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- Right now the prevailing theory of how the Universe came about is commonly called the Big Bang Theory.
- And really it's just this idea that the Universe that this Universe started as kind of an infintely small
- point, this infinitely small singularity, and then it just had a Big Bang, or it just expanded from that
- state to the Universe we know right now. And when I first imagined this, and I think it's also a by-product
- of how its named, Big Bang, you kind of imagine this type of explosion. You kind of imagine this type
- of explosion. That everything was infinitely packed in together and then it exploded. And then it exploded
- outward. Then as all the matter exploded outward it started to condense and then you have all these
- galaxies and super clusters of galaxies and they started to condense and then within them, planets condense
- and stars condense and then we have the type of Universe that we have right now. But this model for
- visualizing the Big Bang has a couple of problems. One is, when we talk about the Big Bang, we're not
- talking about the matter, just the mass or just the matter in the Universe being in one point, we're
- talking about actual space expanding, we are not just talking about something inside of space, like the physical mass expanding
- we are talking about space itself so when you have this type of a model you have all the stuff expanding
- is it expanding into something else? Maybe if the furthest out part of this matter is right over here
- what's this stuff over here? So you say:
- wouldn't that be space, how can you say space itself is expanding?
- And another idea that a Big Bang also implies is that if this is furthest stuff out there
- would this be the edge of the Universe? Does the Universe have an edge?
- And the answer to this question, that's why we are going to try to tackle this is,
- one: **the Universe does not have an edge** and
- two: **there is no outside space**, we are not expanding
- into another space. I am going to explain that,
- hopefully we'll see why this is the case right now.
- So the best way of viewing it is by analogy
- If I were to tell you that I have a two dimensional space
- that has a finite area, so it's not infinite and also has no edge
- this once again, when you first look at it, it seems difficult
- how do I construct something that has a finite area
- but still has no edge? Every time I try to draw an area it looks like I have to have some edges
- and then you might remember, what if that two dimensional space is curved?
- what happens? I think that the easiest example of that is the the surface of the sphere.
- let me draw a sphere over here. So this right here is a sphere.
- let me draw some longitude and latitude lines on this sphere
- on this sphere all of a sudden, I shade it in a little bit, make it look nice,
- this type of a sphere you have a finite area, you can imagine the surface of a balloon
- or the surface of a bubble or the surface of the Earth
- you have a finite area but you have no edge, if you keep going forever in one direction
- you just keep going all the way around and come back to the other side
- now, to imagine a three dimensional space that has the same properties, a finite area and,
- I don't want to say finite area anymore, because we are not talking about
- a three dimensional space anymore, let me draw over here
- so let's think about three dimensional space,
- and instead of area I want to talk about finite volume
- and no edge, how do I do that?
- when you think about it superficially, look, if you had finite volume it's going to be maybe
- contained in some type of cube, we clearly have edges in those situations
- you can even think about a finite volume as being the inside of a sphere, that clearly has an edge
- this entire surface over there.
- so how do you construct an three dimensional space that has finite volume and no edge?
- And than I am going to tell you right now
- it's very hard for us to visualize it, but in order to visualize it
- I am going to draw the same thing that I drew right here
- you have to imagine it, you always have to imagine it by analogy
- (unless you have a profound brain wired for more than three spatial dimensions)
- is a sphere, let me make it clear, this is two dimensional surface.
- right on the surface of the sphere you can only move in two directions.
- two perpendicular directions, you can move like that or you can move like that,
- you can move left and right or you can move up and and down
- two dimensional surface of a three dimensional
- sphere, so if we take it by analogy, let's imagine, and it's hard to imagine, a three dimensional surface
- and you can do it mathematically, the math here is actually not that difficult, three dimensional surface of a four dimensional sphere
- and I'm going to draw up the same way,
- so if we kind of view those three dimensions are just these two dimension of the surface
- it's the same thing, and if imagine that I'm not saying this is the actual shape of the Universe,
- we don't know the shape, but we do know it has a slight curvature, we don't know the actual shape
- but the sphere is the simpliest, there's other ones we can do, a toroid
- would also fit the bill, it would have a finite volume with no edge
- and I think, I want to make it clear, we actually don't know whether it has a finite volume
- it's still an open question, but I want to show you it can have a finite volume and also have
- no edge. And most people believe, and I want to say believe because you know we can, just go based on evidence and all that,
- that we are talking about something with finite volume, especially when you talk about the Big Bang theory
- that kind of some dimensions implies a finite volume, although it could be a super large, unfathomably large volume
- it is finite, now if you have this, imagine, this sphere,
- once again if you're on this surface of this four dimensional sphere, I can't draw a four dimensional sphere, but
- if you are on this surface of this four dimensional sphere if you go in any direction you'll come back to where you started
- if you go that way you'll come back around here, now the Universe is super huge so even light
- maybe light itself would take an unbelievable amount of time to traverse it
- and if this sphere itself is expanding, it may be expanding so fast that light
- might not ever be able to come back around it, but in theory if somethings were fast enough
- if something were to keep going around it could actually go back to this point. Now when we talk about
- a three dimensional surface it's a three dimensional surface of a four dimensional sphere
- that means that any of the three dimensions that are over here on the surface, I can only draw two
- but that means, if this is true, if the Universe is a three dimensional surface of a four dimensional
- sphere, that means if you go up and if you just keep going up, you'll eventually come back from the bottom.
- So if you keep going, you keep going all the way up you'll eventually come back to the point that you where
- it might be an unbelievably large distance but you'll eventually get back where you were
- if you go to the right you'll eventually come back all the way around to the point where you were
- and if you want to go into the page, let me draw it that way, if you go into the page
- you'd eventually come back from above the page, and come back to the point that you are
- so that's what this implication would be that you would actually get back to where you are
- so let's go back to the question of and expanding Universe.
- You know an expanding Universe that is not expanding into any other space
- it is all of the space but it is still expanding
- this is the model, so you can imagine shortly after the Big Bang, our four dimensional sphere look like this
- maybe it was a little small four dimensional sphere, maybe at the Big Bang it was this little unbelievably
- small sphere then a little bit later it is this larger sphere, let me just shade it in
- to show that it is kind of popping out of the page this sphere, and in the later time this sphere might look like this,
- now you temptation might be to say, well isn't this stuff outside of the sphere?
- isn't that some type of a space that is expanding into ?
- isn't that somehow part of the Universe? and I would say if you are talking in three dimension, no it's not.
- The entire Universe is this surface, it is the surface of this four dimensional sphere
- if you start talking about more dimensions, then yes, you could talk about maybe things outside of our
- three dimensional Universe, so as this expands in space-time, you know one way to view
- this fourth dimension is that it is time itself, things are just getting further and further apart.
- And I'll talk about the evidence in future videos for why the Big Bang is the best theory
- we have out there right now. But as you can imagine, if you have two points on this sphere that are that
- far apart, as this sphere expands, this four dimensional sphere, this bubble, blows up, or this balloon
- blows up, those two points; let me draw three points, those three points are just going to get further
- and further apart, that's actually one of the main points that, one of the first reasons why it makes
- sense to believe in the Big Bang is that everything is expanding not from some central point, but everything
- is expanding from everything, that if you go in any direction from any point in the Universe, everything else
- is expanding away and the further away you go it looks like the faster it's expanding away from you,
- so I'll leave there it's something for you to think about a little bit, and then we'll build on some of this
- to think about what it means to observe the observable Universe.

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