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## Cosmology and astronomy

### Unit 1: Lesson 4

Big bang and expansion of the universe- Big bang introduction
- Radius of observable universe
- Radius of observable universe (correction)
- Red shift
- Cosmic background radiation
- Cosmic background radiation 2
- Hubble's law
- A universe smaller than the observable
- How can the universe be infinite if it started expanding 13.8 billion years ago?

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# Big bang introduction

Created by Sal Khan.

## Want to join the conversation?

- If the universe is the surface of the sphere, then what is inside the sphere?(289 votes)
- The difficulty is in imagining or visualizing geometry in more than 3 dimensions.The sphere is merely an analogy for trying to understand how there can be a finite volume with no edges. In reality there is not an actual sphere, so the question of what is inside of it is not really a valid question.(230 votes)

- What did things look like BEFORE the universe had a "big bang" and what caused it?(81 votes)
- We have no idea, there is no way for our current theories can not tell us.

I just posted this on a similar question posted here 4 hours ago. I like the response Stephen Hawking gave to a question like this: Asking what was before the big bang is like asking what is 1 km north of the north pole.(109 votes)

- I've heard that it was Edwin Hubble who first discovered that our universe is expanding, but I read an article recently that claimed there was an astronomer who had come to the same conclusion as Hubble, a few years before.

So who is, currently, credited as first having made this discovery, and what led them to it?(20 votes)- Lemaitre's 1927 paper already contained a version of what is now known as the Hubble's Law. So no. Hubble still didn't discover or figure the equation out. The 2 main reasons why Lemaitre was not credited is that because his scientific paper was published in an obscure Belgian scientific paper rather than a more notable one. And second, the translated English version of his 1927 paper in 1931 omitted the equation. There has been a great deal of debate about this amongst scientists whether this was intentional or not.(5 votes)

- At6:14he says that we know there is a slight curvature to space. I thought this topic was still up for debate and there have been tests indicating it is actually flat.(24 votes)
- Ok, I am not an expert, but as far as I know there are three "shapes" of the universe: Open, Closed, and Flat. Closed is a universe much like a sphere, where if you had a powerful enough telescope, you will eventually be able to look at the back of your head. Open is the exact opposite. Scientists classify the three is based on the curvature of the universe. Think of it like this: C (curvature) =1 if there is no curvature. (It's one because the line is still in existence, similar to how a straight line (180 degrees) is still an angle) C>1 if it is closed, meaning that curvature is positive. An Open shape is C<1. A flat universe is C=1.

The WMAP (Wilkinson Microwave Anisotropy Probe) measurements proved (and I use that word with a grain of salt) that the universe IS CURRENTLY (Have no idea about the shape of the universal expansion.) flat within a 0.4 margin of error.

Was the WMAP what you were referencing?(7 votes)

- Is the theory of the 4th dimension similar to something like the "void?" I mean, is the universe expanding into nothing, or does the universe create space as it expands? Also, if we imagine the 4th dimension as a sphere, and are able to theorize that traveling light would eventually circle back to its origin, are we able to say the universe is expanding? Wouldn't that necessitate that light travels at least slightly faster than the expanding universe, and wouldn't this eventually confuse our perspective of things like stars and planets? Would we have ever seen light from the nearest star if light traveled slower than the expanding universe? I understand that this would happen over an astronomical amount of time, but am I conceptualizing the theory accurately?(16 votes)
- Many questions, I like the spirit.

- The model Sal describes is a finite 3D-surface on a 4D-sphere.

- However, if the universe is infinite, spacetime is stretched but always the same size. Think of all positive integers as one infinity and then stretch it by multiplying every number by 2. The distance increases between numbers but you still have infinity.

- If it is finite, you could argue that it not only stretches, but rather grows into something 'outside' or 'nothing' as you call it (Sal alludes to that around9:25). We don't know which is true - finite or infinite - only that the distance between galaxies increases.

- Sal addresses your question about light in following videos. But to answer: Einstein does allow for objects to move FTL in one sense, by bending space. One analogy is bending a 2D-page of paper curving so much in 3D that the edges touch. Something crossing the edges will travel at a speed not greater than lightspeed but appear to have travelled FTL because it technically 'crossed' the entire length to any outside observer. The reverse is also possible of course that by stretching space, light could appear to travel slowly.

I hope I understood your questions correctly and that this helps.(12 votes)

- Sal talks in his first analogy about how the universe would be two dimensional, would be finite, and would have no edge. Then he has us think of a sphere. I can see how a sphere is finite and has no edges, but it is not two dimensional. Is there a better analogy?(11 votes)
- If one is only talking about the
**surface**of a sphere, that surface is actually only two-dimensional. I can get anywhere I want to on the surface of the earth by going in the East or West direction or by going in the North or South direction or a combination of these two directions. I don't need a "go up or go down" direction to reach any point on the surface of the earth.(14 votes)

- if everything is moving apart from each other, does that mean the we are moving or we might move away from the sun?

thanks a ton!(10 votes)- No, expansion is very weak and only able to overcome the attractive force of gravity over extremely large distances. You have to get past the local galaxies before expansion is capable of overcoming the gravitational bond of objects.(14 votes)

- is it possible that the universe is expanding so fast that the velocity of light relative to the velocity of the expanding universe around it becomes zero(8 votes)
- Very distant parts of the universe are already moving away from us faster than the speed of light. If you were there, you'd measure light moving at the speed of light. From here, we'll just never see that light. I suppose you could think of that as though the "net velocity" of the light toward us is zero, or even negative.(4 votes)

- At5:17, why can't you move diagonally?(6 votes)
- that's just a combination of the other two perpendicular directions(4 votes)

- Two dimension - length x breadth

Three dimension - length x breadth x height

Then what is 4 dimension?(3 votes)- It depends if you mean 4th spatial dimension or just any old 4th dimension. Time can be considered A fourth dimension, but of course it is not a 4th spatial dimension. If there is a 4th spatial dimension that we are unable to perceive or picture in our minds, then it would make sense that we would not have a common word for it to go along with length, breadth, and height, right?(6 votes)

## Video transcript

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.