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PROFESSOR: All right. So today's task is going
to be to outline some of the basic experimental

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facts that we will both have to deal with
and that our aim should be to understand and

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model through the rest of the course.

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Physics doesn't tell you some abstract truth
about why the universe is the way it is. Physics

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gives you models to understand how things
work and predict what will happen next. And

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what we will be aiming to do is develop models
that give us an intuition for the phenomena

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and allow us to make predictions. And these
are going to be the experimental facts I would

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like to both explain, develop an intuition
for, and be able to predict consequences of.

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So we'll start off with-- so let me just outline
them. So, first fact, atoms exist. I'll go

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over some of the arguments for that. Randomness,
definitely present in the world. Atomic spectre

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are discrete and structured. We have a photoelectric
effect, which I'll describe in some detail.

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Electrons do some funny things. In particular
electron diffraction. And sixth and finally,

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Bell's Inequality. Something that we will
come back to at the very end of the class,

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which I like to think of as a sort of a frame
for the entirety of 8.04.

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So... we'll stick with this for the moment.

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So everyone in here knows that atoms are made
of electrons and nuclei. In particular, you

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know that electrons exist because you've seen
a cathode ray tube. I used to be able to say

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you've seen a TV, but you all have flat panel
TVs, so this is useless. So a cathode ray

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tube is a gun that shoots electrons at a phosphorescent
screen. And every time the electron hits the

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screen it induces a little phosphorescence,
a little glow. And that's how you see on a

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CRT.

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And so as was pithily stated long ago by a
very famous physicist, if you can spray them,

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they exist. Pretty good argument. There's
a better argument for the existence of electrons,

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which is that we can actually see them individually.

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And this is one of the most famous images
in high-energy physics. It's from an experiment

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called Gargamelle, which was a 30-cubic meter
tank of liquid freon pulsing just at its vapor

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pressure 60 times a second. And what this
image is is, apart from all the schmut, you're

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watching a trail of bubbles in this de-pressurizing
freon that wants to create bubbles but you

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have to nucleate bubbles. What you're seeing
there in that central line that goes up and

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then curls around is a single electron that
was nailed by a neutrino incident from a beam

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at CERN where currently the LHC is running.

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And this experiment revealed two things. First,
to us it will reveal that you can see individual

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electrons and by studying the images of them
moving through fluids and leaving a disturbing

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wake of bubbles behind them. We can study
their properties in some considerable detail.

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The second thing it taught us is something
new-- we're not going to talk about it in

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detail-- is that it's possible for a neutrino
to hit an electron. And that process is called

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a weak neutral current for sort of stupid
historical reasons. It's actually a really

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good name. And that was awesome and surprising
and so this picture is both a monument to

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the technology of the experiment, but also
to the physics of weak neutral currents and

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electrons. They exist if you can discover
neutrinos by watching them. OK.

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Secondly, nuclei. We know that nuclei exist
because you can shoot alpha particles, which

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come from radioactive decay, at atoms. And
you have your atom which is some sort of vague

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thing, and I'm gonna make the-- I'm gonna
find the atom by making a sheet of atoms.

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Maybe a foil. A very thin foil of stuff. And
then I'm gonna shoot very high-energy alpha

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particles incident of this.

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Probably everyone has heard of this experiment,
it was done by Rutherford and Geiger and Marsden,

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in particular his students at the time or
post-docs. I don't recall-- and you shoot

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these alpha particles in. And if you think
of these guys as some sort of jelly-ish lump

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then maybe they'll deflect a little bit, but
if you shoot a bullet through Jello it just

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sort of maybe gets deflected a little bit.
But Jello, I mean, come on.

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And I think what was shocking is that you
should these alpha particles in and every

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once in a while, they bounce back at, you
know, 180, 160 degrees. Rutherford likened

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this to rolling a bowling ball against a piece
of paper and having it bounce back. Kind of

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surprising. And the explanation here that
people eventually came up upon is that atoms

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are mostly zero density. Except they have
very, very high density cores, which are many

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times smaller than the size of the atom but
where most of the mass is concentrated. And

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as a consequence, most of the inertia.

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And so we know that atoms have substructure,
and the picture we have is that well if you

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scrape this pile of metal, you can pull off
the electrons, leaving behind nuclei which

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have positive charge because you've scraped
off the electrons that have negative charge.

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So we have a picture from these experiments
that there are electrons and there are nuclei--

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which, I'll just write N and plus-- which
are the constituents of atoms.

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Now this leads to a very natural picture of
what an atom is. If you're a 19th-century

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physicist, or even an early 20th-century physicist,
it's very natural to say, aha, well if I know

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if I have a positive charge and I have a negative
charge, then they attract each other with

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a 1 over r minus q1 q2-- sorry, q1 q2 over
r potential. This is just like gravity, right.

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The earth and the sun are attracted with an
inverse-r potential. This leads to Keplerian

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orbits. And so maybe an atom is just some
sort of orbiting classical combination of

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an electron and a nucleus, positively charged
nucleus.

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The problem with this picture, as you explore
in detail in your first problem on the problem

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set, is that it doesn't work. What happens
when you accelerate a charge? It radiates.

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Exactly. So if it's radiating, it's gotta
lose energy. It's dumping energy into this--

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out of the system. So it's gotta fall lower
into the potential. Well it falls lower, it

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speeds up. It radiates more. Because it's
accelerating more to stay in a circular orbit.

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All right, it radiates more, it has to fall
further down.

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So on the problem set you're going to calculate
how long that takes. And it's not very long.

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And so the fact that we persist for more than
a few picoseconds tells you that it's not

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that-- this is not a correct picture of an
atom. OK.

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So in classical mechanics, atoms could not
exist. And yet, atoms exist. So we have to

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explain that. That's gonna be our first challenge.
Now interestingly Geiger who is this collaborator

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of Rutherford, a young junior collaborator
of Rutherford, went on to develop a really

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neat instrument. So suppose you want to see
radiation. We do this all the time. I'm looking

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at you and I'm seeing radiation, seeing light.
But I'm not seeing ultra high energy radiation,

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I'm seeing energy radiation in the electromagnetic
waves in the optical spectrum.

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Meanwhile I'm also not seeing alpha particles.
So what Geiger wanted was a way to detect

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without using your eyes radiation that's hard
to see. So the way he did this is he took

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a capacitor and he filled the-- surrounded
the capacitor with some noble gas. It doesn't

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interact. There's no-- it's very hard to ionize.
And if you crank up the potential across this

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capacitor plate high enough, what do you get?
A spark. You all know this, if you crank up

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a capacitor it eventually breaks down because
the dielectric in between breaks down, you

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get a spontaneous sparking.

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So what do you figure it would look if I take
a capacitor plate and I charge it up, but

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not quite to breakdown. Just a good potential.
And another charged particle comes flying

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through, like an alpha particle, which carries
a charge of plus 2, that positive charge will

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disturb things and will add extra field effectively.
And lead to the nucleation of a spark.

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So the presence of a spark when this potential
is not strong enough to induce a spark spontaneously

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indicates the passage of a charged particle.
Geiger worked later with-- Marsden? Muller.

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Heck. I don't even remember. And developed
this into a device now known as the Geiger

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counter. And so you've probably all seen or
heard Geiger counters going off in movies,

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right. They go ping ping ping ping ping ping
ping ping ping, right. They bounce off randomly.

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This is an extremely important lesson, which
is tantamount to the lesson of our second

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experiment yesterday. The 50-50, when we didn't
expect it. The white electrons into the harness

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box then into a color box again, would come
out 50-50, not 100 percent. And they come

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out in a way that's unpredictable. We have
no ability to our knowledge-- and more than

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our knowledge, we'll come back to that with
Bell's Inequality-- but we have no ability

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to predict which electron will come out of
that third box, white or black, right.

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Similarly with a Geiger counter you hear that
atoms decay, but they decay randomly. The

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radiation comes out of a pile of radioactive
material totally at random. We know the probabilistic

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description of that. We're going to develop
that, but we don't know exactly when. And

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that's a really powerful example-- both of
those experiments are powerful examples of

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randomness.

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And so we're going to have to incorporate
that into our laws of physics into our model

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of quantum phenomena as well. Questions? I
usually have a Geiger counter at this point,

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which is totally awesome, so I'll try to produce
the Geiger counter demo later. But the person

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with the Geiger counter turns out to have
left the continent, so made it a little challenging.

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OK. Just sort of since we're at MIT, an interesting
side note. This strategy of so-called hard

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scattering, of taking some object and sending
it at very high velocity at some other object

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and looking for the rare events when they
bounce off at some large angle, so-called

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hard scattering. Which is used to detect dense
cores of objects. It didn't stop with Rutherford.

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People didn't just give up at that point.

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Similar experience in the '60s and '70s which
are conducted at Slack, were involved not

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alpha particles incident on atoms but individual
electrons incident on protons. So not shooting

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into the nucleus, but shooting and looking
for the effect of hitting individual protons

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inside the nucleus. And through this process
it was discovered that in fact-- so this was

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done in the '60s and '70s, that in fact the
proton itself is also not a fundamental particle.

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The proton is itself composite.

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And in particular, it's made out of-- eventually
people understood that it's made out of, morally

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speaking, and I'm gonna put this in quotation
marks-- ask me about it in office hours--

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three quarks, which are some particles. And
the reason we-- all this tells you is that

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it's some object and we've given it the name
quark. But indeed there are three point-like

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particles that in some sense make up a proton.
It's actually much more complicated than that,

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but these quarks, among other things, have
very strange properties. Like they have fractional

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charge.

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And this was discovered by a large group of
people, in particular led by Kendall and Friedman

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and also Richard Taylor. Kendall and Friedman
were at MIT, Richard Taylor was at Stanford.

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And in 1990 they shared the Nobel Prize for
the discovery of the partonic structure out

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of the nucleons. So these sorts of techniques
that people have been using for a very long

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time continue to be useful and awesome.

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And in particular the experiment, the experimental
version of this that's currently going on,

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that I particularly love is something called
the relativistic heavy ion collider, which

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is going on at Brookhaven. So here what you're
doing is you take two protons and you blow

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them into each other at ultra high energy.
Two protons, collide them and see what happens.

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And that's what happens. You get massive shrapnel
coming flying out. So instead of having a

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simple thing where one of the protons just
bounces because there's some hard quark, instead

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what happens is just shrapnel everywhere,
right. So you might think, well, how do we

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interpret that at all. How do you make sense
out of 14,000 particles coming out of two

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protons bouncing into each other. How does
that make any sense? And the answer turns

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out to be kind of awesome.

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And so this touches on my research. So I want
to make a quick comment on it just for color.

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The answer turns out to be really interesting.
First off, the interior constituents of protons

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interact very strongly with each other. But
at the brief moment when protons collide with

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each other, what you actually form is not
a point-like quirk and another point-like

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quark. In fact, protons aren't made out of
point-like quarks at all. Protons are big

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bags with quarks and gluons and all sorts
of particles fluctuating in and out of existence

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in a complicated fashion.

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And what you actually get is, amazingly, a
liquid. For a brief, brief moment of time

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the parts of those protons that overlap--
think of them as two spheres and they overlap

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in some sort of almond-shaped region. The
parts of those protons that overlap form a

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liquid at ultra high temperature and at ultra
high density. It's called the RHIC fireball

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or the quark-gluon plasma, although it's not
actually a plasma. But it's a liquid like

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water. And what I mean by saying it's a liquid
like water, if you push it, it spreads in

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waves. And like water, it's dissipative. Those
waves dissipate.

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But it's a really funny bit of liquid.

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Imagine you take your cup of coffee. You drink
it, you're drinking your coffee as I am wont

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to do, and it cools down over time. This is
very frustrating. So you pour in a little

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bit of hot coffee and when you pour in that
hot coffee, the system is out of equilibrium.

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It hasn't thermalized. So what you want is
you want to wait for all of the system to

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wait until it's come to equilibrium so you
don't get a swig of hot or swig of cold. You

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want some sort of Goldilocks-ean in between.

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So you can ask how long does it take for this
coffee to come to thermal equilibrium. Well

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it takes a while. You know, a few seconds,
a few minutes, depending on exactly how you

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mess with it. But let me ask you a quick question.
How does that time scale compare to the time

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it takes for light to cross your mug? Much,
much, much slower, right? By orders of magnitude.

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For this liquid that's formed in the ultra
high energy collision of two protons, the

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time it takes for the system-- which starts
out crazy out of equilibrium with all sorts

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of quarks here and gluons there and stuff
flying about-- the time it takes for it to

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come to thermal equilibrium is of order the
time it takes for light to cross the little

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puddle of liquid. This is a crazy liquid,
it's called a quantum liquid. And it has all

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sorts of wonderful properties. And the best
thing about it to my mind is that it's very

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well modeled by black holes. Which is totally
separate issue, but it's a fun example. So

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from these sorts of collisions, we know a
great deal about the existence of atoms and

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randomness, as you can see. That's a fairly
random sorting.

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OK so moving on to more 8.04 things. Back to
atoms. So let's look at specifics of that.

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I'm not kidding, they really are related to
black holes. I get paid for this. So here's

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a nice fact, so let's get to atomic spectra.
So to study atomic spectra, here's the experiment

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I want to run. The experiment I want to run
starts out with some sort of power plant.

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And out of the power plant come two wires.
And I'm going to run these wires across a

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spark gap, you know, a piece of metal here,
a piece of metal here, and put them inside

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a container, which has some gas. Like H2 or
neon or whatever you want. But some simple

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gas inside here.

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So we've got an electric potential established
across it. Again, we don't want so much potential

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that it sparks, but we do want to excite the
H2. So we can even make it spark, it doesn't

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really matter too much. The important thing
is that we're going to excite the hydrogen,

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and in exciting the hydrogen the excited hydrogen
is going to send out light. And then I'm going

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to take this light-- we take the light, and
I'm gonna shine this on a prism, something

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I was taught to do by Newton. And-- metaphorically
speaking-- and look at the image of this light

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having passed through the prism.

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And what you find is you find a very distinct
set of patterns. You do not get a continuous

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band. In fact what you get-- I'm going to
have a hard time drawing this so let me draw

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down here. I'm now going to draw the intensity
of the light incident on the screen on this

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piece of paper-- people really used to use
pieces of paper for this, which is kind of

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awesome-- as a function of the wavelength,
and I'll measure it in angstroms.

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And what you discover is-- here's around 1,000
angstroms-- you get a bunch of lines. Get

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these spikes. And they start to spread out,
and then there aren't so many. And then at

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around 3,000, you get another set. And then
at around 10,000, you get another set.

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This is around 10,000.

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And here's the interesting thing about these.
So the discovery of these lines-- these are

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named after a guy named Lyman, these are--
these are named after a guy named-- Ballmer.

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Thank you. Steve Ballmer. And these are passion,
like passion fruit. So. Everyone needs a mnemonic,

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OK. And so these people identified these lines
and explained various things about them.

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But here's an interesting fact. If you replace
this nuclear power plant with a coal plant,

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it makes no difference. If you replace this
prism by a different prism, it makes no difference

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to where the lines are. If you change this
mechanism of exciting the hydrogen, it makes

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no difference. As long as it's hydrogen--
as long as it's hydrogen in here you get the

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same lines, mainly with different intensities
depending upon how exactly you do the experiment.

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But you get the same position of the lines.
And that's a really striking thing.

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Now if you use a different chemical, a different
gas in here, like neon, you get a very different

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set of lines. And a very different effective
color now when you eyeball this thing. So

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Ballmer, incidentally-- and I think this is
actually why he got blamed for that particular

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series, although I don't know the history--
Ballmer noticed by being-- depending on which

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biography you read-- very clever or very obsessed
that these guys, this particular set, could

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be-- they're wavelengths. If you wrote their
wavelengths and labeled them by an integer

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n, where n ran from 3 to any positive integer
above 3, could be written as 36. So this is

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pure numerology. 36, 46 angstroms times the
function n squared over n squared minus 4,

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where N is equal to 3, 4, dot dot dot-- an
integer.

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And it turns out if you just plug in these
integers, you get a pretty good approximation

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to this series of lines. This is a hallowed
tradition, a phenomenological fit to some

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data. Where did it come from? It came from
his creative or obsessed mind. So this was

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Ballmer. And this is specifically for hydrogen
gas, H2.

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So Rydberg and Ritz, R and R, said, well actually
we can do one better. Now that they realized

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that this is true, they looked at the whole
sequence. And they found a really neat little

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expression, which is that 1 over the wavelength
is equal to a single constant parameter. Not

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just for all these, but for all of them. One
single numerical coefficient times 1 over

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m squared minus 1 over n squared-- n is an
integer greater than zero and greater in particular

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than m. And if you plug in any value of n
and any value of m, for sufficiently reasonable--

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I mean, if you put in 10 million integers
you're not going to see it because it's way

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00:19:43,770 --> 00:19:52,750
out there, but if you put in or-- rather,
in here-- if you put any value of n and m,

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you will get one of these lines. So again,
why? You know, as it's said, who ordered that.

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So this is experimental result three that
we're going to have to deal with. When you

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look at atoms and you look at the specter
of light coming off of them, their spectra

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are discrete. But they're not just stupidly
discrete, they're discrete with real structure.

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Something that begs for an explanation. This
is obviously more than numerology, because

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it explains with one tunable coefficient a
tremendous number of spectral lines. And there's

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a difference-- and crucially, these both work
specifically for hydrogen. For different atoms

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you need a totally different formula.

250
00:20:31,450 --> 00:20:44,740
But again, there's always some formula that
nails those spectral lines. Why? Questions?

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00:20:44,740 --> 00:21:00,120
OK. So speaking of atomic spectra-- whoops,
I went one too far-- here's a different experiment.

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00:21:00,120 --> 00:21:07,470
So people notice the following thing. People
notice that if you take a piece of metal and

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you shine a light at it, by taking the sun
or better yet, you know, these days we'd use

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00:21:12,660 --> 00:21:17,840
a laser, but you shine light on this piece
of metal. Something that is done all the time

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00:21:17,840 --> 00:21:21,640
in condensed matter labs, it's a very useful
technique. We really do use lasers not the

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00:21:21,640 --> 00:21:24,390
sun, but still it continues to be useful in
fact to this day.

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You shine light on a piece of metal and every
once in a while what happens is electrons

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00:21:27,630 --> 00:21:35,049
come flying off. And the more light and the
stronger the light you shine, you see changes

259
00:21:35,049 --> 00:21:39,920
in the way that electrons bounce off. So we'd
like to measure that. I'd like to make that

260
00:21:39,920 --> 00:21:43,429
precise. And this was done in a really lovely
experiment. Here's the experiment. The basic

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00:21:43,429 --> 00:21:47,510
idea of the experiment is I want to check
to see, as I change the features of the light,

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00:21:47,510 --> 00:21:50,660
the intensity, the frequency, whatever, I
want to see how that changes the properties

263
00:21:50,660 --> 00:21:52,059
of the electrons that bounce off.

264
00:21:52,059 --> 00:21:55,690
Now one obvious way-- one obvious feature
of an electron that flew off a piece of metal

265
00:21:55,690 --> 00:21:59,890
is how fast is it going, how much energy does
it have. What's its kinetic energy. So I'd

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00:21:59,890 --> 00:22:03,540
like to build an experiment that measures
the kinetic energy of an electron that's been

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00:22:03,540 --> 00:22:09,400
excited through this photoelectric effect.
Through emission after shining light on a

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00:22:09,400 --> 00:22:10,280
piece of metal. Cool?

269
00:22:10,280 --> 00:22:14,590
So I want to build that experiment. So here's
how that experiment goes. Well if this electron

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00:22:14,590 --> 00:22:20,809
comes flying off with some kinetic energy
and I want to measure that kinetic energy,

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00:22:20,809 --> 00:22:26,390
imagine the following circuit. OK first off
imagine I just take a second piece of metal

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over here, and I'm going to put a little current
meter here, an ammeter. And here's what this

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00:22:33,000 --> 00:22:36,370
circuit does. When you shine light on this
piece of metal-- we'll put a screen to protect

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00:22:36,370 --> 00:22:40,020
the other piece of metal-- the electrons come
flying off, they get over here. And now I've

275
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got a bunch of extra electrons over here and
I'm missing electrons over here. So this is

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00:22:43,230 --> 00:22:47,170
negative, this is positive. And the electrons
will not flow along this wire back here to

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00:22:47,170 --> 00:22:48,330
neutralize the system.

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00:22:48,330 --> 00:22:52,870
The more light I shine, the more electrons
will go through this circuit. And as a consequence,

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00:22:52,870 --> 00:22:58,030
there will be a current running through this
current meter. That cool with everyone? OK.

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00:22:58,030 --> 00:23:01,299
So we haven't yet measured the kinetic energy,
though. How do we measure the kinetic energy?

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00:23:01,299 --> 00:23:04,929
I want to know how much energy, with how much
energy, were these electrons ejected.

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00:23:04,929 --> 00:23:10,210
Well I can do that by the following clever
trick. I'm going to put now a voltage source

283
00:23:10,210 --> 00:23:15,370
here, which I can tune the voltage of, with
the voltage V. And what that's going to do

284
00:23:15,370 --> 00:23:19,960
is set up a potential difference across these
and the energy in that is the charge times

285
00:23:19,960 --> 00:23:24,770
the potential difference. So I know that the
potential difference it takes, so the amount

286
00:23:24,770 --> 00:23:31,020
of energy it takes to overcome this potential
difference, is q times V. That cool?

287
00:23:31,020 --> 00:23:35,990
So now imagine I send in an electron-- I send
in light and it leads an electron to jump

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00:23:35,990 --> 00:23:41,660
across, and it has kinetic energy, kE. Well
if the kinetic energy is less than this, will

289
00:23:41,660 --> 00:23:46,320
it get across? Not so much. It'll just fall
back. But if the kinetic energy is greater

290
00:23:46,320 --> 00:23:51,360
than the energy it takes to cross, it'll cross
and induce a current.

291
00:23:51,360 --> 00:23:58,780
So the upshot is that, as a function of the
voltage, what I should see is that there is

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00:23:58,780 --> 00:24:04,030
some critical minimum voltage. And depending
on how you set up the sign, the sign could

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00:24:04,030 --> 00:24:11,260
be the other way, but there's some critical
minimal voltage where, for less voltage, the

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00:24:11,260 --> 00:24:18,500
electron doesn't get across. And for any greater
voltage-- or, sorry, for any closer to zero

295
00:24:18,500 --> 00:24:24,020
voltage, the electron has enough kinetic energy
to get across. And so the current should increase.

296
00:24:24,020 --> 00:24:28,740
So there's a critical voltage, V-critical,
where the current running through the system

297
00:24:28,740 --> 00:24:35,030
runs to zero. You make it harder for the electrons
by making the voltage in magnitude even larger.

298
00:24:35,030 --> 00:24:38,390
You make it harder for the electrons to get
across. None will get across. Make it a little

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00:24:38,390 --> 00:24:45,470
easier, more and more will get across. And
the current will go up. So what you want to

300
00:24:45,470 --> 00:24:49,830
do to measure this kinetic energy is you want
to measure the critical voltage at which the

301
00:24:49,830 --> 00:24:57,440
current goes to zero.

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00:24:57,440 --> 00:25:01,210
So now the question is what do we expect to
see. And remember that things we can tune

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00:25:01,210 --> 00:25:08,530
in this experiment are the intensity of the
light, which is like e squared plus b squared.

304
00:25:08,530 --> 00:25:14,130
And we can tune the frequency of the light.
We can vary that. Now does the total energy,

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00:25:14,130 --> 00:25:18,919
does that frequency show up in the total energy
of a classical electromagnetic wave? No. If

306
00:25:18,919 --> 00:25:25,950
it's an electromagnetic wave, it cancels out.
You just get the total intensity, which is

307
00:25:25,950 --> 00:25:33,880
a square of the fields. So this is just like
a harmonic oscillator. The energy is in the

308
00:25:33,880 --> 00:25:36,919
amplitude. The frequency of the oscillator
doesn't matter. You push the swing harder,

309
00:25:36,919 --> 00:25:43,440
it gets more kinetic energy. It's got more
energy. OK.

310
00:25:43,440 --> 00:25:48,740
So what do we expect to see as we vary, for
example, the intensity? So here's a natural

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00:25:48,740 --> 00:25:53,220
gas. If you take-- so you can think about
the light here as getting a person literally,

312
00:25:53,220 --> 00:25:57,559
like get the person next to you to take a
bat and hit a piece of metal. If they hit

313
00:25:57,559 --> 00:25:59,970
it really lightly they're probably not going
to excite electrons with a lot of energy.

314
00:25:59,970 --> 00:26:03,840
If they just whack the heck out of it, then
it wouldn't be too surprising if you get much

315
00:26:03,840 --> 00:26:06,860
more energy in the particles that come flying
off. Hit it hard enough, things are just gonna

316
00:26:06,860 --> 00:26:09,980
shrapnel and disintegrate.

317
00:26:09,980 --> 00:26:20,900
The expectation here is the following. That
if you have a more intense beam, then you

318
00:26:20,910 --> 00:26:25,510
should get more-- the electrons coming off
should be more energetic. Because you're hitting

319
00:26:25,510 --> 00:26:37,370
them harder. And remember that the potential,
which I will call V0, the stopping voltage.

320
00:26:37,370 --> 00:26:44,230
So therefore V0 should be greater in magnitude.

321
00:26:44,230 --> 00:26:49,850
So this anticipates that the way this curve
should look as we vary the current as a function

322
00:26:49,850 --> 00:26:57,250
of v, if we have a low voltage-- sorry, if
we have a low-intensity beam-- it shouldn't

323
00:26:57,250 --> 00:27:01,990
take too much potential just to impede the
motion.

324
00:27:01,990 --> 00:27:04,880
But if we have a-- so this is a low intensity.

325
00:27:04,880 --> 00:27:09,960
But if we have a high-intensity beam, it should
take a really large voltage to impede the

326
00:27:09,960 --> 00:27:14,250
electric flow, the electric current, because
high-intensity beam you're just whacking those

327
00:27:14,250 --> 00:27:19,870
electrons really hard and they're coming off
with a lot of kinetic energy. So this is high

328
00:27:19,870 --> 00:27:28,070
intensity. Everyone down with that intuition?
This is what you get from Maxwell's electrodynamics.

329
00:27:28,070 --> 00:27:31,990
This is what you'd expect.

330
00:27:31,990 --> 00:27:40,660
And in particular, as we vary-- so this is
our predictions-- in particular as we vary--

331
00:27:40,660 --> 00:27:50,820
so this is 1, 2, with greater intensity. And
the second prediction is that V-naught should

332
00:27:50,830 --> 00:27:55,169
be independent of frequency. Because the energy
density and electromagnetic wave is independent

333
00:27:55,169 --> 00:28:04,600
of the frequency. It just depends on the amplitude.
And I will use nu to denote the frequency.

334
00:28:04,600 --> 00:28:15,020
So those are the predictions that come from
8.02 and 8.03. But this is 8.04. And here's what

335
00:28:15,020 --> 00:28:21,880
the experimental results actually look like.
So here's the intensity, here's the potential.

336
00:28:21,880 --> 00:28:26,230
And if we look at high potential, it turns
out that-- if we look, sorry, if we look at

337
00:28:26,230 --> 00:28:32,770
intermediate potentials, it's true that the
high intensity leads to a larger current and

338
00:28:32,770 --> 00:28:36,690
the low intensity leads to a lower current.

339
00:28:36,690 --> 00:28:44,330
But here's the funny thing that happens. As
you go down to the critical voltage, their

340
00:28:44,330 --> 00:28:52,440
critical voltages are the same. What that
tells you is that the kinetic energy kicked

341
00:28:52,440 --> 00:28:57,010
out-- or the kinetic energy of an electron
kicked out of this piece of metal by the light

342
00:28:57,010 --> 00:29:03,530
is independent of how intense that beam is.
No matter how intense that beam is, no matter

343
00:29:03,530 --> 00:29:09,120
how strong the light you shine on the material,
the electrons all come out with the same energy.

344
00:29:09,120 --> 00:29:15,600
This would be like taking a baseball and hitting
it with a really powerful swing or a really

345
00:29:15,600 --> 00:29:19,450
weak swing and seeing that the electron dribbles
away with the same amount of energy. This

346
00:29:19,450 --> 00:29:25,140
is very counter-intuitive.

347
00:29:25,140 --> 00:29:32,690
But more surprisingly, V-naught is actually
independent of intensity. But here's the real

348
00:29:32,690 --> 00:29:41,770
shocker. V-naught varies linearly in the frequency.
What does change V-naught is changing the

349
00:29:41,770 --> 00:29:45,960
frequency of the light in this incident. That
means that if you take an incredibly diffuse

350
00:29:45,960 --> 00:29:51,090
light-- incredibly diffuse light, you can
barely see it-- of a very high frequency,

351
00:29:51,090 --> 00:29:56,710
then it takes a lot of energy to impede the
electrons that come popping off.

352
00:29:56,710 --> 00:30:01,900
The electrons that come popping off have a
large energy. But if you take a low-frequency

353
00:30:01,900 --> 00:30:07,720
light with extremely high intensity, then
those electrons are really easy to stop. Powerful

354
00:30:07,720 --> 00:30:11,539
beam but low frequency, it's easy to stop
those electrons. Weak little tiny beam at

355
00:30:11,539 --> 00:30:16,530
high frequency, very hard to stop the electrons
that do come off. So this is very counter-intuitive

356
00:30:16,530 --> 00:30:23,730
and it doesn't fit at all with the Maxwellian
picture. Questions about that?

357
00:30:23,730 --> 00:30:34,340
So this led Einstein to make a prediction.
This was his 1905 result. One of his many

358
00:30:34,340 --> 00:30:38,679
totally breathtaking papers of that year.
And he didn't really propose a model or a

359
00:30:38,679 --> 00:30:42,720
detailed theoretical understanding of this,
but he proposed a very simple idea. And he

360
00:30:42,720 --> 00:30:47,990
said, look, if you want to fit this-- if you
want to fit this experiment with some simple

361
00:30:47,990 --> 00:30:53,850
equations, here's the way to explain it. I
claim-- I here means Einstein, not me-- I

362
00:30:53,850 --> 00:31:09,539
claim that light comes in packets or chunks
with definite energy. And the energy is linearly

363
00:31:09,539 --> 00:31:14,120
proportional to the frequency. And our energy
is equal to something times nu, and we'll

364
00:31:14,120 --> 00:31:18,780
call the coefficient h.

365
00:31:18,780 --> 00:31:31,820
The intensity of light, or the amplitude squared,
the intensity is like the number of packets.

366
00:31:31,820 --> 00:31:36,580
So if you have a more intense beam at the
same frequency, the energy of each individual

367
00:31:36,580 --> 00:31:44,070
chunk of light is the same. There are just
a lot more chunks flying around. And so to

368
00:31:44,070 --> 00:31:48,350
explain the photoelectric effect, Einstein
observed the following. Look, he said, the

369
00:31:48,350 --> 00:31:52,860
electrons are stuck under the metal. And it
takes some work to pull them off. So now what's

370
00:31:52,860 --> 00:31:59,159
the kinetic energy of an electron that comes
flying off-- whoops, k3. Bart might have a

371
00:31:59,159 --> 00:32:03,470
laugh about that one. Kinetic, kE, not 3.

372
00:32:03,470 --> 00:32:07,780
So the kinetic energy of electron that comes
flying off, well, it's the energy deposited

373
00:32:07,780 --> 00:32:13,580
by the photon, the chunk of light, h-nu well
we have to subtract off the work it took.

374
00:32:13,580 --> 00:32:18,070
Minus the work to extract the electron from
the material. And you can think of this as

375
00:32:18,070 --> 00:32:24,820
how much energy does it take to suck it off
the surface. And the consequence of this is

376
00:32:24,820 --> 00:32:34,809
that the kinetic energy of an electron should
be-- look, if h-nu is too small, if the frequency

377
00:32:34,809 --> 00:32:37,850
is too low, then the kinetic energy would
be negative.

378
00:32:37,850 --> 00:32:41,090
But that doesn't make any sense. You can't
have negative kinetic energy. It's a strictly

379
00:32:41,090 --> 00:32:45,679
positive quantity. So it just doesn't work
until you have a critical value where the

380
00:32:45,679 --> 00:32:50,460
frequency times h-- this coefficient-- is
equal to the work it takes to extract. And

381
00:32:50,460 --> 00:32:55,960
after that, the kinetic energy rises with
the frequency with a slope equal to h. And

382
00:32:55,960 --> 00:33:04,000
that fits the data like a champ.

383
00:33:04,000 --> 00:33:08,650
So no matter-- let's think about what this
is saying again. No matter what you do, if

384
00:33:08,650 --> 00:33:13,130
your light is very low-frequency and you pick
some definite piece of metal that has a very

385
00:33:13,130 --> 00:33:17,049
definite work function, very definite amount
of energy it takes to extract electrons from

386
00:33:17,049 --> 00:33:23,610
the surface. No matter how intense your beam,
if the frequency is insufficiently high, no

387
00:33:23,610 --> 00:33:26,799
electrons come off. None.

388
00:33:26,799 --> 00:33:30,840
So it turns out none is maybe a little overstatement
because what you can have is two photon processes,

389
00:33:30,840 --> 00:33:34,309
where two chunks hit one electron at the right,
just at the same time. Roughly speaking the

390
00:33:34,309 --> 00:33:37,950
same time. And they have twice the energy,
but you can imagine that the probability of

391
00:33:37,950 --> 00:33:41,850
two photon hitting one electron at the same
time of pretty low. So the intensity has to

392
00:33:41,850 --> 00:33:45,450
be preposterously high. And you see those
sorts of multi-photon effects. But as long

393
00:33:45,450 --> 00:33:52,730
as we're not talking about insanely high intensities,
this is an absolutely fantastic probe of the

394
00:33:52,730 --> 00:33:53,450
physics.

395
00:33:53,450 --> 00:33:57,650
Now there's a whole long subsequent story
in the development of quantum mechanics about

396
00:33:57,650 --> 00:34:00,320
this particular effect. And it turns out that
the photoelectric effect is a little more

397
00:34:00,320 --> 00:34:07,440
complicated than this. But the story line
is a very useful one for organizing your understanding

398
00:34:07,440 --> 00:34:12,460
of the photoelectric effect. And in particular,
this relation that Einstein proposed out of

399
00:34:12,460 --> 00:34:16,940
the blue, with no other basis. No one else
had ever seen this sort of statement that

400
00:34:16,940 --> 00:34:22,699
the electrons, or that the energy of a beam
of light should be made up of some number

401
00:34:22,699 --> 00:34:27,909
of chunks, each of which has a definite minimum
amount of energy.

402
00:34:27,909 --> 00:34:33,859
So you can take what you've learned from 8.02
and 8.03 and extract a little bit more information

403
00:34:33,859 --> 00:34:39,639
out of this. So here's something you learned
from 8.02. In 8.02 you learned that the energy

404
00:34:39,639 --> 00:34:44,239
of an electromagnetic wave is equal to c times
the momentum carried by that wave-- whoops,

405
00:34:44,239 --> 00:34:51,509
over two. And in 8.03 you should have learned
that the wavelength of an electromagnetic

406
00:34:51,509 --> 00:34:59,099
wave times the frequency is equal to the speed
of light, C.

407
00:34:59,099 --> 00:35:07,539
And we just had Einstein tell us-- or declare,
without further evidence, just saying, look

408
00:35:07,539 --> 00:35:13,809
this fits-- that the energy of a chunk of
light should be h times the frequency. So

409
00:35:13,809 --> 00:35:16,960
if you combine these together, you get another
nice relation that's similar to this one,

410
00:35:16,960 --> 00:35:25,269
which says that the momentum of a chunk of
light is equal to h over lambda. So these

411
00:35:25,269 --> 00:35:29,789
are two enormously influential expressions
which come out of this argument from the photoelectric

412
00:35:29,789 --> 00:35:33,279
effect from Einstein. And they're going to
be-- their legacy will be with us throughout

413
00:35:33,279 --> 00:35:36,789
the rest of the semester.

414
00:35:36,789 --> 00:35:51,989
Now this coefficient has a name, and it was
named after Planck. It's called Planck's Constant.

415
00:35:51,989 --> 00:35:55,339
And the reason that it's called Planck's Constant
has nothing to do with the photoelectric effect.

416
00:35:55,339 --> 00:36:03,489
It was first this idea that an electromagnetic
wave, that light, has an energy which is linearly

417
00:36:03,489 --> 00:36:07,469
proportional not to its intensity squared,
none of that, but just linearly proportional

418
00:36:07,469 --> 00:36:13,339
to the frequency. First came up an analysis
of black body radiation by Planck. And you'll

419
00:36:13,339 --> 00:36:16,690
understand, you'll go through this in some
detail in 8.044 later in the semester. So I'm

420
00:36:16,690 --> 00:36:20,660
not going to dwell on it now, but I do want
to give you a little bit of perspective on it.

421
00:36:20,660 --> 00:36:28,710
So Planck ran across this idea that E is equal
to h/nu. Through the process of trying to

422
00:36:28,710 --> 00:36:34,829
fit an experimental curve. There was a theory
of how much energy should be emitted by an

423
00:36:34,829 --> 00:36:39,329
object that's hot and glowing as a function
of frequency. And that theory turned out to

424
00:36:39,329 --> 00:36:44,019
be in total disagreement with experiment.
Spectacular disagreement. The curve for the

425
00:36:44,019 --> 00:36:48,109
theory went up, the curve for the experiment
went down. They were totally different.

426
00:36:48,109 --> 00:36:52,819
So Planck set about writing down a function
that described the data. Literally curve-fitting,

427
00:36:52,819 --> 00:36:58,069
that's all he was doing. And this is the depths
of desperation to which he was led, was curve-fitting.

428
00:36:58,069 --> 00:37:02,749
He's an adult. He shouldn't be doing this,
but he was curve-fitting. And so he fits the

429
00:37:02,749 --> 00:37:07,339
curve, and in order to get it to fit the only
thing that he can get to work even vaguely

430
00:37:07,339 --> 00:37:13,299
well is if he puts in this calculation of
h/nu. He says, well, maybe when I sum over

431
00:37:13,299 --> 00:37:17,569
all the possible energies I should restrict
the energies which were proportional to the

432
00:37:17,569 --> 00:37:20,759
frequency.

433
00:37:20,759 --> 00:37:24,979
And it was forced on him because it fit from
the function. Just functional analysis. Hated

434
00:37:24,979 --> 00:37:30,910
it. Hated it, he completely hated it. He was
really frustrated by this. It fit perfectly,

435
00:37:30,910 --> 00:37:34,950
he became very famous. He was already famous,
but he became ridiculously famous. Just totally

436
00:37:34,950 --> 00:37:40,539
loathed this idea. OK. So it's now become
a cornerstone of quantum mechanics. But he

437
00:37:40,539 --> 00:37:41,549
wasn't so happy about it.

438
00:37:41,549 --> 00:37:46,579
And to give you a sense for how bold and punchy
this paper by Einstein was that said, look,

439
00:37:46,579 --> 00:37:52,269
seriously. Seriously guys. e equals h/nu.
Here's what Planck had to say when he wrote

440
00:37:52,269 --> 00:37:55,910
a letter of recommendation to get Einstein
into the Prussian Academy of Sciences in 1917,

441
00:37:55,910 --> 00:38:01,170
or 1913. So he said, there is hardly one among
the great problems in physics to which Einstein

442
00:38:01,170 --> 00:38:05,670
has not made an important contribution. That
he may sometimes have missed the target in

443
00:38:05,670 --> 00:38:11,479
his speculations as in his hypothesis of photons
cannot really be held too much against him.

444
00:38:11,479 --> 00:38:18,249
It's not possible to introduce new ideas without
occasionally taking a risk.

445
00:38:18,249 --> 00:38:22,680
Einstein who subsequently went on to develop
special relativity and general relativity

446
00:38:22,680 --> 00:38:28,559
and prove the existence of atoms and the best
measurement of Avogadro's Constant, subsequently

447
00:38:28,559 --> 00:38:33,180
got the Nobel Prize. Not for Avogadro's Constant,
not for proving the existence of atoms, not

448
00:38:33,180 --> 00:38:39,380
for relativity, but for photons. Because of
guys like Planck, right. This is crazy.

449
00:38:39,380 --> 00:38:45,089
So this was a pretty bold idea. And here,
to get a sense for why-- we're gonna leave

450
00:38:45,089 --> 00:38:51,599
that up because it's just sort of fun to see
these guys scowling and smiling-- there is,

451
00:38:51,599 --> 00:38:57,339
incidentally there's a great book about Einstein's
years in Berlin by Tom Levenson, who's a professor

452
00:38:57,339 --> 00:39:04,539
here. A great writer and a sort of historian
of science. You should take a class from him,

453
00:39:04,539 --> 00:39:08,549
which is really great. But I encourage you
to read this book. It talks about why Planck

454
00:39:08,549 --> 00:39:14,650
is not looking so pleased right there, among
many other things. It's a great story.

455
00:39:14,650 --> 00:39:18,630
So let's step back for a second. Why was Planck
so upset by this, and why was in fact everyone

456
00:39:18,630 --> 00:39:24,529
so flustered by this idea that it led to the
best prize you can give a physicist. Apart

457
00:39:24,529 --> 00:39:36,450
from a happy home and, you know. I've got
that one. That's the one that matters to me.

458
00:39:36,450 --> 00:39:42,529
So why is this so surprising? And the answer
is really simple. We know that it's false.

459
00:39:42,529 --> 00:39:47,700
We know empirically, we've known for two hundred
and some years that light is a wave. Empirically.

460
00:39:47,700 --> 00:39:52,069
This isn't like people are like, oh I think
it'd be nice if it was a wave. It's a wave.

461
00:39:52,069 --> 00:39:56,799
So how do we know that? So this goes back
to the double-slit experiment from Young.

462
00:39:56,799 --> 00:40:04,489
Young's performance of this was in 1803. Intimations
of it come much earlier. But this is really

463
00:40:04,489 --> 00:40:09,609
where it hits nails to the wall. And here's
the experiment.

464
00:40:09,609 --> 00:40:15,700
So how many people in here have not seen a
double-slit experiment described? Yeah, exactly.

465
00:40:15,700 --> 00:40:18,880
OK. So I'm just going to quickly remind you
of how this goes.

466
00:40:18,880 --> 00:40:23,339
So we have a source for waves. We let the
waves get big until they're basically plane

467
00:40:23,339 --> 00:40:29,459
waves. And then we take a barrier. And we
poke two slits in it. And these plane waves

468
00:40:29,459 --> 00:40:35,680
induce-- they act like sources at the slits
and we get nu. And you get crests and troughs.

469
00:40:35,680 --> 00:40:38,579
And you look at some distant screen and you
look at the pattern, and the pattern you get

470
00:40:38,579 --> 00:40:45,509
has a maximum. But then it falls off, and
it has these wiggles, these interference fringes.

471
00:40:45,509 --> 00:40:49,799
These interference fringes are, of course,
extremely important. And what's going on here

472
00:40:49,799 --> 00:40:55,579
is that the waves sometimes add in-- so the
amplitude of the wave, the height of the wave,

473
00:40:55,579 --> 00:41:01,160
sometimes adds constructively and sometimes
destructively. So that sometimes you get twice

474
00:41:01,160 --> 00:41:06,369
the height and sometimes you get nothing.

475
00:41:06,369 --> 00:41:11,859
So just because it's fun to see this, here's
Young's actual diagram from his original note

476
00:41:11,859 --> 00:41:18,640
on the double-slit experiment. So a and b
are the slits, and c, d and f are the [INAUDIBLE]

477
00:41:18,640 --> 00:41:27,690
on the screen, the distant screen. He drew
it by hand. It's pretty good.

478
00:41:27,690 --> 00:41:32,039
So we've known for a very long time that light,
because of the double-slit experiment, light

479
00:41:32,039 --> 00:41:35,119
is clearly wavy, it behaves like a wave. And
what are the senses in which it behaves like

480
00:41:35,119 --> 00:41:44,940
a wave? There are two important senses here.
The first is answered by the question, where

481
00:41:44,940 --> 00:41:55,430
did the wave hit the screen? So when we send
in a wave, you know, I drop a stone, one big

482
00:41:55,430 --> 00:41:59,900
pulsive wave comes out. It splits into-- it
leads to new waves being instigated here and

483
00:41:59,900 --> 00:42:07,700
over here. Where did that wave hit the screen?
Anyone?

484
00:42:07,700 --> 00:42:09,040
AUDIENCE: Everywhere.

485
00:42:09,040 --> 00:42:12,259
PROFESSOR: Yeah, exactly. It didn't hit this
wave-- the screen in any one spot. But some

486
00:42:12,259 --> 00:42:15,890
amplitude shows up everywhere. The wave is
a distributed object, it does not exist at

487
00:42:15,890 --> 00:42:20,420
one spot, and it's by virtue of the fact that
it is not a localized object-- it is not a

488
00:42:20,420 --> 00:42:27,910
point-like object-- that it can interfere
with itself. The wave is a big large phenomena

489
00:42:27,910 --> 00:42:31,519
in a liquid, in some thing.

490
00:42:31,519 --> 00:42:37,299
So it's sort of essential that it's not a
localized object. So not localized. The answer

491
00:42:37,299 --> 00:42:45,569
is not localized. And let's contrast this
with what happens if you take this double-slit

492
00:42:45,569 --> 00:42:56,120
experiment and you do it with, you know, I
don't know, take-- who. Hmm. Tim Wakefield.

493
00:42:56,120 --> 00:42:57,979
Let's give some love to that guy.

494
00:42:57,979 --> 00:43:03,729
So, baseball player. And have him throw baseballs
at a screen with two slits in it. OK? Now

495
00:43:03,729 --> 00:43:10,650
he's got pretty good-- well, he's got terrible
accuracy, actually. So every once in a while

496
00:43:10,650 --> 00:43:15,150
he'll make it through the slits. So let's
imagine first blocking off-- what, he's a

497
00:43:15,150 --> 00:43:18,670
knuckle-baller, right-- so every once in a
while it goes, the baseball will go through

498
00:43:18,670 --> 00:43:19,930
the slit.

499
00:43:19,930 --> 00:43:22,719
And let's think about what happens, so let's
cover one slit. And what we expect to happen

500
00:43:22,719 --> 00:43:26,759
is, well, it'll go through more or less straight,
but sometimes it'll scrape the edge, it'll

501
00:43:26,759 --> 00:43:30,769
go off to the side, and sometimes it'll come
over here. But if you take a whole bunch of

502
00:43:30,769 --> 00:43:39,309
baseballs, and-- so any one baseball, where
does it hit? Some spot. Right? One spot. Not

503
00:43:39,309 --> 00:43:40,519
distributed. One spot.

504
00:43:40,519 --> 00:43:44,739
And as a consequence, you know, one goes here,
one goes there, one goes there. And now, there's

505
00:43:44,739 --> 00:43:50,059
nothing like interference effects, but what
happens is as it sort of doesn't-- you get

506
00:43:50,059 --> 00:43:54,309
some distribution if you look at where they
all hit. Yeah? Everyone cool with that? And

507
00:43:54,309 --> 00:43:59,839
if we had covered over this slot, or slit,
and let the baseballs go through this one,

508
00:43:59,839 --> 00:44:00,729
same thing would have happened.

509
00:44:00,729 --> 00:44:04,650
Now if we leave them both open, what happens
is sometimes it goes here, sometimes it goes

510
00:44:04,650 --> 00:44:07,670
here. So now it's pretty useful that we've
got a knuckle-baller. And what you actually

511
00:44:07,670 --> 00:44:12,989
get is the total distribution looks like this.
It's the sum of the two. But at any given

512
00:44:12,989 --> 00:44:16,200
time, any one baseball, you say, aha, the
baseball either went through the top slit,

513
00:44:16,200 --> 00:44:18,650
and more or less goes up here. Or it went
through the bottom slit and more or less goes

514
00:44:18,650 --> 00:44:28,219
down here. So for chunks-- so this is for
waves-- for chunks or localized particles,

515
00:44:28,219 --> 00:44:43,190
they are localized. And as a consequence,
we get no interference.

516
00:44:43,190 --> 00:44:55,509
So for waves, they are not localized, and
we do get interference. Yes, interference.

517
00:44:55,509 --> 00:45:01,849
OK. So on your problem set, you're going to
deal with some calculations involving these

518
00:45:01,849 --> 00:45:05,509
interference effects. And I'm going to brush
over them.

519
00:45:05,509 --> 00:45:13,599
Anyway the point of the double-slit experiment
is that whatever else you want to say about

520
00:45:13,599 --> 00:45:19,769
baseballs or anything else, light, as we've
learned since 1803 in Young's double-slit

521
00:45:19,769 --> 00:45:23,569
experiment, light behaves like a wave. It
is not localized, it hits the screen over

522
00:45:23,569 --> 00:45:28,369
its entire extent. And as a consequence, we
get interference. The amplitudes add. The

523
00:45:28,369 --> 00:45:34,519
intensity is the square of the amplitude.
If the intensities add-- so sorry, if the

524
00:45:34,519 --> 00:45:39,559
amplitudes add-- amplitude total is equal
to a1 plus a2, the intensity, which is the

525
00:45:39,559 --> 00:45:57,920
square of a1 plus a2 squared, has interference
terms, the cross terms, from this square.

526
00:45:57,920 --> 00:46:02,900
So light, from this point of view, is an electromagnetic
wave. It interferes with itself. It's made

527
00:46:02,900 --> 00:46:08,700
of chunks. And I can't help but think about
it this way, this is literally the metaphor

528
00:46:08,700 --> 00:46:18,160
I use in my head-- light is creamy and smooth
like a wave. Chunks are very different. But

529
00:46:18,160 --> 00:46:25,089
here's the funny thing. Light is both smooth
like a wave, it is also chunky. It is super

530
00:46:25,089 --> 00:46:31,900
chunky, as we have learned from the photoelectric
effect. So light is both at once. So it's

531
00:46:31,900 --> 00:46:36,400
the best of both worlds. Everyone will be
satisfied, unless you're not from the US,

532
00:46:36,400 --> 00:46:45,400
in which case this is deeply disturbing. So
of course the original Superchunk is a band.

533
00:46:45,400 --> 00:46:49,309
So we've learned now from Young that light
is a wave. We've learned from the photoelectric

534
00:46:49,309 --> 00:46:58,430
effect that light is a bunch of chunks. OK.
Most experimental results are true. So how

535
00:46:58,430 --> 00:47:02,759
does that work? Well, we're gonna have to
deal with that.

536
00:47:02,759 --> 00:47:07,339
But enough about light. If this is true of
light, if light, depending on what experiment

537
00:47:07,339 --> 00:47:10,739
you do and how you do the experiment, sometimes
it seems like it's a wave, sometimes it seems

538
00:47:10,739 --> 00:47:17,180
like it's a chunk or particle, which is true?
Which is the better description?

539
00:47:17,180 --> 00:47:21,739
So it's actually worthwhile to not think about
light all the time. Let's think about something

540
00:47:21,739 --> 00:47:27,099
more general. Let's stick to electrons. So
as we saw from yesterday's lecture, you probably

541
00:47:27,099 --> 00:47:30,589
want to be a little bit wary when thinking
about individual electrons. Things could be

542
00:47:30,589 --> 00:47:34,999
a little bit different than your classical
intuition. But here's a crucial thing. Before

543
00:47:34,999 --> 00:47:38,449
doing anything else, we can just think, which
one of these two is more likely to describe

544
00:47:38,449 --> 00:47:39,799
electrons well.

545
00:47:39,799 --> 00:47:46,190
Well electrons are localized. When you throw
an electron at a CRT, it does not hit the

546
00:47:46,190 --> 00:47:49,199
whole CRT with a wavy distribution. When you
take a single electron and you throw it at

547
00:47:49,199 --> 00:47:54,699
a CRT, it goes ping and there's a little glowing
spot. Electrons are localized. And we know

548
00:47:54,699 --> 00:48:02,940
that localized things don't lead to interference.

549
00:48:02,940 --> 00:48:06,279
Some guys at Hitachi, really good scientists
and engineers, developed some really awesome

550
00:48:06,279 --> 00:48:10,019
technology a couple of decades ago. They were
trying to figure out a good way to demonstrate

551
00:48:10,019 --> 00:48:13,680
their technology. And they decided that you
know what would be really awesome, this thought

552
00:48:13,680 --> 00:48:16,579
experiment that people have always talked
about that's never been done really well,

553
00:48:16,579 --> 00:48:20,499
of sending an electron through a two-slitted
experiment. In this case it was like ten slits

554
00:48:20,499 --> 00:48:24,910
effectively, it was a grading. Send an electron,
a bunch of electrons, one at a time, throw

555
00:48:24,910 --> 00:48:28,529
the electron, wait. Throw the electron, wait.
Like our French guy with the boat.

556
00:48:28,529 --> 00:48:34,349
So do this experiment with our technology
and let's see what happens. And this really

557
00:48:34,349 --> 00:48:42,269
is one of my favorite-- let's see, how we
close these screens-- aha. OK. This is going

558
00:48:42,269 --> 00:48:50,180
to take a little bit of-- and it's broken.
No, no. Oh that's so sad.

559
00:48:50,180 --> 00:48:57,620
AUDIENCE: [LAUGHTER]

560
00:48:57,620 --> 00:49:07,440
PROFESSOR: Come on. I'm just gonna let-- let's
see if we can, we'll get part of the way.

561
00:49:07,440 --> 00:49:11,729
I don't want to destroy it. So what they actually
did is they said, look, let's-- we want to

562
00:49:11,729 --> 00:49:15,839
see what happens. We want to actually do this
experiment because we're so awesome at Hitachi

563
00:49:15,839 --> 00:49:22,289
Research Labs, so let's do it. So here's what
they did. And I'm going to turn off the light.

564
00:49:22,289 --> 00:49:29,599
And I set this to some music because I like
it.

565
00:49:29,599 --> 00:49:37,529
OK here's what's happening. One at a time,
individual photons.

566
00:49:37,529 --> 00:49:55,280
[MUSIC PLAYING]

567
00:49:55,280 --> 00:50:05,979
PROFESSOR: So they look pretty localized.
There's not a whole lot of structure. Now

568
00:50:05,979 --> 00:50:13,400
they're going to start speeding it up. It's
100 times the actual speed.

569
00:50:13,400 --> 00:50:41,240
[MUSIC PLAYING]

570
00:50:41,240 --> 00:50:43,520
PROFESSOR: Eh? Yeah.

571
00:50:43,540 --> 00:50:49,280
AUDIENCE: [APPLAUSE]

572
00:50:49,280 --> 00:50:55,580
PROFESSOR: So those guys know what they're
doing. Let's-- there were go. So I think I

573
00:50:55,589 --> 00:51:00,509
don't know of a more vivid example of electron
interference than that one. It's totally obvious.

574
00:51:00,509 --> 00:51:04,069
You see individual electrons. They run through
the apparatus. You wait, they run through

575
00:51:04,069 --> 00:51:08,529
the apparatus. You wait. One at a time, single
electron, like a baseball being pitched through

576
00:51:08,529 --> 00:51:12,660
two slits, and what you see is an interference
effect. But you don't see the interference

577
00:51:12,660 --> 00:51:16,400
effect like you do from light, from waves
on the sea.

578
00:51:16,400 --> 00:51:20,079
You see the interference effect by looking
at the cumulative stacking up of all the electrons

579
00:51:20,079 --> 00:51:25,680
as they hit. Look at where all the electrons
hit one at a time. So is an electron behaving

580
00:51:25,680 --> 00:51:35,339
like a wave in a pond? No. Does a wave in
a pond at a spot? No. It's a distributed beast.

581
00:51:35,339 --> 00:51:40,650
OK yes, it interferes, but it's not localized.
Well is it behaving like a baseball? Well

582
00:51:40,650 --> 00:51:41,969
it's localized.

583
00:51:41,969 --> 00:51:47,440
But on-- when I look at a whole bunch of electrons,
they do that. They seem to interfere, but

584
00:51:47,440 --> 00:51:50,079
there's only one electron going through at
a time. So in some sense it's interfering

585
00:51:50,079 --> 00:51:54,239
with itself. How does that work? Is an electron
a wave?

586
00:51:54,239 --> 00:51:56,569
AUDIENCE: Yes.

587
00:51:56,569 --> 00:52:00,130
PROFESSOR: Does an electron hit at many spots
at once?

588
00:52:00,130 --> 00:52:00,880
AUDIENCE: No.

589
00:52:00,880 --> 00:52:08,920
PROFESSOR: No. So is an electron a wave. No.
Is an electron a baseball? No. It's an electron.

590
00:52:08,920 --> 00:52:14,029
So this is something you're going to have
to deal with, that every once in awhile we

591
00:52:14,029 --> 00:52:17,150
have these wonderful moments where it's useful
to think about an electron as behaving in

592
00:52:17,150 --> 00:52:21,699
a wave-like sense. Sometimes it's useful to
think about it as behaving in a particle-like

593
00:52:21,699 --> 00:52:25,630
sense. But it is not a particle like you normally
conceive of a baseball. And it is not a wave

594
00:52:25,630 --> 00:52:35,680
like you normally conceive of a wave on the
surface of a pond. It's an electron.

595
00:52:35,680 --> 00:52:41,229
I like to think about this like an elephant.
If you're closing your eyes and you walk up

596
00:52:41,229 --> 00:52:44,670
to an elephant, you might think like I've
got a snake and I've got a tree trunk and,

597
00:52:44,670 --> 00:52:48,739
you know, there's a fan over here. And you
wouldn't know, like, maybe it's a wave, maybe

598
00:52:48,739 --> 00:52:52,650
it's a particle, I can't really tell. But
if you could just see the thing the way it

599
00:52:52,650 --> 00:52:57,569
is, not through the preconceived sort of notions
you have, you'd see it's an elephant. Yes,

600
00:52:57,569 --> 00:53:03,709
that is the Stata Center. So-- look, everything
has to happen sometime, right?

601
00:53:03,709 --> 00:53:06,780
AUDIENCE: [LAUGHTER]

602
00:53:06,780 --> 00:53:12,600
PROFESSOR: So Heisenberg-- it's often, people
often give the false impression in popular

603
00:53:12,609 --> 00:53:16,369
books on physics, so I want to subvert this,
that in the early days of quantum mechanics,

604
00:53:16,369 --> 00:53:23,609
the early people like Born and Oppenheimer
and Heisenberg who invented quantum mechanics,

605
00:53:23,609 --> 00:53:26,880
they were really tortured about, you know,
is it an electron, is it a wave. It's a wave-particle

606
00:53:26,880 --> 00:53:31,740
duality. It's both. And this is one of the
best subversions of that sort of silliness

607
00:53:31,740 --> 00:53:32,300
that I know of.

608
00:53:32,319 --> 00:53:36,019
And so what Heisenberg says, the two mental
pictures which experiments lead us to form,

609
00:53:36,019 --> 00:53:41,259
the one of particles the other waves, are
both incomplete and have the validity of analogies,

610
00:53:41,259 --> 00:53:46,099
which are accurate only in limited cases.
The apparent duality rises in the limitation

611
00:53:46,099 --> 00:53:50,390
of our language. And then he goes on to say,
look, you developed your intuition by throwing

612
00:53:50,390 --> 00:53:56,239
rocks and, you know, swimming. And, duh, that's
not going to be very good for atoms.

613
00:53:56,239 --> 00:54:01,609
So this will be posted, it's really wonderful.
His whole lecture is really-- the lectures

614
00:54:01,609 --> 00:54:05,440
are really quite lovely. And by the way, that's
him in the middle there, Pauley all the way

615
00:54:05,440 --> 00:54:12,279
on the right. I guess they were pleased. OK
so that's the Hitachi thing.

616
00:54:12,279 --> 00:54:19,539
So now let's pick up on this, though. Let's
pick up on this and think about what happens.

617
00:54:19,539 --> 00:54:23,599
I want to think in a little more detail about
this Hitachi experiment. And I want to think

618
00:54:23,599 --> 00:54:28,099
about it in the context of a simple two-slit
experiment. So here's our source of electrons.

619
00:54:28,099 --> 00:54:31,690
It's literally a gun, an electron gun. And
it's firing off electrons. And here's our

620
00:54:31,690 --> 00:54:37,259
barrier, and it has two slits in it.

621
00:54:37,259 --> 00:54:44,049
And we know that any individual electron hits
its own spot. But when we take many of them,

622
00:54:44,049 --> 00:54:48,380
we get an interference effect. We get interference
fringes. And so the number that hit a given

623
00:54:48,380 --> 00:54:57,390
spot fill up, construct this distribution.
So then here's the question I want to ask.

624
00:54:57,390 --> 00:55:01,839
When I take a single electron, I shoot one
electron at a time through this experiment,

625
00:55:01,839 --> 00:55:06,430
one electron. It could go through the top
slit, it could go through the bottom slit.

626
00:55:06,430 --> 00:55:12,960
While it's inside the apparatus, which path
does it take?

627
00:55:12,960 --> 00:55:15,920
AUDIENCE: Superposition.

628
00:55:15,920 --> 00:55:17,939
PROFESSOR: Good. So did it take the top path?

629
00:55:17,939 --> 00:55:18,799
AUDIENCE: No.

630
00:55:18,799 --> 00:55:20,249
PROFESSOR: How do you know?

631
00:55:20,249 --> 00:55:23,400
[INTERPOSING VOICES]

632
00:55:23,400 --> 00:55:28,959
PROFESSOR: Good, let's block the bottom, OK,
to force it to go through the top slit. So

633
00:55:28,959 --> 00:55:32,619
we'll block the bottom slit. Now the only
electrons that make it through go through

634
00:55:32,619 --> 00:55:37,839
the top slit. Half of them don't make it through.
But those that do make it through give you

635
00:55:37,839 --> 00:55:43,390
this distribution. No interference. But I
didn't tell you these are hundreds of thousands

636
00:55:43,390 --> 00:55:47,430
of kilometers apart, the person who threw
in the electron didn't know whether there

637
00:55:47,430 --> 00:55:50,599
was a barrier here. The electron, how could
it possibly know whether there was a barrier

638
00:55:50,599 --> 00:55:52,089
here if you went through the top.

639
00:55:52,089 --> 00:55:57,719
This is exactly like our boxes. It's exactly
like our box. Did it go through-- an electron,

640
00:55:57,719 --> 00:56:03,229
when the slits are both open and we know that
ensemble average it will give us an interference

641
00:56:03,229 --> 00:56:08,329
effect, did the electron inside the apparatus
go through the top path? No. Did it go through

642
00:56:08,329 --> 00:56:13,489
the bottom path? Did it go through both? Because
we only see one electron. Did it go through

643
00:56:13,489 --> 00:56:14,969
neither? It is in a--

644
00:56:14,969 --> 00:56:16,360
AUDIENCE: Superposition.

645
00:56:16,360 --> 00:56:19,140
PROFESSOR: --of having gone through the top
and the bottom. Of being along the top half

646
00:56:19,150 --> 00:56:25,519
and being along the bottom path. This is a
classic example of the two-box experiment.

647
00:56:25,519 --> 00:56:34,529
OK. So you want to tie that together.

648
00:56:34,529 --> 00:56:37,779
So let's nuance this just a little bit, though,
because it's going to have an interesting

649
00:56:37,779 --> 00:56:47,650
implication for gravity. So here's the nuance
I want to pull on this one. Let's cheat. OK.

650
00:56:47,650 --> 00:56:53,939
Suppose I want to measure which slit the electron
actually did go through. How might I do that?

651
00:56:53,939 --> 00:56:57,630
Well I could do the course thing I've been
doing which is I could block it and just catch

652
00:56:57,630 --> 00:57:02,420
the-- catch electrons that go through in that
spot. But that's a little heavy-handed. Probably

653
00:57:02,420 --> 00:57:03,529
I can do something a little more delicate.

654
00:57:03,529 --> 00:57:11,979
And so here's the more delicate thing I'm
going to do. I want to build a detector that

655
00:57:11,979 --> 00:57:17,259
uses very, very, very weak light, extremely
weak light, to detect whether the particle

656
00:57:17,259 --> 00:57:20,920
went through here or here. And the way I can
do that is I can sort of shine light through

657
00:57:20,920 --> 00:57:27,380
and-- I'm gonna, you know, bounce-- so here's
my source of light. And I'll be able to tell

658
00:57:27,380 --> 00:57:31,779
whether the electron went through this slit
or it went through this slit. Cool?

659
00:57:31,779 --> 00:57:38,479
So imagine I did that. So obviously I don't
want to use some giant, huge, ultra high-energy

660
00:57:38,479 --> 00:57:41,279
laser because it would just blast the thing
out of the way. It would destroy the experiment.

661
00:57:41,279 --> 00:57:45,979
So I wanna something very diffuse, very low
energy, very low intensity electromagnetic

662
00:57:45,979 --> 00:57:51,209
wave. And the idea here is that, OK, it's
true that when I bounce this light off an

663
00:57:51,209 --> 00:57:56,439
electron, let's say it bounces off an electron
here, it's true it's going impart some momentum

664
00:57:56,439 --> 00:58:00,079
and the electron's gonna change its course.
But if it's really, really weak, low energy

665
00:58:00,079 --> 00:58:03,199
light, then it's-- it's gonna deflect only
a little tiny bit.

666
00:58:03,199 --> 00:58:08,569
So it will change the pattern I get over here.
But it will change it in some relatively minor

667
00:58:08,569 --> 00:58:13,749
way because I've just thrown in very, very
low energy light. Yeah? That make sense? So

668
00:58:13,749 --> 00:58:24,320
this is the experiment I want to do. This
experiment doesn't work. Why.

669
00:58:24,320 --> 00:58:27,160
AUDIENCE: You know which slit it went through.

670
00:58:27,180 --> 00:58:31,100
PROFESSOR: No. It's true that it turns out
that those are correlated facts, but here's

671
00:58:31,109 --> 00:58:36,089
the problem. I can run this experiment without
anyone actually knowing what happens until

672
00:58:36,089 --> 00:58:42,170
long afterwards. So knowing doesn't seem to
play any role in it. It's very tempting often

673
00:58:42,170 --> 00:58:46,170
to say, no, but it turns out that it's really
not about what you know. It's really just

674
00:58:46,170 --> 00:58:47,499
about the experiment you're doing.

675
00:58:47,499 --> 00:58:53,140
So what principle that we've already run into
today makes it impossible to make this work?

676
00:58:53,140 --> 00:58:58,269
If I want to shine really low-energy, really
diffuse light through, and have it scatter

677
00:58:58,269 --> 00:59:01,580
weakly. Yeah.

678
00:59:01,580 --> 00:59:05,400
AUDIENCE: Um, light is chunky.

679
00:59:05,400 --> 00:59:10,660
PROFESSOR: Yeah, exactly. That's exactly right.
So when I say really low-energy light, I don't--

680
00:59:10,670 --> 00:59:14,549
I really can't mean, because we've already
done this experiment, I cannot possibly mean

681
00:59:14,549 --> 00:59:20,499
low intensity. Because intensity doesn't control
the energy imparted by the light. The thing

682
00:59:20,499 --> 00:59:25,079
that controls the energy imparted by a collision
of the light with the electron is the frequency.

683
00:59:25,079 --> 00:59:28,999
The energy in a chunk of light is proportional
to the frequency.

684
00:59:28,999 --> 00:59:33,499
So now if I want to make the effect the energy
or the momentum, similarly-- the momentum,

685
00:59:33,499 --> 00:59:39,229
where did it go-- remember the momentum goes
like h over lambda. If I want to make the

686
00:59:39,229 --> 00:59:42,079
energy really low, I need to make the frequency
really low. Or if I want to make the momentum

687
00:59:42,079 --> 00:59:47,369
really low, I need to make the wavelength
what? Really big. Right? So in order to make

688
00:59:47,369 --> 00:59:51,489
the momentum imparted by this photon really
low, I need to make the wavelength really

689
00:59:51,489 --> 00:59:52,089
long.

690
00:59:52,089 --> 00:59:58,299
But now here's the problem. If I make the
wavelength really long, so if I use a really

691
00:59:58,299 --> 01:00:03,380
long-wavelengthed wave, like this long of
a wavelength, are you ever going to be able

692
01:00:03,380 --> 01:00:07,369
to tell which slit it went through? No, because
the particle could have been anywhere. It

693
01:00:07,369 --> 01:00:10,739
could have scattered this light if it was
here, if it was here, if it was here, right?

694
01:00:10,739 --> 01:00:15,569
In order to measure where the electron is
to some reasonable precision-- so, for example,

695
01:00:15,569 --> 01:00:19,599
to this sort of wavelength, I need to be able
to send in light with a wavelength that's

696
01:00:19,599 --> 01:00:25,479
comparable to the scale that I want to measure.
And it turns out that if you run through and

697
01:00:25,479 --> 01:00:30,589
just do the calculation, suppose I send in--
and this is done in the books, in I think

698
01:00:30,589 --> 01:00:37,029
all four, but this is done in the books on
the reading list-- if you send in a wave with

699
01:00:37,029 --> 01:00:41,719
a short enough wavelength to be able to distinguish
between these two slits, which slit did it

700
01:00:41,719 --> 01:00:47,309
go through, the momentum that it imparts precisely
watches-- washes out is just enough to wash

701
01:00:47,309 --> 01:00:52,509
out the interference effect, and break up
these fringes so you don't see interference

702
01:00:52,509 --> 01:00:55,229
effects.

703
01:00:55,229 --> 01:00:59,880
It's not about what you know. It's about the
particulate nature of light and the fact that

704
01:00:59,880 --> 01:01:06,880
the momentum of a chunk of light goes like
h over lambda. OK? But this tells you something

705
01:01:06,880 --> 01:01:13,979
really interesting. Did I have to use light
to do this measurement? I could have sent

706
01:01:13,979 --> 01:01:17,650
in anything, right? I didn't have to bounce
light off these things.

707
01:01:17,650 --> 01:01:24,519
I could have bounced off gravitational waves.
So if I had a gravitational wave detector,

708
01:01:24,519 --> 01:01:29,939
so-- Matt works on gravitational wave detectors,
and so, I didn't tell you this but Matt gave

709
01:01:29,939 --> 01:01:34,420
me a pretty killer gravitational wave detector.
It's, you know, here it is. There's my awesome

710
01:01:34,420 --> 01:01:38,130
gravitational wave detector. And I'm now going
to build supernova. OK.

711
01:01:38,130 --> 01:01:40,519
And they are creeping under this black hole,
and it's going to create giant gravitational

712
01:01:40,519 --> 01:01:44,369
waves. And we're gonna use those gravitational
waves and detect them with the super advanced

713
01:01:44,369 --> 01:01:48,859
LIGO. And I'm gonna detect which slit it went
through. But gravitational waves, those aren't

714
01:01:48,859 --> 01:01:52,670
photons. So I really can make a low-intensity
gravitational wave, and then I can tell which

715
01:01:52,670 --> 01:01:59,429
slit it went through without destroying the
interference effect. That would be awesome.

716
01:01:59,429 --> 01:02:05,699
What does that tell you about gravitational
waves? They must come in chunks. In order

717
01:02:05,699 --> 01:02:09,679
for this all to fit together logically, you
need all the interactions that you could scatter

718
01:02:09,679 --> 01:02:15,029
off this to satisfy these quantization properties.
But the energy is proportional to the frequency.

719
01:02:15,029 --> 01:02:18,979
The line I just gave you is a heuristic. And
making it precise is one of the great challenges

720
01:02:18,979 --> 01:02:23,890
of modern contemporary high-energy physics,
of dealing with the quantum mechanics and

721
01:02:23,890 --> 01:02:24,839
gravity together.

722
01:02:24,839 --> 01:02:30,140
But this gives you a strong picture of why
we need to treat all forces in all interactions

723
01:02:30,140 --> 01:02:39,589
quantum-mechanically in order for the world
to be consistent. OK. Good. OK, questions

724
01:02:39,589 --> 01:02:51,679
at this point? OK. So-- oh, I forgot about
this one-- so there are actually two more.

725
01:02:51,679 --> 01:02:55,029
So I want to just quickly show you-- well,
OK.

726
01:02:55,029 --> 01:02:59,549
So, this is a gorgeous experiment. So remember
I told you the story of the guy with the boat

727
01:02:59,549 --> 01:03:05,029
and the opaque wall and it turns out that's
a cheat. It turns out that this opaque screen

728
01:03:05,029 --> 01:03:11,939
doesn't actually give you quantum mechanically
isolated photons. They're still, in a very

729
01:03:11,939 --> 01:03:17,179
important way, classical. So this experiment
was done truly with a source that gives you

730
01:03:17,179 --> 01:03:20,359
quantum mechanically isolated single photons,
one at a time.

731
01:03:20,359 --> 01:03:26,759
So this is the analogue of the Hitachi experiment.
And it was done by this pretty awesome Japanese

732
01:03:26,759 --> 01:03:30,599
group some number of years ago. And I just
want to emphasize that it gives you exactly

733
01:03:30,599 --> 01:03:34,519
the same effects. We see that photons-- this
should look essentially identical to what

734
01:03:34,519 --> 01:03:37,920
we saw at the end of the Hitachi video. And
that's because it's exactly the same physics.

735
01:03:37,920 --> 01:03:42,369
It's a grating with something like 10 slits
and individual particles going through one

736
01:03:42,369 --> 01:03:45,788
at a time and hitting the screen and going,
bing.

737
01:03:45,788 --> 01:03:53,949
So what you see is the light going, bing,
on a CCD. It's a pretty spectacular experience.

738
01:03:53,949 --> 01:03:58,509
So let's get back to electrons. I want another
probe of whether electrons are really waves

739
01:03:58,509 --> 01:04:03,390
or not. So this other experiment-- again,
you're going to study this on your problem

740
01:04:03,390 --> 01:04:11,259
set-- this other experiment was done by a
couple of characters named Davisson and Germer.

741
01:04:11,259 --> 01:04:15,839
And in this experiment, what they did is they
took a crystal, and a crystal is just a lattice

742
01:04:15,840 --> 01:04:25,600
of regularly-located ions, like diamond or
something. Yeah?

743
01:04:25,600 --> 01:04:27,540
AUDIENCE: Before you go on I guess,

744
01:04:27,540 --> 01:04:33,900
I wanted to ask if the probability of a photon or an electron going through the 10 slits is about the same?

745
01:04:33,900 --> 01:04:35,560
PROFESSOR: Is what, sorry?

746
01:04:35,560 --> 01:04:36,839
AUDIENCE: Is exactly the same.

747
01:04:36,839 --> 01:04:38,549
PROFESSOR: You mean for different electrons?

748
01:04:38,549 --> 01:04:38,839
AUDIENCE: Yeah.

749
01:04:38,839 --> 01:04:42,069
PROFESSOR: Well they can be different if the
initial conditions are different. But they

750
01:04:42,069 --> 01:04:46,599
could be-- if the initial conditions are the
same, then the probabilities are identical.

751
01:04:46,599 --> 01:04:50,379
So every electron behaves identically to every
other electron in that sense. Is that what

752
01:04:50,380 --> 01:04:51,380
you were asking?

753
01:04:51,380 --> 01:04:58,140
AUDIENCE: It is actually like through any [INAUDIBLE] the probability of it going like [INAUDIBLE]?

754
01:04:58,140 --> 01:05:02,200
PROFESSOR: Sure, absolutely. So the issue
there is just a technological one of trying

755
01:05:02,219 --> 01:05:07,049
to build a beam that's perfectly columnated.
And that's just not doable. So there's always

756
01:05:07,049 --> 01:05:11,880
some dispersion in your beam. So in practice
it's very hard to make them identical, but

757
01:05:11,880 --> 01:05:16,939
in principle they could be if you were infinitely
powerful as an experimentalist, which-- again,

758
01:05:16,939 --> 01:05:19,910
I was banned from the lab, so not me.

759
01:05:19,910 --> 01:05:23,469
So here's our crystal. You could think of
this as diamond or nickel or whatever. I think

760
01:05:23,469 --> 01:05:32,140
they actually use nickel but I don't remember
exactly. And they sent in a beam of electrons.

761
01:05:32,140 --> 01:05:38,299
So they send in a beam of electrons, and what
they discover is that if you send in these

762
01:05:38,299 --> 01:05:44,390
electrons and watch how they scatter at various
different angles-- I'm going to call the angle

763
01:05:44,390 --> 01:05:54,059
here of scattering theta-- what they discover
is that the intensity of the reflected beam,

764
01:05:54,059 --> 01:06:03,099
as a function of theta, shows interference
effects.

765
01:06:03,099 --> 01:06:06,059
And in particular they gave a whole calculation
for this, which I'm not going to go through

766
01:06:06,059 --> 01:06:09,640
right now because it's not terribly germane
for us-- you're going to go through it on

767
01:06:09,640 --> 01:06:12,679
your problem set, so that'll be good and it's
a perfect thing for your recitation instructors

768
01:06:12,679 --> 01:06:17,660
to go through. But the important thing is
the upshot. So if the distance between these

769
01:06:17,660 --> 01:06:24,630
crystal planes is L-- or, sorry, d-- let me
call it d. If the distance between the crystal

770
01:06:24,630 --> 01:06:31,059
planes is d, what they discover is that the
interference effects that they observed, these

771
01:06:31,059 --> 01:06:40,429
maxima and minima, are consistent with the
wavelength of light. Or, sorry, with the electrons

772
01:06:40,429 --> 01:06:46,288
behaving as if they were waves with a definite
wavelength, with a wavelength lambda being

773
01:06:46,288 --> 01:06:56,239
equal to some integer, n, over 2d sine theta.

774
01:06:56,239 --> 01:07:01,449
So this is the data-- these are the data they
actually saw, data are plural. And these are

775
01:07:01,449 --> 01:07:06,049
the data they actually saw. And they infer
from this that the electrons are behaving

776
01:07:06,049 --> 01:07:11,079
as if they were wave-like with this wavelength.
And what they actually see are individual

777
01:07:11,079 --> 01:07:13,839
electrons hitting one by one. Although in
their experiment, they couldn't resolve individual

778
01:07:13,839 --> 01:07:15,799
electrons. But that is what they see.

779
01:07:15,799 --> 01:07:21,538
And so in particular, plugging all of this
back into the experiment, you send in the

780
01:07:21,538 --> 01:07:24,660
electrons with some energy, which corresponds
to some definite momentum. This leads us back

781
01:07:24,660 --> 01:07:29,809
to the same expression as before, that the
momentum is equal to h over lambda, with this

782
01:07:29,809 --> 01:07:35,229
lambda associated. So it turns out that this
is correct.

783
01:07:35,229 --> 01:07:40,420
So the electrons diffract off the crystal
as if they have a momentum which comes with

784
01:07:40,420 --> 01:07:48,759
a definite wavelength corresponding to its
momentum. So that's experimental result--

785
01:07:48,759 --> 01:07:53,999
oh, I forgot to check off four-- that's experimental
result five, that electrons diffract. We already

786
01:07:53,999 --> 01:07:57,959
saw the electron diffraction.

787
01:07:57,959 --> 01:08:04,150
So something to emphasize is that-- so these
experiments as we've described them were done

788
01:08:04,150 --> 01:08:09,559
with photons and with electrons, but you can
imagine doing the experiments with soccer

789
01:08:09,559 --> 01:08:14,390
balls. This is of course hard. Quantum effects
for macroscopic objects are usually insignificantly

790
01:08:14,390 --> 01:08:19,830
small. However, this experiment was done with
Buckyballs, which are the same shape as soccer

791
01:08:19,830 --> 01:08:26,189
balls in some sense. But they're huge, they're
gigantic objects. So here's the experiment

792
01:08:26,189 --> 01:08:31,819
in which this was actually done. So these
guys are just totally amazing. So this is

793
01:08:31,819 --> 01:08:38,580
Zellinger's lab. And it doesn't look like
all-- I mean it looks kind of, you know. It's

794
01:08:38,580 --> 01:08:41,420
hideous, right? I mean to a theorist it's
like, come on, you've got to be kidding that

795
01:08:41,420 --> 01:08:42,710
that's--

796
01:08:42,710 --> 01:08:47,640
But here's what a theorist is happy about.
You know, because it looks simple. We really

797
01:08:47,640 --> 01:08:52,318
love lying to ourselves about that. So here's
an over. We're going to cook up some Buckyballs

798
01:08:52,318 --> 01:08:57,000
and emit them with some definite known thermal
energy. Known to some accuracy. We're going

799
01:08:57,000 --> 01:08:59,830
to columnate them by sending them through
a single slit, and then we're going to send

800
01:08:59,830 --> 01:09:03,000
them through a diffraction grating which,
again, is just a whole bunch of slits.

801
01:09:03,000 --> 01:09:09,818
And then we're going to image them using photo
ionization and see where they pop through.

802
01:09:09,818 --> 01:09:16,559
So here is the horizontal position of this
wave along the grating, and this is the number

803
01:09:16,559 --> 01:09:20,660
that come through. This is literally one by
one counts because they're going bing, bing,

804
01:09:20,660 --> 01:09:25,479
bing, as a c60 molecule goes through. So without
the grating, you just get a peek. But with

805
01:09:25,479 --> 01:09:29,540
the grating, you get the side bands. You get
interference fringes.

806
01:09:29,540 --> 01:09:36,910
So these guys, again, they're going through
one by one. A single Buckyball, 60 carbons,

807
01:09:36,910 --> 01:09:41,479
going through one by one is interfering with
itself. This is a gigantic object by any sort

808
01:09:41,479 --> 01:09:47,899
of comparison to single electrons. And we're
seeing these interference fringes.

809
01:09:47,899 --> 01:09:51,160
So this is a pretty tour de force experiment,
but I just want to emphasize that if you could

810
01:09:51,160 --> 01:09:55,910
do this with your neighbor, it would work.
You'd just have to isolate the system well

811
01:09:55,910 --> 01:10:02,559
enough. And that's a technological challenge
but not an in-principle one.

812
01:10:02,559 --> 01:10:16,460
OK. So we have one last experimental facts
to deal with. And this is Bell's Inequality,

813
01:10:16,460 --> 01:10:24,940
and this is my favorite one. So Bell's Inequality
for many years languished in obscurity until

814
01:10:24,940 --> 01:10:28,960
someone realized that it could actually be
done beautifully in an experiment that led

815
01:10:28,960 --> 01:10:32,309
to a very concrete experiment that they could
actually do and that they wanted to do.

816
01:10:32,309 --> 01:10:39,460
And we now think of it as an enormously influential
idea which nails the coffin closed for classical

817
01:10:39,460 --> 01:10:46,110
mechanics. And it starts with a very simple
question. I claim that the following inequality

818
01:10:46,110 --> 01:10:54,720
is true: the number of undergraduate-- of
the number of people in the room who are undergraduates,

819
01:10:54,720 --> 01:11:00,350
which I'll denote as U-- and not blonde, which
I will denote as bar B-- so undergraduates

820
01:11:00,350 --> 01:11:04,840
who are not blonde-- actually let me write
this out in English. It's gonna be easier.

821
01:11:04,840 --> 01:11:18,530
Number who are undergrads and not blonde plus
the number of people in the room who are blonde

822
01:11:18,530 --> 01:11:27,970
but not from Massachusetts is strictly greater
than or equal to the number of people in the

823
01:11:27,980 --> 01:11:36,960
room who are undergraduates and not from Massachusetts.

824
01:11:36,960 --> 01:11:39,960
I claim that this is true. I haven't checked

825
01:11:39,960 --> 01:11:41,860
in this room. But I claim that this is true.

826
01:11:41,860 --> 01:11:47,860
So let's check. How many people are undergraduates
who are not blonde? OK this is going to--

827
01:11:47,860 --> 01:11:56,110
jeez. OK that's-- so, lots. OK. How many people
are blonde but not from Massachusetts? OK.

828
01:11:56,110 --> 01:12:01,860
A smattering. Oh God, this is actually going
to be terrible.

829
01:12:01,860 --> 01:12:11,860
AUDIENCE: [LAUGHTER]

830
01:12:11,870 --> 01:12:21,559
PROFESSOR: Shoot. This is a really large class.
OK. Small. And how many people are undergraduates

831
01:12:21,559 --> 01:12:25,520
who are not from Massachusetts? Yeah, this--
oh God. This counting is going to be-- so

832
01:12:25,520 --> 01:12:28,600
let's-- I'm going to do this just so I can
do the counting with the first two rows here.

833
01:12:28,600 --> 01:12:30,710
OK. My life is going to be easier this way.

834
01:12:30,710 --> 01:12:34,270
So how many people in the first two rows,
in the center section, are undergraduates

835
01:12:34,270 --> 01:12:40,550
but not blonde? One, two, three, four, five,
six, seven, eight, nine, ten, eleven, twelve,

836
01:12:40,550 --> 01:12:45,790
thirteen, fourteen. We could dispute some
of those, but we'll take it for the moment.

837
01:12:45,790 --> 01:12:52,110
So, fourteen. You're probably all undergraduates.
So blonde and not from Massachusetts. One.

838
01:12:52,110 --> 01:13:01,180
Awesome. Undergraduates not from Massachusetts.
One, two, three, four, five, six, seven, eight,

839
01:13:01,180 --> 01:13:07,460
nine, ten, eleven, twelve, thirteen, fourteen,
fifteen. Equality.

840
01:13:07,460 --> 01:13:09,030
AUDIENCE: [LAUGHTER]

841
01:13:09,030 --> 01:13:15,150
PROFESSOR: OK. So that-- you might say well,
look, you should have been nervous there.

842
01:13:15,150 --> 01:13:19,809
You know, and admittedly sometimes there's
experimental error. But I want to convince

843
01:13:19,809 --> 01:13:25,620
you that I should never, ever ever be nervous
about this moment in 8.04. And the reason is

844
01:13:25,620 --> 01:13:28,630
the following. I want to prove this for you.
And the way I'm gonna prove it is slightly

845
01:13:28,630 --> 01:13:33,000
more general, in more generality. And I want
to prove to you that the number-- if I have

846
01:13:33,000 --> 01:13:37,059
a set, or, sorry, if the number of people
who are undergraduates and not blonde which,

847
01:13:37,059 --> 01:13:43,250
all right, is b bar plus the number who are
blonde but not from Massachusetts is greater

848
01:13:43,250 --> 01:13:48,840
than or equal to the number that are undergraduates
and not from Massachusetts.

849
01:13:48,840 --> 01:13:54,040
So how do I prove this? Well if you're an
undergraduate and not blonde, you may or you

850
01:13:54,040 --> 01:13:58,540
may not be from Massachusetts. So this is
equal to the number of undergraduates who

851
01:13:58,540 --> 01:14:03,750
are not blonde and are from Massachusetts
plus the number of undergraduates who are

852
01:14:03,750 --> 01:14:09,920
not blonde and are not from Massachusetts.
It could hardly be otherwise. You either are

853
01:14:09,920 --> 01:14:15,690
or you are not from Massachusetts. Not the
sort of thing that you normally see in physics.

854
01:14:15,690 --> 01:14:19,460
So this is the number of people who are blonde
and not from Massachusetts, number of people

855
01:14:19,460 --> 01:14:23,570
who are blonde, who are-- so if you're blonde
and not from Massachusetts, you may or may

856
01:14:23,570 --> 01:14:27,300
not be an undergraduate. So this is the number
of people who are undergraduates, blonde,

857
01:14:27,300 --> 01:14:32,350
and not from Massachusetts plus the number
of people who are not undergraduates, are

858
01:14:32,350 --> 01:14:36,040
blonde and are not from Massachusetts.

859
01:14:36,040 --> 01:14:42,330
And on the right hand side-- so, adding these
two together gives us plus and plus. On the

860
01:14:42,330 --> 01:14:45,080
right hand side, the number of people that
are undergraduates and not from Massachusetts,

861
01:14:45,080 --> 01:14:49,720
well each one could be either blonde or not
blonde. So this is equal to the number that

862
01:14:49,720 --> 01:14:53,520
are undergraduates, blonde, and not from Massachusetts,

863
01:14:53,520 --> 01:14:56,740
plus-- remember that our undergraduates not

864
01:14:56,750 --> 01:15:00,440
blonde and not from Massachusetts. Agreed?

865
01:15:00,440 --> 01:15:05,460
I am now going to use the awesome power of--
and so this is what we want to prove, and

866
01:15:05,460 --> 01:15:12,150
I'm going to use the awesome power of subtraction.
And note that U, B, M bar, these guys cancel.

867
01:15:12,150 --> 01:15:19,380
And U, B bar, M bar, these guys cancel. And
we're left with the following proposition:

868
01:15:19,380 --> 01:15:23,750
the number of undergraduates who are not blonde
but are from Massachusetts plus the number

869
01:15:23,750 --> 01:15:27,809
of undergrad-- of non-undergraduates who are
blonde but not from Massachusetts must be

870
01:15:27,809 --> 01:15:31,570
greater than or equal to zero.

871
01:15:31,570 --> 01:15:37,800
Can you have a number of people in a room
satisfying some condition be less than zero?

872
01:15:37,800 --> 01:15:44,260
Can minus 3 of you be blonde undergraduates
not from Massachusetts? Not so much. This

873
01:15:44,260 --> 01:15:47,570
is a strictly positive number, because it's
a numerative. It's a counting problem. How

874
01:15:47,570 --> 01:15:53,230
many are undergraduates not blonde and from
Massachusetts. Yeah? Everyone cool with that?

875
01:15:53,230 --> 01:15:56,090
So it could hardly have been otherwise. It
had to work out like this.

876
01:15:56,090 --> 01:16:01,670
And here's the more general statement. The
more general statement is that the number

877
01:16:01,670 --> 01:16:06,410
of people, or the number of elements of any
set where each element in that set has binary

878
01:16:06,410 --> 01:16:12,780
properties a b and c-- a or not a, b or not
b, c or not c. Satisfies the following inequality.

879
01:16:12,780 --> 01:16:19,450
The number who are a but not b plus the number
who are b but not c is greater than or equal

880
01:16:19,450 --> 01:16:27,160
to the number who are a but not c. And this
is exactly the same argument.

881
01:16:27,160 --> 01:16:35,020
And this inequality which is a tautology,
really, is called Bell's Inequality. And it's

882
01:16:35,020 --> 01:16:43,190
obviously true. What did I use to derive this?
Logic and integers, right? I mean, that's

883
01:16:43,190 --> 01:16:46,520
bedrock stuff.

884
01:16:46,520 --> 01:16:53,390
Here's the problem. I didn't mention this
last time, but in fact electrons have a third

885
01:16:53,390 --> 01:16:58,830
property in addition to-- electrons have a
third property in addition to hardness and

886
01:16:58,830 --> 01:17:05,080
color. The third property is called whimsy,
and you can either be whimsical or not whimsical.

887
01:17:05,080 --> 01:17:08,270
And every electron, when measured, is either
whimsical or not whimsical. You never have

888
01:17:08,270 --> 01:17:14,580
a boring electron. You never have an ambiguous
electron. Always whimsical or not whimsical.

889
01:17:14,580 --> 01:17:20,800
So we have hardness, we have color, we have
whimsy. OK. And I can perform the following

890
01:17:20,800 --> 01:17:31,030
experiment. From a set of electrons, I can
measure the number that are hard and not black,

891
01:17:31,030 --> 01:17:40,960
plus the number that are black but not whimsical.
And I can measure the number that are hard

892
01:17:40,960 --> 01:17:45,520
and not whimsical. OK?

893
01:17:45,520 --> 01:17:50,460
And I want to just open up the case a little
bit and tell you that the hardness here really

894
01:17:50,460 --> 01:17:56,380
is the angular momentum of the electron along
the x-axis. Color is the angular momentum

895
01:17:56,380 --> 01:18:01,210
of the electron along the y-axis. And whimsy
is the angular momentum of the electron along

896
01:18:01,210 --> 01:18:05,830
the z-axis. These are things I can measure
because I can measure angular momentum.

897
01:18:05,830 --> 01:18:16,559
So I can perform this experiment with electrons
and it needn't be satisfied. In particular,

898
01:18:16,559 --> 01:18:24,080
we will show that the number of electrons,
just to be very precise, the number of electrons

899
01:18:24,080 --> 01:18:30,470
in a given set, which have positive angular
momentum along the x-axis and down along the

900
01:18:30,470 --> 01:18:38,520
y-axis, plus up along the y-axis and down
along the z-axis, is less than the number

901
01:18:38,520 --> 01:18:46,610
that are up. Actually let me do this in a
very particular way. Up... zero down at theta.

902
01:18:46,610 --> 01:18:53,790
Up at theta, down at-- two theta is greater
than the number that are up at zero and down at theta.

903
01:18:53,790 --> 01:18:59,130
Now here's the thing-- two theta. You can't
at the moment understand what this equation

904
01:18:59,130 --> 01:19:06,030
means. But if I just tell you that these are
three binary properties of the electron, OK,

905
01:19:06,030 --> 01:19:11,850
and that it violates this inequality, there
is something deeply troubling about this result.

906
01:19:11,850 --> 01:19:18,770
Bell's Inequality, which we proved-- trivially,
using integers, using logic-- is false in

907
01:19:18,770 --> 01:19:19,830
quantum mechanics.

908
01:19:19,830 --> 01:19:23,800
And it's not just false in quantum mechanics.
We will at the end of the course derive the

909
01:19:23,800 --> 01:19:27,460
quantum mechanical prediction for this result
and show that at least to a predicted violation

910
01:19:27,460 --> 01:19:33,870
of Bell's Inequality. This experiment has
been done, and the real world violates Bell's

911
01:19:33,870 --> 01:19:39,880
Inequality. Logic and integers and adding
probabilities, as we have done, is misguided.

912
01:19:39,880 --> 01:19:44,460
And our job, which we will begin with the
next lecture, is to find a better way to add

913
01:19:44,460 --> 01:19:49,980
probabilities than classically. And that will
be quantum mechanics See you on Tuesday.

914
01:19:49,980 --> 01:19:56,960
AUDIENCE: [APPLAUSE]