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- This is one of my favorite experiments of all time
because if you think about it deeply enough,
it becomes really counter-intuitive
and you have to dig even deeper than that
to solve the mystery at the core of it.
You may have seen this experiment on YouTube already,
but I can always guarantee
that you haven't seen an explanation of how it works.
I certainly wasn't able to find one.
It's an experiment that shows how sugar in solution
can twist light.
Specifically, it can change the direction
of polarized light.
You probably know what polarized light is already
but just to recap.
So light is an oscillation
in the electric and magnetic fields
that permeate the universe.
So, you know, if light is traveling towards you
that represents an oscillation in the electric field
and perpendicular to that,
an oscillation in the magnetic field.
For simplicity sake,
it's a good idea to just ignore the magnetic field
and just focus on the electric field
just cause it makes diagrams cleaner,
but just know that the magnetic field
is oscillating as well
and it's perpendicular to the electric field.
So you've got light traveling towards you,
here's the oscillation in the electric field
and it's going up and down
but it could just as easily be going side to side.
In fact, it could be oscillating any of those directions.
But because it's a quantum mechanical system,
actually it can be a superposition
of all those different directions.
And that's what unpolarized light is.
It's light that is in a super position of the electric field
oscillating in all different directions.
If you pass unpolarized light through a polarizing filter
like this one,
then it restricts all those oscillations
down into just one direction.
So the light reaching the camera from my face is polarized
and I can change the direction of that polarized light
by, you know, turning the filter like this.
This computer monitor has a polarizing filter in it,
like most computer monitors actually.
So all the light coming from this monitor
is already polarized.
If I put another polarizing filter in front
and change the angle, you can see the effect.
So if I put the polarizing filter at 90 degrees
to the polarization of the light coming from the monitor
then it all gets blocked.
But if I line them up,
then the polarizing filter lets all the light through.
Here's the crazy part though,
if I put this cylinder full of sugar water
between the monitor and the filter,
now look some of the light gets through
and that's because the sugar
is twisting the polarized light.
It's changing the direction of it
so that some of it can now get through the filter.
The more sugar you put in the way,
the more the light turns.
So I've chosen a concentration of sugar
that turns the light about 90 degrees.
It's approximate
because different wavelengths respond differently
which is why the color changes as I rotate the filter.
This whole thing was mind blowing to past Steve.
I couldn't figure out how this jumble of molecules
that are all oriented in different directions
could possibly have this effect,
could possibly lead to a net turning
in the clockwise direction and always clockwise,
never counter-clockwise,
that doesn't make sense.
Like surely if there's a molecule in the solution
that slightly turns the light clockwise
then there's gonna be another molecule
oriented in a different way
that will turn it slightly counter-clockwise.
The net result should be no twist
in the direction of the polarized light at all.
Like it felt like a glitch in the universe.
That's not the solution by the way,
to get to the answer
we need to look again
at the superposition of different polarized states.
So imagine you've got some lights
and it's in a superposition of two states,
one is polarized horizontally,
the other is polarized vertically.
So you've got an electric field
oscillating up and down in one state,
and you've got the electric field
oscillating side to side in the other state.
What does the superposition look like?
We can actually just think about it
like summing up those two waves.
So look at this point in space, for example,
what is the sum of the displacement
of the electric field at this point?
Well, it's displaced a little bit vertically
and a little bit horizontally.
The superposition of those two states
is just this point here, right?
It's a little bit vertical and it's a little bit horizontal.
So it's out here.
If you look at the superposition
of the two states at this point,
well the electric field is not displaced at all from zero,
from the access at this point.
So the superposition is zero as well.
Then at this point, you're a little bit out to the right
and you're a little bit down.
And so the super position
at that point is diagonally down and to the right.
And if we do that for all the points along the axis,
then we get this result here.
In other words, the superposition of these two states
can just be thought of as a third state
which is at 45 degrees to those two.
Let's do that same exercise again
but this time shift, the vertically polarized state
forward through a quarter of a wavelength.
Let's see what happens now,
looking at this point,
the superposition must be just out to the left there
because the vertical component is zero.
At this point,
the superposition must be just vertically downwards
because the horizontal component is zero.
At this point, the superposition must be to the right
because the vertical component is zero.
At this point, the superposition must be vertically upwards
because the horizontal component is zero.
Let's join those points together
and this is the result, this helix, this spiral.
So this is clockwise circularly polarized light
and you can have counter-clockwise
circularly polarized light as well.
So you can think of circularly polarized light
as the superposition of two linearly polarized states
that are perpendicular to each other,
where one of them is offset by a quarter of a wavelength.
You know, if you search online
for things like circularly polarized light
and superposition,
you'll find diagrams like this one.
What's interesting is,
there's a diagram that you won't find,
or at least I wasn't able to find
and it's really important for this explanation.
And it's a diagram of the opposite of what we just did
because it turns out that the superposition
of two circularly polarized states,
one clockwise, one anti-clockwise
gives you linearly polarized light.
So that this is maybe the first time
this diagram is appearing on the internet ever,
something that I have been able to find
almost certainly in video form.
Look, you've got two States here,
one is polarized in the counter-clockwise direction,
one is polarized in the clockwise direction.
Let's look at some points and see how they add up.
So look, at this point the two waves are in the same place,
so the superposition must be there at that point.
Here, you've only got horizontal components in each wave
and they're in opposite directions
so they cancel out.
Here, the two waves meet again,
so the superposition must be at that point.
Here, the two horizontal components cancel out,
so it must be here.
So let's draw all those points in
and see what the result is.
It's linearly, polarized light.
So that's really important.
You can think of linearly polarized light
as the superposition of two polarized states,
one circularly polarized in the clockwise direction,
the other circularly polarized
in the counter-clockwise direction.
So what happens when light like this
passes through a solution of sugar
like the light coming from my monitor?
Well, I want you to imagine
that the solution of sugar is like this bag of pasta.
It's actually nothing like this bag of pasta,
but I want you to imagine that it is just for a minute.
So you've got all these molecules, all jumbled up,
all in different orientations.
Let's have a look at what happens
when the light passes through
a single one of those molecules
and it happens to be oriented vertically like this.
So the light is linearly polarized,
which we can think of as the superposition
of two circularly polarized states
going in opposite directions.
And hopefully you can see that those two states
will have a very different experience
of traveling through this molecule of pasta.
The clockwise circularly polarized state
is in step with the pasta,
it's nestled into the grooves of the pasta.
Whereas the anti-clockwise state
is in opposition to those turns.
It's constantly bumping into those flaps of pasta.
For the purposes of illustration,
I've chosen a wavelength of light
that matches the spacing of the pasta's spirals.
In reality, it's not gonna be like that most of the time
but hopefully you can see regardless of the wavelength
that those two different directions
of circularly polarized light
will have a different experience
of passing through the pasta.
Why does that matter?
Well, you probably already know
that light travels more slowly in glass.
And so the peaks and troughs of the wave
have to bunch up to compensate.
In other words, the wavelength that goes down.
And that's true when light passes through anything
actually not just glass.
It's also true when light passes through a molecule
like our spirally pasta molecule here.
Let's suppose hypothetically
that the clockwise circularly polarized
component of our light
interacts more strongly with the pasta
because it spends more time traveling through those flaps.
Well, in that case we would expect that component
to be slowed down down more.
To relate that back to the language
that we used to talk about light,
you would say that the index of refraction for this pasta
is higher for clockwise circularly polarized light
than anti-clockwise circularly polarized light.
The two components of light see a different refractive index
when they interact with this pasta.
So if the counter-clockwise component of the light
is traveling more quickly through the pasta
than the clockwise component of the light,
it will have traveled further
by the time it exits the pasta at the top there.
In other words,
the counter-clockwise component would have shifted up
relative to the counter-clockwise component.
What does that do to the superposition of these two states?
Hopefully you can see from this animation
that if you shift one of the components or states
of polarized light forward,
it causes the superposition in yellow to rotate.
So if we have a solution of sugar
where all the molecules are all pointing
in the same direction,
they're all aligned vertically like this,
all throughout the solution,
then we would expect the light to twist as it comes up.
And to reiterate why,
that's because this linearly polarized light
is the superposition
of two circularly polarized light states
and they have a different experience as they travel through.
One goes more slowly than the other,
so by the time they leave,
the phase between them has shifted
and that twists the superposition.
But a solution of sugar is not like that,
it's a jumble of molecules in all different directions.
And this is where we have to correct
my miss assumption at the start,
because my thinking was like,
look if you've got a, you know, pasta,
or a molecule oriented this way in space
and that's twisting light like this
and all you need to do is find another molecule
that's oriented the other way
and that will twist it back the way it came.
So the net result of all these jumbled up molecules
should be no rotation at all.
But that's a mistake because look,
what happens if I turn this pasta upside down?
It's genuinely unremarkable, like not very much happens.
Look at the direction of the spiral,
so as you move up through the pasta from bottom to top
the edge moves from left to right.
And if we switch it upside down,
maybe we expect that to reverse
so that it goes from right to left.
But look, as turn it upside down like that,
it stays the same.
The edge of the pasta still goes from left to right
as you move up through the pasta.
In other words, it doesn't matter
if you have the pasta oriented this way or this way,
the experience of light passing through it will be the same.
The clockwise and counterclockwise components
will have a different experience,
and that difference in experience will be the same
regardless of which way up the pasta is,
the experiences don't switch.
You know this about spirals already
from everyday experience.
Look, here's a bolt that has a spiral on it,
and the inside of this nut has a spiral on it,
and I can turn the nut upside down, right?
And it still works.
The explanation isn't complete
because sugar molecules don't look like this.
They look like this.
So what is the fundamental attribute
that these two things have in common
that matters in this scenario?
Well, it's handedness.
They both have a handedness.
In other words, they don't have mirror symmetry.
If you looked at this pasta in a mirror,
the mirror image of the pasta
would be different in a fundamental way,
in the same way that my hands have handedness.
Like if you look at my left hand in a mirror,
you wouldn't see another left-hand you'd see a right hand.
And they're fundamentally different.
Like if you could take that right hand
from inside the mirror like a ghost,
and try and line it up with the left hand,
you wouldn't be able to
there's no way to get them to overlap perfectly.
And not just because my hands are slightly different
and not just because I'm married.
The same is true for these molecules here.
If you took a mirror image of this glucose molecule,
the molecule would be fundamentally different.
You wouldn't be able to rearrange that molecule,
and line it up on top of this one.
To really hammer the point home,
let's see what happens
with molecules that do have mirror symmetry
like these ones here.
So look, let's orient the molecule like that.
And let's imagine light traveling up
through the molecule like this.
And it's again, it's a superposition
of circularly polarized in that direction,
and in that direction.
Maybe you could persuade yourself
that they would have a different experience
passing through this molecule.
How would you then undo that?
How would you reverse that?
What all you need is the mirror image of this molecule
somewhere else in the path of the light.
So let's put the mirror image up here like that.
And they really are the mirror image that they go
see again they're the mirror image there.
And so it passes through one
and then it passes through the other.
And whatever preferential treatment for the left-handed
versus the right-handed is undone with this mirror image.
But of course, because these molecules have mirror symmetry
they're just the same molecule, right?
So you'll find the mirror image
of this orientation floating around elsewhere
in the solution.
What about this sugar molecule then?
Imagine the light passing through this molecule.
Hopefully you can persuade yourselves
that clockwise circularly polarized light
will have a different experience
to counter-clockwise circularly polarized light,
as it passes through this molecule.
To undo that effect,
you would need the light to pass through the same molecule
but a mirror image of itself up here.
And you can't create the in mirror image
by flipping it in any direction,
because the molecule has a handiness.
It doesn't have mirror symmetry.
You can't create the mirror image of itself,
just by reorienting it.
So there you go.
It's because sugar molecules have a handedness
and it's because linearly polarized light,
can be thought of as the superposition
of two states of circularly polarized light,
in opposite directions.
By the way, you may have heard of sugar
being referred to as dextrose.
Dextro meaning to the right,
because dextrose or glucose turns light to the right,
clockwise and counterclockwise.
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I hope you enjoyed this video.
If you did, don't forget to hit subscribe
and I'll see you next time.
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