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Speaker 1: Hey, Orge, I'm going to say a word, and I

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Speaker 1: want you to tell me if you think it sounds

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Speaker 1: like a positive or a negative idea.

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Speaker 2: All right, go for it.

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Speaker 1: The word is flat.

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Speaker 2: I guess it could go either way. You know, nobody

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Speaker 2: likes their soda flat or they are jokes to fall flat.

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Speaker 1: But I sure do like my bed to be flat.

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Speaker 2: But do you like your tires to be flat?

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Speaker 1: No? But I do like my roads to be flat.

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Speaker 2: Does that mean you want the earth to be flat?

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Speaker 1: I like it spherical, But I also like mountains, so

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Speaker 1: I guess I'm anti flat earth.

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Speaker 2: Do you like falling flat from a mountain?

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Speaker 1: I like landing flat on my feet.

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Speaker 2: I think this discussion has run out of air.

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Speaker 3: Hi.

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Speaker 2: I'm Hoorhey, mccartoonist and the author of the book Oliver's

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Speaker 2: Great Big Universe.

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Speaker 1: Hi, I'm Daniel. I'm a particle physicist and a professor

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Speaker 1: at UC Irvine, and I'm also flat footed.

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Speaker 2: Are you saying metaphorically or you know, physiologically?

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Speaker 1: Well, your questions often catch me flat footed, so that's metaphorical,

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Speaker 1: but also literally and physiologically, I have flat feet, so yeah,

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Speaker 1: I wear inserts.

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Speaker 2: Does that have to make you taller you like Tom Cruise,

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Speaker 2: I don't wear heels.

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Speaker 1: No, I wear inserts to avoid crippling pain when running.

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Speaker 2: Sounds like the solution is just not to run life

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Speaker 2: flat on your back.

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Speaker 1: Yeah. I'm working on a floating recliner I can live

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Speaker 1: in for the rest of my life and float around.

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Speaker 2: There you go. You can attach like a bicycle pedal

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Speaker 2: and maybe get your workouts that way.

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Speaker 1: Yeah, that's great for going upstairs.

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Speaker 2: Yeah exactly. But anyways, welcome to our podcast. Daniel and

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Speaker 2: Jorge Explained the Universe, a productive of iHeartRadio.

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Speaker 1: Where we take all the twists and turns and curves

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Speaker 1: of this crazy universe and try to flatten it all

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Speaker 1: out for you. We try to untangle all of the

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Speaker 1: mysteries of the nature of matter, the forces, the energy,

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Speaker 1: the geometry of space time, the size and shape and

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Speaker 1: history of the universe and make a nice, smooth story

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Speaker 1: for you to understand.

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Speaker 2: That's right, because it is an amazing universe full of

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Speaker 2: stuff inflated with amazing and incredible physics and stars and

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Speaker 2: galaxies and planets and particles for us to wonder at

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Speaker 2: and for us to I guess poke it.

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Speaker 1: There's so much that's amazing about the universe. And sometimes

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Speaker 1: you can have two amazing facts that seem to be

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Speaker 1: in conflict, Like, on one hand, it's amazing that we

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Speaker 1: still don't really know so many basic things about the

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Speaker 1: nature of the universe. How big is it? What is

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Speaker 1: its shape? How did it all come to be? We're

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Speaker 1: so ignorant about the environment in which we live. And

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Speaker 1: on the other hand, it's kind of amazing that we

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Speaker 1: know anything about the universe, and then we've only lived

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Speaker 1: on one tiny little dot and one random little corner

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Speaker 1: of the universe and never really left.

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Speaker 2: Yeah, it's amazing what we can learn just from this

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Speaker 2: little corner of the universe. And as you said, how

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Speaker 2: we can ask these big questions about how everything is

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Speaker 2: the way it is and why it is the way

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Speaker 2: it is, Like, for example, we don't know if the

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Speaker 2: universe is flat footed or not.

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Speaker 1: Does the universe even like to run? Or does just

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Speaker 1: want to sit on the couch and eat snacks all day?

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Speaker 2: Yeah, just sit around and spin.

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Speaker 1: It has big consequences for the curvature of the universe.

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Speaker 2: It is getting bigger and bigger, so you know, maybe

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Speaker 2: it could use a little bit of exercise. It's getting

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Speaker 2: wider and wider per second.

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Speaker 1: I think we should be universe positive on this podcast.

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Speaker 1: You know, universe just be whatever shape you are, We

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Speaker 1: love you.

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Speaker 2: Yeah, yeah, true, true, true. I guess we should love

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Speaker 2: the universe the way it is.

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Speaker 1: It's the only universe we got, so might as well

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Speaker 1: love it.

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Speaker 2: Even if we don't understand it. I guess all the

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Speaker 2: time we should, you know, take it for what it is.

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Speaker 2: That's kind of what science is, right, taking things for

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Speaker 2: what they are.

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Speaker 1: Taking things for what they are are, absolutely, but then

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Speaker 1: always asking why are they this way? Why couldn't they

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Speaker 1: be some other way? Why do we live in this universe?

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Speaker 1: Do we live in the only universe that's possible? Or

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Speaker 1: are there many possible universes and we just happen to

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Speaker 1: be in this one. So often we look around as

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Speaker 1: we try to tell the story of the universe, and

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Speaker 1: we ask those kinds of questions like does this make sense?

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Speaker 1: This seems weird? Is it random? Or is there a

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Speaker 1: reason for it?

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Speaker 2: Yeah, because it is pretty perplexing out there the way

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Speaker 2: things are. You know, there are amazing things like black

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Speaker 2: holes that seem unexplainable, and there's sort of really weird

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Speaker 2: things like quantum mechanics out there that kind of keep

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Speaker 2: you guessing about what the universe is going to do.

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Speaker 1: And as we put together this story of physics that

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Speaker 1: tells us how the universe operates, what machinery is going

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Speaker 1: on behind the scenes, that controls like what happens when

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Speaker 1: two particles bump into each other, or house space curves

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Speaker 1: and twists in the presence of mass. We start to

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Speaker 1: tell a story about the universe, we notice, like, hm,

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Speaker 1: the universe seems to do this kind of thing or

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Speaker 1: do that kind of thing. And sometimes the story tells

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Speaker 1: is very weird. It's very surprising. It's not one that

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Speaker 1: makes sense to us or seems intuitive. It makes us

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Speaker 1: wonder if maybe we're missing part of the story or

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Speaker 1: if we're all just very very lucky.

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Speaker 2: Yeah, and as you said, there are big questions about

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Speaker 2: the universe that we still don't know about, like its size,

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Speaker 2: its shape, and what it's going to do in the future,

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Speaker 2: and also a very interesting question about its curvature.

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Speaker 1: Yeah. As we develop our understanding of gravity and general

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Speaker 1: relativity and we understand that space is weird and twisted

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Speaker 1: and curved and that affects how things move, it also

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Speaker 1: affects how the universe itself expands or contracts. So we

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Speaker 1: have a lot of really fun questions to ask about

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Speaker 1: why the universe looks this particular way, especially about the

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Speaker 1: curvature of space.

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Speaker 2: So today on the podcast, we'll be tackling the question

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Speaker 2: why is space so flat? You mean as opposed to bumpy? Like,

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Speaker 2: what would be the opposite of flat overinflated under pressure?

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Speaker 1: Just like my arches, the opposite of flat would be curved, right,

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Speaker 1: everybody likes nice curved arches for their feet, and the

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Speaker 1: opposite of flat in the case of space or the

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Speaker 1: universe would be curved.

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Speaker 2: Well, it could also be well bumpy. I guess bumpy

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Speaker 2: is also kind of curvy. It means you have a

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Speaker 2: lot of little curves. You could have bumpy feet.

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Speaker 1: Yeah, exactly, that's true. You got to sand those down

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Speaker 1: a little bit. But in this case, yeah, we're talking

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Speaker 1: about like the nature of space is space the way

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Speaker 1: Euclid thought about it, You know, two parallel lines will

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Speaker 1: never touch, or a space more complicated twisting and curving

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Speaker 1: on a global sense. We're talking here about the curvature

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Speaker 1: of the entire universe itself.

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Speaker 2: Yeah, and this is I guess a pretty mind bending

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Speaker 2: and space bending topic, because you know, I think we're

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Speaker 2: all used to thinking of space, or at least empty

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Speaker 2: space is being kind of like flat, right, not weird

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Speaker 2: and curved.

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Speaker 1: It's really hard to think about this in the three

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Speaker 1: dimensions of our universe, and even the word flat is

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Speaker 1: kind of confusing there. It comes really from thinking about

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Speaker 1: a two dimensional version of the picture instead of thinking

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Speaker 1: about space like I can move in three different directions,

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Speaker 1: it's easier to think about it in two different directions

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Speaker 1: because then we can like draw it on a piece

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Speaker 1: of paper. So if you imagine like a sheet of

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Speaker 1: graph paper, that's a flat sheet of paper, and two

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Speaker 1: parallel lines on that piece of paper are never going

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Speaker 1: to meet each other. When we talk about whether space

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Speaker 1: is flat, we're asking a similar kind of question, but

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Speaker 1: about three dimensional space, though it's harder to understand, like

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Speaker 1: what curvature means in three dimensions than it is in

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Speaker 1: two dimensions.

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Speaker 2: Are you saying we're going to use a term that

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Speaker 2: doesn't quite work or describe things or is counterintuitive to

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Speaker 2: actually what is actually happening. Are we going to do

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Speaker 2: that again?

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Speaker 1: Yeah, that's exactly right. That's the story of.

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Speaker 2: Physics being inadequate.

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Speaker 1: We think we understand the universe, and then it surprises

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Speaker 1: us and it sort of outgrows even like our ideas

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Speaker 1: and forces us to like generalize these concepts like, oh wait,

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Speaker 1: flattness can apply in three dimensions, not just two.

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Speaker 2: Well, as usual, we were wondering how many people out

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Speaker 2: there had thought about this question whether space and why

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Speaker 2: space is so flat, and so Daniel went out into

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Speaker 2: the internet to ask people this question.

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Speaker 1: Thanks very much to everybody who participates. If you'd like

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Speaker 1: to hear your voice answering these questions for this segment

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Speaker 1: of the podcast, please don't be shy. Write to me

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Speaker 1: two questions at Danielandjorge dot com. You'll have a good time,

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Speaker 1: I promise.

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Speaker 2: So think about it for a second. Why do you

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Speaker 2: think space is flat? Here's what people had to say.

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Speaker 4: I think space is flat because I think at the

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Speaker 4: beginning there wasn't any room for stuff to be clumpy

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Speaker 4: or lumped together or have little dips or gaps. And

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Speaker 4: I assume that everything was shot out from the big

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Speaker 4: Bang in every direction in equal measure, and therefore it

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Speaker 4: stayed flat to this day.

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Speaker 3: I think that we're not one hundred percent certain that

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Speaker 3: space is flat. It just seems like it's flat because

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Speaker 3: space has been inflated so much from our perspective. The

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Speaker 3: analogy that I've heard before is kind of like standing

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Speaker 3: on the surface of the Earth, where the curvature of

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Speaker 3: the Earth is so large relative to us that it

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Speaker 3: seems like it's flat.

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Speaker 1: I'm not sure. I thought it was three dimensional.

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Speaker 5: Plant has to do with two D.

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Speaker 6: I think the flat space is somehow stable equilibrium points,

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Speaker 6: so the space will eventually evolve into the flat version.

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Speaker 7: I was sneaking suspicion it's not so flat, but it

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Speaker 7: just looks that way to us. I know there's some

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Speaker 7: bits of like string theory that posit there are dimensions

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Speaker 7: we simply can't perceive, and so I'm wondering if space

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Speaker 7: just looks flat to us because we just don't have

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Speaker 7: a capacity to see the other dimensions.

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Speaker 5: I don't think it is very flat. I think it

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Speaker 5: is pretty multi dimensional. I don't know what really is

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Speaker 5: meant by that. Maybe like stuff forms discs, like the

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Speaker 5: Solar System or our galaxy, maybe that is meant by flat.

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Speaker 5: I think that is due to so that things tend

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Speaker 5: to take the shape of discs when there's rotation.

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Speaker 2: Involved, all right, and not a lot of flat universes.

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Speaker 1: Yeah. Here, I think you really are scoring some points

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Speaker 1: because a lot of people think flat implies two dimensional.

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Speaker 2: Yeah, that makes sense, right, like if something if the

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Speaker 2: universe was flat, it would be the width of a

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Speaker 2: sheet of paper kind of right.

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Speaker 1: Mm hmm. Yeah. If somebody like bakes your birthday cake

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Speaker 1: and then a truck drives over it and flattens it,

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Speaker 1: then you think of it as like thinner, right, squeeze

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Speaker 1: down to two.

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Speaker 2: Dimensions two dimensional? Yeah, although two dimensional cake would be

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Speaker 2: pretty low calorie.

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Speaker 1: I don't think the calorie squeeze out of it when

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Speaker 1: the truck drives over it, unless there's like fusion that happens,

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Speaker 1: but that would be a pretty heavy truck.

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Speaker 2: As if a truck runs over it, I don't think

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Speaker 2: you want to eat it off the road. It seems

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Speaker 2: like it will make you sick.

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Speaker 1: I think we need to have a highly controlled experiment,

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Speaker 1: one of those like roads smootheners they have in cartoons

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Speaker 1: all the time that's crushing white the coyote. Squeeze a

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Speaker 1: cake and see if it still makes people fat.

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Speaker 2: I'm pretty sure that if you ask YouTube, somebody out

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Speaker 2: there has made a video of a cake being flatted

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Speaker 2: by multiple things.

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Speaker 1: Thank you.

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Speaker 2: YouTube sounds like the kind of thing the Internet likes.

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Speaker 1: If it doesn't exist on the Internet before this podcast,

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Speaker 1: it certainly will after.

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Speaker 2: But yeah, it's an interesting question why is space flat?

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Speaker 2: And I guess also is space flat? I guess is

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Speaker 2: maybe the first question we should be asking, or maybe

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Speaker 2: the question before that should be what does it mean

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Speaker 2: for space to be flat?

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Speaker 1: Yeah, it's a really fascinating question to even think about,

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Speaker 1: like what it means for space to be flat, and

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Speaker 1: to talk about how we measure it's flat and why

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Speaker 1: we're surprised to find that it is flat. But you're right,

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Speaker 1: first we should make sure we're clear about what we

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Speaker 1: mean by flat. And there's sort of two different concepts

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Speaker 1: to there, of course connected that we need to think about.

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Speaker 1: We can think about locally being flat, like is the

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Speaker 1: universe bumpy? And we can think about globally like is

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Speaker 1: the universe curved? On some big scale. Thinking about locally

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Speaker 1: is a little bit easy, though of course still twists

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Speaker 1: your brain a little bit. This is just the idea

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Speaker 1: that matter bends space, that the reason things don't seem

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Speaker 1: to move in straight lines but seem to be bent

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Speaker 1: by gravity. Is not because gravity is a force, but

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Speaker 1: that space itself is curved. So things are moving through

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Speaker 1: that curved space. The Sun bends the space around it,

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Speaker 1: so the Earth moves in that circle, which is the

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Speaker 1: natural inertial motion for an object in that curved space.

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Speaker 1: That's sort of local curvature.

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Speaker 2: Right, right, although I think we always have to give

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Speaker 2: the caveat that. You mean space time, right, Like space

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Speaker 2: time is what's curved.

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Speaker 1: Well, space is a part of space time, and the

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Speaker 1: curvature of space time is a little bit different from

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Speaker 1: the curvature of space. But in this case, space is

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Speaker 1: also curved.

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Speaker 2: But I guess I mean like curved space makes me

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Speaker 2: think of like a road. Like a road is curved,

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Speaker 2: and so anything that tries to follow a straight line

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Speaker 2: on that road is going to follow the same path.

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Speaker 2: But maybe in real life it would kind of depend, right,

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Speaker 2: I don't know how fast you're going or what your

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Speaker 2: mass is or right, isn't it?

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Speaker 1: Yeah, A curved road is a helpful analogy. Things that

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Speaker 1: are moving through space are basically following an invisible road

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Speaker 1: that we can't see. You know, space is curved, but

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Speaker 1: in this way that we can't directly observe it. Like

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Speaker 1: you can look at a road and say, oh, there's

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Speaker 1: a curve coming up ahead, but you can't look at

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Speaker 1: space and see the curvature directly. But it does affect

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Speaker 1: the way things move through it. So you try to

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Speaker 1: drive your car on the curve road of space, and

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Speaker 1: space moves your car forward. You sort of like guides

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Speaker 1: it along the curvature of space and fundamensional space time.

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Speaker 1: It's really fascinating because time and space bend together to

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Speaker 1: make space. Time itself have these invariants, these things that

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Speaker 1: don't actually change, but space curves and time curves due

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Speaker 1: to the presence of mass. Right.

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Speaker 2: But like if I throw a bowling ball at a

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Speaker 2: low speed and a high speed, and I threw a

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Speaker 2: feather at a low speed and as high speed, they

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Speaker 2: would sort of curve through space, or I would see

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Speaker 2: them curve in a different way, or would they all

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Speaker 2: curve the same way.

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Speaker 1: We know that because, for example, you throw a baseball

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Speaker 1: at different speeds, it's going to go a different path, right,

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Speaker 1: So it definitely depends on the velocity of the object

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Speaker 1: as it moves through curve space. So that's all inertial motion.

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Speaker 1: That's motion under no forces, just the curvature of space.

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Speaker 2: So I wonder if it's more accurate to say that

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Speaker 2: space has curvature and not that space is curved.

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Speaker 1: What's the distinction in your mind?

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Speaker 2: Well, space like if you say that space is curved,

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Speaker 2: make me think of it like a tunnel. Like, if

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Speaker 2: a tunnel is curved, then no matter how fast you're

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Speaker 2: going or what you throw, you're going to bend the

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Speaker 2: same way. You can follow the same path. But that's

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Speaker 2: not sort of how space really works, right, Not everything

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Speaker 2: is stuck in the same kind of path.

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Speaker 1: Yeah, you're right, there aren't rigid tunnels that things have

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Speaker 1: to go through. It's not like if you enter a

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Speaker 1: pipe and you get flushed out the bottom or something.

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Speaker 1: The curvature of space does affect how you move, So yeah,

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Speaker 1: that distinction makes sense to me.

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Speaker 2: Okay, So then there's local curvature of space. What you're

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Speaker 2: talking about is sort of like how things go around

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Speaker 2: the Sun, for example, or how the moon goes around.

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Speaker 1: The Earth m or how we stay on the Earth,

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Speaker 1: all that kind of stuff. Things being gravitationally bound, even

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Speaker 1: like the galaxy holding itself together. That's all local curvature

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Speaker 1: in comparison to the global curvature, which is a question

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Speaker 1: about the whole universe and its shape.

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Speaker 2: So there's local and global, and I guess what's the difference,

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Speaker 2: just like the size of it the scale, Like are

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Speaker 2: you saying that? Like if I'm orbiting around the center

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Speaker 2: of the galaxy, it's a different kind of curvature of

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Speaker 2: doue to gravity than the Moon orpening around the Earth.

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Speaker 1: It's not fundamentally different. It's all described by general relativity

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Speaker 1: in Einstein's equations. It's sort of like the difference between

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Speaker 1: the Earth being a sphere and the Earth having mountains.

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Speaker 1: Like the Earth could be flat and it could be

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Speaker 1: a sphere, but it could still have mountains in either case. Right,

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Speaker 1: the Earth could be bumpy locally, it could have valleys

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Speaker 1: and mountains even if it's flat, or even if it's

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Speaker 1: a sphere. So global curvature is more about the question

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Speaker 1: of like is the Earth a sphere or is the

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Speaker 1: Earth flat? Local curvature is about like is the Earth

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Speaker 1: bumpy or is it all perfectly smooth everywhere you go?

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Speaker 2: So we are asking if the universe is bumping.

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Speaker 1: We're asking if the universe is sort of bent Right,

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Speaker 1: is three D space more like the surface of a

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Speaker 1: three sphere? Right? Or is it flat? And morn analogy

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Speaker 1: to like a sheet of paper. So the global curvature

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Speaker 1: space is asking about like the big picture, whereas the

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Speaker 1: local curvature is asking about the little picture right right.

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Speaker 2: But I guess my question was, or is you know

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Speaker 2: where do you draw when do you draw this distinction

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Speaker 2: between local and global, like at the galaxy level, at

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Speaker 2: the galaxy cluster level, or it's only global if it's everything.

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Speaker 1: It's only global if it's everything. And you know, when

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Speaker 1: we solve these equations in general relativity, and by we,

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Speaker 1: I mean those guys who knows all equations in general relativity.

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Speaker 5: Not me.

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Speaker 1: They can only solve those in certain situations, in situations

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Speaker 1: where they assume, like the universe is empty, or the

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Speaker 1: universe is filled with matter, but that matter is perfectly smooth, like.

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Speaker 1: Nobody can solve the general relativity equations for our universe,

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Speaker 1: which has like clumps of matter in it. So when

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Speaker 1: we talk about the whole universe and its curvature, basically

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Speaker 1: we're talking about a simplification of our universe where all

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Speaker 1: the matter is spread out evenly. There are no lumps

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Speaker 1: at all, because that's all they can. And in that case,

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Speaker 1: there's still this question of the global curvature. Is the

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Speaker 1: universe curved on some large scale and how is it curved?

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Speaker 1: Is it flat? Is it open? Is it closed? These

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Speaker 1: are the questions of the global curvature of space time,

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Speaker 1: which are irrelevant to the little details because they still

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Speaker 1: exist even if you smooth all the matter and energy

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Speaker 1: out everywhere like peanut butter.

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Speaker 2: Mmm, but I guess, you know, if it's everything, we

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Speaker 2: don't really know what everything is, right, Like the whole

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Speaker 2: entire observable universe might be just a little bump in

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Speaker 2: a ginormous infinite universe.

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Speaker 1: Well, you're totally right, But the curvature around here is

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Speaker 1: dependent on the energy density, doesn't depend on what's happening

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Speaker 1: out there. And then we assume that what's happening here

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Speaker 1: is what's happening everywhere else, And that's an assumption we

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Speaker 1: don't know. It could be that what we're calling global

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Speaker 1: curvature is actually local on a much larger scale, that

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Speaker 1: if you zoom out from the observable universe to the

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Speaker 1: actual full universe, that we could never see that the

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Speaker 1: curvature is different, right, and that what we were talking

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Speaker 1: about the whole time is quote unquote global curvature is

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Speaker 1: actually the local curvature of the observable universe.

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Speaker 2: I guess it's sort of like how before we used

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Speaker 2: to think that the Earth was flat because we only

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Speaker 2: knew sort of the local area here around this and

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Speaker 2: looks pretty flat. But actually if you sort of keep

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Speaker 2: going or you're taken to account the whole planet, then

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Speaker 2: you see that the whole planet is curved and round.

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Speaker 1: Yeah, exactly. And if you lived on a part of

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Speaker 1: the Earth that was literally flat, like maybe you were

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Speaker 1: really precise about it, and you took out a bunch

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Speaker 1: of tools and you try to measure the curvature of

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Speaker 1: the Earth. Imagine you lived on like a truly flat

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Speaker 1: part of the Earth and you measured it to be flat,

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Speaker 1: and then you left that and you realized, oh, actually

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Speaker 1: the rest of the Earth is curved. And so what

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Speaker 1: I got was a misunderstanding of the bigger picture. So

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Speaker 1: you're right, we can only see the observable universe, and

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Speaker 1: we can measure the global curvature of this part of

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Speaker 1: the universe and then assume that the rest of it

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Speaker 1: is the same. But we'll never know, all.

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Speaker 2: Right, So then a local curvature of space sort of

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Speaker 2: is kind of about how mass spans space, and how

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Speaker 2: the Moon goes around the Earth and the Earth goes

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Speaker 2: around the Sun through curve space time. Now, when you're

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Speaker 2: talking about the global picture, I guess you're not just

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Speaker 2: talking about how things move, but it's more sort of

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Speaker 2: a fundamental property of space about what it contains.

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Speaker 1: Yeah, and it's really hard to think about it in

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Speaker 1: three D. So we do this thing where we talk

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Speaker 1: about two dimensional versions. Sometimes that's helpful and sometimes it's misleading.

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Speaker 1: So you always have to keep in mind, like how

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Speaker 1: those things translate from a two dimensional analogy that's easier

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Speaker 1: for us to think about to the reality of three

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Speaker 1: D space. And it's easier to think about two dimensional

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Speaker 1: analogies because we basically live on a two dimensional surface,

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Speaker 1: the surface of the Earth, right, So it's easy to

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Speaker 1: imagine like living on a flat sheet of paper versus

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Speaker 1: living on the surface of a sphere versus living in

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Speaker 1: like a hyperbola, And so those three shapes have different curvature.

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Speaker 1: An infinite plane is totally flat. If you drew a

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Speaker 1: triangle on the ground, the angles would add up to

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Speaker 1: one hundred and eighty degrees. The surface of a sphere,

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Speaker 1: we say it has positive curvature. You try a triangle

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Speaker 1: that follows the surface of that sphere, its angles are

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Speaker 1: going to add up to more than a hund You

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Speaker 1: live on the surface of a hyperboloid, and you draw

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Speaker 1: a triangle on that surface, the angles are going to

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Speaker 1: add up to less than one eighty. So those are

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Speaker 1: two D examples of curved surfaces. Then you have to

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Speaker 1: extrapolate those two three D space, and it's very similar

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Speaker 1: to a lot of the ideas carry over.

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Speaker 2: I feel like this is getting a little bit technical,

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Speaker 2: So when don't we stretch these thoughts out and try

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Speaker 2: to get them down flat and talk about what it

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Speaker 2: actually means for three D universal space to be flat.

442
00:20:29,440 --> 00:20:31,080
Speaker 2: But first, let's take a quick break.

443
00:20:43,640 --> 00:20:43,919
Speaker 1: All right.

444
00:20:43,960 --> 00:20:47,439
Speaker 2: We're asking the question why is space so flat? And

445
00:20:47,840 --> 00:20:51,160
Speaker 2: I guess the preceding question is is space flat? And

446
00:20:51,200 --> 00:20:53,480
Speaker 2: the preceding preceding question is what does it mean for

447
00:20:53,520 --> 00:20:56,040
Speaker 2: the for space to be flat? Because I guess base

448
00:20:56,119 --> 00:20:58,359
Speaker 2: sort of seems flat to us, you know, it doesn't

449
00:20:58,359 --> 00:21:01,679
Speaker 2: seem curve or bent to us, at least our immediate surroundings.

450
00:21:01,720 --> 00:21:04,440
Speaker 2: But we know that if you expand your your surroundings

451
00:21:04,480 --> 00:21:06,359
Speaker 2: a little bit, you see that space time is flat.

452
00:21:06,640 --> 00:21:08,880
Speaker 2: That's how gravity works, and that's what makes the Moon

453
00:21:08,920 --> 00:21:11,040
Speaker 2: go around the Earth and the Earth around go around

454
00:21:11,200 --> 00:21:15,320
Speaker 2: the Sun. But we're talking now about global curvature of space,

455
00:21:15,440 --> 00:21:19,080
Speaker 2: which really means universal curvature of space, which actually sort

456
00:21:19,080 --> 00:21:22,320
Speaker 2: of means observable universe curvature of space, right yeah.

457
00:21:22,160 --> 00:21:24,439
Speaker 1: And we're trying to use our understanding of two D

458
00:21:24,600 --> 00:21:27,199
Speaker 1: space to sort of bootstrap our way to understand the

459
00:21:27,280 --> 00:21:30,199
Speaker 1: curvature of three D space. So if you're like on

460
00:21:30,320 --> 00:21:34,240
Speaker 1: a flat surface and you shoot two parallel lines out

461
00:21:34,280 --> 00:21:37,280
Speaker 1: like two laser beams, then they'll never cross each other.

462
00:21:37,359 --> 00:21:39,480
Speaker 1: This is Euclid's famous geometry, and that's why we call

463
00:21:39,560 --> 00:21:43,359
Speaker 1: it Euclidean geometry. These two parallel lines will never meet.

464
00:21:43,480 --> 00:21:46,040
Speaker 1: And you can also do that in three dimensional space.

465
00:21:46,119 --> 00:21:48,760
Speaker 1: Right now, just imagine the universe is having three directions

466
00:21:48,760 --> 00:21:51,640
Speaker 1: shoot two parallel lines, but in any direction in xyz

467
00:21:52,040 --> 00:21:55,040
Speaker 1: they will never meet. In flat space, the extension of

468
00:21:55,080 --> 00:21:57,920
Speaker 1: flat space from two D three D is pretty straightforward.

469
00:21:58,000 --> 00:21:59,560
Speaker 2: I wonder if, like we even have to go to

470
00:21:59,560 --> 00:22:01,640
Speaker 2: a two D analogy, why can't we just talk about

471
00:22:01,680 --> 00:22:03,520
Speaker 2: the curvature space in three D.

472
00:22:03,840 --> 00:22:06,360
Speaker 1: Yeah, I think three D flat space is pretty straightforward,

473
00:22:06,400 --> 00:22:08,359
Speaker 1: but it can help us understand the curved space to

474
00:22:08,400 --> 00:22:10,280
Speaker 1: start in two D or at least let's give it

475
00:22:10,320 --> 00:22:13,439
Speaker 1: a shot. In two dimensional curved space, if you fire

476
00:22:13,520 --> 00:22:17,520
Speaker 1: two laser beams in the same direction, they will eventually cross.

477
00:22:18,119 --> 00:22:19,639
Speaker 1: Like if you're on the surface of the Earth and

478
00:22:19,680 --> 00:22:21,520
Speaker 1: you fire two laser beams in the direction in the

479
00:22:21,520 --> 00:22:24,359
Speaker 1: north pole, they'll cross when they hit the north pole.

480
00:22:24,560 --> 00:22:27,399
Speaker 2: Right What I think this is why it's confusing, and

481
00:22:27,440 --> 00:22:29,679
Speaker 2: I wonder if we can just stick with three D

482
00:22:29,880 --> 00:22:32,080
Speaker 2: like three D flat space. If I shoot two lasers

483
00:22:32,080 --> 00:22:34,439
Speaker 2: out in space, they're never going to meet. These two

484
00:22:34,520 --> 00:22:36,320
Speaker 2: laser beams, they're never going to meet. Right now, let's

485
00:22:36,320 --> 00:22:39,480
Speaker 2: talk about curve three D space. I shoot two lasers,

486
00:22:39,520 --> 00:22:42,240
Speaker 2: and the lasers are going to do one of two things, right,

487
00:22:42,280 --> 00:22:45,640
Speaker 2: They're either going to come towards each other or bend

488
00:22:45,680 --> 00:22:46,400
Speaker 2: away from each other.

489
00:22:46,520 --> 00:22:48,800
Speaker 1: That's right. And whether they come towards each other and

490
00:22:48,840 --> 00:22:51,440
Speaker 1: away from each other tells you the sign of the curvature.

491
00:22:51,880 --> 00:22:55,640
Speaker 1: Positive curvature, they'll come towards each other. Negative curvature, they'll

492
00:22:55,720 --> 00:22:57,520
Speaker 1: veer away from each other, never meet.

493
00:22:58,119 --> 00:23:01,280
Speaker 2: Now this is super weird because what's bending the path

494
00:23:01,320 --> 00:23:04,560
Speaker 2: of the lasers just the curvingness of space.

495
00:23:05,600 --> 00:23:08,679
Speaker 1: Lasers and light follow the curvature of space. They're like

496
00:23:08,760 --> 00:23:13,120
Speaker 1: tracers that tell you how space is curved. So light

497
00:23:13,240 --> 00:23:17,679
Speaker 1: moves in straight lines through curved space time, right, But

498
00:23:17,840 --> 00:23:20,400
Speaker 1: that leads to curved motion in space.

499
00:23:20,800 --> 00:23:22,800
Speaker 2: So you're saying that space might have a property to

500
00:23:22,840 --> 00:23:26,560
Speaker 2: it called curvature, which would to us make the light

501
00:23:26,600 --> 00:23:28,359
Speaker 2: beams not go in a straight line.

502
00:23:28,400 --> 00:23:30,840
Speaker 1: That's right. If you assume space is flat, then light

503
00:23:30,880 --> 00:23:33,960
Speaker 1: appears to be moving in a curve. If, however, space

504
00:23:34,000 --> 00:23:37,399
Speaker 1: itself is curved, those grid lines themselves are curving, then

505
00:23:37,480 --> 00:23:39,560
Speaker 1: light is moving along those grid lines. It's just the

506
00:23:39,600 --> 00:23:41,360
Speaker 1: gridlines themselves are curved.

507
00:23:41,440 --> 00:23:43,840
Speaker 2: Okay, So now I feel like there's a third possibility.

508
00:23:44,359 --> 00:23:46,679
Speaker 2: So like, if I have a laser shooter on my

509
00:23:46,800 --> 00:23:49,639
Speaker 2: right hand and a laser shooter on my left hand,

510
00:23:50,119 --> 00:23:52,480
Speaker 2: and I shoot them perfectly parallel to each other. If

511
00:23:52,520 --> 00:23:54,639
Speaker 2: space is flat, they're just going to keep going straight

512
00:23:55,000 --> 00:23:58,600
Speaker 2: parallel forever. But if space is curved, there's some things

513
00:23:58,600 --> 00:24:01,000
Speaker 2: that can do. They can bend towards each other away

514
00:24:01,000 --> 00:24:02,800
Speaker 2: from each other. But I feel like they could also

515
00:24:03,000 --> 00:24:07,080
Speaker 2: like bend perpendicular to each other, like maybe my right

516
00:24:07,160 --> 00:24:11,720
Speaker 2: laser beam drifts up and my left laser being drifts down.

517
00:24:11,960 --> 00:24:12,960
Speaker 2: What does what would that mean?

518
00:24:13,160 --> 00:24:15,160
Speaker 1: Isn't that the same as bending away from each other?

519
00:24:15,240 --> 00:24:18,280
Speaker 2: I guess if I just turn my head sideways, what

520
00:24:18,400 --> 00:24:22,160
Speaker 2: if they spiral around each other? Can space be twisty?

521
00:24:22,400 --> 00:24:25,320
Speaker 1: Space can have all sorts of weird combinations. I mean,

522
00:24:25,400 --> 00:24:27,359
Speaker 1: in general relativity, space can doesn't even have to be

523
00:24:27,440 --> 00:24:30,560
Speaker 1: totally connected. So a laser beam can like disappear and

524
00:24:30,600 --> 00:24:33,959
Speaker 1: appear somewhere else, right, That's basically what a wormhole would be.

525
00:24:34,160 --> 00:24:36,800
Speaker 1: We're trying to talk about pretty simple constructions of space

526
00:24:36,840 --> 00:24:39,639
Speaker 1: where all you have is a single overall curvature.

527
00:24:40,400 --> 00:24:43,119
Speaker 2: I guess if I shoot my laser beams and they

528
00:24:43,720 --> 00:24:47,879
Speaker 2: they go past a large massive object in space, like

529
00:24:47,920 --> 00:24:51,080
Speaker 2: the Sun, they're gonna curve, and if they're maybe on

530
00:24:51,160 --> 00:24:53,920
Speaker 2: opposite or different sides of the Sun, they're gonna curve

531
00:24:53,960 --> 00:24:57,080
Speaker 2: in a different way. And as they go through a galaxy,

532
00:24:57,080 --> 00:24:58,840
Speaker 2: they're gonna get pushed this way and that way. The

533
00:24:58,880 --> 00:25:01,000
Speaker 2: laser beams. But I think you're talking about like if

534
00:25:01,040 --> 00:25:04,640
Speaker 2: I shoot them maybe really far apart from each other,

535
00:25:05,160 --> 00:25:07,240
Speaker 2: and let them go for a really really long time

536
00:25:07,400 --> 00:25:09,960
Speaker 2: on average, Are they going to be moving towards each

537
00:25:10,000 --> 00:25:12,080
Speaker 2: other or away from each other? That's what you mean

538
00:25:12,160 --> 00:25:13,400
Speaker 2: by global curvature.

539
00:25:13,960 --> 00:25:15,919
Speaker 1: Yeah, And your analogy is great because it lets us

540
00:25:16,000 --> 00:25:20,680
Speaker 1: make a connection between local curvature and global curvature. Local curvature,

541
00:25:20,680 --> 00:25:22,360
Speaker 1: as you say, is like, is there a star there

542
00:25:22,400 --> 00:25:24,159
Speaker 1: that's going to bend the path of my life? And

543
00:25:24,200 --> 00:25:26,160
Speaker 1: we sort of got our minds around a little bit

544
00:25:26,200 --> 00:25:29,240
Speaker 1: the general relativity that light is bent by masses. Even

545
00:25:29,280 --> 00:25:32,040
Speaker 1: though light has no mass, it follows the curvature of space,

546
00:25:32,240 --> 00:25:35,119
Speaker 1: and it's bent right now. Instead of having a local

547
00:25:35,160 --> 00:25:37,400
Speaker 1: mass like a star with a single point of really

548
00:25:37,480 --> 00:25:40,399
Speaker 1: high density, take that star and spread it out throughout

549
00:25:40,400 --> 00:25:43,560
Speaker 1: the whole universe instead. So now the universe is filled

550
00:25:43,560 --> 00:25:46,840
Speaker 1: with constant density of matter or energy that creates a

551
00:25:46,840 --> 00:25:49,600
Speaker 1: curvature of space that's constant. It's not like, oh, there's

552
00:25:49,600 --> 00:25:51,720
Speaker 1: a lot of curvature near that star. Let's have a

553
00:25:51,720 --> 00:25:54,960
Speaker 1: little curvature everywhere instead of a lot of curvature in

554
00:25:55,080 --> 00:25:57,040
Speaker 1: just one spot. And that's one way to think about

555
00:25:57,080 --> 00:25:59,960
Speaker 1: the global curvature of space. Think about a universe unit

556
00:26:00,160 --> 00:26:02,760
Speaker 1: formally filled with a certain matter and energy density.

557
00:26:02,960 --> 00:26:05,520
Speaker 2: So like if the universe was infinite and was filled

558
00:26:05,560 --> 00:26:09,879
Speaker 2: with like evenly spread out gas or an evenly spread

559
00:26:09,880 --> 00:26:13,440
Speaker 2: out star, I guess what would happen to a laser beam.

560
00:26:13,440 --> 00:26:15,320
Speaker 2: Would it still curve or would it go straight?

561
00:26:15,480 --> 00:26:18,760
Speaker 1: It depends on the density of that stuff. Right, there's

562
00:26:18,760 --> 00:26:22,240
Speaker 1: a certain critical density of energy in the universe. Below

563
00:26:22,280 --> 00:26:26,040
Speaker 1: a certain level, the universe will be negatively curved. If

564
00:26:26,040 --> 00:26:29,359
Speaker 1: it has exactly the right critical energy at this knife's edge,

565
00:26:29,400 --> 00:26:31,879
Speaker 1: the universe will be flat. If it's more than that

566
00:26:31,920 --> 00:26:35,600
Speaker 1: critical energy, the universe will be curved. So the curvature

567
00:26:35,680 --> 00:26:39,359
Speaker 1: of the universe itself of space is connected to the

568
00:26:39,560 --> 00:26:42,600
Speaker 1: energy density of stuff in the universe relative to this

569
00:26:42,720 --> 00:26:43,800
Speaker 1: critical threshold.

570
00:26:44,040 --> 00:26:46,520
Speaker 2: I guess that's a little counterintuitive, because I would think

571
00:26:46,600 --> 00:26:49,359
Speaker 2: that if the universe is filled evenly with the same

572
00:26:49,520 --> 00:26:53,680
Speaker 2: energy or gas or matter or energy, then the laser

573
00:26:53,680 --> 00:26:56,520
Speaker 2: beam would just go straight because it's being pulled the

574
00:26:56,600 --> 00:26:58,040
Speaker 2: same way in all directions.

575
00:26:58,240 --> 00:27:02,400
Speaker 1: Yeah. Unfortunately, general relativity isn't intuitive, and if you add

576
00:27:02,520 --> 00:27:06,040
Speaker 1: enough stuff to the universe, it curves up. It makes

577
00:27:06,080 --> 00:27:09,480
Speaker 1: the universe effectively like a sphere. That's only consistent with

578
00:27:09,640 --> 00:27:14,160
Speaker 1: universes that have a positive curvature, because imagine you take

579
00:27:14,160 --> 00:27:16,360
Speaker 1: every bit of space and you make it bend y. Now,

580
00:27:16,400 --> 00:27:19,199
Speaker 1: think about, like, what shapes can you build with that?

581
00:27:19,400 --> 00:27:21,560
Speaker 1: If you only have curvy pieces, all you can do

582
00:27:21,600 --> 00:27:23,600
Speaker 1: is build the surface of a sphere, or all you

583
00:27:23,600 --> 00:27:26,119
Speaker 1: can do is build a three dimensional version of the

584
00:27:26,160 --> 00:27:28,919
Speaker 1: surface of a four dimensional sphere if all you have

585
00:27:29,000 --> 00:27:30,000
Speaker 1: are bendy pieces.

586
00:27:31,400 --> 00:27:34,639
Speaker 2: Yeah, I guess I'm still confused because I'm imagine this

587
00:27:34,680 --> 00:27:37,440
Speaker 2: scenario where the whole universe is filled with the same

588
00:27:37,480 --> 00:27:40,600
Speaker 2: gas or evenly distributed star. If I shoot a laser beam,

589
00:27:40,640 --> 00:27:43,760
Speaker 2: which way does it curve? If the universe is positively curve,

590
00:27:43,920 --> 00:27:45,440
Speaker 2: so curve up, down, left right.

591
00:27:45,560 --> 00:27:48,199
Speaker 1: In a universe with positive curvature, if you shoot a

592
00:27:48,280 --> 00:27:50,919
Speaker 1: laser beam, it looks to you like it's going straight,

593
00:27:51,119 --> 00:27:52,840
Speaker 1: but then it hits you in the back of the head.

594
00:27:53,000 --> 00:27:54,920
Speaker 2: What it wouldn't necessarily hit mean in the back of

595
00:27:54,960 --> 00:27:55,320
Speaker 2: my head.

596
00:27:55,880 --> 00:27:59,680
Speaker 1: In a universe that's uniformly filled with matter that's positive curvature,

597
00:28:00,119 --> 00:28:01,960
Speaker 1: it will loop back around. It's like being on the

598
00:28:01,960 --> 00:28:04,640
Speaker 1: two dimensional surface of a three dimensional sphere.

599
00:28:04,680 --> 00:28:07,040
Speaker 2: But I guess it maybe it might loop around a

600
00:28:07,040 --> 00:28:08,560
Speaker 2: few times before it hits me in the back of

601
00:28:08,560 --> 00:28:08,880
Speaker 2: the head.

602
00:28:08,960 --> 00:28:10,399
Speaker 1: Any point on a sphere is the same, so it

603
00:28:10,400 --> 00:28:13,000
Speaker 1: doesn't really matter where you are, which direction you shoot it.

604
00:28:13,040 --> 00:28:15,320
Speaker 1: You always get the same results. From that point of view.

605
00:28:15,800 --> 00:28:17,520
Speaker 2: I feel like then, now it's getting a little bit

606
00:28:17,560 --> 00:28:21,040
Speaker 2: into this idea of the how space is connected to itself,

607
00:28:21,160 --> 00:28:23,639
Speaker 2: which is at the case, is a curvature of space

608
00:28:23,760 --> 00:28:26,480
Speaker 2: necessarily the same as how space is connected to itself,

609
00:28:26,480 --> 00:28:28,159
Speaker 2: whether it loops around itself.

610
00:28:27,960 --> 00:28:30,360
Speaker 1: It's definitely connected. Right, It's not the same, but it's

611
00:28:30,359 --> 00:28:34,040
Speaker 1: definitely connected. If space is flat, then the universe can

612
00:28:34,080 --> 00:28:37,240
Speaker 1: be infinite. If space is positive curvature, then the universe

613
00:28:37,280 --> 00:28:40,040
Speaker 1: can't be infinite. It can be finite but also have

614
00:28:40,160 --> 00:28:43,280
Speaker 1: no boundary, just the way like the two dimensional surface

615
00:28:43,280 --> 00:28:46,760
Speaker 1: of a three D sphere can be finite but unbounded

616
00:28:47,080 --> 00:28:50,120
Speaker 1: because it has positive curvature. So these two ideas are

617
00:28:50,160 --> 00:28:53,800
Speaker 1: definitely connected. The topology of space, the large scale shape

618
00:28:53,840 --> 00:28:56,840
Speaker 1: of space, and the curvature of space. The two things

619
00:28:56,840 --> 00:29:00,239
Speaker 1: are definitely closely linked. The curvature of space you can

620
00:29:00,240 --> 00:29:03,360
Speaker 1: deduce from the density of matter in that space. Because

621
00:29:03,440 --> 00:29:05,280
Speaker 1: general relativity connects those two things.

622
00:29:05,480 --> 00:29:07,160
Speaker 2: Now, that was one laser beam. Now I take two

623
00:29:07,240 --> 00:29:10,120
Speaker 2: laser beams and I shoot it off into three D space.

624
00:29:10,320 --> 00:29:13,880
Speaker 2: And let's say that the universe has positive curvature. What's

625
00:29:13,920 --> 00:29:17,080
Speaker 2: going to happen to these two laser beams. They're eventually

626
00:29:17,160 --> 00:29:17,960
Speaker 2: going to hit each other.

627
00:29:18,080 --> 00:29:19,560
Speaker 1: They will eventually cross. Yeah.

628
00:29:19,800 --> 00:29:23,640
Speaker 2: Mmm. And if the universe is not positively curved, if

629
00:29:23,680 --> 00:29:27,040
Speaker 2: it's negatively curved, then they'll never hit each other.

630
00:29:27,120 --> 00:29:28,840
Speaker 1: They won't hit each other, they'll veer apart.

631
00:29:29,160 --> 00:29:32,800
Speaker 2: M all right. I think that gives us as good

632
00:29:32,800 --> 00:29:35,480
Speaker 2: of an explanation of what the curvature space is in

633
00:29:35,520 --> 00:29:36,680
Speaker 2: the universe, right, m hm.

634
00:29:37,160 --> 00:29:40,320
Speaker 1: And all of these things together control the future of

635
00:29:40,360 --> 00:29:44,520
Speaker 1: the universe, like the curvature and the topology, the matter

636
00:29:44,640 --> 00:29:47,440
Speaker 1: density of the universe. That plus like the dark energy

637
00:29:47,440 --> 00:29:50,400
Speaker 1: of the universe, all these things work together to determine

638
00:29:50,520 --> 00:29:53,520
Speaker 1: how fast the universe is expanding. Is it expanding or

639
00:29:53,600 --> 00:29:57,160
Speaker 1: is it collapsing or is it steady state with no expansion.

640
00:29:57,560 --> 00:30:00,080
Speaker 1: All of these things play a role in determining the

641
00:30:00,080 --> 00:30:02,080
Speaker 1: future of the universe. Cool.

642
00:30:02,320 --> 00:30:05,920
Speaker 2: Well, maybe talk about how you might measure the flatness

643
00:30:05,920 --> 00:30:07,880
Speaker 2: of the universe in like, how do we know whether

644
00:30:07,920 --> 00:30:09,920
Speaker 2: the universe is flat or not.

645
00:30:10,200 --> 00:30:12,280
Speaker 1: So what we do is we measure this energy density.

646
00:30:12,560 --> 00:30:14,480
Speaker 1: And of course the caveat is we can only measure

647
00:30:14,480 --> 00:30:17,280
Speaker 1: it in the observable universe. We can't measure outside, and

648
00:30:17,320 --> 00:30:19,240
Speaker 1: so when we say the universe here, we always really

649
00:30:19,280 --> 00:30:21,520
Speaker 1: just mean the observable universe. All we can do is

650
00:30:21,600 --> 00:30:24,200
Speaker 1: measure the energy density, and we can say, is there

651
00:30:24,320 --> 00:30:27,560
Speaker 1: enough stuff in the universe to make it curved positively

652
00:30:27,960 --> 00:30:30,520
Speaker 1: so it wraps up on itself. Is there the critical

653
00:30:30,560 --> 00:30:32,960
Speaker 1: density so the space is flat? Or is there less

654
00:30:33,000 --> 00:30:35,720
Speaker 1: than the critical density so that the universe is open

655
00:30:35,840 --> 00:30:38,520
Speaker 1: with negative curvature. So the way we do that is

656
00:30:38,520 --> 00:30:41,600
Speaker 1: by measuring the amount of stuff, the energy density of

657
00:30:41,640 --> 00:30:42,720
Speaker 1: stuff in the universe.

658
00:30:42,840 --> 00:30:45,160
Speaker 2: Oh, I see you measure the density of stuff. But

659
00:30:45,280 --> 00:30:47,640
Speaker 2: I guess we never covered why the density of stuff

660
00:30:47,760 --> 00:30:50,000
Speaker 2: determines the curvature of space, Like why is there a

661
00:30:50,000 --> 00:30:53,440
Speaker 2: critical amount that makes it negative or positive? Like wouldn't

662
00:30:53,480 --> 00:30:56,960
Speaker 2: any amount of stuff in the universe make deniverse positively curve?

663
00:30:57,080 --> 00:30:59,760
Speaker 1: Yeah, that is a little counterintuitive, But a totally empty

664
00:30:59,840 --> 00:31:03,640
Speaker 1: un one with no matter or energy in it at all,

665
00:31:03,920 --> 00:31:07,680
Speaker 1: would not have flat space. It would have negatively curved space.

666
00:31:07,880 --> 00:31:09,760
Speaker 1: So you need a little bit of stuff in the

667
00:31:09,880 --> 00:31:11,160
Speaker 1: universe to counteract that.

668
00:31:11,640 --> 00:31:14,600
Speaker 2: Whoa wait, So if I had an empty universe, like

669
00:31:14,680 --> 00:31:16,880
Speaker 2: no stars, no planets, no galaxies in it, and I

670
00:31:16,960 --> 00:31:19,800
Speaker 2: shoot to laser beams, they're going to diverse from each other.

671
00:31:20,120 --> 00:31:22,520
Speaker 2: They're not just going to stay parallel to each other forever.

672
00:31:22,840 --> 00:31:25,000
Speaker 1: Yeah, that's right. This is one of the situations we

673
00:31:25,000 --> 00:31:28,080
Speaker 1: can actually solve in Einstein, the general relativity situation with

674
00:31:28,200 --> 00:31:31,560
Speaker 1: nothing in the universe, totally empty, no matter, no energy,

675
00:31:31,640 --> 00:31:34,600
Speaker 1: no dark energy. And in that case, the universe has

676
00:31:34,720 --> 00:31:37,640
Speaker 1: negative curvature, so you have to add stuff to the

677
00:31:37,720 --> 00:31:41,240
Speaker 1: universe to make it have no curvature or positive curvature.

678
00:31:41,520 --> 00:31:44,760
Speaker 2: Oh so even no dark energy like this sort of

679
00:31:45,000 --> 00:31:48,840
Speaker 2: necessary amount of stuff in it is not related to

680
00:31:48,880 --> 00:31:51,560
Speaker 2: the expansion of the universe either, or do you assume

681
00:31:51,600 --> 00:31:53,400
Speaker 2: the expansion of the universe or not.

682
00:31:53,560 --> 00:31:56,160
Speaker 1: This does not determine the expansion of the universe. All

683
00:31:56,200 --> 00:31:59,560
Speaker 1: these pieces together, the curvature, the density, the dark energy,

684
00:31:59,640 --> 00:32:03,160
Speaker 1: all these things together determine whether the universe is expanding,

685
00:32:03,160 --> 00:32:06,640
Speaker 1: whether that expansion is accelerating. It's a whole complex dance,

686
00:32:07,120 --> 00:32:09,760
Speaker 1: but just the curvature of the universe is determined by

687
00:32:09,760 --> 00:32:12,200
Speaker 1: the matter and energy density. If you have a certain amount,

688
00:32:12,240 --> 00:32:15,000
Speaker 1: then you sort of counteract the natural negative curvature of

689
00:32:15,080 --> 00:32:17,280
Speaker 1: space and you get a flat universe. If you have

690
00:32:17,320 --> 00:32:19,200
Speaker 1: more than that, you get a positive curvature. If you're

691
00:32:19,280 --> 00:32:21,960
Speaker 1: less than that, you get negative curvature. So a flat

692
00:32:22,040 --> 00:32:24,520
Speaker 1: universe is sort of balanced on a knife's edge. You

693
00:32:24,520 --> 00:32:26,920
Speaker 1: have to have like exactly the right amount of stuff,

694
00:32:27,240 --> 00:32:29,479
Speaker 1: and it's not a big number, Like the critical density

695
00:32:29,560 --> 00:32:32,440
Speaker 1: right now is about five protons per cubic meter.

696
00:32:33,040 --> 00:32:37,320
Speaker 2: I guess that's weird that space by itself has negative curvature,

697
00:32:38,120 --> 00:32:41,800
Speaker 2: like pure space OG space. If you shoose laser beams,

698
00:32:41,960 --> 00:32:45,240
Speaker 2: they would diverge. Isn't that weird because shouldn't space be

699
00:32:45,360 --> 00:32:47,040
Speaker 2: like neutral or totally empty.

700
00:32:47,200 --> 00:32:49,480
Speaker 1: Well, intuitive concept of space doesn't even allow it to

701
00:32:49,480 --> 00:32:52,480
Speaker 1: be bent, right, So you have to already let go

702
00:32:52,560 --> 00:32:55,560
Speaker 1: of those intuitive ideas and think that space is something

703
00:32:55,640 --> 00:32:59,200
Speaker 1: quite different from what we imagined as these weird properties.

704
00:32:59,360 --> 00:33:01,880
Speaker 1: It's a little bit more complicated than what we've described

705
00:33:02,360 --> 00:33:04,800
Speaker 1: because the amount of stuff you have to add to

706
00:33:04,960 --> 00:33:08,200
Speaker 1: space to avoid this negative curvature actually changes over time.

707
00:33:08,280 --> 00:33:11,320
Speaker 1: It depends also on the expansion of the universe. So

708
00:33:11,360 --> 00:33:13,680
Speaker 1: there's a lot of complex moving parts here that we're

709
00:33:13,720 --> 00:33:14,680
Speaker 1: trying to distill down.

710
00:33:14,880 --> 00:33:17,200
Speaker 2: But I guess the main takeaway is that space by

711
00:33:17,200 --> 00:33:21,120
Speaker 2: itself has negative curvature, but because we have stuff in it,

712
00:33:21,200 --> 00:33:24,680
Speaker 2: matter and energy, then it's possible for space to be

713
00:33:24,880 --> 00:33:28,200
Speaker 2: flat because that's what the effect of energy and mass

714
00:33:28,480 --> 00:33:31,120
Speaker 2: does to space, is it makes it more positively curvy.

715
00:33:31,280 --> 00:33:33,720
Speaker 1: Yeah, and we can measure the curvature of space by

716
00:33:33,800 --> 00:33:37,880
Speaker 1: measuring the matter and energy density of the universe. So

717
00:33:37,920 --> 00:33:39,920
Speaker 1: we go out we measure that, and that tells us

718
00:33:39,960 --> 00:33:43,520
Speaker 1: what curvature we have in our universe. The magnitude of

719
00:33:43,520 --> 00:33:46,240
Speaker 1: that curvature can also change the sign can't. If you

720
00:33:46,280 --> 00:33:49,800
Speaker 1: have positively curved space, it's always going to be positively curved,

721
00:33:50,080 --> 00:33:53,240
Speaker 1: but it can get more positively curved or less positively curved,

722
00:33:53,360 --> 00:33:56,080
Speaker 1: like the universe has positive curvature, can collapse on itself,

723
00:33:56,120 --> 00:33:59,480
Speaker 1: making itself more and more positively curved, or universe it's

724
00:33:59,520 --> 00:34:02,520
Speaker 1: open can expand really really rapidly and get less and

725
00:34:02,600 --> 00:34:05,040
Speaker 1: less curved. But they can't flip over. You can't start

726
00:34:05,040 --> 00:34:07,160
Speaker 1: from the universe as positively curves and end up with

727
00:34:07,160 --> 00:34:07,600
Speaker 1: the universe.

728
00:34:07,640 --> 00:34:10,840
Speaker 2: That's negatively curved unless maybe the density of energy and

729
00:34:10,960 --> 00:34:14,839
Speaker 2: matter decreases enough. Isn't that possible? No, As like you said,

730
00:34:14,880 --> 00:34:17,680
Speaker 2: it depends on that density. What if the density changes.

731
00:34:17,880 --> 00:34:20,520
Speaker 1: The density definitely does change, right, and we'll talk a

732
00:34:20,520 --> 00:34:22,880
Speaker 1: little bit about how that density is changing and how

733
00:34:22,920 --> 00:34:25,799
Speaker 1: we understand how it's changing. But you can't change the

734
00:34:25,880 --> 00:34:29,080
Speaker 1: curvature of the universe. You can't go from positively curved

735
00:34:29,120 --> 00:34:32,200
Speaker 1: space to negatively curve space. That would correspond to like

736
00:34:32,239 --> 00:34:35,160
Speaker 1: changing from a finite universe to an infinite universe, which

737
00:34:35,200 --> 00:34:38,000
Speaker 1: you can't do right. You can't take the service of

738
00:34:38,000 --> 00:34:40,480
Speaker 1: a sphere and snap it out to an infinite plane.

739
00:34:40,880 --> 00:34:44,040
Speaker 2: You can pop a balloon, you can flat a birthday cake.

740
00:34:44,400 --> 00:34:47,480
Speaker 1: That's one of the confusing things about these two D analogies, right,

741
00:34:48,080 --> 00:34:50,600
Speaker 1: is that you're imagining it in a three D space.

742
00:34:50,680 --> 00:34:52,799
Speaker 1: You're thinking about really a two D service on a

743
00:34:52,840 --> 00:34:55,520
Speaker 1: three D sphere. But in those analogies, the two D

744
00:34:55,600 --> 00:34:58,800
Speaker 1: surface is all there is, so you can't really flatten

745
00:34:58,840 --> 00:34:59,200
Speaker 1: it all.

746
00:34:59,280 --> 00:35:01,960
Speaker 2: Right, Well, into what would happen if you change the

747
00:35:02,000 --> 00:35:05,200
Speaker 2: density of matter and energy in the universe, And then

748
00:35:05,280 --> 00:35:08,760
Speaker 2: let's ask the big question, why is the universe flat?

749
00:35:09,920 --> 00:35:24,960
Speaker 2: But first, let's take another quick break. All right, we're

750
00:35:25,000 --> 00:35:28,359
Speaker 2: asking the question why is space flat? Or I guess

751
00:35:28,360 --> 00:35:31,040
Speaker 2: why space so flat? Because it's maybe flatter than what

752
00:35:31,120 --> 00:35:31,680
Speaker 2: you expected.

753
00:35:31,880 --> 00:35:33,840
Speaker 1: Yeah, when we go out to measure the curvage of

754
00:35:33,840 --> 00:35:36,760
Speaker 1: the universe, we find something kind of surprising. We find

755
00:35:36,840 --> 00:35:40,520
Speaker 1: that it's really pretty flat. Like there's this critical density

756
00:35:40,600 --> 00:35:43,640
Speaker 1: five protons per cubic meter, And we go out to

757
00:35:43,680 --> 00:35:45,640
Speaker 1: measure the amount of stuff in the universe. We add

758
00:35:45,719 --> 00:35:48,959
Speaker 1: up all the mass, the stars, the galaxies, the dark matter,

759
00:35:49,239 --> 00:35:52,040
Speaker 1: and also the dark energy. All of that stuff. It

760
00:35:52,080 --> 00:35:55,400
Speaker 1: adds up to like very very close to exactly the

761
00:35:55,480 --> 00:35:59,080
Speaker 1: critical density. It's within one percent, which is about our

762
00:35:59,160 --> 00:36:02,840
Speaker 1: uncertainty of the critical density, which tells us that space

763
00:36:02,920 --> 00:36:06,200
Speaker 1: is either flat or very very close to flat. And

764
00:36:06,239 --> 00:36:08,400
Speaker 1: that's kind of a surprise because we don't think the

765
00:36:08,480 --> 00:36:10,280
Speaker 1: universe likes to be flat.

766
00:36:11,200 --> 00:36:14,560
Speaker 2: I guess before we go, I have more questions about

767
00:36:14,560 --> 00:36:16,279
Speaker 2: what you just said. Well, first of all, how do

768
00:36:16,320 --> 00:36:19,800
Speaker 2: we measure the mass and energy density of the universe?

769
00:36:20,400 --> 00:36:22,440
Speaker 2: And second of all, how do we know what amount

770
00:36:22,520 --> 00:36:24,200
Speaker 2: you need for the universe to be flat?

771
00:36:24,239 --> 00:36:26,920
Speaker 1: So how we measure it is several different ways. We

772
00:36:26,920 --> 00:36:30,319
Speaker 1: can use like the cosmic microwave background radiation. This is

773
00:36:30,400 --> 00:36:33,720
Speaker 1: radiation from about three hundred thousand years after the Big Bang,

774
00:36:34,000 --> 00:36:36,160
Speaker 1: where the universe was very hot and dense with its

775
00:36:36,239 --> 00:36:38,720
Speaker 1: bright plasma, and then it cooled off and formed neutral

776
00:36:38,760 --> 00:36:41,879
Speaker 1: atoms and light could propagate. We can still see that light.

777
00:36:42,120 --> 00:36:44,399
Speaker 1: That light was made everywhere in the universe, and it's

778
00:36:44,440 --> 00:36:47,960
Speaker 1: flying around everywhere, and some of it has just reached

779
00:36:48,000 --> 00:36:50,560
Speaker 1: Earth from places that used to be very very far away,

780
00:36:50,719 --> 00:36:52,399
Speaker 1: and we can use it to sort of look at

781
00:36:52,440 --> 00:36:54,600
Speaker 1: what the universe looked like at that time, and there

782
00:36:54,600 --> 00:36:57,720
Speaker 1: were little bumps and wiggles in it. It's not completely smooth.

783
00:36:57,719 --> 00:37:00,360
Speaker 1: It's like a little bit of a frothing quantum plasma.

784
00:37:00,520 --> 00:37:02,720
Speaker 1: And from the size of those wiggles, we can tell

785
00:37:02,760 --> 00:37:05,520
Speaker 1: how much energy density there was in the early.

786
00:37:05,360 --> 00:37:07,839
Speaker 2: Universe based on some theory that you have about how

787
00:37:07,840 --> 00:37:11,640
Speaker 2: the universe formed and how these things balance out with space.

788
00:37:11,440 --> 00:37:14,440
Speaker 1: Relying basically just on general relativity. I mean, we assume

789
00:37:14,560 --> 00:37:17,719
Speaker 1: some model of the universe, but it's based in general relativity.

790
00:37:17,920 --> 00:37:20,600
Speaker 1: Doesn't depend on how the universe formed or what came before.

791
00:37:20,600 --> 00:37:23,600
Speaker 1: It just depends on the size of those fluctuations in

792
00:37:23,640 --> 00:37:26,640
Speaker 1: the early universe and then how those propagate through an

793
00:37:26,640 --> 00:37:28,279
Speaker 1: expanding universe to us.

794
00:37:28,640 --> 00:37:30,440
Speaker 2: Okay, so that's one way to measure it.

795
00:37:30,600 --> 00:37:33,759
Speaker 1: So that measures the total energy density like the dark

796
00:37:33,880 --> 00:37:37,000
Speaker 1: energy plus the dark matter plus the normal matter density

797
00:37:37,000 --> 00:37:39,040
Speaker 1: in the early universe. We can also measure it by

798
00:37:39,040 --> 00:37:42,080
Speaker 1: looking at the acceleration of the universe, like looking at

799
00:37:42,080 --> 00:37:44,719
Speaker 1: supernova seeing how fast they're moving away from us, or

800
00:37:44,760 --> 00:37:47,959
Speaker 1: looking at cephids. This expansion rate of the universe also

801
00:37:48,040 --> 00:37:51,600
Speaker 1: helps us measure these various components. So the components of

802
00:37:51,640 --> 00:37:53,920
Speaker 1: the energy density of the universe are the dark energy,

803
00:37:54,280 --> 00:37:56,479
Speaker 1: the normal matter, and the dark matter, and the super

804
00:37:56,560 --> 00:37:59,560
Speaker 1: nova measurements the acceleration of the universe help us measure

805
00:37:59,680 --> 00:38:03,719
Speaker 1: the dark energy component minus the matter component, because that

806
00:38:03,800 --> 00:38:07,120
Speaker 1: determines the expansion of the universe. So there's like a

807
00:38:07,120 --> 00:38:09,359
Speaker 1: bunch of different components here, and we have different ways

808
00:38:09,400 --> 00:38:11,960
Speaker 1: to measure each one's or combinations of each one, to

809
00:38:11,960 --> 00:38:15,719
Speaker 1: help us in down exactly what those contributions are. Dark

810
00:38:15,840 --> 00:38:18,360
Speaker 1: energy is of like seventy percent of the critical density.

811
00:38:18,600 --> 00:38:21,319
Speaker 1: Matter is like thirty percent of the critical density, where

812
00:38:21,320 --> 00:38:23,279
Speaker 1: most of that is dark matter, and they add up

813
00:38:23,320 --> 00:38:25,000
Speaker 1: to basically this critical density.

814
00:38:25,239 --> 00:38:28,080
Speaker 2: This is from this CMB measurement, or from all measurements.

815
00:38:28,400 --> 00:38:31,319
Speaker 1: The CMB measurement tells us the total density. The supernova

816
00:38:31,360 --> 00:38:34,480
Speaker 1: tells us the dark energy minus the matter the difference

817
00:38:34,480 --> 00:38:37,239
Speaker 1: between those two because they work against each other when

818
00:38:37,280 --> 00:38:40,880
Speaker 1: controlling the expansion of the universe. There's another measurement, the

819
00:38:40,920 --> 00:38:44,720
Speaker 1: buryon acoustic oscillations, that tells us about like how matter

820
00:38:44,840 --> 00:38:47,600
Speaker 1: was sloshing around in the early universe and made these

821
00:38:47,640 --> 00:38:50,920
Speaker 1: sound waves back when the universe was super duper dense.

822
00:38:50,960 --> 00:38:53,480
Speaker 1: Sound traveled at nearly half the speed of light, and

823
00:38:53,520 --> 00:38:55,920
Speaker 1: the speed of that sound depends on the density of

824
00:38:56,000 --> 00:38:58,200
Speaker 1: matter in the universe, and we can still sort of

825
00:38:58,239 --> 00:39:02,680
Speaker 1: see the universe ringing from those oscillations in the early universe.

826
00:39:03,040 --> 00:39:06,360
Speaker 1: That separately measures just the matter portion. So we have

827
00:39:06,400 --> 00:39:08,960
Speaker 1: these different pieces of the pie, and they all add

828
00:39:09,040 --> 00:39:11,799
Speaker 1: up to make exactly one pie. And the fascinating thing

829
00:39:12,160 --> 00:39:13,880
Speaker 1: is that they didn't have to write it could have

830
00:39:13,880 --> 00:39:15,520
Speaker 1: added up to anything. It could have added up to

831
00:39:15,560 --> 00:39:18,240
Speaker 1: be twice the critical density or half the critical density,

832
00:39:18,400 --> 00:39:21,040
Speaker 1: but it adds up to bang on just the critical

833
00:39:21,080 --> 00:39:22,520
Speaker 1: density to within one percent.

834
00:39:23,040 --> 00:39:25,560
Speaker 2: I see. So you're saying we've measured the energy density

835
00:39:25,600 --> 00:39:28,319
Speaker 2: of the universe, and according to what we think is

836
00:39:28,680 --> 00:39:31,120
Speaker 2: the laws of the universe, according to general relativity, we

837
00:39:31,200 --> 00:39:33,760
Speaker 2: have just enough mass and density to make the universe flat,

838
00:39:33,800 --> 00:39:36,240
Speaker 2: which means if I shoot two lasers out there in space,

839
00:39:36,800 --> 00:39:39,319
Speaker 2: they're not going to hit each other, they're not going

840
00:39:39,400 --> 00:39:40,880
Speaker 2: to drift the part, they're not going to hit me

841
00:39:40,960 --> 00:39:42,640
Speaker 2: in the back of the head. Those two laser beings

842
00:39:42,680 --> 00:39:45,280
Speaker 2: are just gonna keep going forever exactly.

843
00:39:45,640 --> 00:39:48,640
Speaker 1: And this is kind of a surprise to physicists because

844
00:39:49,000 --> 00:39:51,680
Speaker 1: they think the universe doesn't like to be flat. Like

845
00:39:51,719 --> 00:39:54,000
Speaker 1: the flatness of the universe is not a stable thing.

846
00:39:54,480 --> 00:39:56,880
Speaker 1: If you're just above the critical density, if you're like

847
00:39:56,960 --> 00:39:59,320
Speaker 1: a little bit more in the critical density, then the

848
00:39:59,440 --> 00:40:02,280
Speaker 1: universe tends to collapse and become more and more dense,

849
00:40:02,320 --> 00:40:04,759
Speaker 1: and you move away from the critical density. If you

850
00:40:04,800 --> 00:40:07,359
Speaker 1: have less than the critical density, you're below it, then

851
00:40:07,360 --> 00:40:09,960
Speaker 1: the universe is open. It tends to expand and dilute

852
00:40:10,000 --> 00:40:13,640
Speaker 1: itself away from the critical density. So either you're exactly

853
00:40:13,680 --> 00:40:16,120
Speaker 1: bang on the critical density, in which you're stable like

854
00:40:16,160 --> 00:40:18,840
Speaker 1: a pencil balance on its tip, or you're a little

855
00:40:18,840 --> 00:40:20,960
Speaker 1: bit above and a little bit below, and then you

856
00:40:21,080 --> 00:40:23,640
Speaker 1: very quickly veer away from it. So sort of a

857
00:40:23,680 --> 00:40:26,920
Speaker 1: mystery how we're still so close to the critical density

858
00:40:27,000 --> 00:40:28,680
Speaker 1: after billions of years.

859
00:40:28,760 --> 00:40:31,040
Speaker 2: What do you mean it's unstable like a pencil. What

860
00:40:31,040 --> 00:40:31,520
Speaker 2: does that mean?

861
00:40:31,640 --> 00:40:33,719
Speaker 1: It's unstable, and that if you move away from the

862
00:40:33,719 --> 00:40:36,680
Speaker 1: critical density a little bit, the universe moves away even more.

863
00:40:37,120 --> 00:40:39,600
Speaker 1: It's like a pencil balance on its tip. Right, it's unstable.

864
00:40:39,680 --> 00:40:41,960
Speaker 1: You have it, a tiny little push, a fly lands

865
00:40:41,960 --> 00:40:44,120
Speaker 1: on it, air blows by it really gently. It's going

866
00:40:44,200 --> 00:40:45,080
Speaker 1: to tend to fall over.

867
00:40:45,320 --> 00:40:47,680
Speaker 2: Wait to Like, if you measure the density of the

868
00:40:47,760 --> 00:40:50,759
Speaker 2: universe and it's a little bit more than the critical

869
00:40:51,000 --> 00:40:53,640
Speaker 2: amount of density you need for a flat universe, then

870
00:40:53,680 --> 00:40:56,759
Speaker 2: the density is going to increase over time, Like the

871
00:40:56,840 --> 00:40:58,480
Speaker 2: universe is going to get more and more denser.

872
00:40:58,680 --> 00:41:01,040
Speaker 1: Exactly. If you have more in the critical density, the

873
00:41:01,120 --> 00:41:04,760
Speaker 1: universe will contract, right, and things will get denser and denser.

874
00:41:04,840 --> 00:41:06,200
Speaker 1: You'll end up with like a big crunch.

875
00:41:06,480 --> 00:41:08,600
Speaker 2: You mean, like the expansion of the universe will reverse.

876
00:41:08,800 --> 00:41:11,600
Speaker 1: Yeah, exactly. In the opposite scenario, where you lessen the

877
00:41:11,640 --> 00:41:14,640
Speaker 1: critical density, things expand forever and things get more and

878
00:41:14,719 --> 00:41:18,440
Speaker 1: more dilute, So the density drops right as the universe expands,

879
00:41:18,600 --> 00:41:21,839
Speaker 1: the density of matter drops. As the universe contracts, the

880
00:41:21,840 --> 00:41:25,040
Speaker 1: density of matter increases, and so if you're not at

881
00:41:25,040 --> 00:41:27,120
Speaker 1: the critical density you tend to veer away from it

882
00:41:27,160 --> 00:41:29,759
Speaker 1: pretty quickly. And we're like billions of years into the

883
00:41:29,800 --> 00:41:32,600
Speaker 1: history and we're still super close to the critical density,

884
00:41:32,640 --> 00:41:35,080
Speaker 1: which was a big question in cosmology. How can you

885
00:41:35,120 --> 00:41:37,359
Speaker 1: stay so closely balanced so long?

886
00:41:37,520 --> 00:41:39,480
Speaker 2: I feel like now we're tying it to the expansion

887
00:41:39,520 --> 00:41:41,960
Speaker 2: of the universe. So the critical density is tied to

888
00:41:42,000 --> 00:41:44,759
Speaker 2: the expansion, like if the universe is positively curved, then

889
00:41:44,840 --> 00:41:46,640
Speaker 2: the universe is going to contract eventually.

890
00:41:46,760 --> 00:41:48,880
Speaker 1: The courage of the universe definitely plays a role. The

891
00:41:48,920 --> 00:41:51,640
Speaker 1: critical density and the curvature, together with the amount of

892
00:41:51,680 --> 00:41:55,480
Speaker 1: dark energy, determine the expansion. You can have a universe

893
00:41:55,520 --> 00:41:59,040
Speaker 1: that's positively curved and expanding if you have enough dark energy,

894
00:41:59,120 --> 00:42:02,560
Speaker 1: because dark energy can overcome this critical density, that you

895
00:42:02,560 --> 00:42:05,240
Speaker 1: could have a universe which expands. But in the simple

896
00:42:05,280 --> 00:42:07,280
Speaker 1: scenario where you take out dark energy for the moment

897
00:42:07,360 --> 00:42:09,800
Speaker 1: and just have a universe with only matter and radiation,

898
00:42:10,239 --> 00:42:12,600
Speaker 1: which was basically the scenario of our universe for the

899
00:42:12,640 --> 00:42:15,440
Speaker 1: first nine billion years when dark energy was negligible, and

900
00:42:15,480 --> 00:42:18,560
Speaker 1: then the universe above the critical density will contract and

901
00:42:18,640 --> 00:42:21,880
Speaker 1: increase the density, and the universe below the critical density

902
00:42:21,920 --> 00:42:25,800
Speaker 1: will expand and decrease the density. So they did this calculation.

903
00:42:25,880 --> 00:42:28,520
Speaker 1: They're like, well, in that scenario, how close do the

904
00:42:28,600 --> 00:42:31,000
Speaker 1: universe have to start to the critical density to end

905
00:42:31,080 --> 00:42:33,000
Speaker 1: up at one percent. The answer is we had to

906
00:42:33,000 --> 00:42:35,560
Speaker 1: be within the critical density to within ten to the

907
00:42:35,640 --> 00:42:38,960
Speaker 1: minus sixty two. If you're anything above that, then the

908
00:42:39,040 --> 00:42:43,120
Speaker 1: universe would have expanded like crazy or contracted like crazy.

909
00:42:43,680 --> 00:42:46,480
Speaker 1: So it seems really, really weird that we end up

910
00:42:46,520 --> 00:42:49,040
Speaker 1: with a universe so close to flat when the universe

911
00:42:49,120 --> 00:42:51,040
Speaker 1: likes to veer away from flatness.

912
00:42:51,440 --> 00:42:55,239
Speaker 2: Well, that's a really tight requirement for this density that

913
00:42:55,280 --> 00:42:57,399
Speaker 2: we need at the beginning of the universe. It kind

914
00:42:57,400 --> 00:42:58,880
Speaker 2: of seems like too much of a coincidence.

915
00:42:59,000 --> 00:43:00,960
Speaker 1: It does seem like too much of a coincidence, and

916
00:43:01,000 --> 00:43:03,840
Speaker 1: physicists don't like coincidences because the density of stuff in

917
00:43:03,880 --> 00:43:06,239
Speaker 1: the universe doesn't seem to be determined by anything. It

918
00:43:06,239 --> 00:43:08,440
Speaker 1: could have been anything, So for it to be like

919
00:43:08,600 --> 00:43:12,000
Speaker 1: exactly close to one complete pie of the critical density,

920
00:43:12,000 --> 00:43:14,560
Speaker 1: it seems too neat. Physicists like a reason for these

921
00:43:14,640 --> 00:43:17,560
Speaker 1: numbers to line up, and there is an explanation for it,

922
00:43:17,920 --> 00:43:21,239
Speaker 1: and the explanation is cosmic inflation. So you know how

923
00:43:21,239 --> 00:43:24,160
Speaker 1: the universe is expanding now, and that expansion is accelerating.

924
00:43:24,320 --> 00:43:27,480
Speaker 1: We also think that the universe expanded very very early

925
00:43:27,520 --> 00:43:30,600
Speaker 1: on in its history. But like a huge factor, this

926
00:43:30,719 --> 00:43:33,960
Speaker 1: accelerating expansion we call inflation. It's an expansion of like

927
00:43:34,040 --> 00:43:36,680
Speaker 1: ten to the thirty in like ten to the negative

928
00:43:36,719 --> 00:43:40,279
Speaker 1: thirty seconds. And this kind of accelerating expansion tends to

929
00:43:40,440 --> 00:43:45,280
Speaker 1: push the universe towards flatness. It makes the universe more flat.

930
00:43:45,400 --> 00:43:47,920
Speaker 2: But isn't it still sort of too much of a coincidence,

931
00:43:47,920 --> 00:43:50,480
Speaker 2: Like I wonder if maybe our theories are wrong, or

932
00:43:50,480 --> 00:43:53,960
Speaker 2: maybe there's some sort of mechanism that keeps the universe flat.

933
00:43:54,040 --> 00:43:55,799
Speaker 1: Well, we don't know if inflation is true, and it's

934
00:43:55,840 --> 00:43:58,040
Speaker 1: just one of the possible scenarios, And you know, maybe

935
00:43:58,040 --> 00:44:00,160
Speaker 1: it's just a coincidence, and we just happen to in

936
00:44:00,160 --> 00:44:02,279
Speaker 1: the universe that was that close to flat that we

937
00:44:02,440 --> 00:44:05,200
Speaker 1: ended up in the universe that didn't overexpand or didn't

938
00:44:05,200 --> 00:44:09,200
Speaker 1: collapse on itself. But inflation makes it less sensitive. Inflation says,

939
00:44:09,200 --> 00:44:11,840
Speaker 1: you know, you could have started with lots of different densities,

940
00:44:12,080 --> 00:44:15,000
Speaker 1: and inflation would have made your universe have the critical

941
00:44:15,040 --> 00:44:17,640
Speaker 1: density early on, So you could have started with half

942
00:44:17,640 --> 00:44:20,120
Speaker 1: the density or one and a half times the critical density,

943
00:44:20,160 --> 00:44:23,160
Speaker 1: and inflation would have made your universe super duper close

944
00:44:23,200 --> 00:44:24,720
Speaker 1: to the critical density.

945
00:44:24,880 --> 00:44:27,080
Speaker 2: Meaning like you might have started with too much stuff

946
00:44:27,080 --> 00:44:30,680
Speaker 2: in the universe, but then some mechanism stretched out the

947
00:44:30,760 --> 00:44:34,320
Speaker 2: universe enough so that you had the critical density.

948
00:44:34,160 --> 00:44:37,959
Speaker 1: Exactly the math of inflation. In fact of any accelerating

949
00:44:38,000 --> 00:44:41,520
Speaker 1: expansion in the universe tends to push the universe back

950
00:44:41,600 --> 00:44:44,080
Speaker 1: towards the critical density. So if you had too much,

951
00:44:44,239 --> 00:44:47,399
Speaker 1: inflation would stretch out the universe in just the right

952
00:44:47,440 --> 00:44:49,799
Speaker 1: way to make it have the critical density. Just like

953
00:44:49,800 --> 00:44:51,440
Speaker 1: if you're standing on the surface of a tiny sphere

954
00:44:51,440 --> 00:44:54,040
Speaker 1: like a beach ball, it looks really really curved. But

955
00:44:54,080 --> 00:44:56,799
Speaker 1: then if somebody expands it rapidly by a factor of

956
00:44:56,840 --> 00:44:59,040
Speaker 1: ten to the thirty, then now you're standing on the

957
00:44:59,040 --> 00:45:02,120
Speaker 1: surface of a huge it looks flat. Right, So a

958
00:45:02,200 --> 00:45:05,040
Speaker 1: bigger sphere looks flatter and then a small sphere. In

959
00:45:05,080 --> 00:45:09,080
Speaker 1: the same way inflation pushes the universe towards less.

960
00:45:08,840 --> 00:45:11,759
Speaker 2: Curvature, does it also work the other way, Like if

961
00:45:12,080 --> 00:45:14,880
Speaker 2: the universe had started with too little stuff in it,

962
00:45:14,960 --> 00:45:19,320
Speaker 2: the density was too small. Mood inflation have somehow adjusted

963
00:45:19,480 --> 00:45:22,400
Speaker 2: or slowed down or compress the universe somehow. Would you

964
00:45:22,440 --> 00:45:25,720
Speaker 2: have had deflation in order to keep the universe flat?

965
00:45:26,480 --> 00:45:28,600
Speaker 1: Yeah, that's a great question. It does. It pushes it

966
00:45:28,640 --> 00:45:32,360
Speaker 1: towards critical density from either direction, which is pretty cool

967
00:45:32,719 --> 00:45:33,839
Speaker 1: how the math works out.

968
00:45:34,040 --> 00:45:35,320
Speaker 2: So it does do deflation.

969
00:45:35,560 --> 00:45:38,440
Speaker 1: Well, they still consider it inflation because you're still stretching

970
00:45:38,440 --> 00:45:38,680
Speaker 1: it out.

971
00:45:38,719 --> 00:45:38,880
Speaker 4: You know.

972
00:45:38,920 --> 00:45:42,120
Speaker 1: Imagine like a hyperbolic surface. You stretched it out, so

973
00:45:42,200 --> 00:45:46,680
Speaker 1: the negative curvature goes towards zero curvature. So inflation drives

974
00:45:46,680 --> 00:45:48,480
Speaker 1: you towards zero curvature from either direction.

975
00:45:49,080 --> 00:45:53,080
Speaker 2: So it's more like stackflation or less flation.

976
00:45:54,360 --> 00:45:56,640
Speaker 1: I don't know enough economics to know if an analogy

977
00:45:56,680 --> 00:45:57,480
Speaker 1: is accurate or not.

978
00:45:57,640 --> 00:46:01,880
Speaker 2: Yeah, I mean it sounds like something they say in

979
00:46:01,920 --> 00:46:02,279
Speaker 2: the news.

980
00:46:02,360 --> 00:46:04,879
Speaker 1: And one fascinating thing about that is it means that

981
00:46:04,960 --> 00:46:09,160
Speaker 1: our universe right now is driving back towards flatness. Like

982
00:46:09,200 --> 00:46:11,800
Speaker 1: the brief history of the universe is you have probably inflation,

983
00:46:11,880 --> 00:46:14,600
Speaker 1: which makes the universe mostly flat, and then you have

984
00:46:14,680 --> 00:46:18,080
Speaker 1: a matter in radiation dominated time when the universe is

985
00:46:18,120 --> 00:46:21,040
Speaker 1: then driven by this critical density, and it continues to

986
00:46:21,080 --> 00:46:23,959
Speaker 1: expand that that expansion is decelerating because of the matter

987
00:46:24,040 --> 00:46:26,279
Speaker 1: dominated nature of the universe. And then like six billion

988
00:46:26,360 --> 00:46:29,000
Speaker 1: years ago, dark energy took over, right, because the expanding

989
00:46:29,120 --> 00:46:32,760
Speaker 1: universe dilutes out the matter and radiation, while dark energy

990
00:46:32,760 --> 00:46:35,160
Speaker 1: grows as a fraction. So now we have an accelerating

991
00:46:35,200 --> 00:46:39,200
Speaker 1: expansion again, which does the same thing. Any accelerating expansion

992
00:46:39,239 --> 00:46:42,719
Speaker 1: in the universe pushes you back towards zero curvature.

993
00:46:43,120 --> 00:46:45,680
Speaker 2: Mmm. Interesting. I guess what that makes me think is

994
00:46:45,719 --> 00:46:49,239
Speaker 2: that maybe the universe is flat, Like it's just flat.

995
00:46:49,280 --> 00:46:51,880
Speaker 2: It's infinite and flat, and all these things we're seeing,

996
00:46:51,880 --> 00:46:55,799
Speaker 2: all these measurements and all these theoretical concepts, they kind

997
00:46:55,800 --> 00:46:57,560
Speaker 2: of have to work out to a flat universe, and

998
00:46:57,600 --> 00:46:59,560
Speaker 2: that's what we're seeing. Like maybe it's not sort of

999
00:46:59,600 --> 00:47:02,480
Speaker 2: like this mystery or this universe sitting on a nice edge.

1000
00:47:02,520 --> 00:47:04,480
Speaker 2: It's just that's just the way that the verse is.

1001
00:47:04,960 --> 00:47:07,279
Speaker 2: And to us, the math and the measurements look like

1002
00:47:07,320 --> 00:47:09,000
Speaker 2: it could have gone either way, but it could never

1003
00:47:09,040 --> 00:47:09,560
Speaker 2: had a chance.

1004
00:47:09,719 --> 00:47:12,799
Speaker 1: Yeah, it's possible. Right in the equations of general relativity,

1005
00:47:12,840 --> 00:47:15,920
Speaker 1: this is curvature parameter. It's either plus one zero, or

1006
00:47:16,120 --> 00:47:18,640
Speaker 1: minus one, and it can't change again. Right, You can't

1007
00:47:18,680 --> 00:47:20,960
Speaker 1: go from a negative curvature to a positive curvature, and

1008
00:47:21,000 --> 00:47:24,279
Speaker 1: our universe is just one of those. The interesting thing, though,

1009
00:47:24,640 --> 00:47:27,040
Speaker 1: is that to have k equals zero, to have zero curvature,

1010
00:47:27,200 --> 00:47:30,200
Speaker 1: you really have to have the critical density of matter

1011
00:47:30,280 --> 00:47:32,600
Speaker 1: and energy. So it sort of depends on what question

1012
00:47:32,680 --> 00:47:34,560
Speaker 1: you ask, Like you could ask, well, which of the

1013
00:47:34,600 --> 00:47:36,719
Speaker 1: three curvatures is it? Well, maybe it's just zero, like

1014
00:47:36,800 --> 00:47:38,560
Speaker 1: you say, but if you think about it in terms

1015
00:47:38,560 --> 00:47:41,680
Speaker 1: of the continuous spectrum of matter and energy density, then

1016
00:47:41,680 --> 00:47:44,480
Speaker 1: it has to have exactly the right number, which seems

1017
00:47:44,480 --> 00:47:46,880
Speaker 1: like one option out of an infinite number instead of

1018
00:47:46,880 --> 00:47:47,960
Speaker 1: one option out of three.

1019
00:47:48,440 --> 00:47:51,919
Speaker 2: Or unless the universe sort of like prevents the matter

1020
00:47:52,000 --> 00:47:54,400
Speaker 2: and energy to be anything else, in case that wouldn't

1021
00:47:54,440 --> 00:47:54,719
Speaker 2: make sense.

1022
00:47:54,800 --> 00:47:57,520
Speaker 1: Right, Yeah, we it'd certainly possible. And these questions are

1023
00:47:57,520 --> 00:47:59,680
Speaker 1: really basic and also simple, And in a few hundred

1024
00:47:59,760 --> 00:48:01,399
Speaker 1: years they might look back on this and be like, hah,

1025
00:48:01,920 --> 00:48:04,440
Speaker 1: how do they imagine they lived in a curved universe?

1026
00:48:04,480 --> 00:48:06,480
Speaker 2: What a bunch of idiots, What a bunch of flat

1027
00:48:06,520 --> 00:48:07,360
Speaker 2: footed idiots?

1028
00:48:08,239 --> 00:48:10,160
Speaker 1: But these are the questions we're asking, and we don't

1029
00:48:10,200 --> 00:48:12,479
Speaker 1: know and the equations of general real too. They allow

1030
00:48:12,600 --> 00:48:16,040
Speaker 1: for all three kinds of universe negative curvature, flat or

1031
00:48:16,080 --> 00:48:18,799
Speaker 1: positive curvature. We just don't know which of those we

1032
00:48:18,840 --> 00:48:21,279
Speaker 1: live in and why we've measured its space to be flat.

1033
00:48:21,320 --> 00:48:23,600
Speaker 1: And you're right. Either it just is flat and it

1034
00:48:23,680 --> 00:48:25,680
Speaker 1: started out balanced on that knife's edge and it will

1035
00:48:25,719 --> 00:48:29,200
Speaker 1: always be there, perfectly balanced, or it has a little

1036
00:48:29,200 --> 00:48:31,600
Speaker 1: bit of curvature, but then we don't understand why it's

1037
00:48:31,640 --> 00:48:34,920
Speaker 1: still so flat unless you do something early on, like inflation.

1038
00:48:35,160 --> 00:48:37,480
Speaker 2: Well, I think the idea is that maybe the universe

1039
00:48:37,560 --> 00:48:40,520
Speaker 2: is flat, which means that the pencil is not upside down,

1040
00:48:40,600 --> 00:48:43,400
Speaker 2: like maybe the pencil is hanging from the tail, and

1041
00:48:43,480 --> 00:48:46,800
Speaker 2: that it can only sort of be that hanging down

1042
00:48:46,880 --> 00:48:49,640
Speaker 2: and the universe would push it down if you try

1043
00:48:49,640 --> 00:48:52,080
Speaker 2: to move the pencil. That's a possibility. Sounds like it's

1044
00:48:52,080 --> 00:48:55,400
Speaker 2: still a mystery why the universe is flat. We're measuring

1045
00:48:55,440 --> 00:48:57,880
Speaker 2: it to be flat and it seems to be staying flat,

1046
00:48:58,080 --> 00:49:02,040
Speaker 2: which means that the universe either is flat or the

1047
00:49:02,120 --> 00:49:06,160
Speaker 2: universe is not flat, but something is making it suspiciously flat.

1048
00:49:06,640 --> 00:49:08,360
Speaker 2: Those are the two options, right exactly.

1049
00:49:08,920 --> 00:49:11,799
Speaker 1: If it's not exactly flat, then something is keeping it

1050
00:49:12,000 --> 00:49:13,239
Speaker 1: very very close.

1051
00:49:12,960 --> 00:49:15,400
Speaker 2: To flat, which would be the universe, which means the

1052
00:49:15,480 --> 00:49:16,800
Speaker 2: universe it's flat.

1053
00:49:18,120 --> 00:49:20,640
Speaker 1: The universe is either exactly flat or it likes to

1054
00:49:20,680 --> 00:49:22,080
Speaker 1: stay very close to flat.

1055
00:49:22,320 --> 00:49:26,319
Speaker 2: I'm just trying to propagate flat universe theories and say

1056
00:49:26,320 --> 00:49:28,320
Speaker 2: that it's all just a conspiracy by the universe.

1057
00:49:28,480 --> 00:49:29,440
Speaker 1: You're curving my brain.

1058
00:49:29,520 --> 00:49:29,719
Speaker 5: Man.

1059
00:49:30,040 --> 00:49:32,400
Speaker 2: All right, Well, the next time you look at into space,

1060
00:49:32,520 --> 00:49:35,360
Speaker 2: think about what happens to those photons that you're seeing.

1061
00:49:35,600 --> 00:49:37,959
Speaker 2: Did they come straight at you or did they get

1062
00:49:38,000 --> 00:49:42,040
Speaker 2: bent by space? Are those photons curving their way through

1063
00:49:42,040 --> 00:49:46,359
Speaker 2: the universe, maybe even a close circular universe, or did

1064
00:49:46,360 --> 00:49:48,200
Speaker 2: it come straight at you from really far away.

1065
00:49:48,360 --> 00:49:51,319
Speaker 1: Either way, we're grateful that photons are arriving here on

1066
00:49:51,400 --> 00:49:53,799
Speaker 1: Earth and that we're smart enough to figure out the

1067
00:49:53,840 --> 00:49:57,520
Speaker 1: messages that they send about the nature of this incredible cosmos.

1068
00:49:57,680 --> 00:49:59,480
Speaker 2: Or at least we think we're smart enough. It might

1069
00:49:59,560 --> 00:50:01,520
Speaker 2: just be falling flat on our facebooks.

1070
00:50:01,680 --> 00:50:04,000
Speaker 1: We're feeling good about being smart. Whether or not we

1071
00:50:04,080 --> 00:50:04,839
Speaker 1: are all right.

1072
00:50:04,920 --> 00:50:07,960
Speaker 2: We hope you enjoyed that. Thanks for joining us, See

1073
00:50:08,000 --> 00:50:08,520
Speaker 2: you next time.

1074
00:50:16,440 --> 00:50:19,240
Speaker 1: Thanks for listening, and remember that Daniel and Jorge explain

1075
00:50:19,320 --> 00:50:23,279
Speaker 1: the universe is a production of iHeartRadio. For more podcasts

1076
00:50:23,320 --> 00:50:27,960
Speaker 1: from iHeartRadio, visit the iHeartRadio app, Apple Podcasts, or wherever

1077
00:50:28,040 --> 00:50:29,760
Speaker 1: you listen to your favorite shows.