VARIOUS VOICES FADE IN AND OUT
'I'm Alan Davies...
'And this is a piece of string.
'All I was asked to do is find out how long it is.
'You'd think that would be a piece of cake.'
You can only measure shiny flat things?
'But little did I know that, by the end of the week,
'a centimetre would hold a new meaning and I'd be starting to question the fabric of reality.'
That piece of string could actually be infinite.
Strings can be in more than one place at a time.
Your string does not actually possess a length.
Somehow, by measuring it, we create a length for the string.
THEY LAUGH
'All because I tried to measure string.
VARIOUS VOICES FADE IN AND OUT
'It doesn't look a length till you measure the length.
'The more you measure it, the longer it gets.'
How long is a piece of string? Should be simple.
'Now, I was never a great science enthusiast.
'In fact, at school, I wasn't very good at it.
'But measuring a piece of string, that's something
'I can do. It's just one step up from colouring in, isn't it?
'That's always been a skill of mine.'
I wonder if you can help. I need a piece of string.
A piece of string? Yeah, just a piece. A piece? Say when.
That's good, that is good. A piece of string.
Have you got a ruler?
Yeah, 32 centimetres.
32 centimetres.
That'll be the end of the programme, then.
Thanks for solving that. That's pretty good.
32 centimetres.
Thanks a lot, see you, bye. Thank you. Bye.
Unfortunately, I suspect it won't be that simple,
as I am now about to visit the professor of mathematics.
'Professor Marcus du Sautoy is a maths genius
'but also rather foolish.'
OK, Alan, let me take you into the fourth dimension.
'Last year, he took it upon himself to try to teach me
'some really complicated mathematics.'
LAUGHTER
You've sold me, Marcus.
You've changed my view of the universe.
That's fantastic!
'So who better to help me solve a simple question about string?'
Professor! Hello! Great to see you. How the devil are you? I'm good. How about you? I'm very well.
All I want you to do for me is a simple task this time, shouldn't take long.
OK. I just need to know how long is this piece of string.
Oh... OK, you want the one-minute version? Yeah.
Or the 60-minute version? Well, I've measured it, I know it's 32 centimetres long.
You used a ruler where you bought this? Where did you buy this? The hardware shop. OK.
They had a ruler on the desk, it's been measuring things for years.
And what about this ruler? Do you think it's the same length? It's got centimetres on it, yeah.
You want it in centimetres or inches or cubits? Centimetres, please.
I'm... Or stadia?
LAUGHTER
The problem about measuring things and putting them against...
'I knew he'd be like this. To me, it's a short piece of string.
'But for Marcus, it's a major mathematical problem.'
..measure and make it standard. Measurement is really the beginning of mathematics.
And new numbers arise out of trying to measure things like this,
and the Greeks, they were obsessed...
'Good god, he's giving me the history of geometry.'
Your piece of string is really a fundamental mathematical object.
I've spent the whole morning trying to measure things.
This little Greek symbol here stands for measurement
and it's measuring the size of this double coset - GSP 2 N QP.
OK, tiger. Can I...? Hold on there. MARCUS LAUGHS
I just need to how long this piece of string is. Go back to the string.
There's interesting maths and physics behind the question of how long this piece of string is.
It isn't just 32 centimetres.
You're beginning a journey that mathematicians started 5,000 years ago.
'I knew this wouldn't be as simple as it first appeared,
'but things were going well at this point.
'As far as I was concerned, 32 centimetres was close enough.
'But Marcus wanted to take me somewhere very special,
'a place that's dedicated to just one thing - measurement.'
And that's why we're going to the National Physics Laboratory.
Bits of the bodies were first used as a form of measurement,
so the Egyptians, for example, they had something called a cubit -
the distance from your elbow to the tip of your middle finger.
It's quite a nice distance. Let's measure ours and see...
Look, you've got a huge cubit. Famous for the size of my cubit.
That's no good for measuring, because your house will be bigger or smaller than my house.
It'll be bigger and that's fine. What will it be? Bigger or smaller?
If we have the same number of cubits? It'll be bigger. You'll say,
"My house is six cubits high and it'll be longer." Six cubits high!
I won't be able to get in the door. Whatever. We need something which is gonna be the same for everybody.
You don't really want it depending on whether people are tall or small, or how big things are.
You want something which is gonna be standard.
Do you mind if I ask you a question? Yeah, sure.
How long is that piece of string? Nine inches.
No, no, it's just 12 and a bit. Good guess, though, it's not bad.
Nine inches.
Cheers. Thank you.
He's quite tall, so I bet his cubit is probably a bit bigger than our cubit.
No way you can rely on anything that he says.
Go and ask him how far it is to London.
He thinks that's nine inches, he's 25% out! Yeah.
'Body parts and Egyptian cubits are all very well,
'but they aren't exactly what I had in mind for my string.'
What's needed is some science, and that's what brings us
to the National Physical Laboratory, the scientific home of measurement.
'This is a place filled with priceless treasures carefully locked away.'
It's got this special feet-cleaning sticky floor.
We need to get this for home.
We have to keep the room very, very clean.
'They are the country's measurement standards,
'objects that define the units we use to measure every day.'
This is the UK's primary mass standard.
'That's a kilo to you and me.' It's quite small.
Yes, this little cylinder in here, that's a kilo? Yes.
The size minimises the surface area. There's less to get contaminated. Ah.
'Got them all here, replicas of the cubit.' Wow!
You are an Egyptian man! LAUGHTER
'The definitive yard.'
It's 36 inches at 68 Fahrenheit.
'And a 200-year-old original metre bar.'
How do they decide which metal to make it from?
Well, they commissioned a study to find out the most stable metal
and, after a lot of experiments, decided that a mixture
of 90% platinum and 10% iridium was the most stable material.
This is 90% platinum! 90% platinum. That's quite valuable.
I don't think you'll get that in your trousers. Watch me!
'For hundreds of years, we defined measurements with rods of stone and metal.'
18 fingers. 18 fingers.
Your answer. Happy with that. It's quite cute. How long's a piece of string? 18 fingers.
'But platinum is old hat when it comes to defining length.
'At the NPL, the metre is defined by the speed of light.'
I tell you, this is where we want, the Length Bar Interferometry department.
Let's run out screaming. LAUGHTER
MACHINE HISSES
MARCUS LAUGHS This is really... I love the sound.
I feel like Q in James Bond. Yeah... "Don't touch it, Bond."
One of the problems when you want to measure things very accurately
is keeping them still enough and that's why we have to minimise
the vibration levels that we get in the room.
So this table is floating on air and shining throughout this instrument
is the laser beam that actually performs the measurement.
'A laser! That's the kind of measurement technology I need.'
So I think the amazing thing is that, today, a metre isn't defined
by a piece of metal, but it's defined by light and in particular
how far light will travel in a fraction of a second,
and it's 1 over 299 million.
792458. There you go. Of a second. Of a second, yeah. Yeah.
In that fraction of a second, light will have travelled exactly a metre.
OK.
'If a metre is the distance light travels in three billionths of a second,
'how long is my string in light speed?'
So, Andrew, I was wondering
if I can measure my string here in your interferometer?
It would be a little bit difficult.
I would need to have the ends of the string polished nice and shiny flat
and so I don't think we could measure it in here...
You only measure shiny flat things? In this particular instrument,
but we have got something else which could have a go at measuring it.
A stringometer? A stringometer.
'When they say stringometer, what they mean is this little fellow -
'the fully-automated tracking laser.'
Are you interested in the length of a piece of string?
Do you want us to go?
LAUGHTER
So what you're going to have to do is take your ball,
position it accurately on the end of the piece of string, about there.
Hold it stationary on that end, and tell Andrew when you're ready, he'll record the point.
OK, Andrew. I'm ready.
MACHINE BEEPS
Move to the other end of the piece of string. I'll get out of the way.
MACHINE BEEPS
If he says 320 millimetres, I'm leaving.
Well, according to the laser tracker, the distance between those two points
you just selected is 319 millimetres and 442 micrometres.
It's 319 and a half millimetres?
Just a touch under.
And do you know why it wasn't 320? I didn't add the little bit of fray.
'I thought that was it.
'319.442 millimetres seems a pretty definite length to me.
'But Marcus doesn't agree.
'He thinks we can get an even better measurement,
'something more accurate than the laser can produce.'
It's that long. Yes.
'So we travelled 132.4 miles to the west,
'because Marcus says that my string is actually a famous mathematical conundrum
'and he seems to think that the way to solve it lies in measuring Cornwall.'
Five...six... This could take a while, this is really complicated.
You can do it a bit rough and ready to start with. Do it wrong?
No, it's just quite hard to get inside of all of the little inlets.
I'm prepared to make the effort. I can see you're trying.
This might be the best bit of the show if I get this right.
It could. On the other hand... You deliberately made me lose my place.
Right start again, start again. 133, 143...
'What Marcus wants to demonstrate is that
'how I go about measuring something can change the result.
'With a ruler, from Black Head to Looe is 42 centimetres.'
Down to Looe... It's 42 centimetres.
Now of course the problem you are finding using this is
with a flat edge, it's really difficult to get into all of the inlets and things like that.
What about using your piece of string?
'My string was somewhat better, but produced a different result...'
47 centimetres.
Right, let's do 47. Seems to be growing.
'Finally, a map measuring wheel.'
Gosh, OK! Whoa! Look, this is, this is...
centimetres round the side here. 65.
We've got up to 65 centimetres using this one. So...
with a ruler, we had 42 centimetres.
With your piece of string, 47 centimetres.
If we had an even more accurate way to measure the length here,
we'd probably get the coast going up even more,
because you'd be able to get into all the nooks and crannies.
Each measuring device is effectively zooming in on the coast
looking at in greater detail,
and that reveals more twists and turns.
Each new cove or inlet increases the overall length
all the way down to individual grains of sand.
And the more detail you reveal, the longer the length becomes.
This'll have serious implications for measuring your piece of string,
because this isn't a smooth piece of string.
It's actually also got lots of crinkly bits inside it,
so the length of this piece of string is going to depend on how accurately we measure it.
Oh, boy!
I knew this would happen.
LAUGHTER
So make sure he gets a good night's sleep,
because tomorrow, we're going to find out how long he really is.
'Studying Britain's crinkly coastline
'has actually resulted in a whole new field of mathematics.'
What I want to do is to measure out nine metres.
That's the side of our triangle. 'It's the maths of fractals.'
Excellent.
Brilliant, so this triangle that we're building is
a third the size of the larger triangle.
Now we're going to add even smaller triangles on,
we're going to make it even more complicated. Right.
'Now I was wondering what on earth a fractal looked like.
'But I wish I'd never asked Marcus,
'because he has me drawing triangles in the sand over and over again.'
Brilliant. The sticks are getting a little bit big,
so I think it's chopsticks now. Come on, then. Race you? Race you!
Nice little triangle.
Wow, there you go! OK, shall we do another set of triangles? No.
You got the point? OK. That's enough triangles!
So what we have here is the beginning of a fractal
and does it remind you of anything? Um...
Ice... Dust... Snow. Snow.
It's like a snow flake and in fact this is called the Koch snow flake.
Nice(!) Yes, exactly!
It's the name of the German who discovered the...
EMPHASISING THE END OF THE WORD: The Koch! The Koch, yes, exactly.
All this drawing is so Marcus can show me that fractals
are mathematical shapes that look the same
no matter how zoomed in on they are.
Their shape is repeated over and over and over again.
And he thinks it's the same for my string.
The closer you look at it, the more crinkles appear.
That makes calculating the length of the string a little tricky.
How long do you think the fractal is that we drew here?
How long was the triangle, the big triangle we drew at the beginning?
27 metres. Three times nine. Yeah, nine metres each side,
so we had a triangle which was 27 metres long
and then what we did was to add a smaller triangle on the side
so actually, the length of this has gone up by four-thirds by adding these new triangles,
so every time I add on more triangles, each time, the length increases by four-thirds.
You add one third, but to do the sum, you have to multiply by four and divide by three. Yes.
You've got 27, the original length, and we're adding a third on again
each time we add another triangle. Multiply by four-thirds. Exactly. Now do that again,
add an extra third on by adding more triangles, so maybe you can see what's happening.
Every time I add smaller and smaller triangles on, the length increases
by another factor of four-thirds, and potentially,
the lengths of this fractal... will actually be infinite.
So we've drawn an infinite line in the sand
and because your piece of string is a bit crinkly, a bit fractal-like,
that piece of string could actually be infinite in length.
Right. You've been carrying around infinity in your pocket
all these days without knowing it.
Well, you say that, but look there's the beginning and there's the end.
This is quite theoretical, if you ask me!
You're right, I mean, this is a shape in the beautiful, pure world of mathematics and you're right.
If we kept on adding triangles into the sand, at some point, you're going to hit a grain of sand,
the atom, and you won't be able to divide any further. Yeah, yeah, so!
OK, you're right, but I love this pure world of mathematic where you can just keep on dividing off
into infinity and produce this beautiful fractal thing.
'When I asked Marcus to help me measure my string,
'I thought he would definitely have an answer.
'Instead, he proposes fractals,
'theoretical objects that are infinite.
'But I want a length that works in the real world and that means
'I'm gonna have to leave Marcus and his equations behind.'
My watch says 8:52. What time's it going down?
Doesn't this say when the sun sets?
Yeah, this is the classic 21st-century life.
We're so busy looking at what time the sun sets, we missed the sunset.
LAUGHTER We actually... Oh, it's gone.
It says it's still up at the moment. Oh, does it?! Good, good.
Beautiful sunset. Yeah.
'I've still got my measurement of 319.442 millimetres,
'which is pretty good, but I must be able to do better than that.
'What I need to do is measure it in the smallest units possible
'and surely, that means measuring in atoms.
'So...I guess I'll have to get to grips with some physics.
'Just one problem.
'When it comes to physics, I have a little secret.'
I've been sent back to school to do physics,
which I'm not proud to admit
that I deliberately failed my mock O-level
to get a U, so that I could drop it.
I've been slightly anxious about a physics teacher,
but got my string and actually I'm finding it quite comforting.
SCHOOL BELL RINGS
'This is the Simon Langton School for Boys
'and I'm here to meet one of the country's best physics teachers -
'Becky Parker.'
Hi there! Hi! Are you Becky? Yeah, welcome to the Langton. Nice to meet you. Lovely to meet you.
I've got a bit of a problem - I've been trying to measure the length of this piece of string.
Right, and you want a straightforward simple answer to this one? Wow! Is there one?
When you get down to the really tiny scale, things get complicated
and that's why your problem of measuring really accurately that length of string
is not just straightforward. I need to take you on a bit of a journey through
lots of quite wonderful ideas, which I think you'll find quite mind-blowing.
I had a feeling there'd be a journey.
'This is exactly what I was afraid of -
'being locked in a dark room with a physics teacher.'
'Any minute now, she'll ask me for my homework.'
There you go, just need to get it completely dark... Oh, now, hold on a minute.
SHE IMITATES A FANFARE AND PRESSES A SWITCH Bang...
Oh! Electricity, that's what you need.
Hey, hey, we have light!
Now we're going to try and do some experiments
to understand what's going to happen and it is quite amazing,
almost magical in a way, to see the weird effects which happen
down in this atomic world, but what do you understand the atom as being?
I bet you've probably done that at school? I have a vague recollection of it, yes.
Have you got any picture of what that atom might look like?
Something might come to me.
Would you like to draw a model of the atom on the board?
Why certainly!
Draw an atom. Yeah.
Right...
Well, all I really remember, I remember from school,
I remember there was...
There's something very, very small in the middle. Yeah.
And then, is there not something going round and round it?
Yeah, definitely. Spinning round and round.
So, in the middle, there's protons. Yeah.
And neutrons. Yeah, absolutely brilliant.
And then, what's the thing that's going round? Electrons. Electrons.
That's it. That's all I remember. Yeah.
I mean, this is how the atom is portrayed,
a bit like a little mini solar system that you've got this thing
which is pulling the electrons. An orbit thing. Yeah yeah.
It gives an idea of how tiny this nucleus is with the protons and neutrons compared to the electron.
Most of the atom is nothing. So if you collapsed - here's a question -
if you collapsed, all of what you are as matter,
the whole of the human race into just the massive stuff,
which is the protons and neutrons, what would be the size of...?
If you just took the actual stuff that we're made of
and took the space out, we'd shrink down dramatically.
I mean, I'd come down to just a little bit of... Yeah. ..a crumb.
You be careful, cos you wouldn't see you, you'd be microscopic.
The whole of the human race would be in the volume of a sugar cube.
Everybody? Yeah.
So the matter of everybody in the world amounts to one sugar cube?
Yeah, if you got rid of... The rest is just space? Yeah.
And so, we're all made up of these just tiny little fundamental things.
'Talk about making someone feel inadequate!
'We're all made up of space, of nothing at all.
'At least I've managed to pass my first physics test.
'Quite pleased with my atom.'
The only trouble is, if the atom was like that,
then the actual electrons, if they were accelerating round
orbiting the protons and neutrons, they would lose energy
and so they would actually spiral into the nucleus
and that would mean that all matter would just collapse.
Now we know that matter doesn't. So that's wrong? The only thing I remember.
I know, because that's what you've always been taught
then you have to re-learn it and think that's not a very good model cos it doesn't work at all.
So sorry about that! That's what often happens.
You have to sort of, you know, refine your thinking as you understand more and more.
Atoms aren't what I thought they were,
not neat little solar systems with particle planets.
According to Becky, they're much weirder than that.
So weird, they have their own branch of physics - quantum mechanics.
'And that is a big problem, because in quantum physics,
'the particles in my string can be in two places at once.
'And that makes working out where they are really hard.'
So...the thing about why actually it's important is
when it comes to footballs, for example, which, obviously, are particle-like... Mm-hm.
..they're smeared out, so in the quantum world, they wouldn't just be here.
It'd be all over the place and around and you wouldn't necessarily be able to tell where it was.
So if I throw it at you, in the quantum world, you wouldn't be actually sure where...
A bit like somebody trying to save a penalty, you wouldn't know which way to go.
Oh, there you are, you see. But that was a terrible penalty.
But say, in the quantum world, we wouldn't know exactly in which position the ball was.
It could even be behind me or over your head.
So is this ball that ball? Yeah, exactly. It can be in two places at once? Yeah.
'This is a fundamental tenet of quantum physics.
It's not a weird by-product, but a reality that explains how the smallest objects behave.
The whole question of actually defining where the atoms,
where the footballs are becomes quite a serious measurement problem.
That's the last thing I wanted was a serious measurement problem. It's the nature of the quantum world.
I wanted a simple measurement solution. It's not straightforward,
because you can never be exactly sure at what point your string ends.
Oh, no!
LAUGHTER
'I find it hard to accept
'that particles can be in two places at once,
'not just two places at once, but many places at once.
'Unfortunately, to see this miraculous behaviour
'takes a lot more than a bag of footballs.
'To prove to me that my string can be in many places at once, we need a real physics lab.
'At Imperial College in London, they have the equipment
'to see individual particles and watch how they behave.'
All these flashing lights... A centre for cold matters.
Is that the fridge? SHE LAUGHS
Johnny! Hi, great to see you. Hi. Thanks for seeing us.
Dr Johnny Hudson, Alan Davis. Hello! Hi, good to meet you.
'Becky and Johnny have chosen one of the most common things in the universe
'to provide evidence that objects can be in two places at once.
'It's something that surrounds us all the time - light.'
We'll shine a laser beam through two very narrow slits. Can you see them?
Can you see two? OK. Just. Yes, yes, I can.
They're about the size of a human hair each and they're spaced by about the same amount. OK.
What you can see over on the far wall
are the stripes from the waves coming from each slit interfering.
'Right, let's just stop it there.
'In a minute, I will to see something that was to turn my world upside down.
'But to properly understand it, Becky needed to explain a simple concept.
'It's all to do with how light works.'
Firing laser light at two slits
doesn't create two shafts of light, as you'd think.
It creates stripes.
That's because light is a wave.
The waves of light pass through both slits
and then interfere with each other.
Some add up to give bright bands, others cancel out, leaving darkness.
Becky calls this an interference pattern
and she says it's telltale evidence that the light
has passed through both slits at the same time.
But Johnny is only going to send through
a single particle of light, called a photon, at a time.
Of course, you'd have thought that would just create a dot,
but that wouldn't be quantum.
OK. So what we can see here
is each of these little green splodges of light
is a single photon.
OK, so this is now averaging those successive frames together,
laying them on each other as if you printed them and put them in a stack then held them up to the light.
Where you get more photon impacts, you see a brighter green colour.
Where there are fewer, you see a darker colour. And you can see that?
It's amazing. Stripes. Completely amazing. It's definitely stripes.
'If only one photon at a time goes through the slits,
'how does it create an interference pattern?'
So you've got your photons, they're going through two slits.
And they, they're passing through them, one photon goes through both,
it has to go through both to create the wave effect. Yeah.
But it's one photon. Yes. So it has to be in two places at once? Yes.
It has to be in both slits at once? Yeah, effectively.
It's adding up to a bright band, cancelling out to give nothing...
But the photon's something that... That's as small as you can get.
You can't split it in half and re-form it?
Well, that's because you can't then have that picture of it being a single particle.
It seems to then act as a wave when it goes through the slits.
The thing is, position isn't a good idea any more.
Position is something that's useful for big things.
But when you talk about the smallest things, position is not a good idea any more.
You mean where things are? Yeah, they're not in a place.
They don't really have a position as such, which is surprising, right?
'I thought that Johnny would have a big fancy machine that would count the atoms in the string.
'It's a tricky task, but at least understandable.
'Alas, the real world just isn't like that.
'It turns out, in reality, the fundamental building blocks
'of the universe don't have a fixed position.
'Well, if that's the case, how am I ever going to measure my string?'
I think the philosophical understanding
of how we understand reality has got a long way to go, I think.
Really, we probably need a whole new way of thinking about the world.
Yeah, it's quite difficult to get your head round,
except it turns out out it is possible to get your head round it,
because your head could be in two places at once. Ha-ha!
Yes, so your head could be here and then it would understand.
Yeah, it's getting your head round the fact that you could get your head round it. That's the trouble.
Wow, this whole measuring thing turned out to be
so much more complicated than I thought.
FAIRGROUND MUSIC PLAYS
'Measurement should be easy. I do it all the time
'but according to quantum mechanics, it's an almost impossible challenge.
'Worse than that, it's a science that declares
'that the world is mysterious and confusing.
'I knew that already.'
It sounds like a cop-out to have a theory which says that you can't work out the answer.
Well, Alan, yeah, like you, Einstein grappled with this and never...
I like that sentence. Yeah, you and Einstein.
Like me, Einstein grappled with the laws of physics. No, you did!
Einstein and I have many of the same concerns.
Yeah. You know, people like you and Einstein
expect to be able to understand the world and have it...
We do, we both do. Yeah, have it completely clear exactly what reality is.
You...
You don't get an absolute, definitive answer.
You get probabilities and likely to be here,
and most probable to be there.
I'm gonna go back to 320 millimetres.
'Becky has been trying to help...
'But I think she might've scrambled my mind.'
'Position is not a good idea...'
'I thought she'd give me real world answers,'
'Turns out the real world is stranger than I imagined.
'Now I'm more confused than ever.
'But what does this mean for me and my string?
'We're all made of atoms and particles.
'Does that mean we're also blurry at the edges?
'Can I be in many places at once? VOICE ECHOES
'If I'm here, where else am I? VOICE ECHOES
'I want answers.'
'Quite an amazing journey right right down into the tiniest stuff
'which I think you'll find quite mind-blowing.'
'To find them, I've arranged to meet a professor of quantum physics,
'a man called Seth Lloyd.
'Seth is a master of the quantum.
'He works with particles and atoms all the time and can bend them to his will.
'Seth's the man to bring sense to this quantum madness.
'But I'm not entirely sure why he wants to meet me in a taxidermist's.'
Seth! Oh, Alan! Hello. Good to meet you.
Nice to meet you too. Thanks for inviting me to this place.
You're probably wondering why I asked you down here today. It has crossed my mind.
You have nothing to fear. Good! LAUGHTER
In fact, I brought you here to introduce you to Fluffy.
What a beautiful cat. She WAS a beautiful cat.
LAUGHTER
First, let me ask you a question. Do you think this cat is alive?
No, I think, I think it's stuffed. You think it's stuffed? Yeah.
Now it may not seem to begin with that cats have much to do with measuring string,
but in fact, they have everything to do with measuring string.
About 70 years ago, the German physicist, Erwin Schrodinger,
came up with a thought experiment about a cat,
a thought experiment which I'm now going to ask you to go through.
OK. I'm ready. OK.
So Schrodinger imagined that you had a cat.
But then, as a result of a radioactive decay,
where an atom would decay and emit a photon,
this photon would be absorbed by a detector and, if the photon was absorbed by the detector,
then a small amount of poison would be put in the cat's milk.
The cat would drink the milk and then die.
Right. At the level of quantum mechanics,
a particle isn't in one place or another,
so the photon in some funny sense is both detected and it's somewhere else where it's not detected
and that means that the poison is being put in the milk and not being put in the milk at the same time.
So if a photon can be here and there at the same time, then a cat
can be alive and dead at the same time.
'I was hoping Seth would make things seem less weird,
'but now, things aren't just in two places at once.
'They're also dead and alive at the same time.'
I'm picking up the thought experiment and I get the theory,
but in reality, we're alive, the cat's dead.
The string is a certain length. Well, that's what Einstein would've liked to have thought.
This is why Einstein didn't like quantum mechanics. Right. So what's going on?
How can a cat be alive and dead? We never see the cat alive and dead.
This has to do with observation, crucially.
Looking at the cat is an act of measurement and if the cat is,
in this funny sense, alive and dead at the same time, and we look at it or measure it,
it effectively has to have become either alive or dead,
but not both.
LAUGHTER
I'm getting it, but I just feel as though, even if I don't see it, it's still dead.
Yeah, so it's important here to, to think about what we mean by observation.
Most human beings when they say, "We observe something," it means we're there to see it.
But you have to think that, as every particle of light bounces off this cat,
it's effectively observing it, so if there's anything there to detect whether the cat is alive or dead,
then it's either alive or dead and not alive and dead at the same time.
CAT PURRS
So big things don't show up being two places at once
or cats don't show up being dead and alive at the same time,
cos they're big and interact with their surroundings.
Every interaction with the surroundings is effectively an observation.
The environment observes the cat.
And this is very important for your length of string,
because, just in the same way the photons can be here and there at the same time,
the string can have multiple lengths at one time.
'This isn't the news I was hoping for.
'In fact, it's an utter disaster.'
Your string does not actually possess a length.
Somehow, by measuring it, we create a length for the string.
It hasn't got a length till you measure the length?
It doesn't, and then its length is what you measure it to be.
Then it goes back to not having a length again? It's not even really there until you measure it.
That's what Einstein hated about quantum mechanics,
that things aren't there until you actually look at them.
So reality, in some sense, doesn't exist unless we're actually observing it
and it's our act of observation that makes things real.
Oh, no!
'Right, so let me get this straight.
'My string doesn't have a length until it's observed, and then its length is created.
'But it IS observed, it's in my pocket.
'The last time I looked, it was about 320 millimetres.'
I'm enjoying the theory and the thought experiments.
I can see things and where things are and I'm not really getting the relevance to the real world.
It doesn't really matter.
This is all just theory that isn't really relevant,
because we are observed by the environment, so does it...?
Who are you - Einstein?! Does it really matter? What's your problem(?)
I feel more and more like Einstein every day, which I previously thought was a good thing.
You think that quantum mechanics doesn't matter in a really important way for living things.
Come with me, I'll show you how it matters. Don't knock quantum mechanics, baby!
LAUGHTER
'Seth doesn't need a laser or a lab to demonstrate
'that quantum mechanics isn't only relevant to invisible particles.
'All he needs is a greenhouse.
'He's brought me to Kew Gardens, cos the latest scientific research
'has uncovered a surprising truth.
'That all life on Earth relies on quantum physics.'
You say you don't believe that quantum mechanics is really important at a basic scale.
So what would you say if I told you that every single plant here
is using quantum mechanics in a fundamental fashion in order
to turn light into energy, and to build itself up from scratch?
Nature effectively discovered how to use the same kind of quantum weirdness that allows
particles to be in two places at once
and that underlies Schrodinger's cat in order to make all this happen.
Things have to be in two places at once or there's no plant life?
That's right, exactly.
How do the plants know that?
Even I know that plants turn sunlight, air and water into food
in a process called photosynthesis,
but according to Seth, this relies on quantum physics.
The way that photosynthesis works is that a photon particle of light from the sun comes in,
gets absorbed in a gigantic molecule like a chlorophyll and it creates
an energy state called an exciton, an excited state of electron.
Now this exciton has got to get from this side of the molecule where it's been created
to this side of the molecule where it can be turned into chemical energy and photosynthesis is incredibly
efficient in this energy transfer process, like 99% efficient.
And that's very hard to understand because you can understand if it were maybe, like, 50% efficient,
so if half the energy got there,
but it's quite crazy that 99% of the energy gets from where it's absorbed
to where it actually gets turned into chemical energy.
And the way that these organisms figured out how to make it efficient is by using this wacky quantum state
where you go through all possible paths at once of the molecule
so it's in many, many, many different places at once.
That way it can do it without dissipating all this energy that it's got.
We've gone past two places at once.
We've gone into thousands, millions of places.
Millions of places at once, yeah. Hey! Hey.
It's almost like this quantum process
is trying to find a path through a maze,
and the energy takes every possible path at the same time
but having arrived at the centre,
it appears to have only taken the quickest route.
Without this quantum weirdness that allows plants to be so energy-efficient,
life on earth would be very different.
So without plant life discovering this ability to transfer energy
in that way, there's no dinner on the table, there's no anything?
There's no barley for the beer.
I have new respect for plants now.
The question really is do they have new respect for you?
THEY LAUGH
Quantum physics isn't restricted just to plant life.
It's everywhere. It's even in me.
Apparently quantum physics is going on between my ears.
Alas, not in my brain but up my nose.
Smell that. Very nice.
You couldn't smell if quantum mechanics weren't there to help you.
The role of quantum mechanics in the way we smell
is not yet fully understood, but a research group,
led by Professor Marshall Stoneham, are just beginning to uncover it.
Dr Simon Gain. Hi, there.
The question is what happens when you actually get a smell.
But what we believe is happening is the smell molecule has to pass through various mucus layers
and so forth and it ends up at a receptor, and you have 350 different receptors.
And they're all sitting there waiting to be triggered?
That's right, and only perhaps a dozen of those will be triggered by
any one scent molecule, and then the mixture of those signals is what tells your brain which smell it is.
And if it was a bad egg that you've just opened, then you'd get that effect of the bad egg smell
about a millisecond, about a thousandth of a second after things had gone in.
We can show you because it doesn't happen everywhere in your nose.
It only happens in a specific bit right up at the top between your eyes
and in, just behind the bones of your nose.
So if you're interested, we can put a camera up there and have a look.
And what does this camera look like?
This is the camera.
Holy smoke!
Better you than me, is all I can say.
Yeah, yeah.
To see where the quantum physics is happening, required numbing my nose and face.
And placing a camera just below my brain.
So that's called the nasal vestibule, the hair-bearing part.
Looking into the nose now with the septum on the
right of the picture, we're looking right up just below your brain.
Right here at the top of my nose is a gap in the skull
that allows the smell receptors to connect directly to my brain.
And that's where the lining of your nose changes from the respiratory mucosa
to the olfactory mucosa
which has the nerve endings that bear the receptor that we think works by quantum methods.
Just seeing if you left any equipment.
THEY ALL LAUGH
Thank you!
As a scent molecule travels up the nose, it finds its way to a receptor.
To distinguish different smells, the receptors have to send a signal to the brain.
That signal is triggered by an electron.
The only way for the electron to signal the brain
is to go through the solid scent molecule
though this should be an impenetrable barrier,
but when the right molecule hits the right receptor,
the electron can magically pass through the molecule
and begin its journey to the brain.
This seemingly impossible process is called quantum tunnelling.
What's remarkable, I think, about this is that,
we've known about quantum mechanics for 100 years now
but only in the last few years has it become clear
that nature actually discovered all this quantum weirdness
a billion years before human beings even came on the scene.
You would expect it to be very interesting to go from what seemed to be a purely theoretical
experimental side to something that's actually day to day life.
So are you willing to accept now that quantum mechanics is more important to life than just dead cats?
Yes, I can accept that.
The smell of success!
Yes, I get it.
Quantum physics underlies everything in the world,
and gives us a glimpse of what reality is actually like.
It's amazing and I'm very pleased that smart people like Seth are working all this stuff out
but I just think we've taken a bit of a detour.
I set out to measure a piece of string
and I can't believe that 0.442 of a millimetre
is as accurate as I can get.
Surely, there's a way to go beyond that to get a better length.
So Seth,
come on!
You've shown me a lot of particles and waves and...
I know a bit about quantum mechanics now but I don't know the length of my piece of string.
Fair enough.
Isn't science always like that?
It's turning out that way.
It answers lots of questions but not the one you want to know the answer to.
How long is a piece of string?
Absolutely.
Well, let's look at how accurately you could possibly measure your string. Yes, let's.
All right, so you know that if you can measure your string very
accurately within a millionth of a metre by counting the number of wave lengths of light that go along it.
And then you say hey, I can measure it more accurately
by putting in light with a shorter wavelength, so if the light
has half the wavelength, I can measure it to twice the accuracy.
This is what they were talking about at the National Physical Laboratory,
using the wavelength of laser light to measure my string.
Despite the uncertainties of quantum physics, it's the best way to measure length.
Theoretically, there is almost no limit to how well you can measure with it.
In principle you could actually by making a light wiggle up and down really, really, really, really fast,
you would think, "I can measure my string to any degree of accuracy I want."
Which would make you happy. Yes.
But there's one slight hitch. Yeah, I thought there'd be a "but" after it.
Yeah, yeah, I know.
I know. It's always this way, right?
Yeah. So... Go on then, what is it?
OK, the hitch is that if the light is wiggling up and down faster,
each photon has more and more energy
so if it wiggles up and down twice as fast, you double the energy of the photon.
That's OK, we just put in more energy but we get a better measurement of your piece of string.
But what Einstein taught us is that energy effectively has mass,
and mass gives us gravity, but there's actually a limit
to how densely you can pack a bunch of energy into a sub-class.
What's the limit?
Do the words, "Black hole" ring a bell?
I can make a black hole with my string? Well, you can.
Measuring leads to black holes?
To measure you need to put in energy. Energy causes gravitation.
Excess of gravitation causes black holes.
Oh, that's a terrible disappointment.
I'm going with the black hole, Seth.
You wanted to know the answer.
I don't care any more.
Thanks for everything but...
kaboom!
THEY LAUGH
I've learnt something.
I just thought at the beginning of this, a group of men in white coats
would point a laser at the string and da-da, you'd get a length.
But it turns out that trying to measure
something as simple as string is actually a philosophical journey.
'The whole of the human race would be in the volume of a sugar cube.'
'Everybody in the world?'
It's led me to discover the fundamental building blocks of everything defy reality.
We're only scratching the surface of what's really going on in the world.
'The length of this piece of string is going to depend....'
'It's a simple task, this time, shouldn't take long.'
'The more you measure it, the longer it gets.'
How long is this piece of string?
Right, and you want a simple answer to this one?
319 millimetres and 442 micrometers.
That piece of string could actually be infinite in length.
'Things aren't there until you actually look at them.'
VOICES ECHO
32 centimetres.
That'll be the end of the programme, then.
But after all this maths and physics,
how long is my piece of string?
Well, I promised to tell Marcus the answer.
Hello, how are you! I'm good, how about you?
I'm fine, I'm fine.
My head is full of string now.
So ultimately what's the answer? How long is your piece of string, Alan?
It's 320 millimetres.
That's what you said right at the beginning.
But every time I asked someone how long is it, they took me further and further
down into it and they said, really you can't measure it.
How long's a piece of string? We just don't know.
I think your piece of string might deserve a drink after its long journey.
Shall we take it for a pint? OK.
I still don't really know, though, why I had a six inch needle stuffed up my nose.
I still don't really understand that bit.
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