sense, right, like if something if the
Speaker 2: universe was flat, it would be the width of a
Speaker 2: sheet of paper kind of right.
Speaker 1: Mm hmm. Yeah. If somebody like bakes your birthday cake
Speaker 1: and then a truck drives over it and flattens it,
Speaker 1: then you think of it as like thinner, right, squeeze
Speaker 1: down to two.
Speaker 2: Dimensions two dimensional? Yeah, although two dimensional cake would be
Speaker 2: pretty low calorie.
Speaker 1: I don't think the calorie squeeze out of it when
Speaker 1: the truck drives over it, unless there's like fusion that happens,
Speaker 1: but that would be a pretty heavy truck.
Speaker 2: As if a truck runs over it, I don't think
Speaker 2: you want to eat it off the road. It seems
Speaker 2: like it will make you sick.
Speaker 1: I think we need to have a highly controlled experiment,
Speaker 1: one of those like roads smootheners they have in cartoons
Speaker 1: all the time that's crushing white the coyote. Squeeze a
Speaker 1: cake and see if it still makes people fat.
Speaker 2: I'm pretty sure that if you ask YouTube, somebody out
Speaker 2: there has made a video of a cake being flatted
Speaker 2: by multiple things.
Speaker 1: Thank you.
Speaker 2: YouTube sounds like the kind of thing the Internet likes.
Speaker 1: If it doesn't exist on the Internet before this podcast,
Speaker 1: it certainly will after.
Speaker 2: But yeah, it's an interesting question why is space flat?
Speaker 2: And I guess also is space flat? I guess is
Speaker 2: maybe the first question we should be asking, or maybe
Speaker 2: the question before that should be what does it mean
Speaker 2: for space to be flat?
Speaker 1: Yeah, it's a really fascinating question to even think about,
Speaker 1: like what it means for space to be flat, and
Speaker 1: to talk about how we measure it's flat and why
Speaker 1: we're surprised to find that it is flat. But you're right,
Speaker 1: first we should make sure we're clear about what we
Speaker 1: mean by flat. And there's sort of two different concepts
Speaker 1: to there, of course connected that we need to think about.
Speaker 1: We can think about locally being flat, like is the
Speaker 1: universe bumpy? And we can think about globally like is
Speaker 1: the universe curved? On some big scale. Thinking about locally
Speaker 1: is a little bit easy, though of course still twists
Speaker 1: your brain a little bit. This is just the idea
Speaker 1: that matter bends space, that the reason things don't seem
Speaker 1: to move in straight lines but seem to be bent
Speaker 1: by gravity. Is not because gravity is a force, but
Speaker 1: that space itself is curved. So things are moving through
Speaker 1: that curved space. The Sun bends the space around it,
Speaker 1: so the Earth moves in that circle, which is the
Speaker 1: natural inertial motion for an object in that curved space.
Speaker 1: That's sort of local curvature.
Speaker 2: Right, right, although I think we always have to give
Speaker 2: the caveat that. You mean space time, right, Like space
Speaker 2: time is what's curved.
Speaker 1: Well, space is a part of space time, and the
Speaker 1: curvature of space time is a little bit different from
Speaker 1: the curvature of space. But in this case, space is
Speaker 1: also curved.
Speaker 2: But I guess I mean like curved space makes me
Speaker 2: think of like a road. Like a road is curved,
Speaker 2: and so anything that tries to follow a straight line
Speaker 2: on that road is going to follow the same path.
Speaker 2: But maybe in real life it would kind of depend, right,
Speaker 2: I don't know how fast you're going or what your
Speaker 2: mass is or right, isn't it?
Speaker 1: Yeah, A curved road is a helpful analogy. Things that
Speaker 1: are moving through space are basically following an invisible road
Speaker 1: that we can't see. You know, space is curved, but
Speaker 1: in this way that we can't directly observe it. Like
Speaker 1: you can look at a road and say, oh, there's
Speaker 1: a curve coming up ahead, but you can't look at
Speaker 1: space and see the curvature directly. But it does affect
Speaker 1: the way things move through it. So you try to
Speaker 1: drive your car on the curve road of space, and
Speaker 1: space moves your car forward. You sort of like guides
Speaker 1: it along the curvature of space and fundamensional space time.
Speaker 1: It's really fascinating because time and space bend together to
Speaker 1: make space. Time itself have these invariants, these things that
Speaker 1: don't actually change, but space curves and time curves due
Speaker 1: to the presence of mass. Right.
Speaker 2: But like if I throw a bowling ball at a
Speaker 2: low speed and a high speed, and I threw a
Speaker 2: feather at a low speed and as high speed, they
Speaker 2: would sort of curve through space, or I would see
Speaker 2: them curve in a different way, or would they all
Speaker 2: curve the same way.
Speaker 1: We know that because, for example, you throw a baseball
Speaker 1: at different speeds, it's going to go a different path, right,
Speaker 1: So it definitely depends on the velocity of the object
Speaker 1: as it moves through curve space. So that's all inertial motion.
Speaker 1: That's motion under no forces, just the curvature of space.
Speaker 2: So I wonder if it's more accurate to say that
Speaker 2: space has curvature and not that space is curved.
Speaker 1: What's the distinction in your mind?
Speaker 2: Well, space like if you say that space is curved,
Speaker 2: make me think of it like a tunnel. Like, if
Speaker 2: a tunnel is curved, then no matter how fast you're
Speaker 2: going or what you throw, you're going to bend the
Speaker 2: same way. You can follow the same path. But that's
Speaker 2: not sort of how space really works, right, Not everything
Speaker 2: is stuck in the same kind of path.
Speaker 1: Yeah, you're right, there aren't rigid tunnels that things have
Speaker 1: to go through. It's not like if you enter a
Speaker 1: pipe and you get flushed out the bottom or something.
Speaker 1: The curvature of space does affect how you move, So yeah,
Speaker 1: that distinction makes sense to me.
Speaker 2: Okay, So then there's local curvature of space. What you're
Speaker 2: talking about is sort of like how things go around
Speaker 2: the Sun, for example, or how the moon goes around.
Speaker 1: The Earth m or how we stay on the Earth,
Speaker 1: all that kind of stuff. Things being gravitationally bound, even
Speaker 1: like the galaxy holding itself together. That's all local curvature
Speaker 1: in comparison to the global curvature, which is a question
Speaker 1: about the whole universe and its shape.
Speaker 2: So there's local and global, and I guess what's the difference,
Speaker 2: just like the size of it the scale, Like are
Speaker 2: you saying that? Like if I'm orbiting around the center
Speaker 2: of the galaxy, it's a different kind of curvature of
Speaker 2: doue to gravity than the Moon orpening around the Earth.
Speaker 1: It's not fundamentally different. It's all described by general relativity
Speaker 1: in Einstein's equations. It's sort of like the difference between
Speaker 1: the Earth being a sphere and the Earth having mountains.
Speaker 1: Like the Earth could be flat and it could be
Speaker 1: a sphere, but it could still have mountains in either case. Right,
Speaker 1: the Earth could be bumpy locally, it could have valleys
Speaker 1: and mountains even if it's flat, or even if it's
Speaker 1: a sphere. So global curvature is more about the question
Speaker 1: of like is the Earth a sphere or is the
Speaker 1: Earth flat? Local curvature is about like is the Earth
Speaker 1: bumpy or is it all perfectly smooth everywhere you go?
Speaker 2: So we are asking if the universe is bumping.
Speaker 1: We're asking if the universe is sort of bent Right,
Speaker 1: is three D space more like the surface of a
Speaker 1: three sphere? Right? Or is it flat? And morn analogy
Speaker 1: to like a sheet of paper. So the global curvature
Speaker 1: space is asking about like the big picture, whereas the
Speaker 1: local curvature is asking about the little picture right right.
Speaker 2: But I guess my question was, or is you know
Speaker 2: where do you draw when do you draw this distinction
Speaker 2: between local and global, like at the galaxy level, at
Speaker 2: the galaxy cluster level, or it's only global if it's everything.
Speaker 1: It's only global if it's everything. And you know, when
Speaker 1: we solve these equations in general relativity, and by we,
Speaker 1: I mean those guys who knows all equations in general relativity.
Speaker 5: Not me.
Speaker 1: They can only solve those in certain situations, in situations
Speaker 1: where they assume, like the universe is empty, or the
Speaker 1: universe is filled with matter, but that matter is perfectly smooth, like.
Speaker 1: Nobody can solve the general relativity equations for our universe,
Speaker 1: which has like clumps of matter in it. So when
Speaker 1: we talk about the whole universe and its curvature, basically
Speaker 1: we're talking about a simplification of our universe where all
Speaker 1: the matter is spread out evenly. There are no lumps
Speaker 1: at all, because that's all they can. And in that case,
Speaker 1: there's still this question of the global curvature. Is the
Speaker 1: universe curved on some large scale and how is it curved?
Speaker 1: Is it flat? Is it open? Is it closed? These
Speaker 1: are the questions of the global curvature of space time,
Speaker 1: which are irrelevant to the little details because they still
Speaker 1: exist even if you smooth all the matter and energy
Speaker 1: out everywhere like peanut butter.
Speaker 2: Mmm, but I guess, you know, if it's everything, we
Speaker 2: don't really know what everything is, right, Like the whole
Speaker 2: entire observable universe might be just a little bump in
Speaker 2: a ginormous infinite universe.
Speaker 1: Well, you're totally right, But the curvature around here is
Speaker 1: dependent on the energy density, doesn't depend on what's happening
Speaker 1: out there. And then we assume that what's happening here
Speaker 1: is what's happening everywhere else, And that's an assumption we
Speaker 1: don't know. It could be that what we're calling global
Speaker 1: curvature is actually local on a much larger scale, that
Speaker 1: if you zoom out from the observable universe to the
Speaker 1: actual full universe, that we could never see that the
Speaker 1: curvature is different, right, and that what we were talking
Speaker 1: about the whole time is quote unquote global curvature is
Speaker 1: actually the local curvature of the observable universe.
Speaker 2: I guess it's sort of like how before we used
Speaker 2: to think that the Earth was flat because we only
Speaker 2: knew sort of the local area here around this and
Speaker 2: looks pretty flat. But actually if you sort of keep
Speaker 2: going or you're taken to account the whole planet, then
Speaker 2: you see that the whole planet is curved and round.
Speaker 1: Yeah, exactly. And if you lived on a part of
Speaker 1: the Earth that was literally flat, like maybe you were
Speaker 1: really precise about it, and you took out a bunch
Speaker 1: of tools and you try to measure the curvature of
Speaker 1: the Earth. Imagine you lived on like a truly flat
Speaker 1: part of the Earth and you measured it to be flat,
Speaker 1: and then you left that and you realized, oh, actually
Speaker 1: the rest of the Earth is curved. And so what
Speaker 1: I got was a misunderstanding of the bigger picture. So
Speaker 1: you're right, we can only see the observable universe, and
Speaker 1: we can measure the global curvature of this part of
Speaker 1: the universe and then assume that the rest of it
Speaker 1: is the same. But we'll never know, all.
Speaker 2: Right, So then a local curvature of space sort of
Speaker 2: is kind of about how mass spans space, and how
Speaker 2: the Moon goes around the Earth and the Earth goes
Speaker 2: around the Sun through curve space time. Now, when you're
Speaker 2: talking about the global picture, I guess you're not just
Speaker 2: talking about how things move, but it's more sort of
Speaker 2: a fundamental property of space about what it contains.
Speaker 1: Yeah, and it's really hard to think about it in
Speaker 1: three D. So we do this thing where we talk
Speaker 1: about two dimensional versions. Sometimes that's helpful and sometimes it's misleading.
Speaker 1: So you always have to keep in mind, like how
Speaker 1: those things translate from a two dimensional analogy that's easier
Speaker 1: for us to think about to the reality of three
Speaker 1: D space. And it's easier to think about two dimensional
Speaker 1: analogies because we basically live on a two dimensional surface,
Speaker 1: the surface of the Earth, right, So it's easy to
Speaker 1: imagine like living on a flat sheet of paper versus
Speaker 1: living on the surface of a sphere versus living in
Speaker 1: like a hyperbola, And so those three shapes have different curvature.
Speaker 1: An infinite plane is totally flat. If you drew a
Speaker 1: triangle on the ground, the angles would add up to
Speaker 1: one hundred and eighty degrees. The surface of a sphere,
Speaker 1: we say it has positive curvature. You try a triangle
Speaker 1: that follows the surface of that sphere, its angles are
Speaker 1: going to add up to more than a hund You
Speaker 1: live on the surface of a hyperboloid, and you draw
Speaker 1: a triangle on that surface, the angles are going to
Speaker 1: add up to less than one eighty. So those are
Speaker 1: two D examples of curved surfaces. Then you have to
Speaker 1: extrapolate those two three D space, and it's very similar
Speaker 1: to a lot of the ideas carry over.
Speaker 2: I feel like this is getting a little bit technical,
Speaker 2: So when don't we stretch these thoughts out and try
Speaker 2: to get them down flat and talk about what it
Speaker 2: actually means for three D universal space to be flat.
Speaker 2: But first, let's take a quick break.
Speaker 1: All right.
Speaker 2: We're asking the question why is space so flat? And
Speaker 2: I guess the preceding question is is space flat? And
Speaker 2: the preceding preceding question is what does it mean for
Speaker 2: the for space to be flat? Because I guess base
Speaker 2: sort of seems flat to us, you know, it doesn't
Speaker 2: seem curve or bent to us, at least our immediate surroundings.
Speaker 2: But we know that if you expand your your surroundings
Speaker 2: a little bit, you see that space time is flat.
Speaker 2: That's how gravity works, and that's what makes the Moon
Speaker 2: go around the Earth and the Earth around go around
Speaker 2: the Sun. But we're talking now about global curvature of space,
Speaker 2: which really means universal curvature of space, which actually sort
Speaker 2: of means observable universe curvature of space, right yeah.
Speaker 1: And we're trying to use our understanding of two D
Speaker 1: space to sort of bootstrap our way to understand the
Speaker 1: curvature of three D space. So if you're like on
Speaker 1: a flat surface and you shoot two parallel lines out
Speaker 1: like two laser beams, then they'll never cross each other.
Speaker 1: This is Euclid's famous geometry, and that's why we call
Speaker 1: it Euclidean geometry. These two parallel lines will never meet.
Speaker 1: And you can also do that in three dimensional space.
Speaker 1: Right now, just imagine the universe is having three directions
Speaker 1: shoot two parallel lines, but in any direction in xyz
Speaker 1: they will never meet. In flat space, the extension of
Speaker 1: flat space from two D three D is pretty straightforward.
Speaker 2: I wonder if, like we even have to go to
Speaker 2: a two D analogy, why can't we just talk about
Speaker 2: the curvature space in three D.
Speaker 1: Yeah, I think three D flat space is pretty straightforward,
Speaker 1: but it can help us understand the curved space to
Speaker 1: start in two D or at least let's give it
Speaker 1: a shot. In two dimensional curved space, if you fire
Speaker 1: two laser beams in the same direction, they will eventually cross.
Speaker 1: Like if you're on the surface of the Earth and
Speaker 1: you fire two laser beams in the direction in the
Speaker 1: north pole, they'll cross when they hit the north pole.
Speaker 2: Right What I think this is why it's confusing, and
Speaker 2: I wonder if we can just stick with three D
Speaker 2: like three D flat space. If I shoot two lasers
Speaker 2: out in space, they're never going to meet. These two
Speaker 2: laser beams, they're never going to meet. Right now, let's
Speaker 2: talk about curve three D space. I shoot two lasers,
Speaker 2: and the lasers are going to do one of two things, right,
Speaker 2: They're either going to come towards each other or bend
Speaker 2: away from each other.
Speaker 1: That's right. And whether they come towards each other and
Speaker 1: away from each other tells you the sign of the curvature.
Speaker 1: Positive curvature, they'll come towards each other. Negative curvature, they'll
Speaker 1: veer away from each other, never meet.
Speaker 2: Now this is super weird because what's bending the path
Speaker 2: of the lasers just the curvingness of space.
Speaker 1: Lasers and light follow the curvature of space. They're like
Speaker 1: tracers that tell you how space is curved. So light
Speaker 1: moves in straight lines through curved space time, right, But
Speaker 1: that leads to curved motion in space.
Speaker 2: So you're saying that space might have a property to
Speaker 2: it called curvature, which would to us make the light
Speaker 2: beams not go in a straight line.
Speaker 1: That's right. If you assume space is flat, then light
Speaker 1: appears to be moving in a curve. If, however, space
Speaker 1: itself is curved, those grid lines themselves are curving, then
Speaker 1: light is moving along those grid lines. It's just the
Speaker 1: gridlines themselves are curved.
Speaker 2: Okay, So now I feel like there's a third possibility.
Speaker 2: So like, if I have a laser shooter on my
Speaker 2: right hand and a laser shooter on my left hand,
Speaker 2: and I shoot them perfectly parallel to each other. If
Speaker 2: space is flat, they're just going to keep going straight
Speaker 2: parallel forever. But if space is curved, there's some things
Speaker 2: that can do. They can bend towards each other away
Speaker 2: from each other. But I feel like they could also
Speaker 2: like bend perpendicular to each other, like maybe my right
Speaker 2: laser beam drifts up and my left laser being drifts down.
Speaker 2: What does what would that mean?
Speaker 1: Isn't that the same as bending away from each other?
Speaker 2: I guess if I just turn my head sideways, what
Speaker 2: if they spiral around each other? Can space be twisty?
Speaker 1: Space can have all sorts of weird combinations. I mean,
Speaker 1: in general relativity, space can doesn't even have to be
Speaker 1: totally connected. So a laser beam can like disappear and
Speaker 1: appear somewhere else, right, That's basically what a wormhole would be.
Speaker 1: We're trying to talk about pretty simple constructions of space
Speaker 1: where all you have is a single overall curvature.
Speaker 2: I guess if I shoot my laser beams and they
Speaker 2: they go past a large massive object in space, like
Speaker 2: the Sun, they're gonna curve, and if they're maybe on
Speaker 2: opposite or different sides of the Sun, they're gonna curve
Speaker 2: in a different way. And as they go through a galaxy,
Speaker 2: they're gonna get pushed this way and that way. The
Speaker 2: laser beams. But I think you're talking about like if
Speaker 2: I shoot them maybe really far apart from each other,
Speaker 2: and let them go for a really really long time
Speaker 2: on average, Are they going to be moving towards each
Speaker 2: other or away from each other? That's what you mean
Speaker 2: by global curvature.
Speaker 1: Yeah, And your analogy is great because it lets us
Speaker 1: make a connection between local curvature and global curvature. Local curvature,
Speaker 1: as you say, is like, is there a star there
Speaker 1: that's going to bend the path of my life? And
Speaker 1: we sort of got our minds around a little bit
Speaker 1: the general relativity that light is bent by masses. Even
Speaker 1: though light has no mass, it follows the curvature of space,
Speaker 1: and it's bent right now. Instead of having a local
Speaker 1: mass like a star with a single point of really
Speaker 1: high density, take that star and spread it out throughout
Speaker 1: the whole universe instead. So now the universe is filled
Speaker 1: with constant density of matter or energy that creates a
Speaker 1: curvature of space that's constant. It's not like, oh, there's
Speaker 1: a lot of curvature near that star. Let's have a
Speaker 1: little curvature everywhere instead of a lot of curvature in
Speaker 1: just one spot. And that's one way to think about
Speaker 1: the global curvature of space. Think about a universe unit
Speaker 1: formally filled with a certain matter and energy density.
Speaker 2: So like if the universe was infinite and was filled
Speaker 2: with like evenly spread out gas or an evenly spread
Speaker 2: out star, I guess what would happen to a laser beam.
Speaker 2: Would it still curve or would it go straight?
Speaker 1: It depends on the density of that stuff. Right, there's
Speaker 1: a certain critical density of energy in the universe. Below
Speaker 1: a certain level, the universe will be negatively curved. If
Speaker 1: it has exactly the right critical energy at this knife's edge,
Speaker 1: the universe will be flat. If it's more than that
Speaker 1: critical energy, the universe will be curved. So the curvature
Speaker 1: of the universe itself of space is connected to the
Speaker 1: energy density of stuff in the universe relative to this
Speaker 1: critical threshold.
Speaker 2: I guess that's a little counterintuitive, because I would think
Speaker 2: that if the universe is filled evenly with the same
Speaker 2: energy or gas or matter or energy, then the laser
Speaker 2: beam would just go straight because it's being pulled the
Speaker 2: same way in all directions.
Speaker 1: Yeah. Unfortunately, general relativity isn't intuitive, and if you add
Speaker 1: enough stuff to the universe, it curves up. It makes
Speaker 1: the universe effectively like a sphere. That's only consistent with
Speaker 1: universes that have a positive curvature, because imagine you take
Speaker 1: every bit of space and you make it bend y. Now,
Speaker 1: think about, like, what shapes can you build with that?
Speaker 1: If you only have curvy pieces, all you can do
Speaker 1: is build the surface of a sphere, or all you
Speaker 1: can do is build a three dimensional version of the
Speaker 1: surface of a four dimensional sphere if all you have
Speaker 1: are bendy pieces.
Speaker 2: Yeah, I guess I'm still confused because I'm imagine this
Speaker 2: scenario where the whole universe is filled with the same
Speaker 2: gas or evenly distributed star. If I shoot a laser beam,
Speaker 2: which way does it curve? If the universe is positively curve,
Speaker 2: so curve up, down, left right.
Speaker 1: In a universe with positive curvature, if you shoot a
Speaker 1: laser beam, it looks to you like it's going straight,
Speaker 1: but then it hits you in the back of the head.
Speaker 2: What it wouldn't necessarily hit mean in the back of
Speaker 2: my head.
Speaker 1: In a universe that's uniformly filled with matter that's positive curvature,
Speaker 1: it will loop back around. It's like being on the
Speaker 1: two dimensional surface of a three dimensional sphere.
Speaker 2: But I guess it maybe it might loop around a
Speaker 2: few times before it hits me in the back of
Speaker 2: the head.
Speaker 1: Any point on a sphere is the same, so it
Speaker 1: doesn't really matter where you are, which direction you shoot it.
Speaker 1: You always get the same results. From that point of view.
Speaker 2: I feel like then, now it's getting a little bit
Speaker 2: into this idea of the how space is connected to itself,
Speaker 2: which is at the case, is a curvature of space
Speaker 2: necessarily the same as how space is connected to itself,
Speaker 2: whether it loops around itself.
Speaker 1: It's definitely connected. Right, It's not the same, but it's
Speaker 1: definitely connected. If space is flat, then the universe can
Speaker 1: be infinite. If space is positive curvature, then the universe
Speaker 1: can't be infinite. It can be finite but also have
Speaker 1: no boundary, just the way like the two dimensional surface
Speaker 1: of a three D sphere can be finite but unbounded
Speaker 1: because it has positive curvature. So these two ideas are
Speaker 1: definitely connected. The topology of space, the large scale shape
Speaker 1: of space, and the curvature of space. The two things
Speaker 1: are definitely closely linked. The curvature of space you can
Speaker 1: deduce from the density of matter in that space. Because
Speaker 1: general relativity connects those two things.
Speaker 2: Now, that was one laser beam. Now I take two
Speaker 2: laser beams and I shoot it off into three D space.
Speaker 2: And let's say that the universe has positive curvature. What's
Speaker 2: going to happen to these two laser beams. They're eventually
Speaker 2: going to hit each other.
Speaker 1: They will eventually cross. Yeah.
Speaker 2: Mmm. And if the universe is not positively curved, if
Speaker 2: it's negatively curved, then they'll never hit each other.
Speaker 1: They won't hit each other, they'll veer apart.
Speaker 2: M all right. I think that gives us as good
Speaker 2: of an explanation of what the curvature space is in
Speaker 2: the universe, right, m hm.
Speaker 1: And all of these things together control the future of
Speaker 1: the universe, like the curvature and the topology, the matter
Speaker 1: density of the universe. That plus like the dark energy
Speaker 1: of the universe, all these things work together to determine
Speaker 1: how fast the universe is expanding. Is it expanding or
Speaker 1: is it collapsing or is it steady state with no expansion.
Speaker 1: All of these things play a role in determining the
Speaker 1: future of the universe. Cool.
Speaker 2: Well, maybe talk about how you might measure the flatness
Speaker 2: of the universe in like, how do we know whether
Speaker 2: the universe is flat or not.
Speaker 1: So what we do is we measure this energy density.
Speaker 1: And of course the caveat is we can only measure
Speaker 1: it in the observable universe. We can't measure outside, and
Speaker 1: so when we say the universe here, we always really
Speaker 1: just mean the observable universe. All we can do is
Speaker 1: measure the energy density, and we can say, is there
Speaker 1: enough stuff in the universe to make it curved positively
Speaker 1: so it wraps up on itself. Is there the critical
Speaker 1: density so the space is flat? Or is there less
Speaker 1: than the critical density so that the universe is open
Speaker 1: with negative curvature. So the way we do that is
Speaker 1: by measuring the amount of stuff, the energy density of
Speaker 1: stuff in the universe.
Speaker 2: Oh, I see you measure the density of stuff. But
Speaker 2: I guess we never covered why the density of stuff
Speaker 2: determines the curvature of space, Like why is there a
Speaker 2: critical amount that makes it negative or positive? Like wouldn't
Speaker 2: any amount of stuff in the universe make deniverse positively curve?
Speaker 1: Yeah, that is a little counterintuitive, But a totally empty
Speaker 1: un one with no matter or energy in it at all,
Speaker 1: would not have flat space. It would have negatively curved space.
Speaker 1: So you need a little bit of stuff in the
Speaker 1: universe to counteract that.
Speaker 2: Whoa wait, So if I had an empty universe, like
Speaker 2: no stars, no planets, no galaxies in it, and I
Speaker 2: shoot to laser beams, they're going to diverse from each other.
Speaker 2: They're not just going to stay parallel to each other forever.
Speaker 1: Yeah, that's right. This is one of the situations we
Speaker 1: can actually solve in Einstein, the general relativity situation with
Speaker 1: nothing in the universe, totally empty, no matter, no energy,
Speaker 1: no dark energy. And in that case, the universe has
Speaker 1: negative curvature, so you have to add stuff to the
Speaker 1: universe to make it have no curvature or positive curvature.
Speaker 2: Oh so even no dark energy like this sort of
Speaker 2: necessary amount of stuff in it is not related to
Speaker 2: the expansion of the universe either, or do you assume
Speaker 2: the expansion of the universe or not.
Speaker 1: This does not determine the expansion of the universe. All
Speaker 1: these pieces together, the curvature, the density, the dark energy,
Speaker 1: all these things together determine whether the universe is expanding,
Speaker 1: whether that expansion is accelerating. It's a whole complex dance,
Speaker 1: but just the curvature of the universe is determined by
Speaker 1: the matter and energy density. If you have a certain amount,
Speaker 1: then you sort of counteract the natural negative curvature of
Speaker 1: space and you get a flat universe. If you have
Speaker 1: more than that, you get a positive curvature. If you're
Speaker 1: less than that, you get negative curvature. So a flat
Speaker 1: universe is sort of balanced on a knife's edge. You
Speaker 1: have to have like exactly the right amount of stuff,
Speaker 1: and it's not a big number, Like the critical density
Speaker 1: right now is about five protons per cubic meter.
Speaker 2: I guess that's weird that space by itself has negative curvature,
Speaker 2: like pure space OG space. If you shoose laser beams,
Speaker 2: they would diverge. Isn't that weird because shouldn't space be
Speaker 2: like neutral or totally empty.
Speaker 1: Well, intuitive concept of space doesn't even allow it to
Speaker 1: be bent, right, So you have to already let go
Speaker 1: of those intuitive ideas and think that space is something
Speaker 1: quite different from what we imagined as these weird properties.
Speaker 1: It's a little bit more complicated than what we've described
Speaker 1: because the amount of stuff you have to add to
Speaker 1: space to avoid this negative curvature actually changes over time.
Speaker 1: It depends also on the expansion of the universe. So
Speaker 1: there's a lot of complex moving parts here that we're
Speaker 1: trying to distill down.
Speaker 2: But I guess the main takeaway is that space by
Speaker 2: itself has negative curvature, but because we have stuff in it,
Speaker 2: matter and energy, then it's possible for space to be
Speaker 2: flat because that's what the effect of energy and mass
Speaker 2: does to space, is it makes it more positively curvy.
Speaker 1: Yeah, and we can measure the curvature of space by
Speaker 1: measuring the matter and energy density of the universe. So
Speaker 1: we go out we measure that, and that tells us
Speaker 1: what curvature we have in our universe. The magnitude of
Speaker 1: that curvature can also change the sign can't. If you
Speaker 1: have positively curved space, it's always going to be positively curved,
Speaker 1: but it can get more positively curved or less positively curved,
Speaker 1: like the universe has positive curvature, can collapse on itself,
Speaker 1: making itself more and more positively curved, or universe it's
Speaker 1: open can expand really really rapidly and get less and
Speaker 1: less curved. But they can't flip over. You can't start
Speaker 1: from the universe as positively curves and end up with
Speaker 1: the universe.
Speaker 2: That's negatively curved unless maybe the density of energy and
Speaker 2: matter decreases enough. Isn't that possible? No, As like you said,
Speaker 2: it depends on that density. What if the density changes.
Speaker 1: The density definitely does change, right, and we'll talk a
Speaker 1: little bit about how that density is changing and how
Speaker 1: we understand how it's changing. But you can't change the
Speaker 1: curvature of the universe. You can't go from positively curved
Speaker 1: space to negatively curve space. That would correspond to like
Speaker 1: changing from a finite universe to an infinite universe, which
Speaker 1: you can't do right. You can't take the service of
Speaker 1: a sphere and snap it out to an infinite plane.
Speaker 2: You can pop a balloon, you can flat a birthday cake.
Speaker 1: That's one of the confusing things about these two D analogies, right,
Speaker 1: is that you're imagining it in a three D space.
Speaker 1: You're thinking about really a two D service on a
Speaker 1: three D sphere. But in those analogies, the two D
Speaker 1: surface is all there is, so you can't really flatten
Speaker 1: it all.
Speaker 2: Right, Well, into what would happen if you change the
Speaker 2: density of matter and energy in the universe, And then
Speaker 2: let's ask the big question, why is the universe flat?
Speaker 2: But first, let's take another quick break. All right, we're
Speaker 2: asking the question why is space flat? Or I guess
Speaker 2: why space so flat? Because it's maybe flatter than what
Speaker 2: you expected.
Speaker 1: Yeah, when we go out to measure the curvage of
Speaker 1: the universe, we find something kind of surprising. We find
Speaker 1: that it's really pretty flat. Like there's this critical density
Speaker 1: five protons per cubic meter, And we go out to
Speaker 1: measure the amount of stuff in the universe. We add
Speaker 1: up all the mass, the stars, the galaxies, the dark matter,
Speaker 1: and also the dark energy. All of that stuff. It
Speaker 1: adds up to like very very close to exactly the
Speaker 1: critical density. It's within one percent, which is about our
Speaker 1: uncertainty of the critical density, which tells us that space
Speaker 1: is either flat or very very close to flat. And
Speaker 1: that's kind of a surprise because we don't think the
Speaker 1: universe likes to be flat.
Speaker 2: I guess before we go, I have more questions about
Speaker 2: what you just said. Well, first of all, how do
Speaker 2: we measure the mass and energy density of the universe?
Speaker 2: And second of all, how do we know what amount
Speaker 2: you need for the universe to be flat?
Speaker 1: So how we measure it is several different ways. We
Speaker 1: can use like the cosmic microwave background radiation. This is
Speaker 1: radiation from about three hundred thousand years after the Big Bang,
Speaker 1: where the universe was very hot and dense with its
Speaker 1: bright plasma, and then it cooled off and formed neutral
Speaker 1: atoms and light could propagate. We can still see that light.
Speaker 1: That light was made everywhere in the universe, and it's
Speaker 1: flying around everywhere, and some of it has just reached
Speaker 1: Earth from places that used to be very very far away,
Speaker 1: and we can use it to sort of look at
Speaker 1: what the universe looked like at that time, and there
Speaker 1: were little bumps and wiggles in it. It's not completely smooth.
Speaker 1: It's like a little bit of a frothing quantum plasma.
Speaker 1: And from the size of those wiggles, we can tell
Speaker 1: how much energy density there was in the early.
Speaker 2: Universe based on some theory that you have about how
Speaker 2: the universe formed and how these things balance out with space.
Speaker 1: Relying basically just on general relativity. I mean, we assume
Speaker 1: some model of the universe, but it's based in general relativity.
Speaker 1: Doesn't depend on how the universe formed or what came before.
Speaker 1: It just depends on the size of those fluctuations in
Speaker 1: the early universe and then how those propagate through an
Speaker 1: expanding universe to us.
Speaker 2: Okay, so that's one way to measure it.
Speaker 1: So that measures the total energy density like the dark
Speaker 1: energy plus the dark matter plus the normal matter density
Speaker 1: in the early universe. We can also measure it by
Speaker 1: looking at the acceleration of the universe, like looking at
Speaker 1: supernova seeing how fast they're moving away from us, or
Speaker 1: looking at cephids. This expansion rate of the universe also
Speaker 1: helps us measure these various components. So the components of
Speaker 1: the energy density of the universe are the dark energy,
Speaker 1: the normal matter, and the dark matter, and the super
Speaker 1: nova measurements the acceleration of the universe help us measure
Speaker 1: the dark energy component minus the matter component, because that
Speaker 1: determines the expansion of the universe. So there's like a
Speaker 1: bunch of different components here, and we have different ways
Speaker 1: to measure each one's or combinations of each one, to
Speaker 1: help us in down exactly what those contributions are. Dark
Speaker 1: energy is of like seventy percent of the critical density.
Speaker 1: Matter is like thirty percent of the critical density, where
Speaker 1: most of that is dark matter, and they add up
Speaker 1: to basically this critical density.
Speaker 2: This is from this CMB measurement, or from all measurements.
Speaker 1: The CMB measurement tells us the total density. The supernova
Speaker 1: tells us the dark energy minus the matter the difference
Speaker 1: between those two because they work against each other when
Speaker 1: controlling the expansion of the universe. There's another measurement, the
Speaker 1: buryon acoustic oscillations, that tells us about like how matter
Speaker 1: was sloshing around in the early universe and made these
Speaker 1: sound waves back when the universe was super duper dense.
Speaker 1: Sound traveled at nearly half the speed of light, and
Speaker 1: the speed of that sound depends on the density of
Speaker 1: matter in the universe, and we can still sort of
Speaker 1: see the universe ringing from those oscillations in the early universe.
Speaker 1: That separately measures just the matter portion. So we have
Speaker 1: these different pieces of the pie, and they all add
Speaker 1: up to make exactly one pie. And the fascinating thing
Speaker 1: is that they didn't have to write it could have
Speaker 1: added up to anything. It could have added up to
Speaker 1: be twice the critical density or half the critical density,
Speaker 1: but it adds up to bang on just the critical
Speaker 1: density to within one percent.
Speaker 2: I see. So you're saying we've measured the energy density
Speaker 2: of the universe, and according to what we think is
Speaker 2: the laws of the universe, according to general relativity, we
Speaker 2: have just enough mass and density to make the universe flat,
Speaker 2: which means if I shoot two lasers out there in space,
Speaker 2: they're not going to hit each other, they're not going
Speaker 2: to drift the part, they're not going to hit me
Speaker 2: in the back of the head. Those two laser beings
Speaker 2: are just gonna keep going forever exactly.
Speaker 1: And this is kind of a surprise to physicists because
Speaker 1: they think the universe doesn't like to be flat. Like
Speaker 1: the flatness of the universe is not a stable thing.
Speaker 1: If you're just above the critical density, if you're like
Speaker 1: a little bit more in the critical density, then the
Speaker 1: universe tends to collapse and become more and more dense,
Speaker 1: and you move away from the critical density. If you
Speaker 1: have less than the critical density, you're below it, then
Speaker 1: the universe is open. It tends to expand and dilute
Speaker 1: itself away from the critical density. So either you're exactly
Speaker 1: bang on the critical density, in which you're stable like
Speaker 1: a pencil balance on its tip, or you're a little
Speaker 1: bit above and a little bit below, and then you
Speaker 1: very quickly veer away from it. So sort of a
Speaker 1: mystery how we're still so close to the critical density
Speaker 1: after billions of years.
Speaker 2: What do you mean it's unstable like a pencil. What
Speaker 2: does that mean?
Speaker 1: It's unstable, and that if you move away from the
Speaker 1: critical density a little bit, the universe moves away even more.
Speaker 1: It's like a pencil balance on its tip. Right, it's unstable.
Speaker 1: You have it, a tiny little push, a fly lands
Speaker 1: on it, air blows by it really gently. It's going
Speaker 1: to tend to fall over.
Speaker 2: Wait to Like, if you measure the density of the
Speaker 2: universe and it's a little bit more than the critical
Speaker 2: amount of density you need for a flat universe, then
Speaker 2: the density is going to increase over time, Like the
Speaker 2: universe is going to get more and more denser.
Speaker 1: Exactly. If you have more in the critical density, the
Speaker 1: universe will contract, right, and things will get denser and denser.
Speaker 1: You'll end up with like a big crunch.
Speaker 2: You mean, like the expansion of the universe will reverse.
Speaker 1: Yeah, exactly. In the opposite scenario, where you lessen the
Speaker 1: critical density, things expand forever and things get more and
Speaker 1: more dilute, So the density drops right as the universe expands,
Speaker 1: the density of matter drops. As the universe contracts, the
Speaker 1: density of matter increases, and so if you're not at
Speaker 1: the critical density you tend to veer away from it
Speaker 1: pretty quickly. And we're like billions of years into the
Speaker 1: history and we're still super close to the critical density,
Speaker 1: which was a big question in cosmology. How can you
Speaker 1: stay so closely balanced so long?
Speaker 2: I feel like now we're tying it to the expansion
Speaker 2: of the universe. So the critical density is tied to
Speaker 2: the expansion, like if the universe is positively curved, then
Speaker 2: the universe is going to contract eventually.
Speaker 1: The courage of the universe definitely plays a role. The
Speaker 1: critical density and the curvature, together with the amount of
Speaker 1: dark energy, determine the expansion. You can have a universe
Speaker 1: that's positively curved and expanding if you have enough dark energy,
Speaker 1: because dark energy can overcome this critical density, that you
Speaker 1: could have a universe which expands. But in the simple
Speaker 1: scenario where you take out dark energy for the moment
Speaker 1: and just have a universe with only matter and radiation,
Speaker 1: which was basically the scenario of our universe for the
Speaker 1: first nine billion years when dark energy was negligible, and
Speaker 1: then the universe above the critical density will contract and
Speaker 1: increase the density, and the universe below the critical density
Speaker 1: will expand and decrease the density. So they did this calculation.
Speaker 1: They're like, well, in that scenario, how close do the
Speaker 1: universe have to start to the critical density to end
Speaker 1: up at one percent. The answer is we had to
Speaker 1: be within the critical density to within ten to the
Speaker 1: minus sixty two. If you're anything above that, then the
Speaker 1: universe would have expanded like crazy or contracted like crazy.
Speaker 1: So it seems really, really weird that we end up
Speaker 1: with a universe so close to flat when the universe
Speaker 1: likes to veer away from flatness.
Speaker 2: Well, that's a really tight requirement for this density that
Speaker 2: we need at the beginning of the universe. It kind
Speaker 2: of seems like too much of a coincidence.
Speaker 1: It does seem like too much of a coincidence, and
Speaker 1: physicists don't like coincidences because the density of stuff in
Speaker 1: the universe doesn't seem to be determined by anything. It
Speaker 1: could have been anything, So for it to be like
Speaker 1: exactly close to one complete pie of the critical density,
Speaker 1: it seems too neat. Physicists like a reason for these
Speaker 1: numbers to line up, and there is an explanation for it,
Speaker 1: and the explanation is cosmic inflation. So you know how
Speaker 1: the universe is expanding now, and that expansion is accelerating.
Speaker 1: We also think that the universe expanded very very early
Speaker 1: on in its history. But like a huge factor, this
Speaker 1: accelerating expansion we call inflation. It's an expansion of like
Speaker 1: ten to the thirty in like ten to the negative
Speaker 1: thirty seconds. And this kind of accelerating expansion tends to
Speaker 1: push the universe towards flatness. It makes the universe more flat.
Speaker 2: But isn't it still sort of too much of a coincidence,
Speaker 2: Like I wonder if maybe our theories are wrong, or
Speaker 2: maybe there's some sort of mechanism that keeps the universe flat.
Speaker 1: Well, we don't know if inflation is true, and it's
Speaker 1: just one of the possible scenarios, And you know, maybe
Speaker 1: it's just a coincidence, and we just happen to in
Speaker 1: the universe that was that close to flat that we
Speaker 1: ended up in the universe that didn't overexpand or didn't
Speaker 1: collapse on itself. But inflation makes it less sensitive. Inflation says,
Speaker 1: you know, you could have started with lots of different densities,
Speaker 1: and inflation would have made your universe have the critical
Speaker 1: density early on, So you could have started with half
Speaker 1: the density or one and a half times the critical density,
Speaker 1: and inflation would have made your universe super duper close
Speaker 1: to the critical density.
Speaker 2: Meaning like you might have started with too much stuff
Speaker 2: in the universe, but then some mechanism stretched out the
Speaker 2: universe enough so that you had the critical density.
Speaker 1: Exactly the math of inflation. In fact of any accelerating
Speaker 1: expansion in the universe tends to push the universe back
Speaker 1: towards the critical density. So if you had too much,
Speaker 1: inflation would stretch out the universe in just the right
Speaker 1: way to make it have the critical density. Just like
Speaker 1: if you're standing on the surface of a tiny sphere
Speaker 1: like a beach ball, it looks really really curved. But
Speaker 1: then if somebody expands it rapidly by a factor of
Speaker 1: ten to the thirty, then now you're standing on the
Speaker 1: surface of a huge it looks flat. Right, So a
Speaker 1: bigger sphere looks flatter and then a small sphere. In
Speaker 1: the same way inflation pushes the universe towards less.
Speaker 2: Curvature, does it also work the other way, Like if
Speaker 2: the universe had started with too little stuff in it,
Speaker 2: the density was too small. Mood inflation have somehow adjusted
Speaker 2: or slowed down or compress the universe somehow. Would you
Speaker 2: have had deflation in order to keep the universe flat?
Speaker 1: Yeah, that's a great question. It does. It pushes it
Speaker 1: towards critical density from either direction, which is pretty cool
Speaker 1: how the math works out.
Speaker 2: So it does do deflation.
Speaker 1: Well, they still consider it inflation because you're still stretching
Speaker 1: it out.
Speaker 4: You know.
Speaker 1: Imagine like a hyperbolic surface. You stretched it out, so
Speaker 1: the negative curvature goes towards zero curvature. So inflation drives
Speaker 1: you towards zero curvature from either direction.
Speaker 2: So it's more like stackflation or less flation.
Speaker 1: I don't know enough economics to know if an analogy
Speaker 1: is accurate or not.
Speaker 2: Yeah, I mean it sounds like something they say in
Speaker 2: the news.
Speaker 1: And one fascinating thing about that is it means that
Speaker 1: our universe right now is driving back towards flatness. Like
Speaker 1: the brief history of the universe is you have probably inflation,
Speaker 1: which makes the universe mostly flat, and then you have
Speaker 1: a matter in radiation dominated time when the universe is
Speaker 1: then driven by this critical density, and it continues to
Speaker 1: expand that that expansion is decelerating because of the matter
Speaker 1: dominated nature of the universe. And then like six billion
Speaker 1: years ago, dark energy took over, right, because the expanding
Speaker 1: universe dilutes out the matter and radiation, while dark energy
Speaker 1: grows as a fraction. So now we have an accelerating
Speaker 1: expansion again, which does the same thing. Any accelerating expansion
Speaker 1: in the universe pushes you back towards zero curvature.
Speaker 2: Mmm. Interesting. I guess what that makes me think is
Speaker 2: that maybe the universe is flat, Like it's just flat.
Speaker 2: It's infinite and flat, and all these things we're seeing,
Speaker 2: all these measurements and all these theoretical concepts, they kind
Speaker 2: of have to work out to a flat universe, and
Speaker 2: that's what we're seeing. Like maybe it's not sort of
Speaker 2: like this mystery or this universe sitting on a nice edge.
Speaker 2: It's just that's just the way that the verse is.
Speaker 2: And to us, the math and the measurements look like
Speaker 2: it could have gone either way, but it could never
Speaker 2: had a chance.
Speaker 1: Yeah, it's possible. Right in the equations of general relativity,
Speaker 1: this is curvature parameter. It's either plus one zero, or
Speaker 1: minus one, and it can't change again. Right, You can't
Speaker 1: go from a negative curvature to a positive curvature, and
Speaker 1: our universe is just one of those. The interesting thing, though,
Speaker 1: is that to have k equals zero, to have zero curvature,
Speaker 1: you really have to have the critical density of matter
Speaker 1: and energy. So it sort of depends on what question
Speaker 1: you ask, Like you could ask, well, which of the
Speaker 1: three curvatures is it? Well, maybe it's just zero, like
Speaker 1: you say, but if you think about it in terms
Speaker 1: of the continuous spectrum of matter and energy density, then
Speaker 1: it has to have exactly the right number, which seems
Speaker 1: like one option out of an infinite number instead of
Speaker 1: one option out of three.
Speaker 2: Or unless the universe sort of like prevents the matter
Speaker 2: and energy to be anything else, in case that wouldn't
Speaker 2: make sense.
Speaker 1: Right, Yeah, we it'd certainly possible. And these questions are
Speaker 1: really basic and also simple, And in a few hundred
Speaker 1: years they might look back on this and be like, hah,
Speaker 1: how do they imagine they lived in a curved universe?
Speaker 2: What a bunch of idiots, What a bunch of flat
Speaker 2: footed idiots?
Speaker 1: But these are the questions we're asking, and we don't
Speaker 1: know and the equations of general real too. They allow
Speaker 1: for all three kinds of universe negative curvature, flat or
Speaker 1: positive curvature. We just don't know which of those we
Speaker 1: live in and why we've measured its space to be flat.
Speaker 1: And you're right. Either it just is flat and it
Speaker 1: started out balanced on that knife's edge and it will
Speaker 1: always be there, perfectly balanced, or it has a little
Speaker 1: bit of curvature, but then we don't understand why it's
Speaker 1: still so flat unless you do something early on, like inflation.
Speaker 2: Well, I think the idea is that maybe the universe
Speaker 2: is flat, which means that the pencil is not upside down,
Speaker 2: like maybe the pencil is hanging from the tail, and
Speaker 2: that it can only sort of be that hanging down
Speaker 2: and the universe would push it down if you try
Speaker 2: to move the pencil. That's a possibility. Sounds like it's
Speaker 2: still a mystery why the universe is flat. We're measuring
Speaker 2: it to be flat and it seems to be staying flat,
Speaker 2: which means that the universe either is flat or the
Speaker 2: universe is not flat, but something is making it suspiciously flat.
Speaker 2: Those are the two options, right exactly.
Speaker 1: If it's not exactly flat, then something is keeping it
Speaker 1: very very close.
Speaker 2: To flat, which would be the universe, which means the
Speaker 2: universe it's flat.
Speaker 1: The universe is either exactly flat or it likes to
Speaker 1: stay very close to flat.
Speaker 2: I'm just trying to propagate flat universe theories and say
Speaker 2: that it's all just a conspiracy by the universe.
Speaker 1: You're curving my brain.
Speaker 5: Man.
Speaker 2: All right, Well, the next time you look at into space,
Speaker 2: think about what happens to those photons that you're seeing.
Speaker 2: Did they come straight at you or did they get
Speaker 2: bent by space? Are those photons curving their way through
Speaker 2: the universe, maybe even a close circular universe, or did
Speaker 2: it come straight at you from really far away.
Speaker 1: Either way, we're grateful that photons are arriving here on
Speaker 1: Earth and that we're smart enough to figure out the
Speaker 1: messages that they send about the nature of this incredible cosmos.
Speaker 2: Or at least we think we're smart enough. It might
Speaker 2: just be falling flat on our facebooks.
Speaker 1: We're feeling good about being smart. Whether or not we
Speaker 1: are all right.
Speaker 2: We hope you enjoyed that. Thanks for joining us, See
Speaker 2: you next time.
Speaker 1: Thanks for listening, and remember that Daniel and Jorge explain
Speaker 1: the universe is a production of iHeartRadio. For more podcasts
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