Radius of Observable Universe

Right now, the best estimate
of when the Big Bang occurred--

and once again, I don't like
the term that much because it

kind of implies some
type of explosion.

But what it really is
is kind of an expansion

of space, when space
started to really start

to expand from a singularity.

But our best estimate
of when this occurred

is 13.7 billion years ago.

And even though we're used
to dealing with numbers

in the billions,
especially when we

talk about large amounts
of money and what not,

this is an unbelievable
amount of time.

It seems like something that is
tractable, but it really isn't.

And in future
videos, I'm actually

going to talk about
the time scale.

So we can really
appreciate how long,

or even start to
appreciate, or appreciate

that we can't appreciate how
long 13.7 billion years is.

And I also want to emphasize
that this is the current best

estimate.

Even in my lifetime, even in
my lifetime that I actually

knew about the Big Bang and
that I would pay attention

to what the best estimate
was, this number's

been moving around.

So I suspect that in
the future, this number

might become more accurate
or might move around some.

But this is our best guess.

Now with that said, I want to
think about what this tells us

about the size of the
observable universe.

So if all of the expansion
started 13.7 billion years ago,

that 13.7 billion
years ago, everything

we know in our
three-dimensional universe

was in a single
point, the longest

that any photon of light could
be traveling that's reaching us

right now-- so let's say that
that is my eye right over here.

That's my eyelashes, just like
that-- so some photon of light

is just to getting to
my eye or maybe it's

just getting to the
lens of a telescope.

The longest that that
could have been traveling

is 13.7 billion years.

So it could be traveling
13.7 billion years.

So when we looked
at that depiction--

this I think was two
or three videos ago,

of the observable universe--
I drew, it was this circle.

And when we see light coming
from these remote objects--

that light is getting
to us right here.

This is where we are.

This is where I guess
in the depiction

the remote object was.

But the light from
that remote object

is just now getting to us.

And that light took 13.7
billion years to get to us.

Now, what I'm going
to hesitate to do,

because we're talking
over such large distances

and we're talking on such large
time scales and time scales

over which space
itself is expanding--

we're going to see in this video
that you cannot say that this

object over here, this is
not necessarily, this is NOT,

I'll put it in caps, this is NOT
13.7 billion light years away.

If we were talking about
smaller time scales

or I guess smaller
distances, you

could say approximately that.

The expansion of the universe
itself would not make as much

of a difference.

And let me make it
even more clear.

I'm talking about an
object over there.

But we could even talk about
that coordinate in space.

And actually, I should say
that coordinate in space-time,

because we're viewing it at
a certain instant as well.

But that coordinate is not
13.7 billion light years away

from our current coordinate.

And there's a couple of
reasons to think about it.

First of all, think
about it, that light

was emitted 13.7
billion years ago.

When that light was
emitted, we were

much closer to that coordinate.

This coordinate was
much closer to that.

Where we are in the
universe right now

was much closer to that
point in the universe.

The other thing
to think about is

as this-- let me
actually draw it.

So let's go 300,000 years
after that initial expansion

of that singularity.

So we're just 300,000 years
into the universe's history

right now.

So this is roughly 300,000
years into the universe's life.

I guess we could
view it that way.

And first of all, at that point
things haven't differentiated

in a meaningful
way yet right now.

And we'll talk more
about this when

we talk about the cosmic
microwave background radiation.

But at this point
in the universe,

it was kind of this almost
uniform white-hot plasma

of hydrogen.

And then we're going
to talk about it.

It was emitting
microwave radiation.

And we'll talk more about
that in a future video.

But let's just think about two
points in this early universe.

So in this early universe,
let's say you have that point.

And let's say you have the
coordinate where we are right

now.

You have the coordinate
where we are right now.

And in fact, I'll just make
that roughly-- I won't make it

the center just because I
think it makes it easier

to visualize if
it's not the center.

And let's say at that very
early stage in the universe,

if you were able to just take
some rulers instantaneously

and measure that, you
would measure this distance

to be 30 million light years.

And let's just say
right at that point,

this object over here--
I'll do it in magenta--

this object over here
emits a photon, maybe

in the microwave
frequency range.

And we'll see that that was the
range that it was emitting in.

But it emits a photon.

And that photon is traveling
at the speed of light.

It is light.

And so that photon, says,
you know what, I only

got 30 million light
years to travel.

That's not too bad.

I'm going to get there
in 30 million years.

And I'm going to do it discrete.

The math is more complicated
than what I'm doing here.

But I really just
want to give you

the idea of what's
going on here.

So let's just say,
well, that photon

says in about 10 million years,
in roughly 10 million years,

I should be right about
at that coordinate.

I should be about one
third of the distance.

But what happens over the course
of those 10 million years?

Well, over the course of
those 10 million years,

the universe has expanded some.

The universe has expanded
maybe a good deal.

So let me draw the
expanded universe.

So after 10 million years, the
universe might look like this.

Actually it might even
be bigger than that.

Let me draw it like this.

After 10 million
years, the universe

might have expanded a good bit.

So this is 10 million
years into the future.

Still on a cosmological time
scale, still almost at kind

of the infancy of the
universe because we're

talking about 13.7
billion years.

So let's say 10 million years.

10 million years go by.

The universe has expanded.

This coordinate, where
we're sitting today

at the present time, is
now all the way over here.

That coordinate where the
photon was originally emitted

is now going to be
sitting right over here.

And that photon, it said, OK,
after 10 million light years,

I'm going to get over there.

And I'm approximating.

I'm doing it in a
very discrete way.

But I really just want
to give you the idea.

So that coordinate,
where the photon roughly

gets in 10 million light years,
is about right over here.

The whole universe has expanded.

All the coordinates have gotten
further away from each other.

Now, what just happened here?

The universe has expanded.

This distance that was 30
million light years now--

and I'm just making
rough numbers here.

I don't know the
actual numbers here.

Now, it is actually--
this is really just

for the sake of giving you the
idea of why-- well, giving you

the intuition of
what's going on.

This distance now is no
longer 30 million light years.

Maybe it's 100 million.

So this is now 100 million light
years away from each other.

The universe is expanding.

These coordinates, the space
is actually spreading out.

You could imagine it's
kind of a trampoline

or the surface of a balloon.

It's getting stretched thin.

And so this coordinate
where the light happens

to be after 10
million years, it has

been traveling for
10 million years,

but it's gone a much
larger distance.

That distance now might
be on the order of-- maybe

it's on the order of
30 million light years.

And the math isn't exact here.

I haven't done the
math to figure it out.

So it's done 30
million light years.

And actually I shouldn't even
make it the same proportion.

Because the distance it's gone
and the distance it has to go,

because of the
stretching, it's not

going to be completely linear.

At least when I'm thinking about
it in my head, it shouldn't be,

I think.

But I'm going to make a
hard statement about that.

But the distance that it
reversed, maybe this distance

right here is now 20
million light years

because it got there.

Every time it moved some
distance, the space that it

had traversed is now stretched.

So even though its traveled
for 10 million years,

the space that it
traversed is no longer

just 10 million light years.

It's now stretched to
20 million light years.

And the space that it
has left to traverse

is no longer only 20
million light years.

It might now be 80
million light years.

It is now 80
million light years.

And so this photon might
be getting frustrated.

There's an optimistic
way of viewing it.

It is like, wow, I
was able to cover

20 million light years
in only 10 million years.

It looks like I'm moving
faster than the speed of light.

The reality is it's not
because the space coordinates

themselves are spreading out.

Those are getting thin.

So the photon is just moving
at the speed of light.

But the distance
that it actually

traversed in 10 million
years is more than 10 million

light years.

It's 20 million light years.

So you can't just
multiply a rate times time

on these cosmological scales,
especially when the coordinates

themselves, the distance
coordinates are actually

moving away from each other.

But I think you see,
or maybe you might see,

where this is going.

OK, this photon says, oh, in
another-- let me write this.

This is 80 million light
years-- in another 40 million

light years, maybe I'm
going to get over here.

But the reality is over that
next 40 million light years--

sorry, in 40 million years,
I might get right over here,

because this is 80
million light years.

But the reality is
after 40 million years--

so another 40 million years
go by-- now, all of a sudden,

the universe has
expanded even more.

I won't even draw
the whole bubble.

But the place where the
photon was emitted from

might be over here.

And now our current
position is over here.

Where the light got after 10
million years is now over here.

And now, where the light
is after 40 million years,

maybe it's over here.

So now this distance,
the distance

between these two
points, when we started,

it was 10 million light years.

Then it became 20
million light years.

Maybe now, it's on the order
of-- I don't know-- maybe it's

a billion light years.

Maybe now it's a
billion light years.

And maybe this distance
over here-- and I'm

just making up these numbers.

In fact, that's probably be too
big for that point-- maybe this

is now 100 million light years.

This is now 100
million light years.

And now, maybe
this distance right

here is-- I don't know--
500 million light years.

And maybe now the total
distance between the two points

is a billion light years.

So as you can see, the photon
might getting frustrated.

As it covers more
and more distance,

it looks back and says, wow,
in only 50 million years,

I've been able to cover
600 million light years.

That's pretty good.

But it's frustrated
because what it thought

was it only had to cover
30 million light years

in distance.

That keeps stretching
out because space

itself is stretching.

So the reality, just going
to the original idea,

this photon that is
just reaching us,

that's been traveling
for-- let's say

it's been traveling
for 13.4 billion years.

So it's reaching us is just now.

So let me just fast
forward 13.4 billion years

from this point now to
get to the present day.

So if I draw the whole visible
universe right over here,

this point right
over here is going

to be-- where it was emitted
from is right over there.

We are sitting right over there.

And actually, let me
make something clear.

If I'm drawing the whole
observable universe,

the center actually
should be where we are.

Because we can observe
an equal distance.

If things aren't
really strange, we

can observe an equal
distance in any direction.

So actually maybe we should
put us at the center.

So if this was the entire
observable universe,

and the photon was emitted from
here 13.4 billion years ago--

so 300,000 years after
that initial Big Bang,

and it's just getting
to us, it is true

that the photon
has been traveling

for 13.7 billion years.

But what's kind of nutty about
it is this object, since we've

been expanding away from each
other, this object is now,

in our best
estimates, this object

is going to be about 46 billion
light years away from us.

And I want to make
it very clear.

This object is now 46 billion
light years away from us.

When we just use light to
observe it, it looks like,

just based on light
years, hey, this light

has been traveling 13.7
billion years to reach us.

That's our only way
of kind with light

to kind of think
about the distance.

So maybe it's 13.4
or whatever-- I

keep changing the decimal-- but
13.4 billion light years away.

But the reality is if you had a
ruler today, light year rulers,

this space here has
stretched so much

that this is now 46
billion light years.

And just to give
you a hint of when

we talk about the cosmic
microwave background

radiation, what will
this point in space

look like, this
thing that's actually

46 billion light years
away, but the photon only

took 13.7 billion
years to reach us?

What will this look like?

Well, when we say
look like, it's

based on the photons that
are reaching us right now.

Those photons left
13.4 billion years ago.

So those photons are
the photons being

emitted from this
primitive structure,

from this white-hot
haze of hydrogen plasma.

So what we're going to see
is this white-hot haze.

So we're going to see this kind
of white-hot plasma, white hot,

undifferentiated
not differentiated

into proper stable atoms,
much less stars and galaxies,

but white hot.

We're going to see
this white-hot plasma.

The reality today is
that point in space

that's 46 billion
years from now,

it's probably differentiated
into stable atoms, and stars,

and planets, and galaxies.

And frankly, if that
person, that person,

if there is a civilization
there right now

and if they're sitting right
there, and they're observing

photons being emitted
from our coordinate,

from our point in
space right now,

they're not going to see us.

They're going to see us
13.4 billion years ago.

They're going to see the
super primitive state

of our region of
space when it really

was just a white-hot plasma.

And we're going to talk more
about this in the next video.

But think about it.

Any photon that's coming
from that period in time,

so from any direction,
that's been traveling

for 13.4 billion years
from any direction,

it's going to come from
that primitive state

or it would have been
emitted when the universe was

in that primitive
state, when it was just

that white-hot plasma,
this undifferentiated mass.

And hopefully,
that will give you

a sense of where the
cosmic microwave background

radiation comes from.