Professor Hawking's Universe Horizon

20 years ago, Stephen Hawking,

a young research student

at Cambridge University,

began to show the first symptoms

of an incurable disease

at he was told might kill him

within a few years.

Amyotrophic lateral sclerosis.

Undeterred, he married,

had three children,

and became a great scientist.

His subject is cosmology,

the study of the universe.

STUDENTS CHATTER.

You could pull that down.

Could you shut the door, please?

This week's seminar is given

by Paul Todd from Oxford.

What I was going to talk about is

some applications of Penrose's

quasi-local mass construction.

I'll remind you to begin with,

what that construction is,

because it's something of a novelty.

It's been around for about a year,

and the way the construction works,

or the way the definition works

is...

The Monday seminar is more or less

compulsory for all the relativity

group, especially the students.

Chris is in his third year.

He's working on

supersymmetric theories.

Bruce is studying the early

universe, and like Chris,

he's writing up his Ph.D.

Then you contract the...

Wayne concentrates more on the

mathematical side than the physics.

He is a second-year like me, Julian.

I'm working on quantum gravity.

It's like picking out some specific

bits of spherical harmonic.

Whereas in special relativity...

There are three more

students, all first years.

To get into this group,

you need a good advanced degree,

so most of us are in our early 20s,

except for Simon, who's only 17.

So you get the same answer

integrating it

over any hyper surface.

So if we integrate it over

a hyper surface, like so,

that's a number which depends

on which particular killing vector

I picked and if I picked one

of the translation killing vectors,

that's a component

of the total momentum.

If I picked one of the rotational

killing vectors, it's a component...

Most of us students are under

the charge of Stephen Hawking,

who is the Lucasian Professor

of Mathematics, and head

of the relativity group as well.

That's special relativity.

Now if you consider linearised

general relativity,

if this is the source,

it gives rise to a gravitational

field, so you should be able

to spot that momentum

in the gravitational field.

INAUDIBLE.

Sorry?

What do the self dual

rotations correspond to?

Oh, well I...

The combination of boost

and special rotation.

Yes, that's right.

If it is, if you think of it

as a rotation of the X Y plane,

plus I times a boost and the TZ

plane, they are just one

of the rotations, naturally.

Are they real?

They are real.

So they are real in the Euclidian

space, but they're not

going to be real here.

This is what one might refer

to as old-fashioned relativity,

with plus minus minus minus.

LAUGHTER.

We gave that up ten years ago.

LAUGHTER.

A guy called Stewart

Lowther at Manchester...

INAUDIBLE.

There are two different...

In equivalent?

Ah-ha.

That equal something of the form

like this, then Chi.

It's going to be...

Self dual, then that's

got to be true.

Which if you stick

that in, gives you...

People tend to congregate

from the relativity group, and,

at the time, you find that you learn

almost as much as you do sitting

in your office working or reading.

And that equals something

of the form like this.

Right, so that one just corresponds?

That is what I was wondering.

So it doesn't work with one or two.

You can do a certain amount

of research and creative thinking

each day and then what's really

helpful is discussing with other

people, so that your

ideas are clarified.

Why doesn't it work

with five, for example?

The group is quite close.

We get to talk to each other

about problems and have

discussions all the time,

which is very good in a social

sense, and also in the sense

that there are people here who,

if you asked them a question

about any particular subject,

there's bound to be someone who can

find an answer to it,

and so you don't have to wait

for very long to find an answer!

Because the one...

Because you have much

greater contact with

Stephen as a supervisor,

because he needs your help

all the time, he's always available

to answer questions and to help

you with things you don't

understand, and he's also very,

very clear in the way

he explains it.

And since he knows all his research

students as friends,

he seems much more relaxed and much

less an academic physicist.

He most definitely is number one

an academic physicist.

The most famous of all academic

physicists is Albert Einstein.

The source of his fame,

the general theory of relativity,

burst on the world of

physics in 1915.

But after an initial rush

of enthusiasm, few other academic

physicists took up his theory,

and developed further.

General relativity passed out

of fashion for about 40 years.

The initial?

Sorry?

Stephen Hawking was one of a group

of scientists who resurrected

interest in Einstein's general

theory of relativity

during the 50s and 60s.

Stephen worked on mathematical

theorems in general relativity

which proved the necessity for a big

bang at the beginning

of the universe.

He also investigated

many of the attributes of a bizarre

class of objects whose properties

are predicted by Einstein's theory.

Black holes.

Massive as they are,

black holes are not things

you can actually see,

because a black hole

doesn't emit any light.

But if a black hole passes in front

of a background of stars,

the stars appear to move away

from their real positions,

just as if the black hole

were a giant lens.

In fact, the light from

the background stars is bent

round and round the black hole,

by its intense gravitational field,

so you can see several images

of each star at once.

If you are a long way

away from a black hole,

you are quite safe!

If you're a long way

away from a black hole,

you are quite safe.

If our sun were to become a black

hole,

we would continue to orbit

around it just as we do

at the moment.

In fact, it wouldn't make any

difference to our orbit.

Of course, we would get rather cold!

But if you go close up to a black

hole,

then the gravitational

field becomes stronger.

And at a certain point,

the gravitational field

reaches critical strength.

And if you go beyond there,

you can't get out at all again.

Stephen says that a black hole

is rather like a whirlpool.

Imagine you have a whirlpool, and

you have some little boats nearby.

Far away, there are quite safe,

but if they get within a certain

critical distance of the world pool,

then even if they try to motor

directly away from it,

they will get sucked

in by the current which is much

faster than they are.

From within this critical radius,

nothing, whether little boats,

rays of light or spacecraft

can ever return.

If it was a black hole

with the mass of the sun...

Then you would be torn apart

by tidal forces before you got

inside the black hole.

But if it was a very

large black hole...

Such as we believe may

occur in the centre

of our galaxy, or in quasis...

Then you wouldn't see anything

special

if you passed inside the black hole.

But once you pass a certain

critical point...

Then you would never be

able to get out again,

no matter how much rocket

power you used.

Moreover, we assume you would run

into a singularity...

You would be doomed to run

into a singularity.

In a fairly short time.

Like a few hours.

So far, even though astronomers have

been busily looking for black holes,

none have been definitely

identified, although there

are some strong candidates.

So the properties of black holes

have had to be entirely worked

out using mathematics.

If Einstein's general theory

of relativity is true,

then inside the radius

from which nothing can escape,

called the event horizon,

and at the centre of the black hole

is a singularity.

A place where gravity is infinite,

and space and time come to an end.

It would be a very nice idea.

If one could fall into a black

hole and then come out

of another universe.

And there are some solutions

to the Einstein field equations

which have this property that

you can come out

in another universe.

But all the evidence we have shows

these solutions are very unstable.

So that is, if you disturb them

slightly, for example by falling

into the black hole...

Than a passage which takes

you through to the other universe

gets closed off and you run right

into the singularity.

We all came out of a singularity.

The Big Bang singularity

at the beginning of the universe.

So it wouldn't be that

unnatural if we ended up

in another singularity.

Either a singularity in a black

hole or the collapse

of the whole universe.

You could say, dust to dust

and ashes to ashes,

and singularity to singularity.

It can be very frustrating

when you're working at something

and banging your head

against a wall and never

getting anywhere day in,

day out, but then suddenly it clicks

and everything works

fine for a few days.

An answer comes out.

Whether it's what you want

or what you don't want,

you have to work out later.

Part of it's just a search for

beauty and prettiness in physics.

So what do you want it for?

Just to check on how he did.

I tend to be more on

the mathematical side,

if you are looking at equations

for mathematical consistency rather,

then a physical relevance.

I certainly wouldn't mind doing

relativity all day, or mathematics,

or anything like that.

It just interests you.

I don't think you could explain it,

you would have to ask

a psychologist about that.

And there's certainly

no monetary reward.

Well, there's a bit of monetary

reward, but not much, I could get

more on the outside.

But it's very comfortable.

You can do what you want to do

all your life, if you get

to do it all your life.

You're playing games all your life.

It's pretty good.

All of theoretical physics

is formulated in mathematical terms.

The theory of physics is really

a mathematical model of the world.

But being good at mathematics isn't

enough, one also needs what one

calls physical intuition.

You can't deduce physics purely

deductibly from a set

of basic principles,

you have to make certain intuitive

leaps to introduce new models.

The ability to make these intuitive

leaps is what characterises a good

theoretical physicist.

Stephen is lucky that he chose

one of the few fields

in which his disability is not

a serious handicap.

Because most of his work

is really just thinking.

And his disabilities don't

stop him doing that.

In a way, they give him

more time to think.

In 1973, Stephen started

a new line of research

that was eventually to make him

famous, with the discovery

of Hawking radiation.

Up until then, his work

on black holes was concerned

only with large ones,

with the mass of the sun or bigger.

But then, he began to think

that there might also be very

very small black holes.

Stephen realised, in order

to an designed them,

Einstein's general relativity

would not be enough.

He needed to use a completely

different branch of physics

called quantum mechanics.

Quantum mechanics was formulated

by Werner Heisenberg

and Erwin Schrodinger

in the mid-1920s.

Theirs is a theory of very

small things, like atoms.

Quantum mechanics is the greatest

achievement in physics this century,

even greater than Einstein's general

theory of relativity.

It implies that what we normally

think of as empty space isn't

really empty at all,

but is filled with pairs

of particles and antiparticles.

These appear together at some point

in space, move apart,

and then come together again,

annihilating each other.

They are called virtual particles

because you can't directly measure

them with a particle detector.

According to Hawking, if there's

a small black hole present,

one of the members of these pairs

might fall into it.

Of course, the other

one might fall in, too,

but it's also possible for one

of them to escape, and in that case,

it would appear to be a particle

emitted from the black hole.

In fact, to an observer a long way

away, it appears that the black

hole is emitting particles

and radiation as if

it was a hot body.

Very small black holes

aren't black at all,

they shine with Hawking radiation.

If you have a black hole

with the mass of the sun,

then its temperature is only one

10,000,000th of a degree

above absolute zero.

And the amount of radiation would be

absolutely insignificant.

But if you have one of these small

black holes, then the temperature

would be much higher,

and it would emit

a lot of radiation.

In fact, the most interesting

mass of a black hole

is about a thousand million tonnes,

which is about the mass

of a mountain.

But the actual size of such a black

hole would only be that

of the nucleus of an atom.

But it would emit a lot

of radiation and energy.

Equivalent to about six

nuclear power stations.

So if you could find

such a small black hole,

and if we could harness it properly,

then we would really solve

all our energy problems.

However, we have been

looking for radiation

from the black holes like this,

and we haven't found any so far.

In a way, that's rather

disappointing for Stephen.

Because, had we found one, Stephen

would have got a Nobel Prize!

No biscuit?

Er, yes, please.

I should go and buy some coffee.

Oh, that's right,

it's quarter to 11.

Should I buy some instant?

Try eight ounces.

Eight ounces.

There'll be crowds pouring

into Stephen's lecture.

I mean, we didn't have enough last

week, and it was getting

a bit weak at the end.

Hello.

Tea?

Some of us are mathematicians,

and others physicists,

and we're all working

on different problems.

Do you want the Omega

for the embedding in the cylinder?

These problems are usually either

suggested or allocated by Stephen.

These problems are very

different from each other,

but are basically connected,

in that they are

all trying to unearth

the fundamentals of the universe.

So that's supposed to have...

Does it?

No, it won't, will it?

It is certainly an ambitious task.

People have been working on it for,

I'd say, 50 years or longer,

so I guess it's even more ambitious,

since we don't even know if

the answer is that it can be done.

A zero on the horizon,

on the boundary?

Yes, because r is half pi there.

So it's not right?

Yes.

In that case...!

OK.

Morning, Chris.

Right here!

The boundary partitions...

We are trying to unify

many of the modern ideas of physics.

I'm interested in the almost

philosophical, or even religious,

quest for what actually makes

the universe work.

I mean, certainly the conformal

group corresponding to flat

three space would be 041.

There's an embarrassing

inconsistency at the heart

of modern physics.

Einstein's general theory

of relativity, which describes

the nature of very big things,

disagrees with the theory of very

small things, quantum mechanics,

in apparently unresolvable ways,

even though no one has managed

to prove either theory untrue.

So perhaps the way out

of this dilemma is to find

a more profound theory,

which incorporates both.

Two outstanding partial theories

have been discovered this century.

They are general relativity

and quantum mechanics.

Ultimately we have to find

one consistent theory,

which will describe everything...

Not only general relativity

and quantum mechanics,

but all the other interactions

in physics, as well.

We have had quite

a success recently...

In that we've developed

a theory which unifies

electromagnetism in

the weak nuclear force.

Now we want to go on to unify these

interactions with gravity,

and also unify gravity

with quantum mechanics.

Unfortunately, this is a very

ambitious programme,

but there's quite a reasonable

chance of success.

Stephen would put

the chances at 50-50.

In that you could succeed in this

task by the end of the century.

Now we have a definite candidate...

For the complete unified theory,

which will describe everything,

and this candidate is called N=8

Supergravity.

If it doesn't work, then we have no

idea what will work.

We're working very

hard on this theory.

But at the moment it doesn't seem

to predict the kind of particles

that we actually observe.

But we're hoping that maybe

when we understand the theory

better...

Then we could construct

the particles we observe

out of smaller pieces,

which are the particles

in the N=8 Supergravity theory.

And, in that case, we could actually

say that theoretical physics

was over, we had a complete theory

of the whole universe.

If we had a complete theory

of the universe, we could,

in principle, predict everything.

But in practice, the computations

involved are very, very complicated,

so in effect, we can't predict

anything, apart from

the most simple situations.

In fact, we already know

all the laws which govern all normal

matter and all normal situations...

So, in principle, we can

predict everything that

happens on the earth.

But we haven't had much success

in predicting human behaviour

from mathematical equations.

It's mostly complicated,

a human being contains

about a million million million

million million particles.

I don't think we really

need a very big lunch,

because we felt ourselves up

with doughnuts this

morning, haven't we, Timmy?

She's gone out to lunch with Juliet,

and she's gone swimming.

Well, I can afford to buy

myself a small black...

And I can afford to buy

Stephen half of one.

Neither Mrs Hawking nor their son,

Timmy, are particularly

interested in mathematics,

so that when they come

to lunch we try not to talk

too much about work.

Oh, dear, look, Stephen,

that's a bit much!

White?

Black.

Two white...

How's that?

OK, what Stephen's going to say...

So Stephen will basically be

talking about infinity.

LAUGHTER.

Unfortunately, infinity's

rather hard to talk about,

because it's rather a long,

long way away!

So what Stephen's going to do

is he's going to try

and bring it a lot nearer.

In other words, Stephen's

going to conformally compactify

anti-de Sitter space.

The Einstein static universe

is topologically S3 cross of one...

Where S3 gives the spatial sections

and R1 gives the time.

So the Einstein static universe...

So it's really a sort of cylinder.

With the time being the axis.

Now it just so happens that we

happen to have the universe here.

LAUGHTER.

LAUGHTER.

Sorry!

Unfortunately, we were unable to get

the full 4-dimensional

universe in here today...

But the anti-de Sitter space

is a time-like hyper surface.

And that leads to an

important difference...

Crystal clear.

The way he thinks, he manages

to cut away all the dross,

cut away all the trees,

and just see down to the base

cut away all the trees,

and just see down to the basic

simple, central fact

that is necessary to consider.

And he makes everything

so crystal clear, simple.

It's quite astounding sometimes.

And because he can't write,

because he can't, he finds it

hard to read papers,

hard to read books, he tends to,

he thinks in terms of diagrams

all the time, he thinks very

clearly, and manages to make

everything very, very simple.

That equation is conforming...

It depends upon the taste

of the person in a way,

there is a certain taste people

have, in which they appreciate

mathematical beauty of the theory,

and it's sort of hard to describe,

but this is really one

of the reasons for doing physics,

that you find that there are just

a certain number of laws,

and they are very simple

when written out, mathematically,

and simplicity is quite beautiful,

and the fact it describes

what's happening around us

is quite amazing, really.

And the question is whether we can

keep on simplifying our laws

and postulates, and maybe derive

an ultimate law like that.

APPLAUSE.

Are there any questions?

Either everyone's understood

everything, or no one's

understood anything!

Shall we have a vote?

LAUGHTER.

In the tearoom, we have a number

of portraits of former

professors of mathematics...

And Stephen's not quite

sure what the criterion

are that should determine

whether you get your

portrait in the tearoom...

But one of them seems to be that

you've left the department.

On the wall that this

office is on...

There are the portraits of Stephen's

four immediate predecessors

in the Lucasian chair...

One of them was Paul Dirac...

Who is in fact still alive...

He was one of the founders

of quantum mathematics.

It was he who had

the idea of antimatter.

In the corner, there's

Sir George Gabriel Stokes...

Who was professor

for about 54 years...

Because in those days you didn't

have any retirement age...

And there's a space outside here...

In which it's fairly obvious

they'll put Stephen's

portrait if he leaves...

It gives him a rather

creepy feeling...

It's like seeing your own tombstone.