A Night with the Stars

Where's the reception? Oh, OK...

So nobody knows what this lecture is going to be about...

I know what it's about. It'll be about science, and he'll be promoting that heresy of his.

I hope he's going to unveil a death ray. I don't know.

I'm going to make one, at least one unsuspecting celebrity, do sums.

-I really am so out of my depth...

-LAUGHTER

This is the worst thing that's happened to me as an adult.

The only thing I do know is that I've been roped in to go up

on stage - with Simon Pegg, no less - waving a rope about.

I can see why you've got no hair.

LAUGHTER

I'm so thrilled to have been asked, to be honest.

I never do clever things.

There's a real buzz in this room, and it just makes me feel proud to be a scientist in this day and age.

Perhaps tonight is my chance

to realise what it's all about, and have a big sort of Damascene moment.

I'd like to ask Professor Brian Cox about his hair - it's a shared interest.

-I hope he blows some stuff up.

-Whoa... Ow!

I'm hoping it's going to start simple, for people like me,

and then get slowly more complicated.

Because otherwise, if my brain starts swelling inside my skull

it's just going to pop and I'll distract people.

Thank you.

Welcome to the Royal Institution of Great Britain, established

in 1799 as "an institution for diffusing knowledge",

and perhaps the most iconic lecture theatre in science.

Thomas Huxley championed Charles Darwin's theory of evolution here,

Michael Faraday pioneered our understanding of electricity and magnetism here,

and on this stage he demonstrated the first electric motor.

And the great scientist and lecturer Sir Humphry Davy,

who was also the first director of the Royal Institution

and one of my heroes, spoke here many times.

And he gave the best explanation of the absolute need to do science that I know of -

"Nothing is so fatal to the progress of the human mind

"as to suppose that our views of science are ultimate;

"that there are no mysteries in nature;

"that our triumphs are complete,

"and that there are no new worlds to conquer."

Well, tonight I want to talk about one of the great mysteries,

pillars of our understanding of nature -

the scientific theory that underpins much of the technology

we take for granted in the 21st century,

yet retains its reputation for obscure difficulty and bizarre predictions.

Now, by the time I've finished, I hope that

while your view of reality might have shifted a little,

you'll understand a bit more about how the universe works.

Now, let's start with the contents of this box.

This is a rough diamond. It's worth well over £1 million.

It costs so much because it's rare, and because it's beautiful.

But there's a different kind of beauty here, a more profound

kind of beauty - less superficial, but perhaps far more instructive.

A diamond is one of the hardest known substances -

which is why diamonds are widely used industrially -

but light can stream through it relatively unimpeded.

So there's beauty in a question, which is,

how can something be so ethereal, and yet be

so hard that it can drill through solid rock?

Well, to answer that we need to know about the

structure of the diamond - indeed the structure of all matter itself.

And the best theory we have to describe matter, is quantum theory.

Now, I understand why quantum theory can seem a bit odd.

It makes odd statements.

It says, for example, that things can be many places at once -

in fact, technically it says things can be in an infinite number of places at once.

It says that subatomic building blocks of our bodies

are constantly shifting in response to events that happened at the edge

of the known universe - a billion light years somewhere over there.

Now, this is all true, but that isn't a licence to talk utter drivel.

LAUGHTER

See, quantum theory might SEEM weird and mysterious, but it describes the

world with higher precision than the laws of physics laid down by Newton,

and it's one of the foundations of our modern understanding of nature.

It doesn't, therefore, allow mystical healing,

or ESP or any other manifestation of New Age woo-woo

into the pantheon of the possible.

Always remember, quantum theory is physics, and physics is

usually done by people without star signs tattooed on their bottom.

What makes quantum theory a good scientific theory?

Well, it makes predictions that can be tested against experiment,

and when we test those predictions we find that they agree with observation.

This means quantum theory is not wrong - it's a survivor,

if you like, because it's been put to the test over and over again,

and consistently been found to make correct predictions.

If this changes, then we'll search for a new theory -

there are NO absolute truths in science.

This is how we make scientific progress, and this is how

everything in the world that you take for granted was delivered.

So, remember that however odd it might seem, tonight

I'm going to show you, hopefully, that quantum theory works.

So, I want to explain quantum theory to you in the simplest way that I can.

Ultimately, I'll show you how it gives us insight into the

fundamental building blocks of the universe, and explains the existence

of some of the most spectacular phenomena out there in deep space.

And I'm going to do this now because if I don't point wistfully at the sky at least once,

some of my viewers will get annoyed, so there you go.

That's the only mountain-top pose I'm going to pull...

-LAUGHTER

-..so, to begin...

No helicopters tonight.

To begin, let's zoom into the heart of this diamond.

What I've got here is a sequence of actual photographs of, well,

initially the surface of a diamond, but these photographs

have been taken by a series of increasingly powerful microscopes.

So as we zoom in you see that at first you're seeing a more

detailed picture of the structure of the surface of the diamond.

But as we go right in, you see that a regular pattern,

a regular structure emerges,

so this is an electron microscope photograph of diamond.

And what you're looking at here actually are carbon atoms,

individual atoms.

You see that they appear to be in a kind of a dumbbell shape, and there's a space

and another pair, because you're looking at a two-dimensional image.

But if you take that to three dimensions

and look at this - this is the structure of diamond,

and what you can see is carbon atoms surrounded by four other

carbon atoms, in a regular, beautiful crystalline structure.

Now, in this diamond, this over- a-million-pound piece of diamond,

there are something like 3 million billion billion atoms,

and they are laid out in precisely this beautifully simple way.

I should say, actually, this diamond is as it was when it was found,

so this hasn't been cut. It was found in South Africa well over 100 years ago,

and it's 3 billion years old.

And that structure, its diamond shape -

that's how it naturally appeared, because its structure

is like this, it's built out of carbon atoms exactly like that.

Carbon atoms can't be packed any more tightly together than this.

That's what makes diamonds so tough, and allows them

to cut through virtually anything.

Which makes what I'm about to say quite remarkable.

See, the atoms that make up this diamond -

and pretty much everything else for that matter - are virtually empty.

Now, what do I mean by that? Well, what is an atom?

Well, about 100 years ago now, in the greatest city

known to civilization - which is Manchester! -

APPLAUSE

..Ernest Rutherford discovered that the atom consists of an atomic nucleus,

which is made of particles called protons and neutrons tightly packed together,

and a third kind of particle,

called electrons, orbit somewhere or exist somewhere around the outside.

The nucleus protons are positively charged,

the neutrons are neutral, so it has a positive charge.

The electrons somewhere out here have a negative charge,

and as Faraday would have talked about on this very stage

just under 200 years ago, there is a force that holds

the electron to the nucleus,

because they're both electrically charged.

So that's kind of a sketch, a schematic view of the atom.

We've known that now for around a hundred years.

Protons, neutrons and electrons.

These three particles make up not only the diamond,

but everything we can touch, every structure we can see.

Everything is made up of these same three absolutely identical particles.

So the richness of the natural world, everything on planet Earth,

everything we can see beyond is described by a simple recipe

that determines how these simple particles combine together.

Now, clearly physicists don't call it a recipe, we call that quantum theory.

Now, one of the first great challenges for quantum theory -

indeed, one of the reasons it was developed at the turn of the 20th century,

in Manchester and a few other places - was to understand precisely how these particles

come together to create this diamond, you, me and everything else.

And a hundred years after its discovery, it still provides

our best understanding of the structure of matter.

And admittedly, yes, it is still a bit strange.

Now, one of the particularly strange things about it is the behaviour of electrons inside atoms.

See, these imperceptibly tiny electrons spend

the overwhelming majority of their time in far distant clouds.

So between the nucleus and the electron there is a vast emptiness.

If I were a nucleus, and I perched on the edge of the White Cliffs of Dover,

then the fuzzy edge of the electron cloud would be

somewhere in the farms of northern France.

Looking out towards the electrons I'd see nothing but empty, interatomic space.

So atoms are vast, and they are empty. Actually about -

I've got to count this on my fingers -

99.9999999999999% empty.

That's 13 nines. So, you buy this diamond,

and you're buying about a million quid's worth of mainly empty space, and since

everything is made of atoms, that means you are vast and empty too.

LAUGHTER

Especially you... No, I can't say that, can I?

Never say that to a stand-up comic - what am I doing?

Anyway, if I squeezed all the space out of all the atoms in all

the people on the planet, then you'd be able to fit the whole

of humanity into that diamond, and that's how empty matter is.

So, understanding why atoms are empty and yet so solid,

why light can stream through that diamond, and yet

it sits nicely on the predominantly empty cushion and the predominantly empty floor,

is therefore a prerequisite to understanding the structure of everything in nature.

Now, you might have gathered that the world inside an atom

must be a strange place where things don't behave

much like they appear to behave here in the macroscopic world.

Well, there's one historic experiment

which contains everything you need to know about the bizarre way

that particles behave, and therefore why atoms are the way that they are.

I'm going to need a helping hand for this,

and I know that Sarah Millican has volunteered kindly to help me.

-Where's Sarah?

-I'm here. Hello.

-So Sarah - would you mind...?

Thanks, Sarah. Did you do a science degree, by the way?

No. I've already been asked that by somebody in the audience -

"Did you study physics?"

No, I just sort of gave up after GCSE - is that a problem,

-should I go back to me seat?

-LAUGHTER

-Any other volunteers(?) No...

-Only got a C!

So you may or may not have heard of the double slit experiment, it's something every physics student...

-I've heard of it, but it was something different.

-Was it(?)

-Well, we're going to...

-LAUGHTER

Every physicist is taught this the moment they step through the doors of a university.

It's simple, and it demonstrates the paradoxical world of quantum particles.

So first of all we're going to do it - we're going to do it twice, or even three times.

So I'm going to give you this bucket of sand, which is quite heavy actually.

These are particles of sand, little bits of sand. They're probably your picture,

I suppose, of what a particle might be, a little piece of matter.

So what I'm going to ask you to do is just pour the sand

onto this piece of board, which has got two slits cut in it,

and I suppose before I do it...

-Oh, you bugger!

-It's a bit heavy!

-It is.

You pour it first, then I'll ask you what you think might happen.

Yeah, let's chat for a while, while I'm holding the bucket(!)

It weighs a ton, doesn't it? So just pour it through the slits...

Now, what do you think is going to happen?

So we're just pouring particles of sand over the slits.

Just keep going...

So there we are. That'll do, I think.

So if I remove that... what does that remind you of?

LAUGHTER

I feel like smacking it - does that help?

Pour that sand into there. So that's probably pretty much...

-There you go, you can put it down now.

-Thank you!

That's probably pretty much, I suppose, what you expected would happen.

The sand has just fallen through the slits,

and beneath each slit there's a bigger pile of sand.

Particles fall through slits - pretty obvious.

But...this is a picture of real data.

So this is real experimental data,

of electrons essentially being poured through two slits, so it's electrons

being fired at two slits, and then there's a screen there, and so what

you're seeing are just piles of electrons, so the white spots

really are where electrons hit the screens -

there's a pile, and then there's nothing,

and then there's a pile, and then there's nothing...

Looks nothing like that. But the experiment was the same -

it really is electrons being poured through two slits

onto a screen, and you get that strange pattern.

So, let me show you this, which is a different version of the same experiment.

Now, this is a tank of water, so there's some water in there,

and as you can see there's just a bar that's vibrating up and down,

-and then there's two slits.

-Yeah.

-So you can see the two slits there.

And if you come round here... you can see the screen here.

So there's the two slits, and these are the waves of water.

So there's a flat wave of water hitting the two slits,

and then coming through the slits.

And do you see that there are waves here,

-but here, there's kind of an area where the water's flat.

-Yeah.

Then here there are waves,

then here's an area where the water's flat,

then here are waves, here's an area where the water's flat.

So if I were to, I could sketch it actually on the blackboard.

If I draw that...

We've got those two slits, like that, which you can see there.

and we've got the water wave coming through

and you can sort of see that the waves

when they go through the slits spread out like that.

And I hope you can see that at the front, you're seeing

a kind of a place where there's no waves and then some waves

and then there's a place where there's no waves

and then there's some waves and a place where there's no waves.

-You see that pattern on the front.

-Yes.

So if you were to draw kind of a detector along there,

then you'd see that, right,

because here you'd see nothing, no waves no electrons.

Here you'd see the electrons, here no waves, here waves, here no waves.

So what are we to infer about electrons?

Have you not done your homework today, is that what it is?

I mean this is just the experimental data... This was first done,

by the way, in the 1920s and it was a shock when it was seen,

but the inference is...?

That looks like...that.

-This could be a long game.

-It's the same pattern!

LAUGHTER

GCSE grade C, remember.

This pattern here...

What do you think...?!

You could just tell us.

So, the electrons are behaving more like the waves in the tank

on the water waves and that's a classic pattern you see

when you get waves passing through slits.

Rather than this, which I suppose is what you might have expected

electrons to do, because you might think of electrons as being little grains of sand.

But actually, they don't behave like little grains of sand.

That experiment tells us they behave more like waves and water.

Exactly!

LAUGHTER AND APPLAUSE

Thank you.

Thanks, Sarah!

Thanks, Sarah. That's... Yeah, physics!

Well...

this might all be a bit confusing, as you've just seen,

but if you remember nothing else, remember this - the double slit experiment reveals something

fundamental about particles like the electrons inside the diamond.

Sometimes they behave like particles,

but sometimes experiment says that they behave like waves.

Now there's a deep explanation for this

and I'm going to get to that a little bit later on,

but for now all we need to remember is that electrons behave like waves,

and this is the key to understanding the emptiness of atoms.

Simple? I hope so. So let's clear away the water tank.

So, we've understood that electrons exhibit wavy behaviour,

but how does that explain the emptiness of atoms?

Well, I need some volunteers now and I know that Simon Pegg

and Jim Al-Khalili have kindly volunteered, so would you both like to come down?

APPLAUSE

Have you seen him, there?

Hello!

He's got an earpiece in he's watching really carefully.

So, I've got an experiment for you both to do involving a spring

and your wrists,

so...

What I'd like you to do

is stretch the string a little bit as far away as you can.

Now what I want you to do is start gently oscillating the spring. Very gently.

-Both of us?

-Yeah. You'll see what happens.

Up and down, or longitudinally?

ALL: Ooh!

Shall I sit back down?

Up and down is better. Up and down.

So just a bit more...

There you go... And a bit more.

There you go. So what you're doing is vibrating the spring.

Are you going to jump in?

LAUGHTER

It looks quite painful.

So what you're doing now, just gently vibrating the string,

you notice that it's vibrating in a very particular way.

Cos you're holding it still there and you're holding it still there,

so it's trapped - it's confined, in a sense.

So what you can see is there's only one bit which is moving

with the maximum amplitude if you like, the maximum wave

and it's in the middle there.

So that's called a standing wave. It's called a standing wave

because it's confined.

It's doing nothing, really - it's vibrating up and down.

It's not a wave as you might usually expect it.

Now, if you give it a bit more wrist action...

GIGGLING

Look at that one - now, that...

THAT is the next standing wave up,

so there is a transition from the one where we're just moving here -

this one's got three stationary points.

-I lost me stroke...

-Don't get carried away.

-Sorry, sorry.

Wait, wait, wait -

this has never happened to me before!

LAUGHTER AND APPLAUSE

There - look at that - now there's three stationary bits -

there's one stationary there, one stationary bit there, one stationary bit there

and the amplitude - the maximum amplitude is there and there.

Now, you can get another one going...

if you really try, which is the third one.

There it is! No!

CHEERING

Look at that.

Yes, yes, yes!

Can you see? That's got two stationary points -

-one there and one there. That's a brilliant...

-Oh, it's gone again!

I can see... Hang on... There, there, there!

Two stationary points... 1, 2, 3, 4 stationary points.

-I can see why you've got no air!

-Here it is! There it is!

Ah, that's better now. There's the fourth one.

So, you...

You carry on.

Now it feels like someone else!

It's back! Ah, it's gone!

So if I just sketch... Carry on!

There we go - yes!

-Brian, Brian, Brian, Brian!

-Yeah, yeah, yeah!

APPLAUSE

Perfect.

1, 2, 3, 4, 5 - all right, you can stop now.

Good practice for later!

-Thank you very much!

-Thanks.

APPLAUSE

I sketched what you saw there.

You saw that one very clearly which was this wave

where there were just two stationary points

which were at the ends and then you saw this one,

where there were three stationary points.

And then you saw this one where there were four stationary points

and actually, because you were... That's the best I've ever seen it done,

-there was one with about five, I think, or even six.

-(Yes!)

So, you saw that...

there were only certain waves...

That the spring could vibrate, certain waves it could vibrate

and the reason it behaved like that is because it was trapped at both ends.

So this is what you would call, physicists would call

standing waves and you saw them appear on that spring.

Now, what has that got to do with empty atoms?

Well, just as this wave was trapped between Jim and Simon,

electrons are trapped inside atoms.

The positive electric charge of the nucleus effectively traps

the negatively-charged electron inside an atomic-sized box.

And when an electron is trapped,

just as the spring was trapped between Jim and Simon,

it exhibits the same kind of wave-like behaviour as the spring.

So now we're getting closer to understanding what's happening inside an atom.

But what do standing electron waves around a nucleus actually represent?

Well, the clue is that Jim and Simon had to put more energy in

to switch from one standing wave to another.

So it's tempting to think of those electron standing waves

as waves with different energies inside an atom,

waves that the different energies, the electron can have, if you like

when it's confined around a nucleus and this turns out to be correct.

But, just as there were only certain standing waves on the spring,

inside an atom, there are only certain energies that electrons can have.

Now, quantum theory allows physicists to calculate the shape

of the waves and therefore the allowed energies the electrons can have inside the atom.

And when you do the calculations, you find the lowest energy 'wave',

if you like, so I suppose this standing wave here

that can fit around the nucleus

has a wavelength of around 3 x 10­-10 metres.

Now, let me just write that down, because you might not be familiar with the notation.

It's 1, 2, 3, 4, 5, 6, 7, 8, 9...

0.0000000003 of a metre which sounds

unimaginably small, but it's enormous compared to the size

of the nucleus. It's actually about a quarter of a million times larger.

So that is why atoms are so big and yet so empty.

It's because electrons trapped around a nucleus

behave like waves - in this case standing waves - and there has to be

enough room to fit an electron wave around the atomic nucleus.

But that doesn't answer a very important question.

Now, we've shown why atoms are empty,

But we haven't yet explained

how they become so strongly bound together that they can create solid objects

like our beautiful million-pound diamond here.

Answer that, and we explain the structure of everything we see in the universe.

The early years of quantum theory were dominated by boy wonders,

people actually half my age, believe it or not.

So much so, that it became nicknamed "Knabenphysik",

which translated from German means "boy physics".

The key discovery was made by a man called Wolfgang Pauli.

Pauli published his first paper on Einstein's Theory of General Relativity when he was 18.

And his great contribution to quantum theory was made when he was only 24.

It's known as the Exclusion Principle.

We've seen that electrons can only exist in certain energy levels around the nucleus.

These energy levels, associated with the different standing waves.

Those energy levels correspond to standing waves that can fit in the atomic size box.

But the key point that Pauli realised

is that electrons can't all simply inhabit the lowest energy level.

Now, to a physicist, this should look a bit odd.

I mean, take this apple, for example.

If I lift the apple up, then I have to do work.

I give it energy to lift it up.

And if I let go, so I don't support it any more,

then it falls to the ground.

Now, the explanation of that, for a physicist,

is that the apple is falling into a lower-energy state.

Nature doesn't like to be in high-energy states.

It wants to cascade down into the lowest energy configuration that it can.

But the surprising thing is that electrons don't all live in that lowest energy level in an atom.

It turns out they're forbidden from doing so by an unbreakable law of nature.

That law is called the Pauli Exclusion Principle.

It's kind of like all of you sitting in these rows here.

You aren't allowed to all come down to the front row.

You can't all squash into the front seats, because there isn't room for you.

Electrons don't all occupy the lowest energy slots around an atom.

Instead, they fill each level up in order of increasing energy.

This might sound meaningless,

maybe it sounds a bit abstract.

But let me tell you that it isn't.

You see, Pauli's simple quantum rule is profoundly important.

In fact, it's the key to understanding chemistry.

But don't take my word for it. Time for another volunteer.

I know that James May kindly volunteered to take part in this.

He looks very worried, so maybe he was never asked! But anyway, James.

Now this is doubly amusing for me,

cos I know that you know exactly what's going to happen

because there's a canister of hydrogen gas there

and I know you're a keen aviator, so...

-You think about the story of the Hindenburg...

-Mmm!

-..while I...

-Which was unhappy, wasn't it?

-Oh, I get to wear the goggles?

-You might have to wear the goggles.

It's only a small safety thing, because it went wrong in rehearsal.

So what we're going to do is encourage a small chemical reaction to happen. What we're doing

is bubbling hydrogen through... Hydrogen gas through this, um...

-LAUGHTER

-..through this soap, here.

-Mmm.

What I'd like you to do... Actually, just wet your hands first. Just because it's a safety thing.

It stops your hands catching fire.

It actually... Perhaps roll your sleeves up a little bit.

You'll be all right. I'm sure you'll be fine.

So I'd like you to get - grab - some of that of that hydrogen in the soap bubbles.

Um...

-How's that?

-Don't look...

at what I'm doing.

What I'm going to do is I'm going to encourage a chemical reaction to happen...

from over here.

LAUGHTER

Whoa!

-Ow!

-You all right?

LAUGHTER AND APPLAUSE

LAUGHTER AND APPLAUSE DROWNS SPEECH

Thank you very much for putting yourself at great risk!

Thanks, James. That actually was a lot more fire than I was expecting! Sorry about that.

So what happened there?

What we did was we bubbled hydrogen gas into these bubbles.

James held them, and then I just gave them a little kick of energy

which encouraged them to react with oxygen in the air.

Now if draw the energy levels of oxygen,

then they look something like that.

They don't quite look as neat as when I drew the standing waves on the spring.

That's really because of the shape of the atomic box,

the shape of the box surrounding the oxygen nucleus.

Now oxygen has eight protons and eight neutrons in its nucleus,

which means it needs eight electrons filling up its energy levels.

And the electrons fill up the energy levels like that.

So you get three full energy levels

and two energy levels with a single electron in them.

Now that kind of makes oxygen a voracious consumer of electrons.

It would like, if it can -

it's energetically favourable for it to fill up those missing gaps.

Hydrogen has one proton,

and so it has one electron sat there in its lowest energy level.

Again, it has a space there. It would also like to fill that up.

So what happens, when I give it a little kick with this splint,

is that the hydrogen is encouraged to react with the with the oxygen.

It's energetically favourable for it to share its electron.

So the oxygen shares with the hydrogen,

the hydrogen shares with the oxygen.

There are two gaps, so you get two hydrogens which would like to react.

In doing so, the rearrangement of those electrons in the energy levels

is such a great giver of energy that you saw a flash.

All that flash that you saw, the little explosion, was energy being released

when the electrons in the hydrogen and the oxygen reconfigure -

just like the apple reconfigured itself

by dropping to the ground to get into the lowest energy state.

Two hydrogens, one oxygen. What does that make?

MAN: Water.

-ALL: Water!

-Right!

H2O.

So that is essentially the reason why we get chemistry.

Without Pauli's Exclusion Principle,

all the electrons would crowd down into the lowest energy level and there'd be no chemistry.

Which is worse than it sounds...

LAUGHTER

..because without chemistry, we'd have no magnificent structures in the universe,

like water, diamonds, or indeed, any of you.

Now, there's another consequence of the exclusion principle

that wasn't proved until 1967,

just one year before I was born.

Pauli's principle says that identical electrons

can't occupy the same energy level.

This is an absolute requirement.

So it also means that electrons will avoid each other at all costs.

And that, it was proved, is the actual reason

that I don't fall through the empty atoms that make up the floor.

That's ultimately what gives the illusion of solidity to the empty world of atoms.

And if you think a little bit more deeply about it,

then this throws up a bewildering conclusion, and it's this.

The Pauli Exclusion Principle applies to EVERY electron in the universe.

Not just every electron in a single atom, or a single molecule.

And this leads to a bizarre conclusion.

The particles that make up this diamond

are in communication with particles everywhere.

Inside all of you,

and inside the atoms in the furthest corners of the universe.

Let me explain that a little bit more. The Pauli Exclusion Principle

says no identical electrons can be in precisely the same energy level.

What if you have more than one atom?

For example, in this diamond

there are 3 million billion billion carbon atoms.

So this is a diamond-size box of carbon atoms.

And the Pauli Exclusion Principle still applies.

So all the energy levels

in all those 3 million billion billion atoms

have to be slightly different in order to ensure that

none of the electrons sit in precisely the same energy level.

Pauli's principle holds fast. But it doesn't stop with the diamond.

See, you can think of the whole universe as a vast box of atoms,

with countless numbers of energy levels

all filled by countless numbers of electrons.

So here's the amazing thing - the exclusion principle still applies,

so none of the electrons in the universe can sit in precisely

the same energy level.

But that must mean something very odd.

See, let me take this diamond, and let me just

heat it up a little bit between my hands.

Just gently warming it up,

putting a bit of energy into it, so I'm shifting the electrons around,

some of the electrons are jumping into different energy levels.

But this shift in the configuration of the electrons

inside the diamond has consequences, because the sum total

of all the electrons in the universe must respect Pauli.

Therefore, every electron, around every atom

in the universe, must be shifting as I heat the diamond up,

to make sure that none of them end up in the same energy level.

When I heat this diamond up, all the electrons across the universe

instantly but imperceptibly change their energy levels.

So everything is connected to everything else.

At the beginning, I promised I'd explain everything in the universe,

which I have in some way, but also I said that I'd give you

a deeper explanation of that wavy behaviour of the subatomic world.

So here it is. In my view, this is the deepest explanation we have,

and it's down to the Nobel Prize-winning physicist

Richard Feynman who, his colleague Freeman Dyson once described

as half genius, half buffoon but he subsequently, after having

worked with him for a while, changed that to all genius, all buffoon.

Let's go back to the double slit experiment, but now,

instead of just showing you the pattern...

This is Richard Feynman.

Instead of just showing you the pattern,

I want to show you how that pattern builds up.

Remember, we're firing electrons at two slits,

almost pouring them through two slits

and seeing what happened when they were detected on the other side.

Well, this is one electron at a time being fired through the slits

and hitting the screen, and building up in a pile.

Only when the one electron has gone through, was another one fired

and this is real data, again, a real movie of that happening

and you see the interference pattern.

Electrons, no electrons, electrons, no electrons.

The wavy-type interference pattern building up.

What could be happening there?

So, here it is again. Just electrons

and you see that what emerges is that wave-like behaviour.

So, you might have thought, "Well, I kind of understand

"what's going on with the double slits, there's loads of electrons

"piling through the slits and somehow there's some interference

"just like a big water wave and you build up the interference pattern."

Well, no, because this is one electron at a time,

so, what could possibly be happening?

Well, Feynman was a wonderfully intuitive, logical physicist.

No ordinary genius, he was often described as.

And he said this.

Here are the slits.

Here's the screen.

The electrons starts off here. What happens?

Well, obviously, the particle - electron - must go through a slit

and it must appear somewhere on the screen,

but it needs to be able to interfere with itself -

there've got to be regions on the screen where there are no electrons,

it's prevented from landing there,

so it must, at least, go through the other slit, as well,

and get to that point, and there must be some mechanism

for these paths interfering with each other, but why stop there?

See, that wouldn't be particularly logical.

Why only let it go through two paths?

Why not let it go through that path or maybe

some sort of path like that, or maybe like or maybe, indeed,

off here, out of this lecture theatre

and then maybe through Jonathan's head on its way...

I've got to say through Paul's foot, haven't I? Cos I just have to.

Paul Foot. I don't know - what a rubbish thing to say.

But, anyway, it could go through you, through Jonathan,

off up Oxford Street, up to Newcastle

indeed on to the Andromeda Galaxy

and back again, and land at this point on the screen.

Why not?

Why not allow the particle to travel along every possible path it can,

from one point to the other? And that is indeed what happens,

in the sense that's the way Feynman's theory works.

In principle, it's not too difficult.

You just have to calculate some quantity

associated with each path and find some mathematical machinery

from adding all those things up, and seeing whether or not they all

interfere together and disappear or appear when they land on the screen.

There is a formula that does that

and this is all I really need to say.

Let me turn it around. There it is.

Thank you and good... No, no, I won't say that!

This is called the Feynman path integral,

and this just says,

sum up over all the paths and calculate something

that will tell you the probability

of an electron going from one place to another.

Now, that might look a tremendous mess,

or it might look very simple and illuminating -

I suppose it depends on your point of view.

Probably a tremendous mess, granted.

But this formula is just a little machine,

I think that's a good way to think about it.

It that takes all the possible paths a particle can have,

it adds them up and it spits out the probability

that it'll end up at some particular place.

And that includes the particles that make up the diamond.

Now, for the moment, it's sat on its little cushion there.

Let me put it back in its box.

Now, Feynman's version of quantum theory tells us

something rather shocking.

This diamond is made up of atoms,

and the atoms are behaving according to quantum theory -

according to Feynman's equation.

In other words, they are all currently exploring the universe,

hopping around everywhere, exploring every possible path they can.

And that means this diamond is doing the same thing,

because it's made of atoms.

That means there is a finite chance that it will not

be inside this box at a later time - you can see where I'm going -

but it'll jump, completely out of its own accord,

without me touching it...and that's what I'm going to tell the judge!

But what's remarkable, is that I can calculate what the chance is

by using a simplified version of Feynman's formula.

And this is it.

See, just by doing a bit of maths, you can work that, simplify it,

and turn it into this...

which is an expression for the time you would have to wait,

on the average, to have a reasonable chance of it hopping

out of its box, and it goes like this.

OK, so, that is the distance we want it to hop,

that is the size of the box,

that's the mass of the diamond

and that's something called Planck's constant.

I'm going to need another volunteer here

because I'm going to actually do the maths

because I want to show you that you can do the sum quite simply

and I believe that Jonathan has kindly agreed

to do some sums, so, thank you.

-How's your maths?

-Well, you know, you know that's easy for me.

I do. That's why I asked you, actually.

We're going to do it,

so x - that's the distance we want the diamond to jump.

So let's say the box is about 5cm.

Let's say 6cm for x

and the mass of the diamond is 290-something carats -

-it's about 60g.

-Roughly, yes.

-An expert on diamonds, are you?

So, first of all, we just have to multiply those 3 numbers together.

6cm x 5cm x 60g.

Yeah. 6 x 5 x 6.

So 30 x 60. You just said 6!

60. 60g.

OK, 30 x 6 = 1,800.

Is that right? 60?

-It's heavy.

-It is. The BBC used to pay me in these.

LAUGHTER AND APPLAUSE

-I better take it back. I'm going to get...

-HE LAUGHS NERVOUSLY

-Then, though we get to this.

-Over the thing.

6.6 x 10­-34 kgm­2/s.

That is Planck's constant -

this is a fundamental constant of nature.

It's intrinsic to the way the universe is put together.

It's like the speed of light, like the strength of gravity.

It is THE fundamental THING -

constant, if you like - that sets the scale for quantum phenomena.

So, there's a slight issue here

because you see... You'll have noticed it.

The unit's are kilograms metres squared per second

and we calculated the 1,800 in cm and grams.

Which, by the way, I'm amazed I got that right!

So, first of all, we better another 10­-2 and a 10­-2 and a 10­-3 on,

-so it's 10­-7.

-Yeah.

So all you've got to do is divide that by that.

-All of that with that?

-Divide that by that roughly.

Roughly I don't even know if I can do...

That, for me... That's a kilogram? I don't even know. I do pounds!

-No, I've done the unit conversion for you - you've just got to divide.

-Where's the unit conversion?

1,800 x 10­-7 x 6.6 x 10...

I have no idea what you're doing and why you would want to do this to me!

Help him out, Jim.

Well you've got 10­-34 downstairs. Bring it upstairs

-and it becomes 10­34.

-Where do I put it? Up here?

Yeah, put it next to the 10...

-So then you've got 34 - 7.

-OK 34-7?

-Yeah.

-Yes, OK.

So that's 10­27.

-You've got about 10­3.

-I really... I'm so out of my depth.

This is the worst thing that's happened to me as an adult.

-You've got 10­27.

-OK.

Just for any children watching, I should say,

34 - 7 = 27

So you've got 10­27 and then we've got 6 and we've got 1,800,

so we've got to divide those things so we get about a 3 and another 100.

If you say so!

3 x 10­29...ish.

Once again, I am none the wiser. LAUGHTER

Why couldn't I have done James May's job where you just set fire to me?

And everyone went "Oooh!" And he's so happy he did that

and I'm now sweating.

-We're done.

-We've done it?

-Yeah, you see, this is what that number is you calculated.

See, we just put in the numbers divided by Planck's constant? What this number is

is the number of seconds you would have to wait on the average to have

a reasonable chance of the diamond hopping out of the box on its own.

I could have told you that's not going to happen without any of this.

LAUGHTER

I didn't need the sums. The diamond is safe in the box,

unless it's turned into a dead cat. That's the theory, isn't it?

I'll tell you what this is. Do you know roughly what that is?

-A nine?

-3 x 10­29?

-Why would I know? I'm an idiot!

-In years?

-That's about...

-Well, I'll tell you what it is. It is 600 billion times

the current age of the universe.

I don't know what to do. I'm just going to keep smiling at you.

-LAUGHTER Thank you for sharing that.

-Thank you.

Thanks.

Thanks, Jon.

The point of that... The point of that is to show that quantum theory doesn't just

apply to the inconceivably small world of the atom.

The same rules apply to you, to me, and the diamond.

It's just that for objects out here in the familiar world,

like the diamond, we don't usually see quantum effects.

The reason for that is the smallness of Planck's constant. We had quite a big number here,

but we had to divide it by an extremely small number in order

to work out the time we'd have to wait and that's why that's big.

See, if that was one or something like that, then we wouldn't have had to wait many seconds -

about 1,800 seconds or something like that, for the diamond to hop out of the box.

So it's Planck's constant, this fundamental constant of nature

that means that quantum theory is rather unfamiliar

because it applies to small things, because Planck's constant is small.

Now you could theoretically make the diamond jump sooner.

Look again at this equation.

One way to do it, as I've said, would be to make Planck's constant very big,

but you can't do that. It's a fundamental constant of nature. What you could do, though,

is you could shrink the size of the box, this delta x here.

If I made the box smaller and smaller and smaller,

I'd make the time I had to wait for it to jump out of the box smaller and smaller and smaller.

So this equation says that the more we know the position

of something, the position of this diamond in the box, let's say,

then the more likely it is for the diamond to jump out of the box.

Now this is known as Heisenberg's Uncertainty Principle -

the more you try to pin down a particle's position by trapping it

in a smaller and smaller box, the more likely it is to jump around.

You might have come across Heisenberg's Uncertainty Principle.

It's one of the most famously misunderstood

and misrepresented parts of quantum theory.

It says, precisely, that the more precisely you know

a particle's position, the less certain you can be of its momentum.

And you can see that it emerged... I derived it from a fundamental equation.

It's not complete nonsense. I didn't make it up.

It's often misrepresented by what I would call "mischievous hippies"

to mean that physicists are rubbish at their job

or that the equipment is no good and we're unable to measure

two things about a particle with any accuracy.

But Heisenberg's Uncertainty Principle is a consequence

of the laws of quantum theory. It emerges

from Feynman's equation. It has nothing to do with any of that wishy-washy, drivelly nonsense.

In that spirit, I want to show you that rather than restricting our knowledge of the natural world,

Heisenberg can actually widen it.

In fact, this rule about the unimaginably small particles

can explain some of the most massive and spectacular objects in the universe.

I'm going to end

by explaining how everything I've told you this evening

predicts the existence of diamonds bigger than this -

in fact, bigger than this lecture theatre.

In fact, diamonds as big as a planet and as massive as a star.

Now to understand how this can be, we need to understand something

about the life cycles of the stars themselves.

Stars are big clumps of matter collapsing under their own gravity.

As they collapse, they heat up and they set off a chain reaction

of nuclear fusion reactions where the nuclei of hydrogen

fuse together, initially to form helium, and eventually they fuse

to form carbon and oxygen and all the heavy elements up to and including iron.

That's where the heavy elements come from in the universe.

In this process, vast amounts of energy are released.

That energy creates a pressure that holds the star up

and prevents it from collapsing.

The stars don't have infinite amounts of fuel

and eventually those fusion reactions must cease.

In five billion years, this will happen to our sun.

It'll stop generating enough energy to prevent its own collapse

and so it will collapse.

By the end of their lives, stars like our sun have converted all the hydrogen in their cores

and mainly they've converted it into oxygen and carbon.

Now remember that those carbon atoms,

just like those in our diamond, are almost entirely empty space,

so you might expect that the space can be squashed and compressed almost out of existence

as the dying star collapses.

But as the star collapses and becomes denser,

its electrons get closer and closer together.

Finally, they're so close that they try to occupy the same volume of space as each other.

Then Pauli's Exclusion Principle steps in,

because the electrons cannot occupy the same bit of space -

they are unable to overlap, so they try to arrange themselves

such that they have as much space as they possibly can.

And you might imagine them as being alone inside little boxes like this

and the boxes shrink and shrink and shrink as the star collapses.

But then, as the electrons become more and more confined,

Heisenberg's Uncertainty Principle comes into play. As the electrons' boxes get smaller and smaller,

their tendency to hop out of the box becomes greater and greater,

so you can think of it that they are frantically vibrating

around faster and faster inside these boxes of ever-decreasing size.

This quantum jiggling exerts a pressure, which stops

the star from collapsing any further, leaving something called

a white dwarf star, which is a densely-packed dead star the size of the Earth

but the mass of our sun, and a million times more dense than water.

White dwarfs are so dense that if I were to stand on their surface

the gravitational pull would make me weigh something like 30,000 tonnes.

White dwarfs are strange objects indeed.

But here is the final triumph, I think, of quantum theory.

It is the most powerful example I know of its power to predict how the natural world behaves.

See, it predicts the existence of these strange stars of white dwarfs.

But it does more than that.

In the 1930s, the physicist Subrahmanyan Chandrasekhar

used quantum theory to predict the maximum mass

of a lump of matter that can be held up by the exclusion pressure of electrons

to form a white dwarf. He just used the uncertainty principle, essentially,

and the exclusion principle.

He found that there should be no stars of this type

with masses greater than 1.4 times the mass of our sun.

Now to date, astronomers have found tens of thousands of white dwarf stars

and they have found that not one in the sky exceeds the maximum mass

calculated by Chandrasekhar using the simple laws of quantum theory.

And in amongst those stars, astronomers have found something that I think is quite extraordinary.

Now that diamond is 296 carats.

In the heart of this constellation, Centaurus, which is a few tens of light years away,

they've detected a white dwarf star with the wonderful name BPM 37093(!)

-LAUGHTER

-As it died and cooled, the carbon within the core crystallised.

So BPM 37093, which is somewhere around there, became a diamond,

just like this, but of ten billion trillion trillion carats.

LAUGHTER

We understand in detail why such a thing can exist.

That's a diamond, light years away, intimately connected to this diamond,

and indeed, intimately connected to everything else

in the universe, by the laws of quantum physics.

What a remarkable testament to the power of the wavy behaviour of electrons,

and what a spectacular demonstration of the effectiveness of quantum theory.

Quantum theory is a uniquely potent tool that gives us

our best understanding of how the inconceivably small

can give rise to the inconceivably large.

It is THE most accurate way that we currently possess

to understand our universe.

It explains how atoms are empty yet solid,

how the wave-like behaviour of electrons creates the hardest known substances,

and how the real world emerges from subatomic particles

that explore the universe, the entire universe, in an instant.

There's nothing strange, there's nothing weird, there's no woo-woo.

It is just beautiful physics. Thank you.

APPLAUSE

It was mind-blowing.

I couldn't... Some of it I could understand,

other parts I could not understand. It was so exciting. I loved it.

I love listening to him because he does makes things clear.

He speaks at just the right pace for me to absorb it

and also he's got that very winning smile, so even though

he does insist on telling us how soon it is that the sun's going to die out

and we will all die screaming and flying off into the inky void of space,

you don't mind it because he looks so sweet when he tells you.

What do you now think of quantum physics?

I feel like I maybe should have stuck in at school a little bit more,

but you know, the career that I've chosen is going well, so...

But I have learnt a lot - mainly "don't volunteer for things"!

How are your hands now?

My hands are fine. All it does is singe the very fine hairs on the back.

But I was getting a bit, you know, gorilla-ish anyway, so he's probably done me a favour.

It was great. I loved it. It was fantastic. It was almost exactly about everything

I think about all the time.

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