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ALLAN ADAMS: Hi everyone.

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Welcome to 804 for spring 2013.

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This is the fourth, and
presumably final time

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that I will be
teaching this class.

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So I'm pretty excited about it.

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So my name is Allan Adams.

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I'll be lecturing the course.

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I'm an assistant
professor in Course 8.

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I study string theory
and its applications

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to gravity, quantum gravity,
and condensed matter physics.

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Quantum mechanics, this is a
course in quantam mechanics.

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Quantam mechanics Is
my daily language.

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Quantum mechanics
is my old friend.

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I met quantum
mechanics 20 years ago.

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I just realized that last night.

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It was kind of depressing.

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So, old friend.

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It's also my most powerful tool.

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So I'm pretty psyched about it.

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Our recitation instructors
are Barton Zwiebach, yea!

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And Matt Evans-- yea!

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Matt's new to the
department, so welcome him.

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Hi.

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So he just started
his faculty position,

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which is pretty awesome.

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And our TA is Paolo Glorioso.

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Paolo, are you here?

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Yea!

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There you go.

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OK, so he's the person to
send all complaints to.

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So just out of curiosity, how
many of you all are Course 8?

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Awesome.

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How many of you all
are, I don't know, 18?

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Solid.

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6?

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Excellent.

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9?

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No one?

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This is the first year we
haven't had anyone Course 9.

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That's a shame.

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Last year one of
the best students

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was a Course 9 student.

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So two practical things to know.

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The first thing is
everything that we put out

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will be on the Stellar website.

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Lecture notes, homeworks,
exams, everything

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is going to be done through
Stellar, including your grades.

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The second thing
is that as you may

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notice there are rather
more lights than usual.

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I'm wearing a mic.

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And there are these signs up.

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We're going to be
videotaping this course

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for the lectures for OCW.

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And if you're happy
with that, cool.

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If not, just sit on
the sides and you

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won't appear anywhere on video.

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Sadly, I can't do that.

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But you're welcome
to if you like.

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But hopefully that should
not play a meaningful role

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in any of the lectures.

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So the goal of 804 is for you
to learn quantum mechanics.

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And by learn
quantum mechanics, I

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don't mean to learn
how to do calculations,

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although that's an important
and critical thing.

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I mean learn some intuition.

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I want you to develop
some intuition

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for quantum phenomena.

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Now, quantam
mechanics is not hard.

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It has a reputation
for being a hard topic.

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It is not a super hard topic.

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So in particular,
everyone in this room,

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I'm totally positive, can
learn quantum mechanics.

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It does require
concerted effort.

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It's not a trivial topic.

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And in order to really
develop a good intuition,

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the essential thing
is to solve problems.

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So the way you develop
a new intuition

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is by solving problems
and by dealing

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with new situations, new
context, new regimes, which

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is what we're
going to do in 804.

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It's essential that you work
hard on the problem sets.

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So your job is to devote
yourself to the problem sets.

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My job is to convince you
at the end of every lecture

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that the most interesting
thing you could possibly

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do when you leave
is the problem set.

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So you decide who
has the harder job.

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So the workload is not so bad.

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So we have problem
sets due, they're

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due in the physics box in
the usual places, by lecture,

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by 11 AM sharp on
Tuesdays every week.

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Late work, no, not so much.

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But we will drop one
problem set to make up

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for unanticipated events.

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We'll return the
graded problem sets

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a week later in recitation.

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Should be easy.

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I strongly, strongly
encourage you

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to collaborate with other
students on your problem sets.

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You will learn more,
they will learn more,

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it will be more efficient.

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Work together.

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However, write your
problem sets yourself.

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That's the best way for
you to develop and test

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your understanding.

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There will be two midterms,
dates to be announced,

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and one final.

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I guess we could have
multiple, but that

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would be a little exciting.

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We're going to use clickers,
and clickers will be required.

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We're not going to
take attendance,

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but they will give
a small contribution

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to your overall grade.

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And we'll use them
most importantly

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for non-graded but just
participation concept questions

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and the occasional in class
quiz to probe your knowledge.

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This is mostly so that
you have a real time

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measure of your own conceptual
understanding of the material.

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This has been
enormously valuable.

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And something I want
to say just right off

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is that the way I've
organized this class

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is not so much based on
the classes I was taught.

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It's based to the degree
possible on empirical lessons

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about what works
in teaching, what

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actually makes you learn better.

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And clickers are an
excellent example of that.

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So this is mostly a
standard lecture course,

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but there will be clickers used.

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So by next week I need
you all to have clickers,

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and I need you to register
them on the TSG website.

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I haven't chosen a
specific textbook.

00:05:50.980 --> 00:05:52.939
And this is discussed
on the Stellar web page.

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There are a set of textbooks,
four textbooks that I strongly

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recommend, and a set of others
that are nice references.

00:05:58.019 --> 00:05:59.829
The reason for this is twofold.

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First off, there
are two languages

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that are canonically used
for quantum mechanics.

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One is called wave
mechanics, and the language,

00:06:07.459 --> 00:06:09.979
the mathematical language is
partial differential equations.

00:06:09.980 --> 00:06:11.500
The other is a matrix mechanics.

00:06:11.500 --> 00:06:13.209
They have big names.

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And the language there
is linear algebra.

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And different books
emphasize different aspects

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and use different languages.

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And they also try to aim
at different problems.

00:06:22.350 --> 00:06:23.790
Some books are
aimed towards people

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who are interested in materials
science, some books that

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are aimed towards people
interested in philosophy.

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And depending on
what you want, get

00:06:29.550 --> 00:06:32.300
the book that's suited to you.

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And every week I'll be providing
with your problem sets readings

00:06:35.540 --> 00:06:38.287
from each of the
recommended texts.

00:06:38.286 --> 00:06:40.870
So what I really encourage you
to do is find a group of people

00:06:40.870 --> 00:06:42.810
to work with every
week, and make sure

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that you've got all the
books covered between you.

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This'll give you as
much access to the texts

00:06:47.399 --> 00:06:49.959
as possible without forcing
you to buy four books, which

00:06:49.959 --> 00:06:51.745
I would discourage
you from doing.

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So finally I guess
the last thing to say

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is if this stuff
were totally trivial,

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you wouldn't need to be here.

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So ask questions.

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If you're confused
about something,

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lots of other
people in the class

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are also going to be confused.

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And if I'm not answering your
question without you asking,

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then no one's getting
the point, right?

00:07:12.730 --> 00:07:13.794
So ask questions.

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Don't hesitate to interrupt.

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Just raise your hand, and I
will do my best to call on you.

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And this is true
for both in lecture,

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also go to office
hours and recitations.

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Ask questions.

00:07:23.399 --> 00:07:25.969
I promise, there's no such
thing as a terrible question.

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Someone else will
also be confused.

00:07:28.560 --> 00:07:30.860
So it's a very valuable
to me and everyone else.

00:07:34.180 --> 00:07:36.840
So before I get going
on the actual physics

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content of the class, are there
any other practical questions?

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Yeah.

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AUDIENCE: You said there
was a lateness policy.

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ALLAN ADAMS: Lateness policy.

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No late work is
accepted whatsoever.

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So the deal is given that
every once in a while,

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you know, you'll be
walking to school

00:07:53.970 --> 00:07:55.386
and your leg is
going to fall off,

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or a dog's going to jump out
and eat your person standing

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next to you, whatever.

00:08:01.370 --> 00:08:02.250
Things happen.

00:08:02.250 --> 00:08:04.959
So we will drop your
lowest problem set score

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without any questions.

00:08:05.877 --> 00:08:07.251
At the end of the
semester, we'll

00:08:07.250 --> 00:08:08.599
just dropped your lowest score.

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And if you turn
them all in, great,

00:08:10.139 --> 00:08:11.680
whatever your lowest
score was, fine.

00:08:11.680 --> 00:08:13.550
If you missed one, then gone.

00:08:13.550 --> 00:08:16.350
On the other hand, if
you know next week, I'm

00:08:16.350 --> 00:08:18.160
going to be attacked
by a rabid squirrel,

00:08:18.160 --> 00:08:19.200
it's going to be
horrible, I don't

00:08:19.199 --> 00:08:20.991
want to have to worry
about my problem set.

00:08:20.992 --> 00:08:21.950
Could we work this out?

00:08:21.949 --> 00:08:23.689
So if you know ahead
of time, come to us.

00:08:23.689 --> 00:08:25.009
But you need to do that
well ahead of time.

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The night before doesn't count.

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OK?

00:08:27.769 --> 00:08:28.329
Yeah.

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AUDIENCE: Will we be
able to watch the videos?

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ALLAN ADAMS: You know,
that's an excellent question.

00:08:31.769 --> 00:08:32.699
I don't know.

00:08:32.700 --> 00:08:34.780
I don't think so.

00:08:34.779 --> 00:08:37.178
I think it's going to happen
at the end of the semester.

00:08:37.178 --> 00:08:37.418
Yeah.

00:08:37.418 --> 00:08:37.918
OK.

00:08:37.918 --> 00:08:41.370
So no, you'll be able to watch
them later on the OCW website.

00:08:45.120 --> 00:08:47.019
Other questions.

00:08:47.019 --> 00:08:47.730
Yeah.

00:08:47.730 --> 00:08:48.697
AUDIENCE: Are there
any other videos

00:08:48.697 --> 00:08:51.269
that you'd recommend, just
like other courses on YouTube?

00:08:51.269 --> 00:08:51.949
ALLAN ADAMS: Oh.

00:08:51.950 --> 00:08:54.440
That's an interesting question.

00:08:54.440 --> 00:08:57.156
I don't off the top of my head,
but if you send me an email,

00:08:57.155 --> 00:08:57.779
I'll pursue it.

00:08:57.779 --> 00:08:59.720
Because I do know several
other lecture series

00:08:59.720 --> 00:09:01.029
that I like very
much, but I don't

00:09:01.029 --> 00:09:03.089
know if they're available
on YouTube or publicly.

00:09:03.090 --> 00:09:05.379
So send me an email
and I'll check.

00:09:05.379 --> 00:09:05.909
Yeah.

00:09:05.909 --> 00:09:07.870
AUDIENCE: So how about
the reading assignments?

00:09:07.870 --> 00:09:10.452
ALLAN ADAMS: Reading assignments
on the problem set every week

00:09:10.452 --> 00:09:11.149
will be listed.

00:09:11.149 --> 00:09:13.750
There will be equivalent
reading from every textbook.

00:09:13.750 --> 00:09:15.250
And if there is
something missing,

00:09:15.250 --> 00:09:16.791
like if no textbook
covers something,

00:09:16.791 --> 00:09:18.074
I'll post a separate reading.

00:09:18.073 --> 00:09:20.240
Every once in a while, I'll
post auxiliary readings,

00:09:20.240 --> 00:09:22.430
and they'll be available
on the Stellar website.

00:09:22.429 --> 00:09:25.208
So for example, in your problem
set, first one was posted,

00:09:25.208 --> 00:09:27.000
will be available
immediately after lecture

00:09:27.000 --> 00:09:28.299
on the Stellar website.

00:09:28.299 --> 00:09:32.229
There are three papers
that it refers to, or two,

00:09:32.230 --> 00:09:34.879
and they are posted
on the Stellar website

00:09:34.879 --> 00:09:38.070
and linked from the problem set.

00:09:38.070 --> 00:09:38.570
Others?

00:09:41.090 --> 00:09:41.750
OK.

00:09:41.750 --> 00:09:45.799
So the first lecture.

00:09:45.799 --> 00:09:48.589
The content of the physics
of the first lecture

00:09:48.590 --> 00:09:51.040
is relatively standalone.

00:09:51.039 --> 00:09:53.549
It's going to be an introduction
to a basic idea then is

00:09:53.549 --> 00:09:55.799
going to haunt,
plague, and charm us

00:09:55.799 --> 00:09:57.174
through the rest
of the semester.

00:10:00.580 --> 00:10:02.560
The logic of this
lecture is based

00:10:02.559 --> 00:10:05.256
on a very beautiful discussion
in the first few chapters

00:10:05.256 --> 00:10:07.339
of a book by David Albert
called Quantum Mechanics

00:10:07.340 --> 00:10:09.200
and Experience.

00:10:09.200 --> 00:10:10.700
It's a book for philosophers.

00:10:10.700 --> 00:10:13.528
But the first few chapters,
a really lovely introduction

00:10:13.528 --> 00:10:14.570
at a non-technical level.

00:10:14.570 --> 00:10:16.361
And I encourage you to
take a look at them,

00:10:16.360 --> 00:10:19.460
because they're very lovely.

00:10:19.460 --> 00:10:21.710
But it's to be sure
straight up physics.

00:10:25.389 --> 00:10:27.179
Ready?

00:10:27.179 --> 00:10:30.549
I love this stuff.

00:10:30.549 --> 00:10:34.289
today I want to describe
to you a particular set

00:10:34.289 --> 00:10:35.860
of experiments.

00:10:35.860 --> 00:10:41.460
Now, to my mind, these are the
most unsettling experiments

00:10:41.460 --> 00:10:43.370
ever done.

00:10:43.370 --> 00:10:46.899
These experiments
involve electrons.

00:10:46.899 --> 00:10:49.230
They have been performed,
and the results

00:10:49.230 --> 00:10:53.110
as I will describe
them are true.

00:10:53.110 --> 00:10:56.889
I'm going to focus on two
properties of electrons.

00:10:56.889 --> 00:11:00.569
I will call them
color and hardness.

00:11:05.440 --> 00:11:07.054
And these are not
the technical names.

00:11:07.053 --> 00:11:09.220
We'll learn the technical
names for these properties

00:11:09.220 --> 00:11:10.379
later on in the semester.

00:11:10.379 --> 00:11:13.470
But to avoid distracting you
by preconceived notions of what

00:11:13.470 --> 00:11:16.330
these things mean, I'm going
to use ambiguous labels, color

00:11:16.330 --> 00:11:17.240
and hardness.

00:11:17.240 --> 00:11:27.320
And the empirical fact is that
every electron, every electron

00:11:27.320 --> 00:11:34.450
that's ever been observed
is either black or white

00:11:34.450 --> 00:11:35.670
and no other color.

00:11:35.669 --> 00:11:37.299
We've never seen
a blue electron.

00:11:37.299 --> 00:11:38.969
There are no green electrons.

00:11:38.970 --> 00:11:40.950
No one has ever found
a fluorescent electron.

00:11:40.950 --> 00:11:42.860
They're either black,
or they are white.

00:11:42.860 --> 00:11:45.399
It is a binary property.

00:11:45.399 --> 00:11:50.149
Secondly, their hardness
is either hard or soft.

00:11:50.149 --> 00:11:52.240
They're never squishy.

00:11:52.240 --> 00:11:54.570
No one's ever found
one that dribbles.

00:11:54.570 --> 00:11:56.210
They are either hard,
or they are soft.

00:11:56.210 --> 00:11:57.940
Binary properties.

00:11:57.940 --> 00:12:00.820
OK?

00:12:00.820 --> 00:12:04.170
Now, what I mean
by this is that it

00:12:04.169 --> 00:12:07.620
is possible to
build a device which

00:12:07.620 --> 00:12:09.580
measures the color
and the hardness.

00:12:09.580 --> 00:12:11.500
In particular, it
is possible to build

00:12:11.500 --> 00:12:16.652
a box, which I will call a color
box, that measures the color.

00:12:16.652 --> 00:12:17.860
And the way it works is this.

00:12:17.860 --> 00:12:21.460
It has three apertures,
an in port and two out

00:12:21.460 --> 00:12:25.734
ports, one which sends
out black electrons

00:12:25.734 --> 00:12:27.400
and one which sends
out white electrons.

00:12:32.429 --> 00:12:36.089
And the utility of this
box is that the color

00:12:36.090 --> 00:12:38.259
can be inferred
from the position.

00:12:38.259 --> 00:12:40.360
If you find the particle,
the electron over here,

00:12:40.360 --> 00:12:41.669
it is a white electron.

00:12:41.669 --> 00:12:44.479
If you find the electron
here, it is a black electron.

00:12:44.480 --> 00:12:46.360
Cool?

00:12:46.360 --> 00:12:50.460
Similarly, we can
build a hardness box,

00:12:50.460 --> 00:12:52.700
which again has three
apertures, an in port.

00:12:52.700 --> 00:12:59.050
And hard electrons
come out this port,

00:12:59.049 --> 00:13:00.659
and soft electrons
come out this port.

00:13:10.429 --> 00:13:14.459
Now, if you want, you're free
to imagine that these boxes are

00:13:14.460 --> 00:13:20.440
built by putting
a monkey inside.

00:13:20.440 --> 00:13:22.980
And you send in an
electron, and the monkey,

00:13:22.980 --> 00:13:26.149
you know, with the ears,
looks at the electron,

00:13:26.149 --> 00:13:28.995
and says it's a hard electron,
it sends it out one way,

00:13:28.995 --> 00:13:31.120
or it's a soft electron,
it sends it out the other.

00:13:31.120 --> 00:13:32.894
The workings inside
do not matter.

00:13:32.894 --> 00:13:34.560
And in particular,
later in the semester

00:13:34.559 --> 00:13:37.199
I will describe in
considerable detail

00:13:37.200 --> 00:13:39.600
the workings inside
this apparatus.

00:13:39.600 --> 00:13:41.629
And here's something I
want to emphasize to you.

00:13:41.629 --> 00:13:44.568
It can be built in
principle using monkeys,

00:13:44.568 --> 00:13:46.610
hyper intelligent monkeys
that can see electrons.

00:13:46.610 --> 00:13:50.548
It could also be built using
magnets and silver atoms.

00:13:50.548 --> 00:13:51.840
It could be done with neutrons.

00:13:51.840 --> 00:13:54.256
It could be done with all sorts
of different technologies.

00:13:54.255 --> 00:13:56.679
And they all give
precisely the same results

00:13:56.679 --> 00:13:59.989
as I'm about to describe.

00:13:59.990 --> 00:14:01.830
They all give precisely
the same results.

00:14:01.830 --> 00:14:04.080
So it does not
matter what's inside.

00:14:04.080 --> 00:14:05.639
But if you want a
little idea, you

00:14:05.639 --> 00:14:08.350
could imagine putting a monkey
inside, a hyper intelligent

00:14:08.350 --> 00:14:10.128
monkey.

00:14:10.128 --> 00:14:11.550
I know, it sounds good.

00:14:16.289 --> 00:14:21.929
So a key property of these
hardness boxes and color boxes

00:14:21.929 --> 00:14:23.329
is that they are repeatable.

00:14:23.330 --> 00:14:25.460
And here's what I mean by that.

00:14:25.460 --> 00:14:29.040
If I send in an electron,
and I find that it comes out

00:14:29.039 --> 00:14:32.701
of a color box black, and
then I send it in again,

00:14:32.701 --> 00:14:34.409
then if I send it into
another color box,

00:14:34.409 --> 00:14:35.605
it comes out black again.

00:14:38.809 --> 00:14:44.659
So in diagrams, if I send
in some random electron

00:14:44.659 --> 00:14:48.120
to a color box, and I discover
that it comes out, let's say,

00:14:48.120 --> 00:14:50.840
the white aperture.

00:14:50.840 --> 00:14:53.519
And so here's dot dot dot, and
I take the ones that come out

00:14:53.519 --> 00:14:56.519
the white aperture, and I send
them into a color box again.

00:14:56.519 --> 00:15:02.091
Then with 100% confidence,
100% of the time, the electron

00:15:02.091 --> 00:15:04.340
coming out of the white port
incident on the color box

00:15:04.340 --> 00:15:05.980
will come out the
white aperture again.

00:15:05.980 --> 00:15:09.759
And 0% of the time will it
come out the black aperture.

00:15:09.759 --> 00:15:11.535
So this is a
persistent property.

00:15:11.535 --> 00:15:12.659
You notice that it's white.

00:15:12.659 --> 00:15:14.813
You measure it again,
it's still white.

00:15:14.813 --> 00:15:16.480
Do a little bit later,
it's still white.

00:15:16.480 --> 00:15:17.370
OK?

00:15:17.370 --> 00:15:20.649
It's a persistent property.

00:15:20.649 --> 00:15:21.699
Ditto the hardness.

00:15:21.700 --> 00:15:25.855
If I send in a bunch of
electrons in to a hardness box,

00:15:25.855 --> 00:15:26.980
here is an important thing.

00:15:26.980 --> 00:15:29.269
Well, send them
into a hardness box,

00:15:29.269 --> 00:15:32.329
and I take out the ones
that come out soft.

00:15:32.330 --> 00:15:34.280
And I send them again
into a hardness box,

00:15:34.279 --> 00:15:36.179
and they come out soft.

00:15:36.179 --> 00:15:38.389
They will come
out soft with 100%

00:15:38.389 --> 00:15:40.039
confidence, 100% of the time.

00:15:40.039 --> 00:15:42.939
Never do they come
out the hard aperture.

00:15:52.844 --> 00:15:54.010
Any questions at this point?

00:15:59.802 --> 00:16:01.009
So here's a natural question.

00:16:07.070 --> 00:16:13.530
Might the color and the hardness
of an electron be related?

00:16:13.529 --> 00:16:18.279
And more precisely,
might they be correlated?

00:16:18.279 --> 00:16:21.459
Might knowing the color infer
something about the hardness?

00:16:21.460 --> 00:16:26.530
So for example, so being
male and being a bachelor

00:16:26.529 --> 00:16:28.749
are correlated properties,
because if you're male,

00:16:28.749 --> 00:16:30.540
you don't know if you're
a bachelor or not,

00:16:30.539 --> 00:16:32.122
but if you're a
bachelor, you're male.

00:16:32.123 --> 00:16:34.870
That's the definition
of the word.

00:16:34.870 --> 00:16:36.850
So is it possible that
color and hardness

00:16:36.850 --> 00:16:39.110
are similarly correlated?

00:16:39.110 --> 00:16:41.970
So, I don't know, there
are lots of good examples,

00:16:41.970 --> 00:16:44.651
like wearing a red shirt and
beaming down to the surface

00:16:44.650 --> 00:16:46.149
and making it back
to the Enterprise

00:16:46.149 --> 00:16:48.360
later after the
away team returns.

00:16:48.360 --> 00:16:49.649
Correlated, right?

00:16:49.649 --> 00:16:52.539
Negatively, but correlated.

00:16:52.539 --> 00:16:55.789
So the question
is, suppose, e.g.,

00:16:55.789 --> 00:16:59.879
suppose we know that
an electron is white.

00:17:02.990 --> 00:17:05.214
Does that determine
the hardness?

00:17:10.759 --> 00:17:15.042
So we can answer this
question by using our boxes.

00:17:15.042 --> 00:17:16.333
So here's what I'm going to do.

00:17:16.334 --> 00:17:19.029
I'm going to take some
random set of electrons.

00:17:19.029 --> 00:17:20.789
That's not random.

00:17:20.789 --> 00:17:22.068
Random.

00:17:22.068 --> 00:17:24.813
And I'm going to send
them in to a color box.

00:17:24.814 --> 00:17:26.480
And I'm going to take
the electrons that

00:17:26.480 --> 00:17:27.740
come out the white aperture.

00:17:27.740 --> 00:17:28.849
And here's a useful fact.

00:17:28.849 --> 00:17:31.015
When I say random, here's
operationally what I mean.

00:17:31.016 --> 00:17:33.580
I take some piece of
material, I scrape it,

00:17:33.579 --> 00:17:36.329
I pull off some electrons,
and they're totally

00:17:36.329 --> 00:17:37.788
randomly chosen
from the material.

00:17:37.788 --> 00:17:38.579
And I send them in.

00:17:38.579 --> 00:17:41.179
If I send a random pile of
electrons into a color box,

00:17:41.180 --> 00:17:44.436
useful thing to know, they
come out about half and half.

00:17:44.435 --> 00:17:45.809
It's just some
random assortment.

00:17:45.809 --> 00:17:49.200
Some of them are white,
some of them come out black.

00:17:49.200 --> 00:17:51.900
Suppose I send some random
collection of electrons

00:17:51.900 --> 00:17:52.880
into a color box.

00:17:52.880 --> 00:17:55.007
And I take those which come
out the white aperture.

00:17:55.007 --> 00:17:57.090
And I want to know, does
white determine hardness.

00:17:57.089 --> 00:18:01.139
So I can do that, check, by then
sending these white electrons

00:18:01.140 --> 00:18:03.990
into a hardness box and
seeing what comes out.

00:18:09.099 --> 00:18:11.689
Hard, soft.

00:18:11.690 --> 00:18:17.860
And what we find is that 50%
of those electrons incident

00:18:17.859 --> 00:18:26.059
on the hardness box come out
hard, and 50% come out soft.

00:18:26.059 --> 00:18:27.599
OK?

00:18:27.599 --> 00:18:28.849
And ditto if we reverse this.

00:18:28.849 --> 00:18:32.559
If we take hardness, and take,
for example, a soft electron

00:18:32.559 --> 00:18:40.264
and send it into a color
box, we again get 50-50.

00:18:45.067 --> 00:18:46.900
So if you take a white
electron, you send it

00:18:46.900 --> 00:18:49.232
into a hardness box,
you're at even odds,

00:18:49.231 --> 00:18:50.690
you're at chance
as to whether it's

00:18:50.690 --> 00:18:52.049
going to come out hard or soft.

00:18:52.049 --> 00:18:54.339
And similarly, if you
send a soft electron

00:18:54.339 --> 00:18:56.309
into a color box,
even odds it's going

00:18:56.309 --> 00:18:58.190
to come out black or white.

00:18:58.190 --> 00:18:59.980
So knowing the hardness
does not give you

00:18:59.980 --> 00:19:02.569
any information about the
color, and knowing the color

00:19:02.569 --> 00:19:05.220
does not give you any
information about the hardness.

00:19:05.220 --> 00:19:06.000
cool?

00:19:06.000 --> 00:19:08.910
These are independent facts,
independent properties.

00:19:08.910 --> 00:19:11.590
They're not correlated
in this sense,

00:19:11.589 --> 00:19:15.949
in precisely this
operational sense.

00:19:15.950 --> 00:19:18.100
Cool?

00:19:18.099 --> 00:19:20.134
Questions?

00:19:20.134 --> 00:19:20.634
OK.

00:19:24.279 --> 00:19:26.720
So measuring the color
give zero predictive power

00:19:26.720 --> 00:19:28.553
for the hardness, and
measuring the hardness

00:19:28.553 --> 00:19:31.280
gives zero predictive
power for the color.

00:19:34.119 --> 00:19:36.079
And from that, I will
say that these properties

00:19:36.079 --> 00:19:37.662
are correlated.

00:19:37.662 --> 00:19:45.799
So H, hardness, and color are
in this sense uncorrelated.

00:19:55.130 --> 00:19:59.237
So using these properties of
the color and hardness boxes,

00:19:59.237 --> 00:20:00.820
I want to run a few
more experiment's.

00:20:00.819 --> 00:20:03.068
I want to probe these
properties of color and hardness

00:20:03.068 --> 00:20:04.309
a little more.

00:20:04.309 --> 00:20:06.349
And in particular,
knowing these results

00:20:06.349 --> 00:20:09.109
allows us to make predictions,
to predict the results

00:20:09.109 --> 00:20:10.549
for set a very
simple experiments.

00:20:10.549 --> 00:20:12.508
Now, what we're going to
do for the next bit is

00:20:12.508 --> 00:20:15.111
we're going to run some
simple experiments.

00:20:15.111 --> 00:20:16.610
And we're going to
make predictions.

00:20:16.609 --> 00:20:18.109
And then those
simple experiments

00:20:18.109 --> 00:20:20.548
are going to lead us to more
complicated experiments.

00:20:20.548 --> 00:20:22.589
But let's make sure we
understand the simple ones

00:20:22.589 --> 00:20:23.089
first.

00:20:26.579 --> 00:20:30.980
So for example, let's take
this last experiment, color

00:20:30.980 --> 00:20:33.750
and hardness, and
let's add a color box.

00:20:33.750 --> 00:20:36.089
One more monkey.

00:20:36.089 --> 00:20:41.359
So color in, and
we take those that

00:20:41.359 --> 00:20:44.549
come out the white aperture.

00:20:44.549 --> 00:20:47.669
And we send them
into a hardness box.

00:20:47.670 --> 00:20:49.095
Hard, soft.

00:20:49.095 --> 00:20:50.470
And we take those
electrons which

00:20:50.470 --> 00:20:53.259
come out the soft aperture.

00:20:53.259 --> 00:20:55.829
And now let's send these
again into a color box.

00:20:55.829 --> 00:20:59.220
So it's easy to see
what to predict.

00:20:59.220 --> 00:21:00.420
Black, white.

00:21:02.814 --> 00:21:04.980
So you can imagine a monkey
inside this, going, aha.

00:21:08.829 --> 00:21:11.449
You look at it, you
inspect, it comes out white.

00:21:11.450 --> 00:21:13.670
Here you look at it and
inspect, it comes out soft.

00:21:13.670 --> 00:21:15.259
And you send it
into the color box,

00:21:15.259 --> 00:21:17.480
and what do you
expect to happen?

00:21:17.480 --> 00:21:21.309
Well, let's think
about the logic here.

00:21:21.309 --> 00:21:22.879
Anything reaching
the hardness box

00:21:22.880 --> 00:21:25.851
must have been
measured to be white.

00:21:25.851 --> 00:21:27.600
And we just did the
experiment that if you

00:21:27.599 --> 00:21:29.349
send a white electron
into a hardness box,

00:21:29.349 --> 00:21:31.679
50% of the time it comes
out a hard aperture and 50%

00:21:31.680 --> 00:21:33.910
of the time it comes
out the soft aperture.

00:21:33.910 --> 00:21:35.769
So now we take that
50% of electrons

00:21:35.769 --> 00:21:38.019
that comes out the soft
aperture, which had previously

00:21:38.019 --> 00:21:40.279
been observed to
be white and soft.

00:21:40.279 --> 00:21:42.654
And then we send them into a
color box, and what happens?

00:21:44.990 --> 00:21:46.976
Well, since colors
are repeatable,

00:21:46.976 --> 00:21:49.600
the natural expectation is that,
of course, it comes out white.

00:21:49.599 --> 00:21:53.549
So our prediction,
our natural prediction

00:21:53.549 --> 00:21:58.970
here is that of those electrons
that are incident on this color

00:21:58.970 --> 00:22:09.920
box, 100% should come out white,
and 0% should come out black.

00:22:14.619 --> 00:22:17.339
That seem like a reasonable--
let's just make sure

00:22:17.339 --> 00:22:18.466
that we're all agreeing.

00:22:18.467 --> 00:22:19.050
So let's vote.

00:22:19.049 --> 00:22:21.008
How many people think
this is probably correct?

00:22:23.130 --> 00:22:23.630
OK, good.

00:22:23.630 --> 00:22:26.300
How many people think
this probably wrong?

00:22:26.299 --> 00:22:26.799
OK, good.

00:22:26.799 --> 00:22:29.480
That's reassuring.

00:22:29.480 --> 00:22:31.329
Except you're all wrong.

00:22:31.329 --> 00:22:32.309
Right?

00:22:32.309 --> 00:22:36.899
In fact, what happens is
half of these electrons exit

00:22:36.900 --> 00:22:39.060
white, 50%.

00:22:39.059 --> 00:22:41.919
And 50% percent exit black.

00:22:45.599 --> 00:22:47.349
So let's think about
what's going on here.

00:22:47.349 --> 00:22:48.724
This is really
kind of troubling.

00:22:48.724 --> 00:22:50.449
We've said already
that knowing the color

00:22:50.450 --> 00:22:51.990
doesn't predict the hardness.

00:22:51.990 --> 00:22:54.250
And yet, this electron,
which was previously

00:22:54.250 --> 00:22:57.769
measured to be white, now when
subsequently measured sometimes

00:22:57.769 --> 00:23:00.240
it comes out white,
sometimes it comes out

00:23:00.240 --> 00:23:04.450
black, 50-50% of the time.

00:23:04.450 --> 00:23:05.509
So that's surprising.

00:23:05.509 --> 00:23:07.759
What that tells you is you
can't think of the electron

00:23:07.759 --> 00:23:11.629
as a little ball that has black
and soft written on it, right?

00:23:11.630 --> 00:23:14.216
You can't, because apparently
that black and soft

00:23:14.215 --> 00:23:15.839
isn't a persistent
thing, although it's

00:23:15.839 --> 00:23:17.713
persistent in the sense
that once it's black,

00:23:17.713 --> 00:23:19.649
it stays black.

00:23:19.650 --> 00:23:22.090
So what's going on here?

00:23:22.089 --> 00:23:25.309
Now, I should emphasize
that the same thing happens

00:23:25.309 --> 00:23:30.569
if I had changed this to
taking the black electrons

00:23:30.569 --> 00:23:33.569
and throwing in a hardness and
picking soft and then measuring

00:23:33.569 --> 00:23:35.865
the color, or if I had
used the hard electrons.

00:23:35.865 --> 00:23:37.740
Any of those combinations,
any of these ports

00:23:37.740 --> 00:23:39.448
would have given the
same results, 50-50.

00:23:39.448 --> 00:23:43.190
Is not persistent in this sense.

00:23:43.190 --> 00:23:45.910
Apparently the presence
of the hardness box

00:23:45.910 --> 00:23:48.910
tampers with the color somehow.

00:23:48.910 --> 00:23:52.390
So it's not quite as trivial is
that hyper intelligent monkey.

00:23:52.390 --> 00:23:54.480
Something else is going on here.

00:23:54.480 --> 00:23:56.110
So this is suspicious.

00:23:56.109 --> 00:23:57.750
So here's the
first natural move.

00:23:57.750 --> 00:24:01.119
The first natural move
is, oh, look, surely

00:24:01.119 --> 00:24:04.069
there's some additional
property of the electron

00:24:04.069 --> 00:24:05.829
that we just
haven't measured yet

00:24:05.829 --> 00:24:08.529
that determines whether it
comes out the second color

00:24:08.529 --> 00:24:10.519
box black or white.

00:24:10.519 --> 00:24:15.519
There's got be some property
that determines this.

00:24:15.519 --> 00:24:17.990
And so people have spent
a tremendous amount

00:24:17.990 --> 00:24:20.930
of time and energy looking
at these initial electrons

00:24:20.930 --> 00:24:24.039
and looking with great
care to see whether there's

00:24:24.039 --> 00:24:28.480
any sort of feature of
these incident electrons

00:24:28.480 --> 00:24:30.960
which determines which
port they come out of.

00:24:30.960 --> 00:24:35.170
And the shocker is no one's
ever found such a property.

00:24:35.170 --> 00:24:36.759
No one has ever found
a property which

00:24:36.759 --> 00:24:38.819
determines which
port it comes out of.

00:24:38.819 --> 00:24:41.814
As far as we can tell,
it is completely random.

00:24:45.750 --> 00:24:48.219
Those that flip and
those that don't are

00:24:48.219 --> 00:24:49.509
indistinguishable at beginning.

00:24:49.509 --> 00:24:52.730
And let me just emphasize, if
anyone found such a-- it's not

00:24:52.730 --> 00:24:53.980
like we're not looking, right?

00:24:53.980 --> 00:24:56.849
If anyone found such a
property, fame, notoriety,

00:24:56.849 --> 00:24:59.000
subverting quantum
mechanics, Nobel Prize.

00:24:59.000 --> 00:24:59.930
People have looked.

00:24:59.930 --> 00:25:03.360
And there is none that
anyone's been able to find.

00:25:03.359 --> 00:25:05.829
And as we'll see later on,
using Bell's inequality,

00:25:05.829 --> 00:25:08.799
we can more or less nail
that such things don't exist,

00:25:08.799 --> 00:25:10.134
such a fact doesn't exist.

00:25:10.134 --> 00:25:12.049
But this tells us something
really disturbing.

00:25:12.049 --> 00:25:14.769
This tells us, and this
is the first real shocker,

00:25:14.769 --> 00:25:20.029
that there is something
intrinsically unpredictable,

00:25:20.029 --> 00:25:24.190
non-deterministic, and random
about physical processes

00:25:24.190 --> 00:25:27.100
that we observe in a laboratory.

00:25:27.099 --> 00:25:29.299
There's no way to determine
a priori whether it

00:25:29.299 --> 00:25:32.899
will come out black or
white from the second box.

00:25:32.900 --> 00:25:35.160
Probability in this
experiment, it's

00:25:35.160 --> 00:25:37.080
forced upon us by observations.

00:25:42.190 --> 00:25:45.009
OK, well, there's another
way to come at this.

00:25:45.009 --> 00:25:48.430
You could say, look, you ran
this experiment, that's fine.

00:25:48.430 --> 00:25:52.049
But look, I've met the
guy who built these boxes,

00:25:52.049 --> 00:25:54.200
and look, he's just
some guy, right?

00:25:54.200 --> 00:25:57.080
And he just didn't
do a very good job.

00:25:57.079 --> 00:26:00.519
The boxes are just badly built.

00:26:00.519 --> 00:26:03.269
So here's the way to
defeat that argument.

00:26:03.269 --> 00:26:05.990
No, we've built these things
out of different materials,

00:26:05.990 --> 00:26:09.309
using different technologies,
using electrons, using

00:26:09.309 --> 00:26:14.319
neutrons, using bucky-balls,
C60, seriously, it's been done.

00:26:14.319 --> 00:26:18.961
We've done this experiment, and
this property does not change.

00:26:18.961 --> 00:26:19.670
It is persistent.

00:26:19.670 --> 00:26:22.240
And the thing that's most
upsetting to me is that not

00:26:22.240 --> 00:26:25.890
only do we get the same results
independent of what objects we

00:26:25.890 --> 00:26:29.450
use to run the experiment, we
cannot change the probability

00:26:29.450 --> 00:26:31.970
away from 50-50 at all.

00:26:31.970 --> 00:26:34.920
Within experimental
tolerances, we cannot change,

00:26:34.920 --> 00:26:36.990
no matter how we
build the boxes,

00:26:36.990 --> 00:26:41.441
we cannot change the
probability by part in 100.

00:26:41.441 --> 00:26:41.940
50-50.

00:26:45.880 --> 00:26:49.400
And to anyone who grew up
with determinism from Newton,

00:26:49.400 --> 00:26:52.330
this should hurt.

00:26:52.329 --> 00:26:54.579
This should feel wrong.

00:26:54.579 --> 00:26:56.460
But it's a property
of the real world.

00:26:56.460 --> 00:27:00.084
And our job is going
to be to deal with it.

00:27:00.084 --> 00:27:02.500
Rather, your job is going to
be to deal with it, because I

00:27:02.500 --> 00:27:03.583
went through this already.

00:27:06.940 --> 00:27:08.789
So here's a curious
consequence-- oh,

00:27:08.789 --> 00:27:10.909
any questions before I cruise?

00:27:10.910 --> 00:27:11.470
OK.

00:27:11.470 --> 00:27:15.630
So here's a curious consequence
of this series of experiments.

00:27:15.630 --> 00:27:17.550
Here's something you can't do.

00:27:17.549 --> 00:27:20.049
Are you guys old enough for you
can't do this on television?

00:27:22.829 --> 00:27:24.269
This is so sad.

00:27:24.269 --> 00:27:28.000
OK, so here's
something you can't do.

00:27:28.000 --> 00:27:30.680
We cannot build, it is
impossible to build,

00:27:30.680 --> 00:27:33.717
a reliable color
and hardness box.

00:27:33.717 --> 00:27:35.800
We've built a box that
tells you what color it is.

00:27:35.799 --> 00:27:38.404
We've built a box that tells
you what hardness it is.

00:27:38.404 --> 00:27:42.849
But you cannot build a
meaningful box that tells you

00:27:42.849 --> 00:27:46.719
what color and hardness
an electron is.

00:27:46.720 --> 00:27:49.410
So in particular, what
would this magical box be?

00:27:49.410 --> 00:27:51.700
It would have four ports.

00:27:51.700 --> 00:27:54.840
And its ports would say,
well, one is white and hard,

00:27:54.839 --> 00:27:58.329
and one is white and soft,
one is black and hard,

00:27:58.329 --> 00:28:00.409
and one is black and soft.

00:28:00.410 --> 00:28:02.310
So you can imagine
how you might try

00:28:02.309 --> 00:28:05.609
to build a color
and hardness box.

00:28:05.609 --> 00:28:08.429
So for example, here's
something you might imagine.

00:28:08.430 --> 00:28:12.509
Take your incident
electrons, and first

00:28:12.509 --> 00:28:16.059
send them into a color box.

00:28:16.059 --> 00:28:22.460
And take those white
electrons, and send them

00:28:22.460 --> 00:28:24.779
into a hardness box.

00:28:24.779 --> 00:28:26.579
And take those
electrons, and this

00:28:26.579 --> 00:28:29.089
is going to be white
and hard, and this

00:28:29.089 --> 00:28:31.740
is going to be white and soft.

00:28:31.740 --> 00:28:33.609
And similarly, send
these black electrons

00:28:33.609 --> 00:28:37.779
into the hardness box,
and here's hard and black,

00:28:37.779 --> 00:28:40.339
and here's soft and back.

00:28:45.513 --> 00:28:46.579
Everybody cool with that?

00:28:46.579 --> 00:28:48.266
So this seems to do
the thing I wanted.

00:28:48.267 --> 00:28:50.100
It measures both the
hardness and the color.

00:28:50.099 --> 00:28:53.002
What's the problem with it?

00:28:53.002 --> 00:28:53.877
AUDIENCE: [INAUDIBLE]

00:28:56.715 --> 00:28:58.029
ALLAN ADAMS: Yeah, exactly.

00:28:58.029 --> 00:29:00.019
So the color is not persistent.

00:29:00.019 --> 00:29:03.750
So you tell me this is a soft
and black electron, right?

00:29:03.750 --> 00:29:05.119
That's what you told me.

00:29:05.119 --> 00:29:06.099
Here's the box.

00:29:06.099 --> 00:29:10.159
But if I put a color
box here, that's

00:29:10.160 --> 00:29:12.250
the experiment we just ran.

00:29:12.250 --> 00:29:13.119
And what happens?

00:29:13.119 --> 00:29:15.289
Does this come out black?

00:29:15.289 --> 00:29:17.440
No, this is a crappy
source of black electrons.

00:29:17.440 --> 00:29:19.570
It's 50/50 black and white.

00:29:19.569 --> 00:29:21.705
So this box can't be built.

00:29:21.705 --> 00:29:23.579
And the reason, and I
want to emphasize this,

00:29:23.579 --> 00:29:25.970
the reason we cannot
build this box is not

00:29:25.970 --> 00:29:28.130
because our
experiments are crude.

00:29:28.130 --> 00:29:30.590
And it's not because
I can't build things,

00:29:30.589 --> 00:29:32.189
although that's true.

00:29:32.190 --> 00:29:36.590
I was banned from a lab one
day after joining it, actually.

00:29:36.589 --> 00:29:40.309
So I really can't build,
but other people can.

00:29:40.309 --> 00:29:41.230
And that's not why.

00:29:41.230 --> 00:29:43.490
We can't because of something
much more fundamental,

00:29:43.490 --> 00:29:45.609
something deeper,
something in principle,

00:29:45.609 --> 00:29:50.169
which is encoded in
this awesome experiment.

00:29:50.170 --> 00:29:51.580
This can be done.

00:29:51.579 --> 00:29:55.029
It does not mean anything,
as a consequence.

00:29:55.029 --> 00:29:57.899
It does not mean anything
to say this electron is

00:29:57.900 --> 00:30:04.376
white and hard, because if you
tell me it's white and hard,

00:30:04.375 --> 00:30:06.500
and I measure the white,
well, I know if it's hard,

00:30:06.500 --> 00:30:09.130
it's going to come out 50-50.

00:30:09.130 --> 00:30:11.490
It does not mean anything.

00:30:11.490 --> 00:30:13.309
So this is an important idea.

00:30:13.309 --> 00:30:16.669
This is an idea which
is enshrined in physics

00:30:16.670 --> 00:30:19.420
with a term which
comes with capital

00:30:19.420 --> 00:30:21.509
letters, the
Uncertainty Principle.

00:30:21.509 --> 00:30:24.619
And the Uncertainty Principle
says basically that, look,

00:30:24.619 --> 00:30:27.429
there's some observable,
measurable properties

00:30:27.430 --> 00:30:31.160
of a system which
are incompatible

00:30:31.160 --> 00:30:34.240
with each other in
precisely this way,

00:30:34.240 --> 00:30:36.000
incompatible with each
other in the sense

00:30:36.000 --> 00:30:41.170
not that you can't know, because
you can't know whether it's

00:30:41.170 --> 00:30:43.450
hard and soft
simultaneously, deeper.

00:30:43.450 --> 00:30:47.690
It is not hard and
white simultaneously.

00:30:47.690 --> 00:30:48.600
It cannot be.

00:30:48.599 --> 00:30:50.579
It does not mean
anything to say it

00:30:50.579 --> 00:30:54.769
is hard and white
simultaneously.

00:30:54.769 --> 00:30:56.269
That is uncertainty.

00:30:56.269 --> 00:30:58.289
And again,
uncertainty is an idea

00:30:58.289 --> 00:31:01.289
we're going to come back to
over and over in the class.

00:31:01.289 --> 00:31:02.789
But every time you
think about it,

00:31:02.789 --> 00:31:04.869
this should be the
first place you

00:31:04.869 --> 00:31:06.679
start for the next few weeks.

00:31:09.680 --> 00:31:11.700
Yeah.

00:31:11.700 --> 00:31:14.190
Questions.

00:31:14.190 --> 00:31:16.240
No questions?

00:31:16.240 --> 00:31:16.740
OK.

00:31:16.740 --> 00:31:19.519
So at this point,
it's really tempting

00:31:19.519 --> 00:31:24.325
to think yeah, OK, this
is just about the hardness

00:31:24.325 --> 00:31:25.450
and the color of electrons.

00:31:28.289 --> 00:31:30.619
It's just a weird
thing about electrons.

00:31:30.619 --> 00:31:31.799
It's not a weird thing
about the rest of the world.

00:31:31.799 --> 00:31:33.089
The rest of the world's
completely reasonable.

00:31:33.089 --> 00:31:34.849
And no, that's absolutely wrong.

00:31:34.849 --> 00:31:39.639
Every object in the world
has the same properties.

00:31:39.640 --> 00:31:42.430
If you take bucky-balls,
and you send them

00:31:42.430 --> 00:31:44.180
through the analogous
experiment--

00:31:44.180 --> 00:31:46.340
and I will show you the
data, I think tomorrow,

00:31:46.339 --> 00:31:48.029
but soon, I will
show you the data.

00:31:48.029 --> 00:31:49.529
When you take
bucky-balls and run it

00:31:49.529 --> 00:31:51.980
through a similar experiment,
you get the same effect.

00:31:51.980 --> 00:31:56.870
Now, bucky-balls are huge,
right, 60 carbon atoms.

00:31:56.869 --> 00:31:58.699
But, OK, OK, at
that point, you're

00:31:58.700 --> 00:32:01.430
saying, dude, come on,
huge, 60 carbon atoms.

00:32:01.430 --> 00:32:06.240
So there is a
pendulum, depending

00:32:06.240 --> 00:32:10.870
on how you define building, in
this building, a pendulum which

00:32:10.869 --> 00:32:13.949
is used, in principle which
is used to improve detectors

00:32:13.950 --> 00:32:15.970
to detect gravitational waves.

00:32:15.970 --> 00:32:18.930
There's a pendulum with a,
I think it's 20 kilo mirror.

00:32:21.569 --> 00:32:27.379
And that pendulum exhibits
the same sort of effects here.

00:32:27.380 --> 00:32:29.482
We can see these quantum
mechanical effects

00:32:29.481 --> 00:32:30.190
in those mirrors.

00:32:30.190 --> 00:32:32.259
And this is in breathtakingly
awesome experiments

00:32:32.259 --> 00:32:35.930
done by Nergis Malvalvala, whose
name I can never pronounce,

00:32:35.930 --> 00:32:38.230
but who is totally awesome.

00:32:38.230 --> 00:32:40.015
She's an amazing physicist.

00:32:40.015 --> 00:32:42.390
And she can get these kind of
quantum effects out of a 20

00:32:42.390 --> 00:32:43.720
kilo mirror.

00:32:43.720 --> 00:32:46.259
So before you say something
silly, like, oh, it's

00:32:46.259 --> 00:32:48.400
just electrons, it's
20 kilo mirrors.

00:32:48.400 --> 00:32:50.759
And if I could put you on
a pendulum that accurate,

00:32:50.759 --> 00:32:52.013
it would be you.

00:32:52.013 --> 00:32:53.209
OK?

00:32:53.210 --> 00:32:56.799
These are properties of
everything around you.

00:32:56.799 --> 00:32:59.859
The miracle is not that
electrons behave oddly.

00:32:59.859 --> 00:33:03.189
The miracle is that when you
take 10 to the 27 electrons,

00:33:03.190 --> 00:33:06.570
they behave like cheese.

00:33:06.569 --> 00:33:08.049
That's the miracle.

00:33:08.049 --> 00:33:10.039
This is the underlying
correct thing.

00:33:13.200 --> 00:33:16.490
OK, so this is so far so good.

00:33:16.490 --> 00:33:18.210
But let's go deeper.

00:33:18.210 --> 00:33:21.110
Let's push it.

00:33:21.109 --> 00:33:23.079
And to push it, I
want to design for you

00:33:23.079 --> 00:33:26.960
a slightly more elaborate
apparatus, a slightly more

00:33:26.960 --> 00:33:29.289
elaborate experimental
apparatus.

00:33:29.289 --> 00:33:32.599
And for this, I want you to
consider the following device.

00:33:32.599 --> 00:33:35.490
I'm going to need to introduce a
couple of new features for you.

00:33:35.490 --> 00:33:36.910
Here's a hardness box.

00:33:36.910 --> 00:33:38.740
And it has an in port.

00:33:38.740 --> 00:33:41.250
And the hardness box
has a hard aperture,

00:33:41.250 --> 00:33:43.601
and it has a soft aperture.

00:33:43.601 --> 00:33:45.350
And now, in addition
to this hardness box,

00:33:45.349 --> 00:33:46.849
I'm going to introduce
two elements.

00:33:46.849 --> 00:33:49.674
First, mirrors.

00:33:49.674 --> 00:33:51.799
And what these mirrors do
is they take the incident

00:33:51.799 --> 00:33:53.879
electrons and,
nothing else, they

00:33:53.880 --> 00:33:57.715
change the direction of motion,
change the direction of motion.

00:33:57.714 --> 00:33:59.589
And here's what I mean
by doing nothing else.

00:33:59.589 --> 00:34:02.250
If I take one of these
mirrors, and I take,

00:34:02.250 --> 00:34:03.565
for example, a color box.

00:34:03.565 --> 00:34:05.440
And I take the white
electrons that come out,

00:34:05.440 --> 00:34:08.269
and I bounce it off
the mirror, and then

00:34:08.269 --> 00:34:13.469
I send these into
a color box, then

00:34:13.469 --> 00:34:17.269
they come out white
100% of the time.

00:34:17.269 --> 00:34:19.699
It does not change
the observable color.

00:34:19.699 --> 00:34:20.199
Cool?

00:34:20.199 --> 00:34:21.639
All it does is
change the direction.

00:34:21.639 --> 00:34:22.960
Similarly, with
the hardness box,

00:34:22.960 --> 00:34:24.251
it doesn't change the hardness.

00:34:24.251 --> 00:34:26.780
It just changes the
direction of motion.

00:34:26.780 --> 00:34:29.340
And every experiment we've
ever done on these, guys,

00:34:29.340 --> 00:34:31.860
changes in no way
whatsoever the color

00:34:31.860 --> 00:34:34.539
or the hardness by
subsequent measurement.

00:34:34.539 --> 00:34:35.369
Cool?

00:34:35.369 --> 00:34:37.859
Just changes the
direction of motion.

00:34:37.860 --> 00:34:40.110
And then I'm going to
add another mirror.

00:34:40.110 --> 00:34:43.309
It's actually a slightly
fancy set of mirrors.

00:34:43.309 --> 00:34:45.989
All they do is they join
these beams together

00:34:45.989 --> 00:34:47.001
into a single beam.

00:34:50.688 --> 00:34:52.579
And again, this doesn't
change the color.

00:34:52.579 --> 00:34:53.920
You send in a white
electron, you get out,

00:34:53.920 --> 00:34:55.909
and you measure the
color on the other side,

00:34:55.909 --> 00:34:56.530
you get a white electron.

00:34:56.530 --> 00:34:57.830
You send in a black
electron from here,

00:34:57.829 --> 00:35:00.413
and you measure the color, you
get a black electron again out.

00:35:00.413 --> 00:35:02.137
Cool?

00:35:02.137 --> 00:35:03.095
So here's my apparatus.

00:35:05.509 --> 00:35:07.300
And I'm going to put
this inside a big box.

00:35:09.889 --> 00:35:11.416
And I want to run
some experiments

00:35:11.416 --> 00:35:12.250
with this apparatus.

00:35:22.039 --> 00:35:24.029
Everyone cool with
the basic design?

00:35:24.030 --> 00:35:25.820
Any questions
before I cruise on?

00:35:30.143 --> 00:35:30.809
This part's fun.

00:35:34.724 --> 00:35:36.140
So what I want to
do now is I want

00:35:36.139 --> 00:35:39.440
to run some simple experiments
before we get to fancy stuff.

00:35:39.440 --> 00:35:42.090
And the simple experiments
are just going to warm you up.

00:35:42.090 --> 00:35:43.590
They're going to
prepare you to make

00:35:43.590 --> 00:35:45.430
some predictions and
some calculations.

00:35:45.429 --> 00:35:48.899
And eventually we'd like
to lead back to this guy.

00:35:48.900 --> 00:35:51.690
So the first
experiment, I'm going

00:35:51.690 --> 00:35:53.869
to send in white electrons.

00:35:53.869 --> 00:35:54.405
Whoops.

00:35:54.405 --> 00:35:56.539
Im.

00:35:56.539 --> 00:36:00.320
I'm going to send
in white electrons.

00:36:00.320 --> 00:36:03.620
And I'm going to
measure at the end,

00:36:03.619 --> 00:36:07.869
and in particular at the
output, the hardness.

00:36:15.438 --> 00:36:17.105
So I'm going to send
in white electrons.

00:36:23.367 --> 00:36:24.950
And I'm going to
measure the hardness.

00:36:24.949 --> 00:36:27.500
So this is my apparatus.

00:36:27.501 --> 00:36:29.500
I'm going to measure the
hardness at the output.

00:36:29.500 --> 00:36:30.369
And what I mean by
measure the hardness

00:36:30.369 --> 00:36:32.779
is I throw these electrons
into a hardness box

00:36:32.780 --> 00:36:34.720
and see what comes out.

00:36:34.719 --> 00:36:37.931
So this is experiment 1.

00:36:37.931 --> 00:36:41.889
And let me draw this, let
me biggen the diagram.

00:36:41.889 --> 00:36:49.109
So you send white into-- so the
mechanism is a hardness box.

00:36:49.110 --> 00:36:58.070
Mirror, mirror,
mirrors, and now we're

00:36:58.070 --> 00:36:59.519
measuring the hardness out.

00:37:05.840 --> 00:37:10.950
And the question I want to ask
is how many electrons come out

00:37:10.949 --> 00:37:14.019
the hard aperture, and how
many electrons come out

00:37:14.019 --> 00:37:18.130
the soft aperture of
this final hardness box.

00:37:18.130 --> 00:37:20.220
So I'd like to know what
fraction come out hard,

00:37:20.219 --> 00:37:21.730
and what fraction come out soft.

00:37:21.730 --> 00:37:23.246
I send an initial
white electron,

00:37:23.246 --> 00:37:25.619
for example I took a color
box and took the white output,

00:37:25.619 --> 00:37:28.769
send them into the hardness
box, mirror, mirror,

00:37:28.769 --> 00:37:30.710
hard, hard, soft.

00:37:30.710 --> 00:37:33.030
And what fraction come out
hard, and what fraction

00:37:33.030 --> 00:37:33.680
come out soft.

00:37:38.369 --> 00:37:39.893
So just think about
it for a minute.

00:37:44.530 --> 00:37:47.990
And when you have a prediction
in your head, raise your hand.

00:37:56.630 --> 00:37:57.896
All right, good.

00:37:57.896 --> 00:37:59.230
Walk me through your prediction.

00:38:01.820 --> 00:38:04.390
AUDIENCE: I think
it should be 50-50.

00:38:04.389 --> 00:38:06.980
ALLAN ADAMS: 50-50.

00:38:06.980 --> 00:38:08.295
How come?

00:38:08.295 --> 00:38:10.248
AUDIENCE: [INAUDIBLE]
color doesn't

00:38:10.248 --> 00:38:13.626
have any bearing on hardness.

00:38:13.626 --> 00:38:14.126
[INAUDIBLE]

00:38:20.599 --> 00:38:21.519
ALLAN ADAMS: Awesome.

00:38:21.519 --> 00:38:22.170
So let me say that again.

00:38:22.170 --> 00:38:24.530
So we've done the experiment,
you send a white electron

00:38:24.530 --> 00:38:25.946
into the hardness
box, and we know

00:38:25.945 --> 00:38:27.929
that it's non-predictive, 50-50.

00:38:27.929 --> 00:38:30.904
So if you take a white
electron and you send it

00:38:30.905 --> 00:38:33.879
into the hardness
box, 50% of the time

00:38:33.878 --> 00:38:36.170
it will come out the hard
aperture, and 50% of the time

00:38:36.170 --> 00:38:37.750
it will come out
the soft aperture.

00:38:37.750 --> 00:38:40.726
Now if you take the one that
comes out the hard aperture,

00:38:40.726 --> 00:38:42.559
then you send it up
here or send it up here,

00:38:42.559 --> 00:38:44.929
we know that these
mirrors do nothing

00:38:44.929 --> 00:38:46.719
to the hardness of
the electron except

00:38:46.719 --> 00:38:48.061
change the direction of motion.

00:38:48.061 --> 00:38:49.519
We've already done
that experiment.

00:38:49.519 --> 00:38:52.539
So you measure the hardness at
the output, what do you get?

00:38:52.539 --> 00:38:56.050
Hard, because it came out hard,
mirror, mirror, hardness, hard.

00:38:56.050 --> 00:38:58.060
But it only came out
hard 50% of the time

00:38:58.059 --> 00:39:00.269
because we sent in
initially white electron.

00:39:00.269 --> 00:39:00.869
Yeah?

00:39:00.869 --> 00:39:01.911
What about the other 50%?

00:39:01.911 --> 00:39:04.679
Well, the other 50% of the time,
it comes out the soft aperture

00:39:04.679 --> 00:39:07.211
and follows what I'll
call the soft path

00:39:07.211 --> 00:39:08.849
to the mirror, mirror, hardness.

00:39:08.849 --> 00:39:10.515
And with soft, mirror,
mirror, hardness,

00:39:10.514 --> 00:39:12.096
you know it comes out soft.

00:39:12.097 --> 00:39:13.680
50% of the time it
comes out this way,

00:39:13.679 --> 00:39:14.524
and then it will come out hard.

00:39:14.525 --> 00:39:17.289
50% it follows the soft path,
and then it will come out soft.

00:39:17.289 --> 00:39:18.809
Was this the logic?

00:39:18.809 --> 00:39:20.130
Good.

00:39:20.130 --> 00:39:23.869
How many people agree with this?

00:39:23.869 --> 00:39:24.489
Solid.

00:39:24.489 --> 00:39:27.809
How many people disagree?

00:39:27.809 --> 00:39:29.630
No abstention.

00:39:29.630 --> 00:39:30.280
OK.

00:39:30.280 --> 00:39:35.120
So here's a prediction.

00:39:35.119 --> 00:39:35.839
Oh, yep.

00:39:35.840 --> 00:39:38.220
AUDIENCE: Just a question.

00:39:38.219 --> 00:39:40.599
Could you justify
that prediction

00:39:40.599 --> 00:39:44.411
without talking about oh,
well, half the electrons were

00:39:44.411 --> 00:39:47.000
initially measured to be
hard, and half were initially

00:39:47.000 --> 00:39:48.860
measured to be soft,
by just saying, well,

00:39:48.860 --> 00:39:54.120
we have a hardness box, and
then we joined these electrons

00:39:54.119 --> 00:39:57.045
together again, so we don't
know anything about it.

00:39:57.045 --> 00:40:00.171
So it's just like
sending white electrons

00:40:00.170 --> 00:40:01.801
into one hardness
box instead of two.

00:40:01.802 --> 00:40:04.010
ALLAN ADAMS: Yeah, that's
a really tempting argument,

00:40:04.010 --> 00:40:04.690
isn't it?

00:40:04.690 --> 00:40:05.291
So let's see.

00:40:05.291 --> 00:40:06.750
We're going to see
in a few minutes

00:40:06.750 --> 00:40:09.400
whether that kind of an
argument is reliable or not.

00:40:09.400 --> 00:40:12.389
But so far we've been given two
different arguments that lead

00:40:12.389 --> 00:40:14.759
to the same prediction, 50-50.

00:40:14.760 --> 00:40:15.981
Yeah?

00:40:15.981 --> 00:40:16.480
Question.

00:40:20.414 --> 00:40:23.139
AUDIENCE: Are the electrons
interacting between themselves?

00:40:23.139 --> 00:40:25.932
Like when you get
them to where--

00:40:25.932 --> 00:40:27.641
ALLAN ADAMS: Yeah.

00:40:27.641 --> 00:40:28.849
This is a very good question.

00:40:28.849 --> 00:40:31.900
So here's a question look you're
sending a bunch of electrons

00:40:31.900 --> 00:40:33.519
into this apparatus.

00:40:33.519 --> 00:40:35.813
But if I take--
look, I took 802.

00:40:35.813 --> 00:40:37.230
You take two
electrons and you put

00:40:37.230 --> 00:40:38.769
them close to each
other, what do they do?

00:40:38.769 --> 00:40:39.289
Pyewww.

00:40:39.289 --> 00:40:39.630
Right?

00:40:39.630 --> 00:40:42.140
They interact with each other
through a potential, right?

00:40:42.139 --> 00:40:44.319
So yeah, we're being a
little bold here, throwing

00:40:44.320 --> 00:40:45.080
a bunch of electrons
in and saying,

00:40:45.079 --> 00:40:46.269
oh, they're independent.

00:40:46.269 --> 00:40:47.650
So I'm going to do one better.

00:40:47.650 --> 00:40:49.670
I will send them
in one at a time.

00:40:49.670 --> 00:40:51.950
One electron through
the apparatus.

00:40:51.949 --> 00:40:54.139
And then I will
wait for six weeks.

00:40:54.139 --> 00:40:57.440
[LAUGHTER]

00:40:57.440 --> 00:40:59.280
See, you guys laugh,
you think that's funny.

00:40:59.280 --> 00:41:01.250
But there's a famous
story about a guy

00:41:01.250 --> 00:41:05.190
who did a similar experiment
with photons, French guy.

00:41:05.190 --> 00:41:07.440
And, I mean, the French,
they know what they're doing.

00:41:07.440 --> 00:41:11.720
So he wanted to do the same
experiment with photons.

00:41:11.719 --> 00:41:13.559
But the problem is
if you take a laser

00:41:13.559 --> 00:41:15.219
and you shined it
into your apparatus,

00:41:15.219 --> 00:41:18.189
there there are like, 10
to the 18 photons in there

00:41:18.190 --> 00:41:19.050
at any given moment.

00:41:19.050 --> 00:41:21.633
And the photons, who knows what
they're doing with each other,

00:41:21.632 --> 00:41:23.460
right?

00:41:23.460 --> 00:41:25.925
So I want to send in one
photon, but the problem

00:41:25.925 --> 00:41:28.580
is, it's very hard to get
a single photon, very hard.

00:41:28.579 --> 00:41:31.851
So what he did, I kid you not,
he took an opaque barrier,

00:41:31.851 --> 00:41:34.099
I don't remember what it
was, it was some sort of film

00:41:34.099 --> 00:41:37.619
on top of glass, I think it
was some sort of oil-tar film.

00:41:37.619 --> 00:41:39.389
Barton, do you
remember what he used?

00:41:39.389 --> 00:41:44.650
So he takes a film, and it
has this opaque property,

00:41:44.650 --> 00:41:49.849
such that the photons that are
incident upon it get absorbed.

00:41:49.849 --> 00:41:52.719
Once in a blue moon
a photon manages

00:41:52.719 --> 00:41:53.719
to make its way through.

00:41:53.719 --> 00:41:56.819
Literally, like once
every couple of days,

00:41:56.820 --> 00:41:58.070
or a couple of hours, I think.

00:41:58.070 --> 00:42:01.280
So it's going to
take a long time

00:42:01.280 --> 00:42:02.900
to get any sort of statistics.

00:42:02.900 --> 00:42:05.579
But he this advantage, that
once every couple of hours

00:42:05.579 --> 00:42:07.690
or whatever a photon
makes its way through.

00:42:07.690 --> 00:42:09.273
That means inside
the apparatus, if it

00:42:09.273 --> 00:42:12.280
takes a pico-second to
cross, triumph, right?

00:42:12.280 --> 00:42:13.780
That's the week I
was talking about.

00:42:13.780 --> 00:42:15.850
So he does this experiment.

00:42:15.849 --> 00:42:18.599
But as you can tell, you start
the experiment, you press go,

00:42:18.599 --> 00:42:21.509
and then you wait
for six months.

00:42:21.510 --> 00:42:26.890
Side note on this guy, liked
boats, really liked yachts.

00:42:26.889 --> 00:42:29.253
So he had six months
to wait before doing

00:42:29.253 --> 00:42:31.170
a beautiful experiment
and having the results.

00:42:31.170 --> 00:42:32.650
So what did he do?

00:42:32.650 --> 00:42:35.380
Went on a world
tour in his yacht.

00:42:35.380 --> 00:42:37.990
Comes back, collects the
data, and declares victory,

00:42:37.989 --> 00:42:40.349
because indeed, he saw
the effect he wanted.

00:42:40.349 --> 00:42:41.514
So I was not kidding.

00:42:44.650 --> 00:42:46.389
We really do wait.

00:42:46.389 --> 00:42:49.730
So I will take your challenge.

00:42:49.730 --> 00:42:53.500
And single electron,
throw it in,

00:42:53.500 --> 00:42:56.050
let it go through the
apparatus, takes mere moments.

00:42:56.050 --> 00:42:59.110
Wait for a week, send
in another electron.

00:42:59.110 --> 00:43:02.950
No electrons are
interacting with each other.

00:43:02.949 --> 00:43:07.317
Just a single electron at a time
going through this apparatus.

00:43:07.317 --> 00:43:08.025
Other complaints?

00:43:11.076 --> 00:43:12.579
AUDIENCE: More stories?

00:43:12.579 --> 00:43:13.370
ALLAN ADAMS: Sorry?

00:43:13.369 --> 00:43:14.327
AUDIENCE: More stories?

00:43:14.327 --> 00:43:16.092
ALLAN ADAMS: Oh,
you'll get them.

00:43:16.092 --> 00:43:17.300
I have a hard time resisting.

00:43:17.300 --> 00:43:21.870
So here's a prediction, 50-50.

00:43:21.869 --> 00:43:24.569
We now have two
arguments for this.

00:43:24.570 --> 00:43:26.880
So again, let's vote
after the second argument.

00:43:26.880 --> 00:43:29.710
50-50, how many people?

00:43:29.710 --> 00:43:30.960
You sure?

00:43:30.960 --> 00:43:31.668
Positive?

00:43:31.668 --> 00:43:32.960
How many people don't think so?

00:43:35.670 --> 00:43:37.329
Very small dust.

00:43:37.329 --> 00:43:37.829
OK.

00:43:37.829 --> 00:43:38.949
It's correct.

00:43:38.949 --> 00:43:41.149
Yea.

00:43:41.150 --> 00:43:41.700
So, good.

00:43:46.710 --> 00:43:50.099
I like messing with you guys.

00:43:50.099 --> 00:43:53.346
So remember, we're going to
go through a few experiments

00:43:53.346 --> 00:43:54.719
first where it's
going to be very

00:43:54.719 --> 00:43:55.809
easy to predict the results.

00:43:55.809 --> 00:43:57.509
We've got four experiments
like this to do.

00:43:57.510 --> 00:43:58.890
And then we'll go on to
the interesting examples.

00:43:58.889 --> 00:44:00.900
But we need to go through
them so we know what happens,

00:44:00.900 --> 00:44:03.148
so we can make an empirical
argument rather than an in

00:44:03.148 --> 00:44:03.940
principle argument.

00:44:03.940 --> 00:44:05.272
So there's the first experiment.

00:44:05.273 --> 00:44:07.019
Now, I want to run
the second experiment.

00:44:09.969 --> 00:44:12.480
And the second experiment,
same as the first,

00:44:12.480 --> 00:44:15.199
a little bit louder,
a little bit worse.

00:44:15.199 --> 00:44:16.769
Sorry.

00:44:16.769 --> 00:44:18.960
The second experiment,
we're going

00:44:18.960 --> 00:44:23.590
to send in hard
electrons, and we're

00:44:23.590 --> 00:44:27.900
going to measure color at out.

00:44:31.300 --> 00:44:32.930
So again, let's look
at the apparatus.

00:44:32.929 --> 00:44:34.559
We send in hard electrons.

00:44:34.559 --> 00:44:39.059
And our apparatus
is hardness box

00:44:39.059 --> 00:44:40.704
with a hard and a soft aperture.

00:44:47.728 --> 00:44:50.019
And now we're going to measure
the color at the output.

00:44:53.389 --> 00:44:56.500
Color, what have I been doing?

00:44:58.983 --> 00:45:01.150
And now I want to know what
fraction come out black,

00:45:01.150 --> 00:45:02.525
and what fraction
come out white.

00:45:07.130 --> 00:45:10.269
We're using lots of
monkeys in this process.

00:45:10.269 --> 00:45:11.880
OK, so this is not
rocket science.

00:45:16.030 --> 00:45:17.620
Rocket science isn't
that complicated.

00:45:17.619 --> 00:45:18.786
Neuroscience is much harder.

00:45:18.786 --> 00:45:20.539
This is not neuroscience.

00:45:20.539 --> 00:45:23.710
So let's figure
out what this is.

00:45:23.710 --> 00:45:24.380
Predictions.

00:45:24.380 --> 00:45:25.921
So again, think
about your prediction

00:45:25.920 --> 00:45:27.869
your head, come to
a conclusion, raise

00:45:27.869 --> 00:45:29.202
your hand when you have an idea.

00:45:31.590 --> 00:45:33.339
And just because you
don't raise your hand

00:45:33.340 --> 00:45:34.841
doesn't mean I
won't call on you.

00:45:47.266 --> 00:45:48.599
AUDIENCE: 50-50 black and white.

00:45:48.599 --> 00:45:49.779
ALLAN ADAMS: 50-50
black and white.

00:45:49.780 --> 00:45:50.365
I like it.

00:45:50.364 --> 00:45:51.661
Tell me why.

00:45:51.661 --> 00:45:53.702
AUDIENCE: It's gone through
a hardness box, which

00:45:53.702 --> 00:45:56.269
scrambled the color, and
therefore has to be [INAUDIBLE]

00:45:56.269 --> 00:45:56.570
ALLAN ADAMS: Great.

00:45:56.570 --> 00:45:59.111
So the statement, I'm going to
say that slightly more slowly.

00:45:59.110 --> 00:46:01.629
That was an excellent argument.

00:46:01.630 --> 00:46:02.630
We have a hard electron.

00:46:02.630 --> 00:46:05.097
We know that hardness
boxes are persistent.

00:46:05.097 --> 00:46:07.180
If you send a hard electron
in, it comes out hard.

00:46:07.179 --> 00:46:09.859
So every electron incident
upon our apparatus

00:46:09.860 --> 00:46:13.880
will transit across
the hard trajectory.

00:46:13.880 --> 00:46:16.090
It will bounce, it will
bounce, but it is still hard,

00:46:16.090 --> 00:46:17.309
because we've already
done that experiment.

00:46:17.309 --> 00:46:18.710
The mirrors do nothing
to the hardness.

00:46:18.710 --> 00:46:20.460
So we send a hard electron
into the color box,

00:46:20.460 --> 00:46:21.030
and what comes out?

00:46:21.030 --> 00:46:22.613
Well, we've done
that experiment, too.

00:46:22.612 --> 00:46:24.254
Hard into color, 50-50.

00:46:24.255 --> 00:46:25.640
So the prediction is 50-50.

00:46:25.639 --> 00:46:27.500
This is your prediction.

00:46:27.500 --> 00:46:28.489
Is that correct?

00:46:28.489 --> 00:46:29.089
Awesome.

00:46:29.090 --> 00:46:33.140
OK, let us vote.

00:46:33.139 --> 00:46:36.519
How many people think
this is correct?

00:46:36.519 --> 00:46:37.570
Gusto, I like it.

00:46:37.570 --> 00:46:40.809
How many people think it's not?

00:46:40.809 --> 00:46:41.539
All right.

00:46:41.539 --> 00:46:45.217
Yay, this is correct.

00:46:45.217 --> 00:46:47.050
Third experiment,
slightly more complicated.

00:46:50.409 --> 00:46:54.199
But we have to go through
these to get to the good stuff,

00:46:54.199 --> 00:46:56.219
so humor me for a moment.

00:46:56.219 --> 00:47:02.879
Third, let's send
in white electrons,

00:47:02.880 --> 00:47:10.630
and then measure the
color at the output port.

00:47:10.630 --> 00:47:14.640
So now we send in white
electrons, same beast.

00:47:14.639 --> 00:47:17.519
And our apparatus
is a hardness box

00:47:17.519 --> 00:47:20.605
with a hard path
and a soft path.

00:47:20.606 --> 00:47:26.736
Do-do-do, mirror,
do-do-do, mirror, box,

00:47:26.735 --> 00:47:27.859
join together into our out.

00:47:27.860 --> 00:47:30.720
And now we send those out
electrons into a color box.

00:47:34.960 --> 00:47:39.119
And our color box,
black and white.

00:47:39.119 --> 00:47:41.139
And now the question is
how many come out black,

00:47:41.139 --> 00:47:42.306
and how many come out white.

00:47:44.179 --> 00:47:48.309
Again, think through the
logic, follow the electrons,

00:47:48.309 --> 00:47:49.690
come up with a prediction.

00:47:49.690 --> 00:47:51.481
Raise your hand when
you have a prediction.

00:48:09.958 --> 00:48:18.305
AUDIENCE: Well, earlier
we showed that [INAUDIBLE]

00:48:18.304 --> 00:48:20.098
so it'll take those
paths equally--

00:48:20.099 --> 00:48:21.597
ALLAN ADAMS: With
equal probability.

00:48:21.597 --> 00:48:22.097
Good.

00:48:22.097 --> 00:48:23.032
AUDIENCE: Yeah.

00:48:23.032 --> 00:48:24.795
And then it'll go back
into the color box.

00:48:24.795 --> 00:48:26.378
But earlier when we
did the same thing

00:48:26.378 --> 00:48:29.246
without the weird path-changing,
it came out 50-50 still.

00:48:29.246 --> 00:48:30.372
So I would say still 50-50.

00:48:30.371 --> 00:48:31.161
ALLAN ADAMS: Great.

00:48:31.161 --> 00:48:32.859
So let me say that
again, out loud.

00:48:32.860 --> 00:48:35.980
And tell me if
this is an accurate

00:48:35.980 --> 00:48:37.434
extension of what you said.

00:48:37.434 --> 00:48:38.809
I'm just going to
use more words.

00:48:38.809 --> 00:48:40.409
But it's, I think,
the same logic.

00:48:40.409 --> 00:48:42.539
We have a white electron,
initially white electron.

00:48:42.539 --> 00:48:43.739
We send it into a hardness box.

00:48:43.739 --> 00:48:45.579
When we send a white
electron into a hardness box,

00:48:45.579 --> 00:48:46.579
we know what happens.

00:48:46.579 --> 00:48:49.371
50% of the time it comes
out hard, the hard aperture,

00:48:49.371 --> 00:48:51.329
50% of the time it comes
out the soft aperture.

00:48:51.329 --> 00:48:53.639
Consider those electrons that
came out the hard aperture.

00:48:53.639 --> 00:48:55.029
Those electrons that came
out the hard aperture

00:48:55.030 --> 00:48:56.942
will then transit
across the system,

00:48:56.942 --> 00:48:58.900
preserving their hardness
by virtue of the fact

00:48:58.900 --> 00:49:01.000
that these mirrors preserve
hardness, and end up

00:49:01.000 --> 00:49:01.949
at a color box.

00:49:01.949 --> 00:49:03.859
When they end at
the color box, when

00:49:03.860 --> 00:49:05.860
that electron, the single
electron in the system

00:49:05.860 --> 00:49:07.360
ends at this color
box, then we know

00:49:07.360 --> 00:49:09.450
that a hard electron
entering a color box

00:49:09.449 --> 00:49:11.719
comes out black or
white 50% of the time.

00:49:11.719 --> 00:49:13.919
We've done that experiment, too.

00:49:13.920 --> 00:49:17.320
So for those 50% that came
out hard, we get 50/50.

00:49:17.320 --> 00:49:18.739
Now consider the other 50%.

00:49:18.739 --> 00:49:21.280
The other half of the time, the
single electron in the system

00:49:21.280 --> 00:49:24.059
will come out the soft aperture.

00:49:24.059 --> 00:49:26.350
It will then proceed along
the soft trajectory, bounce,

00:49:26.349 --> 00:49:28.420
bounce, not changing
its hardness,

00:49:28.420 --> 00:49:30.880
and is then a soft electron
incident on the color box.

00:49:30.880 --> 00:49:32.380
But we've also done
that experiment,

00:49:32.380 --> 00:49:34.640
and we get 50-50
out, black and white.

00:49:34.639 --> 00:49:37.469
So those electrons that came
out hard come out 50-50,

00:49:37.469 --> 00:49:40.019
and those electrons that
come out soft come out 50/50.

00:49:40.019 --> 00:49:43.690
And the logic then leads
to 50-50, twice, 50-50.

00:49:46.909 --> 00:49:48.200
Was that an accurate statement?

00:49:48.199 --> 00:49:48.980
Good.

00:49:48.980 --> 00:49:50.579
It's a pretty
reasonable extension.

00:49:50.579 --> 00:49:51.590
OK, let's vote.

00:49:51.590 --> 00:49:54.850
How many people
agree with this one?

00:49:54.849 --> 00:49:58.400
OK, and how many
people disagree?

00:49:58.400 --> 00:49:59.110
Yeah, OK.

00:49:59.110 --> 00:50:01.620
So vast majority agree.

00:50:01.619 --> 00:50:04.500
And the answer is
no, this is wrong.

00:50:04.500 --> 00:50:11.619
In fact, all of these, 100% come
out white and 0 come out black.

00:50:11.619 --> 00:50:15.659
Never ever does an electron
come out the black aperture.

00:50:28.940 --> 00:50:33.159
I would like to quote
what a student just

00:50:33.159 --> 00:50:36.719
said, because it's actually the
next line in my notes, which

00:50:36.719 --> 00:50:38.629
is what the hell is going on?

00:50:42.170 --> 00:50:46.340
So let's the series of
follow up experiments

00:50:46.340 --> 00:50:49.789
to tease out what's
going on here.

00:50:49.789 --> 00:50:51.719
So something very
strange, let's just

00:50:51.719 --> 00:50:55.000
all agree, something very
strange just happened.

00:50:55.000 --> 00:50:57.750
We sent a single electron in.

00:50:57.750 --> 00:50:59.969
And that single electron
comes out the hardness box,

00:50:59.969 --> 00:51:03.864
well, it either came
out the hard aperture

00:51:03.864 --> 00:51:05.109
or the soft aperture.

00:51:05.110 --> 00:51:06.329
And if it came out the
hard, we know what happens,

00:51:06.329 --> 00:51:08.246
if it came out the soft,
we know what happens.

00:51:08.246 --> 00:51:10.930
And it's not 50-50.

00:51:10.929 --> 00:51:16.529
So we need to improve
the situation.

00:51:16.530 --> 00:51:17.846
Hold on a sec.

00:51:17.846 --> 00:51:18.619
Hold on one sec.

00:51:21.192 --> 00:51:22.572
Well, OK, go ahead.

00:51:22.572 --> 00:51:24.780
AUDIENCE: Yeah, it's just
a question about the setup.

00:51:24.780 --> 00:51:27.708
So with the second
hardness box, are we

00:51:27.708 --> 00:51:30.940
collecting both the
soft and hard outputs?

00:51:30.940 --> 00:51:33.816
ALLAN ADAMS: The second, you
mean the first hardness box?

00:51:33.815 --> 00:51:39.019
AUDIENCE: The one-- are
we getting-- no, the--

00:51:39.019 --> 00:51:41.288
ALLAN ADAMS: Which one, sorry?

00:51:41.288 --> 00:51:42.630
This guy?

00:51:42.630 --> 00:51:45.300
Oh, that's a mirror,
not a hardness box.

00:51:45.300 --> 00:51:46.410
Oh, thanks for asking.

00:51:46.409 --> 00:51:47.329
Yeah, sorry.

00:51:47.329 --> 00:51:50.199
I wish I had a better notation
for this, but I don't.

00:51:50.199 --> 00:51:53.909
There's a classic-- well,
I'm not going to go into it.

00:51:53.909 --> 00:51:55.784
Remember that thing
where I can't stop myself

00:51:55.784 --> 00:51:57.839
from telling stories?

00:51:57.840 --> 00:51:59.789
So all this does, it's
just a set of mirrors.

00:51:59.789 --> 00:52:00.956
It's a set of fancy mirrors.

00:52:00.956 --> 00:52:03.019
And all it does is it
takes an electron coming

00:52:03.019 --> 00:52:05.530
this way or an electron coming
this way, and both of them

00:52:05.530 --> 00:52:06.988
get sent out in
the same direction.

00:52:06.987 --> 00:52:08.599
It's like a beam joiner, right?

00:52:08.599 --> 00:52:10.239
It's like a y junction.

00:52:10.239 --> 00:52:11.089
That's all it is.

00:52:11.090 --> 00:52:14.050
So if you will, imagine
the box is a box,

00:52:14.050 --> 00:52:16.830
and you take, I don't
know, Professor Zwiebach,

00:52:16.829 --> 00:52:17.860
and you put him inside.

00:52:17.860 --> 00:52:19.059
And every time an electron
comes up this way,

00:52:19.059 --> 00:52:19.799
he throws it out that
way, and every time

00:52:19.800 --> 00:52:21.440
it comes in this way, he
throws it out that way.

00:52:21.440 --> 00:52:23.856
And he'd be really ticked at
you for putting him in a box,

00:52:23.856 --> 00:52:24.980
but he'd do the job well.

00:52:24.980 --> 00:52:25.480
Yeah.

00:52:25.480 --> 00:52:27.929
AUDIENCE: And this also works if
you go one electron at a time?

00:52:27.929 --> 00:52:30.304
ALLAN ADAMS: This works if
you go one electron at a time,

00:52:30.304 --> 00:52:33.190
this works if you go 14
electrons at a time, it works.

00:52:33.190 --> 00:52:33.940
It works reliably.

00:52:33.940 --> 00:52:34.804
Yeah.

00:52:34.804 --> 00:52:36.704
AUDIENCE: Just,
maybe [INAUDIBLE]

00:52:36.704 --> 00:52:39.018
but what's the difference
between this experiment

00:52:39.018 --> 00:52:39.559
and that one?

00:52:39.559 --> 00:52:41.119
ALLAN ADAMS: Yeah, I know.

00:52:41.119 --> 00:52:41.909
Right?

00:52:41.909 --> 00:52:43.810
Right?

00:52:43.811 --> 00:52:45.559
So the question was,
what's the difference

00:52:45.559 --> 00:52:48.137
between this experiment
and the last one.

00:52:48.137 --> 00:52:48.970
Yeah, good question.

00:52:48.969 --> 00:52:49.969
So we're going to
have to answer that.

00:52:49.969 --> 00:52:50.860
Yeah.

00:52:50.860 --> 00:52:54.788
AUDIENCE: Well, you're
mixing again the hardness.

00:52:54.789 --> 00:52:58.852
So it's like as you weren't
measuring it at all, right?

00:52:58.851 --> 00:53:01.309
ALLAN ADAMS: Apparently it's
a lot we weren't measuring it,

00:53:01.309 --> 00:53:01.809
right?

00:53:01.809 --> 00:53:05.150
Because we send in the white
electron, and at the end

00:53:05.150 --> 00:53:06.869
we get out that
it's still white.

00:53:06.869 --> 00:53:09.639
So somehow this is like
not doing anything.

00:53:09.639 --> 00:53:11.869
But how does that work?

00:53:11.869 --> 00:53:13.329
So that's an
excellent observation.

00:53:13.329 --> 00:53:15.788
And I'm going to build you now
a couple of experiments that

00:53:15.788 --> 00:53:18.630
tease out what's going on.

00:53:18.630 --> 00:53:20.500
And you're not going
to like the answer.

00:53:20.500 --> 00:53:21.001
Yeah.

00:53:21.001 --> 00:53:22.583
AUDIENCE: How were
the white electrons

00:53:22.583 --> 00:53:23.970
generated in this experiment?

00:53:23.969 --> 00:53:24.769
ALLAN ADAMS: The
white electrons were

00:53:24.769 --> 00:53:26.070
generated in the following way.

00:53:26.070 --> 00:53:27.570
I take a random
source of electrons,

00:53:27.570 --> 00:53:31.230
I rub a cat against a balloon
and I charge up the balloon.

00:53:31.230 --> 00:53:33.119
And so I take those
random electrons,

00:53:33.119 --> 00:53:34.519
and I send them
into a color box.

00:53:34.519 --> 00:53:36.275
And we have previously
observed that if you

00:53:36.275 --> 00:53:38.200
take random electrons and
throw them into a color box

00:53:38.199 --> 00:53:40.399
and pull out the electrons that
come out the white aperture,

00:53:40.400 --> 00:53:41.730
if you then send
them into a color box

00:53:41.730 --> 00:53:43.019
again, they're still white.

00:53:43.019 --> 00:53:45.000
So that's how I've
generated them.

00:53:45.000 --> 00:53:47.539
I could have done it by
rubbing the cat against glass,

00:53:47.539 --> 00:53:53.300
or rubbing it against me,
right, just stroke the cat.

00:53:53.300 --> 00:53:55.510
Any randomly selected
set of electrons

00:53:55.510 --> 00:53:57.760
sent into a color box,
and then from which

00:53:57.760 --> 00:53:59.040
you take the white electrons.

00:53:59.039 --> 00:54:01.039
AUDIENCE: So how is it different
from the experiment up there?

00:54:01.039 --> 00:54:01.434
ALLAN ADAMS: Yeah.

00:54:01.434 --> 00:54:02.289
Uh-huh.

00:54:02.289 --> 00:54:03.469
Exactly.

00:54:03.469 --> 00:54:04.256
Yeah.

00:54:04.257 --> 00:54:06.590
AUDIENCE: Is the difference
that you never actually know

00:54:06.590 --> 00:54:07.789
whether the electron's
hard or soft?

00:54:07.789 --> 00:54:09.581
ALLAN ADAMS: That's a
really good question.

00:54:09.581 --> 00:54:12.180
So here's something I'm
going to be very careful not

00:54:12.179 --> 00:54:14.889
to say in this class
to the degree possible.

00:54:14.889 --> 00:54:17.269
I'm not going to use
the word to know.

00:54:17.269 --> 00:54:18.894
AUDIENCE: Well, to
measure. [INAUDIBLE]

00:54:18.894 --> 00:54:19.643
ALLAN ADAMS: Good.

00:54:19.643 --> 00:54:21.289
Measure is a very
slippery word, too.

00:54:21.289 --> 00:54:23.320
I've used it here
because I couldn't really

00:54:23.320 --> 00:54:24.880
get away with not using it.

00:54:24.880 --> 00:54:27.880
But we'll talk about
that in some detail

00:54:27.880 --> 00:54:28.990
later on in the course.

00:54:28.989 --> 00:54:30.447
For the moment, I
want to emphasize

00:54:30.447 --> 00:54:34.409
that it's tempting but dangerous
at this point to talk about

00:54:34.409 --> 00:54:37.069
whether you know or don't
know, or whether someone knows

00:54:37.070 --> 00:54:38.736
or doesn't know, for
example, the monkey

00:54:38.735 --> 00:54:40.250
inside knows or doesn't know.

00:54:40.250 --> 00:54:42.170
So let's try to
avoid that, and focus

00:54:42.170 --> 00:54:44.836
on just operational questions of
what are the things that go in,

00:54:44.836 --> 00:54:46.835
what are the things that
come out, and with what

00:54:46.835 --> 00:54:47.629
probabilities.

00:54:47.630 --> 00:54:49.599
And the reason
that's so useful is

00:54:49.599 --> 00:54:51.889
that it's something
that you can just do.

00:54:51.889 --> 00:54:53.639
There's no ambiguity
about whether you've

00:54:53.639 --> 00:54:55.589
caught a white electron
in a particular spot.

00:54:55.590 --> 00:54:57.374
Now in particular,
the reason these boxes

00:54:57.373 --> 00:55:00.039
are such a powerful tool is that
you don't measure the electron,

00:55:00.039 --> 00:55:01.748
you measure the position
of the electron.

00:55:01.748 --> 00:55:03.990
You get hit by the
electron or you don't.

00:55:03.989 --> 00:55:07.589
And by using these boxes we
can infer from their position

00:55:07.590 --> 00:55:09.690
the color or the hardness.

00:55:09.690 --> 00:55:12.269
And that's the reason
these boxes are so useful.

00:55:12.269 --> 00:55:14.063
So we're inferring from
the position, which

00:55:14.063 --> 00:55:15.480
is easy to measure,
you get beaned

00:55:15.480 --> 00:55:18.130
or you don't, we're
inferring the property

00:55:18.130 --> 00:55:20.300
that we're interested in.

00:55:20.300 --> 00:55:21.800
It's a really good
question, though.

00:55:21.800 --> 00:55:23.230
Keep it in the
back of your mind.

00:55:23.230 --> 00:55:25.188
And we'll talk about it
on and off for the rest

00:55:25.188 --> 00:55:26.809
of the semester.

00:55:26.809 --> 00:55:27.648
Yeah.

00:55:27.648 --> 00:55:29.690
AUDIENCE: So what happens
if you have this setup,

00:55:29.690 --> 00:55:32.510
and you just take away
the bottom right mirror?

00:55:32.510 --> 00:55:33.760
ALLAN ADAMS: Perfect question.

00:55:33.760 --> 00:55:35.385
This leads me into
the next experiment.

00:55:35.385 --> 00:55:36.516
So here's the modification.

00:55:36.516 --> 00:55:38.139
But thank you, that's
a great question.

00:55:38.139 --> 00:55:40.949
Here's the modification
of this experiment.

00:55:40.949 --> 00:55:44.573
So let's rig up a
small-- hold on,

00:55:44.574 --> 00:55:46.740
I want to go through the
next series of experiments,

00:55:46.739 --> 00:55:47.829
and then I'll come
back to questions.

00:55:47.829 --> 00:55:49.079
And these are great questions.

00:55:49.079 --> 00:55:53.360
So I want to rig up a small
movable wall, a small movable

00:55:53.360 --> 00:55:53.910
barrier.

00:55:53.909 --> 00:55:56.049
And here's what this
movable barrier will do.

00:56:00.710 --> 00:56:07.233
If I put the barrier in, so
this would be in the soft path,

00:56:07.233 --> 00:56:08.900
when I put the barrier
in the soft path,

00:56:08.900 --> 00:56:12.590
it absorbs all electrons
incident upon it

00:56:12.590 --> 00:56:15.400
and impedes them
from proceeding.

00:56:15.400 --> 00:56:19.519
So you put a barrier in here,
put a barrier in the soft path,

00:56:19.519 --> 00:56:20.929
no electrons continue through.

00:56:20.929 --> 00:56:24.109
An electron incident
cannot continue through.

00:56:24.110 --> 00:56:27.041
When I say that the
barrier is out, what I mean

00:56:27.041 --> 00:56:28.000
is it's not in the way.

00:56:28.000 --> 00:56:29.739
I've moved it out of the way.

00:56:29.739 --> 00:56:31.159
Cool?

00:56:31.159 --> 00:56:34.449
So I want to run
the same experiment.

00:56:34.449 --> 00:56:38.739
And I want to run this
experiment using the barriers

00:56:38.739 --> 00:56:42.784
to tease out how the electrons
transit through our apparatus.

00:56:47.280 --> 00:56:48.940
So experiment four.

00:56:52.340 --> 00:56:55.519
Let's send in a
white electron again.

00:56:55.519 --> 00:56:57.849
I want to do the same
experiment we just did.

00:56:57.849 --> 00:57:06.900
And color at out, but now with
the wall in the soft path.

00:57:06.900 --> 00:57:10.349
Wall in soft.

00:57:10.349 --> 00:57:13.500
So that's this experiment.

00:57:13.500 --> 00:57:19.670
So we send in white
electrons, and at the output

00:57:19.670 --> 00:57:25.550
we measure the color as before.

00:57:25.550 --> 00:57:33.185
And the question is what
fraction come out black,

00:57:33.184 --> 00:57:34.559
and what fraction
come out white.

00:57:40.028 --> 00:57:42.070
So again, everyone think
through it for a second.

00:57:42.070 --> 00:57:42.861
Just take a second.

00:57:44.759 --> 00:57:46.050
And this one's a little sneaky.

00:57:46.050 --> 00:57:50.267
So feel free to discuss it with
the person sitting next to you.

00:57:50.266 --> 00:57:53.759
[CHATTER]

00:59:00.782 --> 00:59:01.740
ALLAN ADAMS: All right.

00:59:04.380 --> 00:59:06.880
All right, now that everyone
has had a quick second

00:59:06.880 --> 00:59:08.680
to think through
this one, let me just

00:59:08.679 --> 00:59:10.944
talk through what I'd
expect from the point

00:59:10.945 --> 00:59:11.820
of these experiments.

00:59:11.820 --> 00:59:14.950
And then we'll talk about
whether this is reasonable.

00:59:14.949 --> 00:59:16.870
So the first thing I
expect is that, look,

00:59:16.871 --> 00:59:18.619
if I send in a white
electron and I put it

00:59:18.619 --> 00:59:20.993
into a hardness pass, I know
that 50% of the time it goes

00:59:20.994 --> 00:59:22.980
out hard, and 50% of the
time it goes out soft.

00:59:22.980 --> 00:59:24.869
If it goes out
the soft aperture,

00:59:24.869 --> 00:59:27.965
it's going to get eaten
by the barrier, right?

00:59:27.965 --> 00:59:29.589
It's going to get
eaten by the barrier.

00:59:29.590 --> 00:59:31.730
So first thing I predict
is that the output

00:59:31.730 --> 00:59:34.210
should be down by 50%.

00:59:37.170 --> 00:59:39.389
However, here's an
important bit of physics.

00:59:39.389 --> 00:59:41.014
And this comes to
the idea of locality.

00:59:44.110 --> 00:59:47.079
I didn't tell you
this, but these

00:59:47.079 --> 00:59:52.860
armlinks in the experiment I
did, 3,000 kilometers long.

00:59:52.860 --> 00:59:56.000
3,000 kilometers long.

00:59:56.000 --> 00:59:57.380
That's too minor.

00:59:57.380 --> 00:59:59.349
10 million kilometers long.

00:59:59.349 --> 01:00:00.969
Really long.

01:00:00.969 --> 01:00:01.469
Very long.

01:00:04.190 --> 01:00:06.463
Now, imagine an
electron that enters

01:00:06.463 --> 01:00:07.880
this, an initially
white electron.

01:00:07.880 --> 01:00:11.090
If we had the barriers out,
if the barrier was out,

01:00:11.090 --> 01:00:12.015
what do we get?

01:00:14.690 --> 01:00:15.599
100% white, right?

01:00:15.599 --> 01:00:17.639
We just did this
experiment, to our surprise.

01:00:17.639 --> 01:00:18.629
So if we did this, we get 100%.

01:00:18.630 --> 01:00:20.030
And that means an
electron, any electron,

01:00:20.030 --> 01:00:21.780
going along the soft
path comes out white.

01:00:21.780 --> 01:00:24.430
Any electron going along the
hard path goes out white.

01:00:24.429 --> 01:00:27.269
They all come out white.

01:00:27.269 --> 01:00:29.550
So now, imagine I do this.

01:00:29.550 --> 01:00:33.140
Imagine we put a barrier in
here 2 million miles away

01:00:33.139 --> 01:00:36.019
from this path.

01:00:36.019 --> 01:00:37.844
How does a hard
electron along this path

01:00:37.844 --> 01:00:39.260
know that I put
the barrier there?

01:00:39.260 --> 01:00:41.710
And I'm going to make it
even more sneaky for you.

01:00:41.710 --> 01:00:44.500
I'm going to insert the
barrier along the path

01:00:44.500 --> 01:00:49.059
after I launched the
electron into the apparatus.

01:00:49.059 --> 01:00:53.469
And when I send in the electron,
I will not know at that moment,

01:00:53.469 --> 01:00:55.519
nor will the electron
know, because, you

01:00:55.519 --> 01:00:58.070
know, they're not very
smart, whether the barrier is

01:00:58.070 --> 01:00:58.809
in place.

01:00:58.809 --> 01:01:02.329
And this is going to be millions
of miles away from this guy.

01:01:02.329 --> 01:01:05.150
So an electron out
here can't know.

01:01:05.150 --> 01:01:06.220
It hasn't been there.

01:01:06.219 --> 01:01:07.889
It just hasn't been there.

01:01:07.889 --> 01:01:08.819
It can't know.

01:01:08.820 --> 01:01:10.820
But we know that when
we ran this apparatus

01:01:10.820 --> 01:01:14.575
without the barrier in there,
they came out 100% white.

01:01:14.574 --> 01:01:16.699
But it can't possibly know
whether the barrier's in

01:01:16.699 --> 01:01:18.460
there or not, right?

01:01:18.460 --> 01:01:19.340
It's over here.

01:01:22.320 --> 01:01:25.309
So what this tells us is that
we should expect the output

01:01:25.309 --> 01:01:26.949
to be down by 50%.

01:01:26.949 --> 01:01:30.980
But all the electrons
that do make

01:01:30.980 --> 01:01:33.318
it through must come
out white, because they

01:01:33.318 --> 01:01:35.110
didn't know that there
was a barrier there.

01:01:35.110 --> 01:01:36.693
They didn't go along that path.

01:01:40.010 --> 01:01:40.510
Yeah.

01:01:40.510 --> 01:01:42.259
AUDIENCE: Not trying
to be wise, but why

01:01:42.259 --> 01:01:43.860
are you using the word know?

01:01:43.860 --> 01:01:46.035
ALLAN ADAMS: Oh,
sorry, thank you.

01:01:46.034 --> 01:01:48.659
Thank you, thank you, thank you,
that was a slip of the tongue.

01:01:48.659 --> 01:01:50.299
I was making fun
of the electron.

01:01:50.300 --> 01:01:53.810
So in that particular
case, I was not

01:01:53.809 --> 01:01:55.509
referring to my
or your knowledge.

01:01:55.510 --> 01:01:56.884
I was referring
to the electron's

01:01:56.884 --> 01:01:58.630
tragically
impoverished knowledge.

01:02:01.369 --> 01:02:02.177
Yeah.

01:02:02.177 --> 01:02:04.567
AUDIENCE: But if they come
out one at a time white,

01:02:04.568 --> 01:02:06.320
then wouldn't we know
then with certainty

01:02:06.320 --> 01:02:09.826
that that electron is
both hard and white,

01:02:09.826 --> 01:02:11.996
which is like a violation?

01:02:11.996 --> 01:02:14.119
ALLAN ADAMS: Well, here's
the more troubling thing.

01:02:14.119 --> 01:02:17.069
Imagine it didn't
come out 100% white.

01:02:17.070 --> 01:02:20.170
Then the electron would
have demonstrably not

01:02:20.170 --> 01:02:22.990
go along the soft path.

01:02:22.989 --> 01:02:25.239
It would have demonstrably
gone through the hard path,

01:02:25.239 --> 01:02:27.114
because that's the only
path available to it.

01:02:27.114 --> 01:02:29.519
And yet, it would still have
known that millions of miles

01:02:29.519 --> 01:02:31.860
away, there's a barrier
on a path it didn't take.

01:02:31.860 --> 01:02:34.099
So which one's more
upsetting to you?

01:02:36.719 --> 01:02:40.869
And personally, I find this one
the less upsetting of the two.

01:02:40.869 --> 01:02:43.369
So the prediction is our
output should down by 50%,

01:02:43.369 --> 01:02:44.951
because a half of
them get eaten.

01:02:44.952 --> 01:02:46.410
But they should
all come out white,

01:02:46.409 --> 01:02:47.867
because those that
didn't get eaten

01:02:47.867 --> 01:02:50.469
can't possibly know that
there was a barrier here,

01:02:50.469 --> 01:02:53.480
millions of miles away.

01:02:53.480 --> 01:02:55.621
So we run this experiment.

01:02:55.621 --> 01:02:57.079
And here's the
experimental result.

01:02:57.079 --> 01:02:59.319
In fact, the experimental
result is yes, the output

01:02:59.320 --> 01:03:00.510
is down by 50%.

01:03:00.510 --> 01:03:04.340
But no, not 100%
white, 50% white.

01:03:07.869 --> 01:03:08.799
50% white.

01:03:11.849 --> 01:03:14.309
The barrier, if we put the
barrier in the hardness path.

01:03:14.309 --> 01:03:16.549
If we put the barrier
in the hardness path,

01:03:16.550 --> 01:03:20.170
still down by 50%, and
it's at odds, 50-50.

01:03:23.050 --> 01:03:25.295
How could the electron know?

01:03:25.295 --> 01:03:26.170
I'm making fun of it.

01:03:26.170 --> 01:03:27.095
Yeah.

01:03:27.094 --> 01:03:29.309
AUDIENCE: So I
guess my question is

01:03:29.309 --> 01:03:31.110
before we ask how it
knows that there's

01:03:31.110 --> 01:03:34.309
a block in one of the paths,
how does it know, before,

01:03:34.309 --> 01:03:37.072
over there, that there were
two paths, and combine again?

01:03:37.072 --> 01:03:38.030
ALLAN ADAMS: Excellent.

01:03:38.030 --> 01:03:38.630
Exactly.

01:03:38.630 --> 01:03:40.650
So actually, this
problem was there already

01:03:40.650 --> 01:03:41.730
in the experiment we did.

01:03:41.730 --> 01:03:43.480
All we've done here
is tease out something

01:03:43.480 --> 01:03:44.869
that was existing in the
experiment, something

01:03:44.869 --> 01:03:45.889
that was disturbing.

01:03:45.889 --> 01:03:48.619
The presence of those
mirrors, and the option

01:03:48.619 --> 01:03:51.319
of taking two paths,
somehow changed

01:03:51.320 --> 01:03:53.370
the way the electron behaved.

01:03:53.369 --> 01:03:54.829
How is that possible?

01:03:54.829 --> 01:03:56.549
And here, we're seeing
that very sharply.

01:03:56.550 --> 01:03:58.140
Thank you for that
excellent observation.

01:03:58.139 --> 01:03:58.420
Yeah.

01:03:58.420 --> 01:04:00.340
AUDIENCE: What if you
replaced the two mirrors

01:04:00.340 --> 01:04:04.660
with color boxes, so that
both color boxes [INAUDIBLE]

01:04:07.539 --> 01:04:10.039
ALLAN ADAMS: Yeah.

01:04:10.039 --> 01:04:12.909
So the question is basically,
let's take this experiment,

01:04:12.909 --> 01:04:16.000
and let's make it even more
intricate by, for example,

01:04:16.000 --> 01:04:18.429
replacing these
mirrors by color boxes.

01:04:18.429 --> 01:04:20.690
So here's the thing
I want to emphasize.

01:04:23.440 --> 01:04:25.894
I strongly encourage you to
think through that example.

01:04:25.893 --> 01:04:28.559
And in particular, think through
that example, come to my office

01:04:28.559 --> 01:04:31.599
hours, and ask me about it.

01:04:31.599 --> 01:04:33.949
So that's going to be setting
a different experiment.

01:04:33.949 --> 01:04:34.889
And different
experiments are going

01:04:34.889 --> 01:04:36.230
to have different results.

01:04:36.230 --> 01:04:37.340
So we're going to have to
deal with that on a case

01:04:37.340 --> 01:04:38.090
by case basis.

01:04:38.090 --> 01:04:38.994
It's an interesting
example, but it's

01:04:38.994 --> 01:04:41.440
going to take us a bit afar
from where we are right now.

01:04:41.440 --> 01:04:43.869
But after we get to the
punchline from this,

01:04:43.869 --> 01:04:46.619
come to my office hours and
ask me exactly that question.

01:04:46.619 --> 01:04:47.719
Yeah.

01:04:47.719 --> 01:04:51.209
AUDIENCE: So we had a color
box, we put in white electrons

01:04:51.210 --> 01:04:53.470
and we got 50-50, like random.

01:04:53.469 --> 01:04:55.159
How do you know the boxes work?

01:04:55.159 --> 01:04:56.909
ALLAN ADAMS: How do I
know the boxes work?

01:04:56.909 --> 01:04:58.309
These are the same boxes
we used from the beginning.

01:04:58.309 --> 01:04:59.349
We tested them over and over.

01:04:59.349 --> 01:05:01.599
AUDIENCE: How did you first
check that it was working?

01:05:01.599 --> 01:05:03.594
[INAUDIBLE]

01:05:03.594 --> 01:05:04.969
ALLAN ADAMS: How
to say-- there's

01:05:04.969 --> 01:05:07.759
no other way to build a box
that does the properties that we

01:05:07.760 --> 01:05:10.260
want, which is that you send
in color and it comes out color

01:05:10.260 --> 01:05:13.207
again, and the mirrors
behave this way.

01:05:13.206 --> 01:05:15.289
Any box that does those
first set of things, which

01:05:15.289 --> 01:05:17.869
is what I will call a
color box, does this, too.

01:05:17.869 --> 01:05:19.279
There's no other way to do it.

01:05:19.280 --> 01:05:21.484
I don't mean just because
like, no one's tested--

01:05:21.483 --> 01:05:23.400
AUDIENCE: Because you
can't actually check it,

01:05:23.400 --> 01:05:26.499
you can't actually [INAUDIBLE]
you know which one is white.

01:05:26.498 --> 01:05:27.789
ALLAN ADAMS: Oh, sure, you can.

01:05:27.789 --> 01:05:29.170
You take the electron that
came out of the color box.

01:05:29.170 --> 01:05:30.650
That's what we mean
by saying it's white.

01:05:30.650 --> 01:05:31.369
AUDIENCE: [INAUDIBLE]

01:05:31.369 --> 01:05:32.911
ALLAN ADAMS: But
that's what it means

01:05:32.911 --> 01:05:34.579
to say the electron is white.

01:05:34.579 --> 01:05:35.819
It's like, how do you know
that my name is Allan?

01:05:35.820 --> 01:05:37.220
You say, Allan, and I go, what?

01:05:37.219 --> 01:05:37.589
Right?

01:05:37.590 --> 01:05:40.131
But you're like, look that's
not a test of whether I'm Allan.

01:05:40.130 --> 01:05:41.916
It's like, well,
what is the test?

01:05:41.916 --> 01:05:42.750
That's how you test.

01:05:42.750 --> 01:05:43.230
What's your name?

01:05:43.230 --> 01:05:43.449
I'm Allan.

01:05:43.449 --> 01:05:44.739
Oh, great, that's your name.

01:05:44.739 --> 01:05:46.109
So that's what I mean by white.

01:05:46.110 --> 01:05:48.110
Now you might quibble
that that's a stupid thing

01:05:48.110 --> 01:05:49.070
to call an electron.

01:05:49.070 --> 01:05:50.460
And I grant you that.

01:05:50.460 --> 01:05:53.710
But it is nonetheless a property
that I can empirically engage.

01:05:53.710 --> 01:05:55.932
OK, so I've been told
that I never ask questions

01:05:55.931 --> 01:05:57.139
from the people on the right.

01:05:57.139 --> 01:05:57.632
Yeah.

01:05:57.632 --> 01:05:59.715
AUDIENCE: Is it important
whether the experimenter

01:05:59.715 --> 01:06:02.069
knows if the wall
is there or not?

01:06:02.070 --> 01:06:03.140
ALLAN ADAMS: No.

01:06:03.139 --> 01:06:06.929
This experiment has been done
again by some French guys.

01:06:06.929 --> 01:06:08.849
The French, look, dude.

01:06:08.849 --> 01:06:12.860
So there's this guy,
Alain Aspect, ahh,

01:06:12.860 --> 01:06:14.719
great experimentalist,
great physicist.

01:06:14.719 --> 01:06:16.510
And he's done lots of
beautiful experiments

01:06:16.510 --> 01:06:17.590
on exactly this topic.

01:06:17.590 --> 01:06:20.500
And send me an email, and
I'll post some example papers

01:06:20.500 --> 01:06:23.639
and reviews by him-- and he's a
great writer-- on the web page.

01:06:23.639 --> 01:06:25.960
So just send me an email
to remind me of that.

01:06:25.960 --> 01:06:29.554
OK, so we're lowish on
time, so let me move on.

01:06:29.554 --> 01:06:30.970
So what I want to
do now is I want

01:06:30.969 --> 01:06:32.719
to take the lesson of this
experiment and the observation

01:06:32.719 --> 01:06:35.389
that was made a minute ago, that
in fact the same problem was

01:06:35.389 --> 01:06:37.603
present when we ran this
experiment and go 100%.

01:06:37.603 --> 01:06:39.269
We should have been
freaked out already.

01:06:39.269 --> 01:06:41.353
And I want to think through
what that's telling us

01:06:41.353 --> 01:06:43.579
about the electron,
the single electron,

01:06:43.579 --> 01:06:45.324
as it transits the apparatus.

01:06:52.059 --> 01:06:56.969
The thing is, at this point
we're in real trouble.

01:06:56.969 --> 01:06:58.149
And here's the reason.

01:06:58.150 --> 01:07:02.541
Consider a single electron
inside the apparatus.

01:07:02.541 --> 01:07:05.000
And I want to think about the
electron inside the apparatus

01:07:05.000 --> 01:07:06.840
while all walls are out.

01:07:06.840 --> 01:07:09.430
So it's this experiment.

01:07:09.429 --> 01:07:11.889
Consider the single electron.

01:07:11.889 --> 01:07:15.629
We know, with total confidence,
with complete reliability,

01:07:15.630 --> 01:07:17.552
that every electron
will exit this color box

01:07:17.552 --> 01:07:18.510
out the white aperture.

01:07:18.510 --> 01:07:19.380
We've done this experiment.

01:07:19.380 --> 01:07:20.829
We know it will come out white.

01:07:20.829 --> 01:07:21.329
Yes?

01:07:23.922 --> 01:07:26.320
Here's my question.

01:07:26.320 --> 01:07:27.319
Which route did it take?

01:07:34.579 --> 01:07:37.219
AUDIENCE: Spoiler.

01:07:37.219 --> 01:07:39.619
ALLAN ADAMS: Not a spoiler.

01:07:39.619 --> 01:07:41.349
Which route did it take?

01:07:41.349 --> 01:07:43.230
AUDIENCE: Why do
we care what route?

01:07:43.230 --> 01:07:44.938
ALLAN ADAMS: I'm asking
you the question.

01:07:44.938 --> 01:07:46.369
That's why you care.

01:07:46.369 --> 01:07:47.750
I'm the professor here.

01:07:47.750 --> 01:07:49.210
What is this?

01:07:49.210 --> 01:07:51.445
Come on.

01:07:51.445 --> 01:07:52.445
Which route did it take?

01:07:56.219 --> 01:07:58.909
OK, let's think through
the possibilities.

01:07:58.909 --> 01:08:00.836
Grapple with this
question in your belly.

01:08:00.836 --> 01:08:02.420
Let's think through
the possibilities.

01:08:02.420 --> 01:08:05.099
First off, did it take
the hardness path?

01:08:05.099 --> 01:08:07.413
So as it transits through,
the single electron

01:08:07.414 --> 01:08:08.830
transiting through
this apparatus,

01:08:08.829 --> 01:08:10.913
did it take the hard path
or did it take the soft?

01:08:10.913 --> 01:08:13.800
These are millions of miles
long, millions of miles apart.

01:08:13.800 --> 01:08:15.733
This is not a
ridiculous question.

01:08:15.733 --> 01:08:17.649
Did it go millions of
miles in that direction,

01:08:17.649 --> 01:08:19.619
or millions of miles
in that direction?

01:08:19.619 --> 01:08:22.630
Did it take the hardness path?

01:08:22.630 --> 01:08:25.688
Ladies and gentlemen, did
it take the hard path?

01:08:25.688 --> 01:08:26.270
AUDIENCE: Yes.

01:08:29.250 --> 01:08:31.029
ALLAN ADAMS: Well, we
ran this experiment

01:08:31.029 --> 01:08:33.000
by putting a wall
in the soft path.

01:08:33.000 --> 01:08:35.681
And if we put a wall
in the soft path,

01:08:35.681 --> 01:08:37.139
then we know it
took the hard path,

01:08:37.140 --> 01:08:38.539
because no other
electrons come out

01:08:38.539 --> 01:08:40.414
except those that went
through the hard path.

01:08:40.414 --> 01:08:40.979
Correct?

01:08:40.979 --> 01:08:43.850
On the other hand, if it
went through the hard path,

01:08:43.850 --> 01:08:46.189
it would come out
50% of the time white

01:08:46.189 --> 01:08:48.390
and 50% of the time black.

01:08:48.390 --> 01:08:52.069
But in fact, in this apparatus
it comes out always 100% white.

01:08:52.069 --> 01:08:55.221
It cannot have
taken the hard path.

01:08:55.220 --> 01:08:55.719
No.

01:08:59.399 --> 01:09:01.387
Did it take the soft path?

01:09:05.140 --> 01:09:08.579
Same argument,
different side, right?

01:09:08.579 --> 01:09:10.220
No.

01:09:10.220 --> 01:09:12.729
Well, this is not looking good.

01:09:12.729 --> 01:09:16.550
Well, look, this was suggested.

01:09:16.550 --> 01:09:19.260
Maybe it took both.

01:09:19.260 --> 01:09:21.760
Maybe electrons are
sneaky little devils

01:09:21.760 --> 01:09:24.729
that split in two, and part of
it goes one way and part of it

01:09:24.729 --> 01:09:27.539
goes the other.

01:09:27.539 --> 01:09:29.729
Maybe it took both paths.

01:09:29.729 --> 01:09:30.729
So this is easy.

01:09:30.729 --> 01:09:31.609
We can test this one.

01:09:31.609 --> 01:09:35.970
And here is how I'm
going to test this one.

01:09:35.970 --> 01:09:37.220
Oh, sorry.

01:09:37.220 --> 01:09:39.000
Actually, I'm not
going to do that yet.

01:09:39.000 --> 01:09:40.404
So we can test this one.

01:09:40.404 --> 01:09:43.029
So if it took both paths, here's
what you should be able to do.

01:09:43.029 --> 01:09:46.729
You should be able to put
a detector along each path,

01:09:46.729 --> 01:09:48.463
and you'd be able
to follow, if you've

01:09:48.463 --> 01:09:50.028
got half an electron on one
side and half an electron

01:09:50.029 --> 01:09:51.609
on the other, or
maybe two electrons,

01:09:51.609 --> 01:09:53.569
one on each side and
one on the other.

01:09:53.569 --> 01:09:54.770
So this is the thing
that you'd predict

01:09:54.770 --> 01:09:55.720
if you said it went both.

01:09:55.720 --> 01:09:56.720
So here's what we'll do.

01:09:56.720 --> 01:09:57.690
We will take detectors.

01:09:57.689 --> 01:09:59.409
We will put one along
the hard path and one

01:09:59.409 --> 01:10:00.242
along the soft path.

01:10:00.243 --> 01:10:02.620
We will run the experiment
and then observe

01:10:02.619 --> 01:10:05.349
whether, and ask whether,
we see two electrons,

01:10:05.349 --> 01:10:06.890
we see half and
half, what do we see.

01:10:06.890 --> 01:10:10.990
The answer is you always,
always see one electron on one

01:10:10.989 --> 01:10:12.139
of the paths.

01:10:12.140 --> 01:10:14.320
You never see half an electron.

01:10:14.319 --> 01:10:15.750
You never see a
squishy electron.

01:10:15.750 --> 01:10:18.949
You see one electron
on one path, period.

01:10:18.949 --> 01:10:20.539
It did not take both.

01:10:20.539 --> 01:10:25.720
You never see an electron split
in two, divided, confused.

01:10:25.720 --> 01:10:28.275
No.

01:10:28.274 --> 01:10:30.479
Well, it didn't
take the hard path,

01:10:30.479 --> 01:10:33.729
didn't take the soft
path, it didn't take both.

01:10:33.729 --> 01:10:35.579
There's one option left.

01:10:35.579 --> 01:10:36.157
Neither.

01:10:36.157 --> 01:10:36.989
Well, I say neither.

01:10:36.989 --> 01:10:40.724
But what about neither?

01:10:40.724 --> 01:10:41.390
And that's easy.

01:10:41.390 --> 01:10:44.869
Let's put a barrier
in both paths.

01:10:44.869 --> 01:10:46.489
And then what happens?

01:10:46.489 --> 01:10:48.739
Nothing comes out.

01:10:48.739 --> 01:10:49.369
So no.

01:10:55.050 --> 01:10:58.650
So now, to repeat an
earlier prescient remark

01:10:58.649 --> 01:11:01.759
from one of the
students, what the hell?

01:11:01.760 --> 01:11:03.220
So here's the
world we're facing.

01:11:03.220 --> 01:11:04.100
I want you to think about this.

01:11:04.100 --> 01:11:05.020
Take this seriously.

01:11:05.020 --> 01:11:05.930
Here's the world we're facing.

01:11:05.930 --> 01:11:07.846
And when I say, here's
the world we're facing,

01:11:07.845 --> 01:11:09.379
I don't mean just
these experiments.

01:11:09.380 --> 01:11:14.250
I mean the world around you,
20 kilo mirrors, bucky-balls,

01:11:14.250 --> 01:11:15.899
here is what they do.

01:11:15.899 --> 01:11:19.939
When you send them through
an apparatus like this,

01:11:19.939 --> 01:11:22.679
every single object that
goes through this apparatus

01:11:22.680 --> 01:11:25.960
does not take the hard path,
it does not take the soft path,

01:11:25.960 --> 01:11:29.789
it doesn't take both, and
it does not take neither.

01:11:29.789 --> 01:11:31.449
And that pretty much
exhausts the set

01:11:31.449 --> 01:11:34.840
of logical possibilities.

01:11:34.840 --> 01:11:40.300
So what are electrons doing when
they're inside the apparatus?

01:11:40.300 --> 01:11:43.250
How do you describe that
electron inside the apparatus?

01:11:43.250 --> 01:11:44.720
You can't say it's
on one path, you

01:11:44.720 --> 01:11:46.039
can't say it's on the
other, it's not on both,

01:11:46.039 --> 01:11:47.039
and it's not on neither.

01:11:47.039 --> 01:11:51.269
What is it doing halfway
through this experiment?

01:11:51.270 --> 01:11:52.967
So if our experiments
are accurate,

01:11:52.966 --> 01:11:54.799
and to the best of our
ability to determine,

01:11:54.800 --> 01:12:00.890
they are, and if our arguments
are correct, and that's on me,

01:12:00.890 --> 01:12:02.930
then they're doing
something, these electrons

01:12:02.930 --> 01:12:05.300
are doing something we've
just never thought of before,

01:12:05.300 --> 01:12:06.931
something we've never
dreamt of before,

01:12:06.931 --> 01:12:08.389
something for which
we don't really

01:12:08.390 --> 01:12:11.760
have good words in
the English language.

01:12:11.760 --> 01:12:16.710
Apparently, empirically,
electrons have a way of moving,

01:12:16.710 --> 01:12:19.970
electrons have a way of being
which is unlike anything

01:12:19.970 --> 01:12:22.130
that we're used
to thinking about.

01:12:22.130 --> 01:12:23.930
And so do molecules.

01:12:23.930 --> 01:12:25.630
And so do bacteria.

01:12:25.630 --> 01:12:28.170
So does chalk.

01:12:28.170 --> 01:12:32.390
It's just harder to
detect in those objects.

01:12:32.390 --> 01:12:35.430
So physicists have a name
for this new mode of being.

01:12:35.430 --> 01:12:36.682
And we call it superposition.

01:12:39.829 --> 01:12:42.250
Now, at the moment,
superposition

01:12:42.250 --> 01:12:45.649
is code for I have no
idea what's going on.

01:12:48.720 --> 01:12:51.369
Usage of the word superposition
would go something like this.

01:12:51.369 --> 01:12:55.170
An initially white electron
inside this apparatus

01:12:55.170 --> 01:12:59.960
with the walls out is
neither hard, nor soft,

01:12:59.960 --> 01:13:01.029
nor both, nor neither.

01:13:01.029 --> 01:13:04.949
It is, in fact, in a
superposition of being hard

01:13:04.949 --> 01:13:07.929
and of being soft.

01:13:07.930 --> 01:13:09.600
This is why we
can't meaningfully

01:13:09.600 --> 01:13:13.530
say this electron is some
color and some hardness.

01:13:13.529 --> 01:13:16.679
Not because our boxes are crude,
and not because we're ignorant,

01:13:16.680 --> 01:13:20.220
though our boxes are
crude and we are ignorant.

01:13:20.220 --> 01:13:21.240
It's deeper.

01:13:21.239 --> 01:13:25.949
Having a definite color means
not having a definite hardness,

01:13:25.949 --> 01:13:28.849
but rather being in a
superposition of being hard

01:13:28.850 --> 01:13:31.550
and being soft.

01:13:31.550 --> 01:13:40.300
Every electron exits a hardness
box either hard or soft.

01:13:40.300 --> 01:13:43.630
But not every electron
is hard or soft.

01:13:43.630 --> 01:13:48.619
It can also be a superposition
of being hard or being soft.

01:13:48.619 --> 01:13:51.239
The probability
that we subsequently

01:13:51.239 --> 01:13:54.699
measure it to be
hard or soft depends

01:13:54.699 --> 01:13:59.429
on precisely what
superposition it is.

01:13:59.430 --> 01:14:01.900
For example, we know
that if an electron is

01:14:01.899 --> 01:14:05.729
in the superposition
corresponding to being white

01:14:05.729 --> 01:14:08.839
then there are even odds
of it being subsequently

01:14:08.840 --> 01:14:10.960
measured be hard or to be soft.

01:14:13.800 --> 01:14:18.619
So to build a better
definition of superposition

01:14:18.619 --> 01:14:22.029
than I have no idea
what's going on

01:14:22.029 --> 01:14:23.579
is going to require
a new language.

01:14:23.579 --> 01:14:26.309
And that language is
quantum mechanics.

01:14:26.310 --> 01:14:28.630
And the underpinnings
of this language

01:14:28.630 --> 01:14:29.970
are the topic of the course.

01:14:29.970 --> 01:14:31.780
And developing a
better understanding

01:14:31.779 --> 01:14:35.050
of this idea of
superposition is what

01:14:35.050 --> 01:14:38.329
you have to do over
the next three months.

01:14:38.329 --> 01:14:42.380
Now, if all of this
troubles your intuition,

01:14:42.380 --> 01:14:44.800
well, that shouldn't
be too surprising.

01:14:44.800 --> 01:14:49.630
Your intuition was developed
by throwing spears, and running

01:14:49.630 --> 01:14:52.909
from tigers, and catching
toast as it jumps out

01:14:52.909 --> 01:14:58.069
of the toaster, all of
which involves things so big

01:14:58.069 --> 01:15:01.409
and with so much energy that
quantum effects are negligible.

01:15:04.310 --> 01:15:05.920
As a friend of
mine likes to say,

01:15:05.920 --> 01:15:09.777
you don't need to know quantum
mechanics to make chicken soup.

01:15:09.777 --> 01:15:11.984
However, when we work in
very different regimes, when

01:15:11.984 --> 01:15:15.920
we work with atoms, when we work
with molecules, when we work

01:15:15.920 --> 01:15:18.010
in the regime of very
low energies and very

01:15:18.010 --> 01:15:23.869
small objects, your intuition
is just not a reasonable guide.

01:15:23.869 --> 01:15:26.319
It's not that the electrons--
and I cannot emphasize this

01:15:26.319 --> 01:15:30.460
strongly enough-- it is not
that the electrons are weird.

01:15:30.460 --> 01:15:33.159
The electrons do
what electrons do.

01:15:33.159 --> 01:15:34.170
This is what they do.

01:15:34.170 --> 01:15:37.430
And it violates your
intuition, but it's true.

01:15:37.430 --> 01:15:40.100
The thing that's surprising
is that lots of electrons

01:15:40.100 --> 01:15:42.420
behave like this.

01:15:42.420 --> 01:15:47.090
Lots of electrons behave
like cheese and chalk.

01:15:47.090 --> 01:15:49.569
And that's the goal
of 804, to step

01:15:49.569 --> 01:15:52.684
beyond your daily experience
and your familiar intuition

01:15:52.685 --> 01:15:57.039
and to develop an intuition
for this idea of superposition.

01:15:57.039 --> 01:15:59.069
And we'll start in
the next lecture.

01:15:59.069 --> 01:16:01.739
I'll see you on Thursday.