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ALLAN ADAMS: Hi everyone.
Welcome to 804 for spring 2013.
This is the fourth, and
presumably final time
that I will be
teaching this class.
So I'm pretty excited about it.
So my name is Allan Adams.
I'll be lecturing the course.
I'm an assistant
professor in Course 8.
I study string theory
and its applications
to gravity, quantum gravity,
and condensed matter physics.
Quantum mechanics, this is a
course in quantam mechanics.
Quantam mechanics Is
my daily language.
Quantum mechanics
is my old friend.
I met quantum
mechanics 20 years ago.
I just realized that last night.
It was kind of depressing.
So, old friend.
It's also my most powerful tool.
So I'm pretty psyched about it.
Our recitation instructors
are Barton Zwiebach, yea!
And Matt Evans-- yea!
Matt's new to the
department, so welcome him.
Hi.
So he just started
his faculty position,
which is pretty awesome.
And our TA is Paolo Glorioso.
Paolo, are you here?
Yea!
There you go.
OK, so he's the person to
send all complaints to.
So just out of curiosity, how
many of you all are Course 8?
Awesome.
How many of you all
are, I don't know, 18?
Solid.
6?
Excellent.
9?
No one?
This is the first year we
haven't had anyone Course 9.
That's a shame.
Last year one of
the best students
was a Course 9 student.
So two practical things to know.
The first thing is
everything that we put out
will be on the Stellar website.
Lecture notes, homeworks,
exams, everything
is going to be done through
Stellar, including your grades.
The second thing
is that as you may
notice there are rather
more lights than usual.
I'm wearing a mic.
And there are these signs up.
We're going to be
videotaping this course
for the lectures for OCW.
And if you're happy
with that, cool.
If not, just sit on
the sides and you
won't appear anywhere on video.
Sadly, I can't do that.
But you're welcome
to if you like.
But hopefully that should
not play a meaningful role
in any of the lectures.
So the goal of 804 is for you
to learn quantum mechanics.
And by learn
quantum mechanics, I
don't mean to learn
how to do calculations,
although that's an important
and critical thing.
I mean learn some intuition.
I want you to develop
some intuition
for quantum phenomena.
Now, quantam
mechanics is not hard.
It has a reputation
for being a hard topic.
It is not a super hard topic.
So in particular,
everyone in this room,
I'm totally positive, can
learn quantum mechanics.
It does require
concerted effort.
It's not a trivial topic.
And in order to really
develop a good intuition,
the essential thing
is to solve problems.
So the way you develop
a new intuition
is by solving problems
and by dealing
with new situations, new
context, new regimes, which
is what we're
going to do in 804.
It's essential that you work
hard on the problem sets.
So your job is to devote
yourself to the problem sets.
My job is to convince you
at the end of every lecture
that the most interesting
thing you could possibly
do when you leave
is the problem set.
So you decide who
has the harder job.
So the workload is not so bad.
So we have problem
sets due, they're
due in the physics box in
the usual places, by lecture,
by 11 AM sharp on
Tuesdays every week.
Late work, no, not so much.
But we will drop one
problem set to make up
for unanticipated events.
We'll return the
graded problem sets
a week later in recitation.
Should be easy.
I strongly, strongly
encourage you
to collaborate with other
students on your problem sets.
You will learn more,
they will learn more,
it will be more efficient.
Work together.
However, write your
problem sets yourself.
That's the best way for
you to develop and test
your understanding.
There will be two midterms,
dates to be announced,
and one final.
I guess we could have
multiple, but that
would be a little exciting.
We're going to use clickers,
and clickers will be required.
We're not going to
take attendance,
but they will give
a small contribution
to your overall grade.
And we'll use them
most importantly
for non-graded but just
participation concept questions
and the occasional in class
quiz to probe your knowledge.
This is mostly so that
you have a real time
measure of your own conceptual
understanding of the material.
This has been
enormously valuable.
And something I want
to say just right off
is that the way I've
organized this class
is not so much based on
the classes I was taught.
It's based to the degree
possible on empirical lessons
about what works
in teaching, what
actually makes you learn better.
And clickers are an
excellent example of that.
So this is mostly a
standard lecture course,
but there will be clickers used.
So by next week I need
you all to have clickers,
and I need you to register
them on the TSG website.
I haven't chosen a
specific textbook.
And this is discussed
on the Stellar web page.
There are a set of textbooks,
four textbooks that I strongly
recommend, and a set of others
that are nice references.
The reason for this is twofold.
First off, there
are two languages
that are canonically used
for quantum mechanics.
One is called wave
mechanics, and the language,
the mathematical language is
partial differential equations.
The other is a matrix mechanics.
They have big names.
And the language there
is linear algebra.
And different books
emphasize different aspects
and use different languages.
And they also try to aim
at different problems.
Some books are
aimed towards people
who are interested in materials
science, some books that
are aimed towards people
interested in philosophy.
And depending on
what you want, get
the book that's suited to you.
And every week I'll be providing
with your problem sets readings
from each of the
recommended texts.
So what I really encourage you
to do is find a group of people
to work with every
week, and make sure
that you've got all the
books covered between you.
This'll give you as
much access to the texts
as possible without forcing
you to buy four books, which
I would discourage
you from doing.
So finally I guess
the last thing to say
is if this stuff
were totally trivial,
you wouldn't need to be here.
So ask questions.
If you're confused
about something,
lots of other
people in the class
are also going to be confused.
And if I'm not answering your
question without you asking,
then no one's getting
the point, right?
So ask questions.
Don't hesitate to interrupt.
Just raise your hand, and I
will do my best to call on you.
And this is true
for both in lecture,
also go to office
hours and recitations.
Ask questions.
I promise, there's no such
thing as a terrible question.
Someone else will
also be confused.
So it's a very valuable
to me and everyone else.
So before I get going
on the actual physics
content of the class, are there
any other practical questions?
Yeah.
AUDIENCE: You said there
was a lateness policy.
ALLAN ADAMS: Lateness policy.
No late work is
accepted whatsoever.
So the deal is given that
every once in a while,
you know, you'll be
walking to school
and your leg is
going to fall off,
or a dog's going to jump out
and eat your person standing
next to you, whatever.
Things happen.
So we will drop your
lowest problem set score
without any questions.
At the end of the
semester, we'll
just dropped your lowest score.
And if you turn
them all in, great,
whatever your lowest
score was, fine.
If you missed one, then gone.
On the other hand, if
you know next week, I'm
going to be attacked
by a rabid squirrel,
it's going to be
horrible, I don't
want to have to worry
about my problem set.
Could we work this out?
So if you know ahead
of time, come to us.
But you need to do that
well ahead of time.
The night before doesn't count.
OK?
Yeah.
AUDIENCE: Will we be
able to watch the videos?
ALLAN ADAMS: You know,
that's an excellent question.
I don't know.
I don't think so.
I think it's going to happen
at the end of the semester.
Yeah.
OK.
So no, you'll be able to watch
them later on the OCW website.
Other questions.
Yeah.
AUDIENCE: Are there
any other videos
that you'd recommend, just
like other courses on YouTube?
ALLAN ADAMS: Oh.
That's an interesting question.
I don't off the top of my head,
but if you send me an email,
I'll pursue it.
Because I do know several
other lecture series
that I like very
much, but I don't
know if they're available
on YouTube or publicly.
So send me an email
and I'll check.
Yeah.
AUDIENCE: So how about
the reading assignments?
ALLAN ADAMS: Reading assignments
on the problem set every week
will be listed.
There will be equivalent
reading from every textbook.
And if there is
something missing,
like if no textbook
covers something,
I'll post a separate reading.
Every once in a while, I'll
post auxiliary readings,
and they'll be available
on the Stellar website.
So for example, in your problem
set, first one was posted,
will be available
immediately after lecture
on the Stellar website.
There are three papers
that it refers to, or two,
and they are posted
on the Stellar website
and linked from the problem set.
Others?
OK.
So the first lecture.
The content of the physics
of the first lecture
is relatively standalone.
It's going to be an introduction
to a basic idea then is
going to haunt,
plague, and charm us
through the rest
of the semester.
The logic of this
lecture is based
on a very beautiful discussion
in the first few chapters
of a book by David Albert
called Quantum Mechanics
and Experience.
It's a book for philosophers.
But the first few chapters,
a really lovely introduction
at a non-technical level.
And I encourage you to
take a look at them,
because they're very lovely.
But it's to be sure
straight up physics.
Ready?
I love this stuff.
today I want to describe
to you a particular set
of experiments.
Now, to my mind, these are the
most unsettling experiments
ever done.
These experiments
involve electrons.
They have been performed,
and the results
as I will describe
them are true.
I'm going to focus on two
properties of electrons.
I will call them
color and hardness.
And these are not
the technical names.
We'll learn the technical
names for these properties
later on in the semester.
But to avoid distracting you
by preconceived notions of what
these things mean, I'm going
to use ambiguous labels, color
and hardness.
And the empirical fact is that
every electron, every electron
that's ever been observed
is either black or white
and no other color.
We've never seen
a blue electron.
There are no green electrons.
No one has ever found
a fluorescent electron.
They're either black,
or they are white.
It is a binary property.
Secondly, their hardness
is either hard or soft.
They're never squishy.
No one's ever found
one that dribbles.
They are either hard,
or they are soft.
Binary properties.
OK?
Now, what I mean
by this is that it
is possible to
build a device which
measures the color
and the hardness.
In particular, it
is possible to build
a box, which I will call a color
box, that measures the color.
And the way it works is this.
It has three apertures,
an in port and two out
ports, one which sends
out black electrons
and one which sends
out white electrons.
And the utility of this
box is that the color
can be inferred
from the position.
If you find the particle,
the electron over here,
it is a white electron.
If you find the electron
here, it is a black electron.
Cool?
Similarly, we can
build a hardness box,
which again has three
apertures, an in port.
And hard electrons
come out this port,
and soft electrons
come out this port.
Now, if you want, you're free
to imagine that these boxes are
built by putting
a monkey inside.
And you send in an
electron, and the monkey,
you know, with the ears,
looks at the electron,
and says it's a hard electron,
it sends it out one way,
or it's a soft electron,
it sends it out the other.
The workings inside
do not matter.
And in particular,
later in the semester
I will describe in
considerable detail
the workings inside
this apparatus.
And here's something I
want to emphasize to you.
It can be built in
principle using monkeys,
hyper intelligent monkeys
that can see electrons.
It could also be built using
magnets and silver atoms.
It could be done with neutrons.
It could be done with all sorts
of different technologies.
And they all give
precisely the same results
as I'm about to describe.
They all give precisely
the same results.
So it does not
matter what's inside.
But if you want a
little idea, you
could imagine putting a monkey
inside, a hyper intelligent
monkey.
I know, it sounds good.
So a key property of these
hardness boxes and color boxes
is that they are repeatable.
And here's what I mean by that.
If I send in an electron,
and I find that it comes out
of a color box black, and
then I send it in again,
then if I send it into
another color box,
it comes out black again.
So in diagrams, if I send
in some random electron
to a color box, and I discover
that it comes out, let's say,
the white aperture.
And so here's dot dot dot, and
I take the ones that come out
the white aperture, and I send
them into a color box again.
Then with 100% confidence,
100% of the time, the electron
coming out of the white port
incident on the color box
will come out the
white aperture again.
And 0% of the time will it
come out the black aperture.
So this is a
persistent property.
You notice that it's white.
You measure it again,
it's still white.
Do a little bit later,
it's still white.
OK?
It's a persistent property.
Ditto the hardness.
If I send in a bunch of
electrons in to a hardness box,
here is an important thing.
Well, send them
into a hardness box,
and I take out the ones
that come out soft.
And I send them again
into a hardness box,
and they come out soft.
They will come
out soft with 100%
confidence, 100% of the time.
Never do they come
out the hard aperture.
Any questions at this point?
So here's a natural question.
Might the color and the hardness
of an electron be related?
And more precisely,
might they be correlated?
Might knowing the color infer
something about the hardness?
So for example, so being
male and being a bachelor
are correlated properties,
because if you're male,
you don't know if you're
a bachelor or not,
but if you're a
bachelor, you're male.
That's the definition
of the word.
So is it possible that
color and hardness
are similarly correlated?
So, I don't know, there
are lots of good examples,
like wearing a red shirt and
beaming down to the surface
and making it back
to the Enterprise
later after the
away team returns.
Correlated, right?
Negatively, but correlated.
So the question
is, suppose, e.g.,
suppose we know that
an electron is white.
Does that determine
the hardness?
So we can answer this
question by using our boxes.
So here's what I'm going to do.
I'm going to take some
random set of electrons.
That's not random.
Random.
And I'm going to send
them in to a color box.
And I'm going to take
the electrons that
come out the white aperture.
And here's a useful fact.
When I say random, here's
operationally what I mean.
I take some piece of
material, I scrape it,
I pull off some electrons,
and they're totally
randomly chosen
from the material.
And I send them in.
If I send a random pile of
electrons into a color box,
useful thing to know, they
come out about half and half.
It's just some
random assortment.
Some of them are white,
some of them come out black.
Suppose I send some random
collection of electrons
into a color box.
And I take those which come
out the white aperture.
And I want to know, does
white determine hardness.
So I can do that, check, by then
sending these white electrons
into a hardness box and
seeing what comes out.
Hard, soft.
And what we find is that 50%
of those electrons incident
on the hardness box come out
hard, and 50% come out soft.
OK?
And ditto if we reverse this.
If we take hardness, and take,
for example, a soft electron
and send it into a color
box, we again get 50-50.
So if you take a white
electron, you send it
into a hardness box,
you're at even odds,
you're at chance
as to whether it's
going to come out hard or soft.
And similarly, if you
send a soft electron
into a color box,
even odds it's going
to come out black or white.
So knowing the hardness
does not give you
any information about the
color, and knowing the color
does not give you any
information about the hardness.
cool?
These are independent facts,
independent properties.
They're not correlated
in this sense,
in precisely this
operational sense.
Cool?
Questions?
OK.
So measuring the color
give zero predictive power
for the hardness, and
measuring the hardness
gives zero predictive
power for the color.
And from that, I will
say that these properties
are correlated.
So H, hardness, and color are
in this sense uncorrelated.
So using these properties of
the color and hardness boxes,
I want to run a few
more experiment's.
I want to probe these
properties of color and hardness
a little more.
And in particular,
knowing these results
allows us to make predictions,
to predict the results
for set a very
simple experiments.
Now, what we're going to
do for the next bit is
we're going to run some
simple experiments.
And we're going to
make predictions.
And then those
simple experiments
are going to lead us to more
complicated experiments.
But let's make sure we
understand the simple ones
first.
So for example, let's take
this last experiment, color
and hardness, and
let's add a color box.
One more monkey.
So color in, and
we take those that
come out the white aperture.
And we send them
into a hardness box.
Hard, soft.
And we take those
electrons which
come out the soft aperture.
And now let's send these
again into a color box.
So it's easy to see
what to predict.
Black, white.
So you can imagine a monkey
inside this, going, aha.
You look at it, you
inspect, it comes out white.
Here you look at it and
inspect, it comes out soft.
And you send it
into the color box,
and what do you
expect to happen?
Well, let's think
about the logic here.
Anything reaching
the hardness box
must have been
measured to be white.
And we just did the
experiment that if you
send a white electron
into a hardness box,
50% of the time it comes
out a hard aperture and 50%
of the time it comes
out the soft aperture.
So now we take that
50% of electrons
that comes out the soft
aperture, which had previously
been observed to
be white and soft.
And then we send them into a
color box, and what happens?
Well, since colors
are repeatable,
the natural expectation is that,
of course, it comes out white.
So our prediction,
our natural prediction
here is that of those electrons
that are incident on this color
box, 100% should come out white,
and 0% should come out black.
That seem like a reasonable--
let's just make sure
that we're all agreeing.
So let's vote.
How many people think
this is probably correct?
OK, good.
How many people think
this probably wrong?
OK, good.
That's reassuring.
Except you're all wrong.
Right?
In fact, what happens is
half of these electrons exit
white, 50%.
And 50% percent exit black.
So let's think about
what's going on here.
This is really
kind of troubling.
We've said already
that knowing the color
doesn't predict the hardness.
And yet, this electron,
which was previously
measured to be white, now when
subsequently measured sometimes
it comes out white,
sometimes it comes out
black, 50-50% of the time.
So that's surprising.
What that tells you is you
can't think of the electron
as a little ball that has black
and soft written on it, right?
You can't, because apparently
that black and soft
isn't a persistent
thing, although it's
persistent in the sense
that once it's black,
it stays black.
So what's going on here?
Now, I should emphasize
that the same thing happens
if I had changed this to
taking the black electrons
and throwing in a hardness and
picking soft and then measuring
the color, or if I had
used the hard electrons.
Any of those combinations,
any of these ports
would have given the
same results, 50-50.
Is not persistent in this sense.
Apparently the presence
of the hardness box
tampers with the color somehow.
So it's not quite as trivial is
that hyper intelligent monkey.
Something else is going on here.
So this is suspicious.
So here's the
first natural move.
The first natural move
is, oh, look, surely
there's some additional
property of the electron
that we just
haven't measured yet
that determines whether it
comes out the second color
box black or white.
There's got be some property
that determines this.
And so people have spent
a tremendous amount
of time and energy looking
at these initial electrons
and looking with great
care to see whether there's
any sort of feature of
these incident electrons
which determines which
port they come out of.
And the shocker is no one's
ever found such a property.
No one has ever found
a property which
determines which
port it comes out of.
As far as we can tell,
it is completely random.
Those that flip and
those that don't are
indistinguishable at beginning.
And let me just emphasize, if
anyone found such a-- it's not
like we're not looking, right?
If anyone found such a
property, fame, notoriety,
subverting quantum
mechanics, Nobel Prize.
People have looked.
And there is none that
anyone's been able to find.
And as we'll see later on,
using Bell's inequality,
we can more or less nail
that such things don't exist,
such a fact doesn't exist.
But this tells us something
really disturbing.
This tells us, and this
is the first real shocker,
that there is something
intrinsically unpredictable,
non-deterministic, and random
about physical processes
that we observe in a laboratory.
There's no way to determine
a priori whether it
will come out black or
white from the second box.
Probability in this
experiment, it's
forced upon us by observations.
OK, well, there's another
way to come at this.
You could say, look, you ran
this experiment, that's fine.
But look, I've met the
guy who built these boxes,
and look, he's just
some guy, right?
And he just didn't
do a very good job.
The boxes are just badly built.
So here's the way to
defeat that argument.
No, we've built these things
out of different materials,
using different technologies,
using electrons, using
neutrons, using bucky-balls,
C60, seriously, it's been done.
We've done this experiment, and
this property does not change.
It is persistent.
And the thing that's most
upsetting to me is that not
only do we get the same results
independent of what objects we
use to run the experiment, we
cannot change the probability
away from 50-50 at all.
Within experimental
tolerances, we cannot change,
no matter how we
build the boxes,
we cannot change the
probability by part in 100.
50-50.
And to anyone who grew up
with determinism from Newton,
this should hurt.
This should feel wrong.
But it's a property
of the real world.
And our job is going
to be to deal with it.
Rather, your job is going to
be to deal with it, because I
went through this already.
So here's a curious
consequence-- oh,
any questions before I cruise?
OK.
So here's a curious consequence
of this series of experiments.
Here's something you can't do.
Are you guys old enough for you
can't do this on television?
This is so sad.
OK, so here's
something you can't do.
We cannot build, it is
impossible to build,
a reliable color
and hardness box.
We've built a box that
tells you what color it is.
We've built a box that tells
you what hardness it is.
But you cannot build a
meaningful box that tells you
what color and hardness
an electron is.
So in particular, what
would this magical box be?
It would have four ports.
And its ports would say,
well, one is white and hard,
and one is white and soft,
one is black and hard,
and one is black and soft.
So you can imagine
how you might try
to build a color
and hardness box.
So for example, here's
something you might imagine.
Take your incident
electrons, and first
send them into a color box.
And take those white
electrons, and send them
into a hardness box.
And take those
electrons, and this
is going to be white
and hard, and this
is going to be white and soft.
And similarly, send
these black electrons
into the hardness box,
and here's hard and black,
and here's soft and back.
Everybody cool with that?
So this seems to do
the thing I wanted.
It measures both the
hardness and the color.
What's the problem with it?
AUDIENCE: [INAUDIBLE]
ALLAN ADAMS: Yeah, exactly.
So the color is not persistent.
So you tell me this is a soft
and black electron, right?
That's what you told me.
Here's the box.
But if I put a color
box here, that's
the experiment we just ran.
And what happens?
Does this come out black?
No, this is a crappy
source of black electrons.
It's 50/50 black and white.
So this box can't be built.
And the reason, and I
want to emphasize this,
the reason we cannot
build this box is not
because our
experiments are crude.
And it's not because
I can't build things,
although that's true.
I was banned from a lab one
day after joining it, actually.
So I really can't build,
but other people can.
And that's not why.
We can't because of something
much more fundamental,
something deeper,
something in principle,
which is encoded in
this awesome experiment.
This can be done.
It does not mean anything,
as a consequence.
It does not mean anything
to say this electron is
white and hard, because if you
tell me it's white and hard,
and I measure the white,
well, I know if it's hard,
it's going to come out 50-50.
It does not mean anything.
So this is an important idea.
This is an idea which
is enshrined in physics
with a term which
comes with capital
letters, the
Uncertainty Principle.
And the Uncertainty Principle
says basically that, look,
there's some observable,
measurable properties
of a system which
are incompatible
with each other in
precisely this way,
incompatible with each
other in the sense
not that you can't know, because
you can't know whether it's
hard and soft
simultaneously, deeper.
It is not hard and
white simultaneously.
It cannot be.
It does not mean
anything to say it
is hard and white
simultaneously.
That is uncertainty.
And again,
uncertainty is an idea
we're going to come back to
over and over in the class.
But every time you
think about it,
this should be the
first place you
start for the next few weeks.
Yeah.
Questions.
No questions?
OK.
So at this point,
it's really tempting
to think yeah, OK, this
is just about the hardness
and the color of electrons.
It's just a weird
thing about electrons.
It's not a weird thing
about the rest of the world.
The rest of the world's
completely reasonable.
And no, that's absolutely wrong.
Every object in the world
has the same properties.
If you take bucky-balls,
and you send them
through the analogous
experiment--
and I will show you the
data, I think tomorrow,
but soon, I will
show you the data.
When you take
bucky-balls and run it
through a similar experiment,
you get the same effect.
Now, bucky-balls are huge,
right, 60 carbon atoms.
But, OK, OK, at
that point, you're
saying, dude, come on,
huge, 60 carbon atoms.
So there is a
pendulum, depending
on how you define building, in
this building, a pendulum which
is used, in principle which
is used to improve detectors
to detect gravitational waves.
There's a pendulum with a,
I think it's 20 kilo mirror.
And that pendulum exhibits
the same sort of effects here.
We can see these quantum
mechanical effects
in those mirrors.
And this is in breathtakingly
awesome experiments
done by Nergis Malvalvala, whose
name I can never pronounce,
but who is totally awesome.
She's an amazing physicist.
And she can get these kind of
quantum effects out of a 20
kilo mirror.
So before you say something
silly, like, oh, it's
just electrons, it's
20 kilo mirrors.
And if I could put you on
a pendulum that accurate,
it would be you.
OK?
These are properties of
everything around you.
The miracle is not that
electrons behave oddly.
The miracle is that when you
take 10 to the 27 electrons,
they behave like cheese.
That's the miracle.
This is the underlying
correct thing.
OK, so this is so far so good.
But let's go deeper.
Let's push it.
And to push it, I
want to design for you
a slightly more elaborate
apparatus, a slightly more
elaborate experimental
apparatus.
And for this, I want you to
consider the following device.
I'm going to need to introduce a
couple of new features for you.
Here's a hardness box.
And it has an in port.
And the hardness box
has a hard aperture,
and it has a soft aperture.
And now, in addition
to this hardness box,
I'm going to introduce
two elements.
First, mirrors.
And what these mirrors do
is they take the incident
electrons and,
nothing else, they
change the direction of motion,
change the direction of motion.
And here's what I mean
by doing nothing else.
If I take one of these
mirrors, and I take,
for example, a color box.
And I take the white
electrons that come out,
and I bounce it off
the mirror, and then
I send these into
a color box, then
they come out white
100% of the time.
It does not change
the observable color.
Cool?
All it does is
change the direction.
Similarly, with
the hardness box,
it doesn't change the hardness.
It just changes the
direction of motion.
And every experiment we've
ever done on these, guys,
changes in no way
whatsoever the color
or the hardness by
subsequent measurement.
Cool?
Just changes the
direction of motion.
And then I'm going to
add another mirror.
It's actually a slightly
fancy set of mirrors.
All they do is they join
these beams together
into a single beam.
And again, this doesn't
change the color.
You send in a white
electron, you get out,
and you measure the
color on the other side,
you get a white electron.
You send in a black
electron from here,
and you measure the color, you
get a black electron again out.
Cool?
So here's my apparatus.
And I'm going to put
this inside a big box.
And I want to run
some experiments
with this apparatus.
Everyone cool with
the basic design?
Any questions
before I cruise on?
This part's fun.
So what I want to
do now is I want
to run some simple experiments
before we get to fancy stuff.
And the simple experiments
are just going to warm you up.
They're going to
prepare you to make
some predictions and
some calculations.
And eventually we'd like
to lead back to this guy.
So the first
experiment, I'm going
to send in white electrons.
Whoops.
Im.
I'm going to send
in white electrons.
And I'm going to
measure at the end,
and in particular at the
output, the hardness.
So I'm going to send
in white electrons.
And I'm going to
measure the hardness.
So this is my apparatus.
I'm going to measure the
hardness at the output.
And what I mean by
measure the hardness
is I throw these electrons
into a hardness box
and see what comes out.
So this is experiment 1.
And let me draw this, let
me biggen the diagram.
So you send white into-- so the
mechanism is a hardness box.
Mirror, mirror,
mirrors, and now we're
measuring the hardness out.
And the question I want to ask
is how many electrons come out
the hard aperture, and how
many electrons come out
the soft aperture of
this final hardness box.
So I'd like to know what
fraction come out hard,
and what fraction come out soft.
I send an initial
white electron,
for example I took a color
box and took the white output,
send them into the hardness
box, mirror, mirror,
hard, hard, soft.
And what fraction come out
hard, and what fraction
come out soft.
So just think about
it for a minute.
And when you have a prediction
in your head, raise your hand.
All right, good.
Walk me through your prediction.
AUDIENCE: I think
it should be 50-50.
ALLAN ADAMS: 50-50.
How come?
AUDIENCE: [INAUDIBLE]
color doesn't
have any bearing on hardness.
[INAUDIBLE]
ALLAN ADAMS: Awesome.
So let me say that again.
So we've done the experiment,
you send a white electron
into the hardness
box, and we know
that it's non-predictive, 50-50.
So if you take a white
electron and you send it
into the hardness
box, 50% of the time
it will come out the hard
aperture, and 50% of the time
it will come out
the soft aperture.
Now if you take the one that
comes out the hard aperture,
then you send it up
here or send it up here,
we know that these
mirrors do nothing
to the hardness of
the electron except
change the direction of motion.
We've already done
that experiment.
So you measure the hardness at
the output, what do you get?
Hard, because it came out hard,
mirror, mirror, hardness, hard.
But it only came out
hard 50% of the time
because we sent in
initially white electron.
Yeah?
What about the other 50%?
Well, the other 50% of the time,
it comes out the soft aperture
and follows what I'll
call the soft path
to the mirror, mirror, hardness.
And with soft, mirror,
mirror, hardness,
you know it comes out soft.
50% of the time it
comes out this way,
and then it will come out hard.
50% it follows the soft path,
and then it will come out soft.
Was this the logic?
Good.
How many people agree with this?
Solid.
How many people disagree?
No abstention.
OK.
So here's a prediction.
Oh, yep.
AUDIENCE: Just a question.
Could you justify
that prediction
without talking about oh,
well, half the electrons were
initially measured to be
hard, and half were initially
measured to be soft,
by just saying, well,
we have a hardness box, and
then we joined these electrons
together again, so we don't
know anything about it.
So it's just like
sending white electrons
into one hardness
box instead of two.
ALLAN ADAMS: Yeah, that's
a really tempting argument,
isn't it?
So let's see.
We're going to see
in a few minutes
whether that kind of an
argument is reliable or not.
But so far we've been given two
different arguments that lead
to the same prediction, 50-50.
Yeah?
Question.
AUDIENCE: Are the electrons
interacting between themselves?
Like when you get
them to where--
ALLAN ADAMS: Yeah.
This is a very good question.
So here's a question look you're
sending a bunch of electrons
into this apparatus.
But if I take--
look, I took 802.
You take two
electrons and you put
them close to each
other, what do they do?
Pyewww.
Right?
They interact with each other
through a potential, right?
So yeah, we're being a
little bold here, throwing
a bunch of electrons
in and saying,
oh, they're independent.
So I'm going to do one better.
I will send them
in one at a time.
One electron through
the apparatus.
And then I will
wait for six weeks.
[LAUGHTER]
See, you guys laugh,
you think that's funny.
But there's a famous
story about a guy
who did a similar experiment
with photons, French guy.
And, I mean, the French,
they know what they're doing.
So he wanted to do the same
experiment with photons.
But the problem is
if you take a laser
and you shined it
into your apparatus,
there there are like, 10
to the 18 photons in there
at any given moment.
And the photons, who knows what
they're doing with each other,
right?
So I want to send in one
photon, but the problem
is, it's very hard to get
a single photon, very hard.
So what he did, I kid you not,
he took an opaque barrier,
I don't remember what it
was, it was some sort of film
on top of glass, I think it
was some sort of oil-tar film.
Barton, do you
remember what he used?
So he takes a film, and it
has this opaque property,
such that the photons that are
incident upon it get absorbed.
Once in a blue moon
a photon manages
to make its way through.
Literally, like once
every couple of days,
or a couple of hours, I think.
So it's going to
take a long time
to get any sort of statistics.
But he this advantage, that
once every couple of hours
or whatever a photon
makes its way through.
That means inside
the apparatus, if it
takes a pico-second to
cross, triumph, right?
That's the week I
was talking about.
So he does this experiment.
But as you can tell, you start
the experiment, you press go,
and then you wait
for six months.
Side note on this guy, liked
boats, really liked yachts.
So he had six months
to wait before doing
a beautiful experiment
and having the results.
So what did he do?
Went on a world
tour in his yacht.
Comes back, collects the
data, and declares victory,
because indeed, he saw
the effect he wanted.
So I was not kidding.
We really do wait.
So I will take your challenge.
And single electron,
throw it in,
let it go through the
apparatus, takes mere moments.
Wait for a week, send
in another electron.
No electrons are
interacting with each other.
Just a single electron at a time
going through this apparatus.
Other complaints?
AUDIENCE: More stories?
ALLAN ADAMS: Sorry?
AUDIENCE: More stories?
ALLAN ADAMS: Oh,
you'll get them.
I have a hard time resisting.
So here's a prediction, 50-50.
We now have two
arguments for this.
So again, let's vote
after the second argument.
50-50, how many people?
You sure?
Positive?
How many people don't think so?
Very small dust.
OK.
It's correct.
Yea.
So, good.
I like messing with you guys.
So remember, we're going to
go through a few experiments
first where it's
going to be very
easy to predict the results.
We've got four experiments
like this to do.
And then we'll go on to
the interesting examples.
But we need to go through
them so we know what happens,
so we can make an empirical
argument rather than an in
principle argument.
So there's the first experiment.
Now, I want to run
the second experiment.
And the second experiment,
same as the first,
a little bit louder,
a little bit worse.
Sorry.
The second experiment,
we're going
to send in hard
electrons, and we're
going to measure color at out.
So again, let's look
at the apparatus.
We send in hard electrons.
And our apparatus
is hardness box
with a hard and a soft aperture.
And now we're going to measure
the color at the output.
Color, what have I been doing?
And now I want to know what
fraction come out black,
and what fraction
come out white.
We're using lots of
monkeys in this process.
OK, so this is not
rocket science.
Rocket science isn't
that complicated.
Neuroscience is much harder.
This is not neuroscience.
So let's figure
out what this is.
Predictions.
So again, think
about your prediction
your head, come to
a conclusion, raise
your hand when you have an idea.
And just because you
don't raise your hand
doesn't mean I
won't call on you.
AUDIENCE: 50-50 black and white.
ALLAN ADAMS: 50-50
black and white.
I like it.
Tell me why.
AUDIENCE: It's gone through
a hardness box, which
scrambled the color, and
therefore has to be [INAUDIBLE]
ALLAN ADAMS: Great.
So the statement, I'm going to
say that slightly more slowly.
That was an excellent argument.
We have a hard electron.
We know that hardness
boxes are persistent.
If you send a hard electron
in, it comes out hard.
So every electron incident
upon our apparatus
will transit across
the hard trajectory.
It will bounce, it will
bounce, but it is still hard,
because we've already
done that experiment.
The mirrors do nothing
to the hardness.
So we send a hard electron
into the color box,
and what comes out?
Well, we've done
that experiment, too.
Hard into color, 50-50.
So the prediction is 50-50.
This is your prediction.
Is that correct?
Awesome.
OK, let us vote.
How many people think
this is correct?
Gusto, I like it.
How many people think it's not?
All right.
Yay, this is correct.
Third experiment,
slightly more complicated.
But we have to go through
these to get to the good stuff,
so humor me for a moment.
Third, let's send
in white electrons,
and then measure the
color at the output port.
So now we send in white
electrons, same beast.
And our apparatus
is a hardness box
with a hard path
and a soft path.
Do-do-do, mirror,
do-do-do, mirror, box,
join together into our out.
And now we send those out
electrons into a color box.
And our color box,
black and white.
And now the question is
how many come out black,
and how many come out white.
Again, think through the
logic, follow the electrons,
come up with a prediction.
Raise your hand when
you have a prediction.
AUDIENCE: Well, earlier
we showed that [INAUDIBLE]
so it'll take those
paths equally--
ALLAN ADAMS: With
equal probability.
Good.
AUDIENCE: Yeah.
And then it'll go back
into the color box.
But earlier when we
did the same thing
without the weird path-changing,
it came out 50-50 still.
So I would say still 50-50.
ALLAN ADAMS: Great.
So let me say that
again, out loud.
And tell me if
this is an accurate
extension of what you said.
I'm just going to
use more words.
But it's, I think,
the same logic.
We have a white electron,
initially white electron.
We send it into a hardness box.
When we send a white
electron into a hardness box,
we know what happens.
50% of the time it comes
out hard, the hard aperture,
50% of the time it comes
out the soft aperture.
Consider those electrons that
came out the hard aperture.
Those electrons that came
out the hard aperture
will then transit
across the system,
preserving their hardness
by virtue of the fact
that these mirrors preserve
hardness, and end up
at a color box.
When they end at
the color box, when
that electron, the single
electron in the system
ends at this color
box, then we know
that a hard electron
entering a color box
comes out black or
white 50% of the time.
We've done that experiment, too.
So for those 50% that came
out hard, we get 50/50.
Now consider the other 50%.
The other half of the time, the
single electron in the system
will come out the soft aperture.
It will then proceed along
the soft trajectory, bounce,
bounce, not changing
its hardness,
and is then a soft electron
incident on the color box.
But we've also done
that experiment,
and we get 50-50
out, black and white.
So those electrons that came
out hard come out 50-50,
and those electrons that
come out soft come out 50/50.
And the logic then leads
to 50-50, twice, 50-50.
Was that an accurate statement?
Good.
It's a pretty
reasonable extension.
OK, let's vote.
How many people
agree with this one?
OK, and how many
people disagree?
Yeah, OK.
So vast majority agree.
And the answer is
no, this is wrong.
In fact, all of these, 100% come
out white and 0 come out black.
Never ever does an electron
come out the black aperture.
I would like to quote
what a student just
said, because it's actually the
next line in my notes, which
is what the hell is going on?
So let's the series of
follow up experiments
to tease out what's
going on here.
So something very
strange, let's just
all agree, something very
strange just happened.
We sent a single electron in.
And that single electron
comes out the hardness box,
well, it either came
out the hard aperture
or the soft aperture.
And if it came out the
hard, we know what happens,
if it came out the soft,
we know what happens.
And it's not 50-50.
So we need to improve
the situation.
Hold on a sec.
Hold on one sec.
Well, OK, go ahead.
AUDIENCE: Yeah, it's just
a question about the setup.
So with the second
hardness box, are we
collecting both the
soft and hard outputs?
ALLAN ADAMS: The second, you
mean the first hardness box?
AUDIENCE: The one-- are
we getting-- no, the--
ALLAN ADAMS: Which one, sorry?
This guy?
Oh, that's a mirror,
not a hardness box.
Oh, thanks for asking.
Yeah, sorry.
I wish I had a better notation
for this, but I don't.
There's a classic-- well,
I'm not going to go into it.
Remember that thing
where I can't stop myself
from telling stories?
So all this does, it's
just a set of mirrors.
It's a set of fancy mirrors.
And all it does is it
takes an electron coming
this way or an electron coming
this way, and both of them
get sent out in
the same direction.
It's like a beam joiner, right?
It's like a y junction.
That's all it is.
So if you will, imagine
the box is a box,
and you take, I don't
know, Professor Zwiebach,
and you put him inside.
And every time an electron
comes up this way,
he throws it out that
way, and every time
it comes in this way, he
throws it out that way.
And he'd be really ticked at
you for putting him in a box,
but he'd do the job well.
Yeah.
AUDIENCE: And this also works if
you go one electron at a time?
ALLAN ADAMS: This works if
you go one electron at a time,
this works if you go 14
electrons at a time, it works.
It works reliably.
Yeah.
AUDIENCE: Just,
maybe [INAUDIBLE]
but what's the difference
between this experiment
and that one?
ALLAN ADAMS: Yeah, I know.
Right?
Right?
So the question was,
what's the difference
between this experiment
and the last one.
Yeah, good question.
So we're going to
have to answer that.
Yeah.
AUDIENCE: Well, you're
mixing again the hardness.
So it's like as you weren't
measuring it at all, right?
ALLAN ADAMS: Apparently it's
a lot we weren't measuring it,
right?
Because we send in the white
electron, and at the end
we get out that
it's still white.
So somehow this is like
not doing anything.
But how does that work?
So that's an
excellent observation.
And I'm going to build you now
a couple of experiments that
tease out what's going on.
And you're not going
to like the answer.
Yeah.
AUDIENCE: How were
the white electrons
generated in this experiment?
ALLAN ADAMS: The
white electrons were
generated in the following way.
I take a random
source of electrons,
I rub a cat against a balloon
and I charge up the balloon.
And so I take those
random electrons,
and I send them
into a color box.
And we have previously
observed that if you
take random electrons and
throw them into a color box
and pull out the electrons that
come out the white aperture,
if you then send
them into a color box
again, they're still white.
So that's how I've
generated them.
I could have done it by
rubbing the cat against glass,
or rubbing it against me,
right, just stroke the cat.
Any randomly selected
set of electrons
sent into a color box,
and then from which
you take the white electrons.
AUDIENCE: So how is it different
from the experiment up there?
ALLAN ADAMS: Yeah.
Uh-huh.
Exactly.
Yeah.
AUDIENCE: Is the difference
that you never actually know
whether the electron's
hard or soft?
ALLAN ADAMS: That's a
really good question.
So here's something I'm
going to be very careful not
to say in this class
to the degree possible.
I'm not going to use
the word to know.
AUDIENCE: Well, to
measure. [INAUDIBLE]
ALLAN ADAMS: Good.
Measure is a very
slippery word, too.
I've used it here
because I couldn't really
get away with not using it.
But we'll talk about
that in some detail
later on in the course.
For the moment, I
want to emphasize
that it's tempting but dangerous
at this point to talk about
whether you know or don't
know, or whether someone knows
or doesn't know, for
example, the monkey
inside knows or doesn't know.
So let's try to
avoid that, and focus
on just operational questions of
what are the things that go in,
what are the things that
come out, and with what
probabilities.
And the reason
that's so useful is
that it's something
that you can just do.
There's no ambiguity
about whether you've
caught a white electron
in a particular spot.
Now in particular,
the reason these boxes
are such a powerful tool is that
you don't measure the electron,
you measure the position
of the electron.
You get hit by the
electron or you don't.
And by using these boxes we
can infer from their position
the color or the hardness.
And that's the reason
these boxes are so useful.
So we're inferring from
the position, which
is easy to measure,
you get beaned
or you don't, we're
inferring the property
that we're interested in.
It's a really good
question, though.
Keep it in the
back of your mind.
And we'll talk about it
on and off for the rest
of the semester.
Yeah.
AUDIENCE: So what happens
if you have this setup,
and you just take away
the bottom right mirror?
ALLAN ADAMS: Perfect question.
This leads me into
the next experiment.
So here's the modification.
But thank you, that's
a great question.
Here's the modification
of this experiment.
So let's rig up a
small-- hold on,
I want to go through the
next series of experiments,
and then I'll come
back to questions.
And these are great questions.
So I want to rig up a small
movable wall, a small movable
barrier.
And here's what this
movable barrier will do.
If I put the barrier in, so
this would be in the soft path,
when I put the barrier
in the soft path,
it absorbs all electrons
incident upon it
and impedes them
from proceeding.
So you put a barrier in here,
put a barrier in the soft path,
no electrons continue through.
An electron incident
cannot continue through.
When I say that the
barrier is out, what I mean
is it's not in the way.
I've moved it out of the way.
Cool?
So I want to run
the same experiment.
And I want to run this
experiment using the barriers
to tease out how the electrons
transit through our apparatus.
So experiment four.
Let's send in a
white electron again.
I want to do the same
experiment we just did.
And color at out, but now with
the wall in the soft path.
Wall in soft.
So that's this experiment.
So we send in white
electrons, and at the output
we measure the color as before.
And the question is what
fraction come out black,
and what fraction
come out white.
So again, everyone think
through it for a second.
Just take a second.
And this one's a little sneaky.
So feel free to discuss it with
the person sitting next to you.
[CHATTER]
ALLAN ADAMS: All right.
All right, now that everyone
has had a quick second
to think through
this one, let me just
talk through what I'd
expect from the point
of these experiments.
And then we'll talk about
whether this is reasonable.
So the first thing I
expect is that, look,
if I send in a white
electron and I put it
into a hardness pass, I know
that 50% of the time it goes
out hard, and 50% of the
time it goes out soft.
If it goes out
the soft aperture,
it's going to get eaten
by the barrier, right?
It's going to get
eaten by the barrier.
So first thing I predict
is that the output
should be down by 50%.
However, here's an
important bit of physics.
And this comes to
the idea of locality.
I didn't tell you
this, but these
armlinks in the experiment I
did, 3,000 kilometers long.
3,000 kilometers long.
That's too minor.
10 million kilometers long.
Really long.
Very long.
Now, imagine an
electron that enters
this, an initially
white electron.
If we had the barriers out,
if the barrier was out,
what do we get?
100% white, right?
We just did this
experiment, to our surprise.
So if we did this, we get 100%.
And that means an
electron, any electron,
going along the soft
path comes out white.
Any electron going along the
hard path goes out white.
They all come out white.
So now, imagine I do this.
Imagine we put a barrier in
here 2 million miles away
from this path.
How does a hard
electron along this path
know that I put
the barrier there?
And I'm going to make it
even more sneaky for you.
I'm going to insert the
barrier along the path
after I launched the
electron into the apparatus.
And when I send in the electron,
I will not know at that moment,
nor will the electron
know, because, you
know, they're not very
smart, whether the barrier is
in place.
And this is going to be millions
of miles away from this guy.
So an electron out
here can't know.
It hasn't been there.
It just hasn't been there.
It can't know.
But we know that when
we ran this apparatus
without the barrier in there,
they came out 100% white.
But it can't possibly know
whether the barrier's in
there or not, right?
It's over here.
So what this tells us is that
we should expect the output
to be down by 50%.
But all the electrons
that do make
it through must come
out white, because they
didn't know that there
was a barrier there.
They didn't go along that path.
Yeah.
AUDIENCE: Not trying
to be wise, but why
are you using the word know?
ALLAN ADAMS: Oh,
sorry, thank you.
Thank you, thank you, thank you,
that was a slip of the tongue.
I was making fun
of the electron.
So in that particular
case, I was not
referring to my
or your knowledge.
I was referring
to the electron's
tragically
impoverished knowledge.
Yeah.
AUDIENCE: But if they come
out one at a time white,
then wouldn't we know
then with certainty
that that electron is
both hard and white,
which is like a violation?
ALLAN ADAMS: Well, here's
the more troubling thing.
Imagine it didn't
come out 100% white.
Then the electron would
have demonstrably not
go along the soft path.
It would have demonstrably
gone through the hard path,
because that's the only
path available to it.
And yet, it would still have
known that millions of miles
away, there's a barrier
on a path it didn't take.
So which one's more
upsetting to you?
And personally, I find this one
the less upsetting of the two.
So the prediction is our
output should down by 50%,
because a half of
them get eaten.
But they should
all come out white,
because those that
didn't get eaten
can't possibly know that
there was a barrier here,
millions of miles away.
So we run this experiment.
And here's the
experimental result.
In fact, the experimental
result is yes, the output
is down by 50%.
But no, not 100%
white, 50% white.
50% white.
The barrier, if we put the
barrier in the hardness path.
If we put the barrier
in the hardness path,
still down by 50%, and
it's at odds, 50-50.
How could the electron know?
I'm making fun of it.
Yeah.
AUDIENCE: So I
guess my question is
before we ask how it
knows that there's
a block in one of the paths,
how does it know, before,
over there, that there were
two paths, and combine again?
ALLAN ADAMS: Excellent.
Exactly.
So actually, this
problem was there already
in the experiment we did.
All we've done here
is tease out something
that was existing in the
experiment, something
that was disturbing.
The presence of those
mirrors, and the option
of taking two paths,
somehow changed
the way the electron behaved.
How is that possible?
And here, we're seeing
that very sharply.
Thank you for that
excellent observation.
Yeah.
AUDIENCE: What if you
replaced the two mirrors
with color boxes, so that
both color boxes [INAUDIBLE]
ALLAN ADAMS: Yeah.
So the question is basically,
let's take this experiment,
and let's make it even more
intricate by, for example,
replacing these
mirrors by color boxes.
So here's the thing
I want to emphasize.
I strongly encourage you to
think through that example.
And in particular, think through
that example, come to my office
hours, and ask me about it.
So that's going to be setting
a different experiment.
And different
experiments are going
to have different results.
So we're going to have to
deal with that on a case
by case basis.
It's an interesting
example, but it's
going to take us a bit afar
from where we are right now.
But after we get to the
punchline from this,
come to my office hours and
ask me exactly that question.
Yeah.
AUDIENCE: So we had a color
box, we put in white electrons
and we got 50-50, like random.
How do you know the boxes work?
ALLAN ADAMS: How do I
know the boxes work?
These are the same boxes
we used from the beginning.
We tested them over and over.
AUDIENCE: How did you first
check that it was working?
[INAUDIBLE]
ALLAN ADAMS: How
to say-- there's
no other way to build a box
that does the properties that we
want, which is that you send
in color and it comes out color
again, and the mirrors
behave this way.
Any box that does those
first set of things, which
is what I will call a
color box, does this, too.
There's no other way to do it.
I don't mean just because
like, no one's tested--
AUDIENCE: Because you
can't actually check it,
you can't actually [INAUDIBLE]
you know which one is white.
ALLAN ADAMS: Oh, sure, you can.
You take the electron that
came out of the color box.
That's what we mean
by saying it's white.
AUDIENCE: [INAUDIBLE]
ALLAN ADAMS: But
that's what it means
to say the electron is white.
It's like, how do you know
that my name is Allan?
You say, Allan, and I go, what?
Right?
But you're like, look that's
not a test of whether I'm Allan.
It's like, well,
what is the test?
That's how you test.
What's your name?
I'm Allan.
Oh, great, that's your name.
So that's what I mean by white.
Now you might quibble
that that's a stupid thing
to call an electron.
And I grant you that.
But it is nonetheless a property
that I can empirically engage.
OK, so I've been told
that I never ask questions
from the people on the right.
Yeah.
AUDIENCE: Is it important
whether the experimenter
knows if the wall
is there or not?
ALLAN ADAMS: No.
This experiment has been done
again by some French guys.
The French, look, dude.
So there's this guy,
Alain Aspect, ahh,
great experimentalist,
great physicist.
And he's done lots of
beautiful experiments
on exactly this topic.
And send me an email, and
I'll post some example papers
and reviews by him-- and he's a
great writer-- on the web page.
So just send me an email
to remind me of that.
OK, so we're lowish on
time, so let me move on.
So what I want to
do now is I want
to take the lesson of this
experiment and the observation
that was made a minute ago, that
in fact the same problem was
present when we ran this
experiment and go 100%.
We should have been
freaked out already.
And I want to think through
what that's telling us
about the electron,
the single electron,
as it transits the apparatus.
The thing is, at this point
we're in real trouble.
And here's the reason.
Consider a single electron
inside the apparatus.
And I want to think about the
electron inside the apparatus
while all walls are out.
So it's this experiment.
Consider the single electron.
We know, with total confidence,
with complete reliability,
that every electron
will exit this color box
out the white aperture.
We've done this experiment.
We know it will come out white.
Yes?
Here's my question.
Which route did it take?
AUDIENCE: Spoiler.
ALLAN ADAMS: Not a spoiler.
Which route did it take?
AUDIENCE: Why do
we care what route?
ALLAN ADAMS: I'm asking
you the question.
That's why you care.
I'm the professor here.
What is this?
Come on.
Which route did it take?
OK, let's think through
the possibilities.
Grapple with this
question in your belly.
Let's think through
the possibilities.
First off, did it take
the hardness path?
So as it transits through,
the single electron
transiting through
this apparatus,
did it take the hard path
or did it take the soft?
These are millions of miles
long, millions of miles apart.
This is not a
ridiculous question.
Did it go millions of
miles in that direction,
or millions of miles
in that direction?
Did it take the hardness path?
Ladies and gentlemen, did
it take the hard path?
AUDIENCE: Yes.
ALLAN ADAMS: Well, we
ran this experiment
by putting a wall
in the soft path.
And if we put a wall
in the soft path,
then we know it
took the hard path,
because no other
electrons come out
except those that went
through the hard path.
Correct?
On the other hand, if it
went through the hard path,
it would come out
50% of the time white
and 50% of the time black.
But in fact, in this apparatus
it comes out always 100% white.
It cannot have
taken the hard path.
No.
Did it take the soft path?
Same argument,
different side, right?
No.
Well, this is not looking good.
Well, look, this was suggested.
Maybe it took both.
Maybe electrons are
sneaky little devils
that split in two, and part of
it goes one way and part of it
goes the other.
Maybe it took both paths.
So this is easy.
We can test this one.
And here is how I'm
going to test this one.
Oh, sorry.
Actually, I'm not
going to do that yet.
So we can test this one.
So if it took both paths, here's
what you should be able to do.
You should be able to put
a detector along each path,
and you'd be able
to follow, if you've
got half an electron on one
side and half an electron
on the other, or
maybe two electrons,
one on each side and
one on the other.
So this is the thing
that you'd predict
if you said it went both.
So here's what we'll do.
We will take detectors.
We will put one along
the hard path and one
along the soft path.
We will run the experiment
and then observe
whether, and ask whether,
we see two electrons,
we see half and
half, what do we see.
The answer is you always,
always see one electron on one
of the paths.
You never see half an electron.
You never see a
squishy electron.
You see one electron
on one path, period.
It did not take both.
You never see an electron split
in two, divided, confused.
No.
Well, it didn't
take the hard path,
didn't take the soft
path, it didn't take both.
There's one option left.
Neither.
Well, I say neither.
But what about neither?
And that's easy.
Let's put a barrier
in both paths.
And then what happens?
Nothing comes out.
So no.
So now, to repeat an
earlier prescient remark
from one of the
students, what the hell?
So here's the
world we're facing.
I want you to think about this.
Take this seriously.
Here's the world we're facing.
And when I say, here's
the world we're facing,
I don't mean just
these experiments.
I mean the world around you,
20 kilo mirrors, bucky-balls,
here is what they do.
When you send them through
an apparatus like this,
every single object that
goes through this apparatus
does not take the hard path,
it does not take the soft path,
it doesn't take both, and
it does not take neither.
And that pretty much
exhausts the set
of logical possibilities.
So what are electrons doing when
they're inside the apparatus?
How do you describe that
electron inside the apparatus?
You can't say it's
on one path, you
can't say it's on the
other, it's not on both,
and it's not on neither.
What is it doing halfway
through this experiment?
So if our experiments
are accurate,
and to the best of our
ability to determine,
they are, and if our arguments
are correct, and that's on me,
then they're doing
something, these electrons
are doing something we've
just never thought of before,
something we've never
dreamt of before,
something for which
we don't really
have good words in
the English language.
Apparently, empirically,
electrons have a way of moving,
electrons have a way of being
which is unlike anything
that we're used
to thinking about.
And so do molecules.
And so do bacteria.
So does chalk.
It's just harder to
detect in those objects.
So physicists have a name
for this new mode of being.
And we call it superposition.
Now, at the moment,
superposition
is code for I have no
idea what's going on.
Usage of the word superposition
would go something like this.
An initially white electron
inside this apparatus
with the walls out is
neither hard, nor soft,
nor both, nor neither.
It is, in fact, in a
superposition of being hard
and of being soft.
This is why we
can't meaningfully
say this electron is some
color and some hardness.
Not because our boxes are crude,
and not because we're ignorant,
though our boxes are
crude and we are ignorant.
It's deeper.
Having a definite color means
not having a definite hardness,
but rather being in a
superposition of being hard
and being soft.
Every electron exits a hardness
box either hard or soft.
But not every electron
is hard or soft.
It can also be a superposition
of being hard or being soft.
The probability
that we subsequently
measure it to be
hard or soft depends
on precisely what
superposition it is.
For example, we know
that if an electron is
in the superposition
corresponding to being white
then there are even odds
of it being subsequently
measured be hard or to be soft.
So to build a better
definition of superposition
than I have no idea
what's going on
is going to require
a new language.
And that language is
quantum mechanics.
And the underpinnings
of this language
are the topic of the course.
And developing a
better understanding
of this idea of
superposition is what
you have to do over
the next three months.
Now, if all of this
troubles your intuition,
well, that shouldn't
be too surprising.
Your intuition was developed
by throwing spears, and running
from tigers, and catching
toast as it jumps out
of the toaster, all of
which involves things so big
and with so much energy that
quantum effects are negligible.
As a friend of
mine likes to say,
you don't need to know quantum
mechanics to make chicken soup.
However, when we work in
very different regimes, when
we work with atoms, when we work
with molecules, when we work
in the regime of very
low energies and very
small objects, your intuition
is just not a reasonable guide.
It's not that the electrons--
and I cannot emphasize this
strongly enough-- it is not
that the electrons are weird.
The electrons do
what electrons do.
This is what they do.
And it violates your
intuition, but it's true.
The thing that's surprising
is that lots of electrons
behave like this.
Lots of electrons behave
like cheese and chalk.
And that's the goal
of 804, to step
beyond your daily experience
and your familiar intuition
and to develop an intuition
for this idea of superposition.
And we'll start in
the next lecture.
I'll see you on Thursday.
