If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:11:03

Right now, the prevailing theory
of how the universe came about is commonly called
the Big Bang theory. And really is just this idea
that the universe started as kind of this infinitely
small point, this infinitely small singularity. And then it just had a big
bang or it just expanded from that state to the universe
that we know right now. And when I first
imagined this-- and I think if it's also a byproduct
of how it's named-- Big Bang, you kind of imagine
this type of explosion, that everything was
infinitely packed in together and then it exploded. And then it exploded outward. And then as all of the
matter exploded outward, it started to condense. And then you have
these little galaxies and super clusters of galaxies. And they started to condense. And then within them, planets
condensed and stars condensed. 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. So we're not just talking about
something inside of space, like the physical mass, the
physical matter expanding. We're talking
about space itself. And so when you have
this type of model, you have all of this
stuff expanding. But you're like,
whoa, look, isn't it expanding into something else? Maybe if the furthest
out parts of this matter is right over here, what's
this stuff over here? And so you say, well,
wouldn't that be space? So how can you say space
itself is expanding? And another idea
that a Big Bang also implies is if this is the
furthest stuff out there, would this be the
edge of the universe? Does the universe have an edge? And the answer to either
of those questions, and that's what we're going
to try to tackle in this, is that, one, the universe
does not have an edge. And two, there is
no outside space. We are not expanding
into another space. And I'm going to explain that. Hopefully, we'll see why
that is the case right now. So the best way to
view it-- and we're going to view it by analogy. If I were tell you that I have
a two-dimensional space that has a finite area, so
it has a finite area-- so it's not infinite. And it also has no edge. This once again, when you first
look at it, seems difficult. How do I just
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? And I think the
easiest example of that is the surface of a sphere. Let me draw a sphere over here. So this right here is a sphere. Let me draw some
longitude and latitudinal lines on this sphere. On this sphere, all
of a sudden-- and I'll shade it in a
little bit, make it look nice-- this type of a
sphere, you have a finite area. You could 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're going to go all the
way around and come back to the other side. Now, to imagine a
three-dimensional space that has these same
properties, a finite area and-- and I don't want to
say finite area anymore, because we're not talking about
a three-dimensional space. Let me draw it over here. So let's think about a
three-dimensional space, so a three-dimensional space. Instead of area, since we're
in three dimensions now, I want to talk about a
finite volume and no edge. How do I do that? And when you think
about it superficially, well, look, if I
have a finite volume, maybe it'll be contained
in some type of a cube. And then we clearly have
edges in those situations. Or you could even think
about a finite volume as being the inside of a sphere. And that clearly has an edge,
this entire surface over there. So how do you construct
a three-dimensional space that has a finite
volume and no edge? And that I'm going to
tell you right now, it's very hard for
us to visualize it. But in order to
visualize it, I'm essentially going to
draw the same thing as I drew right here. What you have to
imagine, and you almost have to imagine it by
analogy, unless you have some type of a
profound brain wired for more than three spatial
dimensions, is a sphere. So let me make it clear. This is a
two-dimensional surface. On the surface of
the sphere, you can only move into directions,
two perpendicular directions. You could move like that or
you could move like that. You could move left and right
or you could move up and down. So it's a
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. It's a three-dimensional surface
of a four-dimensional sphere. And I'm going to
draw it the same way. So if we kind of view
those three dimensions are just these two dimensions
of the surface, the same thing. It's the same thing. And if you imagine
that-- I'm not saying that this is actually
the shape of the universe. We don't know the actual shape. But we do know that it does
have a slight curvature. We don't know the actual shape,
but a sphere is the simplest. There's other ones we could do. A toroid would also fit the
bill of having a finite volume with no edge. And another thing, I
want to make it clear, we actually don't
even know whether it has just a finite volume. That's still an open question. But what I want
to do is show you that it can have a finite
volume and also have no edge. And most people believe-- and
I want to say "believe" here because we can just go
based on evidence and all that-- that we are talking about
something with a finite volume, especially when you talk
about the Big Bang theory. That kind of, on some dimension,
implies a finite volume, although it could be a super
large, unfathomably large volume, it is finite. Now, if you have this,
let's imagine this sphere. Let's imagine this sphere. Once again, if you're
on this surface of this four-dimensional
sphere-- I obviously can not draw
a four-dimensional sphere. But if you're on the surface of
this four-dimensional sphere, if you go in any direction,
you'll come back out and 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 will take an unbelievable
amount of time to traverse it. And if this sphere
itself is expanding, it might be expanding so fast
that light might not ever be able to come back around it. But in theory, if
something were fast enough, if something were to
keep going around, it could eventually
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-- 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 that if you go up
and you just keep going up, you'll eventually come
back from the bottom. So if you keep going
all the way up, you'll eventually come back
to the point that you were. 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 were to
go into the page-- so if you were to
go into the page-- let me draw it that way--
if you go into the page, you would 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 eventually
get back to where you are. So let's go back to the question
of an expanding universe, a expanding universe that's not
expanding into any other space. That is all of the space,
but it's still expanding. Well, this is the model. So you could imagine
shortly after the Big Bang, our four-dimensional
sphere looked like this. Maybe it was a little small
four-dimensional sphere. Maybe right at the
Big Bang, it was like this little
unbelievably small sphere. Then a little bit later,
it's this larger sphere. Let me just shade
it in to show you that it's kind of popping out of
the page, that's it's a sphere. And then at a later time, the
sphere might look like this. The sphere might look like this. Now, your temptation
might be to say, wait, Sal, isn't this stuff
outside of this sphere, isn't that some type of a
space that it's expanding into? Isn't that somehow
part of the universe? And I would say if you're
talking in three dimensions, no, it's not. The entire universe
is this surface. It is this 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-- so one way to view
the fourth dimension is it is time itself--
things are just getting further
and further apart. And I'll talk about more
evidence in future videos for why the Big Bang is the best
theory we have out there right now. But as you could
imagine, if you have two points on this sphere
that are that far apart, as this sphere expands, this
four-dimensional sphere, as this bubble blows up or
this balloon blows up, those two points are just--
let me draw three points. Let's say those
are three points. Those three points
are just going to get further
and further apart. And that's actually one of
the main points that-- or one of the first reasons why it made
sense to believe 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 you
there, something for you to kind of think
about a little bit. And then we'll build
on some of this to think about what it
means to kind of observe the observable universe.