WEBVTT

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Prof: So this is a very
exciting day for me,

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because today,
we're going to start quantum

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mechanics and that's all we'll
do till the end of the term.

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Now I've got bad news and good
news.

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The bad news is that it's a
subject that's kind of hard to

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follow intuitively,
and the good news is that

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nobody can follow it
intuitively.

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Richard Feynman,
one of the big figures in

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physics, used to say,
"No one understands

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quantum mechanics."

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So in some sense,
the pressure is off for you

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guys, because I don't get it and
you don't get it and Feynman

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doesn't get it.

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The point is, here is my goal.

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Right now, I'm the only one who
doesn't understand quantum

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mechanics.

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In about seven days,
all of you will be unable to

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understand quantum mechanics.

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Then you can go back and spread
your ignorance everywhere else.

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That's the only legacy a
teacher can want.

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All right, so that's the spirit
in which we are doing this.

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I want you to think about this
as a real adventure.

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Try to think beyond the exams
and grades and everything.

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It's one of the biggest
discoveries in physics,

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in science, and it's marvelous
how people even figured out this

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is what's going on.

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So I want to tell you in some
fashion, but not strictly

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historical fashion.

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Purely historical fashion is
pedagogically not the best way,

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because you go through all the
wrong tracks and get confused,

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and there are a lot of battles
going on.

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When the dust settles down,
a certain picture emerges and

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that's the picture I wanted to
give you.

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In a way, I will appeal to
experiments that were perhaps

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not done in the sequence in
which I describe them,

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but we know that if you did
them, this is what the answer

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would be,
and everyone agrees,

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and they are the simplest
experiments.

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All right, so today we're going
to shoot down Newtonian

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mechanics and Maxwell's theory.

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So we are like the press.

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We build somebody up,
only to destroy them.

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Built up Newton;
shot down.

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Built up Maxwell;
going to get shot down.

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So again, I have tried to drill
into all of you the notion that

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people get shot down because
somebody else does a new

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experiment that probes an
entirely new regime which had

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not been seen before.

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So it's not that people were
dumb;

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it's that given the information
they had, they built the best

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theory that they could.

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And if you give me more
additional information,

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more refined measurements,
something to the tenth decimal

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place, I may have to change what
I do.

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That's how it's going to be.

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So there's always going to
be--for example,

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in the big collider,
people are expecting to see new

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stuff,
hopefully stuff that hasn't

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been explained by any existing
theory.

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And we all want that,
because we want some

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excitement, we want to find out
new things.

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The best way not to worry about
your old theories is to not do

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any experiments.

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Then you can go home.

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But that's not how it goes.

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You probe more and more stuff.

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So here's what you do to find
out what's wrong with

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electrodynamics,
I mean, with Maxwell's theory.

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It all starts with a double
slit experiment.

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You have this famous double
slit and some waves are coming

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from here.

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You have some wavelength l.

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Then in the back,
I'm going to put a photographic

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plate.

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A photographic plate,
as you know,

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is made of these tiny little
pixels which change color when

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light hits them and then you see
your picture.

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And that's the way to detect
light, a perfectly good way to

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detect light.

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So first thing we do is,
we block this hole or this

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slit.

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This is slit 1 and slit 2.

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We block this and we look at
what happened to the

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photographic plate.

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What you will find is that the
region in front of it got pretty

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dark,
or let's say had an image,

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whereas if you go too far from
the slit,

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you don't see anything.

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So that's called intensity,
when one is open.

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Then you close that guy and you
get similar pattern.

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Then you open both.

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Then I told you,
you may expect that,

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but what you get instead--let's
see, I've got to pick my graph

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properly-- is something that
looks like this.

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Now that is the phenomenon of
interference,

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which we studied last time.

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So what's the part that's funny?

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What's the part that makes you
wonder is if you go to some

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location like this,
go to a location like this.

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This used to be a bright
location when one slit was open.

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It was also a bright location,
reasonably bright,

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when the other slit was open.

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But when both are open,
it becomes dark.

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You can ask,
"How can it be that I open

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two windows, room gets darker?

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Why doesn't it happen there,
and why does it happen

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here?"

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The answer is that you're
sending light of definite

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wavelength and the wave
function,

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Y, whatever measures the
oscillation,

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maybe electric field,
magnetic field,

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obeys the superposition
principle.

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And when two slits are open,
what you're supposed to add is

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the electric field,
not the intensity.

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The intensity is proportional
to the square of the electric

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field.

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You don't add E^(2);
you add E.

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E is what obeys the wave
equation.

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E_1 is a
solution, E_2

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is a solution.

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E_1
E_2 is a

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solution.

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No one tells you that if you
add the two sources,

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I_1
I_2 is going to be

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the final answer.

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The correct answer is to find
E_1

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E_2 and then
square that.

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But when you do
E_1

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E_2,
since E_1 and

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E_2 are not
necessarily positive definite,

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when you add them,
sometimes they can add with the

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same sign,
sometimes they can add with

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opposite signs,
and sometimes in between,

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so you get this pattern.

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So we're not surprised.

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And I've told you many times
why we don't see it when we open

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big windows,
first of all,

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when you open a window,
the slit sizes are all many,

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many, many million times bigger
than the wavelength of light.

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Plus the light is not just one
color and so on.

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So you don't pick up these
oscillations.

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These oscillations are very
fine.

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I draw them this way so you can
see them.

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In a real life thing,
if this were really windows and

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this was the back wall of your
house,

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the oscillations would be so
tightly spaced,

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I'll just draw some of them,
that the human eye cannot

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detect these oscillations.

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It will only pick up the
average value.

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The average value will in fact
look like I_1

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I_2.

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So this is all very nice.

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This is how Young discovered
that light is a wave.

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By doing the interference,
I told you,

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he could even find a
wavelength, because it's a

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simple matter of geometry to see
where you've got to go for two

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guys to cancel.

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And once you know that angle,
you know where on that screen

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you will get a minimum or a
maximum.

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So you've got the wavelength.

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He didn't know what was doing
it.

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He didn't know it was
electromagnetic,

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but you can get the wavelength.

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So interference is a hallmark
of waves.

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Any wave will do interference.

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Water will do the same thing.

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For example,
this is your beach house.

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You've got some ocean front
property.

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This is a little lagoon and you
have a wall to keep the ocean

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waves out of your mansion.

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And then suddenly one day,
there is a break in the wall.

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Break in the wall,
the waves start coming in and

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you're having a little boat
here, trying to get some rest.

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The boat starts jumping up and
down because of the waves.

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So you have two options.

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One options is to go and try to
plug that thing,

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but let's say you've got no
bricks, no mortar,

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no time, no nothing.

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You've just got a sledgehammer.

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What you can do,
you can make another hole.

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If these water waves are a
definite wavelength,

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only in that case,
you can make another hole so

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these two add up to 0 where you
are.

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Similarly, if you don't like
the music your roommate's

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playing,
if you can manufacture the same

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music with a phase shift of p,
you can add them together,

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you get 0.

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But you've got to figure out
what the roommate's about to do

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and be synchronous with the
person,

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but get a wavelength of p--I
mean, a phase shift of p.

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So you can cancel waves.

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That's the idea behind all
kinds of noise cancelation,

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but you've got to know the
exact phase of the one signal

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that you're trying to cancel.

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All right, so everything looks
good for Maxwell,

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till you start doing the
following experiment.

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You make the source of light,
whatever it is,

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dimmer and dimmer,
okay?

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So you may not be able to turn
down the brightness.

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Maybe you can,
maybe you cannot,

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but you can imagine moving the
source further and further back.

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You move it further and further
back, you know the energy falls

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like 1/r^(2),
so you can make it weak.

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So here's what we try to do.

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We put a new photographic film.

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We take the light source way
back, then we wait for something

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to happen.

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We come the next morning,
we find there's a very faint

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pattern that's taken place over
night, because the film got

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exposed all through the night.

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Now we can see a faint pattern.

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Then you go and turn it down
even more.

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You come back the next day,
you look at the film.

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You find no pattern,
just two or three spots which

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have been exposed.

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If you look at the screen--so
let me show you a view of the

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screen.

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Normally you will have bright
and dark and bright and dark

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patterns on the back wall if you
turn on a powerful light.

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But I'm telling you,
if you have a really weak

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source, you just find that got
exposed, that got exposed and

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that got exposed,
that's it.

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Only three points on the film
are exposed, and that is very

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strange.

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Because if light is a wave,
no matter how weak it is,

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it should hit the entire
screen.

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It cannot hit certain parts of
it.

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Waves don't hit certain parts.

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In fact, how can it hit just
one?

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For example,
if you make it weak enough,

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you can have a situation where
in the whole day,

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you just get one hit.

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So something is hitting that
screen and it's not a wave,

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because a wave is spread out
over its full transverse

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dimension,
but this is hitting one point

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on the screen.

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So you make further
observations and you find out

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that what happens here is there
is a certain amount of momentum

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and energy are delivered during
that hit.

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If you could measure the recoil
of that film,

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you will find it gets hit and
the momentum you get per hit

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looks like ℏ x
k.

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I'll tell you what it means.

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This is 2p
h/l,

11:44.735 --> 11:48.025
where l is your
wavelength, h is the new

11:48.033 --> 11:50.653
constant called the Planck's
constant.

11:50.649 --> 11:59.989
And its value is 6.6 x 10^(-34
)joule seconds.

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You also find,
every time you get a hit here,

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there's a certain energy
deposited here and the energy

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deposited here happens to be
ℏw where

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w,
as you know,

12:12.345 --> 12:15.615
is 2pf.

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So here's what I'm telling you.

12:18.408 --> 12:23.808
If you send light of a known
frequency and known wavelength

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and you make it extremely dim,
and you put a photographic

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plate and you wait till
something happens,

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what happens is not a thin blur
over the whole screen.

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What happens is a hit at one
location.

12:38.259 --> 12:41.429
And what comes to that location
seems to be a bundle of energy

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and momentum,
i.e.

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a particle, right?

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When something hits you in the
face, it's got energy,

12:47.186 --> 12:48.246
it's got momentum.

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So this film is getting hit at
one point by a particle,

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and what we can say about the
particle is the following - it

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has a momentum.

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It has the same momentum every
time.

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You get this hit,
you get that hit,

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you get that hit.

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As long as you don't screw
around with the wavelength of

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incoming light,
the momentum and energy of each

13:08.734 --> 13:10.434
packet is identical.

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It's more than saying light
seems to be made of particles.

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Made of particles,
each one of them carries an

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energy and momentum that's
absolutely correlated with a

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wavelength and frequency.

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Now let me remind you that
w = kc for light

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waves.

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We've done this many,
many times.

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That means the energy,
which is

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ℏw,
and the momentum is

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ℏk,
are related by the relation

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E = pc.

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So these particles have a
momentum which is related to

13:50.687 --> 13:53.617
energy by the formula E =
pc.

13:53.620 --> 13:58.280
When you go back to your
relativity notes from the last

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semester, you'll find the
following relation is true.

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Any particle,
E^(2) = c^(2)p^(2)

14:06.724 --> 14:09.344
m^(2)c^(4).

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That's the connection between
energy and momentum.

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Therefore this looks like a
particle whose m is 0.

14:19.450 --> 14:23.420
If m is 0, E = pc.

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So these particles are massless.

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They have no rest mass and you
know, something with no rest

14:29.581 --> 14:32.931
mass, if it is to have a
momentum, it must travel at the

14:32.932 --> 14:34.092
speed of light.

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Because normally,
the momentum of anything with

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mass is mv,
in the old days,

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divided by this,
after Einstein.

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And if you don't want to have
an m, and yet you want to

14:48.428 --> 14:51.068
have a p,
the only way it can happen is

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that v = c.

14:52.360 --> 14:54.600
Then you have 0/0,
there is some chance,

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and nature seems to take
advantage of that 0/0.

14:57.408 --> 14:59.528
These are the massless
particles.

14:59.529 --> 15:06.579
So these photons are massless
particles.

15:06.580 --> 15:08.490
So what is the shock?

15:08.490 --> 15:12.400
The shock is that light,
which you thought was a

15:12.402 --> 15:16.312
continuous wave,
is actually made up of discrete

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particles.

15:17.480 --> 15:20.080
In order to see them,
your light source has to be

15:20.076 --> 15:22.916
extremely weak,
because if you turn on a light

15:22.923 --> 15:26.273
source like this one,
millions of these photons come

15:26.274 --> 15:29.024
and the pattern is formed
instantaneously.

15:29.019 --> 15:31.559
The minute you turn on the
light, the film is exposed,

15:31.558 --> 15:34.348
you see these dark and light
and dark and light fringes,

15:34.350 --> 15:37.530
you think it's happening due to
waves that come instantaneously.

15:37.529 --> 15:41.709
But if you look under the hood,
every pattern is formed by tiny

15:41.708 --> 15:45.618
little dots which occur so fast
that you don't see them.

15:45.620 --> 15:49.170
That's where you've got to turn
down the intensity to actually

15:49.168 --> 15:49.808
see them.

15:49.808 --> 15:56.088
When you see that,
you see the corpuscular nature

15:56.090 --> 15:57.530
of light.

15:57.529 --> 16:00.459
But here is the problem - if
somebody told you light is made

16:00.456 --> 16:02.436
of particles and it's not
continuous,

16:02.440 --> 16:05.550
it's not so disturbing,
because water,

16:05.548 --> 16:08.808
which you think is continuous,
is actually made of water

16:08.807 --> 16:09.517
molecules.

16:09.519 --> 16:12.329
Everything that you think of as
continuous is made up of little

16:12.331 --> 16:15.521
molecules and in a bigger scale,
much bigger than the atomic or

16:15.522 --> 16:18.902
molecular size,
it looks like it's continuous.

16:18.899 --> 16:21.319
That's not the bad news.

16:21.320 --> 16:28.120
The bad news really has to do
with the fact that if you have

16:28.120 --> 16:34.490
these particles called photons,
if it really were a particle,

16:34.490 --> 16:38.110
namely a standard,
garden variety particle,

16:38.110 --> 16:39.880
what should you find?

16:39.879 --> 16:44.259
If you emit a particle from
here, and only one slit is open,

16:44.259 --> 16:48.419
it will take some path going
through the slit and it will

16:48.416 --> 16:49.526
come there.

16:49.529 --> 16:54.089
So let us say on a given day,
10 photons will come here,

16:54.094 --> 16:59.244
or let's say 4 photons will
come here, with this one closed.

16:59.240 --> 17:02.550
Then let's close this one and
open this one.

17:02.548 --> 17:06.158
In that, case,
maybe 3 photons will come here.

17:06.160 --> 17:09.330
Or let's say again, 4.

17:09.328 --> 17:18.168
Now I'm claiming that when both
are open, I get no photons.

17:18.170 --> 17:22.060
How can it be that when you
open a second hole,

17:22.060 --> 17:25.360
you get fewer particles coming
there?

17:25.358 --> 17:32.338
Particles normally either take
path number 1 or path number 2.

17:32.339 --> 17:34.979
Either this slit or this slit.

17:34.980 --> 17:38.170
To all the guys going this way,
they don't care if this slit is

17:38.165 --> 17:39.035
open or closed.

17:39.038 --> 17:40.628
They don't even know about the
other slit.

17:40.630 --> 17:43.570
They do their thing,
and guys going through this

17:43.567 --> 17:46.877
slit should do their thing,
therefore you should get a

17:46.881 --> 17:49.571
number equal to the sum,
but you don't.

17:49.568 --> 17:51.378
In other words,
for particles,

17:51.384 --> 17:53.394
which have definite
trajectories,

17:53.388 --> 17:56.828
opening a second slit should
not affect the number going

17:56.834 --> 17:58.654
through the first slit.

17:58.650 --> 17:59.270
Do you understand that?

17:59.269 --> 18:01.069
Particles are local.

18:01.068 --> 18:03.838
They're moving along and they
feel the local forces acting on

18:03.836 --> 18:05.586
them and they bend or twist or
turn.

18:05.588 --> 18:07.828
They don't really care what's
happening far away,

18:07.830 --> 18:09.980
whether a second slit may be
open or closed.

18:09.980 --> 18:13.690
Therefore logically,
the number coming here must be

18:13.686 --> 18:18.356
the sum of the number that would
come with 1 open and 2 open.

18:18.358 --> 18:20.548
How can you cancel a positive
number of particles coming

18:20.550 --> 18:22.900
somewhere with more positive
number of particles coming from

18:22.902 --> 18:23.662
somewhere else?

18:23.660 --> 18:25.500
How do you get a 0?

18:25.500 --> 18:29.600
That is where the wave comes in.

18:29.598 --> 18:32.458
The wave has no trouble knowing
how many slits are open,

18:32.463 --> 18:34.343
because the wave is not
localized.

18:34.339 --> 18:36.049
The wave comes like this.

18:36.048 --> 18:39.438
It can hit both the slits and
certainly cares about how many

18:39.435 --> 18:40.465
slits there are.

18:40.470 --> 18:43.500
Because there's only one,
that wave will go.

18:43.500 --> 18:45.630
You'll have some amplitude
here, which is kind of

18:45.628 --> 18:46.248
featureless.

18:46.250 --> 18:47.750
If that's open,
it will be featureless.

18:47.750 --> 18:53.350
If both are open,
there'll be interference.

18:53.348 --> 18:59.398
So we need that wave to
understand what the photon will

18:59.396 --> 19:01.756
do,
because when you send millions

19:01.760 --> 19:04.580
of photons and if you get the
pattern like this--

19:04.578 --> 19:07.878
let's say you sent lots and
lots of photons and you got a

19:07.881 --> 19:09.061
pattern like this.

19:09.058 --> 19:14.038
Now I'm going to send million 1
photon.

19:14.039 --> 19:17.689
Where will it go?

19:17.690 --> 19:20.090
We do not know where it will go.

19:20.088 --> 19:24.478
We only know that if you repeat
the experiment a million times,

19:24.480 --> 19:26.110
you get this pattern.

19:26.108 --> 19:28.988
But on the million 1th attempt,
where it will go,

19:28.990 --> 19:29.950
we don't know.

19:29.950 --> 19:34.100
We just know that the odds are
high when the function is high,

19:34.098 --> 19:36.878
or the intensity,
and the odds are low when the

19:36.876 --> 19:40.616
function is small and the odds
are 0 when the function is 0.

19:40.618 --> 19:45.728
So the role of the wave is to
determine the probability that

19:45.734 --> 19:50.334
the photon will arrive at some
point on the screen.

19:50.328 --> 19:54.848
And the probability is computed
by adding one wave function to

19:54.854 --> 19:57.974
another wave function and then
squaring.

19:57.970 --> 19:58.950
So you've got to be very clear.

19:58.950 --> 20:02.520
If someone says to you,
"Is the photon a particle

20:02.520 --> 20:03.330
or a wave?

20:03.328 --> 20:06.438
Make up your mind,
what is it?"

20:06.440 --> 20:10.490
Well, the answer is,
it's not going to be a yes or

20:10.491 --> 20:11.651
no question.

20:11.650 --> 20:13.270
People always ask you,
"Is matter made of

20:13.267 --> 20:14.697
particles or waves,
electron particles or

20:14.703 --> 20:15.283
waves?"

20:15.278 --> 20:18.448
Well, sometimes the vocabulary
we have is not big enough to

20:18.448 --> 20:20.358
describe what's really
happening.

20:20.359 --> 20:22.299
It is what it is.

20:22.299 --> 20:23.769
It is the following.

20:23.769 --> 20:27.769
It is a particle in the sense
that the entire energy is

20:27.770 --> 20:31.550
carried in these localized
places, unlike a wave.

20:31.548 --> 20:35.408
When the wave hits the beach,
the energy's over the entire

20:35.409 --> 20:36.289
wave front.

20:36.288 --> 20:39.208
This wave here is not a
physical wave.

20:39.210 --> 20:43.000
It does not carry any energy
and it's not even a property of

20:42.996 --> 20:44.276
a beam of photons.

20:44.279 --> 20:46.999
It's a property of one photon.

20:47.000 --> 20:51.060
Here's what I want you to
understand - you send one photon

20:51.059 --> 20:54.189
at a time, many,
many times, and you get this

20:54.194 --> 20:55.054
pattern.

20:55.048 --> 20:59.218
Each time you throw the die and
ask where will the photon land,

20:59.217 --> 21:03.177
this function is waiting to
tell you the probability it will

21:03.182 --> 21:04.462
land somewhere.

21:04.460 --> 21:06.490
So we have to play this game in
two ways.

21:06.490 --> 21:09.810
It is particles,
but its future is determined by

21:09.805 --> 21:10.435
a wave.

21:10.440 --> 21:12.430
The wave is purely mathematical.

21:12.430 --> 21:15.330
You cannot put an instrument
that measures the energy due to

21:15.329 --> 21:15.919
that wave.

21:15.920 --> 21:20.270
It's a construct we use to
determine what will happen in

21:20.273 --> 21:21.703
this experiment.

21:21.700 --> 21:24.840
So we have no trouble
predicting this experiment,

21:24.843 --> 21:27.663
but we only make statistical
predictions.

21:27.660 --> 21:30.290
So if someone tells you,
"I got light from some

21:30.290 --> 21:33.330
mercury vapor or something,
it's got a certain wavelength,

21:33.325 --> 21:34.855
therefore a certain frequency.

21:34.858 --> 21:38.838
I'm going to take two slits and
I'm going to send the light from

21:38.838 --> 21:41.428
the left so weak that at a given
time,

21:41.430 --> 21:45.240
only one photon leaves the
source and hits the screen.

21:45.240 --> 21:47.100
What will happen?"

21:47.098 --> 21:49.538
We will say we don't know what
it will do.

21:49.538 --> 21:51.308
We don't know where it will
land.

21:51.308 --> 21:53.558
But we tell you if you do it
enough times,

21:53.555 --> 21:56.235
millions of times,
soon a pattern will develop.

21:56.240 --> 21:58.870
Namely, if you plot your
histogram on where everybody

21:58.865 --> 22:00.325
landed, you'll get a graph.

22:00.328 --> 22:02.978
It's the graph that I can
predict.

22:02.980 --> 22:04.500
And how do I predict that graph.

22:04.500 --> 22:09.070
I say, "What was the
energy momentum of your

22:09.070 --> 22:10.500
photon?"

22:10.500 --> 22:15.140
If it was p,
I will introduce a wave whose

22:15.141 --> 22:19.301
momentum is
2pℏ/p.

22:19.298 --> 22:20.968
Oh, I'm sorry,
I forgot to tell you guys one

22:20.969 --> 22:21.279
thing.

22:21.279 --> 22:21.979
I apologize.

22:21.980 --> 22:25.180
I've been writing
ℏ and h.

22:25.180 --> 22:28.940
I should have mentioned it long
back, ℏ is

22:28.935 --> 22:30.315
h/2p.

22:30.318 --> 22:32.728
Since the combination occurs so
often, people write

22:32.733 --> 22:33.703
ℏ.

22:33.700 --> 22:37.340
So you can write l =
2pℏ/p,

22:37.338 --> 22:38.378
or h/p.

22:38.380 --> 22:40.310
It doesn't matter.

22:40.309 --> 22:41.639
So I've stopped using h.

22:41.640 --> 22:44.750
Most people now in the business
use ℏ,

22:44.750 --> 22:47.510
because the energy is
ℏw,

22:47.509 --> 22:49.799
the momentum is
ℏk.

22:49.798 --> 22:51.858
If you want,
you can write this

22:51.857 --> 22:55.697
2phk and k
is 2p/l.

22:55.700 --> 22:57.820
Then you find p is
h/l.

22:57.818 --> 23:00.558
That's how some people used to
write it in the old days,

23:00.559 --> 23:03.799
but now we write it in terms of
ℏ and k.

23:03.798 --> 23:08.418
Anyway, I can make these
predictions, if I knew the

23:08.417 --> 23:10.817
momentum of the photons.

23:10.818 --> 23:12.728
The photons were of a definite
momentum, therefore there's a

23:12.728 --> 23:13.438
definite wavelength.

23:13.440 --> 23:19.000
I can predict the interference
pattern.

23:19.000 --> 23:22.340
So where is the photon when it
goes from start to finish?

23:22.339 --> 23:23.109
We don't know.

23:23.108 --> 23:25.218
I'll come back to that question
now.

23:25.220 --> 23:29.140
But I want to mention to you a
historical fact,

23:29.142 --> 23:33.242
which is, photons were not
really found this way,

23:33.236 --> 23:37.496
by looking at the recoil of an
emulsion plate.

23:37.500 --> 23:40.880
Just for completeness,
I'm going to make a five minute

23:40.878 --> 23:43.938
digression to tell you how
photons were found.

23:43.940 --> 23:46.160
So they were actually predicted
by Einstein.

23:46.160 --> 23:48.890
He got the Nobel Prize for
predicting the photon,

23:48.886 --> 23:52.066
rather than for the Theory of
Relativity, which was still

23:52.067 --> 23:53.827
controversial at that time.

23:53.828 --> 23:57.958
So he predicted the photons,
based on actually fairly

23:57.957 --> 24:02.717
complicated thermodynamic
statistical mechanics arguments.

24:02.720 --> 24:06.850
But one way to understand it is
in terms of what's called the

24:06.854 --> 24:08.444
photoelectric effect.

24:08.440 --> 24:12.380
If you take a metal and you say
"Where are the electrons in

24:12.375 --> 24:13.495
the metal?"

24:13.500 --> 24:17.470
As you know most electrons are
orbiting the parent nucleus.

24:17.470 --> 24:20.710
But in a metal,
some electrons are communal.

24:20.710 --> 24:24.430
Each atom donates one or two
electrons to the whole metal.

24:24.430 --> 24:26.700
They can run all over the metal.

24:26.700 --> 24:29.400
They don't have to be near
their parent nucleus.

24:29.400 --> 24:31.370
They cannot leave the metal.

24:31.369 --> 24:33.449
So in a way, they are like this.

24:33.450 --> 24:36.730
There's a little tank whose
depth is h,

24:36.734 --> 24:40.464
and let's say mgh I want
to call W.

24:40.460 --> 24:44.070
So these guys are somewhere in
the bottom.

24:44.069 --> 24:48.569
They can run around;
they cannot get out.

24:48.568 --> 24:51.998
So if you want to yank an
electron out of the metal,

24:51.998 --> 24:54.948
you have to give an energy
equal to W,

24:54.954 --> 24:57.514
which is called the work
function.

24:57.509 --> 25:00.739
So how are you going to get an
electron to acquire some energy?

25:00.740 --> 25:01.480
We all know.

25:01.480 --> 25:03.610
Electron is an electric charge.

25:03.608 --> 25:06.388
I have to apply an electric
field and I know electromagnetic

25:06.386 --> 25:08.926
waves are nothing but electric
and magnetic fields,

25:08.930 --> 25:11.960
so I shine a light,
a source of light,

25:11.960 --> 25:13.530
towards this.

25:13.528 --> 25:16.278
The electric field comes and
grabs the electron and shakes it

25:16.281 --> 25:16.651
loose.

25:16.650 --> 25:19.810
Hopefully it will shake it
loose from the metal,

25:19.808 --> 25:22.228
giving it enough energy to
escape.

25:22.230 --> 25:26.650
And once it escapes,
it can take off.

25:26.650 --> 25:30.610
So they took some light source
and they aimed it at the metal,

25:30.607 --> 25:32.617
to see if electrons come out.

25:32.619 --> 25:35.039
They didn't.

25:35.038 --> 25:41.488
So what do you think you will
do to get some action?

25:41.490 --> 25:42.010
Yes?

25:42.009 --> 25:44.579
Student:
>

25:44.578 --> 25:46.268
Prof: So you make it
brighter.

25:46.269 --> 25:47.659
You say, "Okay,
let me crank up--"

25:47.657 --> 25:48.657
that's what anybody would do.

25:48.660 --> 25:51.500
They cranked up the intensity
of light, make it brighter and

25:51.496 --> 25:52.646
brighter and brighter.

25:52.650 --> 25:55.810
Nothing happened.

25:55.808 --> 25:59.668
Then by accident they found out
that instead of cranking up the

25:59.669 --> 26:03.309
brightness of the light,
if you cranked up the frequency

26:03.305 --> 26:06.575
of light,
slowly, suddenly beyond some

26:06.576 --> 26:09.716
frequency,
you start getting electrons

26:09.724 --> 26:11.244
escaping the metal.

26:11.240 --> 26:16.820
So here's the graph you get.

26:16.818 --> 26:19.878
Let me just plot it if you
like, ℏ times

26:19.884 --> 26:20.724
the w.

26:20.720 --> 26:22.880
In those days,
they didn't know too much about

26:22.880 --> 26:23.840
ℏ.

26:23.839 --> 26:24.799
You can even plot w.

26:24.799 --> 26:26.119
It doesn't matter.

26:26.118 --> 26:31.218
And you plot here the kinetic
energy of the emitted electron.

26:31.220 --> 26:35.290
And what you find is that below
some minimum value,

26:35.287 --> 26:37.237
no electrons come out.

26:37.240 --> 26:39.640
There's nothing to plot.

26:39.640 --> 26:44.570
And once you cross a magical
w, and anything higher

26:44.567 --> 26:48.977
than that, you get a kinetic
energy that's linear in

26:48.976 --> 26:50.096
w.

26:50.098 --> 26:59.268
Now the kinetic energy is the
energy you gave to the electron

26:59.270 --> 27:01.870
minus W.

27:01.868 --> 27:05.248
Energy given to the electron -
W, because you paid

27:05.250 --> 27:08.750
W to get it out of the
well, and whatever is left is

27:08.750 --> 27:10.140
the kinetic energy.

27:10.140 --> 27:13.480
So Einstein predicted photons
from independent arguments,

27:13.480 --> 27:16.050
and according to him,
light and frequency w is

27:16.051 --> 27:19.301
made up of particles,
each of which contains energy

27:19.295 --> 27:21.205
ℏw.

27:21.210 --> 27:23.820
So you can see what's happening.

27:23.818 --> 27:27.738
If you've got low frequency
light, you're sending millions

27:27.738 --> 27:31.308
of photons, each carries an
energy ℏw

27:31.313 --> 27:32.623
somewhere here.

27:32.618 --> 27:35.558
None of them has the energy to
lift the electron out of the

27:35.563 --> 27:35.973
metal.

27:35.970 --> 27:40.600
It's like sending a million
little kids to lift something

27:40.596 --> 27:42.576
and they cannot do it.

27:42.578 --> 27:46.238
They cannot do it,
but if you send 10 tall,

27:46.238 --> 27:49.808
powerful people,
they will lift it out.

27:49.808 --> 27:53.098
So what's happening with light
is that as you crank up the

27:53.096 --> 27:55.226
w,
even if it's not very bright,

27:55.227 --> 27:57.947
the individual packets are
carrying more and more energy

27:57.952 --> 28:01.162
and more and more momentum,
and that's why they succeed in

28:01.157 --> 28:02.657
knocking the electron out.

28:02.660 --> 28:04.860
And in fact,
if you set the energy of each

28:04.862 --> 28:06.842
photon,
it's ℏw,

28:06.836 --> 28:09.656
then the kinetic energy of the
electron is the energy you gave

28:09.664 --> 28:11.604
with 1 photon,
take away the W,

28:11.602 --> 28:13.762
that's the price you pay to
leave the metal.

28:13.759 --> 28:16.239
The rest of it is kinetic
energy.

28:16.240 --> 28:19.320
So when plotted as a function
of w, K should

28:19.319 --> 28:22.129
look like a straight line with
intercept W.

28:22.130 --> 28:23.920
And that's what you find.

28:23.920 --> 28:27.700
In fact, this is one way to
measure the work function.

28:27.700 --> 28:30.800
How much energy do we need to
rip an electron out of a metal

28:30.800 --> 28:32.010
depends on the metal.

28:32.009 --> 28:34.489
And you shine light and you
crank up the frequency,

28:34.490 --> 28:35.730
till something happens.

28:35.730 --> 28:39.100
And just to be sure,
you go a little beyond that and

28:39.096 --> 28:42.726
you find that the kinetic energy
grows linearly in w.

28:42.730 --> 28:46.170
Anyway, this is how one
confirmed the existence,

28:46.165 --> 28:48.575
indirect existence,
of photons.

28:48.578 --> 28:52.378
There's another experiment that
also confirmed the existence of

28:52.376 --> 28:52.986
photons.

28:52.990 --> 28:53.840
Look, that's the beauty.

28:53.838 --> 28:58.508
Once you've got the right
answer, everything is going to

28:58.510 --> 29:00.040
be on your side.

29:00.038 --> 29:02.318
Before I forget,
I should mention to you,

29:02.316 --> 29:05.446
you've probably heard that
Einstein is very unhappy with

29:05.446 --> 29:06.696
quantum mechanics.

29:06.700 --> 29:09.420
And yet if you look at the
history, he made enormous

29:09.417 --> 29:11.387
contributions to quantum
mechanics.

29:11.390 --> 29:14.990
Even Planck didn't have the
courage to stand behind the

29:14.992 --> 29:18.132
photons that were implied in his
own formula.

29:18.130 --> 29:21.600
Einstein took it to be very
real and pursued it.

29:21.598 --> 29:23.428
So when you say he doesn't like
quantum mechanics,

29:23.432 --> 29:25.232
it's not that he couldn't do
the problem sets.

29:25.230 --> 29:28.230
It's that he had problems with
the problems.

29:28.230 --> 29:31.460
He did not like the
probabilistic nature of quantum

29:31.457 --> 29:35.457
mechanics, but he had no trouble
divining what was going on.

29:35.460 --> 29:36.520
So it's quite different.

29:36.519 --> 29:38.999
It's like saying,
"I don't like that

29:39.002 --> 29:39.812
joke."

29:39.809 --> 29:40.459
There are two reasons.

29:40.460 --> 29:42.920
Some guys don't get it and they
don't like it.

29:42.920 --> 29:45.130
Some guys get it and don't
think it's funny.

29:45.130 --> 29:47.630
So this was like Einstein
certainly understood all the

29:47.631 --> 29:49.331
complexities of quantum
mechanics.

29:49.328 --> 29:51.218
He said he had spent more time
on quantum,

29:51.220 --> 29:55.120
much more on either the special
or the general theory of

29:55.116 --> 29:57.406
relativity,
because he said that was a real

29:57.412 --> 29:57.792
problem.

29:57.788 --> 30:00.288
That's a problem I couldn't
track.

30:00.288 --> 30:03.938
Now it turns out that even till
the end, he didn't find an

30:03.942 --> 30:06.382
answer that was satisfactory to
him.

30:06.380 --> 30:08.320
The answer I'm giving you
certainly works,

30:08.317 --> 30:10.917
makes all the predictions,
never said anything wrong.

30:10.920 --> 30:15.090
Until something better comes to
replace it, we will keep using

30:15.087 --> 30:15.427
it.

30:15.430 --> 30:18.550
Anyway, going back,
the second experiment that

30:18.550 --> 30:20.980
confirmed the reality of
photons.

30:20.980 --> 30:24.060
See, if you say light is made
of particles and each one has an

30:24.063 --> 30:26.343
energy and momentum,
do you understand why the

30:26.337 --> 30:28.357
photoelectric effect is a good
test.

30:28.359 --> 30:30.339
It agrees with that picture.

30:30.339 --> 30:31.809
Individual particles come.

30:31.808 --> 30:34.928
Some have the energy to
liberate the electron and some

30:34.929 --> 30:35.399
don't.

30:35.400 --> 30:37.510
And if individually,
they cannot do it,

30:37.509 --> 30:39.619
it doesn't matter how many you
send.

30:39.618 --> 30:43.108
Now you may have thought of one
scenario in which all of these

30:43.107 --> 30:46.027
tiny little kids can get
something lifted out of the

30:46.025 --> 30:46.535
well.

30:46.539 --> 30:51.749
How will they do that?

30:51.750 --> 30:55.250
Maybe 10 kids together,
like ants, can lift the thing

30:55.246 --> 30:55.646
out.

30:55.650 --> 30:59.330
So if you had 10 photons which
can collectively excite the

30:59.334 --> 31:01.054
electron,
it can happen,

31:01.049 --> 31:04.279
but in those days,
they didn't have a light whose

31:04.276 --> 31:08.036
intensity was enough to send
enough of these photons.

31:08.038 --> 31:10.188
But nowadays,
it turns out that if you

31:10.193 --> 31:13.113
really, really crank up the
intensity, you can make

31:13.105 --> 31:15.955
electrons come out,
even below the frequency.

31:15.960 --> 31:19.120
That's because more than one
photon is involved in ejecting

31:19.122 --> 31:19.942
the electron.

31:19.940 --> 31:22.690
So luckily, we didn't have that
intensity then,

31:22.693 --> 31:25.333
so we go the picture of the
photons right.

31:25.328 --> 31:29.808
Anyway, Compton said the
following thing - it turns out

31:29.807 --> 31:34.367
that if you have an electron
here and you send a beam of

31:34.366 --> 31:37.246
light,
it scatters off the electron

31:37.248 --> 31:41.468
and comes off in some direction
at an angle q to the original

31:41.465 --> 31:42.375
direction.

31:42.380 --> 31:48.150
The wavelength here changes by
an amount Dl,

31:48.154 --> 31:53.354
and Dl happens to be
2pℏ

31:53.351 --> 31:58.781
/mc x 1 - cosine
q.

31:58.779 --> 31:59.809
Are you with me?

31:59.808 --> 32:03.238
You send light in at a known
wavelength.

32:03.240 --> 32:06.080
It scatters off the electron
and comes at an angle q,

32:06.076 --> 32:09.016
no longer preserving its
wavelength, having a different

32:09.020 --> 32:09.840
wavelength.

32:09.838 --> 32:13.198
And the shift in the wavelength
is connected to the angle of

32:13.199 --> 32:13.939
scattering.

32:13.940 --> 32:16.340
For example,
if q is 0, Dl is 0 in the

32:16.335 --> 32:17.625
forward direction.

32:17.630 --> 32:20.680
If it bounces right back,
that cos q is -1.

32:20.680 --> 32:23.980
That number is 2 and you get a
huge Dl.

32:23.980 --> 32:29.210
And you can find the l of it by
putting a diffraction grating.

32:29.210 --> 32:35.020
Now, what one could show is
that if you took this to be made

32:35.015 --> 32:37.865
of particles,
and each particle has an

32:37.865 --> 32:40.785
energy, ℏw,
and each particle has a

32:40.788 --> 32:44.408
momentum, ℏk,
and that that collides with an

32:44.405 --> 32:46.905
electron,
then you just balance energy

32:46.906 --> 32:49.556
conservation and momentum
conservation.

32:49.558 --> 32:52.148
In any collision,
energy and momentum before =

32:52.148 --> 32:53.758
energy and momentum after.

32:53.759 --> 32:55.789
You set them equal and you
fiddle around,

32:55.790 --> 32:58.280
you can find the new momentum
after scattering.

32:58.279 --> 33:00.549
From the new momentum,
you can extract the new

33:00.547 --> 33:03.517
wavelength and you will find
this formula actually works.

33:03.519 --> 33:07.399
So I did that in Physics 200,
I think, so if you want,

33:07.404 --> 33:11.514
you can go look at that,
or maybe it was done for you.

33:11.509 --> 33:11.999
I don't know.

33:12.000 --> 33:15.540
But Compton's scattering,
the scattering due to Compton,

33:15.538 --> 33:19.308
can be completely understood if
you think of the incoming beam

33:19.310 --> 33:22.960
of light as made up of particles
with that momentum and that

33:22.959 --> 33:23.639
energy.

33:23.640 --> 33:26.310
In other words,
you're always going to go back

33:26.307 --> 33:27.017
and forth.

33:27.019 --> 33:30.579
Light will be characterized by
a wavelength and by a momentum.

33:30.578 --> 33:34.368
It will be characterized by a
frequency and by an energy.

33:34.368 --> 33:36.638
When you think about the
particles, you'll think of the

33:36.635 --> 33:37.555
energy and momentum.

33:37.558 --> 33:41.838
When you think about the waves,
you'll think of frequency and

33:41.840 --> 33:42.840
wave number.

33:42.838 --> 33:45.188
So this is what really nailed
it.

33:45.190 --> 33:51.000
After this, you could not doubt
the reality of the photons.

33:51.000 --> 33:55.830
Okay, now I go back to my old
story.

33:55.829 --> 33:57.419
Let's remember what it is.

33:57.420 --> 34:00.890
The shock is that light,
which we were willing to

34:00.891 --> 34:03.531
believe was waves,
because Young had done the

34:03.528 --> 34:06.578
interference experiment,
is actually made up of

34:06.576 --> 34:07.536
particles.

34:07.539 --> 34:08.839
That's the first thing.

34:08.840 --> 34:10.550
So who needs the wave?

34:10.550 --> 34:13.000
If you send a single photon
into a double slit,

34:13.003 --> 34:14.713
we don't know what it will do.

34:14.710 --> 34:17.050
We can only give the odds.

34:17.050 --> 34:20.230
To find the odds,
we take the photon's wavelength

34:20.233 --> 34:23.023
and we form this wave,
and then we form the

34:23.021 --> 34:24.681
interference pattern.

34:24.679 --> 34:28.389
And we find out that whenever
it is high, it is very likely to

34:28.393 --> 34:28.823
come.

34:28.820 --> 34:31.090
Wherever it's low,
it's very unlikely,

34:31.085 --> 34:32.675
but at 0, it won't come.

34:32.679 --> 34:35.179
So to test this theory,
it's not enough to send 1

34:35.181 --> 34:35.651
photon.

34:35.650 --> 34:39.260
1 photon may come here;
that doesn't show you anything.

34:39.260 --> 34:42.290
You've got to send millions of
photons, because if a prediction

34:42.293 --> 34:44.493
is probabilistic,
to test it, you've got to do

34:44.494 --> 34:45.234
many times.

34:45.230 --> 34:47.770
If I give you a coin,
and I tell you it's a fair

34:47.768 --> 34:50.738
coin, I toss it a couple of
times and I get 1 head and 1

34:50.739 --> 34:52.629
tail, it doesn't mean anything.

34:52.630 --> 34:55.220
You want to toss it 500,000
times and see if roughly half

34:55.219 --> 34:57.579
the time it's heads and half the
time it's tails.

34:57.579 --> 35:00.119
That's when a probabilistic
theory is verified.

35:00.119 --> 35:02.979
It's not verified by
individuals.

35:02.980 --> 35:06.440
Insurance companies are always
drawing pictures of when I'm

35:06.436 --> 35:07.326
going to die.

35:07.329 --> 35:12.089
They've got some plot,
and that's my average chance.

35:12.090 --> 35:15.120
I don't know when I will be
part of that statistic,

35:15.123 --> 35:18.343
because in fact--sorry,
it usually looks like this.

35:18.340 --> 35:22.010
Life expectancy of people looks
like that, but doesn't mean

35:22.007 --> 35:23.777
everybody dies at one day.

35:23.780 --> 35:27.370
People are dying left and
right, so there's probability on

35:27.367 --> 35:28.247
either side.

35:28.250 --> 35:31.440
So to verify this table that
companies have got,

35:31.440 --> 35:34.020
you have to watch a huge
population.

35:34.018 --> 35:36.758
Then you can do the histogram
and then you get the profile.

35:36.760 --> 35:40.470
So whenever you do statistical
theories, you've got to run it

35:40.474 --> 35:41.284
many times.

35:41.280 --> 35:43.350
I'll tell you more about
statistics and quantum

35:43.349 --> 35:43.889
mechanics.

35:43.889 --> 35:46.529
It's different from statistics
and classical mechanics and

35:46.529 --> 35:47.779
we'll come to that later.

35:47.780 --> 35:50.200
But for now,
you must understand the

35:50.197 --> 35:52.337
peculiar behavior of photons.

35:52.340 --> 35:55.130
They are not particles
entirely, they are not waves

35:55.126 --> 35:55.736
entirely.

35:55.739 --> 35:59.099
They are particles in the sense
they're localized energy and

35:59.099 --> 36:02.459
momentum, but they don't travel
like Newtonian particles.

36:02.460 --> 36:04.760
If they were Newtonian
particles, you'll never

36:04.755 --> 36:07.965
understand why opening a second
slit reduced the amount of light

36:07.967 --> 36:09.037
coming somewhere.

36:09.039 --> 36:10.899
All right, so this is the story.

36:10.900 --> 36:15.160
So now comes the French
physicist,

36:15.159 --> 36:19.589
de Broglie, and he argued as
follows - you'll find his

36:19.592 --> 36:24.352
argument quite persuasive,
and this is what he did for his

36:24.353 --> 36:24.733
PhD.

36:24.730 --> 36:29.590
He said, "If light,
which I thought was a

36:29.585 --> 36:32.325
particle--
I'm sorry, which I thought was

36:32.333 --> 36:34.063
a wave,
is actually made up of

36:34.056 --> 36:37.156
particles, perhaps things which
I always thought of as

36:37.159 --> 36:39.279
particles,
like electrons,

36:39.282 --> 36:42.762
have a wave associated with
them."

36:42.760 --> 36:45.310
And he said,
"Let me postulate that

36:45.309 --> 36:48.899
electrons also have a wave
associated with them and that

36:48.904 --> 36:52.964
the wavelength associated with
an electron of momentum p

36:52.956 --> 36:56.286
will be 2pℏ
/p;

36:56.289 --> 37:01.159
and that this wave will produce
the same interference pattern

37:01.159 --> 37:06.109
when you do it with electrons,
as you did with light."

37:06.110 --> 37:07.500
So what does that mean?

37:07.500 --> 37:11.240
It means if you did a double
slit experiment,

37:11.239 --> 37:13.809
and you sent electrons of
momentum p,

37:13.809 --> 37:16.069
one at a time,
and you sit here with an

37:16.070 --> 37:20.090
electron detector,
or you have an array of

37:20.085 --> 37:25.415
electron detectors,
he claims that the pattern will

37:25.418 --> 37:29.368
look like this,
where this pattern is obtained

37:29.373 --> 37:34.283
by using a certain wavelength
that corresponds to the momentum

37:34.282 --> 37:37.262
of the incoming beam of
electrons.

37:37.260 --> 37:40.520
Now there the shock is not that
the electron hits one point on

37:40.516 --> 37:41.206
the screen.

37:41.210 --> 37:43.390
It supposed to;
it's a particle.

37:43.389 --> 37:46.269
What is shocking is that when
two slits are open,

37:46.268 --> 37:49.868
you don't get any electrons in
the location where you used to

37:49.869 --> 37:50.949
get electrons.

37:50.949 --> 37:54.229
That is the surprising thing,
because if an electron is a

37:54.226 --> 37:58.086
Newtonian particle and you used
to go like that through hole 1,

37:58.090 --> 38:00.390
and you used to go like that
through hole 2,

38:00.389 --> 38:02.149
if you open the two holes and
two slits,

38:02.150 --> 38:06.290
you've got to get the sum of
the two numbers.

38:06.289 --> 38:10.169
You cannot escape that,
because in Newtonian mechanics,

38:10.170 --> 38:14.410
an electron either goes through
slit 1 or through slit 2.

38:14.409 --> 38:16.319
And therefore,
the number coming here is

38:16.320 --> 38:19.260
simply the sum of the ones that
went here, the ones that went

38:19.259 --> 38:19.699
here.

38:19.699 --> 38:22.219
Now sometimes people think,
"Well,

38:22.219 --> 38:24.769
if you have a lot of electrons
coming here,

38:24.768 --> 38:28.438
maybe these guys bumped into
these guys and collided and

38:28.443 --> 38:32.053
therefore didn't hit the screen
at that point."

38:32.050 --> 38:33.370
That's a fake.

38:33.369 --> 38:35.409
You know you don't have much of
a chance with that explanation,

38:35.409 --> 38:37.109
because if there are random
collisions,

38:37.110 --> 38:39.010
what are the odds they'll form
this beautiful,

38:39.010 --> 38:40.540
repeatable pattern?

38:40.539 --> 38:42.199
Not very big.

38:42.199 --> 38:44.719
Furthermore,
you can silence that criticism

38:44.719 --> 38:48.379
by making the electron gun that
emits electrons so feeble that

38:48.380 --> 38:51.310
at a given time,
there's only one electron.

38:51.309 --> 38:53.339
There's only one electron in
the lab.

38:53.340 --> 38:55.710
It left here,
then it arrived there.

38:55.710 --> 38:57.810
And it cannot collide with
itself.

38:57.809 --> 39:02.599
And yet it knows two slits are
open.

39:02.599 --> 39:07.149
A Newtonian particle cannot
know that two slits are open.

39:07.150 --> 39:11.730
So it has an associated wave,
and if you do this calculation

39:11.733 --> 39:16.323
and you find the interference
pattern, that's what electrons

39:16.315 --> 39:16.855
do.

39:16.860 --> 39:18.980
Originally, it was not done
with a double slit.

39:18.980 --> 39:20.210
It was done with a crystal.

39:20.210 --> 39:23.860
I have given you one homework
problem where you can see how a

39:23.858 --> 39:27.318
crystal of atoms regularly
arranged can also help you find

39:27.324 --> 39:29.214
the wavelength of anything.

39:29.210 --> 39:31.940
And you shine a beam of
electrons on a crystal,

39:31.940 --> 39:35.280
you find out that they come out
in only one particular angle,

39:35.280 --> 39:37.060
and using the angle,
you can find the wavelength,

39:37.059 --> 39:39.559
and the wavelength agrees with
the momentum.

39:39.559 --> 39:40.799
The momentum of the electron is
known,

39:40.800 --> 39:44.490
because if you accelerate them
between two plates with a

39:44.492 --> 39:47.422
certain voltage,
V, and the electron

39:47.420 --> 39:50.880
drops down the voltage,
it gains an energy eV,

39:53.070 --> 39:56.030
which you can also write as
p^(2)/2m.

39:56.030 --> 40:00.990
So you can find the momentum of
an electron before you send it

40:00.992 --> 40:01.402
in.

40:01.400 --> 40:07.730
Okay, so this is the
peculiarity of particles now.

40:07.730 --> 40:13.290
Electron also behaves like a
particle or a wave.

40:13.289 --> 40:19.389
So now you can ask yourself the
following question.

40:19.389 --> 40:22.359
Why is it that microscopic
bodies--first of all,

40:22.360 --> 40:25.330
I hope you understand how
surprising this is.

40:25.329 --> 40:26.589
Suppose it was not electrons.

40:26.590 --> 40:29.480
Suppose this was not an
electron gun,

40:29.481 --> 40:31.571
but a machine gun,
okay?

40:31.570 --> 40:34.180
And these are some concrete
barriers.

40:34.179 --> 40:38.479
The barrier has a hole in it
and that's you.

40:38.480 --> 40:42.380
They've tied you to the back
wall and they're firing bullets

40:42.378 --> 40:44.438
at you,
and you're of course very

40:44.438 --> 40:47.458
anxious when a friend of yours
comes along and says,

40:47.460 --> 40:49.390
"I want to help you."

40:49.389 --> 40:54.699
So let me do that.

40:54.699 --> 40:57.749
So you know that that's not a
friend, and if you do it with

40:57.753 --> 40:59.073
bullets, it won't help.

40:59.070 --> 41:00.320
You cannot reduce the number of
bullets.

41:00.320 --> 41:03.040
And why is it with
electrons--if instead of the big

41:03.036 --> 41:05.126
scenario,
we scale the whole thing down

41:05.134 --> 41:07.494
to atomic dimensions,
and you're talking about

41:07.494 --> 41:10.284
electrons and slits which are a
few micrometers away,

41:10.280 --> 41:13.590
why is it that with electrons,
you can do that?

41:13.590 --> 41:16.250
Why is it with bullets you
don't do that?

41:16.250 --> 41:21.940
The answer has to do with this
wavelength p.

41:21.940 --> 41:26.200
If you put for p,
m x v and you put

41:26.202 --> 41:30.312
for m the mass of a
cannonball or a bullet,

41:30.309 --> 41:35.169
say 1 kilogram,
you will find this wavelength

41:35.168 --> 41:37.818
is 10^(-27 )something.

41:37.820 --> 41:43.050
That means these oscillations
will have maybe 10^(20

41:43.054 --> 41:49.014
)oscillations per centimeter and
you cannot detect that.

41:49.010 --> 41:51.470
So oscillation,
the human eye cannot detect

41:51.474 --> 41:54.884
that, and everything else looks
like you're just adding the

41:54.878 --> 41:57.578
intensities, not adding the wave
function.

41:57.579 --> 42:00.989
It looks like the probabilities
are additive,

42:00.985 --> 42:04.465
and you don't see the
interference pattern.

42:04.469 --> 42:07.959
Now there's another very
interesting twist on this

42:07.963 --> 42:10.393
experiment, which is as follows.

42:10.389 --> 42:12.889
You go back to that experiment,
and you say,

42:12.885 --> 42:16.425
"Look, I do not buy this
notion that an electron does not

42:16.425 --> 42:17.815
go through one slit.

42:17.820 --> 42:18.750
I mean, come on.

42:18.750 --> 42:22.000
How can it not go through one
particular slit?"

42:22.000 --> 42:23.800
So here's what I'm going to do.

42:23.800 --> 42:28.610
I'm going to put a light bulb
here.

42:28.610 --> 42:31.410
I'm going to have the light
bulb look at the slit,

42:31.409 --> 42:35.319
and when this guy goes past,
I will see whether the guy went

42:35.315 --> 42:38.025
through this slit or through
that slit.

42:38.030 --> 42:40.290
Then there's no talk about
going through both slits or not

42:40.289 --> 42:42.709
going through a definite slit or
not having the trajectory.

42:42.710 --> 42:45.180
All that's wrong,
because I'm going to actually

42:45.179 --> 42:48.509
catch the electron in the act of
going through one or the other

42:48.509 --> 42:50.119
by putting a light source.

42:50.119 --> 42:52.219
So you put a light source,
and whenever it hits an

42:52.217 --> 42:54.867
electron, you will see a flash
and you will know whether it was

42:54.869 --> 42:56.239
near this hole or that hole.

42:56.239 --> 42:58.479
You make a tally.

42:58.480 --> 43:01.430
So you find that a certain
number went through hole 1,

43:01.434 --> 43:03.614
a certain number went through
hole 2.

43:03.610 --> 43:05.590
You add them up,
you get the number,

43:05.590 --> 43:07.740
you cannot avoid getting the
number.

43:07.739 --> 43:12.769
Let's imagine that of our 1,000
electrons, about 20 got by

43:12.768 --> 43:15.148
without your seeing them.

43:15.150 --> 43:15.860
It can happen.

43:15.860 --> 43:17.490
When you turn the light,
you don't see it;

43:17.489 --> 43:19.819
it misses.

43:19.820 --> 43:24.400
Then you will find a pattern
that looks like this.

43:24.400 --> 43:29.900
There'll be a 2 percent wiggle
on top of this featureless

43:29.902 --> 43:30.692
curve.

43:30.690 --> 43:33.220
In other words,
the electrons that you caught

43:33.219 --> 43:36.209
and identified as going through
slit 1 or slit 2,

43:36.210 --> 43:39.830
their numbers add up the way
they do in Newtonian mechanics,

43:39.829 --> 43:42.119
but the electrons you did not
catch,

43:42.119 --> 43:45.049
who slipped by,
pretend as if they went through

43:45.045 --> 43:48.525
both the slits,
or at least they showed the

43:48.525 --> 43:50.425
interference pattern.

43:50.429 --> 43:53.059
That's a very novel thing,
that whether you see the

43:53.063 --> 43:55.333
electron or not,
makes such a difference.

43:55.329 --> 43:56.429
That's all I did.

43:56.429 --> 43:58.759
In one case,
I caught the electron.

43:58.760 --> 44:00.120
In the other case, I slipped by.

44:00.119 --> 44:04.759
And whenever it's not observed,
it seems to be able to somehow

44:04.755 --> 44:06.575
be aware of two slits.

44:06.579 --> 44:09.989
And this was a big surprise,
because normally when we study

44:09.990 --> 44:13.750
anything in Newtonian mechanics,
you say here's a collision,

44:13.751 --> 44:17.161
ball 1 collides and goes there,
you do all the calculations.

44:17.159 --> 44:19.509
Meanwhile, we are watching it.

44:19.510 --> 44:20.920
Maybe we are not watching it.

44:20.920 --> 44:21.800
Who cares?

44:21.800 --> 44:24.260
The answer doesn't depend on
whether we are watching or not?

44:24.260 --> 44:25.800
For example,
if you have a football game,

44:25.800 --> 44:28.030
and somebody throws the pass,
and you close your eyes,

44:28.030 --> 44:30.250
which sometimes my kids do,
because they don't know what's

44:30.253 --> 44:32.603
happening,
that doesn't change the outcome

44:32.601 --> 44:33.731
of the experiment.

44:33.730 --> 44:36.000
It follows its own trajectory.

44:36.000 --> 44:38.940
So what does seeing do to
anything?

44:38.940 --> 44:42.330
And you can say maybe he didn't
see it, but maybe people in the

44:42.327 --> 44:44.457
stadium were looking at the
football.

44:44.460 --> 44:46.820
So turn off all the lights.

44:46.820 --> 44:49.590
Then does the football have a
definite trajectory from start

44:49.594 --> 44:50.164
to finish?

44:50.159 --> 44:54.719
It does, because it's colliding
with all these air molecules.

44:54.719 --> 44:56.729
To remove all the air
molecules, of course,

44:56.731 --> 44:59.371
first you remove all the
spectators, then you remove all

44:59.365 --> 45:00.415
the air molecules.

45:00.420 --> 45:02.000
Then does it have a definite
trajectory?

45:02.000 --> 45:03.430
You might say,
"Of course it does.

45:03.429 --> 45:04.949
What difference does it
make?"

45:04.949 --> 45:07.229
But then you would be wrong.

45:07.230 --> 45:09.450
You would be wrong to think it
had a trajectory,

45:09.449 --> 45:11.899
because the minute you said it
had a trajectory,

45:11.900 --> 45:14.040
you will never understand
interference,

45:14.039 --> 45:16.589
which even a football can show.

45:16.590 --> 45:19.100
But the condition is,
for a football to show this

45:19.099 --> 45:21.869
kind of quantum effects,
it should not be disturbed by

45:21.869 --> 45:22.549
anything.

45:22.550 --> 45:24.850
It should not be seen.

45:24.849 --> 45:27.139
Nothing can collide with it.

45:27.139 --> 45:30.159
The minute you interact with a
quantum system,

45:30.155 --> 45:33.965
it stops doing this wishy-washy
business of "Where am

45:33.974 --> 45:34.784
I?"

45:34.780 --> 45:36.650
Till you see it,
it's not anywhere.

45:36.650 --> 45:38.850
Once you see it,
it's in a different location.

45:38.849 --> 45:41.079
Till you see it,
it's not taking any particular

45:41.079 --> 45:41.419
path.

45:41.420 --> 45:44.550
To assume it took this or that
path is simply wrong.

45:44.550 --> 45:47.840
But the act of observation
nails it.

45:47.840 --> 45:50.120
So why is observation so
important?

45:50.119 --> 45:52.049
You have to ask how we observe
things.

45:52.050 --> 45:53.900
We shine light.

45:53.900 --> 45:56.620
You've already seen,
the light is made of quanta,

45:56.617 --> 45:59.677
and each quantum carries a
certain momentum and certain

45:59.675 --> 46:00.295
energy.

46:00.300 --> 46:05.000
If I want to locate the
electron with some waves,

46:05.000 --> 46:07.640
with some light,
I want the momentum of the

46:07.641 --> 46:10.191
light to be weak,
because I don't want to slam

46:10.193 --> 46:12.413
the electron too hard in the act
of finding it.

46:12.409 --> 46:14.429
So I want p to be very
small.

46:14.429 --> 46:17.769
If p is very small,
l,

46:17.768 --> 46:20.338
which is 2pℏ
/p becomes large,

46:20.340 --> 46:23.780
and once l's bigger than
the spacing between the slits,

46:23.780 --> 46:25.870
the picture you get will be so
fuzzy,

46:25.869 --> 46:28.619
you cannot tell which slit it
went through.

46:28.619 --> 46:31.149
In other words,
to make a fine observation in

46:31.152 --> 46:34.322
optics, you need a wavelength
smaller than the distances

46:34.320 --> 46:35.990
you're trying to resolve.

46:35.989 --> 46:38.709
So you've got to use a
wavelength smaller than these

46:38.710 --> 46:39.350
two slits.

46:39.349 --> 46:44.199
So this p should be such
that this l is comparable

46:44.204 --> 46:46.674
to this slit,
or even smaller.

46:46.670 --> 46:50.650
But then you will find the act
of observing the electron

46:50.650 --> 46:53.980
imparts to it an unknown amount
of momentum.

46:53.980 --> 46:58.480
Once you change the momentum,
you change the interference

46:58.476 --> 46:59.276
pattern.

46:59.280 --> 47:03.640
So the act of observation,
which is pretty innocuous for

47:03.639 --> 47:06.939
you and me--
right now, I'm getting slammed

47:06.942 --> 47:11.302
by millions of photons,
but I'm taking it like a man.

47:11.300 --> 47:13.610
But for the electron,
it is not that simple.

47:13.610 --> 47:16.760
One collision with a photon is
like getting hit by a truck.

47:16.760 --> 47:19.830
The momentum of the photon is
enormous in the scale of the

47:19.827 --> 47:20.417
electron.

47:20.420 --> 47:22.550
So it matters a lot to the
electron.

47:22.550 --> 47:24.200
For example,
when I observe you,

47:24.199 --> 47:26.859
I see you because photons
bounce back and forth.

47:26.860 --> 47:29.930
Suppose it's a dark room and I
was swinging one of those things

47:29.925 --> 47:31.405
you see in Gladiator.

47:31.409 --> 47:32.629
What's that thing called?

47:32.630 --> 47:33.910
Trying to locate you.

47:33.909 --> 47:36.659
So the act of location,
you realize it will be

47:36.663 --> 47:39.363
memorable for you,
because it's a destructive

47:39.355 --> 47:40.085
process.

47:40.090 --> 47:43.630
But in Newtonian mechanics,
we can imagine finding gentler

47:43.628 --> 47:47.228
ways to observe somebody and
there's no limit to how gentle

47:47.228 --> 47:47.848
it is.

47:47.849 --> 47:51.089
You just say make the light
dimmer and dimmer and dimmer

47:51.092 --> 47:52.922
till the person doesn't care.

47:52.920 --> 47:56.490
But in quantum theory,
it's not how dim the light is.

47:56.489 --> 47:59.199
If the light is too dim,
there are too few photons and

47:59.197 --> 48:00.727
nobody catches the electron.

48:00.730 --> 48:03.480
In order to see the electron,
you've got to send enough

48:03.480 --> 48:03.990
photons.

48:03.989 --> 48:07.159
But the point is,
each one carries a punch which

48:07.161 --> 48:08.041
is minimum.

48:08.039 --> 48:10.969
It cannot be smaller than this
number, because if the

48:10.965 --> 48:14.335
wavelength is bigger than this,
you cannot tell which hole it

48:14.342 --> 48:15.302
went through.

48:15.300 --> 48:19.000
That's why in quantum theory,
the act of observation is very

48:18.996 --> 48:21.686
important, and it can change the
outcome.

48:21.690 --> 48:28.310
Okay, so what can we figure out
from this.

48:28.309 --> 48:32.469
Well, it looks like the act of
observing somehow affects the

48:32.474 --> 48:34.384
momentum of the electron.

48:34.380 --> 48:37.380
So people often say that's why,
when you try to measure the

48:37.380 --> 48:40.070
position of the electron,
you do something bad to the

48:40.068 --> 48:41.568
momentum of the electron.

48:41.570 --> 48:44.260
We change it,
because you need a large

48:44.255 --> 48:46.935
momentum to see it very
accurately.

48:46.940 --> 48:51.280
But that statement is partly
correct but partly incomplete

48:51.279 --> 48:53.639
and I'll tell you what it is.

48:53.639 --> 48:56.719
The trouble is not that you use
a high momentum photon to see an

48:56.715 --> 48:57.735
electron precisely.

48:57.739 --> 49:00.059
That's not a problem.

49:00.059 --> 49:02.659
The problem is that when it
bounces off the electron and

49:02.664 --> 49:04.894
comes back to you,
it would have changed,

49:04.893 --> 49:07.813
the momentum by an amount that
you cannot predict,

49:07.809 --> 49:10.239
and I'll tell you why that is
the case.

49:10.239 --> 49:14.519
So I told you long back that if
you have a hole and light comes

49:14.516 --> 49:18.026
in through it,
it doesn't go straight,

49:18.032 --> 49:21.642
it fans out,
that the profile of light looks

49:21.637 --> 49:22.407
like this.

49:22.409 --> 49:28.679
It spreads out and the angle by
which it spreads out obeys the

49:28.679 --> 49:32.379
condition dsinq =
l.

49:32.380 --> 49:35.360
Remember that part from wave
theory of light.

49:35.360 --> 49:39.110
Now here is the person trying
to catch an electron,

49:39.114 --> 49:41.974
which is somewhere around this
line.

49:41.969 --> 49:47.279
And he or she brings a
microscope that looks like this.

49:47.280 --> 49:51.620
Here's the opening of the
microscope, and you send some

49:51.617 --> 49:52.257
light.

49:52.260 --> 49:58.560
This opening of the microscope
has some extent d.

49:58.559 --> 50:05.609
Let's say it's got a sharp
opening here of width d.

50:05.610 --> 50:08.610
The light comes,
hits an electron,

50:08.612 --> 50:12.342
if it is there,
and goes right back to the

50:12.344 --> 50:13.714
microscope.

50:13.710 --> 50:16.520
If I see a flicker of reflected
light, I know the electron had

50:16.519 --> 50:18.459
to be somewhere here,
because if it's here,

50:18.456 --> 50:20.526
it's not going to collide with
the light.

50:20.530 --> 50:23.670
So you agree,
this is a way to locate the

50:23.666 --> 50:28.056
electron's position with an
uncertainty, which is roughly

50:28.061 --> 50:29.631
d, right?

50:29.630 --> 50:33.140
The electron had to be in front
of the opening of the microscope

50:33.141 --> 50:35.151
for me to actually see that
flash.

50:35.150 --> 50:37.940
So I make an electron
microscope with a very tiny

50:37.943 --> 50:39.693
hole,
and I'm scanning back and

50:39.688 --> 50:42.808
forth, hoping one day I will hit
an electron and one day I hit

50:42.809 --> 50:45.659
the electron,
it sends the light right back.

50:45.659 --> 50:47.509
This has momentum p.

50:47.510 --> 50:49.850
It also sends back with
momentum p,

50:49.853 --> 50:51.343
but there's one problem.

50:51.340 --> 50:58.980
You know that light entering an
aperture will spread out.

50:58.980 --> 50:59.790
It won't go straight through.

50:59.789 --> 51:00.909
This is this process.

51:00.909 --> 51:04.179
So if you think of this light
entering your microscope,

51:04.179 --> 51:05.209
it spreads out.

51:05.210 --> 51:09.330
If it spreads out,
it means the photon that

51:09.329 --> 51:14.919
bounced back can have a momentum
anywhere in this cone.

51:14.920 --> 51:17.050
And we don't know where it is.

51:17.050 --> 51:19.430
All we know is it re-entered
the microscope,

51:19.429 --> 51:21.669
entered this cone,
but anywhere in this cone is

51:21.673 --> 51:23.963
possible,
because there's a sizeable

51:23.961 --> 51:27.571
chance the light will come
anywhere into this diffracted

51:27.565 --> 51:28.215
region.

51:28.219 --> 51:31.779
That means the final photon's
momentum magnitude may be

51:31.778 --> 51:35.208
p_0,
but its direction is indefinite

51:35.206 --> 51:36.456
by an amount q.

51:36.460 --> 51:40.540
Therefore the photon's momentum
has a horizontal part,

51:40.539 --> 51:44.459
p_0sine q,
which is an uncertainty in the

51:44.460 --> 51:47.970
momentum of the photon in the
x direction.

51:47.969 --> 51:52.329
This is my x direction.

51:52.329 --> 51:55.809
So now you can see that
Dpx =

51:55.807 --> 51:58.207
p_0sine q.

51:58.210 --> 52:03.720
Sine q is l over the
width of the slit.

52:03.719 --> 52:07.019
And l was
2pℏ

52:07.018 --> 52:11.478
/p_0
over d.

52:11.480 --> 52:16.720
You can see that these
p_0's cancel,

52:16.715 --> 52:20.235
then you get d x
Dpx =

52:20.237 --> 52:23.357
2pℏ.

52:23.360 --> 52:26.770
By the way, another good news
is I'm going to give you very

52:26.773 --> 52:29.013
detailed notes on quantum
mechanics.

52:29.010 --> 52:31.600
I'm not following the textbook,
and I know you have to choose

52:31.599 --> 52:33.929
between listening to me and
writing down everything.

52:33.929 --> 52:36.619
So everything I'm saying here,
you will find in those notes,

52:36.621 --> 52:38.721
so don't worry if you didn't
get everything.

52:38.719 --> 52:41.039
You will have a second chance
to look at it.

52:41.039 --> 52:43.859
But what you find here is that
d x Dpx is

52:43.862 --> 52:46.802
2pℏ,
but d is the uncertainty

52:46.797 --> 52:49.697
in the location of the electron,
so you get Dx,

52:49.704 --> 52:52.184
Dpx, I'm not going to
say =,

52:52.179 --> 52:56.589
roughly of order,
ℏ.

52:56.590 --> 52:59.020
Forget the 2p's and everything.

52:59.018 --> 53:03.808
This is a very tiny number,
10^(-34), so we don't care if

53:03.806 --> 53:05.256
there are 2p's.

53:05.260 --> 53:10.730
But what this tells you is that
in the act of locating the

53:10.733 --> 53:14.193
electron--so let's understand
why.

53:14.190 --> 53:16.950
It's a constant going back and
forth between waves and

53:16.951 --> 53:17.891
particles, okay?

53:17.889 --> 53:20.359
That's why this happens.

53:20.360 --> 53:23.970
I want to see an electron and I
want to know exactly where I saw

53:23.972 --> 53:24.262
it.

53:24.260 --> 53:26.760
So I take a microscope with a
very small opening,

53:26.764 --> 53:29.634
so that if I see that guy,
I know it has to be somewhere

53:29.632 --> 53:30.992
in front of that hole.

53:30.989 --> 53:34.719
But the photon that came down
and bounced off it,

53:34.719 --> 53:38.159
if you now use wave theory,
the wave will spread out when

53:38.157 --> 53:40.857
it re-enters the cone by minimal
angle q,

53:40.860 --> 53:43.470
given by dsine q =
l.

53:43.469 --> 53:47.139
That means the photon will also
come at a range of angles,

53:47.137 --> 53:50.027
spread out, but if it comes at
a tilted angle,

53:50.032 --> 53:52.672
it certainly has horizontal
momentum.

53:52.670 --> 53:55.550
That extra horizontal momentum
should be imparted to the

53:55.545 --> 53:58.575
particle, because initially,
the momentum of this thing was

53:58.579 --> 53:59.729
strictly vertical.

53:59.730 --> 54:03.230
So the photon has given a
certain horizontal momentum to

54:03.228 --> 54:06.788
the electron and you don't know
how much it has given.

54:06.789 --> 54:10.319
And smaller your opening,
so the better you try to locate

54:10.320 --> 54:13.090
the electron,
bigger will be the spreading

54:13.086 --> 54:16.536
out, and bigger will be the
uncertainty in the reflected

54:16.539 --> 54:20.809
photon and therefore uncertainty
in the electron after collision.

54:20.809 --> 54:23.519
So before the collision,
you could have had an electron

54:23.518 --> 54:25.978
with perfectly well known
momentum in the x

54:25.976 --> 54:26.676
direction.

54:26.679 --> 54:29.089
But after you saw it,
you don't know its x

54:29.090 --> 54:31.500
momentum very well,
because the photon's x

54:31.503 --> 54:32.813
momentum is not known.

54:32.809 --> 54:35.279
I want you to appreciate,
it's not the fact that the

54:35.277 --> 54:37.937
photon came in its large
momentum that's the problem;

54:37.940 --> 54:41.200
it is that it went back into
the microscope with a slight

54:41.197 --> 54:44.397
uncertainty in its angle,
that comes from diffraction of

54:44.398 --> 54:44.978
light.

54:44.980 --> 54:47.060
It's the uncertainty of the
angle that turns into

54:47.056 --> 54:49.476
uncertainty in the x
component of the momentum.

54:49.480 --> 54:51.630
So basically,
collision of light with

54:51.630 --> 54:55.040
electrons leaves the electron
with an extra momentum whose

54:55.038 --> 54:58.778
value we don't know precisely,
because the act of seeing the

54:58.784 --> 55:01.874
photon with the microscope
necessarily means it accepts

55:01.867 --> 55:03.807
photons with a range of angles.

55:03.809 --> 55:11.209
Okay, so now I want to tell you
a little more about the

55:11.210 --> 55:17.240
uncertainty principle in another
language.

55:17.239 --> 55:23.219
The language is this - here is
a slit.

55:23.219 --> 55:26.289
Okay, here's one way to state
the uncertainty principle.

55:26.289 --> 55:30.649
I challenge you to produce for
me an electron whose location is

55:30.646 --> 55:34.156
known to arbitrary accuracy and
whose momentum,

55:34.159 --> 55:36.129
in the same dimension,
same direction,

55:36.130 --> 55:38.690
is also known to arbitrary
accuracy.

55:38.690 --> 55:40.420
I dare you to make it.

55:40.420 --> 55:45.020
In Newtonian mechanics,
that's not a big deal.

55:45.018 --> 55:48.478
So let's say this is the
y direction,

55:48.480 --> 55:52.710
and you say,
"I'll give you an electron

55:52.710 --> 55:56.350
with precisely known y
coordinate,

55:56.349 --> 55:59.519
and no uncertainty in y
momentum by the following trick.

55:59.518 --> 56:03.698
I'll send a beam of electrons
going in this direction,

56:03.699 --> 56:05.799
in the x direction,
with some momentum

56:05.795 --> 56:08.365
p_0 and I put a
hole in the middle.

56:08.369 --> 56:13.029
The only guys escaping have to
come out like this.

56:13.030 --> 56:16.930
So right outside,
what do I have?

56:16.929 --> 56:20.869
I have an electron whose
vertical momentum is exactly 0,

56:20.869 --> 56:23.799
because the beam had no
vertical momentum,

56:23.804 --> 56:27.534
whose vertical position = the
width of the slit.

56:27.530 --> 56:30.220
It's uncertain by the width of
the slit, and I can make the

56:30.219 --> 56:31.519
width as narrow as I like.

56:31.518 --> 56:33.808
I can make my filter finer and
finer and finer,

56:33.809 --> 56:36.379
till I'm able to give the
electrons a perfectly well

56:36.378 --> 56:39.198
defined position and perfectly
well defined momentum,

56:39.199 --> 56:41.289
namely 0.

56:41.289 --> 56:43.389
That's true in Newtonian
mechanics,

56:43.389 --> 56:45.439
but it's not true in the
quantum theory,

56:45.440 --> 56:48.280
because as you know,
this incoming beam of electrons

56:48.282 --> 56:51.892
is associated with a wave,
the wave is going to fan out

56:51.889 --> 56:53.239
when it comes out.

56:53.239 --> 56:56.409
And we sort of know how much
it's going to fan out.

56:56.409 --> 56:59.759
That's why I did that
diffraction for you.

56:59.760 --> 57:05.450
It fans out by an angle
q, so that dsine

57:05.447 --> 57:07.927
q = l.

57:07.929 --> 57:12.919
That means light can come
anywhere in this cone to your

57:12.918 --> 57:13.748
screen.

57:13.750 --> 57:17.200
That means the electrons
leaving could have had a

57:17.204 --> 57:19.944
momentum in any of these
directions.

57:19.940 --> 57:22.630
So the initial photon at a
momentum p_0,

57:22.630 --> 57:25.230
the final one has a momentum of
magnitude p_0,

57:25.230 --> 57:28.100
but whose direction is
uncertain.

57:28.099 --> 57:32.579
The uncertainty in the y
momentum, simply

57:32.577 --> 57:36.197
p_0sine
q.

57:36.199 --> 57:37.219
You understand?

57:37.219 --> 57:39.189
Take a vector
p_0.

57:39.190 --> 57:41.610
If that angle is q,
this is

57:41.606 --> 57:44.226
p_0sine
q.

57:44.230 --> 57:45.060
And we don't know.

57:45.059 --> 57:47.249
Look, it's not that we know
exactly where it's going to

57:47.246 --> 57:47.526
land.

57:47.530 --> 57:50.500
It can land anywhere inside
this bell shaped curve,

57:50.498 --> 57:53.168
so it can have any momentum in
this region.

57:53.170 --> 57:55.980
So the electrons you produce,
even though the position was

57:55.978 --> 57:57.898
well known to the width of the
slit,

57:57.900 --> 58:01.220
right after leaving the slit,
are capable of coming all over

58:01.224 --> 58:01.624
here.

58:01.619 --> 58:04.939
That means they have momenta
which can point in any of these

58:04.938 --> 58:06.118
allowed directions.

58:06.119 --> 58:08.999
So let's find the uncertainty
in y momentum as this.

58:09.000 --> 58:12.480
The uncertainty in y
position is just the width of

58:12.476 --> 58:13.156
the slit.

58:13.159 --> 58:16.599
So take the product now of D py.

58:16.599 --> 58:18.649
Let me call it Dy.

58:18.650 --> 58:24.340
That happens then to be
p_0sine q times

58:24.338 --> 58:29.408
d but dsine
q is l and l is

58:29.405 --> 58:33.435
2pℏ/p
_0.

58:33.440 --> 58:34.850
Cancel the
p_0,

58:34.849 --> 58:35.849
you get some number.

58:35.849 --> 58:38.629
Forget the 2p's that look like
ℏ.

58:38.630 --> 58:47.880
So this is the uncertainty
principle.

58:47.880 --> 58:51.420
So the origin of the
uncertainty principle is that

58:51.416 --> 58:55.166
the fate of the electrons is
determined by a wave.

58:55.170 --> 58:58.830
And when you try to localize
the wave in one direction,

58:58.829 --> 58:59.779
it fans out.

58:59.780 --> 59:03.230
And when it fans out,
the probability of finding the

59:03.231 --> 59:06.551
electron is not 0 in the
non-forward direction.

59:06.550 --> 59:09.390
It's got a good chance of being
in the range of non-forward

59:09.391 --> 59:10.031
directions.

59:10.030 --> 59:13.670
That means momentum has a good
chance of lying all the way from

59:13.670 --> 59:14.610
there to here.

59:14.610 --> 59:18.320
That means the y
momentum has an uncertainty.

59:18.320 --> 59:23.810
And more you make the purchase
smaller to nail its position,

59:23.809 --> 59:28.739
broader this will be,
keeping the product constant.

59:28.739 --> 59:31.089
So it's not hard mathematically
to understand.

59:31.090 --> 59:35.350
What is hard to understand is
the notion that somehow you need

59:35.353 --> 59:38.083
this wave, but it was forced
upon us.

59:38.079 --> 59:40.589
The wave is forced upon us,
because there's no way to

59:40.590 --> 59:42.910
understand interference,
except through waves.

59:42.909 --> 59:44.929
So when people saw the
interference pattern of the

59:44.934 --> 59:46.924
electrons, they said there's got
to be a wave.

59:46.920 --> 59:49.270
They said, "What is the
role of that wave?"

59:49.268 --> 59:51.828
That's what I want you to
understand.

59:51.829 --> 59:56.699
With every electron now--so
let's summarize what we have

59:56.695 --> 59:57.575
learned.

59:57.579 --> 1:00:00.089
When I say electron,
I mean any other particle you

1:00:00.085 --> 1:00:02.125
like, photon,
neutron, doesn't matter.

1:00:02.130 --> 1:00:03.240
They all do this.

1:00:03.239 --> 1:00:06.779
Quantum mechanics applies to
everything.

1:00:06.780 --> 1:00:11.580
Therefore, with every electron,
I'm going to associate a

1:00:11.581 --> 1:00:14.851
function,
Y(x)--or

1:00:14.853 --> 1:00:21.513
Y(x,y,z),
so that if you find its

1:00:21.514 --> 1:00:24.814
absolute value,
that gives--or absolute value

1:00:24.811 --> 1:00:29.531
squared,
that gives the odds of finding

1:00:29.534 --> 1:00:33.884
it at the point x,
y, z.

1:00:33.880 --> 1:00:39.650
Let me say it's proportional.

1:00:39.650 --> 1:00:40.810
This function is stuck.

1:00:40.809 --> 1:00:42.509
We are stuck with this function.

1:00:42.510 --> 1:00:44.680
And what else do we know about
the function?

1:00:44.679 --> 1:00:51.529
We know that if the electron
has momentum p,

1:00:51.532 --> 1:00:58.392
then the function Y has
wavelength l,

1:00:58.385 --> 1:01:05.235
which is 2pℏ
/p.

1:01:05.239 --> 1:01:08.199
This is all we know from
experiment.

1:01:08.199 --> 1:01:12.979
So experiment has forced us to
write this function Y.

1:01:12.980 --> 1:01:14.890
And the theory will make
predictions.

1:01:14.889 --> 1:01:19.989
Later on we'll find out how to
calculate the Y in every

1:01:19.987 --> 1:01:20.987
situation.

1:01:20.989 --> 1:01:23.279
But the question is,
what is the kinematics of

1:01:23.275 --> 1:01:25.915
quantum mechanics compared to
kinematics of classical

1:01:25.918 --> 1:01:26.628
mechanics?

1:01:26.630 --> 1:01:29.400
In classical mechanics,
a particle has a definite

1:01:29.398 --> 1:01:31.648
position, it has a definite
momentum.

1:01:31.650 --> 1:01:36.960
That describes the state of the
particle now.

1:01:36.960 --> 1:01:39.410
Then you want to predict the
future, so you want to know the

1:01:39.405 --> 1:01:41.185
coordinate and momentum of a
future time.

1:01:41.190 --> 1:01:43.420
How are you going to find that?

1:01:43.420 --> 1:01:47.930
Anybody know?

1:01:47.929 --> 1:01:54.449
How do you find the future of
x and p?

1:01:54.449 --> 1:01:56.859
In Newtonian mechanics;
I'm not talking about quantum

1:01:56.856 --> 1:01:57.336
mechanics.

1:01:57.340 --> 1:02:01.540
Student:
>

1:02:01.539 --> 1:02:04.319
Prof: Which one?

1:02:04.320 --> 1:02:05.710
Just use Newton's laws.

1:02:05.710 --> 1:02:07.030
That's what Newton's law does
for you.

1:02:07.030 --> 1:02:09.770
It tells you what the
acceleration is in a given

1:02:09.766 --> 1:02:10.346
context.

1:02:10.349 --> 1:02:12.899
Then you find the acceleration
to find the new velocity.

1:02:12.900 --> 1:02:16.030
Find the old velocity to find
the new position a little later

1:02:16.032 --> 1:02:18.592
and keep on doing it,
or you solve an equation.

1:02:18.590 --> 1:02:20.520
So the cycle of Newtonian
mechanics is give me the

1:02:20.516 --> 1:02:22.976
x and p,
and I know what they mean,

1:02:22.983 --> 1:02:26.283
and I'll tell you x and
p later if you tell me

1:02:26.280 --> 1:02:27.740
the forces acting on it.

1:02:27.739 --> 1:02:30.919
Or if you want to write the
force as a gradient of a

1:02:30.922 --> 1:02:34.232
potential, you will have to be
given the potential.

1:02:34.230 --> 1:02:36.950
In quantum mechanics,
you are given a function

1:02:36.954 --> 1:02:37.624
Y.

1:02:37.619 --> 1:02:41.829
Suppose the particle lives in
only one dimension,

1:02:41.829 --> 1:02:44.839
then for one particle,
not for a swarm of particles,

1:02:44.840 --> 1:02:48.690
for one particle,
for every particle there can be

1:02:48.688 --> 1:02:53.178
a function Y associated
with it at any instant.

1:02:53.179 --> 1:02:55.349
That tells you the full story.

1:02:55.349 --> 1:02:59.929
Remember, we've gone from two
numbers, x and p,

1:02:59.929 --> 1:03:01.609
to a whole function.

1:03:01.610 --> 1:03:03.930
What does the function do?

1:03:03.929 --> 1:03:07.799
If you squared the function at
this point--

1:03:07.800 --> 1:03:10.450
square will look roughly the
same thing--

1:03:10.449 --> 1:03:14.379
that height is proportional to
the odds of finding it here,

1:03:14.380 --> 1:03:17.040
and that means it's a very high
chance of being found here,

1:03:17.039 --> 1:03:22.299
maybe no chance of being found
here and so on.

1:03:22.300 --> 1:03:24.540
That's called the wave function.

1:03:24.539 --> 1:03:28.399
The name for this guy is the
wave function.

1:03:28.400 --> 1:03:32.670
So far we know only one wave
function.

1:03:32.670 --> 1:03:36.090
In a double slit experiment,
if you send electrons of

1:03:36.088 --> 1:03:39.168
momentum p,
that wave function seems to

1:03:39.173 --> 1:03:42.653
have a wavelength l
connected to p by this

1:03:42.646 --> 1:03:43.716
formula, this.

1:03:43.719 --> 1:03:52.019
This is all we know.

1:03:52.018 --> 1:03:59.068
So let's ask the following
question - take a particle of

1:03:59.074 --> 1:04:01.644
momentum p.

1:04:01.639 --> 1:04:04.939
What do you think the
corresponding wave function is

1:04:04.938 --> 1:04:07.008
in the double slit experiment?

1:04:07.010 --> 1:04:18.650
Can you cook up the function in
the double slit experiment at

1:04:18.650 --> 1:04:21.950
any given time?

1:04:21.949 --> 1:04:26.379
So I want to write a function
that can describe the electron

1:04:26.382 --> 1:04:30.972
in that double slit experiment,
and I'll tell you the momentum

1:04:30.967 --> 1:04:32.167
is p.

1:04:32.170 --> 1:04:34.720
So what can you tell from wave
theory?

1:04:34.719 --> 1:04:37.509
Let's say the wave is
traveling, this is the x

1:04:37.514 --> 1:04:38.164
direction.

1:04:38.159 --> 1:04:42.699
What can you say about
Y(x) at some given

1:04:42.701 --> 1:04:43.291
time?

1:04:43.289 --> 1:04:48.509
It's got some amplitude and
it's oscillating,

1:04:48.510 --> 1:04:53.730
so it's cosine
2px/l.

1:04:53.730 --> 1:04:54.950
Forget the time dependence.

1:04:54.949 --> 1:04:57.919
At one instant of time,
it's going to look like this.

1:04:57.920 --> 1:05:01.900
This is the wavelength l
for anything.

1:05:01.900 --> 1:05:05.390
But now I know that l is
connected to momentum as follows

1:05:05.391 --> 1:05:08.161
- l is 2pℏ
/p,

1:05:08.164 --> 1:05:09.554
so let's put that in.

1:05:09.550 --> 1:05:19.950
So 2p/l
= Acosine p

1:05:19.945 --> 1:05:24.445
over ℏx.

1:05:24.449 --> 1:05:27.209
This has the right wavelength
for the given momentum.

1:05:27.210 --> 1:05:29.670
In other words,
if you send electrons of

1:05:29.672 --> 1:05:32.692
momentum p,
and you put that p into this

1:05:32.690 --> 1:05:35.410
function exactly where it's
supposed to go,

1:05:35.409 --> 1:05:37.609
it determines a wavelength in
just the right way,

1:05:37.610 --> 1:05:42.330
that if you did interference,
you'll get a pattern you

1:05:42.329 --> 1:05:43.219
observe.

1:05:43.219 --> 1:05:47.369
But this is not the right
answer.

1:05:47.369 --> 1:05:52.319
This is not the right answer,
because if you took the square

1:05:52.315 --> 1:05:54.155
of the Y, it's real.

1:05:54.159 --> 1:05:56.829
I don't care whether it's
absolute square or square,

1:05:56.829 --> 1:05:59.019
you get cosine squared
px over

1:05:59.021 --> 1:06:05.701
ℏ,
and if you plot that function,

1:06:05.699 --> 1:06:12.139
it's going to look like this,
the incoming wave.

1:06:12.139 --> 1:06:15.709
I'm talking not about
interference but the incoming

1:06:15.706 --> 1:06:17.916
wave, if I write it this way.

1:06:17.920 --> 1:06:19.650
But incoming wave,
if it looks like this,

1:06:19.650 --> 1:06:22.910
I have a problem,
because the uncertainty

1:06:22.909 --> 1:06:27.309
principle says Dx
Dpx is of

1:06:27.307 --> 1:06:29.587
order ℏ.

1:06:29.590 --> 1:06:32.390
It cannot be smaller,
so the correct statement is,

1:06:32.391 --> 1:06:34.851
it's bigger than
ℏ over some

1:06:34.849 --> 1:06:35.479
number.

1:06:35.480 --> 1:06:37.930
Take this function here.

1:06:37.929 --> 1:06:42.629
Its momentum is exactly know,
do you agree?

1:06:42.630 --> 1:06:46.420
The uncertainty principle says
if you know the position well,

1:06:46.422 --> 1:06:48.892
you don't know the momentum too
well.

1:06:48.889 --> 1:06:51.849
If you know the momentum
exactly, so Dpx is 0,

1:06:51.851 --> 1:06:55.271
Dx is infinity,
that means you don't know where

1:06:55.269 --> 1:06:55.839
it is.

1:06:55.840 --> 1:06:59.670
A particle of perfectly known
momentum has perfectly unknown

1:06:59.666 --> 1:07:00.376
position.

1:07:00.380 --> 1:07:04.660
That means the probability of
finding it everywhere should be

1:07:04.659 --> 1:07:05.159
flat.

1:07:05.159 --> 1:07:07.069
This is not flat.

1:07:07.070 --> 1:07:10.280
It says I'm likely to be here,
not likely to be here,

1:07:10.280 --> 1:07:13.490
likely to be there,
so this function is ruled out.

1:07:13.489 --> 1:07:15.869
Because I want for
Y^(2),

1:07:15.873 --> 1:07:19.873
for a situation where it has a
well defined momentum,

1:07:19.873 --> 1:07:22.953
I want the answer to look like
this.

1:07:22.949 --> 1:07:25.519
The odds of finding it should
be independent of where you are,

1:07:25.521 --> 1:07:27.041
because we don't know where it
is.

1:07:27.039 --> 1:07:30.709
Every place is equally likely.

1:07:30.710 --> 1:07:37.050
And yet this function has no
wavelength.

1:07:37.050 --> 1:07:42.000
So how do I sneak in a
wavelength, but not affect this

1:07:41.998 --> 1:07:44.518
flatness of Y^(2)?

1:07:44.518 --> 1:07:46.958
Is there a way to write a
function that will have a

1:07:46.956 --> 1:07:49.876
magnitude which is constant but
has a wavelength hidden in it

1:07:49.878 --> 1:07:53.828
somewhere,
so that it can take part in

1:07:53.829 --> 1:07:55.499
interference?

1:07:55.500 --> 1:07:56.870
Pardon me?

1:07:56.869 --> 1:07:59.099
Any guess?

1:07:59.099 --> 1:07:59.799
Yes?

1:07:59.800 --> 1:08:00.520
Student:
>

1:08:00.519 --> 1:08:01.539
Prof: A complex function.

1:08:01.539 --> 1:08:04.289
So I'm going to tell you what
the answer is.

1:08:04.289 --> 1:08:07.169
We are driven to that answer.

1:08:07.170 --> 1:08:09.620
Here's a function I can write
down,

1:08:09.619 --> 1:08:14.199
which has all the good
properties I want -

1:08:14.201 --> 1:08:20.801
Y(x) looks like
some number Ae^(ipx/

1:08:20.795 --> 1:08:23.025
ℏ).

1:08:23.029 --> 1:08:27.789
This is just cosine(px
i) sine(px/ℏ).

1:08:27.788 --> 1:08:32.448
It's got a wavelength,
but the absolute value of

1:08:32.453 --> 1:08:37.613
Y is just A^(2),
because the absolute value of

1:08:37.613 --> 1:08:39.403
this guy is 1.

1:08:39.399 --> 1:08:42.059
Ae to the thing looks
like this.

1:08:42.060 --> 1:08:48.190
This is the number A,
this is px/ℏ is the

1:08:48.193 --> 1:08:49.073
angle.

1:08:49.069 --> 1:08:55.709
That complex number Y at
a given point x has got a

1:08:55.707 --> 1:08:59.077
magnitude which is just A^(2).

1:08:59.078 --> 1:09:02.128
So we are driven to the
conclusion that the correct way

1:09:02.125 --> 1:09:04.715
to describe an electron with
wave function,

1:09:04.720 --> 1:09:09.540
with a momentum p,
is some number in front times

1:09:09.537 --> 1:09:13.187
e^(ipx/ℏ),
because it's got a wavelength

1:09:13.186 --> 1:09:16.316
associated with it,
and it also has an absolute

1:09:16.317 --> 1:09:17.727
value that is flat.

1:09:17.729 --> 1:09:19.339
Do you understand why it had to
be flat?

1:09:19.340 --> 1:09:21.950
The uncertainty principle says
if you know its momentum

1:09:21.951 --> 1:09:23.721
precisely,
and you seem to know it,

1:09:23.719 --> 1:09:25.759
because you put a definite
p here,

1:09:25.760 --> 1:09:28.950
you cannot know where it is.

1:09:28.948 --> 1:09:32.728
That means the probability for
finding it cannot be dependent

1:09:32.728 --> 1:09:33.608
on position.

1:09:33.609 --> 1:09:36.759
Any trigonometric function you
take with some wavelength will

1:09:36.761 --> 1:09:39.341
necessarily oscillate,
preferring some points over

1:09:39.336 --> 1:09:40.226
other points.

1:09:40.229 --> 1:09:43.439
The exponential function,
it will oscillate and yet its

1:09:43.443 --> 1:09:45.053
magnitude is independent.

1:09:45.050 --> 1:09:47.550
That's a remarkable function.

1:09:47.550 --> 1:09:49.920
It's fair to say that if you
did not know complex

1:09:49.920 --> 1:09:51.940
exponentials,
you wouldn't have got beyond

1:09:51.944 --> 1:09:54.664
this point in the development of
quantum mechanics.

1:09:54.658 --> 1:09:59.228
The wave function of an
electron of definite momentum is

1:09:59.226 --> 1:10:01.216
a complex exponential.

1:10:01.220 --> 1:10:05.020
This is the sense in which
complex functions enter quantum

1:10:05.020 --> 1:10:07.220
mechanics in an inevitable way.

1:10:07.220 --> 1:10:10.040
It's not that the function is
really cosine px/ℏ and

1:10:10.038 --> 1:10:12.528
I'm trying to write it as a real
part of something.

1:10:12.529 --> 1:10:15.519
You need this complex beast.

1:10:15.520 --> 1:10:17.630
So the wave functions of
quantum mechanics.

1:10:17.630 --> 1:10:20.260
There are electrons which could
be doing many things,

1:10:20.259 --> 1:10:22.029
each one has a function
Y.

1:10:22.029 --> 1:10:24.869
Electron of definite momentum
we know is a reality.

1:10:24.869 --> 1:10:26.279
It happens all the time.

1:10:26.279 --> 1:10:29.959
In CERN they're producing
protons of a definite momentum,

1:10:29.962 --> 1:10:32.202
4 point whatever,
3 point p tev.

1:10:32.199 --> 1:10:33.379
So you know the momentum.

1:10:33.380 --> 1:10:36.100
You can ask what function
describes it in quantum theory;

1:10:36.100 --> 1:10:39.420
this is the answer.

1:10:39.420 --> 1:10:40.470
This is not derived.

1:10:40.470 --> 1:10:42.400
In a way, this is a postulate.

1:10:42.399 --> 1:10:44.189
I'm only trying to motivate it.

1:10:44.189 --> 1:10:46.849
You cannot derive any of
quantum mechanics,

1:10:46.850 --> 1:10:50.320
except looking at experiments
and trying to see if there is

1:10:50.323 --> 1:10:53.443
some theoretical structure that
will fit the data.

1:10:53.439 --> 1:10:55.759
So I'm going to conclude with
what we have found today,

1:10:55.762 --> 1:10:57.272
and it's probably a little
weird.

1:10:57.270 --> 1:11:01.170
I try to pay attention to that
and I will repeat it every time,

1:11:01.172 --> 1:11:03.442
maybe adding a little extra
stuff.

1:11:03.439 --> 1:11:06.179
So what have you found so far?

1:11:06.180 --> 1:11:11.100
It looks like electrons and
photons are all particles and

1:11:11.099 --> 1:11:13.189
waves,
except it's more natural to

1:11:13.194 --> 1:11:15.854
think of light in terms of waves
with the wavelength and

1:11:15.850 --> 1:11:16.480
frequency.

1:11:16.479 --> 1:11:19.849
What's surprising is that it's
made up of particles whose

1:11:19.851 --> 1:11:21.961
energy is
ℏw,

1:11:21.960 --> 1:11:24.670
and whose momentum is
ℏk.

1:11:24.670 --> 1:11:28.190
Conversely, particles like
electrons, which have a definite

1:11:28.186 --> 1:11:31.276
momentum, have a wavelength
associated with them.

1:11:31.279 --> 1:11:33.269
And when does the wavelength
come into play?

1:11:33.270 --> 1:11:36.060
Whenever you do an experiment
in which that wavelength is

1:11:36.064 --> 1:11:38.164
comparable to the geometric
dimensions,

1:11:38.158 --> 1:11:41.728
like a double slit experiment
at a single slit diffraction,

1:11:41.729 --> 1:11:45.919
it's the wave that decides
where the electron will go.

1:11:45.920 --> 1:11:49.550
The height squared of the wave
function is proportional to the

1:11:49.546 --> 1:11:52.456
probability the electron will
end up somewhere.

1:11:52.460 --> 1:11:55.670
And also, in a double slit
experiment, it is no longer

1:11:55.673 --> 1:11:59.073
possible to think that the
electron went through one slit

1:11:59.069 --> 1:11:59.979
or another.

1:11:59.979 --> 1:12:02.799
You make that assumption,
you cannot avoid the fact that

1:12:02.796 --> 1:12:05.816
when both slits are open,
the numbers should be additive.

1:12:05.819 --> 1:12:08.879
The fact they are not means an
electron knows how many slits

1:12:08.877 --> 1:12:12.087
are open, and only a wave knows
how many slits are open because

1:12:12.091 --> 1:12:13.441
it's going everywhere.

1:12:13.439 --> 1:12:16.479
A particle can only look at one
slit at a time.

1:12:16.479 --> 1:12:19.589
In fact, it doesn't know
anything, how many slits there

1:12:19.594 --> 1:12:19.944
are.

1:12:19.939 --> 1:12:22.899
It usually bangs itself into
the wall most of the time,

1:12:22.898 --> 1:12:25.248
but sometimes when it goes
through the hole,

1:12:25.252 --> 1:12:26.132
it comes up.

1:12:26.130 --> 1:12:30.020
And so what do you think one
should do to complete the

1:12:30.015 --> 1:12:30.745
picture?

1:12:30.750 --> 1:12:32.940
What do we need to know?

1:12:32.939 --> 1:12:35.329
We need to know many things.

1:12:35.328 --> 1:12:39.088
Y(x)^(2) is the
probability that if you look for

1:12:39.091 --> 1:12:41.391
it, you will find it somewhere.

1:12:41.390 --> 1:12:44.040
Instead of saying the particle
is at this x in Newtonian

1:12:44.042 --> 1:12:46.122
mechanics,
we're saying it can be at any

1:12:46.118 --> 1:12:48.948
x where Y doesn't
vanish and the odds are

1:12:48.947 --> 1:12:51.877
proportional to the square of
Y at that point.

1:12:51.880 --> 1:12:54.720
Then you can say,
what does the wave function

1:12:54.720 --> 1:12:57.820
look like for a particle of
definite momentum?

1:12:57.819 --> 1:13:00.579
Either you postulate it or try
to follow the arguments I gave,

1:13:00.581 --> 1:13:02.031
but this simply is the answer.

1:13:02.029 --> 1:13:04.929
This is the state of definite
momentum.

1:13:04.930 --> 1:13:07.840
And the uncertainty principle
tells you this is an agreement

1:13:07.844 --> 1:13:10.764
to the uncertainty principle
that any attempt to localize an

1:13:10.759 --> 1:13:13.719
electron in space by an amount
Dx leads to a spread in

1:13:13.722 --> 1:13:15.652
momentum in an amount
Dpx.

1:13:15.649 --> 1:13:17.139
That's because it's given by a
wave.

1:13:17.140 --> 1:13:19.710
If you're trying to squeeze the
wave this way,

1:13:19.707 --> 1:13:21.817
it blows up in the other
direction.

1:13:21.819 --> 1:13:24.199
And the odds for finding in
other directions are non 0,

1:13:24.199 --> 1:13:26.759
that means the momentum can
point in many directions coming

1:13:26.757 --> 1:13:27.637
out of the slit.

1:13:27.640 --> 1:13:29.370
That's the origin of the
uncertainty principle.

1:13:29.368 --> 1:13:33.678
So I'm going to post whatever I
told you today online.

1:13:33.680 --> 1:13:35.680
You should definitely read it
and it's something you should

1:13:35.676 --> 1:13:37.476
talk about,
not only with your analyst,

1:13:37.479 --> 1:13:39.339
because this can really disturb
you,

1:13:39.340 --> 1:13:41.420
talk about it with your
friends, your neighbors,

1:13:41.420 --> 1:13:43.860
talk about it with senior
students.

1:13:43.859 --> 1:13:46.969
The best thing in quantum is
discussing it with people and

1:13:46.967 --> 1:13:48.547
getting over the weirdness.

1:13:48.550 --> 1:13:54.000