
Title:
17. Hubble's Law and the Big Bang (cont.)

Description:
Frontiers/Controversies in Astrophysics (ASTR 160)
Class begins with a review of magnitudes and the problem set involving magnitude equations. Implications of the Hubble Law and Hubble Diagram are discussed. Professor Bailyn elaborates on the Big Bang theory of cosmology and addresses controversial questions related to the age, development, and boundaries of the universe. The fate of the universe, and possibly its end (known as the Big Crunch) are addressed. Imagining an expanding threedimensional universe is proposed. The lecture ends with a questionandanswer session during which students inquire about a variety of topics related to cosmology, such as the center of the universe, its current expansion, and hypothetical collapse.
00:00  Chapter 1. Review of Magnitudes
07:38  Chapter 2. Implications of Hubble's Discoveries on the Aging Universe
26:36  Chapter 3. Conceptualizing a ThreeDimensional Universe
34:22  Chapter 4. Q&A: The Big Bang, the Expansion, and the Big Crunch
Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses
This course was recorded in Spring 2007.

Professor Charles
Bailyn: Okay,

welcome back for more
cosmology.

What I want to do today is
quickly review what we were

doing about magnitudes and make
a comment or two about the

problem set,
and then, go back and talk

about the implications of the
Hubble Law and the Hubble

Diagram,
which are formidable,

to put it mildly.
Okay, magnitudes.

There's a couple of these
magnitude equations.

I'm just going to write them
down.

The first of them looks like
this.


And this equation is usedokay.
So, this equation is used to

relate magnitudes of two
different objects to each other.

So, we've got two different
objects.

And it can be used for either
kind of magnitudeeither

absolute or apparent magnitude,
just so long as you don't mix

them.
So, it's two different objects,

but only one of the magnitudes.
One kind of magnitude.

And depending on which kind of
magnitude you use,

this brightness ratioit's
either the ratio of how bright

it looks or the ratio of how
bright it iswhatever's

appropriate.
Now, on the help sheet on the

web, I have this equation in a
somewhat different form,

and it's important to realize
that it's the exact same

equation.
Watch this.

Let's see.
Let's multiply both halves by 

2/5 which is  0.4.
So, this is 0.4

(M_1 –
M_2) = log

(b_1 /
b_2).

And then, let's take 10 to the
power of that.

That gets rid of the log.
And this is now the form that

it is on the help sheet on the
web.

So, it's exactly the same
equation, just expressed

differently.
And you can use either form,

whichever is more convenient.
Okay.

The other equation looks like
this.

5 log (D/10 parsecs).
And this relates one object,

but it relates both kinds of
magnitude to each other.


So, the first one is two
different objects,

but only one of the magnitudes.
The other is one object and it

relates the two different kinds
of magnitudes to each other,

and to the distance to the
object.

And as you can see,
thisboth of these equations,

actually, have three unknowns.
One, two, three.

That means you've got to know
two things in order to find out

the third.
And that brings me to the

comment I want to make about
problem 2a on the current

problem set.
You are asked in this problem

to determine the difference
between the absolute magnitude

of one kind of star,
called Type 1 Cepheid,

so I label it C1.
And another kind of star,

Type 2 Cepheids,
which I label C2.

And if you're asked toand
this difference is called,

I don't know,
delta M_C or

something like that.
And having been asked to do

this, the logical thing that you
might try to do is say,

all right, I'm going to use one
or the other of these

equationsI'm not sure,
in advance, which,

to compute this one.
Then I'm going to compute this

one.
And I'm going to subtract the

two, and that's going to give me
the answer.

That approach will fail.
Okay?

That doesn't work in this
particular case,

because you don't actually have
enough information to compute

either one of these things.
You do have enough information

to compute the difference.
And let me just give you a very

brief hint on how you might go
about doing that.

Let's see.
Let me take a new piece of

paper here.
Write down

m_C1 
M_C1 = 5 log

(D_C1 /
10parsecs).

And now write the exact same
equation down for C2,

where the two different
distances are the distances you

get by assuming one or the other
kinds of these magnitudes.

This is equation one.
This is equation two.

Now, let's subtract.
1 – 2.

So, then, you get
m_C1 

m_C2 
[M_C1 

M_C2]
= 5 (log D_C1

 log D_C2).
Okay, now.

Here's the trick.
Turns out for reasons that you

had better tell meand TFs
[teaching fellows],

take note that we really want
them to say why this is true,

now that I've told them it is.
This is zero.

The two apparent magnitudes are
the same.

And so, that means that this
side of the equation is what you

want.
It's the difference between

these two magnitudes.
And then, over here,

you have to use one of these
log rules: log (x)  log

(y),
if you remember back to

eleventh grade,
is log (x / y).

And if you use that,
it turns out that you have

information elsewhere in the
problem, which will tell you

what you need to know about the
distances.


And so, in this way,
you can solve for the

difference without actually
being able to determine either

one of these two things.
So, we'll just leave it at that

for the moment.
If you have problems there's

the usual forum,
there's the usual office hours,

but ponder this.
That's basically how the

problem has to go.
Okay?

Problems with magnitudes?


Okay.
If you do have some,

let us know,
because this is going to be

critical for solving,
basically, problems for the

whole rest of the class.
All right.

Yes go ahead.
Student: What is the

locationthe last thing in
green Professor Charles

Bailyn: This?
Student: 5 logis it

over log?
Professor Charles

Bailyn: This is log
(D_C1 / 10

parsecs)  log
(D_C2 / 10

parsecs).
That's just subtracting the two

righthand sides of this
equation.

But then, you get to do the log
thing and divide them instead,

which is this to this on this
log subtraction.

Okay.
Let me remind you why we're

putting ourselves through this
pain.

Okay?
Recall why we started doing

this in the first place.
The goal was to figure out how

to measure the Hubble Diagram.
The Hubble Diagram is this

diagram of velocity,
which you can measure by

redshift versus distance.
And the whole reason we

embarked on this adventure in
magnitudes was because that's a

critical component in how you
determine the distance.

But if you've got a bunch of
galaxies and you measure these

two quantities for each one of
them,

what you discoverwhat Hubble
discoveredwhat Edwin Hubble

discovered many years ago,
is that they line up.

You get this perfect;
well, not quite perfect,

but close to itthis beautiful
straight line,

if you measure a bunch of these
things.

And the way you represent that
straight line is with this

equation, where H is
Hubble's Constant.

And so, that's the purpose of
all this magnitude stuff,

is to be able to determine the
yaxis of this plot.

What I now want to do is talk
about the implications of this

observational fact that galaxies
line up on this line.

It turns out,
this is one of the most

profound plots in all of
astrophysics,

and possibly all of science.
Because what this implies is,

first of all,
that the Universe is expanding,

and hence, it's the basis for
the whole Big Bang Theory of

cosmology.
And by performing relatively

simple calculations using this
quantity H,

you can determine the age of
the Universe,

and the ultimate fate of the
Universe.


Not bad for a relatively simple
algebraic equation.

Yes?
Student: [Inaudible]

Professor Charles
Bailyn: Huh?

Student: [Inaudible]
Professor Charles

Bailyn: Oh,
fate.

I'll get back to that.
The big question in cosmology

is, you knowthe Universe is
now expanding.

The question is,
will it continue to expand,

in which case,
the Universe just gets sparse

and cold and boring,
and expands forever until

there's, you know,
one pathetic hydrogen atom

every cubic megaparsec of space.
Or, alternatively,

it could stop,
slow down, and recollapse into

something called a Big Crunch,
which is sort of the Big Bang

run backwards,
and basically the whole thing

turns into a massive black hole.
These areyou know,

this is ending in fire or in
ice, I guess.

And it can be computed in ways
we'll describe later.

Okay, so, here's what I want to
do.

I want to start understanding
how this plot and this little

equation gives you all these
wonderful things.

I'm going to go on for a little
while, then we'll pause,

and we'll do one of these Q
& A sessions,

because this is sort of the
heart of the Big Bang Theory.

And so, we'll do one of these
things that we did when we were

talking about relativity,
where you talk to each other

and come up with questions.
So, if you've got questions

along the way,
by all means,

ask them, but we will have a
specific moment a little ways

down the line where we actually
pause and do this on purpose.

So, everybody,
keep thinking as we go along,

what are your questions?
What don't you understand or

what questions could you ask to
understand more than what I've

just told you?
Okay.

Here we go.
Imagine a onedimensional

Universe, just because it's easy
for me to write down.

And here's our onedimensional
Universe.

It's all strung out on a line.
Here's the line.

And it's got a bunch of
galaxies on it.

Let's label these galaxies,
A, B,

C, D,
E, and F.

And these galaxies are spaced
evenly, let us imagine.

And we'll give them coordinates.
So this is at 0,1,

2, and so forth.
Okay?

Now, next thing we're going to
do: the Universe is going to

double in size.
So, we're just going to stretch

the thing.
The whole thing is going to get

stretched.
So, here's our Universe.

And now A,
B, C,

D, E and F
are further apart by a factor of

two.
A, B,

C, D, E,
F. And if A,

we imagine stays at the same
coordinateif our coordinate

system starts with A,
this means B is now at 2.

C is 46,8 and 10.
Okay.

And let us imagine that it
takes one time unitone year or

something like that,
for this doubling to take

place.
Now, we're going to ask,

if you sitif you live in
galaxy A,

if you live on planet A,
and you observe the distance

and velocity of all these other
galaxies, what's it going to

look like?
So, observer on A.

And so, we're going to observe
a particular galaxyone of

these other galaxies.
We're going to write down the

distance.
We'll choose the distance at

the start, because it's going to
change.

Then we're going to evaluate
how that galaxy has moved,

and then the distance changed.
And then, over here,

we're going to get the
velocity.

The velocity is going to be the
change in distance divided by

the change in time,
which we've defined to be one

time unit.
Okay?

So, galaxy B.
Galaxy B starts at a

distance of 1 away from us,
because it starts 1.

A starts at 0.
It moved from 1 to 2,

and that gives it a change in
distance of 1 and therefore its

velocity over this time,
it's changed in distance by 1,

it's taken 1 time unit.
The velocity is 1 divided by 1,

equals 1.
Okay?

The algebra is easy.
Okay, so, how about C?

C starts 2 away.
Its motionit goes from 2 away

to 4 away, and so,
the change in its distance is

2.
And since it takes 1 time unit

to do, its velocity is 2/1,
which is equal to 2.

See, the algebra is simple,
but I screw it up.

Bethany is laughing at me and
well she might,

but I caught myself.
All right.

And so on down the line.
I could repeat this simple

exercise.
D, E,

F start at 3,4,
and 5.

Goes from 3 to 6,
from 4 to 8,

from 5 to 10,
and their velocities are 3,4,

and 5, respectively.
And so, if I plot distance

versus velocity,
I'll get points lined up just

like this.
And so, basically,

what happens is this.
If you take a set of points on

a coordinate system and you
simply stretch the coordinate

system,
what happens is that the

further away you start,
the greater the stretch is.

And so, there is a correlation
between how far away you start

and how fast the thing recedes
from you.

Now, this is true regardless of
which point you sit on.

Let's imagine that we sit on
pointthat the observer is on

point E.
So, on point E, we're

now going towhich galaxy,
initial distance,

motion, velocity.
So, this is the same

plotchart as before.
Elet's look at

F, starts at a distance
of 1 because it's 1 unit away.

The motionokay,
at the start it'slet's take a

quick look at how this is set up
here.

Yes, E is at 4.
So, at the start,

the distance is between 4 and
5, which is 1.

And it goes to a distance of 8,
which is where E ends

up, and 10, which is where
F ends up.

So that is a change of 2.
No a change of 1, right?

Because it's gone from 1 away
to 2 away, and the velocity is

1.
If we look at D,

it starts at a distance of 1,
goesstarts at 4 to 3,

that's one separation.
Goes to 8 to 6,

that's a separation of 2.
Delta D is again equal

to 1.
Velocity is equal to 1.

Let's look, for example,
at B.

That starts 3 away.
And it starts from 4B,

C, yeahfrom 4 to 1.
And it goes from 8 to 2.

So, that's a difference of 6
here, a difference 3 there.

And so delta D is equal
to 3.

And so, the velocity is once
again 3.

And so, you get the exact same
plot with different galaxies,

because you're sitting in a
different place.

So, it doesn't matter which
galaxy you're sitting on.

You see the exact same ratio of
distance to velocity and you

create the exact same Hubble
flow no matter which galaxy you

sit on in this little toy
Universe.


So, that's the key pointthat
if you take a coordinate system

and you expand it,
you naturally get this

relationship between distance
and velocity.

Or to turn it around,
if you observe this

relationship between distance
and velocity,

then what you're looking at is
a system in which all the

coordinates arein which you've
simply stretched the coordinate

system.
Okay.

Now, this gives rise tothis
analogy, with these stretching

onedimensional lines gives rise
to two questions people have,

which I like to call
unquestions,

because they're actually
questions that arise because of

the analogy,
not because of the way the

Universe works.
One question is,

Q1: "Where is the center?"
You know, here's your line.

It's expanding.
But somewhere in the middle

here, around C or
D in our thing,

is the center away from which
everything is expanding.

So that's one question.
And the second question is,

"What is it expanding into?"


You know, here you have a
little Universe and it's moving

outwards.
And so, what's going on over

here?
What was there before the

Universe moved into it?
These kinds of questions.

And those kinds of questions
come about because this is

actually a bad analogythis
straight line Universe.

So, let me give you a slightly
better one.

We'll stick with the
onedimensional Universe,

but now we'll do it this way.
Here's a onedimensional

Universe.
You have to stay on the line.

So here's A,
B, C, D, E, F,

whatever.
And it's going to expand.

And it's going to expand into
something that looks like this:

A, B, C, D,
E, F. And all of what we

just did about the velocity,
and so forth,

remains the same.
But, notice that this system is

unbounded.
There's no edge.

There's no edge.
There's no place where you can

say, this is the end of the
Universe, because if you

traveled around it you'd just
come back to where you were,

and therefore,
there's also no center.


And where does it expand into?
It expands into a dimension

that, if you're a
onedimensional creature,

you can't experience because
the whole thing is being pushed

out.
But if you're forced to live on

this circle you can't evenyou
have no comprehension of what it

expands into.
It expands into a higher

dimension.


But all of this stuff about,
you know, velocity and

distance, remains basically the
same.

Here's a twodimensional
analogy.

Let's see, this isso,
I made a little diagram of the

Old Campus [an area of the Yale
campus].

Here's Linsley–Chittenden [a
classroom building]

where we're sitting right now,
yes?

Here's the statue of Abraham
Pierson.

This is the gate between Durfee
and Wright [two undergraduate

dorm buildings].
Here's Phelps Gate [a classroom

building and the entrance to Old
Campus].

Here's Vanderbilt [a dorm
building].

This is Harkness Tower and
here's Starbucks.

Okay, that's all that's
important, right?

So, you following me with that?
And what I did was,

I took this little picture and
I took it to the Xerox machine

and I blew it up by 20%.
So, here's the exact same

diagram blown up by 20%.
So, now, supposing we're

sitting in LinsleyChittenden,
which we happen to be doing,

and the Universe expanded by
20%or, our little corner of

the Universe expanded by 20%,
here's what would happen.

Now, notice what's happening.
Every object in the Universe is

moving away from us.
See?

Here's where Harkness was,
and now it's moved a little

further, in a straight line away
from us.

Here is Pierson,
and he's moved a little

further, straight away from us.
And here's Phelps,

and it's moved a little
further, straight away from us.

And let me erase those lines,
because what I want to

demonstrate is that if you're
anywhere else in this Universe,

the exact same thing happens.
Here we're now sitting on that

statue, and LinsleyChittenden
is moving away from us.

Harkness is moving away from us.
Phelps is moving away from.

Starbucks is moving away from
us, and so forth.

Similarly, if you're sitting in
Starbucks, waiting for students

to come by or something,
the exact same thing happens.

And now, because the distances
are greater, you can see the

effect that the velocity is
greater at greater distances.

If I'm looking down at
Vanderbilt, it moves straight

away from me,
but only a little bit.

If I'm looking all the way
across Old Campus,

this gate moves a lot away from
me.

And so, once again,
you have a situation in which

the further away
someeverything is moving

straight away from you,
but the further away it is,

the faster it's moving away,
right?

And that's just a consequence
of the fact that you have taken

this geometry and expanded it.
And so, wherever you sit in an

expanding geometry,
every object you see will be

moving directly away from you.
And the further away it is,

the faster it will be moving,
which is Hubble's law.


Oh, and one other thing about
this nice analogy,

here.
Let us imagine for a second

that this tiny piece of a tiny
Universe is actually not a flat

plane,
but is sitting on a curved

surface, which is curved all the
way round into a big ball.

That's actually not so hard to
imagine because it's true.

This sits on the surface of the
Earth.

And so, what is happening when
this thing blows up by 20% is,

basically, somebody has taken a
valve to the Earth and has blown

the Earth up by a factor of 20%.
And that would have this effect.

And it would have the exact
same effect everywhere else on

the surface of the Earth.
And the Earth,

you knowwhere is the center
of the surface of the Earth?

You can answer the question:
"Where is the center of the

Earth?"
But you can't answer the

question of where is the center
of the surface of the Earth.

Because wherever you sit,
whether you're sitting at

Starbucks or in Phelps Gate or,
you know, in Los Angeles

somewhere or wherever,
if they blow the Earth up by

20% you're going to see this
exact same effect.

Everything will be moving away
from you.

The further away something is
the faster it will be moving.


So that's the oneyes,
go ahead.

Student: Someone in the
back apparently [inaudible]

Professor Charles
Bailyn: Yeah,

talk.
Student: If something's

far enough away from you would
it appear to be moving at the

speed of light?
Professor Charles

Bailyn: Yes,
yes, good question.

If something's far away from
you, will it appear to be moving

at the speed of light?
Yes, it will,

and that's one of the
fundamental differences between

the motion of an object due to
what's called the Hubble Flow,

due to the expansion,
and ordinary motion of objects.

Now, if something's moving
faster than the speed of light,

of course, you can't see it,
because the light from that is

redshifted down to greater than
infinite wavelengths.

So, the photons don't have any
energy left.

But, let me come back to the
question after I do one more

thing.
That's a good question.

Here's the thing I want to do.
So, we've had the

onedimensional case,
the circle.

We've had the twodimensional
case, the expanding sphere.

Of course, what we want is the
threedimensional space.

Okay, here we are in three
dimensions.

Someone is expanding the
Universe, so everywhere we look,

everything is going away from
us, and the further away it is,

the faster it's going.
What's it expanding into?

Well, that, we have a little
more trouble visualizing,

right?
Because in one dimension,

you can visualize this circle
expanding onto the plane.

In two dimensions,
you can imagine this spherical

surface expanding.
In three dimensions,

we can't imagine what it's
expanding into.

That's beyond us.
And so, having had this failure

of the imagination,
what do you do?

You resort to mathematics.
That's what we always do.

And so, imagine that every
object has a position,

which is denoted by three
coordinates,

three spatial coordinates
x, y,

and z. But now,
let's imagine that every

object's position has this
coordinate system times a scale

factor,
which is a function of T.

So, it's a scale factor times a
coordinate position.


And there are two ways that
things can change their

position.
One is, they can move;

they can change their x,
y, z position.

This is the equivalent of
somebody walking across the Old

Campus.
You walk from Starbucks to

Phelps Gate, or something like
that, and you change your x,

y, z coordinate position by
moving through space.

So, changes in position,
which is to say,

velocity, can be accomplished
in two ways.


One is motion through the
coordinate systemthat is to

say, changing your x,
y, and z.

This is called peculiar motion.
That's a jargon.

And it's called peculiar
because one object can have a

different peculiar motion from
every other.

It's peculiar in the
oldfashioned sense meaning

specific to one object.
So, you have a peculiar motion

that's all your own.
I have one that's all mine as

we move through x,
y, and z.

But the other is just the
effect of the change.

And in particular,
in the case of the current

Universe, the increase in the
scale factor.


And these two kinds of velocity
are conceptually different from

each other.
Because you don't have to do

anything to change your position
in this way.

You just sit there.
You don't expend any energy.

You don't have any requirement
to expend energy or to exert a

force or to do any of these
things that we ordinarily do to

change our position.
You just sit there and the

Universe expands you,
or expands your position.

And that's why,
going back to your question,

that's why it's possible for
this kind of velocity to turn

out to be greater than the speed
of light,

if it's far enough away,
whereas, it's not possible

here.
What the effect of having this

kind of velocity be faster than
the speed of light does,

is it makes the object
impossible to see,

because photons coming off them
would be redshifted into

oblivion.
And so, you can't actually see

them.
And this imposes a kind of

cosmic event horizon,
similar in kind to the event

horizons around black holes.
You can't see events on the

other side of these horizons.
All right, let me go backwards

in time.
Back in time to when this scale

factor A of T is
equal to 0.

So, if the scale factor is
expanding, you know,

the Old Campus,
whatever, is expanding,

and you reverse time and you
think about what happened long

ago, it must have been smaller.
So this A factor must

have been smaller.
And if you go back a sufficient

amount in time,
you go back to the point where

A is equal to 0.
So then, what does the Old

Campus look like?
Looks like this, right?

It's all beenimagine I take a
Xerox machine and I demagnify

the thing down to 0% of its
original size,

or 0 plus epsilon,
perhaps.

What does that little diagram
look like?

It looks like a tiny little dot.
A single point,

except it isn't a single point.
What it is, is it's many points

superposed on each other.
And not only is the Old Campus

in thereimagine you've taken
this sphere that is the Earth

and collapsed its radius down to
0.

Not only the Old Campus is
there, but so is the rest of New

Haven, so is Connecticut,
so is Los Angeles,

so is the whole rest of the
surface of the Earth.

All of the points that will
eventually make the surface of

the Earth are superposed on one
another.

And yet, the whole geometry of
the Earth, of the Old Campus,

whatever, is already somehow
encoded in that point.

Because, you know,
you're taking 0 times x,

y, z for every
point.

But then, if you increase this
so that it becomes epsilon or

some nonzero number,
times x,

y, z, then you
already get the geometry of the

Old Campus and everything else
on the surface of the Earth.

So, it is wrong to think of the
Big Bang as starting at a point

and expanding into space.
That's kind of the impression

that word the Big Bang gives
you.

And you think,
naturally enough,

of an explosion,
where something at a point

explodes into empty space.
But that's not right.

All the space,
all the empty space is

contained in that point.
It's all in there.

It's just, it's all multiplied
by 0, so it all comes out to be

on top of each other in the same
place.

How are we doing?
Wonderful.

Okay, that's the essence of the
Big Bangthe whole idea of the

Big Bangthat what is happening
is that the whole coordinate

system of the Universe is
multiplied by this constant.

And that constant changes in
time.

It gets bigger.
And that fact is inferred from

the observations of these
galaxies.

That you observe galaxies,
and that they're moving away

from us.
But more than thatthat

there's a linear relationship
between how far away from us

they are and how fast they're
moving.

That implies this kind of
coordinate expansion.

And if you run it in reverse,
it implies an origin to the

Universe at some specific time
in the past.

All right.
Let's have questions.

I'll tell you what.
Talk to each other.

Come up with good questions,
and remember how we do this.

When you come up with a
questiona question can be

either to explain some of this
or to expand upon it.

When you're ready with a
question, put your hand up.

I'll answer a few of them while
other people are getting their

questions together.
And then we'll answer as many

of them as we have time for in
the remainder of the class.

So, talk to each other.
Talk amongst yourselves.

Come up with a question,
any question.

All questions are good,
and see what you can do.

I'll come around and try and
answer some of these.

Yeah – so,
talk to each other by all

means.
Yes?

Student: There is a
center of the Universe,

isn't there?
Professor Charles

Bailyn: No.
Student: Well,

I mean, like,
there's got to be a point in

the Universe at which,
like, all other pointsor all

other points that are furthest
away from that point are

expanding equally fast,
right?

Professor Charles
Bailyn: No.

Well, that's true of every
point in the Universe.

That's true of every point in
the Universe.

If you're sitting on the statue
of Pierson, everything at the

same distance is moving away
from you by the same amount.

That's true of every point.
Student: Oh, I see.

Professor Charles
Bailyn: Yeah.

Student: So,
wait, so, like,

is it, like,
in four dimensions,

then?
Professor Charles

Bailyn: Imagine a
threedimensional thing

expanding into the fourth
dimension the way the surface of

a sphere expands into three.
Student: Okay, thank you.

Student: If you switched
from the expansion to getting

close together,
would it precipitate the point

at which the expansion
[inaudible]

Professor Charles
Bailyn: Oh we'll talk about

that later.
You can imagine that gravity is

going to slow the expansion
down.

But at the moment I'm just
thinking about running backwards

in time.
Student: Okay,

and at some point you got to do
expansion [inaudible]

Professor Charles
Bailyn: Yeah,

or could.
Yeah?

Student: I don't
thinkso have you had like one

of those fake event horizons
where something could be

likeappear to be moving faster
than the speed of light?

Could you then likein like a
normal event horizon you can't

pass information between them
[inaudible]

Professor Charles
Bailyn: Right.

Student: But could you,
like relay information?

Professor Charles
Bailyn: Yes,

but by the time you had done
thatthat is to say,

the Universe is expanding
faster than the information

would get to you.
So, you know,

by the time you've moved your
information from here to here,

the distance from here to here
has expanded.

And so, it's not actually
getting any closer.


Okay, let's have a few of these.
Yes, go ahead.

Student: Well I
havefirst, just simply,

I didn't understand why it's 0
times the coordinate,

why there's a point at all and
why there's just nothing.

Why there's not [inaudible]
Professor Charles

Bailyn: Well,
okay.

So, if A is equal to 0
here, then all events are at

0,0, 0.
So, that point of 0,0,

0 is occupied,
if you want to think of it that

way.
It's the pointthe point in

question is the one at 0,0,
0.

And if you have anything in
here times 0,

that's where you're going to
end up.

And as you go backwards and run
this scale factor down to 0 as

you think about going back in
time,

everything's going to end up
closer and closer to 0.

And then, at the moment when
this equals 0,

it's all piled on top of
itself.

Does that make sense?
Yeah go ahead.

Student: Everything has
to be equidistant [Inaudible]

Professor Charles
Bailyn: No,

no, no, no, no.
Imagine Student:

[Inaudible]
Professor Charles

Bailyn: Oh,
in the other dimension.

Student: Yes.
Professor Charles

Bailyn: Yeah,
okay.

In the higher dimension,
that's true.

Well, okay, let me back off.
That's true if you have

constant curvature.
You could imagine something

that, you know,
looks like this,

that also expands in exactly
the same way.

And what creates the curvature
of spacetime?

Gravity.
And so, we're going to end up

in a situation where we're going
to be able to determine what the

curvature of space is by seeing
how much mass there is.

So, this actually relates back
to part two of the course.

Student: So,
is that why time could move

differently?
Professor Charles

Bailyn: Huh?
Student: Time could move

differently.
Professor Charles

Bailyn: Time could move
differently, too.

Yep.
Yes?

Student: Isn'tin the
onedimensional circle and you

said that thing's expanding to a
higher dimensionwhat does that

mean?
Professor Charles

Bailyn: Okay.
So, imagine you're a

onedimensional creature.
You can only go on a line.

But your line,
unbeknownst to you,

is curved, so that it ends on
itself.

That thenthe line expands.
The circle expands.

What do you think is happening?
You think suddenly all the

distances are greater,
but you can't perceive what

it's expanding into,
because that's a second

dimension, and you're
constrained to move on the line.

Similarly, if you're an ant,
or something moving on the

surface of the Earth,
and you have no understanding

that there's up and down,
and the Earth suddenly

increases in size,
you have no perception of the

dimension you're moving into.
Student: So then,

they just keep moving into
higher dimensions?

Professor Charles
Bailyn: Well,

our perception is of a
threedimensional Universe.

So, if you say,
okay, what happens when the

scale factor gets bigger?
You can write it down

mathematically into all these
calculations,

and what you have to imagine,
if you want to have a

conceptual understanding of
this, is that there's some

fourth spatial dimension into
which this threedimensional

space is moving into.
But we can't perceive that.

So, it's better to do it
mathematically,

because it's hard on the brain
to imagine that fourth

dimension.
And there's basically two ways

to think about this.
One is by analogy.

You think of the
onedimensional creature and

what it thinks about the second
dimension,

or the twodimensional
creaturewhat it thinks about

the third dimension.
And then, you just,

sort of, take this leap of
faith into us moving into the

fourth.
Or, you have to write things

down mathematically.
Those are the only two options

you have.
Actually picturing this is not

going to happen.
Yes?

Student: If we were to
speed up this process would we

be able to see things getting
farther away from us?

Professor Charles
Bailyn: Ah,

interesting question.
Would we, if we cranked up this

process some,
would we actually,

you know, be able to take out
our tape measure and notice that

the distance between here and
Starbucks has increased?

No.
Here's why.

We are notwethat is to say,
you, me, our bodies,

whateverare not participating
in the expansion of the Universe

at the moment.
Why?

Because the molecules in our
body are being held together by

other forceschemical forces.
We are beingthe Earth is held

together by gravitational forces
and those forces have stopped

the expansion of the Universe
locally,

but not globally.
And that's why you have to go

out and measure this stuff with
galaxies.

Otherwise, you'd be able to,
you know, measure it with this.

Now, of course,
then, there's the problem,

the ruler also expands,
all this kind of stuff.

But, in fact,
what happens is that

locallylocal objects,
by which I mean,

our own galaxy and anything
smaller, are held together by

other forces.
Picture a balloon expanding,

so that's the twodimensional
case, this balloon expands.

And put a bunch of leather
patches on the balloon.

So, those leather patches don't
expand, but the distance

betweenbecause they're held
together by something elsebut

the distance between them does.
Yes?

Student: So,
what causes the expansion?

Professor Charles
Bailyn: What causes the

expansion?
Oh, that's theology.

No, no, seriously,
it's an initial condition.

Something at the start,
at T equals 0,

where this A is 0.
So, you're starting with

A ofwith this scale
factor of 0, but the derivative

isn't 0.
It's expanding,

A is increasing.
Why?

Why is it increasing by the
particular amount it is?

You have to think of that as
being a parameter of the

Universe.
It's one of the things about

thesort of like the speed of
light.

Why is that the quantity it is?
Or why is the gravitational

constant the value it is?
It's one of the parameters that

governs our Universe.
Why those particular parameters?

That's not quite a science
question, and we don't know.

You can turn it around.
You can make the following

interesting point.
If it wasn't expanding at

approximately the rate it is,
we wouldn't be here to notice

it.
Because if it was expanding a

whole lot slower,
then it would never have gotten

big enough for stars to condense
out.

If it was expanding a whole lot
faster, all the atoms would be

spread out so far that,
again, stars could never form.

So, you can make this
interesting argument that while

you don't know why it has this
particular value,

it's very important that it
does, because otherwise we

wouldn't be here to observe it.
This is a form of argumentation

called the anthropic principle.
It is highly debated among

scientists whether this is a
scientific argument or not.

But it's amusing either way.
Soyes?

Student: So if
derivative A is positive,

then A should have been
0 for that, right?

Professor Charles
Bailyn: Well,

you go back before A and
you're in trouble.

So  Student: What's
that mean?

Professor Charles
Bailyn: Okay.

So, this is another one of
these unquestions.

It's usually phrased as,
well, what happened before the

Big Bang, right?
That's the equivalent question.

And, again, that's a
theological question.

It's like asking the question:
"What's going on inside an

event horizon?"
You can write down equations.

You can talk about it.
But it's untestable by its

very nature.
And so, something– This,

by the way, is why the
Catholics like the Big Bang

Theory so much.
In fact, the mathematics,

the relativistic mathematics
that describe the Big Bang and

the expansion of the Universe,
were worked out by a man named

Lemaitre, who was a Catholic
priest, who was a Jesuit.

They love this because it gives
you a creation moment.

It kind of gives you a
scientifically verified creation

moment.
John Paul was very enthusiastic

about astrophysics.
He used to throw big

conferences in the Vatican,
give afterdinner speeches.

There's a thing called the
Vatican Astrophysical

Observatory.
They have a bunch of Jesuits.

They run a telescope in Arizona.
They do research into this.

And so, you know,
if you want to see science and

religion converge,
you want to run away from

biology as fast you can and talk
to us about cosmology.

And what I don't understand is
why the, sort of,

fundamentalist type worry so
much about biology,

where all the science is
deadset against them.

Whereas, in the case of
astrophysicsnow,

of course, it is possible,
if you take an atheistic point

of view,
to come up with all kinds of

clever ways to avoid this
creation event.

But again, it stops being
science at a certain point.

It becomes another odd kind of
theology, and we'll talk about

that, perhaps,
a little bit.

But if you want a place where
science turned out to be the

congruent to,
at least,

certain kinds of
nonfundamentalist religious

beliefs, you're way better off
in astrophysics than you are in

biology.
Yeah, go ahead.

Student: Back to the
fourth dimension,

is that a time dimension or a
space dimension?

Professor Charles
Bailyn: No,

that's a fourth spatial
dimension that I'm talking about

in this case.
Student: So,

in other words,
spatial dimension [Inaudible]

Professor Charles
Bailyn: It's expanding into

a dimension which we don't
perceive.

Or, at least,
that's one way of

conceptualizing it.
We don't get to deal with that

dimension.
So, again, it's a concept.

It's not necessarily a physical
thing.

Yes?
Student: Back to that

one point, I was just wondering,
is that like anything that will

ever [Inaudible]
Professor Charles

Bailyn: Right.
Student: [inaudible]

and anything that will ever
expand?

Professor Charles
Bailyn: Yeah,

yeah, yeah.
It has to be.

Think of all the points that
now exist in the Universe.

Multiply them by 0,
and they're all on top of each

other.
Yes?

Student: So if you were
to go really,

really fast in a straight line
in any direction,

would it eventually end at a
[Inaudible]

Professor Charles
Bailyn: So,

this is the question of what is
the curvature of the Universe.

Is it, in fact,
like this analogy,

with the circle or the surface
of the sphere.

If you go forever,
do you come back to where you

are?
That depends on what the

overall curvature of the
Universe turns out to be.

That depends on how much mass
it contains, because mass curves

space.
And so, that is a question

that's empirically answerable.
We think the answer is no.

In any case,
though, it would take you

longer, at the speed of light,
than the age of the Universe to

accomplish it.
So, even if it were positively

curved, in this sense that it
rejoined itself,

you wouldn't actually be able
to make that voyage.

Student: [Inaudible]
Professor Charles

Bailyn: No.
Student: [Inaudible]

Professor Charles
Bailyn: Well,

you might, eventually,
unless the Universe is

expanding faster than you can
move.

This goes back to the question
of can parts of it expand faster

than the speed of light,
and the answer is yes.

So, yeah.
You take off on this voyage to

the back of your own head.
Going in that direction,

you're going to end up
hereexcept the Universe is

expanding faster than you can
go,

and so, you don't necessarily
end up back there.

Yes?
Student: How does the

Big Crunch happen in the
expansion?

Professor Charles
Bailyn: Oh,

one of the things that we
haven't talked about is the

expansion rate constant.
Might it be that the Universe

is expanding,
but perhaps slowing down?

Why would it slow down?
It's full of mass.

Gravity slows things down.
And so, in principle,

if you've got enough mass,
the Universe will stop,

turn around,
and fall backwards.

And you can compute fromwe
will compute,

next period,
how fast you have to go to make

that happen.
Or contrary,

how dense the Universe has to
be to stop it.

And so, what you expect is the
Universe is slowing down.

Because you know you don't know
how much it's slowing down,

whether it will stop the
expansion or not,

but you expect it to be slowing
down.

The punch line of this whole
part of the course,

in order to anticipate where
we're going,

is that, in fact,
we can measure the change in

the expansion rate,
and it's speeding up,

not slowing down.
This is very disturbing,

because it means there's some
kind of pervasive cosmic

antigravity,
which we call dark energy,

because we don't know what it
is.

And that's basically the punch
line of this whole section of

the course.
But you could imagine that

there is a change in the
expansion rate,

either positive or negative,
and that, therefore,

various different outcomes are
possible.

Yeah?
Student: Would a

hypothetical of the Big Crunch
be sort of different from Big

Bang in that the Big Bang sort
of expanded the whole geometry

of the Universe where as the Big
Crunch being motivated by

gravity would only cause the
object [inaudible]

Professor Charles
Bailyn: No,

no, no, no, no.
It turns out ityou might

imagine that,
but you'd be wrong.

It turns out that this scale
factoryou can write down a

differential equation for the
scale factor,

and that it's the scale factor
that stops, turns around and

comes back.
Now, it is the case that when

it's going out,
the particular objects the

Universe contains are different
because of the peculiar motions.

It starts out much more evenly
spread, and then gradually stuff

accumulates due to gravity,
and you getwhen you're coming

back, you get a lot of
individual points,

rather than a smooth
distribution of matter.

But that has to do with
peculiar motions,

not the overall motion of the
Universe.

One more and then we got to
continue this next time.

Yes, go ahead.
Student: Before the Big

Bang, what happens when the
minusnegative number did

[Inaudible]
Professor Charles

Bailyn: Right.
So, before the Big Bang,

can you put a negative number
into that A?

This gets you into exactly the
same kind of mathematical

difficulty as moving inside an
event horizon.

You can actually write down a
metric for the whole Universe

and you change all the signs
when that happens.

And you get into a very similar
kind of problem.

So, mathematically,
you could compute a bunch of

stuff.
The physical meaning of that is

notfirst of all,
the fact that that mathematics

actually works in the real world
is impossible to determine,

and the physical nature of
consequences of that are

questionable.
All right, stop.
