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In fact, quantum mechanics almost
could not be more obvious.
At least, to those of us fortunate enough
to have color vision.
Look at some object, such as these toy bricks here.
These nice blue toy bricks.
Or possibly this tennis ball that I have here.
It's a kind of glaring, fluorescent, yellow.
Now, we could say that each of these contains some
appropriately colored pigment, a dye or something.
Based on some material with an intrinsic color.
But that's not much of a theory.
We're really not much further forward in our understanding
of why these things are the color that they are.
And, if we don't know that, then we could be stuck in
Medieval times, when artists had to find nearly all their
pigments in the colors in natural objects.
Sometimes at very great cost.
This is a painting here by the Italian
Renaissance, artist Raphael.
It's from 1503, and it's known as the Diotalevi Madonna.
Now, if a painting at that time in this particularly
rich, deep, blue as you see in the cloak here, you would know
it was very expensive.
Good blue pigment was hard to come by, and typically a blue
like this at that time, would be what is known as an
ultramarine blue.
Which quite literally means that it had to come from
across the sea.
Ultra Marine.
They are actually relatively few naturally occurring
materials that are deep blue and are
suitable for use in paints.
Ultramarine blue is made from a semi-precious stone called
lapis lazuli.
And that name means stone from Lahzward, which was a place
that the stone was originally mined.
In Raphael's time, the lapis lazuli probably came from
Afghanistan, where it has actually been mined for over
4,000 years.
The words for blue in French, "azur," Italian, "azzurro,"
and Spanish "azul" or "azul," and I apologize for my
pronunciations there, all come from the same root, the word
"lazuli." The fact that all these languages adopted the
same word for blue, shows how unusual a color this is in the
natural materials that we have available to us.
And indirectly, how little ability we had to make
materials of a given color.
Part of the difficulty there is that there's no classical
theory that explains why materials have the
colors that they have.
It's really a complete mystery in classical physics.
And as a result, something over which we
had very little control.
Now modern blue coloring, like you see in these bricks here,
is probably made from a man-made material.
A very common one is copper phthalocyanine.
And that's a material that was discovered actually by
accident, in the 1930's, as a very good
blue color, by a chemist.
And as a result of our modern understanding of chemistry,
which to a large extent is based in its microscopic
science on quantum mechanics, we understand how to make
materials of the colors that we want.
And as I say, we can make those nice blue bricks.
Or we can even make colors that don't exist in nature.
Like the fluorescent yellow of this tennis ball here.
Actually, it was a related problem of color that got us
started in quantum mechanics.
Of course, people had known for a long time that hot
objects give off light.
So a fire, or a candle flame are good examples.
And for many years, these were the main kinds of sources of
light that we had in the evening.
Blacksmiths also knew empirically how to gauge the
temperature of materials, like iron, based on how it glows
when it's hot.
And in the latter two decades of the 19th century, electric
lighting was becoming increasingly popular,
especially after the successful invention of
relatively long lasting, so-called incandescent light
bulbs, the electric bulbs that we've known for many years.
And incandescent here simply means that something is
glowing because it's hot.
Now, with care and operation at low power, such bulbs can
actually lost a very long time.
This carbon filament bulb that you see here is in a fire
station in Livermore, California.
And it has apparently been running for 110 years.
However, a key problem with such filament light bulbs is
that they're not very efficient at conducting the
electric power into light power.
And depending a little bit on the detail of how we define
efficiency, that conversion is only a few percent.
Hence, it became rather important to understand just
how efficient such light bulbs could be.
Now the history of that, and what happened in understanding
efficiency of light bulbs, is something that took place
largely in the latter years of the 19th century.
And it's a particularly interesting interaction
between science and engineering.
In 1887 the German government, stimulated in part by Werner
von Siemens, the inventor of the dynamo - and you may have
heard of the Siemens Company, which still exists today - the
German government founded the Physikalisch-Technische
Reichsanstalt, or PTR, the Imperial Institute of Physics
and Technology near Berlin.
And over the next decade or so, this became a very well
equipped to research facility.
One of its priorities was to understand exactly this
question, the light emission from hot bodies.
With the goal of understanding how to make
better light bulbs.
Now it was already understood by this time that if you made
something that perfectly absorbed light, then you
heated it up, it would become the best possible emitter of
such thermal radiation.
This is known as Kirchhoff's law of thermal radiation.
And there's a bit of an irony here in the terminology, but
because that best possible emitter is therefore the best
absorber of light, it's called a black body.
So our best possible emitters are
called black-body emitters.
Now at this Institute, by the late 1890's, quite precise
measurements could be made of this so-called black-body
spectrum - the different colors that came off as you
heated bodies up to different temperatures.
And the problem about this was explaining why this black-body
spectrum had the shape.
So we see here an example of a black-body emission spectrum,
which shows the amount of light emitted as a function of
the wavelength.
This spectrum is for a body at 5,800 degrees Kelvin, which is
approximately the temperature of the sun.
In fact at the sun's surface, before the sunlight has been
somewhat filtered by absorption and scattering in
the atmosphere, that is pretty much what the sun's emission
spectrum would look like.
A cooler body at 3,000 degrees Kelvin, is a similar shape,
but it emits much less light, and it's peak emission is
shifted to longer wavelengths.
And to see the challenges incidentally for practical
light bulbs, we can look in more detail at these spectra
in the visible range.
And up the top here, we've added in an approximate
representation, the color of all of the different
wavelengths in the visible spectrum there.
We can see that the power of the sun is relatively uniform
per unit wavelength across the visible spectrum.
But if we look at our 3,000 degrees Kelvin light bulb
filament, first of all, it's much, much weaker.
About 25 times weaker.
And also, it's not such a nice distribution of colors across
the visible spectrum.
So let's go back to our black-body spectrum at 5,800
degrees Kelvin for a moment.
The key question is, why is it this shape?
Which is the same thing as saying, why is it this color
when you heat something up.
Now the model that followed from the best understanding of
classical physics at that time, was called the
Rayleigh-Jeans model.
And first of all, at the longer wavelengths over
towards the right here, it somewhat overestimated the
black-body emission.
But more importantly, at short wavelengths, it predicted that
the amount of radiated power would keep on increasing.
And empirical measurements just did not agree with that.
It would also have created more basic problems
theoretically, because it would predict an unlimited
amount of power could be radiated by warm body at short
wavelengths.
Hence, this difficulty was called the ultraviolet
catastrophe.
So we certainly need another model for the shape.
And it needed some new assumptions.
Wilhelm Wien, working at the PTR Institute, had come up
with some important relations, One of which, his displacement
law, so-called, has stood the test of time.
We still use that today.
Another formula he had for the shape of the spectrum,
initially seemed to be working, but eventually it
became clear it simply did not work at long wavelengths.
Max Planck, who was then a professor at Berlin
University, in fact he had taken over Kirchoff's former
position there, was quite aware of all of this work.
And he had a particularly strong background in the
necessary thermal physics.
And he worked *** this problem.
He came up basically empirically, not based on any
fundamental physics, with a mathematical formula.
And this was October 1900.
And this formula fit all of the
experimental data very well.
But as I said, he actually had no physical model as to where
this came from.
He continued working in this problem, and just before the
end of 1900, on December the 14th, he presented his
proposal at the Physical Society in Berlin.
And this proposal is now regarded as a
start of quantum mechanics.
Planck made one key assumption.
He said, let's just presume, for some reason we don't know,
that light is emitted in chunks, or quanta, as he
called them, of an amount proportional to the
frequency of light.
So we get this formula, e equals h times nu.
In the way this is usually written, the Greek letter nu,
stands for the frequency Hertz, which means cycles per
second of the light.
Now it was already very well understood at that time the
light was an electromagnetic wave.
That's just like radio waves, for example, are
electromagnetic waves.
Although the frequency of light is very much higher.
It's about 10 to the power 15 Hertz.
And that's much larger than we find in radio waves, but still
we believed, and we do believe today, of course, that light
is electromagnetic waves.
The proportionality constant, h, that he chose, is known as
Plank's constant.
And that's simply a number that he chose so that he could
get his calculated black-body emission spectrum to agree
with the measurement.
This constant is about 6.626 times 10 to the power minus
34, in units of Joules, the unit of energy, times seconds,
the unit of time.
And the value we're showing here is the best accepted
value as set in 2010.
Now an important point here is that when the Planck was
proposing these quanta of emission, he was not actually
proposing that light existed only in such quanta.
That would have caused quite a conflict with what people then
understood about light, that we had this extremely
successful theory of electromagnetism, and that
theory had light as waves, not particles.
And this was an old battle.
Back in the 1600's, the late 1600's, Isaac Newton, the very
famous inventor of classical mechanics, had done a lot of
work on light.
In fact, he did some very good work on light.
And his idea was that light was made out of what he
called, corpuscles.
Little particles, essentially.
And he said this because, he said, well sound is waves,
because sound can go around corners, but light doesn't go
around corners.
You can't see somebody around a corner.
So he said, I think light is made up out of particles that
go in straight lines.
So that was Newton's idea.
But then at the same time, Christiaan Huygens, working in
what is now Holland in the late 1600's, had apparently
been won over quite convincingly by the idea that
these were actually waves.
He had a very good theory of waves, I wasn't quite dead
right, but it was actually a pretty good theory of wave
propagation.
And it wasn't until the early 1800's that this controversy
between the corpuscular model of Newton and the wave model
of Huygens really became resolved.
There were some profound experiments, one of which we
will get back to later on, called Young's slits, that
show rather convincingly that light is actually
made up out of waves.
And at this time in the late 1890's and on into the early
1900's of course, we already had available to us they
extremely successful and deep theory of electromagnetism
from James Clark Maxwell working
in Britain or Scotland.
And he had constructed what are known as Maxwell's
equations, which are one of the major triumphs of 19th
century physics and underlie everything that we do with
electromagnetic waves today.
So that theory was very strong.
It showed light is waves.
There's no doubt about that.
So Planck was not proposing that somehow, light only
existed as corpuscles or particles.
He was saying, light is waves, but for some reason in these
so-called black bodies, it's emitted in chunks.
There was, however, another set of odd observations, first
made by Heinrich Hertz, the same man whose name is on the
cycles per second, in 1887, that if you took some metal
plates, put a voltage between them, and then shone
ultraviolet light on one of them, the spark between the
plates became brighter.
Now the light that he shone on these pieces of metal had to
be ultraviolet light.
And he knew this, in this particular set of metals it
had to be ultraviolet, because if he put in a glass plate in
front of the light, this additional sort of sparking
affect stopped.
Various people looked at this phenomenon after that, and
Hertz himself sort of moved on, and it remained a puzzle
for many years.
Now in 1902 Philipp Leonard, who had been Hertz's
assistant, continued these experiments.
And was able to clarify that there was a flow of negative
charge between the plates, if we had them in a vacuum, when
you shone light on them.
And by biasing the plates with a voltage to stop the current,
he was able to deduce how much kinetic energy the negative
charges had when they left the plate.
That is, if these charges come of the plate with some amount
of kinetic energy, that would allow them to keep on moving.
And some of them would be moving exactly towards the
collecting plate here.
And to stop those, and stop them getting to the collecting
plate, we would have to somehow put enough force on
them, from the election voltage applied across here,
to just stop them from getting there.
Now, the surprise here is that with an obvious classical way
of looking at this effect, we might think that shining a
brighter light on the plate would lead to electrons with
more kinetic energy.
And so they would be harder to stop.
And so we have to put more voltage on the plates to sort
of stop them from getting there, more repelling force on
them to stop them from getting to our collecting plate on the
right here.
For example, if we were heating the plate up with the
light, we might expect that with a brighter light, the
electrons would naturally be hotter and they would have
more kinetic energy, just because there was more power
in the light beam.
But this is not what happens.
Instead, when we shine the light, yeah we get more
electrons off, but the stopping
voltage remains the same.
That is, the electrons always seem to be emitted with the
same kinetic energy.
And furthermore, if we change to a shorter wavelength, say
moving from blue or ultraviolet further into the
ultraviolet, then we have to increase the stopping voltage
to stop the flow of current.
With shorter wavelengths, the kinetic energy of the
electrons was greater.
And it didn't matter how bright light was.
We still needed the same stopping voltage to stop the
electrons managing to get to the collecting plate, no
matter how bright we turned up the bulb.
In 1905, Einstein made a proposal to explain this
strange effect.
He said, light is actually made up out of particles.
And these particles, we're going to call them photons,
and we will say that they actually have energy h nu.
So this is the same formula that Planck had.
But here, we're actually saying light really is made up
out of these particles that have this energy, h nu.
So this is a step beyond Planck, who as I said, was
only proposing light was emitted in these chunks, but
he wasn't trying to leave behind the wave theory of
electromagnetism and substitute a corpuscular one.
So the explanation of the photoelectric effect is as
shown in this diagram.
We presume that electrons in a metal sit in
some sort of pool.
And there is an energy barrier called the work function, here
the Greek letter phi.
And the electrons have to overcome this work function to
get out of the metal.
So a photon with energy h nu that exceeds the height of the
barrier, it exceeds this work function phi, will have enough
energy to allow the electron to be
extracted from the metal.
And the excess energy the electron gets from the photon,
will be given to the electron as kinetic energy.
And the worst case, as I said before, all of that kinetic
energy will correspond to motion in the direction
towards the other electrode.
And we will need the full stopping voltage to slow that
electron down to zero velocity, so it never quite
gets to the other electrode.
It was this proposal, which explains the photoelectric
measurements of Leonard so well, that led to Einstein's
Nobel Prize by the way.
He got his Nobel Prize for his proposal of the photon, not
for his proposals about relativity.
And so we come to something we call wave-particle duality.
We are saying here that light is displaying both wave
character, and it certainly does do that, and is also made
of particles.
But how can this be?
How can light simultaneously be a wave and be a particle?
That simply does not seem to make any sense to us in our
classical view of particles and waves.
And it certainly did not make sense to Planck.
Now strangely enough, in the end, once we've constructed
our quantum mechanical theories, this wave-particle
duality is actually not a problem
within quantum mechanics.
However, the key thing we have to do is we have to avoid
bringing everything along from our classical ideas of what we
think a particle is and everything that we think of a
wave, in the classical world as having as its properties,
we can only bring some of those properties.
That's how we get rid of the contradiction.
And we will see how we do that later on.
But we need to do some more quantum mechanics before we
can get there.
And incidentally, in case we were in any doubt about
wave-particle duality, we can note that we can verify it
literally trillions of times a day.
Modern telecommunications that we use for the internet is
carried over optical fibers.
They carry essentially all of our long distance information
on the internet.
When we design the optical fibers themselves, they are
hair thin pieces of glass, they're designed by
considering light as waves, the electromagnetic waves of
Maxwell's equations and 19th century physics.
And the devices that generate the light beams that go down
the fibers are lasers.
And the devices that detect them at the other end are
photo detectors.
Both those lasers and photo detectors are fully quantum
mechanical devices.
They generate photons and they detect photons.
And since we send trillions of bits per second over the
internet every day, we are actually verifying the
photoelectric effect on this quantum mechanical description
and the wave-particle duality all these times, every day.
So now, we are beginning to see quantum
mechanics take shape.
As it starts to explain aspects of light that we could
not understand before, even if it's introducing some ideas,
like wave-particle duality, that seem very bizarre.
And indeed, even though Einstein got the Nobel Prize
for his explanation of the photoelectric effect, it was,
at that time, by no means clear to physicists that this
actually made sense.
Incidentally, it's amusing to think that that light bulb I
showed you, that is burning in Livermore, California, has
actually been burning, since it's been burning for over 110
years, since before Einstein proposed the photon.
Having started quantum mechanics with light, for the
next chapter in this story, we will be moving on to the early
history of the quantum mechanics of matter.
How do we understand materials and their properties?