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Speaker 1: Or Hey, if you were designing a universe, would you

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Speaker 1: make it the shape of a snack food? M M.

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Speaker 1: It's a very specific question, Daniel. Can I make it

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Speaker 1: like a cheeto shaped or dorito shaped? Hey? If you're

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Speaker 1: making a universe, there are no rules. Oh, I can

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Speaker 1: go nuts or bananas? Hey? Can I make the universe

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Speaker 1: banana shape? How about you? I think instead of going

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Speaker 1: for fruity inspiration, I might draw my inspiration from chocolate.

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Speaker 1: What shape is chocolate? Well, you know, I like my

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Speaker 1: universe the way I like my chocolate, flat, dark, infinite.

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Speaker 1: You make it sound a little inappropriate. There isn't the

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Speaker 1: universe expanding? Also? Is that due to dark chocolate energy?

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Speaker 1: That's also the reason that I'm expanding? Are you going

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Speaker 1: to be shaped like a banana? Soon? I'm going to

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Speaker 1: be the size of the universe Eventually. We all have

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Speaker 1: a dreamy. Hi am or Hammon, cartoonists and the creator

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Speaker 1: of PhD comics. Hi, I'm Daniel. I'm a particle physicist

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Speaker 1: and a professor a UC Irvine, and I really do

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Speaker 1: feel like I have an infinite appetite for dark chocolate infinite. Wow,

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Speaker 1: that's a that's a lot. You know, if and it's

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Speaker 1: no joke. The music can eat it forever all the time. Yeah,

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Speaker 1: I feel like I've never reached the limit. You know,

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Speaker 1: somebody puts a plate of chocolate there, I just keep

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Speaker 1: snacking on it and eventually I gotta take it away.

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Speaker 1: So I've never reached the port where I'm like stop.

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Speaker 1: It sounds like you haven't tried hard enough, Daniel. I

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Speaker 1: need to do more experiments, that's what you're saying. That's right.

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Speaker 1: You need to explore the whole range of possibility, the

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Speaker 1: upper limits and the lower limits. There's got to be

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Speaker 1: a boundary, and I am devoted to finding it wherever

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Speaker 1: the cost, even if it causes your belt line to

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Speaker 1: go to be on bounded But anyways, welcome to our

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Speaker 1: podcast Daniel and Jorge Explain the Universe, a production of

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Speaker 1: I Heart Radio in which we snack our way to

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Speaker 1: an understanding of the craziest questions of the universe. We

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Speaker 1: try to take bite sized pieces out of some of

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Speaker 1: the biggest questions in the universe. How big is it,

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Speaker 1: what shape is it, where does it come from, where

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Speaker 1: is it going to end, what is it made out of?

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Speaker 1: And fundamentally, how does it all work? We talked about

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Speaker 1: all of these questions, and we try to explain all

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Speaker 1: of them to you while you sample your favorite snack food. Yes,

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Speaker 1: it is a very tasty or, as Daniel says, crazy universe,

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Speaker 1: crazy tasty universe for us to sample and enjoy and

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Speaker 1: savor because it is out there. It's very dark and

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Speaker 1: interesting and full of amazing things that we have yet

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Speaker 1: to discover. Speaking of snack foods, I know that people

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Speaker 1: like to munch on something while they watch TV. Do

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Speaker 1: you think people munch on something while they listen to podcasts? Wait?

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Speaker 1: I thought people fell asleep while listening to our podcasts.

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Speaker 1: Are they eating and sleeping at the same time? Isn't

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Speaker 1: it dangerous? I don't know. Do they fall asleep with

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Speaker 1: their hand in the Cheeto's bowl or something. I'm sure

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Speaker 1: there are people who snack while listening to us. I

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Speaker 1: mean I watched this year Is while listening to podcasts. Well,

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Speaker 1: I wondered if the crunching with interviewer they're listening. Well, anyway,

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Speaker 1: let us know if you have a favorite Daniel and

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Speaker 1: Jorhey snack food, maybe we can get them to sponsor

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Speaker 1: an episode. Yeah, it's great. I mean, you're feeding your

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Speaker 1: stomach and your mind at the same time, you're expanding

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Speaker 1: in all directions everywhere. Let's get episodes on dark energy

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Speaker 1: funded by dark chocolate makers. That's no joke, Daniel, we

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Speaker 1: could do it. Yeah, exactly happened to some of those

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Speaker 1: Swiss chocolate funds. Yeah, it happens a big chocolate moundy.

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Speaker 1: But anyways, it is a pretty interesting universe out there

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Speaker 1: that we can see from our little perch out here

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Speaker 1: and then sitting on top of a round rock in

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Speaker 1: the corner of the Milk Way gaxy in a small

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Speaker 1: corner of the gigantic universe that we are surrounded by.

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Speaker 1: And even though we are stuck on this rock so far,

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Speaker 1: we can still ask some of the biggest, craziest questions

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Speaker 1: about the whole universe, about what's going on super duper

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Speaker 1: far away, because of course, we could look out into

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Speaker 1: the universe sort of like we're trapped in a tiny

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Speaker 1: lighthouse and we're looking out at the horizon and wondering

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Speaker 1: what's going on over there. We can't go visit it,

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Speaker 1: but it's sending us messages that let us find answers

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Speaker 1: to some of our biggest questions. Yeah, it to be

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Speaker 1: amazing that from our little point of view here in

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Speaker 1: the little rock floating out in space, we've managed to

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Speaker 1: know so much about the universe and what's out there,

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Speaker 1: But you've got to kind of wonder what else is

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Speaker 1: out there or what happens if you keep going out

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Speaker 1: there in space, what are you going to encounter? And

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Speaker 1: what is the overall shape of the universe. I think

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Speaker 1: it's a great metaphor for our curiosity. You know, we

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Speaker 1: think about what's going on on our planet, what's going

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Speaker 1: on in our solar system, what's going on in the galaxy.

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Speaker 1: No matter how far you explain, people will always wonder

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Speaker 1: what's going on further than that. Right, there's a no

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Speaker 1: limit to our curiosity, just like there's no limit to

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Speaker 1: my capacity to eat dark chocolate. No matter how far

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Speaker 1: you explained, people want to know what's past the edge

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Speaker 1: of the universe. One of those habits seems healthier than

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Speaker 1: the other, then I think they're tied together. I think

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Speaker 1: dark chocolate fuels my curiosity. What did your doctor say

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Speaker 1: about this type of curiosity? This is why I stop

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Speaker 1: going to doctors. Really, sorry, you are a doctor, so

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Speaker 1: really you don't need another doctor. That's right, I tell

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Speaker 1: myself to take off my pants because I no longer

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Speaker 1: fit into them. But I think the two questions are connected.

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Speaker 1: You know, could there be an infinite amount of dark

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Speaker 1: chocolate in the universe for me to eat? Only if

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Speaker 1: the universe is literally infinite? I see you're saying we're

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Speaker 1: sort of like humans are kind of like the eternal

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Speaker 1: busy buddies. You know, we're always wondering what's going on

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Speaker 1: out there beyond the horizon. Yeah, exactly. We want to

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Speaker 1: know what's just beyond our ability to understand. Will never

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Speaker 1: be satisfiment go you know what, a hundred billion light

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Speaker 1: years that's enough for me. There's always going to be

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Speaker 1: somebody who wonders. But what's past that? What if you

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Speaker 1: kept going? And I think the reason for that is

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Speaker 1: that the universe and history of science is filled with

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Speaker 1: crazy surprises. Every time we've looked further than we imagined,

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Speaker 1: we found crazy stuff. Think all the way back to

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Speaker 1: Edwin Hubble discovering that there are other galaxies out there.

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Speaker 1: What a mind blowing realization to think it's not just

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Speaker 1: our galaxy sitting in space, but that there are hundreds, thousands,

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Speaker 1: trillions of other galaxies. That's the kind of realization we're

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Speaker 1: going for. Yeah, it's pretty mind blowing. And so far

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Speaker 1: we can see pretty far out there into the universe.

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Speaker 1: We can see up to about forty five forty six

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Speaker 1: billion light years. That's as far as we can see, right,

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Speaker 1: that's as far as humans are able and can see, right,

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Speaker 1: because of the limitations of the speed of light. Yeah,

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Speaker 1: it's a bit of a subtle question how far we

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Speaker 1: can see in the universe. You might imagine it would

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Speaker 1: be the age of the universe times the speed of

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Speaker 1: light that photons would be racing through space to us,

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Speaker 1: and then we couldn't see anything past thirteen or fourteen

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Speaker 1: billion light years away. But because the universe is expanding,

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Speaker 1: some of the stuff that sent us photons a long

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Speaker 1: time ago is now much much further away, and so

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Speaker 1: we can see light from things that are now very

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Speaker 1: very far away, out to about forty five billion light years,

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Speaker 1: and it actually we'll even see after about sixty two

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Speaker 1: billion light years. Yeah, so that's kind of as far

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Speaker 1: as we can see, Like, that's the range of our

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Speaker 1: vision as human beings in this universe. But I guess,

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Speaker 1: like you said, there are people who wonder what's beyond that.

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Speaker 1: You know, if I keep going past sixty five billion

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Speaker 1: light years, what am I going to find a Am

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Speaker 1: I gonna hit a wall? Is this the universe gonna

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Speaker 1: go on forever? Or is it going to do something

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Speaker 1: even crazier? Yeah, we'll put me in that category. I'm

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Speaker 1: not satisfied to only see sixty two billion light years away.

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Speaker 1: I want to know all of it. I want to

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Speaker 1: know what's beyond that. I want to know if it

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Speaker 1: goes on forever, if it curves on back on itself,

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Speaker 1: if there's some huge cosmic store of dark chocolate just

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Speaker 1: past the edge of our vision. That's your carrot, Daniel, like,

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Speaker 1: you know, the the character that's driving you to do science.

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Speaker 1: You just want to discover dark chocolate everywhere, even among

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Speaker 1: the fundamental particles. When I know there's a dark chocko Latino, Yeah,

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Speaker 1: there could be a secret dark chocolate reservoir past the

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Speaker 1: edge of the observable universe. You know what in my

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Speaker 1: next grant, I'm gonna put funds for dark chocolate, and

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Speaker 1: I'm gonna argue that it's essential for doing science, at

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Speaker 1: least for Daniel. For Daniel to do science, you need

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Speaker 1: a little motivation in the morning. Well, you know, there

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Speaker 1: is a clear correlation between chocolate consumption and Nobel Prize winning.

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Speaker 1: I'm not saying it's causal, but there's a correlation. So

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Speaker 1: you know, when I do apply to the Nestly Foundation

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Speaker 1: for Chocolate Research, then I think I'm gonna put that in.

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Speaker 1: There is a causation, I think, you know, I think

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Speaker 1: winning Nobel Prices makes you hungrier for chocolate, right, there's

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Speaker 1: something about that, you know, Northern European, you know flair

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Speaker 1: that makes you create the chocolate. I don't know. I

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Speaker 1: think it works either way. If you win the Nobel Prize,

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Speaker 1: you celebrate byating chocolate. If you don't win the Nobel Prize,

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Speaker 1: you console yourself by eating chocolate. I see. So the

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Speaker 1: correlation doesn't make sense to your physics, at least the

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Speaker 1: way you do it, not the way that I eat chocolate.

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Speaker 1: But it is an interesting question. What's out there beyond

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Speaker 1: the universe, beyond the sixty five billion light years that

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Speaker 1: we might be able to see some day or you're

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Speaker 1: gonna hit a wall, is it going to come around?

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Speaker 1: What is the size and shape of the universe? And

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Speaker 1: I love thinking about this question, the shape of the universe,

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Speaker 1: because it feels like something really deep and fundamental. It's

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Speaker 1: something that must be like written into the real source

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Speaker 1: code of the universe. It's not just like, oh, where

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Speaker 1: is the planet or where are there aliens? Things that

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Speaker 1: are affected by randomness. Is something which is a deep

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Speaker 1: truth about the universe. It's something which reveals its nature. Yeah,

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Speaker 1: you're basically asking the biggest question you can ask, right,

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Speaker 1: Like when you're asking about the size and shape of

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Speaker 1: the universe, you're asking what is the cion shape of

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Speaker 1: the entire universe? Like it has to encompass all of it,

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Speaker 1: not just like a part of it, all of it. Yeah,

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Speaker 1: I guess you could ask what is the shape of

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Speaker 1: the multiverse? That might be a bigger question. Oh what,

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Speaker 1: you just blew my mind? What is the shape of

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Speaker 1: the multiverse? Shape like a Marble movie? It's shaped like

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Speaker 1: a dollar bill, I'm pretty sure, shaped like the money

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Speaker 1: they're they're breaking in. I hope they're spending some of

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Speaker 1: that money on chocolate to celebrate. But it is the

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Speaker 1: biggest question we can ask, and it's a question we

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Speaker 1: don't know the answer to, right. I mean, first of all,

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Speaker 1: we can't see out to the edge of the universe, right,

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Speaker 1: at least we haven't seen an edge to it, and

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Speaker 1: so it's kind of a weird question to ask what

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Speaker 1: is the size and shape of the universe if we

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Speaker 1: can't see all of it. It's like sitting in the

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Speaker 1: middle of the United States and asking what is the

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Speaker 1: shape of the United States if you've never been to

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Speaker 1: or can ever get to the coast? That's right. But

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Speaker 1: although it seems impossible, science always finds a way to

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Speaker 1: like take the first nibble off of the question, to think, well, well,

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Speaker 1: what can we do if we can't answer the entire

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Speaker 1: question directly? Then? You know, can we find some way

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Speaker 1: to limit the possible answers? What can we do with

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Speaker 1: our limited data and our limited view of the universe?

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Speaker 1: And to me, it's incredible what we have learned where

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Speaker 1: we have been able to rule out about the universe

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Speaker 1: just from looking around. Wait, are you saying we can

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Speaker 1: just ask the universe what its size and shape is?

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Speaker 1: You know, I emailed the universe and invited to be

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Speaker 1: on the podcast, but it hasn't answered yet, and so

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Speaker 1: I'm gonna have to resort to the classic way, which

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Speaker 1: is doing physics experiment, which is basically asking the universe

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Speaker 1: question interesting. Yeah. I guess if you ask anyone by

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Speaker 1: email what their size and shape is that you probably

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Speaker 1: won't get an answer. I got a cease and desist

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Speaker 1: from the universe legal department. Yeah, stay away from me,

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Speaker 1: blocked blocked by the universe. Wow, that's harsh. But it

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Speaker 1: is an interesting question. And so today on the podcast

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Speaker 1: we'll be asking is the universe shaped like a doughnut?

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Speaker 1: And does it taste like a donut? To Daniel, this

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Speaker 1: this seems like a very specific question. It's a specific question,

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Speaker 1: an idea motivated by some hints we've seen in some

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Speaker 1: recent studies that suggested that maybe the universe is chocolate

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Speaker 1: filled after all, chocolate filled or shaped like a donut

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Speaker 1: or like a donut wood chocolate in it exactly, the

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Speaker 1: universe might be a chocolate field donut in the end.

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Speaker 1: I don't think I've ever heard of a chocolate field donut.

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Speaker 1: Usually chocolate is on top. You've never heard of a

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Speaker 1: chocolate filled donut? Are you serious? Well, if it has

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Speaker 1: something in the inside, then it's not a donut, is it. Man?

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Speaker 1: What's a jelly filled donut? Then? Is it a jelly

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Speaker 1: filled not donut? It's a jelly filled cake and p

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Speaker 1: have a hole in the middle. Right to be a donut,

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Speaker 1: doesn't it? Oh? Man, this is turned into a food

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Speaker 1: argument podcast. I hear those are more popular than the

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Speaker 1: science podcast. Let's roll with it. We've done the murder

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Speaker 1: mystery podcast recently and now we're doing the food argument podcast. Absolutely.

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Speaker 1: I think there's lots of different shapes donuts can be.

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Speaker 1: I think the classic shape, you know, it was basically

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Speaker 1: a tourist with a hole in the middle. But you

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Speaker 1: could still put chocolate inside that taurus right, Oh, you

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Speaker 1: mean along like the ring of it you can stuff

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Speaker 1: with with chocolate. Ring of chocolate? Why not? Sounds delicious

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Speaker 1: to me? It sounds like a heart attack. Well, we'll

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Speaker 1: see if the universe agrees with me or with you

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Speaker 1: by the end of the episode. But anyways, apparently it's

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Speaker 1: a possibility that the universe could be shaped like a doughnut,

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Speaker 1: which sounds both bulgeous and filling. And so that's the

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Speaker 1: question we'll be trying to answer today. And so, as usual,

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Speaker 1: we were wondering how many people out there had thought

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Speaker 1: about equating the universe with a treat like a donut. So,

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Speaker 1: thanks to our ever rotating group of volunteers who answer

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Speaker 1: the questions for us on the podcast. It's always fun

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Speaker 1: to hear your answers, and it gives us a sense

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Speaker 1: for what people are thinking. If you'd like to participate

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Speaker 1: for a future episode, please don't be shy. I know

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Speaker 1: you're out there waiting for an invitation. There's right to

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Speaker 1: me two questions at Daniel and Jorge dot com and

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Speaker 1: Dennie will send your donut if you answer the question right.

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Speaker 1: You're a digital donut, a little emoji donut. Well, think

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Speaker 1: about it for a second. Do you think the universe

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Speaker 1: is shaped like a donut? Here's what people have to say.

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Speaker 1: I think the universe could be shaped like a donut,

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Speaker 1: and it could be that we just don't see all

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Speaker 1: of the universe from our advantage point. But I doubt

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Speaker 1: that it is because I would think we would see

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Speaker 1: some kind of evidence of it in the microwave background.

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Speaker 1: So from that, it really appears that the universe, uh

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Speaker 1: does not have curvature to it. I don't think the

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Speaker 1: universe has shaped like a donut unless initial expansion was

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Speaker 1: not uniform in every direction. I would guess it's more

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Speaker 1: likely to be a hollow sphere. Yeah, I mean could

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Speaker 1: it be as an interesting question? I uh, yeah, I

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Speaker 1: mean I imagine it could be. I think I've heard

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Speaker 1: about this before. I remember at some point somebody, maybe

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Speaker 1: in a documentary or something, saying that if you look straightforward,

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Speaker 1: if you were able to like see into infinity, you

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Speaker 1: would look at the back of your head, which I

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Speaker 1: guess if you were on a donut you could probably

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Speaker 1: do that if space was like sort of bat like that.

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Speaker 1: I don't think the universe has shaped like a donut.

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Speaker 1: I think if it was, we would have noticed by now,

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Speaker 1: because there'll be a lot less potions and activity coming

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Speaker 1: from the center of the donut. I think so long

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Speaker 1: as information is consistently available across the entire universe, it

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Speaker 1: really doesn't matter what the shape is. And as long

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Speaker 1: as time and space are concentric, I think the universe

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Speaker 1: can be any shape, and there are probably universes of

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Speaker 1: all ships and sizes out there. Frankly, I think that

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Speaker 1: the universe could be shaped like anything, and it wouldn't

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Speaker 1: surprise me. There's this idea that you know, you start

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Speaker 1: in one place, and you go in one direction, and

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Speaker 1: then eventually you're just back at that place, and yeah,

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Speaker 1: that fits. Donut shaped to me. It's me, all right,

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Speaker 1: a pretty wide range of answers. Some people seem skeptical,

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Speaker 1: some people were like, sure, why not? The universe is

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Speaker 1: is weird and surprising. It could be shaped like anything exactly,

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Speaker 1: and some people even commenting that donuts have jam inside

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Speaker 1: of them, and so they're arguing, I think they agree

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Speaker 1: with you. You know that the shape we're talking about,

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Speaker 1: it's more like a bagel than a donut. Interesting, whoa

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Speaker 1: should we rename the episode? Then? Could the universe be

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Speaker 1: shaped like a bagel? Well, the question then is can

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Speaker 1: you put chocolate inside of a bagel? Obviously, yes, Daniel,

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Speaker 1: you can put chocolate inside of anything, all right, then

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Speaker 1: I'm fine with it, what I call it whatever, as

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Speaker 1: long as you with chocolate inside of it. Man, you

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Speaker 1: really hungry here to day, Daniel? Have you had your

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Speaker 1: daily dose of chocolate yet? I'll reward myself after the podcast.

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Speaker 1: I mean, this podcast is not infinite, I guess. So. Yeah,

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Speaker 1: So let's get into this idea of the shape of

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Speaker 1: the universe, because it's kind of weird to think about

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Speaker 1: the universe having a shape, right, because it could the

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Speaker 1: universe could be infinite, and even if it's not infinite.

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Speaker 1: Are you saying, like the walls of the universe are

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Speaker 1: shaped like a donut? What exactly do you mean by

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Speaker 1: the shape of space? So the shape of space refers

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Speaker 1: to basically how the universe is connected on a really

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Speaker 1: really big scale. You know, we are used to thinking

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Speaker 1: about space is like something we are floating in, and

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Speaker 1: we're also used to thinking about space is like maybe

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Speaker 1: being curved. General relativity tells us that mass and energy

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Speaker 1: and all this kind of stuff can curve space. That's

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Speaker 1: sort of a local curvature. But you know, if you

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Speaker 1: have curvature in space, if space bends in some way,

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Speaker 1: and you can imagine putting it together into some big shape.

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Speaker 1: Like if space doesn't curve, if it's flat, you can

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Speaker 1: make an infinite sheet. That would be the shape of space.

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Speaker 1: Where space does curve, you can imagine it being like

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Speaker 1: a sphere or a donut or some other weird shape.

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Speaker 1: So the curvature of space is connected to this other

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Speaker 1: question of the shape of space. Curvature sort of local,

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Speaker 1: the shape of space is sort of global. It's asking like,

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Speaker 1: how is all of space put together? Think in two

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Speaker 1: dimensions for a moment, because it's easier imagine you have

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Speaker 1: a bunch of rings and you have to connect them

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Speaker 1: together into a two D surface. You could loop them

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Speaker 1: together into a flat sheet, or you could make it

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Speaker 1: into a sphere or something else. These are different shapes

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Speaker 1: because they have fundamentally different properties, And mathematically speaking, two

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Speaker 1: shapes are fundamentally the same if you can smoothly morph

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Speaker 1: one into another. So two different shaped spheres, or even

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Speaker 1: a sphere and ellipsoid are basically the same shape. But

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Speaker 1: a sphere and an infinite flat sheet are not the same.

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Speaker 1: One is infinite, the other is finite. There are other shapes,

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Speaker 1: like ones with a hole in it, like a donut,

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Speaker 1: that are not the same as a sphere or a

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Speaker 1: flat sheet. That's the meaning of shape in a global sense,

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Speaker 1: which is related to, but different from curvature in a

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Speaker 1: local sense. Mm hmm, I see, And I guess just

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Speaker 1: to be clear, you actually mean space time, right, because

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Speaker 1: when you're talking about gravity kind of bending or giving

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Speaker 1: space curvature, you're actually talking about the curvature of space time. Right.

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Speaker 1: You kind of have to take time into consideration as well. Well.

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Speaker 1: We do think about how the shape of space evolves

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Speaker 1: with time, and the shape also contributes to how the

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Speaker 1: universe expands or contracts or doesn't. So, yes, this is

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Speaker 1: a dynamical thing. The shape of the universe, the curvature

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Speaker 1: of the universe can change, although it's fundamental shape cannot. Yes,

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Speaker 1: it is interesting to think about it as a function

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Speaker 1: of time, right, And it's kind of interesting that you

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Speaker 1: related to this idea because I know we've talked a

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Speaker 1: lot in this podcast about how gravity and energy kind

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Speaker 1: of bends space time in the sense that you know,

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Speaker 1: we're not going around the Sun because it's pulling on us.

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Speaker 1: We're going around the Sun because the space time around

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Speaker 1: it is sort of shaped like a bowl on so

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Speaker 1: we're kind of stuck in this loop around it. Is

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Speaker 1: that sort of what you're saying, Like, on a global

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Speaker 1: or universal scale, does the universe have some sort of

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Speaker 1: like curvature to it. It's a really fascinating idea that

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Speaker 1: you know, space is curved, that gravity is not like

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Speaker 1: a force the way we think about other forces, but

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Speaker 1: instead it's a fictitious force, the force that appears to

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Speaker 1: act because we can't see that space is curved. Like

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Speaker 1: if I look at a piece of space, I can't

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Speaker 1: tell you is it curved? But I could shine a

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Speaker 1: light through it, and if I see where that light goes,

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Speaker 1: then I can tell you whether space is curved. So

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Speaker 1: we can see the effect of curved space even though

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Speaker 1: we can't see the curvature directly. So now imagine you're

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Speaker 1: building a universe and I'm giving you pieces of it,

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Speaker 1: and each piece has curvature. So if I only give

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Speaker 1: you curved pieces, what kind of big universe shape can

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Speaker 1: you build? But you can't build like an infinitely flat space,

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Speaker 1: like a huge sheet, But you can build like a

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Speaker 1: sphere or a circle, or a donut or something else

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Speaker 1: that has a curved surface. So the building blocks of

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Speaker 1: the local curvature I'm giving you do constrain the kind

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Speaker 1: of overall shape that you can build for the universe.

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Speaker 1: M I think what you're saying is it's kind of like,

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Speaker 1: you know, if I measure the land around me, and

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Speaker 1: I see that the land occurs around me downwards or

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Speaker 1: towards the end of the Earth, then it kind of

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Speaker 1: tells you that me the whole Earth is round exactly.

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Speaker 1: If you can measure the curvature on the surface of

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Speaker 1: the Earth, then you know that the Earth can't go

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Speaker 1: on forever or can't be flat because you see that

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Speaker 1: it's curved. Right. If you imagine that the rest of

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Speaker 1: the Earth is curved the way the piece you're standing

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Speaker 1: on its curved, then that suggests that probably it's a

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Speaker 1: big sphere, although you know, it could also be a donut,

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Speaker 1: or I guess it could also be kind of like

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Speaker 1: a dome, right, a dome goes on forever, Like if

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Speaker 1: you're standing on a parable at the bottom of parable,

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Speaker 1: you think it's it's curved, but it could keep going forever. Right. Mathematically,

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Speaker 1: a problem has the opposite curvature of a sphere. But yeah,

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Speaker 1: parabola is an open construction, so you can have curvature

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Speaker 1: and still have an infinite shape, so that curvature is

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Speaker 1: negative instead of positive. But that's a detail, right. So

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Speaker 1: you're saying that, you know, somehow we can't see the

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Speaker 1: entire universe, but maybe by measuring the curvature around us,

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Speaker 1: we could maybe you know, get a sense or an

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Speaker 1: idea of what the overall shape to the universe is exactly.

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Speaker 1: And what we want is the curvature on the biggest scale.

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Speaker 1: We don't really care about how much the Sun is

426
00:21:16,160 --> 00:21:19,240
Speaker 1: bending the shape of space in our neighborhood that doesn't

427
00:21:19,280 --> 00:21:22,080
Speaker 1: affect the overall shape of the universe. We want to know,

428
00:21:22,160 --> 00:21:24,640
Speaker 1: like how much is all the stuff in the universe

429
00:21:24,880 --> 00:21:27,760
Speaker 1: bending the shape of space? What shape of spaces that

430
00:21:27,800 --> 00:21:30,159
Speaker 1: consistent with just in the same way, like if you

431
00:21:30,200 --> 00:21:32,240
Speaker 1: want to measure the surface of the Earth, you could

432
00:21:32,280 --> 00:21:35,240
Speaker 1: be standing locally on something flat or something point de

433
00:21:35,480 --> 00:21:37,840
Speaker 1: or you know, in a bowl or something, doesn't change

434
00:21:37,880 --> 00:21:41,119
Speaker 1: the overall structure. So when we measure the curvature universe,

435
00:21:41,160 --> 00:21:43,679
Speaker 1: we want to make measurements on as big a scale

436
00:21:43,720 --> 00:21:47,320
Speaker 1: as possible to avoid like the local fluctuations and deviations.

437
00:21:47,520 --> 00:21:50,000
Speaker 1: Are you saying that the universe might have a curvature

438
00:21:50,400 --> 00:21:52,960
Speaker 1: to it, or that space might have a curvature to

439
00:21:53,080 --> 00:21:56,800
Speaker 1: it without stuff in it, you know, like um or

440
00:21:57,160 --> 00:21:59,440
Speaker 1: are you saying space as a curvature to it because

441
00:21:59,440 --> 00:22:01,680
Speaker 1: there's stuff in it? This is a really important point

442
00:22:01,720 --> 00:22:06,320
Speaker 1: and a subtle one. Universe has some curvature and some shape, right,

443
00:22:06,680 --> 00:22:09,320
Speaker 1: Either the curvature is positive like a sphere, or it's

444
00:22:09,359 --> 00:22:12,439
Speaker 1: flat like an infinite surface, or it's negative like a

445
00:22:12,440 --> 00:22:15,439
Speaker 1: parabola as you described, And that just is part of

446
00:22:15,440 --> 00:22:18,160
Speaker 1: the nature of the universe. And you can put stuff

447
00:22:18,160 --> 00:22:21,480
Speaker 1: in the universe, and that can change the amount of curvature.

448
00:22:21,720 --> 00:22:24,000
Speaker 1: You can make the universe more or less curved by

449
00:22:24,080 --> 00:22:27,120
Speaker 1: putting stuff into it, but you can't change the fundamental

450
00:22:27,280 --> 00:22:30,359
Speaker 1: nature of the curvature or topology of the universe. You

451
00:22:30,400 --> 00:22:33,920
Speaker 1: can't like make a sphere universe into a flat universe

452
00:22:33,960 --> 00:22:36,399
Speaker 1: by putting stuff into it or the other way around.

453
00:22:36,560 --> 00:22:39,080
Speaker 1: M I see, because I think you know, there's sort

454
00:22:39,080 --> 00:22:41,920
Speaker 1: of two things, right, there's stuff and energy and then

455
00:22:41,960 --> 00:22:44,119
Speaker 1: there's space. Those are two kind of separate things, and

456
00:22:44,240 --> 00:22:46,800
Speaker 1: so you can imagine that an empty universe where it's

457
00:22:46,840 --> 00:22:49,240
Speaker 1: just space, or like if you took out all the

458
00:22:49,280 --> 00:22:51,520
Speaker 1: stuff and energy in our universe, we would just be

459
00:22:51,640 --> 00:22:54,159
Speaker 1: left with the space we have. And so you're saying, like,

460
00:22:54,200 --> 00:22:56,520
Speaker 1: without any stuff in it, what is the shape of

461
00:22:56,560 --> 00:22:58,919
Speaker 1: that space? Does that space have curvature or is it

462
00:22:59,000 --> 00:23:02,159
Speaker 1: totally like flat? Then even yeah, although we're interested in

463
00:23:02,160 --> 00:23:04,480
Speaker 1: our universe, which does have stuff in it, and the

464
00:23:04,560 --> 00:23:07,720
Speaker 1: stuff affects the amount of curvature. You know, for example,

465
00:23:07,720 --> 00:23:10,399
Speaker 1: one of the things in our universe is dark energy,

466
00:23:10,400 --> 00:23:12,919
Speaker 1: which we don't understand at all, but it's expanding the

467
00:23:13,000 --> 00:23:15,720
Speaker 1: universe that tends to decrease the curvature of the universe

468
00:23:15,920 --> 00:23:18,680
Speaker 1: like stretches everything out. Imagine you're like the little prints.

469
00:23:18,720 --> 00:23:20,679
Speaker 1: You're standing on a tiny little planet, and then that

470
00:23:20,720 --> 00:23:24,040
Speaker 1: planet expands to be huge. The curvature you experience decreases,

471
00:23:24,080 --> 00:23:27,080
Speaker 1: the amount that planet curves away under you decreases. So

472
00:23:27,160 --> 00:23:30,240
Speaker 1: the stuff that's in the universe can affect the amount

473
00:23:30,280 --> 00:23:32,679
Speaker 1: of curvature, but it can't affect the shape, right, Like

474
00:23:32,760 --> 00:23:34,920
Speaker 1: you can't take a curved universe and put stuff into

475
00:23:34,960 --> 00:23:37,159
Speaker 1: it and make it flat. You can contract it. Like

476
00:23:37,200 --> 00:23:39,560
Speaker 1: you put a bunch of mass into a universe that's

477
00:23:39,560 --> 00:23:42,880
Speaker 1: a sphere, it's going to make that collapse into a point. Interesting,

478
00:23:42,920 --> 00:23:44,360
Speaker 1: So you're saying that if I take out of all

479
00:23:44,400 --> 00:23:46,560
Speaker 1: the stuff and energy in the universe, I would be

480
00:23:46,640 --> 00:23:48,800
Speaker 1: left foot space and that space could be in the

481
00:23:48,800 --> 00:23:51,159
Speaker 1: shape of a sphere or a donut or something and

482
00:23:51,280 --> 00:23:52,960
Speaker 1: the stuff and it wouldn't be able to change that

483
00:23:53,040 --> 00:23:55,199
Speaker 1: wouldn't be able to change that. And it's connected to

484
00:23:55,200 --> 00:23:57,760
Speaker 1: this other idea that you know the shape of space.

485
00:23:57,800 --> 00:24:01,159
Speaker 1: It's apology. It's global curvature plus the amount of stuff,

486
00:24:01,240 --> 00:24:03,400
Speaker 1: the mount of the density, and the dark energy all

487
00:24:03,440 --> 00:24:08,000
Speaker 1: those together determine like whether the universe is expanding or contracting.

488
00:24:08,080 --> 00:24:10,080
Speaker 1: This is one element of that. We're talking about the

489
00:24:10,119 --> 00:24:12,320
Speaker 1: shape of space, which is not something that can be

490
00:24:12,440 --> 00:24:16,160
Speaker 1: changed by dark energy or dark matter or the arrangement

491
00:24:16,160 --> 00:24:18,480
Speaker 1: of stuff. It's just like it's something that's deep and

492
00:24:18,520 --> 00:24:21,920
Speaker 1: true about the universe itself. It's just baked in. I mean,

493
00:24:21,920 --> 00:24:25,160
Speaker 1: it's it's it's it's sape right, like you know nothing,

494
00:24:25,160 --> 00:24:27,240
Speaker 1: but the universe can change its safe yeah, and shape

495
00:24:27,280 --> 00:24:29,040
Speaker 1: in a very specific way, right. You know, we're not

496
00:24:29,080 --> 00:24:31,240
Speaker 1: talking about size. You can have a universe that's a

497
00:24:31,280 --> 00:24:33,439
Speaker 1: sphere and it can grow or it can collapse. In

498
00:24:33,480 --> 00:24:36,359
Speaker 1: that sense, the universe can change, but it can't change

499
00:24:36,359 --> 00:24:39,399
Speaker 1: from like a sphere to an infinitely flat universe or

500
00:24:39,440 --> 00:24:43,000
Speaker 1: to a parabolic universe. That kind of thing can't change, right,

501
00:24:43,040 --> 00:24:45,800
Speaker 1: And you know that sort of mathematically or how do

502
00:24:45,840 --> 00:24:47,600
Speaker 1: you know that it can change? Well, I guess we

503
00:24:47,640 --> 00:24:49,760
Speaker 1: know that mathematically, but you can also just think about

504
00:24:49,800 --> 00:24:53,680
Speaker 1: it intuitively, like how could you take a finite universe

505
00:24:53,680 --> 00:24:56,920
Speaker 1: which is a sphere and suddenly transform it into an

506
00:24:56,960 --> 00:24:59,720
Speaker 1: infinite flat plane. And you can imagine a sphere even

507
00:24:59,760 --> 00:25:02,240
Speaker 1: grow going you know, arbitrarily large, But then how do

508
00:25:02,280 --> 00:25:07,320
Speaker 1: you suddenly transform that smoothly into a flat universe. You know,

509
00:25:07,359 --> 00:25:09,920
Speaker 1: the universe can change, it can't evolve, but it has

510
00:25:09,960 --> 00:25:12,359
Speaker 1: to happen in a smooth way. You can't have like

511
00:25:12,400 --> 00:25:14,760
Speaker 1: a sudden jump where the universe is all of a

512
00:25:14,800 --> 00:25:17,520
Speaker 1: sudden completely different. This is like a basic element of

513
00:25:17,560 --> 00:25:19,439
Speaker 1: the nature of the universe. It doesn't seem like you

514
00:25:19,440 --> 00:25:21,840
Speaker 1: could change it from one moment to the next. All right, well,

515
00:25:21,880 --> 00:25:25,480
Speaker 1: let's get into what are the possible shapes and curvatures

516
00:25:25,480 --> 00:25:28,320
Speaker 1: of the universe and what it all means. But first

517
00:25:28,359 --> 00:25:42,920
Speaker 1: let's take a quick break. Right then, we're talking about

518
00:25:42,920 --> 00:25:45,399
Speaker 1: the size and shape of the universe, which seems a

519
00:25:45,440 --> 00:25:47,680
Speaker 1: little rude to be asking these questions about the universe.

520
00:25:47,920 --> 00:25:50,960
Speaker 1: Maybe the universe is very bashful about these things. Physics

521
00:25:51,000 --> 00:25:56,880
Speaker 1: asking rude questions since fifteen four, being nosy about people's

522
00:25:56,880 --> 00:26:00,200
Speaker 1: size and shape exactly upsetting the apple carts. Since for ever,

523
00:26:00,520 --> 00:26:02,320
Speaker 1: that's our goal. You know, we don't care if the

524
00:26:02,359 --> 00:26:07,800
Speaker 1: truth is offensive. We just want to know. Discarding with

525
00:26:07,840 --> 00:26:10,920
Speaker 1: social conventions since the beginning of the ton of time,

526
00:26:11,119 --> 00:26:13,920
Speaker 1: as if we understood social conventions, right, that's the reason

527
00:26:13,960 --> 00:26:16,240
Speaker 1: we went into physics, because we just don't know how

528
00:26:16,280 --> 00:26:19,400
Speaker 1: to do the other stuff. Oh man, your meetings would

529
00:26:19,560 --> 00:26:23,680
Speaker 1: must be pretty interesting or not or not. You know,

530
00:26:23,680 --> 00:26:26,080
Speaker 1: a world without subtlety might be a little boring. You know,

531
00:26:26,200 --> 00:26:29,439
Speaker 1: that's a fun stereotype. But you know, physicists are social creatures.

532
00:26:29,480 --> 00:26:31,720
Speaker 1: I work in a collaboration of thousands of people, and

533
00:26:31,720 --> 00:26:33,879
Speaker 1: we have lots of meetings and politics and have to

534
00:26:33,920 --> 00:26:36,720
Speaker 1: deal with each other. And you know, people work together

535
00:26:36,920 --> 00:26:39,399
Speaker 1: and don't work together, and it's all sorts of stuff

536
00:26:39,640 --> 00:26:42,280
Speaker 1: exactly the same way you find in every other field

537
00:26:42,359 --> 00:26:45,119
Speaker 1: of human endeavors. Right right, it is a human endeavor.

538
00:26:45,200 --> 00:26:47,080
Speaker 1: And we were talking about the size and shape to

539
00:26:47,119 --> 00:26:49,159
Speaker 1: the universe, and you were telling me that, you know,

540
00:26:49,200 --> 00:26:51,320
Speaker 1: the the universe can have a shape even if I

541
00:26:51,359 --> 00:26:52,800
Speaker 1: take like if I take out all this stuff and

542
00:26:52,920 --> 00:26:55,240
Speaker 1: energy in it, put it somewhere out of nowhere, But

543
00:26:55,280 --> 00:26:57,879
Speaker 1: you put it somewhere, the universe that's left over would

544
00:26:57,880 --> 00:27:01,040
Speaker 1: have a shape to it. What exactly does mean a shape?

545
00:27:01,520 --> 00:27:04,199
Speaker 1: Does it mean it has walls and a boundary like

546
00:27:04,440 --> 00:27:06,840
Speaker 1: edges to it? It tells you how space is connected.

547
00:27:06,880 --> 00:27:10,840
Speaker 1: I think about space not it's just like where stuff happens.

548
00:27:11,040 --> 00:27:12,960
Speaker 1: But I think if it's sort of like a fabric

549
00:27:13,160 --> 00:27:16,560
Speaker 1: and it's woven together, and if I move to the left,

550
00:27:16,720 --> 00:27:19,160
Speaker 1: then I'm moving into a new bit of space. And

551
00:27:19,200 --> 00:27:21,000
Speaker 1: then you can ask, like, well, what happens if you

552
00:27:21,080 --> 00:27:25,680
Speaker 1: keep going you just encounter a new space or potentially

553
00:27:25,760 --> 00:27:28,399
Speaker 1: space could be connected in such a way that if

554
00:27:28,400 --> 00:27:31,200
Speaker 1: you keep going, you come back to where you started right,

555
00:27:31,200 --> 00:27:34,880
Speaker 1: sort of like a Packman universe. And so that's entirely possible,

556
00:27:34,920 --> 00:27:37,280
Speaker 1: and that tells you something about the shape of space.

557
00:27:37,960 --> 00:27:40,199
Speaker 1: So when we say, like, what if space was a sphere,

558
00:27:40,400 --> 00:27:42,560
Speaker 1: what do we mean by that? We don't mean that

559
00:27:42,680 --> 00:27:45,960
Speaker 1: space is literally a three D sphere. We're talking about

560
00:27:45,960 --> 00:27:48,520
Speaker 1: the surface of the sphere, the two D surface of

561
00:27:48,520 --> 00:27:52,760
Speaker 1: the sphere, as an analogy to our three dimensional space,

562
00:27:52,800 --> 00:27:55,399
Speaker 1: because it's hard to think about three D surfaces of

563
00:27:55,480 --> 00:27:57,879
Speaker 1: four D spheres. But if you're on the surface of

564
00:27:57,880 --> 00:28:01,639
Speaker 1: a sphere, that surface is finite. It doesn't go on forever,

565
00:28:01,800 --> 00:28:04,840
Speaker 1: but it also doesn't have an edge. That's an example

566
00:28:04,880 --> 00:28:07,760
Speaker 1: of how space could be connected. So really we're talking about, like,

567
00:28:07,760 --> 00:28:11,080
Speaker 1: how do we've bits of space together into a larger fabric,

568
00:28:11,119 --> 00:28:13,520
Speaker 1: and then what is the shape of that fabric? Right?

569
00:28:13,560 --> 00:28:15,440
Speaker 1: But I think it sounds to me like you're making

570
00:28:15,440 --> 00:28:18,200
Speaker 1: an assumption about the universe, which is that it doesn't

571
00:28:18,280 --> 00:28:21,439
Speaker 1: have an edge or a wall to it, right, Like,

572
00:28:21,520 --> 00:28:24,239
Speaker 1: it doesn't seem like you're considering that possibility that if

573
00:28:24,280 --> 00:28:26,040
Speaker 1: I just hop on a spaceship and I keep going

574
00:28:26,119 --> 00:28:29,040
Speaker 1: for you know, a ninety billion light years, eventually I'm

575
00:28:29,119 --> 00:28:30,760
Speaker 1: maybe you're gonna hit a wall. Like that's not a

576
00:28:30,800 --> 00:28:33,399
Speaker 1: possibility that physicists seemed to consider because it maybe it

577
00:28:33,440 --> 00:28:35,960
Speaker 1: doesn't make sense to you. That's a possibility I'm totally

578
00:28:36,040 --> 00:28:38,680
Speaker 1: open to considering. You're right that it doesn't make sense

579
00:28:38,720 --> 00:28:41,120
Speaker 1: to me. It would break a lot of things and

580
00:28:41,160 --> 00:28:44,120
Speaker 1: be very very odd. That would make it super fun

581
00:28:44,160 --> 00:28:47,160
Speaker 1: and interesting to discover. I wouldn't think it's something that's

582
00:28:47,320 --> 00:28:50,080
Speaker 1: likely as a description of our universe, because it would

583
00:28:50,120 --> 00:28:52,680
Speaker 1: mean that one part of the universe is very different

584
00:28:52,680 --> 00:28:54,960
Speaker 1: from another part of the universe. The edge would have

585
00:28:55,000 --> 00:28:57,600
Speaker 1: to have a different nature than the rest of the universe.

586
00:28:57,600 --> 00:28:59,760
Speaker 1: And so far, what we've seen is that every part

587
00:28:59,760 --> 00:29:01,160
Speaker 1: of the of our sort of seems to be the

588
00:29:01,200 --> 00:29:03,800
Speaker 1: same as every other part. But you know, maybe it's

589
00:29:03,800 --> 00:29:05,160
Speaker 1: like we're in the very center of a huge lake

590
00:29:05,200 --> 00:29:07,200
Speaker 1: and we just can't see the edges, but they are there.

591
00:29:07,400 --> 00:29:10,520
Speaker 1: It's possible that the universe has edges, that there's another

592
00:29:10,640 --> 00:29:13,560
Speaker 1: kind of space, an edgy kind of space that's different.

593
00:29:13,720 --> 00:29:15,920
Speaker 1: That's a possibility. We can't rule it out that it

594
00:29:15,960 --> 00:29:18,080
Speaker 1: would be weird, right, Right, So then when we're talking

595
00:29:18,080 --> 00:29:20,480
Speaker 1: about the shape of base, I mean if it does

596
00:29:20,560 --> 00:29:23,040
Speaker 1: have walls and a boundary could be shaped by anything, right,

597
00:29:23,080 --> 00:29:25,160
Speaker 1: could be shaped like a cube or a banana or

598
00:29:25,320 --> 00:29:28,440
Speaker 1: you know, like um, like being trapped inside of a banana,

599
00:29:28,280 --> 00:29:30,400
Speaker 1: because that could be one way to talk about the

600
00:29:30,400 --> 00:29:33,240
Speaker 1: shape of the universe. But I think for our discussion today,

601
00:29:33,280 --> 00:29:35,160
Speaker 1: what do you actually mean by the shape of the

602
00:29:35,240 --> 00:29:37,880
Speaker 1: universe is like, let's assume that that's not possible. Like,

603
00:29:37,960 --> 00:29:41,720
Speaker 1: let's assume that the universe can't have walls or boundaries.

604
00:29:42,040 --> 00:29:45,400
Speaker 1: Then what are the possibilities left? Yeah, and so if

605
00:29:45,440 --> 00:29:47,960
Speaker 1: you assume that every point in space is the same

606
00:29:48,000 --> 00:29:50,680
Speaker 1: as every other point, right, you have like one kind

607
00:29:50,680 --> 00:29:52,280
Speaker 1: of lego piece, and you have to build a whole

608
00:29:52,400 --> 00:29:55,520
Speaker 1: universe with just that one lego pieast then what are

609
00:29:55,520 --> 00:29:57,959
Speaker 1: your options? So, for example, if I only give you

610
00:29:58,040 --> 00:30:00,400
Speaker 1: those flat pieces of lego, then what can you do?

611
00:30:00,600 --> 00:30:02,960
Speaker 1: You can just make a big flat sheet, right, just

612
00:30:03,080 --> 00:30:05,680
Speaker 1: like quilt together space, so that every piece is just

613
00:30:05,960 --> 00:30:08,440
Speaker 1: next to other pieces adjacent to it, and nothing is

614
00:30:08,440 --> 00:30:13,000
Speaker 1: more complicated. Space just goes on forever, totally flat. Right.

615
00:30:13,040 --> 00:30:15,960
Speaker 1: That's one simple idea for what space might be. Right,

616
00:30:15,960 --> 00:30:17,480
Speaker 1: because I think, you know, maybe a lot of people

617
00:30:17,600 --> 00:30:19,480
Speaker 1: might be confused with this, because you know, if you

618
00:30:19,520 --> 00:30:22,200
Speaker 1: tell me that the universe can have boundaries or like

619
00:30:22,320 --> 00:30:24,920
Speaker 1: walls or edges to it, then to me, I would

620
00:30:24,960 --> 00:30:27,800
Speaker 1: think that it has to go on forever. Then, you know,

621
00:30:27,840 --> 00:30:29,840
Speaker 1: to me, it seems like the only possibilities for the

622
00:30:29,920 --> 00:30:33,120
Speaker 1: universe to be infinite and have no shape. But I think,

623
00:30:33,240 --> 00:30:35,200
Speaker 1: you know, I physicists think about it differently, like it

624
00:30:35,240 --> 00:30:38,320
Speaker 1: could still be sort of infinite and continuous without boundaries

625
00:30:38,600 --> 00:30:40,560
Speaker 1: and still have a shape. No, I think you're right.

626
00:30:40,600 --> 00:30:43,880
Speaker 1: If it's flat and it's infinite, that is, it doesn't

627
00:30:43,960 --> 00:30:47,520
Speaker 1: repeat and there's no special edges to it, then it

628
00:30:47,600 --> 00:30:49,920
Speaker 1: has to be infinite. I can't think of another way

629
00:30:49,960 --> 00:30:52,520
Speaker 1: to arrange space. It is possible, though, for space to

630
00:30:52,560 --> 00:30:56,320
Speaker 1: be flat and not infinite, right. Imagine the pac Man

631
00:30:56,480 --> 00:30:59,360
Speaker 1: universe or the Asteroids universe, where at some point space

632
00:30:59,440 --> 00:31:01,600
Speaker 1: just repeat. You know, you get to some point in

633
00:31:01,640 --> 00:31:04,120
Speaker 1: space and it just is now connected to a spot

634
00:31:04,160 --> 00:31:07,239
Speaker 1: you've already been without any curvature. Right. It's just like

635
00:31:07,320 --> 00:31:09,760
Speaker 1: the way space is sort of the same way we

636
00:31:09,840 --> 00:31:13,360
Speaker 1: talked about for wormholes. Space can have non trivial connections,

637
00:31:13,360 --> 00:31:15,560
Speaker 1: like you can connect this bit of space to that

638
00:31:15,640 --> 00:31:17,640
Speaker 1: bit of space and just say, these two bits are

639
00:31:17,680 --> 00:31:20,360
Speaker 1: now next to each other, meaning you can step from

640
00:31:20,440 --> 00:31:23,640
Speaker 1: one to the other, even though in the larger fabric

641
00:31:23,640 --> 00:31:25,520
Speaker 1: of space they seem to be far apart. In the

642
00:31:25,520 --> 00:31:27,800
Speaker 1: same sense, you could have like a whole seam where

643
00:31:27,800 --> 00:31:30,160
Speaker 1: you connect like a whole line of space to another

644
00:31:30,200 --> 00:31:34,320
Speaker 1: whole line of space, effectively making like an infinitely sized wormhole.

645
00:31:34,480 --> 00:31:36,880
Speaker 1: I think what's interesting is that the idea that space

646
00:31:36,960 --> 00:31:40,120
Speaker 1: can have no it could have no boundaries, no walls,

647
00:31:40,160 --> 00:31:42,360
Speaker 1: but still have a shape. And I think what you're

648
00:31:42,360 --> 00:31:44,080
Speaker 1: telling me is that the one way it can do

649
00:31:44,120 --> 00:31:47,520
Speaker 1: that is if it's if space sort of wraps around itself,

650
00:31:47,840 --> 00:31:49,760
Speaker 1: sort of like if I keep going in one direction,

651
00:31:49,840 --> 00:31:53,360
Speaker 1: I eventually come back from the other direction, like somehow

652
00:31:53,400 --> 00:31:57,600
Speaker 1: space is curved or connected to itself in a strange

653
00:31:57,640 --> 00:32:00,320
Speaker 1: way so that I can't keep going forever, but I

654
00:32:00,360 --> 00:32:02,960
Speaker 1: sort of keep going around circles, and in that case,

655
00:32:03,040 --> 00:32:05,160
Speaker 1: the universe sort of has the shape, but it has

656
00:32:05,200 --> 00:32:08,320
Speaker 1: no edges to it. And there's two possibilities there. One

657
00:32:08,480 --> 00:32:12,200
Speaker 1: is space is actually curved, sort of like a sphere, right,

658
00:32:12,240 --> 00:32:14,360
Speaker 1: and so it's natural to put it together in that

659
00:32:14,400 --> 00:32:17,320
Speaker 1: way that space is curved and finite, and if you

660
00:32:17,520 --> 00:32:19,320
Speaker 1: keep going in one direction, you come back to where

661
00:32:19,360 --> 00:32:22,680
Speaker 1: you are. There's another possibility, which is that space is flat,

662
00:32:22,720 --> 00:32:25,640
Speaker 1: it doesn't have curvature, and yet it doesn't have edges

663
00:32:25,760 --> 00:32:28,200
Speaker 1: and it's finite. And that's like the asteroids or the

664
00:32:28,240 --> 00:32:31,520
Speaker 1: pac Man universe, where without space being curved, it's just

665
00:32:31,720 --> 00:32:34,959
Speaker 1: connected in that way. That's why local curvature is a

666
00:32:34,960 --> 00:32:37,840
Speaker 1: little bit different from this question of like global topology

667
00:32:37,960 --> 00:32:40,720
Speaker 1: the connectedness or shape of space, right right, But maybe

668
00:32:40,800 --> 00:32:42,440
Speaker 1: let's take a step back and break it down. So

669
00:32:42,480 --> 00:32:45,120
Speaker 1: it's possible for the universe to for it to be

670
00:32:45,240 --> 00:32:48,400
Speaker 1: sort of continuous all the way through, no boundaries, no edges,

671
00:32:48,440 --> 00:32:50,400
Speaker 1: but still be finite. And you're telling me, I think

672
00:32:50,400 --> 00:32:53,719
Speaker 1: that there are different ways in which that can happen.

673
00:32:53,920 --> 00:32:55,800
Speaker 1: So one of those ways has to do with curvature

674
00:32:55,840 --> 00:32:58,800
Speaker 1: and the other one doesn't. So let's maybe break it

675
00:32:58,840 --> 00:33:00,480
Speaker 1: down a little bit more about what this idea of

676
00:33:00,600 --> 00:33:03,280
Speaker 1: curvature is, Like, what does what does curvature mean for you?

677
00:33:03,360 --> 00:33:06,280
Speaker 1: Like for me, curvature means that the ground is uneven

678
00:33:06,400 --> 00:33:07,760
Speaker 1: or it has a slope to it. But what does

679
00:33:07,800 --> 00:33:10,000
Speaker 1: it mean in terms of space? In terms of space?

680
00:33:10,080 --> 00:33:13,120
Speaker 1: It locally, it means what is the path of a photon?

681
00:33:13,600 --> 00:33:16,280
Speaker 1: If you shine a laser beam through a chunk of space,

682
00:33:16,760 --> 00:33:20,440
Speaker 1: where does it go? And if space is curved, then

683
00:33:20,600 --> 00:33:23,200
Speaker 1: you can't see that curvature, but it affects the flight

684
00:33:23,280 --> 00:33:26,720
Speaker 1: of the photon, and so the photon will bend. It's

685
00:33:26,760 --> 00:33:30,840
Speaker 1: taking what's actually the shortest distance through that space, right,

686
00:33:30,840 --> 00:33:33,800
Speaker 1: because photons always take the shortest path. But the shortest

687
00:33:33,800 --> 00:33:36,400
Speaker 1: path is now something that looks bent to you because

688
00:33:36,440 --> 00:33:39,720
Speaker 1: you can't see the relationships between those bits of space. Remember,

689
00:33:39,720 --> 00:33:42,959
Speaker 1: the curvature of space is intrinsic, meaning it just changes

690
00:33:43,320 --> 00:33:47,000
Speaker 1: the relative distances between bits of space. So that's what

691
00:33:47,040 --> 00:33:48,960
Speaker 1: I mean by the curvature of space. I mean like

692
00:33:49,000 --> 00:33:51,760
Speaker 1: the path of a photon through that piece of space.

693
00:33:52,480 --> 00:33:54,720
Speaker 1: And again I think it means space time, right, or

694
00:33:54,800 --> 00:33:57,080
Speaker 1: I guess that the lump it all together. Yeah, Well,

695
00:33:57,120 --> 00:34:00,640
Speaker 1: relativity definitely mixes space and time together. There's a connected

696
00:34:00,680 --> 00:34:03,280
Speaker 1: effects there, but you know, space and time are also different.

697
00:34:03,440 --> 00:34:05,960
Speaker 1: You know, space has these properties that time doesn't have.

698
00:34:06,400 --> 00:34:09,160
Speaker 1: And here we're talking specifically about the spatial part of

699
00:34:09,200 --> 00:34:11,880
Speaker 1: space time. But yeah, you can't really think about space

700
00:34:11,880 --> 00:34:14,520
Speaker 1: without thinking about the four D structure that it sits

701
00:34:14,560 --> 00:34:17,120
Speaker 1: images space time. Well, and another thing that I think

702
00:34:17,120 --> 00:34:19,520
Speaker 1: I've read is that, you know, this idea of curvature

703
00:34:19,680 --> 00:34:21,480
Speaker 1: is not just about whether one ft like if you

704
00:34:21,480 --> 00:34:24,000
Speaker 1: shoot one photon and it leans to the right or

705
00:34:24,000 --> 00:34:26,080
Speaker 1: to the left. It's more about, like, if you shoot

706
00:34:26,239 --> 00:34:29,480
Speaker 1: two photons, do they curve away from each other or

707
00:34:29,560 --> 00:34:32,839
Speaker 1: towards each other. That's really more about the curvature of space, right, Yeah,

708
00:34:32,960 --> 00:34:35,320
Speaker 1: one way to measure the curvature of space is to

709
00:34:35,440 --> 00:34:37,919
Speaker 1: look at the path of two photons. Another way, which

710
00:34:37,920 --> 00:34:41,520
Speaker 1: is equivalent, is to like draw a triangle and ask, like,

711
00:34:41,640 --> 00:34:44,480
Speaker 1: what are the angles of that triangle. If you draw

712
00:34:44,520 --> 00:34:47,359
Speaker 1: a triangle on a flat surface, then it's angles add

713
00:34:47,400 --> 00:34:49,760
Speaker 1: up two, And if you draw triangle on the surface

714
00:34:49,800 --> 00:34:51,719
Speaker 1: of a sphere, it's angles are bigger than one a

715
00:34:51,800 --> 00:34:53,759
Speaker 1: d um and that's the same notion, right, if you

716
00:34:53,760 --> 00:34:55,560
Speaker 1: shoot two photons, and they have to move along the

717
00:34:55,560 --> 00:34:57,880
Speaker 1: surface of a sphere, then they can appear to curve

718
00:34:57,920 --> 00:35:01,319
Speaker 1: towards each other, for example, And if you're on a parabola,

719
00:35:01,400 --> 00:35:03,799
Speaker 1: then they appear to curve away from each other. And

720
00:35:03,800 --> 00:35:06,320
Speaker 1: it's equivalent to saying that a triangle on that surface

721
00:35:06,480 --> 00:35:10,000
Speaker 1: as angles less than degrees. Well, it's kind of strange

722
00:35:10,080 --> 00:35:13,440
Speaker 1: to think of a sears and converted between two the

723
00:35:13,480 --> 00:35:16,080
Speaker 1: and four D three D. But I think what you're

724
00:35:16,080 --> 00:35:18,520
Speaker 1: saying is like if the universe, like if the curvature

725
00:35:18,560 --> 00:35:20,520
Speaker 1: of the universe is flat, or at least around us,

726
00:35:21,080 --> 00:35:23,920
Speaker 1: things are flat, it means that if I shoot two photons,

727
00:35:24,040 --> 00:35:25,600
Speaker 1: they're not going to curve, or at least they're gonna

728
00:35:25,600 --> 00:35:27,960
Speaker 1: curve together maybe, but they're not gonna sort of move

729
00:35:28,000 --> 00:35:30,239
Speaker 1: away from each other or move towards each other. Right,

730
00:35:30,239 --> 00:35:32,600
Speaker 1: They're just gonna keep going in the same direction, side

731
00:35:32,600 --> 00:35:34,719
Speaker 1: by side forever. That's what it means for space to

732
00:35:34,760 --> 00:35:37,080
Speaker 1: be flat, Right, that's the way to test it. In

733
00:35:37,200 --> 00:35:40,800
Speaker 1: flat space, two photons moving in parallel will not approach

734
00:35:40,840 --> 00:35:44,480
Speaker 1: each other, whereas in curved space, two photons initially moving

735
00:35:44,760 --> 00:35:47,760
Speaker 1: what appears to be parallel to you will either approach

736
00:35:47,800 --> 00:35:49,839
Speaker 1: each other or divert from each other the same way

737
00:35:49,840 --> 00:35:51,759
Speaker 1: as if you're on the equator of the Earth, which

738
00:35:51,800 --> 00:35:54,320
Speaker 1: is a curved surface, and you and your friend both

739
00:35:54,440 --> 00:35:56,879
Speaker 1: walk north due north, which feels like you know, we're

740
00:35:56,920 --> 00:35:59,840
Speaker 1: moving parallel. You'll notice that you get closer and closer

741
00:35:59,880 --> 00:36:02,000
Speaker 1: to each other because eventually you're gonna hit the same point.

742
00:36:02,040 --> 00:36:05,560
Speaker 1: It's a motion constrained along a curved surface, or motion

743
00:36:05,600 --> 00:36:08,760
Speaker 1: through curved space can make things that initially were parallel

744
00:36:09,080 --> 00:36:11,880
Speaker 1: moved towards each other. So the Earth is not flat.

745
00:36:14,200 --> 00:36:16,840
Speaker 1: Need slash, it's not slash, right. I mean, if the

746
00:36:16,840 --> 00:36:18,839
Speaker 1: Earth was flat and you and I started walking in

747
00:36:18,840 --> 00:36:22,000
Speaker 1: one direction, we would keep walking at the same distance

748
00:36:22,000 --> 00:36:24,040
Speaker 1: from each other all the time. But but that doesn't

749
00:36:24,040 --> 00:36:25,719
Speaker 1: happen on Earth, right. That's one way we know the

750
00:36:25,760 --> 00:36:27,840
Speaker 1: Earth is not flat exactly, although I don't know what

751
00:36:27,960 --> 00:36:30,440
Speaker 1: north would mean on an infinite flat Earth, though I'm

752
00:36:30,440 --> 00:36:32,440
Speaker 1: sure the flat Earth earths have figured that out somehow.

753
00:36:32,760 --> 00:36:35,920
Speaker 1: All right, So that's flat universe and you're seeing a

754
00:36:36,040 --> 00:36:39,879
Speaker 1: curved universe. Means that the two photons would eventually either

755
00:36:41,160 --> 00:36:44,319
Speaker 1: collide or move away from each other forever, depending on

756
00:36:44,400 --> 00:36:46,520
Speaker 1: the sign of the curvature. So if you're on a sphere,

757
00:36:46,560 --> 00:36:49,120
Speaker 1: for example, then those photons eventually will hit each other.

758
00:36:49,200 --> 00:36:51,279
Speaker 1: They'll come closer to each other. If you're on a

759
00:36:51,320 --> 00:36:54,600
Speaker 1: parabola or in three D it's called a hyperbolic paraboloid,

760
00:36:54,920 --> 00:36:57,080
Speaker 1: then they will eventually move away from each other. Right,

761
00:36:57,080 --> 00:36:59,160
Speaker 1: And that's what you mean by like positive curvature and

762
00:36:59,200 --> 00:37:02,399
Speaker 1: negative curvature. If the universe has positive culture, then two

763
00:37:02,400 --> 00:37:04,840
Speaker 1: photons would eventually hit each other, even if you shoot

764
00:37:04,840 --> 00:37:07,280
Speaker 1: in parallel to each other. And if it has negative curvature,

765
00:37:07,360 --> 00:37:12,040
Speaker 1: deligious diverge and never hit each other exactly. But that's curvature.

766
00:37:12,080 --> 00:37:14,000
Speaker 1: What does that tells about the shape of the universe,

767
00:37:14,160 --> 00:37:18,520
Speaker 1: Because the curvature of space determines what shapes are possible.

768
00:37:18,960 --> 00:37:21,560
Speaker 1: Like if the curvature is positive, like on the surface

769
00:37:21,600 --> 00:37:24,280
Speaker 1: of a sphere, then you are building up your universe.

770
00:37:24,440 --> 00:37:27,240
Speaker 1: You can't make a parabloh, you can't make an infinite

771
00:37:27,239 --> 00:37:30,080
Speaker 1: flat universe. Right, you can make a sphere. You could

772
00:37:30,080 --> 00:37:32,279
Speaker 1: make a donut. You can make a donut with more

773
00:37:32,320 --> 00:37:34,960
Speaker 1: holes in it. Right, you have to build a universe

774
00:37:34,960 --> 00:37:37,640
Speaker 1: where every piece of space has that curvature and sort

775
00:37:37,680 --> 00:37:40,040
Speaker 1: of like have it all fit together without any edges.

776
00:37:40,360 --> 00:37:42,719
Speaker 1: There are only a few shapes that are possible. The

777
00:37:42,760 --> 00:37:45,680
Speaker 1: curvature of the universe on the large scales determines the

778
00:37:45,719 --> 00:37:48,320
Speaker 1: shapes that are possible. So if you measure the curvature

779
00:37:48,520 --> 00:37:51,120
Speaker 1: doesn't tell you the shape, it tells you what shapes

780
00:37:51,160 --> 00:37:54,000
Speaker 1: are allowed. M I see. So you're saying, like, if

781
00:37:54,040 --> 00:37:59,719
Speaker 1: it's positively curved everywhere, then there's only one sort of

782
00:37:59,760 --> 00:38:02,759
Speaker 1: shape ish that the universe can be, which is a

783
00:38:02,800 --> 00:38:06,440
Speaker 1: sphere or closed right like something that wraps around itself,

784
00:38:06,560 --> 00:38:09,080
Speaker 1: although it could be other shapes than just a sphere

785
00:38:09,200 --> 00:38:11,320
Speaker 1: like a donut, but not here there's the mid of

786
00:38:11,360 --> 00:38:14,840
Speaker 1: a subtle point of geometry, the picture you have in

787
00:38:14,880 --> 00:38:17,560
Speaker 1: your mind. If a donut has lots of spots on

788
00:38:17,600 --> 00:38:20,600
Speaker 1: it with positive curvature, they sort of bend away from you.

789
00:38:21,000 --> 00:38:24,600
Speaker 1: But not everywhere on the donut has positive curvature. There

790
00:38:24,600 --> 00:38:27,279
Speaker 1: are spots there with negative curvature. And if you talk

791
00:38:27,320 --> 00:38:31,680
Speaker 1: to professional geometrs like mathematicians, they think of a donut

792
00:38:31,800 --> 00:38:35,440
Speaker 1: is actually like a flat plane connected on itself, like

793
00:38:35,480 --> 00:38:38,120
Speaker 1: the pac Man universe we were talking about. So there's

794
00:38:38,160 --> 00:38:40,439
Speaker 1: the donut you eat, which has curvature, and then there's

795
00:38:40,440 --> 00:38:43,800
Speaker 1: a mathematical donut which is actually flat on the surface,

796
00:38:43,920 --> 00:38:46,520
Speaker 1: and we could also consider more exotic shapes like a

797
00:38:46,600 --> 00:38:48,759
Speaker 1: donut with two holes in it. I don't even know

798
00:38:48,800 --> 00:38:51,160
Speaker 1: what you call that, like a double bagel. But yes,

799
00:38:51,200 --> 00:38:54,440
Speaker 1: it couldn't be totally flat if space is curved positively,

800
00:38:54,760 --> 00:38:56,880
Speaker 1: I see. But if we measured space to be flat,

801
00:38:56,920 --> 00:38:59,680
Speaker 1: then there's no shape. It can't beat has to be

802
00:38:59,719 --> 00:39:02,040
Speaker 1: in it kind of. That's right. A space is flat,

803
00:39:02,040 --> 00:39:04,080
Speaker 1: and it can't be a sphere. It could still be

804
00:39:04,120 --> 00:39:06,640
Speaker 1: that weird Pacman universe or as you say, it could

805
00:39:06,640 --> 00:39:09,960
Speaker 1: have a weird edge to it right beyond what we're measuring,

806
00:39:10,080 --> 00:39:11,759
Speaker 1: but it can't be a sphere, or it can't be

807
00:39:11,800 --> 00:39:14,480
Speaker 1: a paraboloid or a hyperboloid or anything like that. So

808
00:39:14,560 --> 00:39:18,080
Speaker 1: measuring the curvature of space does rule out some possibilities

809
00:39:18,320 --> 00:39:20,480
Speaker 1: for the shape of space. Okay, So depending on the

810
00:39:20,520 --> 00:39:23,600
Speaker 1: curvature that we measure around is in all space, they'll

811
00:39:23,640 --> 00:39:27,160
Speaker 1: determine whether the universe is shaped like an infinite sort

812
00:39:27,200 --> 00:39:31,000
Speaker 1: of space sheet, or whether it's shape maybe closed like

813
00:39:31,080 --> 00:39:33,480
Speaker 1: a ball, like a sphere, or whether it has a

814
00:39:33,640 --> 00:39:36,080
Speaker 1: more interesting shape like I don't. And so let's talk

815
00:39:36,120 --> 00:39:38,680
Speaker 1: about what we've measured out there whether the universe is

816
00:39:38,680 --> 00:39:54,080
Speaker 1: flat or curved. But first let's take another quick break. Okay.

817
00:39:54,160 --> 00:39:55,800
Speaker 1: I know we are talking about the size and shape

818
00:39:55,840 --> 00:39:58,080
Speaker 1: of the universe, and now we're doing something even router,

819
00:39:58,280 --> 00:40:01,000
Speaker 1: which is actually measuring the size in shape of the universe. Like,

820
00:40:01,000 --> 00:40:02,480
Speaker 1: wouldn't that be rude? Or something came up to and

821
00:40:02,520 --> 00:40:04,319
Speaker 1: be like, hey, I wonder how big you are? Let

822
00:40:04,320 --> 00:40:06,120
Speaker 1: me measure? Well? You know, I think if you're a tailor,

823
00:40:06,160 --> 00:40:09,080
Speaker 1: for example, you ask somebody to waste size and then

824
00:40:09,120 --> 00:40:11,439
Speaker 1: you measure it because you want to deliver a suit

825
00:40:11,520 --> 00:40:14,520
Speaker 1: that fits, not an aspirational suit that they hoped to

826
00:40:14,560 --> 00:40:17,560
Speaker 1: one day fit into. Oh I see our physicists, the

827
00:40:17,600 --> 00:40:20,000
Speaker 1: tailors of the universe. What kind of suit are we

828
00:40:20,040 --> 00:40:22,040
Speaker 1: making for the universe? I don't know, But if we

829
00:40:22,040 --> 00:40:23,920
Speaker 1: asked the universe it's size and it gives us an answer,

830
00:40:24,040 --> 00:40:26,000
Speaker 1: I'd still want to go out and measure just to

831
00:40:26,080 --> 00:40:29,319
Speaker 1: make sure it wasn't being modest. Oh man, you think

832
00:40:29,320 --> 00:40:32,279
Speaker 1: the universe is lying to you? Maybe you always got

833
00:40:32,360 --> 00:40:34,440
Speaker 1: a double check and then double check your double checks.

834
00:40:34,680 --> 00:40:36,319
Speaker 1: I guess the universe could have been eating more dark

835
00:40:36,400 --> 00:40:40,160
Speaker 1: chocolate than it thought, and you know its measurements are outdated.

836
00:40:40,239 --> 00:40:42,279
Speaker 1: That's right. Maybe in between the time it's sent in

837
00:40:42,320 --> 00:40:44,640
Speaker 1: its measurements, it had a bunch more snacks, and so hey,

838
00:40:44,840 --> 00:40:46,239
Speaker 1: we just want to make sure to make a suit

839
00:40:46,320 --> 00:40:49,320
Speaker 1: that fits. We were talking about how knowing the curvature

840
00:40:49,360 --> 00:40:52,279
Speaker 1: space tells you at least not maybe the total or

841
00:40:52,360 --> 00:40:54,600
Speaker 1: exact shape of the universe tell you kind of what

842
00:40:54,760 --> 00:40:56,960
Speaker 1: kinds of shape the universe can be, whether it's sort

843
00:40:57,000 --> 00:41:00,880
Speaker 1: of closed like a sphere, or open like a infinite sheet,

844
00:41:01,040 --> 00:41:03,319
Speaker 1: or maybe has some weird shaped like a doughnut or

845
00:41:03,360 --> 00:41:06,040
Speaker 1: a hyperbola. And so I guess the big question now

846
00:41:06,120 --> 00:41:08,400
Speaker 1: is how do we measure the curvature of space? Like,

847
00:41:08,480 --> 00:41:11,239
Speaker 1: how do we measure if its curving one way or another? Yeah,

848
00:41:11,239 --> 00:41:13,360
Speaker 1: the best way to do it would be to have

849
00:41:13,480 --> 00:41:16,600
Speaker 1: a huge triangle, right, to like draw out a huge

850
00:41:16,680 --> 00:41:19,960
Speaker 1: triangle in space and to measure its angles. You know,

851
00:41:20,040 --> 00:41:23,920
Speaker 1: shoot photons in straight lines between three points and then

852
00:41:24,040 --> 00:41:27,319
Speaker 1: measure the opening angles between those photons, and that would

853
00:41:27,360 --> 00:41:28,680
Speaker 1: tell you just like if you did that on the

854
00:41:28,719 --> 00:41:31,239
Speaker 1: surface of the Earth, you could literally measure the curvature

855
00:41:31,360 --> 00:41:34,000
Speaker 1: of the Earth because you would measure that a triangle

856
00:41:34,040 --> 00:41:36,680
Speaker 1: actually has more than eight degrees in it if you

857
00:41:36,760 --> 00:41:39,080
Speaker 1: laid it out on the surface of the Earth. So

858
00:41:39,080 --> 00:41:40,640
Speaker 1: that would be the best way to do it. You know,

859
00:41:40,880 --> 00:41:44,359
Speaker 1: huge lasers really really far apart deep in space. Oh

860
00:41:44,400 --> 00:41:46,759
Speaker 1: I see. I mean, like you send out three satellites,

861
00:41:47,160 --> 00:41:52,080
Speaker 1: put arrangement a triangle, and you shoot lasers at each other. Yeah,

862
00:41:52,120 --> 00:41:54,320
Speaker 1: you make sure they're in a triangle by shooting lasers

863
00:41:54,320 --> 00:41:56,680
Speaker 1: at each other. This is totally fantastical, right, you never

864
00:41:56,680 --> 00:42:00,040
Speaker 1: actually do it. Imagine one satellite in this galaxy and

865
00:42:00,040 --> 00:42:03,440
Speaker 1: and Andromeda one and another galaxy, and they shoot lasers

866
00:42:03,480 --> 00:42:05,320
Speaker 1: at each other so you know they're lined up, and

867
00:42:05,360 --> 00:42:07,759
Speaker 1: then you just measure the angles between those lasers. So

868
00:42:07,840 --> 00:42:09,960
Speaker 1: like if I'm shooting an Andromeda from here and I'm

869
00:42:10,000 --> 00:42:13,440
Speaker 1: shooting at Alphas, another gassy from here, I would literally

870
00:42:13,480 --> 00:42:16,520
Speaker 1: just us take like a protractor and measure the angle

871
00:42:16,560 --> 00:42:18,640
Speaker 1: between the lasers. That would tell me whether the universe

872
00:42:18,719 --> 00:42:21,120
Speaker 1: is curved. Yeah, in the same way you could on

873
00:42:21,160 --> 00:42:23,480
Speaker 1: the surface of the Earth. Right, You've got two friends,

874
00:42:23,840 --> 00:42:26,200
Speaker 1: you guys stand in the triangle and you spool out

875
00:42:26,280 --> 00:42:29,640
Speaker 1: string between yourselves. You could just measure the angle between

876
00:42:29,680 --> 00:42:31,560
Speaker 1: those strings, and that would tell you the curvature of

877
00:42:31,600 --> 00:42:34,000
Speaker 1: the Earth same way you could do it with photons

878
00:42:34,080 --> 00:42:36,759
Speaker 1: deep in space. What you want is a really really

879
00:42:36,800 --> 00:42:39,640
Speaker 1: big triangle because the curvature, if it exists, it's going

880
00:42:39,680 --> 00:42:41,640
Speaker 1: to be pretty small. Just like on the surface of

881
00:42:41,680 --> 00:42:43,880
Speaker 1: the Earth. You'd want a really big triangle because it's

882
00:42:43,920 --> 00:42:46,080
Speaker 1: pretty hard to measure the curvature of the Earth in

883
00:42:46,120 --> 00:42:48,360
Speaker 1: just your bedroom. I see, Well, technically you could do

884
00:42:48,400 --> 00:42:50,320
Speaker 1: it in your bedroom. You just need like a super

885
00:42:50,880 --> 00:42:54,080
Speaker 1: precise protractor, right, Yeah, but then you're also measuring the

886
00:42:54,120 --> 00:42:57,319
Speaker 1: curvature of your bedroom instead of the Earth. But if

887
00:42:57,320 --> 00:43:00,280
Speaker 1: your bedroom follows the perfect curvature of the Earth Earth,

888
00:43:00,440 --> 00:43:02,800
Speaker 1: then yes, and so that's what you'd like to do ideally.

889
00:43:02,840 --> 00:43:05,160
Speaker 1: Obviously we can't do that. So what we have to

890
00:43:05,200 --> 00:43:08,840
Speaker 1: do is sort of look for existing triangles in space,

891
00:43:09,320 --> 00:43:12,080
Speaker 1: Like you know, is there a place where two photons

892
00:43:12,160 --> 00:43:15,400
Speaker 1: were sent to us from really distant locations and we

893
00:43:15,400 --> 00:43:19,640
Speaker 1: can sort of reconstruct like an existing cosmic triangle. Mmmmm.

894
00:43:20,040 --> 00:43:22,520
Speaker 1: It's so meaning like looking at galaxies, are looking at

895
00:43:22,560 --> 00:43:24,680
Speaker 1: sort of like the background of the universe. Yeah, so

896
00:43:24,719 --> 00:43:27,800
Speaker 1: the oldest light in the universe is a really helpful

897
00:43:27,880 --> 00:43:30,200
Speaker 1: resource for this. So we're talking about light from the

898
00:43:30,280 --> 00:43:33,920
Speaker 1: cosmic microwave background back when the universe was really hot

899
00:43:34,080 --> 00:43:37,160
Speaker 1: and really dense and only a few hundred thousand years old,

900
00:43:37,280 --> 00:43:40,279
Speaker 1: there was a moment when those particles came together and

901
00:43:40,320 --> 00:43:44,360
Speaker 1: became transparent, and we still see light from that plasma glowing.

902
00:43:44,480 --> 00:43:46,800
Speaker 1: That light is really really helpful because it's so old,

903
00:43:46,840 --> 00:43:49,520
Speaker 1: so it's traversed a lot of the universe and we

904
00:43:49,520 --> 00:43:51,759
Speaker 1: can kind of put it together in a sort of

905
00:43:51,800 --> 00:43:54,840
Speaker 1: cosmic triangle to get a sense for whether the universe

906
00:43:54,960 --> 00:43:57,480
Speaker 1: is curved in one way or another or whether it's

907
00:43:57,520 --> 00:44:00,360
Speaker 1: flat right. And this light is kind of interesting because

908
00:44:00,400 --> 00:44:02,640
Speaker 1: it's like the earliest light in the universe, so it's

909
00:44:02,760 --> 00:44:05,759
Speaker 1: very kind of like primal right like it it's sort

910
00:44:05,800 --> 00:44:08,080
Speaker 1: of like the o G light, like the original light

911
00:44:08,160 --> 00:44:10,279
Speaker 1: of the universe, like when it was born, they didn't

912
00:44:10,280 --> 00:44:12,160
Speaker 1: have a curvature to it. And you can tell from

913
00:44:12,200 --> 00:44:15,400
Speaker 1: the you said, the wiggles of the this light. What

914
00:44:15,480 --> 00:44:17,000
Speaker 1: we do is we look in this light for lumps.

915
00:44:17,040 --> 00:44:19,360
Speaker 1: We don't really just measure the angles between things. What

916
00:44:19,440 --> 00:44:22,200
Speaker 1: we look for is the size of lumps that are

917
00:44:22,239 --> 00:44:24,920
Speaker 1: evidenced in the cosmic microwave background light. So if you

918
00:44:24,920 --> 00:44:26,960
Speaker 1: look in one direction. If you look in another direction,

919
00:44:27,040 --> 00:44:28,719
Speaker 1: you see this light, But it turns out this light

920
00:44:28,760 --> 00:44:31,880
Speaker 1: has slightly different temperatures if you look in different directions.

921
00:44:32,000 --> 00:44:35,080
Speaker 1: It's really really minute, like one part in tens of thousands.

922
00:44:35,360 --> 00:44:37,840
Speaker 1: Mostly it's just the same, But there are these little wiggles,

923
00:44:37,880 --> 00:44:40,080
Speaker 1: and if you look for the size of those wiggles,

924
00:44:40,120 --> 00:44:42,200
Speaker 1: like how big is a hot spot or how big

925
00:44:42,280 --> 00:44:44,800
Speaker 1: is a cold spot, you can use the apparent size

926
00:44:44,800 --> 00:44:47,960
Speaker 1: of those wiggles to tell you whether the universe is

927
00:44:48,000 --> 00:44:50,759
Speaker 1: curved and how it's curved. Yeah, this is pretty cool

928
00:44:50,800 --> 00:44:52,480
Speaker 1: because I was thinking about this. It's almost like the

929
00:44:52,560 --> 00:44:55,680
Speaker 1: universe is acting like a lens, right, Like if the

930
00:44:55,800 --> 00:44:59,880
Speaker 1: universe is curved in one way positively, say, for example,

931
00:45:00,040 --> 00:45:01,920
Speaker 1: and maybe the universe is sort of like a sphere,

932
00:45:02,080 --> 00:45:04,799
Speaker 1: then the universe could acts like a magnifying glass. Right,

933
00:45:04,840 --> 00:45:07,360
Speaker 1: So you should see these um spots in the background

934
00:45:07,440 --> 00:45:10,680
Speaker 1: radiation kind of bigger than they actually are exactly, And

935
00:45:10,719 --> 00:45:13,520
Speaker 1: we have an idea for how big we expect those

936
00:45:13,560 --> 00:45:16,680
Speaker 1: spots to be, right, That's key. We have some idea

937
00:45:16,800 --> 00:45:19,719
Speaker 1: for like how matter and dark matter and the photons

938
00:45:19,719 --> 00:45:22,439
Speaker 1: were all slashing back and forth together against each other,

939
00:45:22,719 --> 00:45:25,640
Speaker 1: how big should those lumps be, we can predict how

940
00:45:25,640 --> 00:45:27,239
Speaker 1: big they should be, and then we can go and

941
00:45:27,280 --> 00:45:30,120
Speaker 1: measure how big they are. And as you say, if

942
00:45:30,160 --> 00:45:33,640
Speaker 1: the universe is curved, then photons, for example, from really

943
00:45:33,640 --> 00:45:36,560
Speaker 1: far apart, will curve towards each other, and so those

944
00:45:36,680 --> 00:45:39,800
Speaker 1: lumps will appear to be slightly bigger than they actually

945
00:45:39,840 --> 00:45:42,440
Speaker 1: are because you look in one direction, you look in

946
00:45:42,480 --> 00:45:45,000
Speaker 1: another direction, you'll be seeing like two sides of the

947
00:45:45,040 --> 00:45:48,080
Speaker 1: same lump. But really those edges were closer than what

948
00:45:48,160 --> 00:45:51,360
Speaker 1: you're seeing spaces flat than the photons are just flying straight.

949
00:45:51,640 --> 00:45:54,040
Speaker 1: And so that's sort of like a cosmic triangle because

950
00:45:54,080 --> 00:45:56,919
Speaker 1: you have these like two different sources of light all

951
00:45:56,960 --> 00:45:59,320
Speaker 1: coming at you, and you can look at the angle.

952
00:45:59,360 --> 00:46:01,759
Speaker 1: Basically we know those photons and tell whether they've been

953
00:46:01,760 --> 00:46:05,600
Speaker 1: bent together or bent apart or flown true right, And

954
00:46:05,640 --> 00:46:09,319
Speaker 1: like if the universe has negative curvature, then it sort

955
00:46:09,320 --> 00:46:12,560
Speaker 1: of acts like what's the opposite of a magnifying glass

956
00:46:12,560 --> 00:46:16,279
Speaker 1: glass if you're near sighted or something magnifying glass, you know,

957
00:46:16,320 --> 00:46:18,839
Speaker 1: like a piece of glass, it has the opposite kind

958
00:46:18,880 --> 00:46:21,239
Speaker 1: of curve, like the curse inwards in the middle, then

959
00:46:21,360 --> 00:46:24,279
Speaker 1: things sord have looked smaller through it. Right, so the

960
00:46:24,320 --> 00:46:27,080
Speaker 1: spots to look smaller, and we can do these simulations.

961
00:46:27,080 --> 00:46:29,000
Speaker 1: We say, here's where the hot spots and cold spots

962
00:46:29,040 --> 00:46:31,400
Speaker 1: should look like if the universe was flat, And then

963
00:46:31,440 --> 00:46:33,440
Speaker 1: we can dial up the curvature of the universe. And

964
00:46:33,480 --> 00:46:35,440
Speaker 1: in our simulations we can say, oh, look the spots

965
00:46:35,440 --> 00:46:38,360
Speaker 1: get bigger. And then we can dial down the curvature

966
00:46:38,400 --> 00:46:40,480
Speaker 1: to negative and say, oh, look the spots get smaller.

967
00:46:40,680 --> 00:46:41,880
Speaker 1: And then we go out and we look in the

968
00:46:41,920 --> 00:46:45,560
Speaker 1: actual universe and we say which of these best describes

969
00:46:45,719 --> 00:46:48,719
Speaker 1: what we see? You know, is the universe look like

970
00:46:48,800 --> 00:46:50,960
Speaker 1: it's flat or does it look like it's curved one

971
00:46:51,000 --> 00:46:53,960
Speaker 1: way or the other. So this is a very powerful

972
00:46:53,960 --> 00:46:56,400
Speaker 1: way to measure the curved to the universe over a

973
00:46:56,560 --> 00:46:59,880
Speaker 1: very very large scale, because even though those photons started

974
00:47:00,000 --> 00:47:03,080
Speaker 1: out not that far apart from each other, they traversed

975
00:47:03,320 --> 00:47:06,919
Speaker 1: a huge amount of the universe because of that expansion. Right, yeah,

976
00:47:07,000 --> 00:47:12,040
Speaker 1: so is the universe amplifying or shrinking the cosmic microwave background?

977
00:47:12,160 --> 00:47:14,319
Speaker 1: And so what we found when we measure this is

978
00:47:14,360 --> 00:47:17,640
Speaker 1: that the universe seems to be very very close to flat,

979
00:47:18,000 --> 00:47:21,440
Speaker 1: within zero point four percent. It's flat, Like this is

980
00:47:21,440 --> 00:47:23,719
Speaker 1: a number we measure, so it's not an exact thing.

981
00:47:23,800 --> 00:47:26,120
Speaker 1: You can never get like zero point zero zero zero

982
00:47:26,200 --> 00:47:29,359
Speaker 1: zero zero with infinite zeros. We measure is zero point

983
00:47:29,640 --> 00:47:33,400
Speaker 1: zero zero four curvature, meaning that as far as we think,

984
00:47:33,880 --> 00:47:36,399
Speaker 1: the universe is not curved, it's flat. That's right. It's

985
00:47:36,400 --> 00:47:39,160
Speaker 1: consistent with zero that we measure something a little bit

986
00:47:39,200 --> 00:47:41,759
Speaker 1: above zero. It's like if you've flipped a coin a

987
00:47:41,840 --> 00:47:44,840
Speaker 1: thousand times and it's a fair coin, you'd expect on

988
00:47:44,880 --> 00:47:47,719
Speaker 1: average to get of those to be heads, but you know,

989
00:47:47,840 --> 00:47:50,399
Speaker 1: sometimes you get a fluctuation up or down. So that's

990
00:47:50,400 --> 00:47:53,080
Speaker 1: what we see here. Space is either perfectly flat or

991
00:47:53,360 --> 00:47:56,920
Speaker 1: it's slightly positively curved, but it's consistent with flat. But

992
00:47:57,040 --> 00:47:58,560
Speaker 1: I guess you know, one question I would have as

993
00:47:58,600 --> 00:48:01,279
Speaker 1: a skeptic is that you just told me that this

994
00:48:01,400 --> 00:48:03,719
Speaker 1: is based on our measurement of the universe compared to

995
00:48:03,760 --> 00:48:06,520
Speaker 1: what we expect, But isn't what we expect also sort

996
00:48:06,520 --> 00:48:08,840
Speaker 1: of warped by our view of the universe, Like what

997
00:48:08,960 --> 00:48:12,640
Speaker 1: if what we expect is somehow distorted to absolutely this

998
00:48:12,719 --> 00:48:15,160
Speaker 1: could be wrong. Right, It's one measurement, and there are

999
00:48:15,160 --> 00:48:18,279
Speaker 1: always assumptions built into any measurement. We have other ways

1000
00:48:18,360 --> 00:48:20,759
Speaker 1: to measure the curvature of the universe, and those other

1001
00:48:20,800 --> 00:48:23,520
Speaker 1: ways agree with this measurement. Another way to measure the

1002
00:48:23,520 --> 00:48:25,279
Speaker 1: curvature of the universe is to go back to something

1003
00:48:25,280 --> 00:48:28,000
Speaker 1: we were talking about earlier, like what stuff is there

1004
00:48:28,040 --> 00:48:31,800
Speaker 1: in the universe? You sort of like way the whole universe,

1005
00:48:31,840 --> 00:48:33,800
Speaker 1: Like add up all the mass of all the stuff

1006
00:48:33,840 --> 00:48:36,040
Speaker 1: that's in the universe, the matter, the dark matter, the

1007
00:48:36,120 --> 00:48:38,560
Speaker 1: dark energy, and that will tell you like, is there

1008
00:48:38,640 --> 00:48:40,760
Speaker 1: enough stuff in the universe to be consistent with flat

1009
00:48:41,160 --> 00:48:42,759
Speaker 1: or is there too much stuff in the universe that

1010
00:48:42,760 --> 00:48:45,960
Speaker 1: the universe has to be closed, has to have positive curvature.

1011
00:48:46,000 --> 00:48:49,480
Speaker 1: And so that's another completely separate, totally independent way to

1012
00:48:49,600 --> 00:48:52,720
Speaker 1: measure the curvature of the universe, and that also comes

1013
00:48:52,800 --> 00:48:55,520
Speaker 1: up consistent with flat. Well, wait, you teld me earlier

1014
00:48:55,560 --> 00:48:57,440
Speaker 1: that the curvature of the universe doesn't depend on the

1015
00:48:57,480 --> 00:49:00,680
Speaker 1: stuff in it. Well, the overall shape, the way it's connected,

1016
00:49:00,719 --> 00:49:04,439
Speaker 1: whether it's infinite or looped or finite, that cannot be

1017
00:49:04,560 --> 00:49:07,920
Speaker 1: changed by the stuff in the universe. But the stuff

1018
00:49:07,920 --> 00:49:11,680
Speaker 1: in the universe can change the amount of curvature. Collapsing

1019
00:49:11,719 --> 00:49:14,480
Speaker 1: a large sphere into a smaller one, for example, if

1020
00:49:14,480 --> 00:49:17,680
Speaker 1: it has more than the critical density. And knowing the

1021
00:49:17,760 --> 00:49:20,719
Speaker 1: amount of stuff in the universe helps us measure the curvature,

1022
00:49:21,000 --> 00:49:25,680
Speaker 1: which determines what shapes it can be. Mm hmmm, I see.

1023
00:49:25,760 --> 00:49:29,040
Speaker 1: So okay, so we we've measured out the cosmic microwave

1024
00:49:29,080 --> 00:49:32,600
Speaker 1: background and we it fits our predictions for a flat universe,

1025
00:49:32,640 --> 00:49:35,480
Speaker 1: which means that probably the universe is flat. What does

1026
00:49:35,480 --> 00:49:37,560
Speaker 1: that mean for the shape of the universe. Probably the

1027
00:49:37,640 --> 00:49:42,480
Speaker 1: universe is flat, which means probably is infinite and boring

1028
00:49:42,520 --> 00:49:45,120
Speaker 1: in that sense and goes on forever and that sort

1029
00:49:45,160 --> 00:49:47,480
Speaker 1: of naive sense. But you know, people look at these

1030
00:49:47,560 --> 00:49:50,239
Speaker 1: measurements and they see some weird stuff in there, Like,

1031
00:49:50,400 --> 00:49:52,960
Speaker 1: first of all, it's flat, but you know, there's a

1032
00:49:53,000 --> 00:49:56,160
Speaker 1: little bit of positive curvature there, so maybe it's something different.

1033
00:49:56,239 --> 00:49:58,480
Speaker 1: And when they look in more detail at these wiggles,

1034
00:49:58,520 --> 00:50:02,120
Speaker 1: they see something a little bit unexpected, something a little surprising,

1035
00:50:02,160 --> 00:50:06,560
Speaker 1: which makes them think about donuts, Are you sure less

1036
00:50:06,600 --> 00:50:09,840
Speaker 1: much just because it's lunchtime maybe, or you need to

1037
00:50:09,960 --> 00:50:12,239
Speaker 1: sugar fix But wait, it's like I said, bag, you said,

1038
00:50:12,239 --> 00:50:15,320
Speaker 1: so we measured the universe speed probably flat, mostly flat,

1039
00:50:15,480 --> 00:50:17,360
Speaker 1: and what does that mean for the shape of the universe, Like,

1040
00:50:17,360 --> 00:50:18,879
Speaker 1: if it is flat, what does that mean? It means

1041
00:50:18,880 --> 00:50:20,560
Speaker 1: it doesn't have a shape, right, It means that it

1042
00:50:20,640 --> 00:50:23,560
Speaker 1: can only be infinite and go on forever, meaning doesn't

1043
00:50:23,560 --> 00:50:25,600
Speaker 1: have a shape. Well, I mean that is a shape, right,

1044
00:50:26,000 --> 00:50:28,800
Speaker 1: you know, mathematically speaking, that the shape If the universe

1045
00:50:28,960 --> 00:50:31,800
Speaker 1: is flat and has no boundaries and goes on forever,

1046
00:50:32,200 --> 00:50:35,359
Speaker 1: that's a shape. Yeah, I see. And if it was closed,

1047
00:50:35,400 --> 00:50:37,480
Speaker 1: if it had positive curvature, it would be a sphere.

1048
00:50:37,600 --> 00:50:40,400
Speaker 1: But we are not measuring that. Yeah, although remember, positive

1049
00:50:40,400 --> 00:50:43,040
Speaker 1: curvature can also be consistent with a donut. A donut

1050
00:50:43,400 --> 00:50:46,600
Speaker 1: is positively curved on its surface. That's for a physical donut.

1051
00:50:46,680 --> 00:50:51,080
Speaker 1: A mathematically donut is technically flat. So remember that little subtlety. Okay,

1052
00:50:51,080 --> 00:50:54,080
Speaker 1: so we're measuring the university a little positive curvature. Is

1053
00:50:54,080 --> 00:50:55,520
Speaker 1: that what you're saying? It has a little bit of

1054
00:50:55,520 --> 00:50:58,120
Speaker 1: a positive curvature, a little bit of a positive curvature.

1055
00:50:58,239 --> 00:51:02,640
Speaker 1: And also some details the cosmic microwave background radiation are

1056
00:51:02,719 --> 00:51:06,040
Speaker 1: really interesting and tantalizing, and I've led some people to

1057
00:51:06,080 --> 00:51:09,120
Speaker 1: suspect that maybe a doughnut is the best description of

1058
00:51:09,160 --> 00:51:12,680
Speaker 1: our universe. As the universe expands, we get these lumps

1059
00:51:12,840 --> 00:51:15,440
Speaker 1: in the cosmic microwave background. Right, These lumps come from

1060
00:51:15,520 --> 00:51:19,400
Speaker 1: quantum fluctuations in the very early universe during inflation. But

1061
00:51:19,480 --> 00:51:22,640
Speaker 1: as the universe is inflating, you're getting fluctuations all the time,

1062
00:51:22,680 --> 00:51:25,480
Speaker 1: So you should see lumps at all different sizes. It's

1063
00:51:25,520 --> 00:51:27,640
Speaker 1: like the biggest lump. And that's when we're using to

1064
00:51:27,680 --> 00:51:30,120
Speaker 1: measure the curvature. You should see big lumps, you should

1065
00:51:30,120 --> 00:51:32,480
Speaker 1: see small lumps, you should see very very small lumps.

1066
00:51:32,520 --> 00:51:35,480
Speaker 1: And so when we look at these fluctuations the amounts

1067
00:51:35,480 --> 00:51:38,200
Speaker 1: of lumpiness in the universe, we should see big lumps

1068
00:51:38,200 --> 00:51:40,640
Speaker 1: and small lumps, and smaller lumps and even smaller lumps.

1069
00:51:40,680 --> 00:51:42,320
Speaker 1: And so when people go out and measure this stuff,

1070
00:51:42,440 --> 00:51:44,640
Speaker 1: they see that mostly, but they see that sort of

1071
00:51:44,640 --> 00:51:47,480
Speaker 1: like the biggest scales, some of those lumps seem to

1072
00:51:47,520 --> 00:51:51,520
Speaker 1: be missing, Like you don't see necessarily correlations between things

1073
00:51:51,520 --> 00:51:54,439
Speaker 1: that are as far apart as you expect. Wait, let's

1074
00:51:54,440 --> 00:51:56,279
Speaker 1: maybe take a step back. We measure the unms be

1075
00:51:56,360 --> 00:51:59,319
Speaker 1: a little bit positive curvature, which means that it can

1076
00:51:59,320 --> 00:52:01,520
Speaker 1: still be a spear. Couldn't it connects to still be

1077
00:52:01,560 --> 00:52:03,839
Speaker 1: a sphere? Could be a sphere? I see, but there's

1078
00:52:03,840 --> 00:52:05,919
Speaker 1: something about the doughnut that makes it makes you think

1079
00:52:05,920 --> 00:52:07,880
Speaker 1: that it could be a donut. What's special about a

1080
00:52:07,920 --> 00:52:10,640
Speaker 1: donut that would fit what you're saying, Well, what we're

1081
00:52:10,640 --> 00:52:14,399
Speaker 1: seeing is that at very very large angles, there aren't

1082
00:52:14,440 --> 00:52:17,560
Speaker 1: as many correlations as we expect. You know, we're talking

1083
00:52:17,600 --> 00:52:21,080
Speaker 1: about a very small effect here, and above sixty degrees

1084
00:52:21,160 --> 00:52:25,239
Speaker 1: in the sky we should see fluctuations about a hundred microclevins,

1085
00:52:25,280 --> 00:52:28,520
Speaker 1: but what we see is fluctuations like twenty microclevin's. So

1086
00:52:28,640 --> 00:52:32,399
Speaker 1: it's a small effect. But a donut topology turns out

1087
00:52:32,400 --> 00:52:35,799
Speaker 1: to suppress these large scale fluctuations because it makes the

1088
00:52:35,920 --> 00:52:39,200
Speaker 1: universe finite. And donuts have a sort of a smaller

1089
00:52:39,400 --> 00:52:42,160
Speaker 1: radius than a sphere for the same curvature. A donut

1090
00:52:42,160 --> 00:52:44,920
Speaker 1: has sort of like shorter length scales, right, then a

1091
00:52:44,960 --> 00:52:47,000
Speaker 1: sphere does. Well. I guess maybe we need to talk

1092
00:52:47,000 --> 00:52:51,360
Speaker 1: about the differences between donuts and meatball standing because a

1093
00:52:51,440 --> 00:52:55,680
Speaker 1: donut is interesting, right because it's it's a close shape, um,

1094
00:52:55,760 --> 00:52:57,160
Speaker 1: but it has a hole in it, and it's kind

1095
00:52:57,160 --> 00:52:59,680
Speaker 1: of interesting because like if you go in one direction,

1096
00:52:59,719 --> 00:53:02,000
Speaker 1: like a around the wide rim of the doughnut, you

1097
00:53:02,080 --> 00:53:04,000
Speaker 1: go in a circle. And also if you go towards

1098
00:53:04,040 --> 00:53:05,960
Speaker 1: the center of the doughnut, you also go in a circle,

1099
00:53:06,000 --> 00:53:08,200
Speaker 1: so it sort of loops around in all directions, sort

1100
00:53:08,200 --> 00:53:10,439
Speaker 1: of like a sphere, but it's not a sphere. It's

1101
00:53:10,480 --> 00:53:13,399
Speaker 1: more like a like a closed cylinder. Yeah, and it's

1102
00:53:13,400 --> 00:53:15,640
Speaker 1: got two different length scales, as you say, It's got

1103
00:53:15,680 --> 00:53:17,920
Speaker 1: like the one way around and the other way around,

1104
00:53:17,920 --> 00:53:20,719
Speaker 1: whereas a sphere only has one length scale, it's just

1105
00:53:20,760 --> 00:53:23,960
Speaker 1: the radius. And you know, even if the universe is

1106
00:53:24,000 --> 00:53:25,919
Speaker 1: curved and it's a sphere or a donut, we're talking

1107
00:53:25,960 --> 00:53:29,839
Speaker 1: about something very slightly curved, so really really huge, right,

1108
00:53:30,080 --> 00:53:33,280
Speaker 1: really un enormous scales, just just so nobody is confused.

1109
00:53:33,440 --> 00:53:35,279
Speaker 1: We're not like the little prints here standing on a

1110
00:53:35,280 --> 00:53:37,759
Speaker 1: tiny donuts, the ginormous donut. Yeah. But they did a

1111
00:53:37,760 --> 00:53:40,080
Speaker 1: bunch of simulations and they discovered that a donut is

1112
00:53:40,120 --> 00:53:42,799
Speaker 1: better at causing the sort of lack of ripples that

1113
00:53:42,880 --> 00:53:45,520
Speaker 1: they see in CMB. You know, in the cosmic microwave

1114
00:53:45,520 --> 00:53:48,480
Speaker 1: background radiation, we don't see some of the bigger ripples

1115
00:53:48,480 --> 00:53:51,759
Speaker 1: that we expect, and a donut is better suppressing those

1116
00:53:51,760 --> 00:53:53,759
Speaker 1: because it has these two length scales, the long way

1117
00:53:53,800 --> 00:53:55,640
Speaker 1: around and the short way around and so you just

1118
00:53:55,640 --> 00:53:57,880
Speaker 1: sort of like don't get as big lumps on a

1119
00:53:57,920 --> 00:53:59,880
Speaker 1: donut as you do on a sphere, and so that

1120
00:54:00,000 --> 00:54:03,520
Speaker 1: makes people wonder maybe the universe is shaped like a donut, right,

1121
00:54:03,760 --> 00:54:06,680
Speaker 1: So it's the difference between these lengths the scales that

1122
00:54:06,800 --> 00:54:08,920
Speaker 1: it is giving you the clues like you're seeing some

1123
00:54:09,040 --> 00:54:12,799
Speaker 1: weird kind of like oblong shaped and the cosmic microwave background. Yes,

1124
00:54:12,840 --> 00:54:15,040
Speaker 1: the fact that you don't see as big lumps as

1125
00:54:15,040 --> 00:54:17,759
Speaker 1: you expect from a flat universe or even from a

1126
00:54:17,800 --> 00:54:21,880
Speaker 1: spherical universe. It's not impossible to suppress these long distance

1127
00:54:21,880 --> 00:54:24,160
Speaker 1: effects on a sphere. It's just that you would need

1128
00:54:24,200 --> 00:54:27,480
Speaker 1: a radius of curvature that's not consistent with what we

1129
00:54:27,600 --> 00:54:31,080
Speaker 1: have measured. A doughnut gives you another length scale to

1130
00:54:31,080 --> 00:54:35,279
Speaker 1: play with, so it's easier to suppress the long distance correlations. Now,

1131
00:54:35,280 --> 00:54:37,520
Speaker 1: this is not a smoking gun. This is like a

1132
00:54:37,640 --> 00:54:40,880
Speaker 1: weird little hint that could just be random noise, right.

1133
00:54:40,920 --> 00:54:43,600
Speaker 1: It could be theorists getting too excited and eating too

1134
00:54:43,640 --> 00:54:46,360
Speaker 1: much chocolate and thinking about donuts. But it's sort of

1135
00:54:46,360 --> 00:54:48,799
Speaker 1: like a fun hint, and we'll get more data and

1136
00:54:48,800 --> 00:54:51,279
Speaker 1: we'll see if this holds up. But it's fascinating to

1137
00:54:51,320 --> 00:54:54,239
Speaker 1: me that this question is the universe flat or is

1138
00:54:54,280 --> 00:54:56,239
Speaker 1: it it's deer or is it even a donut is

1139
00:54:56,239 --> 00:54:59,040
Speaker 1: still unanswered. It's still something we don't know the actual

1140
00:54:59,080 --> 00:55:02,080
Speaker 1: answer to. Oh, but it seems like we have a

1141
00:55:02,120 --> 00:55:05,200
Speaker 1: sort of a big clue, which is that the university

1142
00:55:05,280 --> 00:55:07,360
Speaker 1: is flat around us. Could it be that we're just

1143
00:55:07,400 --> 00:55:11,080
Speaker 1: measuring local curvature, like are we just a dimple or

1144
00:55:11,280 --> 00:55:16,359
Speaker 1: like a flat spot in a you know, teacup shape universe? Absolutely,

1145
00:55:16,640 --> 00:55:18,480
Speaker 1: you know, what we're doing is we're assuming that the

1146
00:55:18,480 --> 00:55:20,680
Speaker 1: curvature we measure here is the same as the curvature

1147
00:55:20,680 --> 00:55:23,520
Speaker 1: we're measuring somewhere else. And we're hoping that that's true

1148
00:55:23,560 --> 00:55:25,799
Speaker 1: because we're measuring in lots of different ways, and we're

1149
00:55:25,800 --> 00:55:28,839
Speaker 1: trying to measure in different directions. But in the end,

1150
00:55:28,960 --> 00:55:31,919
Speaker 1: our vantage point is limited, right, And so it could

1151
00:55:32,000 --> 00:55:34,960
Speaker 1: be that we're a flat spot on a very large doughnut,

1152
00:55:35,200 --> 00:55:37,360
Speaker 1: or that we could be a slightly curved spot on

1153
00:55:37,480 --> 00:55:41,759
Speaker 1: otherwise flat universe. Um, you know, we can't really confidently

1154
00:55:41,800 --> 00:55:45,120
Speaker 1: extrapolate path what we can see. The Remember that the

1155
00:55:45,120 --> 00:55:48,160
Speaker 1: CMB measurements do cover a lot of space. It's not

1156
00:55:48,360 --> 00:55:51,960
Speaker 1: that local. Interesting or so you're saying kind of stay tuned,

1157
00:55:52,040 --> 00:55:54,960
Speaker 1: like we actually don't know what the shape of the

1158
00:55:55,040 --> 00:55:57,920
Speaker 1: universe is. That's right. If you're betting, I think flat

1159
00:55:57,960 --> 00:56:01,480
Speaker 1: is the best bet. It's the simplest, it's harmonious. It's

1160
00:56:01,520 --> 00:56:03,920
Speaker 1: what most physicists believe. If you ask them if the

1161
00:56:04,160 --> 00:56:06,600
Speaker 1: is the universe slat, they would say yes. But you know,

1162
00:56:06,640 --> 00:56:10,080
Speaker 1: the data say it's either flat or slightly positively curved.

1163
00:56:10,360 --> 00:56:13,480
Speaker 1: And there are these interesting wiggles that are more consistent

1164
00:56:13,520 --> 00:56:16,120
Speaker 1: with a donut shape than a sphere or a flat universe.

1165
00:56:16,120 --> 00:56:19,879
Speaker 1: So yeah, stay tuned. We still got big realizations ahead

1166
00:56:19,920 --> 00:56:22,600
Speaker 1: of us. So if you're the gamping type, maybe invest

1167
00:56:22,640 --> 00:56:26,319
Speaker 1: in donuts, that's what you're saying. And if you win,

1168
00:56:26,400 --> 00:56:28,440
Speaker 1: eat a donut, and if you lose, eat a doughnut.

1169
00:56:28,840 --> 00:56:31,840
Speaker 1: Either way you win said. If you don't win, you don't.

1170
00:56:32,000 --> 00:56:34,719
Speaker 1: You win, you don't, but you don't don't donut. If

1171
00:56:34,719 --> 00:56:39,279
Speaker 1: you win. If the is still dark chocolate, how would

1172
00:56:39,280 --> 00:56:41,640
Speaker 1: that change the curvature, Daniel M. I think would make

1173
00:56:41,640 --> 00:56:45,200
Speaker 1: it more closed exactly. Dark chocolate is pretty dense stuff

1174
00:56:45,239 --> 00:56:47,200
Speaker 1: and so we tend to compact on itself. And how

1175
00:56:47,239 --> 00:56:49,960
Speaker 1: would mean the universe is not infinitely filled with chocolate,

1176
00:56:50,000 --> 00:56:53,120
Speaker 1: and eventually my snacking days must end, right, But if

1177
00:56:53,120 --> 00:56:56,640
Speaker 1: it's closed, then there's a finite amount of dark chocolate,

1178
00:56:56,680 --> 00:56:59,359
Speaker 1: So eventually you might eat physicists might eat at all.

1179
00:56:59,480 --> 00:57:01,000
Speaker 1: That's right, I better go ahead and get started on

1180
00:57:01,040 --> 00:57:03,200
Speaker 1: my snack. You might might want to buy some new

1181
00:57:03,239 --> 00:57:06,640
Speaker 1: belts or pants, assuming you wear pants. I mean, we

1182
00:57:06,719 --> 00:57:09,560
Speaker 1: talked about social conventions and physicists. Who knows, right, he

1183
00:57:09,600 --> 00:57:12,040
Speaker 1: talked about not making assumptions, right, you know, we're exploring

1184
00:57:12,040 --> 00:57:15,720
Speaker 1: the university in mind. What shape is Daniel or Daniel's

1185
00:57:15,719 --> 00:57:18,840
Speaker 1: pants he doesn't have pants. Maybe it's a good question.

1186
00:57:19,200 --> 00:57:22,480
Speaker 1: There actually is a pants diagram for black hole mergers.

1187
00:57:22,520 --> 00:57:24,440
Speaker 1: We're going to talk about a few weeks, all right.

1188
00:57:24,880 --> 00:57:27,680
Speaker 1: Is that rude to ask what black Hole's pants are?

1189
00:57:29,320 --> 00:57:32,600
Speaker 1: We'll find out? Are they bill bottoms or tapered low

1190
00:57:32,680 --> 00:57:36,200
Speaker 1: rising and they wear shorts over their socks and sand

1191
00:57:36,520 --> 00:57:42,320
Speaker 1: neither mom jeans or that cargo pants. All right. Well,

1192
00:57:42,360 --> 00:57:44,520
Speaker 1: it's interesting to think that, you know, from our little

1193
00:57:44,560 --> 00:57:46,600
Speaker 1: spot in the universe, we can, you know, have these

1194
00:57:46,600 --> 00:57:49,919
Speaker 1: conversations about what the shape of the universe is when

1195
00:57:49,920 --> 00:57:53,040
Speaker 1: it's so far away, you know, nineties, sixty billion light

1196
00:57:53,080 --> 00:57:55,520
Speaker 1: years away. We're still we can still have conversations about it,

1197
00:57:55,560 --> 00:57:58,520
Speaker 1: and we we might be right, which is the crazy thing. Yeah,

1198
00:57:58,680 --> 00:58:01,200
Speaker 1: and thank you very much duper users, Leo, Stein and

1199
00:58:01,240 --> 00:58:03,680
Speaker 1: Evans gonna be echo for consulting with us on this

1200
00:58:03,720 --> 00:58:08,600
Speaker 1: tricky topic. Any remaining inaccuracies and ambiguities are our responsibility,

1201
00:58:08,720 --> 00:58:11,920
Speaker 1: not there. And no matter how big and how crazy

1202
00:58:11,960 --> 00:58:15,040
Speaker 1: the question is, we can eventually always think about some

1203
00:58:15,160 --> 00:58:18,480
Speaker 1: way to try to answer it, some clever wrinkle in

1204
00:58:18,520 --> 00:58:21,160
Speaker 1: the nature of the universe that forces it to answer

1205
00:58:21,240 --> 00:58:26,080
Speaker 1: our questions. But even the biggest, hardest, craziest questions were

1206
00:58:26,080 --> 00:58:29,520
Speaker 1: the craziest answers. That's right, even the tasty and crazy

1207
00:58:29,560 --> 00:58:32,600
Speaker 1: answers about the universe. Well, we hope you enjoyed that.

1208
00:58:32,640 --> 00:58:43,080
Speaker 1: Thanks for joining us, See you next time. Thanks for listening,

1209
00:58:43,120 --> 00:58:45,840
Speaker 1: and remember that Daniel and Jorge explained. The universe is

1210
00:58:45,920 --> 00:58:49,400
Speaker 1: a production of I Heart Radio. For more podcast from

1211
00:58:49,400 --> 00:58:53,160
Speaker 1: my Heart Radio, visit the I Heart Radio app, Apple Podcasts,

1212
00:58:53,280 --> 00:59:01,240
Speaker 1: or wherever you listen to your favorite shows. No