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Speaker 1: Hey Jorge, 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 3: All right, go for it.

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Speaker 1: The word is flat.

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Speaker 3: I guess it could go either way. You know, nobody

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Speaker 3: 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 3: 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 3: Does that mean you want the Earth to be flat?

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

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

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Speaker 3: 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 3: I think this discussion has run out of air. Hi,

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Speaker 3: I'm Hojorhey mc, cartoonist and the author of the book

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Speaker 3: Oliver's 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 3: Are you saying metaphorically or you know, physiologically, Well, your.

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Speaker 1: Questions often catch me flat footed, so that's metaphorical, but

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Speaker 1: also literally and physiologically, I have flat feet. So yeah,

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Speaker 1: I wear inserts.

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Speaker 3: Does that have to make you taller? You like Tom Cruise,

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Speaker 3: 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 3: Sounds like the solution is just not to run life

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Speaker 3: 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 3: There you go. You can attach like a bicycle pedal

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Speaker 3: 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 3: Yeah exactly. But anyways, welcome to our podcast Daniel and

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Speaker 3: Jorge Explain the Universe, a production 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 3: That's right, because it is an amazing universe full of

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Speaker 3: stuff inflated with amazing and incredible physics and stars and

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Speaker 3: galaxies and planets and particles for us to wonder at

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Speaker 3: 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, given that 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 3: Yeah, it's amazing what we can learn just from this

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Speaker 3: little corner of the universe, and as you said, how

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Speaker 3: we can ask these big questions about how everything is

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Speaker 3: the way it is and why it is the way

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Speaker 3: it is, Like, for example, we don't know if the

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Speaker 3: 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?

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Speaker 5: All day.

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Speaker 3: 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 3: It is getting bigger and bigger, so you know, maybe

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Speaker 3: it could use a little bit of exercise. It's getting

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Speaker 3: 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 3: Yeah, yeah, true, true, true. I guess we should love

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Speaker 3: 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 3: Love it even if we don't understand it. I guess

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Speaker 3: all the time we should, you know, take it for

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Speaker 3: what it is. That's kind of what science is, right,

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Speaker 3: taking things for what they are.

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

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

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Speaker 1: 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 3: Yeah, because it is pretty perplexing out there the way

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Speaker 3: things are. You know, there are amazing things like black

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Speaker 3: holes that seem unexplainable, and there's sort of really weird

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Speaker 3: things like quantum mechanics out there that kind of keep

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Speaker 3: 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 how 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 the

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

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Speaker 1: that kind of thing, and sometimes the story tells is

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

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

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

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

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Speaker 3: Yeah, And as you said, there are big questions about

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Speaker 3: the universe that we still don't know about, like its size,

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Speaker 3: its shape, and what it's going to do in the future.

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Speaker 3: 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 relativity,

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Speaker 1: and we understand that space is weird and twisted and curved,

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Speaker 1: and that affects how things move. It also affects how

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Speaker 1: the universe itself expands or contracts. So we have a

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Speaker 1: lot of really one questions to ask about why the

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Speaker 1: universe looks this particular way, especially about the curvature of space.

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Speaker 3: To be on the podcast, we'll be tackling the question

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Speaker 3: why is space so flat? You mean as opposed to bumpy? Like,

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Speaker 3: what would be the opposite of flat overinflated, under pressure tight?

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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 3: M Well, it could also be well bumpy. I guess

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Speaker 3: bumpy is also kind of curvy. It means you have

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Speaker 3: a lot of little curves. You could have bumpy feet.

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Speaker 1: Yeah, exactly, that's true. You got to send 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 3: Yeah, and this is I guess, a pretty mind bending

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Speaker 3: and space bending topic because you know, I think we're

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Speaker 3: all used to thinking of space, or at least empty

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Speaker 3: space is being kind of like flat, right, not weirder

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Speaker 3: in curve.

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

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Speaker 3: doesn't quite work or describe things or is counter into

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Speaker 3: what is actually happening. Are we gonna do that again?

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

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Speaker 3: 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: flatness can apply in three dimensions, not just two.

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Speaker 3: Well, as usual, we were wondering how many people out

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Speaker 3: there had thought about this question whether space and why

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Speaker 3: space is so flat, and so Daniel went out into

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Speaker 3: 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 3: So think about it for a second. Why do you

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Speaker 3: think space is flat? Here's what people had to say.

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Speaker 6: I think space is flat because I think at the

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Speaker 6: beginning there wasn't any room for stuff to be clumpy

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Speaker 6: or lumped together, or have little dips or gaps, and

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Speaker 6: I assume that everything shot out from the Big Bang

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Speaker 6: in every direction in equal measure, and therefore it stayed

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Speaker 6: flat to this day.

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Speaker 7: I think that we're not one hundred percent certain that

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Speaker 7: space is flat. It just seems like it's flat because

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Speaker 7: space has been inflated so much from our perspective. The

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Speaker 7: analogy that I've heard before is kind of like standing

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Speaker 7: on the surface of the Earth, where the curvature of

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Speaker 7: the Earth is so large relative to us that it

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Speaker 7: seems like it's flat.

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Speaker 8: I'm not sure.

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Speaker 1: I thought it was three dimension on the plant has

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Speaker 1: to do with two D.

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Speaker 9: I think the flat space is somehow stable equilibrium points,

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Speaker 9: so the space will eventually evolve into the flat version.

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Speaker 8: I was sneaking suspicion it's not so flat, but it

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Speaker 8: just looks that way to us. I know there's some

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Speaker 8: bits of like string theory that posit there are dimensions

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Speaker 8: we simply can't perceive, and so I'm wondering if space

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Speaker 8: just looks flat to us because we just don't have

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Speaker 8: a capacity to see the other dimensions.

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Speaker 10: I don't think it is very flat. I think it

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Speaker 10: is pretty multi dimensional. I don't know what really is

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Speaker 10: meant by that maybe like stuff forms discs, like the

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Speaker 10: Solar system or our galaxy, maybe that is meant by flat.

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Speaker 10: I think that is due to that things tend to

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Speaker 10: take the shape of discs when there's rotation involved.

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Speaker 3: All right, 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 3: Yeah, that makes sense, right, Like if something, if the

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Speaker 3: universe was flat, it would be the width of a

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Speaker 3: sheet of paper, kind of right.

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Speaker 1: M Yeah. If somebody like bakes your birthday cake and

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

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

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Speaker 1: to two.

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Speaker 3: Dimensions two dimensional? Yeah, although two dimensional cake would be

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Speaker 3: pretty oh 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 3: As if a truck runs over it, I don't think

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Speaker 3: you want to eat it off the road. It seems

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Speaker 3: 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 wily coyote. Squeeze a cake

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

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Speaker 3: I'm pretty sure that if you ask YouTube, somebody out

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Speaker 3: there has made a video of a cake being flatted

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Speaker 3: by multiple things.

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Speaker 1: Thank you.

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Speaker 3: 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 3: But yeah, it's an interesting question why is space flat?

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Speaker 3: And I guess also is space flat? I guess is

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Speaker 3: maybe the first question we should be asking, or maybe

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Speaker 3: the question before that should be what does it mean

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Speaker 3: 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: of 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, think about locally

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Speaker 1: is a little bit easier, though of course it still

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

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Speaker 1: idea that matter bends space. That the reason things don't

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

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Speaker 1: bent by gravity is not because gravity is a force,

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Speaker 1: but that space itself is curved, so things are moving

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Speaker 1: through 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.

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Speaker 3: Curvature, right, although I think we always have to give

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Speaker 3: the caveat that. You mean space time, right, like space

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Speaker 3: 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 3: But I guess I mean like curve space makes me

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Speaker 3: think of like a road. Like a road is curved,

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Speaker 3: and so anything that tries to follow a stradeline on

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Speaker 3: that road is going to follow the same path. But

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Speaker 3: maybe in real life it would kind of depend. Right,

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Speaker 3: I don't know how fast you're going or what your

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Speaker 3: mass is, or right, isn't it.

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Speaker 1: Yeah, curve road is a helpful analogy. Things that are

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

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

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Speaker 1: this way that we can't directly observe it, Like you

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

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

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

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

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

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

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Speaker 1: along the curvature of space and fundamensional space time. It's

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Speaker 1: really fascinating because time and space bend together to make

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Speaker 1: space time itself have these invariants, these things that don't

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Speaker 1: actually change, but space curves and time curves due to

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Speaker 1: the presence of mass.

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Speaker 3: Right, But like if I throw a bowling ball at

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Speaker 3: a low speed and a high speed, and I threw

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Speaker 3: a feather at a low speed and as high speed,

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Speaker 3: they would sort of curve through space, or I would

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Speaker 3: see them curve in a different way, or would they

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Speaker 3: all 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 3: So I wonder if it's more accurate to say that

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Speaker 3: 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 3: Well, space like if you say that space is curved,

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Speaker 3: make me think of it like a tunnel. Like, if

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Speaker 3: a tunnel is curved, then no matter how fast you're

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Speaker 3: going or what you throw, you're going to bend the

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Speaker 3: same way. You can follow the same path. But that's

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Speaker 3: not sort of how space really works, right, Not everything

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Speaker 3: 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. Like if you enter a pipe and

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Speaker 1: you get flushed out the bottom or something. The curvature

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Speaker 1: of space does affect how you move. So yeah, that

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Speaker 1: distinction makes sense to me.

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Speaker 3: Okay, so then there's local curvature of space. What you're

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Speaker 3: talking about is sort of like how things go around

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Speaker 3: the Sun, for example, or how the moon goes around

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Speaker 3: the Earth, or how.

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Speaker 1: We stay on the Earth. All that kind of stuff,

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Speaker 1: things being gravitationally bound, even like the galaxy holding itself together.

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Speaker 1: That's all local curvature in comparison to the global curvature,

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Speaker 1: which is a question about the whole universe and its shape.

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Speaker 3: So there's local and global, and I guess what's the difference,

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Speaker 3: just like the size of it, the scale, Like are

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Speaker 3: you saying that? Like if I'm orbiting around the center

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Speaker 3: of the galaxy, it's a different kind of curvature of

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Speaker 3: doue to gravity than the Moon orbiting 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 3: 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 more an

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

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

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Speaker 1: whereas the local curvature is asking about the little picture

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Speaker 1: right right.

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Speaker 3: But I guess my question was, or is you know

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Speaker 3: where do you draw when do you draw this distinction

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Speaker 3: between local and global, like at the galaxy level, at

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Speaker 3: 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 know it's all equations in

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Speaker 1: general relativity, not me. They can only solve those in

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Speaker 1: certain situations, in situations where the who like the universe

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Speaker 1: is empty or the universe is filled with matter, but

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Speaker 1: that matter is perfectly smooth, like, nobody can solve the

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Speaker 1: general relativit equations for our universe, which has like clumps

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Speaker 1: of matter in it. So when we talk about the

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Speaker 1: whole universe and its curvature. Basically, we're talking about a

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Speaker 1: simplification of our universe where all the matter is spread

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Speaker 1: out evenly, there are no lumps at all, because that's

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Speaker 1: all they can solve. And in that case, there's still

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Speaker 1: this question of the global curvature. Is the universe curved

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

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

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

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

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

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Speaker 1: everywhere like peanut butter.

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Speaker 3: Mmm, but I guess, you know, if it's everything, we

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Speaker 3: don't really know what everything is, right, Like, the whole

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Speaker 3: entire observable universe might be just a little bump in

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Speaker 3: 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 3: I guess it's sort of like how before we used

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Speaker 3: to think that the Earth was flat because we only

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Speaker 3: knew sort of the local area here around this and

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Speaker 3: looks pretty flat. But actually if you sort of keep

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Speaker 3: going or you're taken to account the whole planet, then

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Speaker 3: 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

442
00:20:52,280 --> 00:20:54,800
Speaker 1: part of the Earth and you measured it to be flat,

443
00:20:55,080 --> 00:20:57,040
Speaker 1: and then you left that and you realized, oh, actually

444
00:20:57,080 --> 00:20:59,040
Speaker 1: the rest of the Earth is curved. And so what

445
00:20:59,080 --> 00:21:02,080
Speaker 1: I got was a misunderstanding of the bigger picture. So

446
00:21:02,119 --> 00:21:04,560
Speaker 1: you're right, we can only see the observable universe, and

447
00:21:04,600 --> 00:21:07,320
Speaker 1: we can measure the global curvature of this part of

448
00:21:07,359 --> 00:21:09,920
Speaker 1: the universe and then assume that the rest of it

449
00:21:09,960 --> 00:21:12,480
Speaker 1: is the same, but we'll never know, all.

450
00:21:12,440 --> 00:21:15,359
Speaker 3: Right, So then a local curvature of space sort of

451
00:21:15,960 --> 00:21:19,000
Speaker 3: is kind of about how mass spans space, and how

452
00:21:19,040 --> 00:21:20,920
Speaker 3: the Moon goes around the Earth and the Earth goes

453
00:21:21,000 --> 00:21:24,120
Speaker 3: around the Sun through curve space time. Now, when you're

454
00:21:24,119 --> 00:21:27,080
Speaker 3: talking about the global picture, I guess you're not just

455
00:21:27,119 --> 00:21:29,399
Speaker 3: talking about how things move, but it's more sort of

456
00:21:29,440 --> 00:21:33,200
Speaker 3: a fundamental property of space, about what it contains.

457
00:21:33,359 --> 00:21:35,040
Speaker 1: Yeah, and it's really hard to think about it in

458
00:21:35,040 --> 00:21:36,760
Speaker 1: three D. So we do this thing where we talk

459
00:21:36,800 --> 00:21:40,400
Speaker 1: about two dimensional versions. Sometimes that's helpful and sometimes it's misleading.

460
00:21:40,440 --> 00:21:42,320
Speaker 1: So you always have to keep in mind, like how

461
00:21:42,359 --> 00:21:45,879
Speaker 1: those things translate from a two dimensional analogy that's easier

462
00:21:45,880 --> 00:21:48,080
Speaker 1: for us to think about to the reality of three

463
00:21:48,160 --> 00:21:51,280
Speaker 1: D space. And it's easier to think about two dimensional

464
00:21:51,359 --> 00:21:54,119
Speaker 1: analogies because we basically live on a two dimensional surface,

465
00:21:54,200 --> 00:21:56,679
Speaker 1: the surface of the Earth, right, So it's easy to

466
00:21:56,720 --> 00:22:00,000
Speaker 1: imagine like living on a flat sheet of paper versus

467
00:22:00,240 --> 00:22:02,840
Speaker 1: on the surface of a sphere versus living in like

468
00:22:02,880 --> 00:22:06,960
Speaker 1: a hyperbola, and so those three shapes have different curvature.

469
00:22:07,119 --> 00:22:10,239
Speaker 1: An infinite plane is totally flat. If you drew a

470
00:22:10,280 --> 00:22:12,760
Speaker 1: triangle on the ground, the angles would add up to

471
00:22:12,760 --> 00:22:15,640
Speaker 1: one hundred and eighty degrees. The surface of a sphere,

472
00:22:15,920 --> 00:22:18,440
Speaker 1: we say it has positive curvature. You try a triangle

473
00:22:18,480 --> 00:22:21,359
Speaker 1: that follows the surface of that sphere, its angles are

474
00:22:21,400 --> 00:22:23,200
Speaker 1: going to add up to more than one hundred and eighty.

475
00:22:23,240 --> 00:22:25,240
Speaker 1: If you live on the surface of a hyperboloid and

476
00:22:25,320 --> 00:22:27,679
Speaker 1: you draw a triangle on that surface, the angles are

477
00:22:27,680 --> 00:22:29,800
Speaker 1: going to add up to less than one eighty. So

478
00:22:29,800 --> 00:22:33,399
Speaker 1: those are two D examples of curved surfaces. Then you

479
00:22:33,440 --> 00:22:36,440
Speaker 1: have to extrapolate those two three D space, and it's

480
00:22:36,520 --> 00:22:38,560
Speaker 1: very similar to a lot of the ideas carry over.

481
00:22:39,440 --> 00:22:41,200
Speaker 3: I feel like this is getting a little bit technical,

482
00:22:41,359 --> 00:22:45,760
Speaker 3: So when't we stretch these thoughts out and try to

483
00:22:45,760 --> 00:22:48,280
Speaker 3: get them down flat and talk about what it actually

484
00:22:48,359 --> 00:22:52,640
Speaker 3: means for three D universal space to be flat. But first,

485
00:22:52,720 --> 00:22:54,080
Speaker 3: let's take a quick break.

486
00:22:58,440 --> 00:23:01,359
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537
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538
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540
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541
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543
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545
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554
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Speaker 3: All Right, we're asking the question why is space so flat?

555
00:26:39,240 --> 00:26:42,640
Speaker 3: And I guess the preceding question is is space flat?

556
00:26:42,920 --> 00:26:45,280
Speaker 3: And the preceding preceding question is what does it mean

557
00:26:45,320 --> 00:26:47,720
Speaker 3: for this for space to be flat? Because I guess

558
00:26:47,760 --> 00:26:49,959
Speaker 3: base sort of seems flat to us. You know, it

559
00:26:49,960 --> 00:26:52,560
Speaker 3: doesn't seem curve or bent to us, at least our

560
00:26:52,600 --> 00:26:55,159
Speaker 3: immediate surroundings. But we know that if you expand your

561
00:26:55,680 --> 00:26:57,800
Speaker 3: your surroundings a little bit, you see that space time

562
00:26:57,880 --> 00:27:00,520
Speaker 3: is flat. That's how gravity works, and that what makes

563
00:27:00,520 --> 00:27:02,240
Speaker 3: the Moon go around the Earth and the Earth around

564
00:27:02,280 --> 00:27:05,920
Speaker 3: go around the Sun. But we're talking now about global

565
00:27:06,040 --> 00:27:09,800
Speaker 3: curvature of space, which really means universal curvature of space,

566
00:27:09,960 --> 00:27:14,240
Speaker 3: which actually sort of means observable universe curvature of space, right, Yeah.

567
00:27:14,080 --> 00:27:16,359
Speaker 1: And we're trying to use our understanding of two D

568
00:27:16,520 --> 00:27:19,119
Speaker 1: space to sort of bootstrap our way to understand the

569
00:27:19,200 --> 00:27:22,119
Speaker 1: curvature of three D space. So if you're like on

570
00:27:22,200 --> 00:27:26,160
Speaker 1: a flat surface and you shoot two parallel lines out

571
00:27:26,200 --> 00:27:29,160
Speaker 1: like two laser beams, then they'll never cross each other.

572
00:27:29,280 --> 00:27:31,440
Speaker 1: This is Euclid's famous geometry, and that's why we call

573
00:27:31,440 --> 00:27:35,280
Speaker 1: it Euclidean geometry. These two parallel lines will never meet.

574
00:27:35,400 --> 00:27:37,920
Speaker 1: And you can also do that in three dimensional space

575
00:27:38,040 --> 00:27:40,680
Speaker 1: right now, just imagine the universe is having three directions

576
00:27:40,680 --> 00:27:43,560
Speaker 1: shoot two parallel lines, but in any direction in xyz

577
00:27:43,960 --> 00:27:46,960
Speaker 1: they will never meet. In flat space, the extension of

578
00:27:46,960 --> 00:27:49,840
Speaker 1: flat space from two D three D is pretty straightforward.

579
00:27:49,920 --> 00:27:51,480
Speaker 3: I wonder if, like we even have to go to

580
00:27:51,520 --> 00:27:53,560
Speaker 3: a two D analogy. Why can't we just talk about

581
00:27:53,560 --> 00:27:55,480
Speaker 3: the curvature space in three D?

582
00:27:55,760 --> 00:27:58,280
Speaker 1: Yeah, I think three D flat space is pretty straightforward,

583
00:27:58,320 --> 00:28:00,280
Speaker 1: but it can help us understand the curved space to

584
00:28:00,320 --> 00:28:02,560
Speaker 1: starting two D, or at least let's give it a shot.

585
00:28:02,680 --> 00:28:06,119
Speaker 1: In two dimensional curve space, if you fire two laser

586
00:28:06,160 --> 00:28:10,119
Speaker 1: beams in the same direction, they will eventually cross, Like

587
00:28:10,240 --> 00:28:11,679
Speaker 1: if you're on the surface of the Earth and you

588
00:28:11,720 --> 00:28:13,920
Speaker 1: fire two laser beams in the direction in the north pole,

589
00:28:14,200 --> 00:28:16,680
Speaker 1: bill cross when they hit the north pole, right.

590
00:28:16,880 --> 00:28:19,399
Speaker 3: What I think this is why it's confusing, And I

591
00:28:19,440 --> 00:28:21,879
Speaker 3: wonder if you can just stick with three D, like

592
00:28:22,080 --> 00:28:24,160
Speaker 3: three D flat space. If I shoot two lasers out

593
00:28:24,160 --> 00:28:26,880
Speaker 3: in space, they're never going to meet. These two laser beams,

594
00:28:26,920 --> 00:28:29,119
Speaker 3: they're never gonna meet. Right now, let's talk about curve

595
00:28:29,240 --> 00:28:32,480
Speaker 3: three D space. I shoot two lasers, and the lasers

596
00:28:32,520 --> 00:28:34,360
Speaker 3: are going to do one of two things, right, They're

597
00:28:34,400 --> 00:28:37,800
Speaker 3: either going to come towards each other or bend away

598
00:28:37,800 --> 00:28:38,320
Speaker 3: from each other.

599
00:28:38,440 --> 00:28:40,720
Speaker 1: That's right. And whether they come towards each other and

600
00:28:40,760 --> 00:28:43,320
Speaker 1: away from each other tells you the sign of the curvature.

601
00:28:43,800 --> 00:28:47,560
Speaker 1: Positive curvature, they'll come towards each other, negative curvature, they'll

602
00:28:47,640 --> 00:28:49,440
Speaker 1: veer away from each other, never meet.

603
00:28:50,040 --> 00:28:53,200
Speaker 3: Now, this is super weird because what's bending the path

604
00:28:53,240 --> 00:28:56,479
Speaker 3: of the lasers just the curveness of space.

605
00:28:57,480 --> 00:29:00,600
Speaker 1: Lasers and light follow the curvature of space. They're like

606
00:29:00,680 --> 00:29:05,000
Speaker 1: tracers that tell you how space is curved. So light

607
00:29:05,120 --> 00:29:09,640
Speaker 1: moves in straight lines through curved space time, right, but

608
00:29:09,720 --> 00:29:12,320
Speaker 1: that leads to curved motion in space.

609
00:29:12,720 --> 00:29:14,720
Speaker 3: So you're saying that space might have a property to

610
00:29:14,760 --> 00:29:18,480
Speaker 3: it called curvature, which would to us make the light

611
00:29:18,520 --> 00:29:20,280
Speaker 3: beams not go in a street line.

612
00:29:20,320 --> 00:29:22,760
Speaker 1: That's right. If you assume space is flat, then light

613
00:29:22,800 --> 00:29:25,880
Speaker 1: appears to be moving in a curve. If, however, space

614
00:29:25,920 --> 00:29:29,320
Speaker 1: itself is curved, those grid lines themselves are curving, then

615
00:29:29,400 --> 00:29:31,480
Speaker 1: light is moving along those grid lines. It's just the

616
00:29:31,480 --> 00:29:33,240
Speaker 1: grid lines themselves are curved.

617
00:29:33,360 --> 00:29:35,760
Speaker 3: Okay, So now I feel like there's a third possibility.

618
00:29:36,280 --> 00:29:38,600
Speaker 3: So like, if I have a laser shooter on my

619
00:29:38,720 --> 00:29:41,560
Speaker 3: right hand and a laser shooter on my left hand,

620
00:29:42,040 --> 00:29:44,400
Speaker 3: and I shoot them perfectly parallel to each other. If

621
00:29:44,440 --> 00:29:46,560
Speaker 3: space is flat, they're just going to keep going straight

622
00:29:46,920 --> 00:29:50,520
Speaker 3: parallel forever. But if space is curved, there's some things

623
00:29:50,520 --> 00:29:52,920
Speaker 3: that can do. They can bend towards each other, away

624
00:29:52,920 --> 00:29:54,720
Speaker 3: from each other, but I feel like they could also

625
00:29:54,920 --> 00:29:59,000
Speaker 3: like bend perpendicular to each other. Like maybe my right

626
00:29:59,080 --> 00:30:03,640
Speaker 3: laser beam drifts up and my left laser being drips down.

627
00:30:03,840 --> 00:30:04,880
Speaker 3: What does what would that mean?

628
00:30:05,080 --> 00:30:07,080
Speaker 1: Isn't that the same as bending away from each other?

629
00:30:07,160 --> 00:30:10,200
Speaker 3: I guess if I just turn my head sideways, what

630
00:30:10,280 --> 00:30:14,080
Speaker 3: if they spiral around each other? Can space be twisty?

631
00:30:14,320 --> 00:30:17,240
Speaker 1: Space can have all sorts of weird combinations. I mean,

632
00:30:17,320 --> 00:30:19,280
Speaker 1: in general relativity, space can doesn't even have to be

633
00:30:19,320 --> 00:30:22,920
Speaker 1: totally connected. So a laser beam can disappear and appear

634
00:30:23,000 --> 00:30:25,880
Speaker 1: somewhere else, right. That's basically what a wormhole would be.

635
00:30:26,080 --> 00:30:28,720
Speaker 1: We're trying to talk about pretty simple constructions of space

636
00:30:28,760 --> 00:30:31,560
Speaker 1: where all you have is a single overall curvature.

637
00:30:32,320 --> 00:30:35,040
Speaker 3: I guess if I shoot my laser beams and they

638
00:30:35,640 --> 00:30:39,800
Speaker 3: they go past a large massive objects in space, like

639
00:30:39,800 --> 00:30:42,960
Speaker 3: the Sun, they're gonna curve, And if they're maybe on

640
00:30:43,080 --> 00:30:45,840
Speaker 3: opposite or different sides of the Sun, they're gonna curve

641
00:30:45,880 --> 00:30:48,960
Speaker 3: in a different way. And as they go through a galaxy,

642
00:30:49,000 --> 00:30:50,720
Speaker 3: they're gonna get pushed this way and that way the

643
00:30:50,800 --> 00:30:52,920
Speaker 3: laser beams. But I think you're talking about, like if

644
00:30:52,960 --> 00:30:56,520
Speaker 3: I shoot them maybe really far apart from each other

645
00:30:57,080 --> 00:30:59,160
Speaker 3: and let them go for a really really long time

646
00:30:59,320 --> 00:31:01,880
Speaker 3: on average, are they going to be moving towards each

647
00:31:01,880 --> 00:31:04,000
Speaker 3: other or away from each other? That's what you mean

648
00:31:04,080 --> 00:31:05,320
Speaker 3: by global curvature.

649
00:31:05,840 --> 00:31:07,840
Speaker 1: Yeah, And your analogy is great because it lets us

650
00:31:07,880 --> 00:31:12,600
Speaker 1: make a connection between local curvature and global curvature. Local curvature,

651
00:31:12,600 --> 00:31:14,280
Speaker 1: as you say, is like is there a star there

652
00:31:14,320 --> 00:31:16,040
Speaker 1: that's going to bend the path of my life. And

653
00:31:16,080 --> 00:31:18,080
Speaker 1: we sort of got our minds around a little bit.

654
00:31:18,120 --> 00:31:21,160
Speaker 1: The general reativity that light is bent by masses. Even

655
00:31:21,160 --> 00:31:23,959
Speaker 1: though light has no mass, it follows the curvature of space,

656
00:31:24,160 --> 00:31:27,040
Speaker 1: and it's bent. Right now, instead of having a local

657
00:31:27,080 --> 00:31:29,320
Speaker 1: mass like a star with a single point of really

658
00:31:29,400 --> 00:31:32,280
Speaker 1: high density, take that star and spread it out throughout

659
00:31:32,320 --> 00:31:35,480
Speaker 1: the whole universe instead. So now the universe is filled

660
00:31:35,480 --> 00:31:38,760
Speaker 1: with constant density of matter or energy. That creates a

661
00:31:38,760 --> 00:31:41,520
Speaker 1: curvature of space that's constant. It's not like, oh, there's

662
00:31:41,520 --> 00:31:43,600
Speaker 1: a lot of curvature near that star. Let's have a

663
00:31:43,640 --> 00:31:46,880
Speaker 1: little curvature everywhere instead of a lot of curvature in

664
00:31:47,000 --> 00:31:49,000
Speaker 1: just one spot. And that's one way to think about

665
00:31:49,000 --> 00:31:52,440
Speaker 1: the global curvature of space. Think about a universe uniformly

666
00:31:52,480 --> 00:31:54,640
Speaker 1: filled with a certain matter and energy density.

667
00:31:54,880 --> 00:31:57,440
Speaker 3: So like if the universe was infinite and was filled

668
00:31:57,480 --> 00:32:01,800
Speaker 3: with like evenly spread out gas or an evenly spread

669
00:32:01,800 --> 00:32:05,320
Speaker 3: out star, I guess what would happen to a laser beam.

670
00:32:05,360 --> 00:32:07,280
Speaker 3: Would it still curve or would it go straight?

671
00:32:07,360 --> 00:32:10,680
Speaker 1: It depends on the density of that stuff. Right, there's

672
00:32:10,680 --> 00:32:14,160
Speaker 1: a certain critical density of energy in the universe. Below

673
00:32:14,200 --> 00:32:17,920
Speaker 1: a certain level, the universe will be negatively curved. If

674
00:32:17,960 --> 00:32:21,280
Speaker 1: it has exactly the right critical energy at this knife's edge,

675
00:32:21,320 --> 00:32:23,800
Speaker 1: the universe will be flat. If it's more than that

676
00:32:23,800 --> 00:32:27,520
Speaker 1: critical energy, the universe will be curved. So the curvature

677
00:32:27,600 --> 00:32:31,280
Speaker 1: of the universe itself of space is connected to the

678
00:32:31,440 --> 00:32:34,520
Speaker 1: energy density of stuff in the universe relative to this

679
00:32:34,640 --> 00:32:35,720
Speaker 1: critical threshold.

680
00:32:35,960 --> 00:32:38,440
Speaker 3: I guess that's a little counterintuitive because I would think

681
00:32:38,520 --> 00:32:41,280
Speaker 3: that if the universe is filled evenly with the same

682
00:32:41,400 --> 00:32:45,600
Speaker 3: energy or gas or matter or energy, then the laser

683
00:32:45,600 --> 00:32:48,440
Speaker 3: beam would just go straight because it's being pulled the

684
00:32:48,480 --> 00:32:49,960
Speaker 3: same way in all directions.

685
00:32:50,160 --> 00:32:54,000
Speaker 1: Yeah, Unfortunately, general relativity isn't always intuitive, and if you

686
00:32:54,080 --> 00:32:57,719
Speaker 1: add enough stuff to the universe, it curves up. It

687
00:32:57,760 --> 00:33:01,320
Speaker 1: makes the universe effectively like a sphere. That's only consistent

688
00:33:01,360 --> 00:33:05,760
Speaker 1: with universes that have a positive curvature, because imagine you

689
00:33:05,920 --> 00:33:08,280
Speaker 1: take every bit of space and you make it bend y. Now,

690
00:33:08,320 --> 00:33:11,080
Speaker 1: think about like what shapes can you build with that.

691
00:33:11,320 --> 00:33:13,479
Speaker 1: If you only have curvy pieces, all you can do

692
00:33:13,520 --> 00:33:15,520
Speaker 1: is build the surface of a sphere, or all you

693
00:33:15,520 --> 00:33:18,040
Speaker 1: can do is build a three dimensional version of the

694
00:33:18,080 --> 00:33:20,840
Speaker 1: surface of a four dimensional sphere. If all you have

695
00:33:20,920 --> 00:33:21,960
Speaker 1: are bendy pieces.

696
00:33:23,320 --> 00:33:26,560
Speaker 3: Yeah, I guess I'm still confused because I'm imagine this

697
00:33:26,600 --> 00:33:29,360
Speaker 3: scenario where the whole universe is filled with the same

698
00:33:29,400 --> 00:33:32,520
Speaker 3: gas or evenly distributed star. If I shoot a laser beam,

699
00:33:32,560 --> 00:33:35,680
Speaker 3: which way does it curve? If the universe is positively curve,

700
00:33:35,840 --> 00:33:37,320
Speaker 3: so curve up, down, left to right.

701
00:33:37,480 --> 00:33:40,120
Speaker 1: In a universe with positive curvature, if you shoot a

702
00:33:40,200 --> 00:33:42,840
Speaker 1: laser beam, it looks to you like it's going straight,

703
00:33:43,040 --> 00:33:44,720
Speaker 1: but then it hits you in the back of the head.

704
00:33:44,920 --> 00:33:46,800
Speaker 3: What it wouldn't necessarily hit me in the back of

705
00:33:46,880 --> 00:33:47,480
Speaker 3: my head.

706
00:33:47,800 --> 00:33:51,600
Speaker 1: In a universe that's uniformly filled with matter that's positive curvature,

707
00:33:52,000 --> 00:33:53,880
Speaker 1: it will loop back around. It's like being on the

708
00:33:53,880 --> 00:33:56,520
Speaker 1: two dimensional surface of a three dimensional sphere.

709
00:33:56,560 --> 00:33:58,920
Speaker 3: But I guess it maybe it might loop around a

710
00:33:58,960 --> 00:34:00,440
Speaker 3: few times before it hits me in the back of

711
00:34:00,480 --> 00:34:00,760
Speaker 3: the head.

712
00:34:00,840 --> 00:34:02,280
Speaker 1: Any point on a sphere is the same, so it

713
00:34:02,320 --> 00:34:04,880
Speaker 1: doesn't really matter where you are which direction you shoot it.

714
00:34:04,920 --> 00:34:06,240
Speaker 1: You always get the same results.

715
00:34:06,360 --> 00:34:08,440
Speaker 3: From that point of view, I feel like then now

716
00:34:08,440 --> 00:34:11,040
Speaker 3: it's getting a little bit into this idea of the

717
00:34:11,320 --> 00:34:14,080
Speaker 3: how space is connected to itself, which is at the

718
00:34:14,160 --> 00:34:16,759
Speaker 3: case is a curvature of space necessarily the same as

719
00:34:16,760 --> 00:34:20,000
Speaker 3: how space is connected to itself, whether loops around itself.

720
00:34:19,880 --> 00:34:22,279
Speaker 1: It's definitely connected. Right, It's not the same, but it's

721
00:34:22,280 --> 00:34:25,919
Speaker 1: definitely connected. If space is flat, then the universe can

722
00:34:26,000 --> 00:34:29,160
Speaker 1: be infinite. If space is positive curvature, then the universe

723
00:34:29,200 --> 00:34:31,960
Speaker 1: can't be infinite. It can be finite but also have

724
00:34:32,080 --> 00:34:35,160
Speaker 1: no boundary, just the way like the two dimensional surface

725
00:34:35,200 --> 00:34:38,680
Speaker 1: of a three D sphere can be finite but unbounded

726
00:34:39,000 --> 00:34:42,040
Speaker 1: because it has positive curvature. So these two ideas are

727
00:34:42,040 --> 00:34:45,720
Speaker 1: definitely connected. The topology of space, the large scale shape

728
00:34:45,760 --> 00:34:48,719
Speaker 1: of space, and the curvature of space. The two things

729
00:34:48,719 --> 00:34:52,120
Speaker 1: are definitely closely linked. The curvature of space you can

730
00:34:52,120 --> 00:34:55,320
Speaker 1: deduce from the density of matter in that space, because

731
00:34:55,360 --> 00:34:57,240
Speaker 1: general relativity connects those two things.

732
00:34:57,400 --> 00:34:59,080
Speaker 3: Now that was one laser beam. Now I take two

733
00:34:59,160 --> 00:35:02,040
Speaker 3: laser beams and they shoot it off into three D space.

734
00:35:02,200 --> 00:35:05,799
Speaker 3: And let's say that the universe has positive curvature. What's

735
00:35:05,800 --> 00:35:09,040
Speaker 3: going to happen to these two laser beams. They're eventually

736
00:35:09,040 --> 00:35:10,000
Speaker 3: going to hit each other.

737
00:35:10,000 --> 00:35:11,480
Speaker 1: They will eventually cross. Yeah.

738
00:35:11,719 --> 00:35:11,919
Speaker 8: Mmm.

739
00:35:12,840 --> 00:35:15,759
Speaker 3: And if the universe is not positively curved, if it's

740
00:35:15,800 --> 00:35:18,920
Speaker 3: negatively curved. Then they'll never hit each other.

741
00:35:19,040 --> 00:35:20,760
Speaker 1: They won't hit each other, they'll veer apart.

742
00:35:21,080 --> 00:35:24,719
Speaker 3: M all right. I think that gives us as good

743
00:35:24,719 --> 00:35:27,400
Speaker 3: of an explanation of what the curvature space is in

744
00:35:27,440 --> 00:35:28,239
Speaker 3: the universe, right.

745
00:35:28,239 --> 00:35:28,600
Speaker 8: M hm.

746
00:35:29,080 --> 00:35:32,239
Speaker 1: And all of these things together control the future of

747
00:35:32,280 --> 00:35:36,440
Speaker 1: the universe, like the curvature and the topology, the matter

748
00:35:36,560 --> 00:35:39,319
Speaker 1: density of the universe. That plus like the dark energy

749
00:35:39,360 --> 00:35:42,319
Speaker 1: of the universe, all these things work together to determine

750
00:35:42,440 --> 00:35:45,400
Speaker 1: how fast the universe is expanding. Is it expanding or

751
00:35:45,520 --> 00:35:49,080
Speaker 1: is it collapsing, or is it steady state with no expansion.

752
00:35:49,480 --> 00:35:51,960
Speaker 1: All of these things play a role in determining the

753
00:35:51,960 --> 00:35:53,360
Speaker 1: future of the universe.

754
00:35:53,680 --> 00:35:57,239
Speaker 3: Cool, Well, maybe talk about how you might measure the

755
00:35:57,280 --> 00:35:59,359
Speaker 3: flatness of the universe, in like, how do we know

756
00:35:59,520 --> 00:36:01,840
Speaker 3: whether the universe is flat or not?

757
00:36:02,120 --> 00:36:04,200
Speaker 1: So what we do is we measure this energy density.

758
00:36:04,480 --> 00:36:06,400
Speaker 1: And of course the caveat is we can only measure

759
00:36:06,400 --> 00:36:09,200
Speaker 1: it in the observable universe. We can't measure outside, and

760
00:36:09,239 --> 00:36:11,160
Speaker 1: so when we say the universe here, we always really

761
00:36:11,200 --> 00:36:13,480
Speaker 1: just mean the observable universe. All we can do is

762
00:36:13,520 --> 00:36:16,120
Speaker 1: measure the energy density, and we can say is there

763
00:36:16,239 --> 00:36:19,440
Speaker 1: enough stuff in the universe to make it curved positively

764
00:36:19,880 --> 00:36:22,440
Speaker 1: so it wraps up on itself. Is there the critical

765
00:36:22,480 --> 00:36:24,879
Speaker 1: density so the space is flat? Or is there less

766
00:36:24,920 --> 00:36:27,600
Speaker 1: than the critical density so that the universe is open

767
00:36:27,760 --> 00:36:30,400
Speaker 1: with negative curvature. So the way we do that is

768
00:36:30,440 --> 00:36:33,520
Speaker 1: by measuring the amount of stuff, the energy density of

769
00:36:33,560 --> 00:36:34,640
Speaker 1: stuff in the universe.

770
00:36:34,760 --> 00:36:37,080
Speaker 3: Oh, I see, you measure the density of stuff. But

771
00:36:37,160 --> 00:36:39,560
Speaker 3: I guess we never covered why the density of stuff

772
00:36:39,680 --> 00:36:41,880
Speaker 3: determines the curvature of space, Like why is there a

773
00:36:41,920 --> 00:36:45,280
Speaker 3: critical amount that makes it negative or positive? Like wouldn't

774
00:36:45,400 --> 00:36:47,800
Speaker 3: any amount of stuff in the universe make the universe

775
00:36:48,000 --> 00:36:48,879
Speaker 3: positively curve?

776
00:36:49,000 --> 00:36:52,280
Speaker 1: Yeah, that is a little counterintuitive. But a totally empty universe,

777
00:36:52,360 --> 00:36:55,479
Speaker 1: one with no matter or energy in it at all,

778
00:36:55,840 --> 00:36:59,600
Speaker 1: would not have flat space. It would have negatively curved space.

779
00:37:00,200 --> 00:37:02,319
Speaker 1: Need a little bit of stuff in the universe to

780
00:37:02,360 --> 00:37:03,080
Speaker 1: counteract that.

781
00:37:03,560 --> 00:37:06,520
Speaker 3: Whoa wait, So if I had an empty universe, like

782
00:37:06,600 --> 00:37:08,800
Speaker 3: no stars, no planets, no galaxies in it, and I

783
00:37:08,840 --> 00:37:11,719
Speaker 3: shoot to laser beams, they're going to diverge from each other.

784
00:37:12,000 --> 00:37:14,440
Speaker 3: They're not just going to stay parallel to each other forever.

785
00:37:14,719 --> 00:37:16,880
Speaker 1: Yeah, that's right. This is one of the situations we

786
00:37:16,920 --> 00:37:20,520
Speaker 1: can actually solve in Einstein's general relativity situation with nothing

787
00:37:20,640 --> 00:37:23,640
Speaker 1: in the universe totally empty, no matter, no energy, no

788
00:37:23,800 --> 00:37:27,640
Speaker 1: dark energy. In that case, the universe has negative curvature.

789
00:37:28,000 --> 00:37:30,360
Speaker 1: So you have to add stuff to the universe to

790
00:37:30,400 --> 00:37:33,160
Speaker 1: make it have no curvature or positive curvature.

791
00:37:33,440 --> 00:37:36,680
Speaker 3: Oh so even no dark energy, like this sort of

792
00:37:36,920 --> 00:37:40,759
Speaker 3: necessary amount of stuff in it is not related to

793
00:37:40,800 --> 00:37:43,480
Speaker 3: the expansion of the universe either or do you assume

794
00:37:43,480 --> 00:37:45,319
Speaker 3: the expansion of the universe or not.

795
00:37:45,480 --> 00:37:48,080
Speaker 1: This does not determine the expansion of the universe. All

796
00:37:48,120 --> 00:37:51,480
Speaker 1: these pieces together, the curvature, the density, the dark energy,

797
00:37:51,560 --> 00:37:55,080
Speaker 1: all these things together determine whether the universe is expanding,

798
00:37:55,080 --> 00:37:58,560
Speaker 1: whether that expansion is accelerating. It's a whole complex dance,

799
00:37:59,040 --> 00:38:01,640
Speaker 1: but just the curve of the universe is determined by

800
00:38:01,680 --> 00:38:04,160
Speaker 1: the matter and energy density. If you have a certain amount,

801
00:38:04,160 --> 00:38:06,920
Speaker 1: then you sort of counteract the natural negative curvature of

802
00:38:06,960 --> 00:38:09,200
Speaker 1: space and you get a flat universe. If you have

803
00:38:09,239 --> 00:38:11,120
Speaker 1: more than that, you get a positive curvature. If you're

804
00:38:11,160 --> 00:38:13,880
Speaker 1: less than that, you get negative curvature. So a flat

805
00:38:13,960 --> 00:38:16,440
Speaker 1: universe is sort of balanced on a knife's edge. You

806
00:38:16,440 --> 00:38:18,840
Speaker 1: have to have like exactly the right amount of stuff,

807
00:38:19,120 --> 00:38:21,400
Speaker 1: and it's not a big number, like the critical density

808
00:38:21,480 --> 00:38:24,359
Speaker 1: right now is about five protons per cubic meter.

809
00:38:24,960 --> 00:38:28,680
Speaker 3: I guess that's weird that space by itself has negative

810
00:38:28,719 --> 00:38:33,720
Speaker 3: curvature like pure space OG space. If you choose laser beams,

811
00:38:33,880 --> 00:38:37,160
Speaker 3: they would diverge. Isn't that weird because shouldn't space be

812
00:38:37,280 --> 00:38:38,960
Speaker 3: like neutral or totally empty.

813
00:38:39,080 --> 00:38:41,360
Speaker 1: Well, intuitive concept of space doesn't even allow it to

814
00:38:41,400 --> 00:38:44,400
Speaker 1: be bent, right, So you have to already let go

815
00:38:44,480 --> 00:38:47,480
Speaker 1: of those intuitive ideas and think that space is something

816
00:38:47,560 --> 00:38:51,080
Speaker 1: quite different from what we imagined as these weird properties.

817
00:38:51,280 --> 00:38:53,800
Speaker 1: It's a little bit more complicated than what we've described

818
00:38:54,280 --> 00:38:56,680
Speaker 1: because the amount of stuff you have to add to

819
00:38:56,880 --> 00:38:59,920
Speaker 1: space to avoid this negative curvature actually changes over time.

820
00:39:00,200 --> 00:39:03,239
Speaker 1: It depends also on the expansion of the universe. So

821
00:39:03,280 --> 00:39:05,600
Speaker 1: there's a lot of complex moving parts here that we're

822
00:39:05,640 --> 00:39:06,560
Speaker 1: trying to distill down.

823
00:39:06,800 --> 00:39:09,080
Speaker 3: But I guess the main takeaway is that space by

824
00:39:09,120 --> 00:39:13,040
Speaker 3: itself has negative curvature. But because we have stuff in it,

825
00:39:13,120 --> 00:39:17,120
Speaker 3: matter and energy, then it's possible for space to be flat,

826
00:39:17,320 --> 00:39:20,640
Speaker 3: because that's what the effect of energy and mess does

827
00:39:20,760 --> 00:39:23,040
Speaker 3: to space is it makes it more positively curvy.

828
00:39:23,160 --> 00:39:25,640
Speaker 1: Yeah, and we can measure the curvature of space by

829
00:39:25,719 --> 00:39:29,799
Speaker 1: measuring the matter and energy density of the universe. So

830
00:39:29,840 --> 00:39:31,839
Speaker 1: we go out, we measure that, and that tells us

831
00:39:31,880 --> 00:39:35,400
Speaker 1: what curvature we have in our universe. The magnitude of

832
00:39:35,440 --> 00:39:38,160
Speaker 1: that curvature can also change, the sign can't. If you

833
00:39:38,200 --> 00:39:41,720
Speaker 1: have positively curved space, it's always going to be positively curved,

834
00:39:41,960 --> 00:39:45,160
Speaker 1: but it can get more positively curved or less positively curved,

835
00:39:45,239 --> 00:39:48,000
Speaker 1: like the universe has positive curvature can collapse on itself,

836
00:39:48,040 --> 00:39:51,399
Speaker 1: making itself more and more positively curved, or universe that's

837
00:39:51,440 --> 00:39:54,440
Speaker 1: open can expand really really rapidly and get less and

838
00:39:54,520 --> 00:39:56,919
Speaker 1: less curved. But they can't flip over. You can't start

839
00:39:56,960 --> 00:39:59,040
Speaker 1: from the universe has positively curves and end up with

840
00:39:59,080 --> 00:40:00,239
Speaker 1: the universe that's negative the.

841
00:40:00,280 --> 00:40:04,359
Speaker 3: Curved, unless maybe the density of energy and matter decreases enough.

842
00:40:04,640 --> 00:40:07,280
Speaker 3: Isn't that possible. No, As like you said, it depends

843
00:40:07,280 --> 00:40:09,600
Speaker 3: on that density. What if the density changes.

844
00:40:09,760 --> 00:40:12,440
Speaker 1: The density definitely does change, right, and we'll talk a

845
00:40:12,440 --> 00:40:14,799
Speaker 1: little bit about how that density is changing and how

846
00:40:14,840 --> 00:40:17,719
Speaker 1: we understand how it's changing. But you can't change the

847
00:40:17,800 --> 00:40:21,000
Speaker 1: curvature of the universe. You can't go from positively curved

848
00:40:21,040 --> 00:40:24,080
Speaker 1: space to negatively curve space. That would correspond to like

849
00:40:24,160 --> 00:40:27,080
Speaker 1: changing from a finite universe to an infinite universe, which

850
00:40:27,120 --> 00:40:29,920
Speaker 1: you can't do, right. You can't take the service of

851
00:40:29,920 --> 00:40:32,360
Speaker 1: a sphere and snap it out to an infinite plane.

852
00:40:32,800 --> 00:40:35,960
Speaker 3: You can pop a balloon, you can flat that birthday cake.

853
00:40:36,320 --> 00:40:39,439
Speaker 1: That's one of the confusing things about these two D analogies, right,

854
00:40:40,000 --> 00:40:42,520
Speaker 1: is that you're imagining it in a three D space.

855
00:40:42,560 --> 00:40:44,719
Speaker 1: You're thinking about really a two D service on a

856
00:40:44,760 --> 00:40:47,400
Speaker 1: three D sphere. But in those analogies, the two D

857
00:40:47,520 --> 00:40:50,920
Speaker 1: surface is all there is, so you can't really flatten it.

858
00:40:51,000 --> 00:40:53,239
Speaker 3: All right, Well, let's dig into what would happen if

859
00:40:53,280 --> 00:40:56,040
Speaker 3: you change the density of matter and energy in the universe,

860
00:40:56,680 --> 00:40:59,680
Speaker 3: and then let's ask the big question why is the

861
00:40:59,760 --> 00:41:03,600
Speaker 3: universe flat? But first, let's take another quick break.

862
00:41:08,280 --> 00:41:10,080
Speaker 1: When you pop a piece of cheese into your mouth,

863
00:41:10,200 --> 00:41:13,320
Speaker 1: or enjoy a rich spoonful of Greek yogurt, you're probably

864
00:41:13,360 --> 00:41:17,400
Speaker 1: not thinking about the environmental impact of each and every bite,

865
00:41:17,440 --> 00:41:20,080
Speaker 1: But the people in the dairy industry are. US Dairy

866
00:41:20,120 --> 00:41:24,400
Speaker 1: has set themselves some ambitious sustainability goals, including being greenhouse

867
00:41:24,440 --> 00:41:27,000
Speaker 1: gas neutral by twenty to fifty. That's why they're working

868
00:41:27,040 --> 00:41:29,359
Speaker 1: hard every day to find new ways to reduce waste,

869
00:41:29,440 --> 00:41:33,680
Speaker 1: conserve natural resources, and drive down greenhouse gas emissions. Take water,

870
00:41:33,719 --> 00:41:36,800
Speaker 1: for example, most dairy farms reuse water up to four

871
00:41:36,880 --> 00:41:40,319
Speaker 1: times the same water cools the milk, cleans equipment, washes

872
00:41:40,360 --> 00:41:43,160
Speaker 1: the barn, and irrigates the crops. How is US dairy

873
00:41:43,200 --> 00:41:46,960
Speaker 1: tackling greenhouse gases. Many farms use anaerobic digestors that turn

874
00:41:47,000 --> 00:41:50,880
Speaker 1: the methane from maneuver into renewable energy that can power farms, towns,

875
00:41:50,920 --> 00:41:53,000
Speaker 1: and electric cars. So the next time you grab a

876
00:41:53,040 --> 00:41:55,040
Speaker 1: slice of pizza or lick an ice cream cone, know

877
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Speaker 3: All right, we're asking the question, why is space flat

908
00:43:33,719 --> 00:43:36,080
Speaker 3: or I guess why space so flat because it's maybe

909
00:43:36,120 --> 00:43:37,360
Speaker 3: flatter than what you expected.

910
00:43:37,600 --> 00:43:39,560
Speaker 1: Yeah, when we go out to measure the curvage of

911
00:43:39,560 --> 00:43:42,440
Speaker 1: the universe, we find something kind of surprising. We find

912
00:43:42,560 --> 00:43:46,240
Speaker 1: that it's really pretty flat, Like there's this critical density

913
00:43:46,320 --> 00:43:49,360
Speaker 1: five protons per cubic meter. And we go out to

914
00:43:49,400 --> 00:43:51,359
Speaker 1: measure the amount of stuff in the universe. We add

915
00:43:51,440 --> 00:43:54,680
Speaker 1: up all the mass, the stars, the galaxies, the dark matter,

916
00:43:54,960 --> 00:43:57,759
Speaker 1: and also the dark energy. All of that stuff. It

917
00:43:57,760 --> 00:44:01,120
Speaker 1: adds up to like very very close to exactly the

918
00:44:01,200 --> 00:44:04,799
Speaker 1: critical density. It's within one percent, which is about our

919
00:44:04,880 --> 00:44:08,560
Speaker 1: uncertainty of the critical density, which tells us that space

920
00:44:08,640 --> 00:44:11,920
Speaker 1: is either flat or very very close to flat. And

921
00:44:11,960 --> 00:44:14,120
Speaker 1: that's kind of a surprise because we don't think the

922
00:44:14,200 --> 00:44:16,000
Speaker 1: universe likes to be flat.

923
00:44:16,920 --> 00:44:19,720
Speaker 3: I guess before we go on, I have more questions

924
00:44:20,000 --> 00:44:21,920
Speaker 3: about what you just said. Well, first of all, how

925
00:44:21,920 --> 00:44:25,480
Speaker 3: do we measure the mass and energy density of the universe?

926
00:44:26,120 --> 00:44:28,160
Speaker 3: And second of all, how do we know what amount

927
00:44:28,239 --> 00:44:29,879
Speaker 3: you need for the universe to be flat?

928
00:44:29,920 --> 00:44:32,640
Speaker 1: So how we measure it is several different ways. We

929
00:44:32,640 --> 00:44:36,000
Speaker 1: can use like the cosmic microwave background radiation. This is

930
00:44:36,120 --> 00:44:39,440
Speaker 1: radiation from about three hundred thousand years after the Big Bang,

931
00:44:39,719 --> 00:44:41,920
Speaker 1: where the universe was very hot and dense with its

932
00:44:41,920 --> 00:44:44,440
Speaker 1: bright plasma, and then it cooled off and formed neutral

933
00:44:44,480 --> 00:44:47,560
Speaker 1: atoms and light could propagate. We can still see that light.

934
00:44:47,840 --> 00:44:50,120
Speaker 1: That light was made everywhere in the universe, and it's

935
00:44:50,160 --> 00:44:53,640
Speaker 1: flying around everywhere, and some of it has just reached

936
00:44:53,719 --> 00:44:56,280
Speaker 1: Earth from places that used to be very very far away,

937
00:44:56,440 --> 00:44:58,120
Speaker 1: and we can use it to sort of look at

938
00:44:58,120 --> 00:45:00,319
Speaker 1: what the universe looked like at that time, and there

939
00:45:00,320 --> 00:45:03,440
Speaker 1: were little bumps and wiggles in it. It's not completely smooth.

940
00:45:03,440 --> 00:45:06,120
Speaker 1: It's like a little bit of a frothing quantum plasma.

941
00:45:06,200 --> 00:45:08,399
Speaker 1: And from the size of those wiggles, we can tell

942
00:45:08,440 --> 00:45:10,680
Speaker 1: how much energy density there was in the.

943
00:45:10,640 --> 00:45:13,400
Speaker 3: Early universe based on some theory that you have about

944
00:45:13,400 --> 00:45:16,279
Speaker 3: how the universe formed and how these things balance out

945
00:45:16,520 --> 00:45:17,319
Speaker 3: with space.

946
00:45:17,160 --> 00:45:20,160
Speaker 1: Relying basically just on general relativity. I mean, we assume

947
00:45:20,280 --> 00:45:23,440
Speaker 1: some model of the universe, but it's based in general relativity.

948
00:45:23,640 --> 00:45:26,320
Speaker 1: Doesn't depend on how the universe formed or what came before.

949
00:45:26,320 --> 00:45:29,319
Speaker 1: It just depends on the size of those fluctuations in

950
00:45:29,360 --> 00:45:32,359
Speaker 1: the early universe and then how those propagate through an

951
00:45:32,360 --> 00:45:34,000
Speaker 1: expanding universe to us.

952
00:45:34,320 --> 00:45:36,160
Speaker 3: Okay, so that's one way to measure it.

953
00:45:36,280 --> 00:45:39,480
Speaker 1: So that measures the total energy density like the dark

954
00:45:39,600 --> 00:45:42,719
Speaker 1: energy plus the dark matter plus the normal matter density

955
00:45:42,719 --> 00:45:44,759
Speaker 1: in the early universe. We can also measure it by

956
00:45:44,760 --> 00:45:47,799
Speaker 1: looking at the acceleration of the universe, like looking at

957
00:45:47,800 --> 00:45:50,400
Speaker 1: supernova seeing how fast they're moving away from us, or

958
00:45:50,480 --> 00:45:53,680
Speaker 1: looking at cephids. This expansion rate of the universe also

959
00:45:53,760 --> 00:45:57,319
Speaker 1: helps us measure these various components. So the components of

960
00:45:57,320 --> 00:45:59,600
Speaker 1: the energy density of the universe are the dark energy,

961
00:46:00,040 --> 00:46:02,200
Speaker 1: the normal matter, and the dark matter and the super

962
00:46:02,239 --> 00:46:05,280
Speaker 1: KNOVEA measurements the acceleration of the universe help us measure

963
00:46:05,440 --> 00:46:09,440
Speaker 1: the dark energy component minus the matter component, because that

964
00:46:09,480 --> 00:46:12,840
Speaker 1: determines the expansion of the universe. So there's like a

965
00:46:12,840 --> 00:46:15,080
Speaker 1: bunch of different components here, and we have different ways

966
00:46:15,120 --> 00:46:17,680
Speaker 1: to measure each one's or combinations of each one, to

967
00:46:17,680 --> 00:46:21,399
Speaker 1: help us in down exactly what those contributions are. Dark

968
00:46:21,520 --> 00:46:24,080
Speaker 1: energy is of like seventy percent of the critical density,

969
00:46:24,280 --> 00:46:27,279
Speaker 1: matters like thirty percent of the critical density, where most

970
00:46:27,280 --> 00:46:29,080
Speaker 1: of that is dark matter, and they add up to

971
00:46:29,120 --> 00:46:30,680
Speaker 1: basically this critical density.

972
00:46:30,920 --> 00:46:34,359
Speaker 3: This is from this CMB measurement or from all measurements.

973
00:46:34,120 --> 00:46:36,960
Speaker 1: The CMB measurement tells us the total density. The supernova

974
00:46:37,080 --> 00:46:40,200
Speaker 1: tells us the dark energy minus the matter the difference

975
00:46:40,200 --> 00:46:42,960
Speaker 1: between those two because they work against each other when

976
00:46:43,000 --> 00:46:46,560
Speaker 1: controlling the expansion of the universe. There's another measurement, the

977
00:46:46,640 --> 00:46:50,440
Speaker 1: buryon acoustic oscillations, that tells us about like how matter

978
00:46:50,560 --> 00:46:53,319
Speaker 1: was sloshing around in the early universe and made these

979
00:46:53,360 --> 00:46:56,640
Speaker 1: sound waves back when the universe was super duper dense.

980
00:46:56,680 --> 00:46:59,200
Speaker 1: Sound traveled at nearly half the speed of light, and

981
00:46:59,239 --> 00:47:02,000
Speaker 1: the speed of that depends on the density of matter

982
00:47:02,120 --> 00:47:04,240
Speaker 1: in the universe, and we can still sort of see

983
00:47:04,280 --> 00:47:08,400
Speaker 1: the universe ringing from those oscillations in the early universe.

984
00:47:08,760 --> 00:47:12,040
Speaker 1: That separately measures just the matter portion. So we have

985
00:47:12,080 --> 00:47:14,680
Speaker 1: these different pieces of the pie, and they all add

986
00:47:14,760 --> 00:47:17,520
Speaker 1: up to make exactly one pie. And the fascinating thing

987
00:47:17,840 --> 00:47:19,600
Speaker 1: is that they didn't have to write It could have

988
00:47:19,600 --> 00:47:21,279
Speaker 1: added up to anything. It could have added up to

989
00:47:21,280 --> 00:47:23,920
Speaker 1: be twice the critical density or half the critical density,

990
00:47:24,120 --> 00:47:26,760
Speaker 1: but it adds up to bang on just the critical

991
00:47:26,760 --> 00:47:28,240
Speaker 1: density to within one percent.

992
00:47:28,719 --> 00:47:31,280
Speaker 3: I see. So you're saying, we've measured the energy density

993
00:47:31,320 --> 00:47:34,040
Speaker 3: of the universe and according to what we think is

994
00:47:34,400 --> 00:47:36,840
Speaker 3: the laws of the universe, according to general relativity, we

995
00:47:36,880 --> 00:47:39,480
Speaker 3: have just enough mass and density to make the universe flat,

996
00:47:39,520 --> 00:47:41,920
Speaker 3: which means if I shoot two lasers out there in space,

997
00:47:42,480 --> 00:47:45,040
Speaker 3: they're not going to hit each other, they're not going

998
00:47:45,120 --> 00:47:46,600
Speaker 3: to drift the part, they're not going to hit me

999
00:47:46,640 --> 00:47:48,359
Speaker 3: in the back of the head. Those two laser beings

1000
00:47:48,360 --> 00:47:51,000
Speaker 3: are just gonna keep going forever, exactly.

1001
00:47:51,360 --> 00:47:54,360
Speaker 1: And this is kind of a surprise to physicists because

1002
00:47:54,719 --> 00:47:57,360
Speaker 1: they think the universe doesn't like to be flat, Like

1003
00:47:57,440 --> 00:47:59,719
Speaker 1: the flatness of the universe is not a stable thing.

1004
00:48:00,200 --> 00:48:02,640
Speaker 1: If you're just above the critical density, if you're like

1005
00:48:02,680 --> 00:48:05,080
Speaker 1: a little bit more than the critical density, then the

1006
00:48:05,160 --> 00:48:08,000
Speaker 1: universe tends to collapse and become more and more dense,

1007
00:48:08,040 --> 00:48:10,480
Speaker 1: and you move away from the critical density. If you

1008
00:48:10,520 --> 00:48:13,080
Speaker 1: have less than the critical density, you're below it, then

1009
00:48:13,080 --> 00:48:15,680
Speaker 1: the universe is open. It tends to expand and dilute

1010
00:48:15,719 --> 00:48:19,360
Speaker 1: itself away from the critical density. So either you're exactly

1011
00:48:19,360 --> 00:48:21,840
Speaker 1: bang on the critical density in which you're stable like

1012
00:48:21,880 --> 00:48:24,520
Speaker 1: a pencil balance on its tip, or you're a little

1013
00:48:24,560 --> 00:48:26,680
Speaker 1: bit above and a little bit below and then you

1014
00:48:26,800 --> 00:48:29,319
Speaker 1: very quickly veer away from it. So sort of a

1015
00:48:29,360 --> 00:48:32,640
Speaker 1: mystery how we're still so close to the critical density

1016
00:48:32,719 --> 00:48:34,400
Speaker 1: after billions of years.

1017
00:48:34,480 --> 00:48:36,759
Speaker 3: What do you mean it's unstable like a pencil. What

1018
00:48:36,760 --> 00:48:37,239
Speaker 3: does that mean?

1019
00:48:37,320 --> 00:48:39,400
Speaker 1: It's unstable in that if you move away from the

1020
00:48:39,440 --> 00:48:42,440
Speaker 1: critical density a little bit, the universe moves away even more.

1021
00:48:42,840 --> 00:48:45,320
Speaker 1: It's like a pencil balance on its tip. Right, it's unstable.

1022
00:48:45,360 --> 00:48:47,680
Speaker 1: You have it, a tiny little push, a fly lands

1023
00:48:47,680 --> 00:48:49,840
Speaker 1: on it, air blows by it really gently, it's going

1024
00:48:49,920 --> 00:48:50,799
Speaker 1: to tend to fall over.

1025
00:48:51,040 --> 00:48:53,400
Speaker 3: Wait to Like, if you measure the density of the

1026
00:48:53,480 --> 00:48:56,480
Speaker 3: universe and it's a little bit more than the critical

1027
00:48:56,719 --> 00:48:59,319
Speaker 3: amount of density you need for a flat universe, then

1028
00:48:59,360 --> 00:49:02,440
Speaker 3: the density is going to increase over time, like the

1029
00:49:02,520 --> 00:49:04,200
Speaker 3: universe is going to get more and more denser.

1030
00:49:04,400 --> 00:49:06,759
Speaker 1: Exactly. If you have more than the critical density, the

1031
00:49:06,840 --> 00:49:10,480
Speaker 1: universe will contract, right, and things will get denser and denser.

1032
00:49:10,560 --> 00:49:11,920
Speaker 1: You'll end up with like a big crunch.

1033
00:49:12,160 --> 00:49:14,320
Speaker 3: You mean, like the expansion of the universe will reverse.

1034
00:49:14,520 --> 00:49:17,320
Speaker 1: Yeah, exactly. In the opposite scenario, where you lessen the

1035
00:49:17,320 --> 00:49:20,400
Speaker 1: critical density, things expand forever and things get more and

1036
00:49:20,400 --> 00:49:24,160
Speaker 1: more dilute, So the density drops right as the universe expands,

1037
00:49:24,320 --> 00:49:27,520
Speaker 1: the density of matter drops. As the universe contracts, the

1038
00:49:27,560 --> 00:49:30,759
Speaker 1: density of matter increases, and so if you're not at

1039
00:49:30,760 --> 00:49:32,840
Speaker 1: the critical density, you tend to veer away from it

1040
00:49:32,840 --> 00:49:35,480
Speaker 1: pretty quickly. And we're like billions of years into the

1041
00:49:35,520 --> 00:49:38,320
Speaker 1: history and we're still super close to the critical density,

1042
00:49:38,360 --> 00:49:40,759
Speaker 1: which was a big question in cosmology. How can you

1043
00:49:40,800 --> 00:49:43,080
Speaker 1: stay so closely balanced so long?

1044
00:49:43,239 --> 00:49:45,200
Speaker 3: I feel like now we're tying it to the expansion

1045
00:49:45,239 --> 00:49:47,680
Speaker 3: of the universe, So the critical density is tied to

1046
00:49:47,719 --> 00:49:50,480
Speaker 3: the expansion, like if the universe is positively curved, then

1047
00:49:50,560 --> 00:49:52,360
Speaker 3: the universe is going to contract eventually.

1048
00:49:52,480 --> 00:49:54,600
Speaker 1: The couragere of the universe definitely plays a role. The

1049
00:49:54,640 --> 00:49:57,320
Speaker 1: critical density and the curvature, together with the amount of

1050
00:49:57,400 --> 00:50:01,200
Speaker 1: dark energy, determine the expansion. You can have a universe

1051
00:50:01,239 --> 00:50:04,760
Speaker 1: that's positively curved and expanding if you have enough dark energy,

1052
00:50:04,840 --> 00:50:08,279
Speaker 1: because dark energy can overcome this critical density, that you

1053
00:50:08,280 --> 00:50:10,960
Speaker 1: could have a universe which expands. But in the simple

1054
00:50:10,960 --> 00:50:13,000
Speaker 1: scenario where you take out dark energy for the moment

1055
00:50:13,040 --> 00:50:15,520
Speaker 1: and just have a universe with only matter and radiation,

1056
00:50:15,960 --> 00:50:18,319
Speaker 1: which was basically the scenario of our universe for the

1057
00:50:18,320 --> 00:50:21,160
Speaker 1: first nine billion years when dark energy was negligible, and

1058
00:50:21,200 --> 00:50:24,279
Speaker 1: then the universe above the critical density will contract and

1059
00:50:24,360 --> 00:50:27,600
Speaker 1: increase the density and the universe below the critical density

1060
00:50:27,640 --> 00:50:31,520
Speaker 1: will expand and decrease the density. So they did this calculation.

1061
00:50:31,600 --> 00:50:34,239
Speaker 1: They're like, well, in that scenario, how close do the

1062
00:50:34,280 --> 00:50:36,719
Speaker 1: universe have to start to the critical density to end

1063
00:50:36,760 --> 00:50:38,680
Speaker 1: up at one percent. The answer is we had to

1064
00:50:38,719 --> 00:50:41,279
Speaker 1: be within the critical density to within ten to the

1065
00:50:41,360 --> 00:50:44,680
Speaker 1: minus sixty two. If you're anything above that, then the

1066
00:50:44,760 --> 00:50:48,840
Speaker 1: universe would have expanded like crazy or contracted like crazy.

1067
00:50:49,400 --> 00:50:52,160
Speaker 1: So it seems really, really weird that we end up

1068
00:50:52,200 --> 00:50:54,760
Speaker 1: with a universe so close to flat when the universe

1069
00:50:54,840 --> 00:50:56,600
Speaker 1: likes to veer away from flatness.

1070
00:50:57,160 --> 00:51:00,960
Speaker 3: Well, that's a really tight requirement for this density that

1071
00:51:01,000 --> 00:51:03,080
Speaker 3: we needed at the beginning of the universe. It kind

1072
00:51:03,120 --> 00:51:04,560
Speaker 3: of seems like too much of a coincidence.

1073
00:51:04,719 --> 00:51:06,680
Speaker 1: It does seem like too much of a coincidence, and

1074
00:51:06,719 --> 00:51:09,560
Speaker 1: physicists don't like coincidences because the density of stuff in

1075
00:51:09,560 --> 00:51:11,920
Speaker 1: the universe doesn't seem to be determined by anything. It

1076
00:51:11,960 --> 00:51:14,120
Speaker 1: could have been anything, So for it to be like

1077
00:51:14,320 --> 00:51:17,680
Speaker 1: exactly close to one complete pie of the critical density,

1078
00:51:17,719 --> 00:51:20,279
Speaker 1: it seems too neat. Physicists like a reason for these

1079
00:51:20,360 --> 00:51:23,279
Speaker 1: numbers to line up, and there is an explanation for it,

1080
00:51:23,640 --> 00:51:26,960
Speaker 1: and the explanation is cosmic inflation. So you know, how

1081
00:51:26,960 --> 00:51:29,879
Speaker 1: the universe is expanding now, and that expansion is accelerating.

1082
00:51:30,040 --> 00:51:33,200
Speaker 1: We also think that the universe expanded very very early

1083
00:51:33,239 --> 00:51:36,319
Speaker 1: on in its history, but like a huge factor, this

1084
00:51:36,440 --> 00:51:39,680
Speaker 1: accelerating expansion we call inflation. It's an expansion of like

1085
00:51:39,760 --> 00:51:42,400
Speaker 1: ten to the thirty in like ten to the negative

1086
00:51:42,440 --> 00:51:46,000
Speaker 1: thirty seconds. And this kind of accelerating expansion tends to

1087
00:51:46,160 --> 00:51:50,880
Speaker 1: push the universe towards flatness. It makes the universe more flat.

1088
00:51:51,080 --> 00:51:53,600
Speaker 3: But isn't it still sort of too much of a coincidence,

1089
00:51:53,640 --> 00:51:56,160
Speaker 3: Like I wonder if maybe our theories are wrong, or

1090
00:51:56,200 --> 00:51:59,560
Speaker 3: maybe there's some sort of mechanism that keeps the universe flat.

1091
00:51:59,719 --> 00:52:01,640
Speaker 1: We don't know if inflation is true, and it's just

1092
00:52:01,719 --> 00:52:03,920
Speaker 1: one of the possible scenarios, And you know, maybe it's

1093
00:52:03,960 --> 00:52:05,840
Speaker 1: just a coincidence. And we just happened to live in

1094
00:52:05,880 --> 00:52:08,040
Speaker 1: a universe that was that close to flat that we

1095
00:52:08,160 --> 00:52:10,879
Speaker 1: ended up in the universe that didn't overexpand or didn't

1096
00:52:10,920 --> 00:52:14,879
Speaker 1: collapse on itself. But inflation makes it less sensitive. Inflation says,

1097
00:52:14,920 --> 00:52:17,560
Speaker 1: you know, you could have started with lots of different densities,

1098
00:52:17,800 --> 00:52:20,719
Speaker 1: and inflation would have made your universe have the critical

1099
00:52:20,760 --> 00:52:23,319
Speaker 1: density early on, So you could have started with half

1100
00:52:23,360 --> 00:52:25,800
Speaker 1: the density or one and a half times the critical density,

1101
00:52:25,880 --> 00:52:28,879
Speaker 1: and inflation would have made your universe super duper close

1102
00:52:28,920 --> 00:52:30,440
Speaker 1: to the critical density.

1103
00:52:30,560 --> 00:52:32,759
Speaker 3: Meaning like you might have started with too much stuff

1104
00:52:32,800 --> 00:52:36,360
Speaker 3: in the universe, but then some mechanism stretched out the

1105
00:52:36,440 --> 00:52:40,040
Speaker 3: universe enough so that you had the critical density.

1106
00:52:39,880 --> 00:52:43,680
Speaker 1: Exactly the math of inflation. In fact of any accelerating

1107
00:52:43,719 --> 00:52:47,239
Speaker 1: expansion in the universe tends to push the universe back

1108
00:52:47,280 --> 00:52:49,800
Speaker 1: towards the critical density. So if you had too much,

1109
00:52:49,960 --> 00:52:53,120
Speaker 1: inflation would stretch out the universe in just the right

1110
00:52:53,160 --> 00:52:55,480
Speaker 1: way to make it have the critical density. Just like

1111
00:52:55,520 --> 00:52:57,160
Speaker 1: if you're standing on the surface of a tiny sphere

1112
00:52:57,160 --> 00:52:59,680
Speaker 1: like a beach ball, it looks really really curved, but

1113
00:52:59,719 --> 00:53:02,759
Speaker 1: then somebody expands it rapidly by a factor of ten

1114
00:53:02,800 --> 00:53:05,120
Speaker 1: to the thirty. Then now you're standing on the surface

1115
00:53:05,120 --> 00:53:07,880
Speaker 1: of a huge sphere. It looks flat, right, So a

1116
00:53:07,920 --> 00:53:10,759
Speaker 1: bigger sphere looks flatter, and then a small sphere. In

1117
00:53:10,760 --> 00:53:14,799
Speaker 1: the same way inflation pushes the universe towards less.

1118
00:53:14,560 --> 00:53:17,480
Speaker 3: Curvature, does it also work the other way, Like if

1119
00:53:17,800 --> 00:53:20,239
Speaker 3: the universe had started with too little stuff in it,

1120
00:53:20,640 --> 00:53:25,040
Speaker 3: the density was too small mood inflation have somehow adjusted

1121
00:53:25,200 --> 00:53:28,120
Speaker 3: or slowed down or compress the universe somehow. Would you

1122
00:53:28,160 --> 00:53:31,440
Speaker 3: have had deflation in order to keep the universe flat?

1123
00:53:32,200 --> 00:53:34,319
Speaker 1: Yeah, that's a great question. It does. It pushes it

1124
00:53:34,360 --> 00:53:38,120
Speaker 1: towards critical density from either direction, which is pretty cool

1125
00:53:38,440 --> 00:53:39,480
Speaker 1: how the math works out.

1126
00:53:39,719 --> 00:53:41,040
Speaker 3: So it does do deflation.

1127
00:53:41,280 --> 00:53:44,120
Speaker 1: Well, they still consider it inflation because you're still stretching

1128
00:53:44,160 --> 00:53:46,800
Speaker 1: it out. You know, imagine like a hyperbolic surface, you

1129
00:53:46,920 --> 00:53:50,880
Speaker 1: stretched it out, so the negative curvature goes towards zero curvature.

1130
00:53:51,400 --> 00:53:54,200
Speaker 1: So inflation drives you towards zero curvature from either direction.

1131
00:53:54,800 --> 00:53:58,800
Speaker 3: So it's more like stackflation or less flation.

1132
00:54:00,080 --> 00:54:02,360
Speaker 1: I don't know enough economics to know if an analogy

1133
00:54:02,400 --> 00:54:03,239
Speaker 1: is accurate or not.

1134
00:54:05,440 --> 00:54:08,000
Speaker 3: But it sounds like something they say in the news.

1135
00:54:08,080 --> 00:54:10,560
Speaker 1: And one fascinating thing about that is it means that

1136
00:54:10,680 --> 00:54:14,880
Speaker 1: our universe right now is driving back towards flatness. Like

1137
00:54:14,920 --> 00:54:17,520
Speaker 1: the brief history of the universe is you have probably inflation,

1138
00:54:17,600 --> 00:54:20,319
Speaker 1: which makes the universe mostly flat, and then you have

1139
00:54:20,360 --> 00:54:23,680
Speaker 1: a matter in a radiation dominated time when the universe

1140
00:54:23,719 --> 00:54:26,640
Speaker 1: is then driven by this critical density and it continues

1141
00:54:26,680 --> 00:54:29,360
Speaker 1: to expand that that expansion is decelerating because of the

1142
00:54:29,440 --> 00:54:31,680
Speaker 1: matter dominated nature of the universe. And then like six

1143
00:54:31,760 --> 00:54:34,200
Speaker 1: billion years ago, dark energy took over, right, because the

1144
00:54:34,239 --> 00:54:38,040
Speaker 1: expanding universe dilutes out the matter and radiation, while dark

1145
00:54:38,120 --> 00:54:40,319
Speaker 1: energy grows as a fraction. So now we have an

1146
00:54:40,360 --> 00:54:44,480
Speaker 1: accelerating expansion again, which does the same thing. Any accelerating

1147
00:54:44,480 --> 00:54:48,440
Speaker 1: expansion in the universe pushes you back towards zero curvature.

1148
00:54:48,840 --> 00:54:49,200
Speaker 4: Mmm.

1149
00:54:49,440 --> 00:54:51,520
Speaker 3: Interesting, I guess what that makes me think is that

1150
00:54:51,640 --> 00:54:55,160
Speaker 3: maybe the universe is flat. Like it's just flat. It's

1151
00:54:55,160 --> 00:54:57,719
Speaker 3: infinite and flat, and all these things we're seeing, all

1152
00:54:57,760 --> 00:55:01,600
Speaker 3: these measurements and all these theoretic concepts, they kind of

1153
00:55:01,600 --> 00:55:03,480
Speaker 3: have to work out to a flat universe, and that's

1154
00:55:03,480 --> 00:55:05,400
Speaker 3: what we're seeing. Like maybe it's not sort of like

1155
00:55:05,440 --> 00:55:08,200
Speaker 3: this mystery or this universe sitting on a nice edge.

1156
00:55:08,200 --> 00:55:10,200
Speaker 3: It's just that's just the way that the universe is.

1157
00:55:10,680 --> 00:55:13,000
Speaker 3: And to us, the math and the measurements look like

1158
00:55:13,040 --> 00:55:14,719
Speaker 3: it could have gone either way, but it could never

1159
00:55:14,760 --> 00:55:15,239
Speaker 3: had a chance.

1160
00:55:15,400 --> 00:55:18,440
Speaker 1: Yeah, it's possible. Right, in the equations of general relativity,

1161
00:55:18,560 --> 00:55:21,600
Speaker 1: this is curvature parameter. It's either plus one, zero or

1162
00:55:21,840 --> 00:55:24,399
Speaker 1: minus one and it can't change again, right, you can't

1163
00:55:24,400 --> 00:55:26,680
Speaker 1: go from a negative curvature to a positive curvature, and

1164
00:55:26,680 --> 00:55:30,000
Speaker 1: our universe is just one of those. The interesting thing, though,

1165
00:55:30,360 --> 00:55:32,760
Speaker 1: is that to have k equals zero, to have zero curvature,

1166
00:55:32,920 --> 00:55:35,879
Speaker 1: you really have to have the critical density of matter

1167
00:55:36,000 --> 00:55:38,320
Speaker 1: and energy. So it sort of depends on what question

1168
00:55:38,360 --> 00:55:40,279
Speaker 1: you ask. Like you could ask, well, which of the

1169
00:55:40,320 --> 00:55:42,440
Speaker 1: three curvatures is it? Well, maybe it's just zero, like

1170
00:55:42,480 --> 00:55:44,239
Speaker 1: you say, but if you think about it in terms

1171
00:55:44,280 --> 00:55:47,359
Speaker 1: of the continuous spectrum of matter and energy density, then

1172
00:55:47,400 --> 00:55:50,160
Speaker 1: it has to have exactly the right number, which seems

1173
00:55:50,200 --> 00:55:52,600
Speaker 1: like one option out of an infinite number instead of

1174
00:55:52,600 --> 00:55:53,680
Speaker 1: one option out of three.

1175
00:55:54,080 --> 00:55:57,640
Speaker 3: Well, unless the universe sort of like prevents the matter

1176
00:55:57,719 --> 00:56:00,439
Speaker 3: and energy to be anything else, Chase makes sense.

1177
00:56:00,480 --> 00:56:03,479
Speaker 1: Right, Yeah, it's certainly possible. And these questions are really

1178
00:56:03,520 --> 00:56:05,640
Speaker 1: basic and also simple, And in a few hundred years

1179
00:56:05,680 --> 00:56:07,120
Speaker 1: they might look back on us and be like, hah,

1180
00:56:07,640 --> 00:56:10,160
Speaker 1: how do they imagine they lived in a curved universe?

1181
00:56:10,160 --> 00:56:12,239
Speaker 3: What a bunch of idiots, What a bunch of flat

1182
00:56:12,239 --> 00:56:13,080
Speaker 3: footed idiots?

1183
00:56:13,920 --> 00:56:16,040
Speaker 1: But these are the questions we're asking, and we don't know,

1184
00:56:16,360 --> 00:56:18,640
Speaker 1: And the equations of general relatio they allow for all

1185
00:56:18,640 --> 00:56:22,640
Speaker 1: three kinds of universe. Negative curvature, flat or positive curvature.

1186
00:56:22,719 --> 00:56:24,960
Speaker 1: We just don't know which of those we live in

1187
00:56:25,000 --> 00:56:27,400
Speaker 1: and why we've measured space to be flat. And you're right,

1188
00:56:27,440 --> 00:56:30,240
Speaker 1: Either it just is flat and it started out balanced

1189
00:56:30,239 --> 00:56:32,319
Speaker 1: on that knife's edge and it will always be there,

1190
00:56:32,360 --> 00:56:35,719
Speaker 1: perfectly balanced, or it has a little bit of curvature,

1191
00:56:35,840 --> 00:56:38,320
Speaker 1: but then we don't understand why it's still so flat

1192
00:56:38,400 --> 00:56:40,640
Speaker 1: unless you do something early on, like inflation.

1193
00:56:40,880 --> 00:56:43,200
Speaker 3: Well, I think the idea is that maybe the universe

1194
00:56:43,280 --> 00:56:45,600
Speaker 3: is flat, which would mean that the pencil is not

1195
00:56:45,680 --> 00:56:48,080
Speaker 3: upside down, like maybe the pencil is hanging from the

1196
00:56:48,120 --> 00:56:51,480
Speaker 3: tam and that it can only sort of be that

1197
00:56:51,840 --> 00:56:54,920
Speaker 3: hanging down and the universe would push it down if

1198
00:56:55,000 --> 00:56:57,560
Speaker 3: you try to move the pencil. That's a possibility. Sounds

1199
00:56:57,560 --> 00:57:00,560
Speaker 3: like it's still a mystery why the universe is flat.

1200
00:57:00,600 --> 00:57:02,480
Speaker 3: We're measuring it to be flat, and it seems to

1201
00:57:02,640 --> 00:57:06,480
Speaker 3: be staying flat, which means that the universe either is

1202
00:57:06,520 --> 00:57:09,680
Speaker 3: flat or the universe is not flat but something is

1203
00:57:09,719 --> 00:57:14,080
Speaker 3: making it suspiciously flat. Those are the two options, right exactly.

1204
00:57:14,640 --> 00:57:17,520
Speaker 1: If it's not exactly flat, then something is keeping it

1205
00:57:17,720 --> 00:57:18,920
Speaker 1: very very close.

1206
00:57:18,680 --> 00:57:21,120
Speaker 3: To flat, which would be the universe, which means the

1207
00:57:21,200 --> 00:57:22,520
Speaker 3: universe is flat.

1208
00:57:23,840 --> 00:57:26,360
Speaker 1: The universe is either exactly flat or it likes to

1209
00:57:26,360 --> 00:57:27,760
Speaker 1: stay very close to flat.

1210
00:57:28,040 --> 00:57:32,040
Speaker 3: I'm just trying to propagate flat universe theories and say

1211
00:57:32,040 --> 00:57:34,040
Speaker 3: that it's all just a conspiracy by the universe.

1212
00:57:34,200 --> 00:57:35,920
Speaker 1: You're curving my brain, man, All.

1213
00:57:35,960 --> 00:57:38,120
Speaker 3: Right, Well, the next time you look at into space,

1214
00:57:38,240 --> 00:57:41,080
Speaker 3: think about what happens to those photons that you're seeing.

1215
00:57:41,320 --> 00:57:43,680
Speaker 3: Did they come straight at you or did they get

1216
00:57:43,720 --> 00:57:47,760
Speaker 3: bent by space? Are those photons curving their way through

1217
00:57:47,760 --> 00:57:52,040
Speaker 3: the universe, maybe even a close circular universe, or did

1218
00:57:52,080 --> 00:57:53,920
Speaker 3: it come straight at you from really far away.

1219
00:57:54,040 --> 00:57:57,040
Speaker 1: Either way, we're grateful that photons are arriving here on

1220
00:57:57,120 --> 00:57:59,440
Speaker 1: Earth and that we're smart enough to figure out the

1221
00:57:59,480 --> 00:58:03,240
Speaker 1: messages that they send about the nature of this incredible cosmos.

1222
00:58:03,440 --> 00:58:05,480
Speaker 3: At least we think we're smart enough. Might just be

1223
00:58:05,680 --> 00:58:07,200
Speaker 3: falling flat on our facebooks.

1224
00:58:07,400 --> 00:58:09,720
Speaker 1: We're feeling good about being smart. Whether or not we

1225
00:58:09,800 --> 00:58:10,560
Speaker 1: are all right.

1226
00:58:10,640 --> 00:58:13,720
Speaker 3: We hope you enjoyed that. Thanks for joining us, See

1227
00:58:13,720 --> 00:58:14,240
Speaker 3: you next time.

1228
00:58:22,160 --> 00:58:24,960
Speaker 1: Thanks for listening, and remember that. Daniel and Jorge Explain

1229
00:58:25,000 --> 00:58:28,960
Speaker 1: the Universe is a production of iHeartRadio. For more podcasts

1230
00:58:29,040 --> 00:58:33,680
Speaker 1: from iHeartRadio, visit the iHeartRadio app. Apple podcasts or wherever

1231
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