20 years ago, Stephen Hawking, a young research student
at Cambridge University, began to show the first symptoms
of an incurable disease that 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.
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.