Professor Hawking's Universe Horizon


Professor Hawking's Universe

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20 years ago, Stephen Hawking,

a young research student

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at Cambridge University,

began to show the first symptoms

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of an incurable disease

at he was told might kill him

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within a few years.

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Amyotrophic lateral sclerosis.

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Undeterred, he married,

had three children,

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and became a great scientist.

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His subject is cosmology,

the study of the universe.

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STUDENTS CHATTER.

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You could pull that down.

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Could you shut the door, please?

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This week's seminar is given

by Paul Todd from Oxford.

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What I was going to talk about is

some applications of Penrose's

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quasi-local mass construction.

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I'll remind you to begin with,

what that construction is,

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because it's something of a novelty.

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It's been around for about a year,

and the way the construction works,

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or the way the definition works

is...

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The Monday seminar is more or less

compulsory for all the relativity

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group, especially the students.

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Chris is in his third year.

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He's working on

supersymmetric theories.

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Bruce is studying the early

universe, and like Chris,

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he's writing up his Ph.D.

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Then you contract the...

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Wayne concentrates more on the

mathematical side than the physics.

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He is a second-year like me, Julian.

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I'm working on quantum gravity.

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It's like picking out some specific

bits of spherical harmonic.

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Whereas in special relativity...

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There are three more

students, all first years.

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To get into this group,

you need a good advanced degree,

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so most of us are in our early 20s,

except for Simon, who's only 17.

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So you get the same answer

integrating it

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over any hyper surface.

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So if we integrate it over

a hyper surface, like so,

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that's a number which depends

on which particular killing vector

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I picked and if I picked one

of the translation killing vectors,

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that's a component

of the total momentum.

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If I picked one of the rotational

killing vectors, it's a component...

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Most of us students are under

the charge of Stephen Hawking,

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who is the Lucasian Professor

of Mathematics, and head

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of the relativity group as well.

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That's special relativity.

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Now if you consider linearised

general relativity,

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if this is the source,

it gives rise to a gravitational

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field, so you should be able

to spot that momentum

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in the gravitational field.

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INAUDIBLE.

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Sorry?

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What do the self dual

rotations correspond to?

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Oh, well I...

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The combination of boost

and special rotation.

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Yes, that's right.

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If it is, if you think of it

as a rotation of the X Y plane,

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plus I times a boost and the TZ

plane, they are just one

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of the rotations, naturally.

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Are they real?

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They are real.

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So they are real in the Euclidian

space, but they're not

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going to be real here.

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This is what one might refer

to as old-fashioned relativity,

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with plus minus minus minus.

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LAUGHTER.

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We gave that up ten years ago.

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LAUGHTER.

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A guy called Stewart

Lowther at Manchester...

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INAUDIBLE.

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There are two different...

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In equivalent?

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Ah-ha.

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That equal something of the form

like this, then Chi.

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It's going to be...

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Self dual, then that's

got to be true.

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Which if you stick

that in, gives you...

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People tend to congregate

from the relativity group, and,

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at the time, you find that you learn

almost as much as you do sitting

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in your office working or reading.

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And that equals something

of the form like this.

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Right, so that one just corresponds?

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That is what I was wondering.

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So it doesn't work with one or two.

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You can do a certain amount

of research and creative thinking

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each day and then what's really

helpful is discussing with other

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people, so that your

ideas are clarified.

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Why doesn't it work

with five, for example?

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The group is quite close.

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We get to talk to each other

about problems and have

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discussions all the time,

which is very good in a social

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sense, and also in the sense

that there are people here who,

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if you asked them a question

about any particular subject,

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there's bound to be someone who can

find an answer to it,

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and so you don't have to wait

for very long to find an answer!

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Because the one...

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Because you have much

greater contact with

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Stephen as a supervisor,

because he needs your help

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all the time, he's always available

to answer questions and to help

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you with things you don't

understand, and he's also very,

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very clear in the way

he explains it.

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And since he knows all his research

students as friends,

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he seems much more relaxed and much

less an academic physicist.

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He most definitely is number one

an academic physicist.

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The most famous of all academic

physicists is Albert Einstein.

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The source of his fame,

the general theory of relativity,

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burst on the world of

physics in 1915.

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But after an initial rush

of enthusiasm, few other academic

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physicists took up his theory,

and developed further.

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General relativity passed out

of fashion for about 40 years.

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The initial?

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Sorry?

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Stephen Hawking was one of a group

of scientists who resurrected

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interest in Einstein's general

theory of relativity

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during the 50s and 60s.

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Stephen worked on mathematical

theorems in general relativity

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which proved the necessity for a big

bang at the beginning

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of the universe.

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He also investigated

many of the attributes of a bizarre

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class of objects whose properties

are predicted by Einstein's theory.

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Black holes.

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Massive as they are,

black holes are not things

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you can actually see,

because a black hole

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doesn't emit any light.

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But if a black hole passes in front

of a background of stars,

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the stars appear to move away

from their real positions,

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just as if the black hole

were a giant lens.

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In fact, the light from

the background stars is bent

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round and round the black hole,

by its intense gravitational field,

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so you can see several images

of each star at once.

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If you are a long way

away from a black hole,

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you are quite safe!

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If you're a long way

away from a black hole,

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you are quite safe.

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If our sun were to become a black

hole,

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we would continue to orbit

around it just as we do

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at the moment.

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In fact, it wouldn't make any

difference to our orbit.

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Of course, we would get rather cold!

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But if you go close up to a black

hole,

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then the gravitational

field becomes stronger.

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And at a certain point,

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the gravitational field

reaches critical strength.

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And if you go beyond there,

you can't get out at all again.

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Stephen says that a black hole

is rather like a whirlpool.

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Imagine you have a whirlpool, and

you have some little boats nearby.

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Far away, there are quite safe,

but if they get within a certain

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critical distance of the world pool,

then even if they try to motor

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directly away from it,

they will get sucked

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in by the current which is much

faster than they are.

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From within this critical radius,

nothing, whether little boats,

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rays of light or spacecraft

can ever return.

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If it was a black hole

with the mass of the sun...

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Then you would be torn apart

by tidal forces before you got

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inside the black hole.

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But if it was a very

large black hole...

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Such as we believe may

occur in the centre

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of our galaxy, or in quasis...

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Then you wouldn't see anything

special

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if you passed inside the black hole.

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But once you pass a certain

critical point...

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Then you would never be

able to get out again,

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no matter how much rocket

power you used.

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Moreover, we assume you would run

into a singularity...

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You would be doomed to run

into a singularity.

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In a fairly short time.

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Like a few hours.

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So far, even though astronomers have

been busily looking for black holes,

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none have been definitely

identified, although there

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are some strong candidates.

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So the properties of black holes

have had to be entirely worked

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out using mathematics.

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If Einstein's general theory

of relativity is true,

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then inside the radius

from which nothing can escape,

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called the event horizon,

and at the centre of the black hole

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is a singularity.

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A place where gravity is infinite,

and space and time come to an end.

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It would be a very nice idea.

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If one could fall into a black

hole and then come out

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of another universe.

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And there are some solutions

to the Einstein field equations

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which have this property that

you can come out

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in another universe.

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But all the evidence we have shows

these solutions are very unstable.

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So that is, if you disturb them

slightly, for example by falling

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into the black hole...

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Than a passage which takes

you through to the other universe

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gets closed off and you run right

into the singularity.

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We all came out of a singularity.

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The Big Bang singularity

at the beginning of the universe.

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So it wouldn't be that

unnatural if we ended up

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in another singularity.

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Either a singularity in a black

hole or the collapse

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of the whole universe.

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You could say, dust to dust

and ashes to ashes,

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and singularity to singularity.

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It can be very frustrating

when you're working at something

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and banging your head

against a wall and never

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getting anywhere day in,

day out, but then suddenly it clicks

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and everything works

fine for a few days.

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An answer comes out.

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Whether it's what you want

or what you don't want,

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you have to work out later.

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Part of it's just a search for

beauty and prettiness in physics.

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So what do you want it for?

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Just to check on how he did.

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I tend to be more on

the mathematical side,

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if you are looking at equations

for mathematical consistency rather,

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then a physical relevance.

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I certainly wouldn't mind doing

relativity all day, or mathematics,

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or anything like that.

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It just interests you.

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I don't think you could explain it,

you would have to ask

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a psychologist about that.

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And there's certainly

no monetary reward.

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Well, there's a bit of monetary

reward, but not much, I could get

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more on the outside.

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But it's very comfortable.

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You can do what you want to do

all your life, if you get

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to do it all your life.

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You're playing games all your life.

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It's pretty good.

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All of theoretical physics

is formulated in mathematical terms.

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The theory of physics is really

a mathematical model of the world.

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But being good at mathematics isn't

enough, one also needs what one

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calls physical intuition.

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You can't deduce physics purely

deductibly from a set

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of basic principles,

you have to make certain intuitive

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leaps to introduce new models.

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The ability to make these intuitive

leaps is what characterises a good

0:21:050:21:08

theoretical physicist.

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Stephen is lucky that he chose

one of the few fields

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in which his disability is not

a serious handicap.

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Because most of his work

is really just thinking.

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And his disabilities don't

stop him doing that.

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In a way, they give him

more time to think.

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In 1973, Stephen started

a new line of research

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that was eventually to make him

famous, with the discovery

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of Hawking radiation.

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Up until then, his work

on black holes was concerned

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only with large ones,

with the mass of the sun or bigger.

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But then, he began to think

that there might also be very

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very small black holes.

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Stephen realised, in order

to an designed them,

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Einstein's general relativity

would not be enough.

0:22:410:22:43

He needed to use a completely

different branch of physics

0:22:430:22:45

called quantum mechanics.

0:22:450:22:47

Quantum mechanics was formulated

by Werner Heisenberg

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and Erwin Schrodinger

in the mid-1920s.

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Theirs is a theory of very

small things, like atoms.

0:22:530:22:58

Quantum mechanics is the greatest

achievement in physics this century,

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even greater than Einstein's general

theory of relativity.

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It implies that what we normally

think of as empty space isn't

0:23:060:23:09

really empty at all,

but is filled with pairs

0:23:090:23:11

of particles and antiparticles.

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These appear together at some point

in space, move apart,

0:23:150:23:18

and then come together again,

annihilating each other.

0:23:180:23:22

They are called virtual particles

because you can't directly measure

0:23:220:23:24

them with a particle detector.

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According to Hawking, if there's

a small black hole present,

0:23:320:23:35

one of the members of these pairs

might fall into it.

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Of course, the other

one might fall in, too,

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but it's also possible for one

of them to escape, and in that case,

0:23:420:23:45

it would appear to be a particle

emitted from the black hole.

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In fact, to an observer a long way

away, it appears that the black

0:24:000:24:04

hole is emitting particles

and radiation as if

0:24:040:24:06

it was a hot body.

0:24:060:24:07

Very small black holes

aren't black at all,

0:24:070:24:09

they shine with Hawking radiation.

0:24:090:24:12

If you have a black hole

with the mass of the sun,

0:24:120:24:20

then its temperature is only one

10,000,000th of a degree

0:24:220:24:24

above absolute zero.

0:24:240:24:31

And the amount of radiation would be

absolutely insignificant.

0:24:310:24:39

But if you have one of these small

black holes, then the temperature

0:24:440:24:48

would be much higher,

and it would emit

0:24:480:24:49

a lot of radiation.

0:24:490:24:57

In fact, the most interesting

mass of a black hole

0:25:010:25:05

is about a thousand million tonnes,

which is about the mass

0:25:050:25:08

of a mountain.

0:25:080:25:16

But the actual size of such a black

hole would only be that

0:25:230:25:27

of the nucleus of an atom.

0:25:270:25:32

But it would emit a lot

of radiation and energy.

0:25:320:25:40

Equivalent to about six

nuclear power stations.

0:25:430:25:51

So if you could find

such a small black hole,

0:25:590:26:04

and if we could harness it properly,

then we would really solve

0:26:040:26:07

all our energy problems.

0:26:070:26:15

However, we have been

looking for radiation

0:26:260:26:29

from the black holes like this,

and we haven't found any so far.

0:26:290:26:37

In a way, that's rather

disappointing for Stephen.

0:26:420:26:50

Because, had we found one, Stephen

would have got a Nobel Prize!

0:27:000:27:03

No biscuit?

0:27:040:27:04

Er, yes, please.

0:27:040:27:12

I should go and buy some coffee.

0:27:330:27:37

Oh, that's right,

it's quarter to 11.

0:27:370:27:39

Should I buy some instant?

0:27:390:27:40

Try eight ounces.

0:27:400:27:41

Eight ounces.

0:27:410:27:45

There'll be crowds pouring

into Stephen's lecture.

0:27:450:27:46

I mean, we didn't have enough last

week, and it was getting

0:27:460:27:49

a bit weak at the end.

0:27:490:27:51

Hello.

0:27:510:27:52

Tea?

0:27:520:27:54

Some of us are mathematicians,

and others physicists,

0:27:570:27:59

and we're all working

on different problems.

0:27:590:28:02

Do you want the Omega

for the embedding in the cylinder?

0:28:030:28:08

These problems are usually either

suggested or allocated by Stephen.

0:28:080:28:16

These problems are very

different from each other,

0:28:180:28:23

but are basically connected,

in that they are

0:28:230:28:25

all trying to unearth

the fundamentals of the universe.

0:28:250:28:28

So that's supposed to have...

0:28:280:28:29

Does it?

0:28:290:28:37

No, it won't, will it?

0:28:390:28:44

It is certainly an ambitious task.

0:28:440:28:47

People have been working on it for,

I'd say, 50 years or longer,

0:28:470:28:54

so I guess it's even more ambitious,

since we don't even know if

0:28:540:28:57

the answer is that it can be done.

0:28:570:29:00

A zero on the horizon,

on the boundary?

0:29:000:29:04

Yes, because r is half pi there.

0:29:040:29:11

So it's not right?

0:29:110:29:13

Yes.

0:29:130:29:15

In that case...!

0:29:150:29:18

OK.

0:29:180:29:21

Morning, Chris.

0:29:490:29:52

Right here!

0:29:520:29:58

The boundary partitions...

0:30:070:30:15

We are trying to unify

many of the modern ideas of physics.

0:30:250:30:29

I'm interested in the almost

philosophical, or even religious,

0:30:290:30:33

quest for what actually makes

the universe work.

0:30:330:30:41

I mean, certainly the conformal

group corresponding to flat

0:30:430:30:49

three space would be 041.

0:30:490:30:57

There's an embarrassing

inconsistency at the heart

0:31:020:31:03

of modern physics.

0:31:030:31:04

Einstein's general theory

of relativity, which describes

0:31:040:31:06

the nature of very big things,

disagrees with the theory of very

0:31:060:31:09

small things, quantum mechanics,

in apparently unresolvable ways,

0:31:090:31:11

even though no one has managed

to prove either theory untrue.

0:31:110:31:13

So perhaps the way out

of this dilemma is to find

0:31:130:31:16

a more profound theory,

which incorporates both.

0:31:160:31:23

Two outstanding partial theories

have been discovered this century.

0:31:310:31:36

They are general relativity

and quantum mechanics.

0:31:360:31:44

Ultimately we have to find

one consistent theory,

0:31:570:32:01

which will describe everything...

0:32:010:32:09

Not only general relativity

and quantum mechanics,

0:32:110:32:14

but all the other interactions

in physics, as well.

0:32:140:32:22

We have had quite

a success recently...

0:32:310:32:39

In that we've developed

a theory which unifies

0:32:420:32:44

electromagnetism in

the weak nuclear force.

0:32:440:32:52

Now we want to go on to unify these

interactions with gravity,

0:33:000:33:03

and also unify gravity

with quantum mechanics.

0:33:030:33:11

Unfortunately, this is a very

ambitious programme,

0:33:120:33:20

but there's quite a reasonable

chance of success.

0:33:230:33:31

Stephen would put

the chances at 50-50.

0:33:350:33:43

In that you could succeed in this

task by the end of the century.

0:33:430:33:51

Now we have a definite candidate...

0:33:560:34:04

For the complete unified theory,

which will describe everything,

0:34:050:34:13

and this candidate is called N=8

Supergravity.

0:34:160:34:24

If it doesn't work, then we have no

idea what will work.

0:34:300:34:38

We're working very

hard on this theory.

0:34:520:35:00

But at the moment it doesn't seem

to predict the kind of particles

0:35:050:35:08

that we actually observe.

0:35:080:35:16

But we're hoping that maybe

when we understand the theory

0:35:180:35:22

better...

0:35:220:35:30

Then we could construct

the particles we observe

0:35:430:35:45

out of smaller pieces,

which are the particles

0:35:450:35:47

in the N=8 Supergravity theory.

0:35:470:35:55

And, in that case, we could actually

say that theoretical physics

0:36:100:36:13

was over, we had a complete theory

of the whole universe.

0:36:130:36:21

If we had a complete theory

of the universe, we could,

0:36:310:36:39

in principle, predict everything.

0:36:420:36:50

But in practice, the computations

involved are very, very complicated,

0:37:210:37:23

so in effect, we can't predict

anything, apart from

0:37:230:37:25

the most simple situations.

0:37:250:37:33

In fact, we already know

all the laws which govern all normal

0:37:370:37:39

matter and all normal situations...

0:37:390:37:47

So, in principle, we can

predict everything that

0:37:590:38:01

happens on the earth.

0:38:010:38:09

But we haven't had much success

in predicting human behaviour

0:38:110:38:13

from mathematical equations.

0:38:130:38:21

It's mostly complicated,

a human being contains

0:38:310:38:34

about a million million million

million million particles.

0:38:340:38:41

I don't think we really

need a very big lunch,

0:39:460:39:48

because we felt ourselves up

with doughnuts this

0:39:480:39:50

morning, haven't we, Timmy?

0:39:500:39:56

She's gone out to lunch with Juliet,

and she's gone swimming.

0:39:560:40:04

Well, I can afford to buy

myself a small black...

0:40:060:40:09

And I can afford to buy

Stephen half of one.

0:40:090:40:11

Neither Mrs Hawking nor their son,

Timmy, are particularly

0:40:110:40:13

interested in mathematics,

so that when they come

0:40:130:40:15

to lunch we try not to talk

too much about work.

0:40:150:40:21

Oh, dear, look, Stephen,

that's a bit much!

0:40:210:40:23

White?

0:40:230:40:24

Black.

0:40:240:40:25

Two white...

0:40:250:40:29

How's that?

0:40:290:40:36

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

0:40:550:40:59

So Stephen will basically be

talking about infinity.

0:40:590:41:07

LAUGHTER.

0:41:110:41:13

Unfortunately, infinity's

rather hard to talk about,

0:41:130:41:14

because it's rather a long,

long way away!

0:41:140:41:22

So what Stephen's going to do

is he's going to try

0:41:240:41:27

and bring it a lot nearer.

0:41:270:41:34

In other words, Stephen's

going to conformally compactify

0:41:340:41:36

anti-de Sitter space.

0:41:360:41:43

The Einstein static universe

is topologically S3 cross of one...

0:41:510:41:59

Where S3 gives the spatial sections

and R1 gives the time.

0:42:050:42:13

So the Einstein static universe...

0:42:140:42:22

So it's really a sort of cylinder.

0:42:220:42:27

With the time being the axis.

0:42:270:42:34

Now it just so happens that we

happen to have the universe here.

0:42:340:42:37

LAUGHTER.

0:42:370:42:44

LAUGHTER.

0:42:440:42:45

Sorry!

0:42:450:42:53

Unfortunately, we were unable to get

the full 4-dimensional

0:43:000:43:02

universe in here today...

0:43:020:43:10

But the anti-de Sitter space

is a time-like hyper surface.

0:43:170:43:20

And that leads to an

important difference...

0:43:200:43:22

Crystal clear.

0:43:220:43:25

The way he thinks, he manages

to cut away all the dross,

0:43:250:43:29

cut away all the trees,

and just see down to the base

0:43:290:43:34

cut away all the trees,

and just see down to the basic

0:43:340:43:37

simple, central fact

that is necessary to consider.

0:43:370:43:39

And he makes everything

so crystal clear, simple.

0:43:390:43:40

It's quite astounding sometimes.

0:43:400:43:48

And because he can't write,

because he can't, he finds it

0:43:490:43:51

hard to read papers,

hard to read books, he tends to,

0:43:510:43:54

he thinks in terms of diagrams

all the time, he thinks very

0:43:540:43:57

clearly, and manages to make

everything very, very simple.

0:43:570:44:04

That equation is conforming...

0:44:040:44:07

It depends upon the taste

of the person in a way,

0:44:070:44:12

there is a certain taste people

have, in which they appreciate

0:44:120:44:17

mathematical beauty of the theory,

and it's sort of hard to describe,

0:44:170:44:20

but this is really one

of the reasons for doing physics,

0:44:200:44:24

that you find that there are just

a certain number of laws,

0:44:240:44:32

and they are very simple

when written out, mathematically,

0:44:320:44:35

and simplicity is quite beautiful,

and the fact it describes

0:44:350:44:39

what's happening around us

is quite amazing, really.

0:44:390:44:43

And the question is whether we can

keep on simplifying our laws

0:44:430:44:48

and postulates, and maybe derive

an ultimate law like that.

0:44:480:44:56

APPLAUSE.

0:44:580:45:00

Are there any questions?

0:45:000:45:07

Either everyone's understood

everything, or no one's

0:45:140:45:15

understood anything!

0:45:150:45:18

Shall we have a vote?

0:45:180:45:20

LAUGHTER.

0:45:200:45:23

In the tearoom, we have a number

of portraits of former

0:45:280:45:32

professors of mathematics...

0:45:320:45:40

And Stephen's not quite

sure what the criterion

0:45:510:45:53

are that should determine

whether you get your

0:45:530:45:55

portrait in the tearoom...

0:45:550:46:03

But one of them seems to be that

you've left the department.

0:46:050:46:13

On the wall that this

office is on...

0:46:160:46:24

There are the portraits of Stephen's

four immediate predecessors

0:46:310:46:35

in the Lucasian chair...

0:46:350:46:41

One of them was Paul Dirac...

0:46:410:46:49

Who is in fact still alive...

0:46:540:46:56

He was one of the founders

of quantum mathematics.

0:46:560:47:03

It was he who had

the idea of antimatter.

0:47:030:47:11

In the corner, there's

Sir George Gabriel Stokes...

0:47:170:47:25

Who was professor

for about 54 years...

0:47:290:47:37

Because in those days you didn't

have any retirement age...

0:47:370:47:44

And there's a space outside here...

0:47:470:47:55

In which it's fairly obvious

they'll put Stephen's

0:48:060:48:08

portrait if he leaves...

0:48:080:48:16

It gives him a rather

creepy feeling...

0:48:190:48:25

It's like seeing your own tombstone.

0:48:250:48:33

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