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[00:21] ALLAN ADAMS: Hi everyone.
[00:24] Welcome to 804 for spring 2013.
[00:27] This is the fourth, and
presumably final time
[00:29] that I will be
teaching this class.
[00:31] So I'm pretty excited about it.
[00:33] So my name is Allan Adams.
[00:34] I'll be lecturing the course.
[00:37] I'm an assistant
professor in Course 8.
[00:40] I study string theory
and its applications
[00:43] to gravity, quantum gravity,
and condensed matter physics.
[00:48] Quantum mechanics, this is a
course in quantam mechanics.
[00:52] Quantam mechanics Is
my daily language.
[00:54] Quantum mechanics
is my old friend.
[00:57] I met quantum
mechanics 20 years ago.
[00:59] I just realized that last night.
[01:00] It was kind of depressing.
[01:01] So, old friend.
[01:03] It's also my most powerful tool.
[01:07] So I'm pretty psyched about it.
[01:10] Our recitation instructors
are Barton Zwiebach, yea!
[01:15] And Matt Evans-- yea!
[01:18] Matt's new to the
department, so welcome him.
[01:20] Hi.
[01:23] So he just started
his faculty position,
[01:25] which is pretty awesome.
[01:26] And our TA is Paolo Glorioso.
[01:28] Paolo, are you here?
[01:29] Yea!
[01:30] There you go.
[01:30] OK, so he's the person to
send all complaints to.
[01:35] So just out of curiosity, how
many of you all are Course 8?
[01:41] Awesome.
[01:41] How many of you all
are, I don't know, 18?
[01:45] Solid.
[01:46] 6?
[01:47] Excellent.
[01:49] 9?
[01:51] No one?
[01:52] This is the first year we
haven't had anyone Course 9.
[01:54] That's a shame.
[01:57] Last year one of
the best students
[01:58] was a Course 9 student.
[01:59] So two practical things to know.
[02:01] The first thing is
everything that we put out
[02:04] will be on the Stellar website.
[02:06] Lecture notes, homeworks,
exams, everything
[02:09] is going to be done through
Stellar, including your grades.
[02:12] The second thing
is that as you may
[02:14] notice there are rather
more lights than usual.
[02:16] I'm wearing a mic.
[02:17] And there are these signs up.
[02:19] We're going to be
videotaping this course
[02:21] for the lectures for OCW.
[02:23] And if you're happy
with that, cool.
[02:27] If not, just sit on
the sides and you
[02:29] won't appear anywhere on video.
[02:31] Sadly, I can't do that.
[02:33] But you're welcome
to if you like.
[02:36] But hopefully that should
not play a meaningful role
[02:39] in any of the lectures.
[02:47] So the goal of 804 is for you
to learn quantum mechanics.
[02:50] And by learn
quantum mechanics, I
[02:51] don't mean to learn
how to do calculations,
[02:54] although that's an important
and critical thing.
[02:56] I mean learn some intuition.
[02:57] I want you to develop
some intuition
[02:59] for quantum phenomena.
[03:00] Now, quantam
mechanics is not hard.
[03:03] It has a reputation
for being a hard topic.
[03:05] It is not a super hard topic.
[03:10] So in particular,
everyone in this room,
[03:12] I'm totally positive, can
learn quantum mechanics.
[03:15] It does require
concerted effort.
[03:17] It's not a trivial topic.
[03:20] And in order to really
develop a good intuition,
[03:24] the essential thing
is to solve problems.
[03:26] So the way you develop
a new intuition
[03:28] is by solving problems
and by dealing
[03:31] with new situations, new
context, new regimes, which
[03:34] is what we're
going to do in 804.
[03:36] It's essential that you work
hard on the problem sets.
[03:40] So your job is to devote
yourself to the problem sets.
[03:43] My job is to convince you
at the end of every lecture
[03:47] that the most interesting
thing you could possibly
[03:49] do when you leave
is the problem set.
[03:53] So you decide who
has the harder job.
[03:57] So the workload is not so bad.
[04:00] So we have problem
sets due, they're
[04:02] due in the physics box in
the usual places, by lecture,
[04:05] by 11 AM sharp on
Tuesdays every week.
[04:10] Late work, no, not so much.
[04:13] But we will drop one
problem set to make up
[04:14] for unanticipated events.
[04:18] We'll return the
graded problem sets
[04:20] a week later in recitation.
[04:22] Should be easy.
[04:23] I strongly, strongly
encourage you
[04:26] to collaborate with other
students on your problem sets.
[04:28] You will learn more,
they will learn more,
[04:31] it will be more efficient.
[04:32] Work together.
[04:34] However, write your
problem sets yourself.
[04:37] That's the best way for
you to develop and test
[04:39] your understanding.
[04:42] There will be two midterms,
dates to be announced,
[04:45] and one final.
[04:46] I guess we could have
multiple, but that
[04:48] would be a little exciting.
[04:50] We're going to use clickers,
and clickers will be required.
[04:53] We're not going to
take attendance,
[04:54] but they will give
a small contribution
[04:56] to your overall grade.
[04:57] And we'll use them
most importantly
[04:59] for non-graded but just
participation concept questions
[05:02] and the occasional in class
quiz to probe your knowledge.
[05:06] This is mostly so that
you have a real time
[05:08] measure of your own conceptual
understanding of the material.
[05:13] This has been
enormously valuable.
[05:15] And something I want
to say just right off
[05:16] is that the way I've
organized this class
[05:18] is not so much based on
the classes I was taught.
[05:21] It's based to the degree
possible on empirical lessons
[05:24] about what works
in teaching, what
[05:27] actually makes you learn better.
[05:29] And clickers are an
excellent example of that.
[05:31] So this is mostly a
standard lecture course,
[05:34] but there will be clickers used.
[05:36] So by next week I need
you all to have clickers,
[05:40] and I need you to register
them on the TSG website.
[05:49] I haven't chosen a
specific textbook.
[05:50] And this is discussed
on the Stellar web page.
[05:52] There are a set of textbooks,
four textbooks that I strongly
[05:55] recommend, and a set of others
that are nice references.
[05:58] The reason for this is twofold.
[05:59] First off, there
are two languages
[06:01] that are canonically used
for quantum mechanics.
[06:03] One is called wave
mechanics, and the language,
[06:07] the mathematical language is
partial differential equations.
[06:09] The other is a matrix mechanics.
[06:11] They have big names.
[06:13] And the language there
is linear algebra.
[06:15] And different books
emphasize different aspects
[06:18] and use different languages.
[06:20] And they also try to aim
at different problems.
[06:22] Some books are
aimed towards people
[06:23] who are interested in materials
science, some books that
[06:25] are aimed towards people
interested in philosophy.
[06:27] And depending on
what you want, get
[06:29] the book that's suited to you.
[06:32] And every week I'll be providing
with your problem sets readings
[06:35] from each of the
recommended texts.
[06:38] So what I really encourage you
to do is find a group of people
[06:40] to work with every
week, and make sure
[06:42] that you've got all the
books covered between you.
[06:45] This'll give you as
much access to the texts
[06:47] as possible without forcing
you to buy four books, which
[06:49] I would discourage
you from doing.
[06:54] So finally I guess
the last thing to say
[06:56] is if this stuff
were totally trivial,
[06:59] you wouldn't need to be here.
[07:02] So ask questions.
[07:04] If you're confused
about something,
[07:06] lots of other
people in the class
[07:07] are also going to be confused.
[07:08] And if I'm not answering your
question without you asking,
[07:11] then no one's getting
the point, right?
[07:12] So ask questions.
[07:13] Don't hesitate to interrupt.
[07:14] Just raise your hand, and I
will do my best to call on you.
[07:17] And this is true
for both in lecture,
[07:19] also go to office
hours and recitations.
[07:21] Ask questions.
[07:23] I promise, there's no such
thing as a terrible question.
[07:25] Someone else will
also be confused.
[07:28] So it's a very valuable
to me and everyone else.
[07:34] So before I get going
on the actual physics
[07:36] content of the class, are there
any other practical questions?
[07:42] Yeah.
[07:43] AUDIENCE: You said there
was a lateness policy.
[07:45] ALLAN ADAMS: Lateness policy.
[07:45] No late work is
accepted whatsoever.
[07:49] So the deal is given that
every once in a while,
[07:52] you know, you'll be
walking to school
[07:53] and your leg is
going to fall off,
[07:55] or a dog's going to jump out
and eat your person standing
[07:58] next to you, whatever.
[08:01] Things happen.
[08:02] So we will drop your
lowest problem set score
[08:04] without any questions.
[08:05] At the end of the
semester, we'll
[08:07] just dropped your lowest score.
[08:08] And if you turn
them all in, great,
[08:10] whatever your lowest
score was, fine.
[08:11] If you missed one, then gone.
[08:13] On the other hand, if
you know next week, I'm
[08:16] going to be attacked
by a rabid squirrel,
[08:18] it's going to be
horrible, I don't
[08:19] want to have to worry
about my problem set.
[08:20] Could we work this out?
[08:21] So if you know ahead
of time, come to us.
[08:23] But you need to do that
well ahead of time.
[08:25] The night before doesn't count.
[08:26] OK?
[08:27] Yeah.
[08:28] AUDIENCE: Will we be
able to watch the videos?
[08:30] ALLAN ADAMS: You know,
that's an excellent question.
[08:31] I don't know.
[08:32] I don't think so.
[08:34] I think it's going to happen
at the end of the semester.
[08:37] Yeah.
[08:37] OK.
[08:37] So no, you'll be able to watch
them later on the OCW website.
[08:45] Other questions.
[08:47] Yeah.
[08:47] AUDIENCE: Are there
any other videos
[08:48] that you'd recommend, just
like other courses on YouTube?
[08:51] ALLAN ADAMS: Oh.
[08:51] That's an interesting question.
[08:54] I don't off the top of my head,
but if you send me an email,
[08:57] I'll pursue it.
[08:57] Because I do know several
other lecture series
[08:59] that I like very
much, but I don't
[09:01] know if they're available
on YouTube or publicly.
[09:03] So send me an email
and I'll check.
[09:05] Yeah.
[09:05] AUDIENCE: So how about
the reading assignments?
[09:07] ALLAN ADAMS: Reading assignments
on the problem set every week
[09:10] will be listed.
[09:11] There will be equivalent
reading from every textbook.
[09:13] And if there is
something missing,
[09:15] like if no textbook
covers something,
[09:16] I'll post a separate reading.
[09:18] Every once in a while, I'll
post auxiliary readings,
[09:20] and they'll be available
on the Stellar website.
[09:22] So for example, in your problem
set, first one was posted,
[09:25] will be available
immediately after lecture
[09:27] on the Stellar website.
[09:28] There are three papers
that it refers to, or two,
[09:32] and they are posted
on the Stellar website
[09:34] and linked from the problem set.
[09:38] Others?
[09:41] OK.
[09:41] So the first lecture.
[09:45] The content of the physics
of the first lecture
[09:48] is relatively standalone.
[09:51] It's going to be an introduction
to a basic idea then is
[09:53] going to haunt,
plague, and charm us
[09:55] through the rest
of the semester.
[10:00] The logic of this
lecture is based
[10:02] on a very beautiful discussion
in the first few chapters
[10:05] of a book by David Albert
called Quantum Mechanics
[10:07] and Experience.
[10:09] It's a book for philosophers.
[10:10] But the first few chapters,
a really lovely introduction
[10:13] at a non-technical level.
[10:14] And I encourage you to
take a look at them,
[10:16] because they're very lovely.
[10:19] But it's to be sure
straight up physics.
[10:25] Ready?
[10:27] I love this stuff.
[10:30] today I want to describe
to you a particular set
[10:34] of experiments.
[10:35] Now, to my mind, these are the
most unsettling experiments
[10:41] ever done.
[10:43] These experiments
involve electrons.
[10:46] They have been performed,
and the results
[10:49] as I will describe
them are true.
[10:53] I'm going to focus on two
properties of electrons.
[10:56] I will call them
color and hardness.
[11:05] And these are not
the technical names.
[11:07] We'll learn the technical
names for these properties
[11:09] later on in the semester.
[11:10] But to avoid distracting you
by preconceived notions of what
[11:13] these things mean, I'm going
to use ambiguous labels, color
[11:16] and hardness.
[11:17] And the empirical fact is that
every electron, every electron
[11:27] that's ever been observed
is either black or white
[11:34] and no other color.
[11:35] We've never seen
a blue electron.
[11:37] There are no green electrons.
[11:38] No one has ever found
a fluorescent electron.
[11:40] They're either black,
or they are white.
[11:42] It is a binary property.
[11:45] Secondly, their hardness
is either hard or soft.
[11:50] They're never squishy.
[11:52] No one's ever found
one that dribbles.
[11:54] They are either hard,
or they are soft.
[11:56] Binary properties.
[11:57] OK?
[12:00] Now, what I mean
by this is that it
[12:04] is possible to
build a device which
[12:07] measures the color
and the hardness.
[12:09] In particular, it
is possible to build
[12:11] a box, which I will call a color
box, that measures the color.
[12:16] And the way it works is this.
[12:17] It has three apertures,
an in port and two out
[12:21] ports, one which sends
out black electrons
[12:25] and one which sends
out white electrons.
[12:32] And the utility of this
box is that the color
[12:36] can be inferred
from the position.
[12:38] If you find the particle,
the electron over here,
[12:40] it is a white electron.
[12:41] If you find the electron
here, it is a black electron.
[12:44] Cool?
[12:46] Similarly, we can
build a hardness box,
[12:50] which again has three
apertures, an in port.
[12:52] And hard electrons
come out this port,
[12:59] and soft electrons
come out this port.
[13:10] Now, if you want, you're free
to imagine that these boxes are
[13:14] built by putting
a monkey inside.
[13:20] And you send in an
electron, and the monkey,
[13:22] you know, with the ears,
looks at the electron,
[13:26] and says it's a hard electron,
it sends it out one way,
[13:28] or it's a soft electron,
it sends it out the other.
[13:31] The workings inside
do not matter.
[13:32] And in particular,
later in the semester
[13:34] I will describe in
considerable detail
[13:37] the workings inside
this apparatus.
[13:39] And here's something I
want to emphasize to you.
[13:41] It can be built in
principle using monkeys,
[13:44] hyper intelligent monkeys
that can see electrons.
[13:46] It could also be built using
magnets and silver atoms.
[13:50] It could be done with neutrons.
[13:51] It could be done with all sorts
of different technologies.
[13:54] And they all give
precisely the same results
[13:56] as I'm about to describe.
[13:59] They all give precisely
the same results.
[14:01] So it does not
matter what's inside.
[14:04] But if you want a
little idea, you
[14:05] could imagine putting a monkey
inside, a hyper intelligent
[14:08] monkey.
[14:10] I know, it sounds good.
[14:16] So a key property of these
hardness boxes and color boxes
[14:21] is that they are repeatable.
[14:23] And here's what I mean by that.
[14:25] If I send in an electron,
and I find that it comes out
[14:29] of a color box black, and
then I send it in again,
[14:32] then if I send it into
another color box,
[14:34] it comes out black again.
[14:38] So in diagrams, if I send
in some random electron
[14:44] to a color box, and I discover
that it comes out, let's say,
[14:48] the white aperture.
[14:50] And so here's dot dot dot, and
I take the ones that come out
[14:53] the white aperture, and I send
them into a color box again.
[14:56] Then with 100% confidence,
100% of the time, the electron
[15:02] coming out of the white port
incident on the color box
[15:04] will come out the
white aperture again.
[15:05] And 0% of the time will it
come out the black aperture.
[15:09] So this is a
persistent property.
[15:11] You notice that it's white.
[15:12] You measure it again,
it's still white.
[15:14] Do a little bit later,
it's still white.
[15:16] OK?
[15:17] It's a persistent property.
[15:20] Ditto the hardness.
[15:21] If I send in a bunch of
electrons in to a hardness box,
[15:25] here is an important thing.
[15:26] Well, send them
into a hardness box,
[15:29] and I take out the ones
that come out soft.
[15:32] And I send them again
into a hardness box,
[15:34] and they come out soft.
[15:36] They will come
out soft with 100%
[15:38] confidence, 100% of the time.
[15:40] Never do they come
out the hard aperture.
[15:52] Any questions at this point?
[15:59] So here's a natural question.
[16:07] Might the color and the hardness
of an electron be related?
[16:13] And more precisely,
might they be correlated?
[16:18] Might knowing the color infer
something about the hardness?
[16:21] So for example, so being
male and being a bachelor
[16:26] are correlated properties,
because if you're male,
[16:28] you don't know if you're
a bachelor or not,
[16:30] but if you're a
bachelor, you're male.
[16:32] That's the definition
of the word.
[16:34] So is it possible that
color and hardness
[16:36] are similarly correlated?
[16:39] So, I don't know, there
are lots of good examples,
[16:41] like wearing a red shirt and
beaming down to the surface
[16:44] and making it back
to the Enterprise
[16:46] later after the
away team returns.
[16:48] Correlated, right?
[16:49] Negatively, but correlated.
[16:52] So the question
is, suppose, e.g.,
[16:55] suppose we know that
an electron is white.
[17:02] Does that determine
the hardness?
[17:10] So we can answer this
question by using our boxes.
[17:15] So here's what I'm going to do.
[17:16] I'm going to take some
random set of electrons.
[17:19] That's not random.
[17:20] Random.
[17:22] And I'm going to send
them in to a color box.
[17:24] And I'm going to take
the electrons that
[17:26] come out the white aperture.
[17:27] And here's a useful fact.
[17:28] When I say random, here's
operationally what I mean.
[17:31] I take some piece of
material, I scrape it,
[17:33] I pull off some electrons,
and they're totally
[17:36] randomly chosen
from the material.
[17:37] And I send them in.
[17:38] If I send a random pile of
electrons into a color box,
[17:41] useful thing to know, they
come out about half and half.
[17:44] It's just some
random assortment.
[17:45] Some of them are white,
some of them come out black.
[17:49] Suppose I send some random
collection of electrons
[17:51] into a color box.
[17:52] And I take those which come
out the white aperture.
[17:55] And I want to know, does
white determine hardness.
[17:57] So I can do that, check, by then
sending these white electrons
[18:01] into a hardness box and
seeing what comes out.
[18:09] Hard, soft.
[18:11] And what we find is that 50%
of those electrons incident
[18:17] on the hardness box come out
hard, and 50% come out soft.
[18:26] OK?
[18:27] And ditto if we reverse this.
[18:28] If we take hardness, and take,
for example, a soft electron
[18:32] and send it into a color
box, we again get 50-50.
[18:45] So if you take a white
electron, you send it
[18:46] into a hardness box,
you're at even odds,
[18:49] you're at chance
as to whether it's
[18:50] going to come out hard or soft.
[18:52] And similarly, if you
send a soft electron
[18:54] into a color box,
even odds it's going
[18:56] to come out black or white.
[18:58] So knowing the hardness
does not give you
[18:59] any information about the
color, and knowing the color
[19:02] does not give you any
information about the hardness.
[19:05] cool?
[19:06] These are independent facts,
independent properties.
[19:08] They're not correlated
in this sense,
[19:11] in precisely this
operational sense.
[19:15] Cool?
[19:18] Questions?
[19:20] OK.
[19:24] So measuring the color
give zero predictive power
[19:26] for the hardness, and
measuring the hardness
[19:28] gives zero predictive
power for the color.
[19:34] And from that, I will
say that these properties
[19:36] are correlated.
[19:37] So H, hardness, and color are
in this sense uncorrelated.
[19:55] So using these properties of
the color and hardness boxes,
[19:59] I want to run a few
more experiment's.
[20:00] I want to probe these
properties of color and hardness
[20:03] a little more.
[20:04] And in particular,
knowing these results
[20:06] allows us to make predictions,
to predict the results
[20:09] for set a very
simple experiments.
[20:10] Now, what we're going to
do for the next bit is
[20:12] we're going to run some
simple experiments.
[20:15] And we're going to
make predictions.
[20:16] And then those
simple experiments
[20:18] are going to lead us to more
complicated experiments.
[20:20] But let's make sure we
understand the simple ones
[20:22] first.
[20:26] So for example, let's take
this last experiment, color
[20:30] and hardness, and
let's add a color box.
[20:33] One more monkey.
[20:36] So color in, and
we take those that
[20:41] come out the white aperture.
[20:44] And we send them
into a hardness box.
[20:47] Hard, soft.
[20:49] And we take those
electrons which
[20:50] come out the soft aperture.
[20:53] And now let's send these
again into a color box.
[20:55] So it's easy to see
what to predict.
[20:59] Black, white.
[21:02] So you can imagine a monkey
inside this, going, aha.
[21:08] You look at it, you
inspect, it comes out white.
[21:11] Here you look at it and
inspect, it comes out soft.
[21:13] And you send it
into the color box,
[21:15] and what do you
expect to happen?
[21:17] Well, let's think
about the logic here.
[21:21] Anything reaching
the hardness box
[21:22] must have been
measured to be white.
[21:25] And we just did the
experiment that if you
[21:27] send a white electron
into a hardness box,
[21:29] 50% of the time it comes
out a hard aperture and 50%
[21:31] of the time it comes
out the soft aperture.
[21:33] So now we take that
50% of electrons
[21:35] that comes out the soft
aperture, which had previously
[21:38] been observed to
be white and soft.
[21:40] And then we send them into a
color box, and what happens?
[21:44] Well, since colors
are repeatable,
[21:46] the natural expectation is that,
of course, it comes out white.
[21:49] So our prediction,
our natural prediction
[21:53] here is that of those electrons
that are incident on this color
[21:58] box, 100% should come out white,
and 0% should come out black.
[22:14] That seem like a reasonable--
let's just make sure
[22:17] that we're all agreeing.
[22:18] So let's vote.
[22:19] How many people think
this is probably correct?
[22:23] OK, good.
[22:23] How many people think
this probably wrong?
[22:26] OK, good.
[22:26] That's reassuring.
[22:29] Except you're all wrong.
[22:31] Right?
[22:32] In fact, what happens is
half of these electrons exit
[22:36] white, 50%.
[22:39] And 50% percent exit black.
[22:45] So let's think about
what's going on here.
[22:47] This is really
kind of troubling.
[22:48] We've said already
that knowing the color
[22:50] doesn't predict the hardness.
[22:51] And yet, this electron,
which was previously
[22:54] measured to be white, now when
subsequently measured sometimes
[22:57] it comes out white,
sometimes it comes out
[23:00] black, 50-50% of the time.
[23:04] So that's surprising.
[23:05] What that tells you is you
can't think of the electron
[23:07] as a little ball that has black
and soft written on it, right?
[23:11] You can't, because apparently
that black and soft
[23:14] isn't a persistent
thing, although it's
[23:15] persistent in the sense
that once it's black,
[23:17] it stays black.
[23:19] So what's going on here?
[23:22] Now, I should emphasize
that the same thing happens
[23:25] if I had changed this to
taking the black electrons
[23:30] and throwing in a hardness and
picking soft and then measuring
[23:33] the color, or if I had
used the hard electrons.
[23:35] Any of those combinations,
any of these ports
[23:37] would have given the
same results, 50-50.
[23:39] Is not persistent in this sense.
[23:43] Apparently the presence
of the hardness box
[23:45] tampers with the color somehow.
[23:48] So it's not quite as trivial is
that hyper intelligent monkey.
[23:52] Something else is going on here.
[23:54] So this is suspicious.
[23:56] So here's the
first natural move.
[23:57] The first natural move
is, oh, look, surely
[24:01] there's some additional
property of the electron
[24:04] that we just
haven't measured yet
[24:05] that determines whether it
comes out the second color
[24:08] box black or white.
[24:10] There's got be some property
that determines this.
[24:15] And so people have spent
a tremendous amount
[24:17] of time and energy looking
at these initial electrons
[24:20] and looking with great
care to see whether there's
[24:24] any sort of feature of
these incident electrons
[24:28] which determines which
port they come out of.
[24:30] And the shocker is no one's
ever found such a property.
[24:35] No one has ever found
a property which
[24:36] determines which
port it comes out of.
[24:38] As far as we can tell,
it is completely random.
[24:45] Those that flip and
those that don't are
[24:48] indistinguishable at beginning.
[24:49] And let me just emphasize, if
anyone found such a-- it's not
[24:52] like we're not looking, right?
[24:53] If anyone found such a
property, fame, notoriety,
[24:56] subverting quantum
mechanics, Nobel Prize.
[24:59] People have looked.
[24:59] And there is none that
anyone's been able to find.
[25:03] And as we'll see later on,
using Bell's inequality,
[25:05] we can more or less nail
that such things don't exist,
[25:08] such a fact doesn't exist.
[25:10] But this tells us something
really disturbing.
[25:12] This tells us, and this
is the first real shocker,
[25:14] that there is something
intrinsically unpredictable,
[25:20] non-deterministic, and random
about physical processes
[25:24] that we observe in a laboratory.
[25:27] There's no way to determine
a priori whether it
[25:29] will come out black or
white from the second box.
[25:32] Probability in this
experiment, it's
[25:35] forced upon us by observations.
[25:42] OK, well, there's another
way to come at this.
[25:45] You could say, look, you ran
this experiment, that's fine.
[25:48] But look, I've met the
guy who built these boxes,
[25:52] and look, he's just
some guy, right?
[25:54] And he just didn't
do a very good job.
[25:57] The boxes are just badly built.
[26:00] So here's the way to
defeat that argument.
[26:03] No, we've built these things
out of different materials,
[26:05] using different technologies,
using electrons, using
[26:09] neutrons, using bucky-balls,
C60, seriously, it's been done.
[26:14] We've done this experiment, and
this property does not change.
[26:18] It is persistent.
[26:19] And the thing that's most
upsetting to me is that not
[26:22] only do we get the same results
independent of what objects we
[26:25] use to run the experiment, we
cannot change the probability
[26:29] away from 50-50 at all.
[26:31] Within experimental
tolerances, we cannot change,
[26:34] no matter how we
build the boxes,
[26:36] we cannot change the
probability by part in 100.
[26:41] 50-50.
[26:45] And to anyone who grew up
with determinism from Newton,
[26:49] this should hurt.
[26:52] This should feel wrong.
[26:54] But it's a property
of the real world.
[26:56] And our job is going
to be to deal with it.
[27:00] Rather, your job is going to
be to deal with it, because I
[27:02] went through this already.
[27:06] So here's a curious
consequence-- oh,
[27:08] any questions before I cruise?
[27:10] OK.
[27:11] So here's a curious consequence
of this series of experiments.
[27:15] Here's something you can't do.
[27:17] Are you guys old enough for you
can't do this on television?
[27:22] This is so sad.
[27:24] OK, so here's
something you can't do.
[27:28] We cannot build, it is
impossible to build,
[27:30] a reliable color
and hardness box.
[27:33] We've built a box that
tells you what color it is.
[27:35] We've built a box that tells
you what hardness it is.
[27:38] But you cannot build a
meaningful box that tells you
[27:42] what color and hardness
an electron is.
[27:46] So in particular, what
would this magical box be?
[27:49] It would have four ports.
[27:51] And its ports would say,
well, one is white and hard,
[27:54] and one is white and soft,
one is black and hard,
[27:58] and one is black and soft.
[28:00] So you can imagine
how you might try
[28:02] to build a color
and hardness box.
[28:05] So for example, here's
something you might imagine.
[28:08] Take your incident
electrons, and first
[28:12] send them into a color box.
[28:16] And take those white
electrons, and send them
[28:22] into a hardness box.
[28:24] And take those
electrons, and this
[28:26] is going to be white
and hard, and this
[28:29] is going to be white and soft.
[28:31] And similarly, send
these black electrons
[28:33] into the hardness box,
and here's hard and black,
[28:37] and here's soft and back.
[28:45] Everybody cool with that?
[28:46] So this seems to do
the thing I wanted.
[28:48] It measures both the
hardness and the color.
[28:50] What's the problem with it?
[28:53] AUDIENCE: [INAUDIBLE]
[28:56] ALLAN ADAMS: Yeah, exactly.
[28:58] So the color is not persistent.
[29:00] So you tell me this is a soft
and black electron, right?
[29:03] That's what you told me.
[29:05] Here's the box.
[29:06] But if I put a color
box here, that's
[29:10] the experiment we just ran.
[29:12] And what happens?
[29:13] Does this come out black?
[29:15] No, this is a crappy
source of black electrons.
[29:17] It's 50/50 black and white.
[29:19] So this box can't be built.
[29:21] And the reason, and I
want to emphasize this,
[29:23] the reason we cannot
build this box is not
[29:25] because our
experiments are crude.
[29:28] And it's not because
I can't build things,
[29:30] although that's true.
[29:32] I was banned from a lab one
day after joining it, actually.
[29:36] So I really can't build,
but other people can.
[29:40] And that's not why.
[29:41] We can't because of something
much more fundamental,
[29:43] something deeper,
something in principle,
[29:45] which is encoded in
this awesome experiment.
[29:50] This can be done.
[29:51] It does not mean anything,
as a consequence.
[29:55] It does not mean anything
to say this electron is
[29:57] white and hard, because if you
tell me it's white and hard,
[30:04] and I measure the white,
well, I know if it's hard,
[30:06] it's going to come out 50-50.
[30:09] It does not mean anything.
[30:11] So this is an important idea.
[30:13] This is an idea which
is enshrined in physics
[30:16] with a term which
comes with capital
[30:19] letters, the
Uncertainty Principle.
[30:21] And the Uncertainty Principle
says basically that, look,
[30:24] there's some observable,
measurable properties
[30:27] of a system which
are incompatible
[30:31] with each other in
precisely this way,
[30:34] incompatible with each
other in the sense
[30:36] not that you can't know, because
you can't know whether it's
[30:41] hard and soft
simultaneously, deeper.
[30:43] It is not hard and
white simultaneously.
[30:47] It cannot be.
[30:48] It does not mean
anything to say it
[30:50] is hard and white
simultaneously.
[30:54] That is uncertainty.
[30:56] And again,
uncertainty is an idea
[30:58] we're going to come back to
over and over in the class.
[31:01] But every time you
think about it,
[31:02] this should be the
first place you
[31:04] start for the next few weeks.
[31:09] Yeah.
[31:11] Questions.
[31:14] No questions?
[31:16] OK.
[31:16] So at this point,
it's really tempting
[31:19] to think yeah, OK, this
is just about the hardness
[31:24] and the color of electrons.
[31:28] It's just a weird
thing about electrons.
[31:30] It's not a weird thing
about the rest of the world.
[31:31] The rest of the world's
completely reasonable.
[31:33] And no, that's absolutely wrong.
[31:34] Every object in the world
has the same properties.
[31:39] If you take bucky-balls,
and you send them
[31:42] through the analogous
experiment--
[31:44] and I will show you the
data, I think tomorrow,
[31:46] but soon, I will
show you the data.
[31:48] When you take
bucky-balls and run it
[31:49] through a similar experiment,
you get the same effect.
[31:51] Now, bucky-balls are huge,
right, 60 carbon atoms.
[31:56] But, OK, OK, at
that point, you're
[31:58] saying, dude, come on,
huge, 60 carbon atoms.
[32:01] So there is a
pendulum, depending
[32:06] on how you define building, in
this building, a pendulum which
[32:10] is used, in principle which
is used to improve detectors
[32:13] to detect gravitational waves.
[32:15] There's a pendulum with a,
I think it's 20 kilo mirror.
[32:21] And that pendulum exhibits
the same sort of effects here.
[32:27] We can see these quantum
mechanical effects
[32:29] in those mirrors.
[32:30] And this is in breathtakingly
awesome experiments
[32:32] done by Nergis Malvalvala, whose
name I can never pronounce,
[32:35] but who is totally awesome.
[32:38] She's an amazing physicist.
[32:40] And she can get these kind of
quantum effects out of a 20
[32:42] kilo mirror.
[32:43] So before you say something
silly, like, oh, it's
[32:46] just electrons, it's
20 kilo mirrors.
[32:48] And if I could put you on
a pendulum that accurate,
[32:50] it would be you.
[32:52] OK?
[32:53] These are properties of
everything around you.
[32:56] The miracle is not that
electrons behave oddly.
[32:59] The miracle is that when you
take 10 to the 27 electrons,
[33:03] they behave like cheese.
[33:06] That's the miracle.
[33:08] This is the underlying
correct thing.
[33:13] OK, so this is so far so good.
[33:16] But let's go deeper.
[33:18] Let's push it.
[33:21] And to push it, I
want to design for you
[33:23] a slightly more elaborate
apparatus, a slightly more
[33:26] elaborate experimental
apparatus.
[33:29] And for this, I want you to
consider the following device.
[33:32] I'm going to need to introduce a
couple of new features for you.
[33:35] Here's a hardness box.
[33:36] And it has an in port.
[33:38] And the hardness box
has a hard aperture,
[33:41] and it has a soft aperture.
[33:43] And now, in addition
to this hardness box,
[33:45] I'm going to introduce
two elements.
[33:46] First, mirrors.
[33:49] And what these mirrors do
is they take the incident
[33:51] electrons and,
nothing else, they
[33:53] change the direction of motion,
change the direction of motion.
[33:57] And here's what I mean
by doing nothing else.
[33:59] If I take one of these
mirrors, and I take,
[34:02] for example, a color box.
[34:03] And I take the white
electrons that come out,
[34:05] and I bounce it off
the mirror, and then
[34:08] I send these into
a color box, then
[34:13] they come out white
100% of the time.
[34:17] It does not change
the observable color.
[34:19] Cool?
[34:20] All it does is
change the direction.
[34:21] Similarly, with
the hardness box,
[34:22] it doesn't change the hardness.
[34:24] It just changes the
direction of motion.
[34:26] And every experiment we've
ever done on these, guys,
[34:29] changes in no way
whatsoever the color
[34:31] or the hardness by
subsequent measurement.
[34:34] Cool?
[34:35] Just changes the
direction of motion.
[34:37] And then I'm going to
add another mirror.
[34:40] It's actually a slightly
fancy set of mirrors.
[34:43] All they do is they join
these beams together
[34:45] into a single beam.
[34:50] And again, this doesn't
change the color.
[34:52] You send in a white
electron, you get out,
[34:53] and you measure the
color on the other side,
[34:55] you get a white electron.
[34:56] You send in a black
electron from here,
[34:57] and you measure the color, you
get a black electron again out.
[35:00] Cool?
[35:02] So here's my apparatus.
[35:05] And I'm going to put
this inside a big box.
[35:09] And I want to run
some experiments
[35:11] with this apparatus.
[35:22] Everyone cool with
the basic design?
[35:24] Any questions
before I cruise on?
[35:30] This part's fun.
[35:34] So what I want to
do now is I want
[35:36] to run some simple experiments
before we get to fancy stuff.
[35:39] And the simple experiments
are just going to warm you up.
[35:42] They're going to
prepare you to make
[35:43] some predictions and
some calculations.
[35:45] And eventually we'd like
to lead back to this guy.
[35:48] So the first
experiment, I'm going
[35:51] to send in white electrons.
[35:53] Whoops.
[35:54] Im.
[35:56] I'm going to send
in white electrons.
[36:00] And I'm going to
measure at the end,
[36:03] and in particular at the
output, the hardness.
[36:15] So I'm going to send
in white electrons.
[36:23] And I'm going to
measure the hardness.
[36:24] So this is my apparatus.
[36:27] I'm going to measure the
hardness at the output.
[36:29] And what I mean by
measure the hardness
[36:30] is I throw these electrons
into a hardness box
[36:32] and see what comes out.
[36:34] So this is experiment 1.
[36:37] And let me draw this, let
me biggen the diagram.
[36:41] So you send white into-- so the
mechanism is a hardness box.
[36:49] Mirror, mirror,
mirrors, and now we're
[36:58] measuring the hardness out.
[37:05] And the question I want to ask
is how many electrons come out
[37:10] the hard aperture, and how
many electrons come out
[37:14] the soft aperture of
this final hardness box.
[37:18] So I'd like to know what
fraction come out hard,
[37:20] and what fraction come out soft.
[37:21] I send an initial
white electron,
[37:23] for example I took a color
box and took the white output,
[37:25] send them into the hardness
box, mirror, mirror,
[37:28] hard, hard, soft.
[37:30] And what fraction come out
hard, and what fraction
[37:33] come out soft.
[37:38] So just think about
it for a minute.
[37:44] And when you have a prediction
in your head, raise your hand.
[37:56] All right, good.
[37:57] Walk me through your prediction.
[38:01] AUDIENCE: I think
it should be 50-50.
[38:04] ALLAN ADAMS: 50-50.
[38:06] How come?
[38:08] AUDIENCE: [INAUDIBLE]
color doesn't
[38:10] have any bearing on hardness.
[38:13] [INAUDIBLE]
[38:20] ALLAN ADAMS: Awesome.
[38:21] So let me say that again.
[38:22] So we've done the experiment,
you send a white electron
[38:24] into the hardness
box, and we know
[38:25] that it's non-predictive, 50-50.
[38:27] So if you take a white
electron and you send it
[38:30] into the hardness
box, 50% of the time
[38:33] it will come out the hard
aperture, and 50% of the time
[38:36] it will come out
the soft aperture.
[38:37] Now if you take the one that
comes out the hard aperture,
[38:40] then you send it up
here or send it up here,
[38:42] we know that these
mirrors do nothing
[38:44] to the hardness of
the electron except
[38:46] change the direction of motion.
[38:48] We've already done
that experiment.
[38:49] So you measure the hardness at
the output, what do you get?
[38:52] Hard, because it came out hard,
mirror, mirror, hardness, hard.
[38:56] But it only came out
hard 50% of the time
[38:58] because we sent in
initially white electron.
[39:00] Yeah?
[39:00] What about the other 50%?
[39:01] Well, the other 50% of the time,
it comes out the soft aperture
[39:04] and follows what I'll
call the soft path
[39:07] to the mirror, mirror, hardness.
[39:08] And with soft, mirror,
mirror, hardness,
[39:10] you know it comes out soft.
[39:12] 50% of the time it
comes out this way,
[39:13] and then it will come out hard.
[39:14] 50% it follows the soft path,
and then it will come out soft.
[39:17] Was this the logic?
[39:18] Good.
[39:20] How many people agree with this?
[39:23] Solid.
[39:24] How many people disagree?
[39:27] No abstention.
[39:29] OK.
[39:30] So here's a prediction.
[39:35] Oh, yep.
[39:35] AUDIENCE: Just a question.
[39:38] Could you justify
that prediction
[39:40] without talking about oh,
well, half the electrons were
[39:44] initially measured to be
hard, and half were initially
[39:47] measured to be soft,
by just saying, well,
[39:48] we have a hardness box, and
then we joined these electrons
[39:54] together again, so we don't
know anything about it.
[39:57] So it's just like
sending white electrons
[40:00] into one hardness
box instead of two.
[40:01] ALLAN ADAMS: Yeah, that's
a really tempting argument,
[40:04] isn't it?
[40:04] So let's see.
[40:05] We're going to see
in a few minutes
[40:06] whether that kind of an
argument is reliable or not.
[40:09] But so far we've been given two
different arguments that lead
[40:12] to the same prediction, 50-50.
[40:14] Yeah?
[40:15] Question.
[40:20] AUDIENCE: Are the electrons
interacting between themselves?
[40:23] Like when you get
them to where--
[40:25] ALLAN ADAMS: Yeah.
[40:27] This is a very good question.
[40:28] So here's a question look you're
sending a bunch of electrons
[40:31] into this apparatus.
[40:33] But if I take--
look, I took 802.
[40:35] You take two
electrons and you put
[40:37] them close to each
other, what do they do?
[40:38] Pyewww.
[40:39] Right?
[40:39] They interact with each other
through a potential, right?
[40:42] So yeah, we're being a
little bold here, throwing
[40:44] a bunch of electrons
in and saying,
[40:45] oh, they're independent.
[40:46] So I'm going to do one better.
[40:47] I will send them
in one at a time.
[40:49] One electron through
the apparatus.
[40:51] And then I will
wait for six weeks.
[40:54] [LAUGHTER]
[40:57] See, you guys laugh,
you think that's funny.
[40:59] But there's a famous
story about a guy
[41:01] who did a similar experiment
with photons, French guy.
[41:05] And, I mean, the French,
they know what they're doing.
[41:07] So he wanted to do the same
experiment with photons.
[41:11] But the problem is
if you take a laser
[41:13] and you shined it
into your apparatus,
[41:15] there there are like, 10
to the 18 photons in there
[41:18] at any given moment.
[41:19] And the photons, who knows what
they're doing with each other,
[41:21] right?
[41:23] So I want to send in one
photon, but the problem
[41:25] is, it's very hard to get
a single photon, very hard.
[41:28] So what he did, I kid you not,
he took an opaque barrier,
[41:31] I don't remember what it
was, it was some sort of film
[41:34] on top of glass, I think it
was some sort of oil-tar film.
[41:37] Barton, do you
remember what he used?
[41:39] So he takes a film, and it
has this opaque property,
[41:44] such that the photons that are
incident upon it get absorbed.
[41:49] Once in a blue moon
a photon manages
[41:52] to make its way through.
[41:53] Literally, like once
every couple of days,
[41:56] or a couple of hours, I think.
[41:58] So it's going to
take a long time
[42:01] to get any sort of statistics.
[42:02] But he this advantage, that
once every couple of hours
[42:05] or whatever a photon
makes its way through.
[42:07] That means inside
the apparatus, if it
[42:09] takes a pico-second to
cross, triumph, right?
[42:12] That's the week I
was talking about.
[42:13] So he does this experiment.
[42:15] But as you can tell, you start
the experiment, you press go,
[42:18] and then you wait
for six months.
[42:21] Side note on this guy, liked
boats, really liked yachts.
[42:26] So he had six months
to wait before doing
[42:29] a beautiful experiment
and having the results.
[42:31] So what did he do?
[42:32] Went on a world
tour in his yacht.
[42:35] Comes back, collects the
data, and declares victory,
[42:37] because indeed, he saw
the effect he wanted.
[42:40] So I was not kidding.
[42:44] We really do wait.
[42:46] So I will take your challenge.
[42:49] And single electron,
throw it in,
[42:53] let it go through the
apparatus, takes mere moments.
[42:56] Wait for a week, send
in another electron.
[42:59] No electrons are
interacting with each other.
[43:02] Just a single electron at a time
going through this apparatus.
[43:07] Other complaints?
[43:11] AUDIENCE: More stories?
[43:12] ALLAN ADAMS: Sorry?
[43:13] AUDIENCE: More stories?
[43:14] ALLAN ADAMS: Oh,
you'll get them.
[43:16] I have a hard time resisting.
[43:17] So here's a prediction, 50-50.
[43:21] We now have two
arguments for this.
[43:24] So again, let's vote
after the second argument.
[43:26] 50-50, how many people?
[43:29] You sure?
[43:30] Positive?
[43:31] How many people don't think so?
[43:35] Very small dust.
[43:37] OK.
[43:37] It's correct.
[43:38] Yea.
[43:41] So, good.
[43:46] I like messing with you guys.
[43:50] So remember, we're going to
go through a few experiments
[43:53] first where it's
going to be very
[43:54] easy to predict the results.
[43:55] We've got four experiments
like this to do.
[43:57] And then we'll go on to
the interesting examples.
[43:58] But we need to go through
them so we know what happens,
[44:00] so we can make an empirical
argument rather than an in
[44:03] principle argument.
[44:03] So there's the first experiment.
[44:05] Now, I want to run
the second experiment.
[44:09] And the second experiment,
same as the first,
[44:12] a little bit louder,
a little bit worse.
[44:15] Sorry.
[44:16] The second experiment,
we're going
[44:18] to send in hard
electrons, and we're
[44:23] going to measure color at out.
[44:31] So again, let's look
at the apparatus.
[44:32] We send in hard electrons.
[44:34] And our apparatus
is hardness box
[44:39] with a hard and a soft aperture.
[44:47] And now we're going to measure
the color at the output.
[44:53] Color, what have I been doing?
[44:58] And now I want to know what
fraction come out black,
[45:01] and what fraction
come out white.
[45:07] We're using lots of
monkeys in this process.
[45:10] OK, so this is not
rocket science.
[45:16] Rocket science isn't
that complicated.
[45:17] Neuroscience is much harder.
[45:18] This is not neuroscience.
[45:20] So let's figure
out what this is.
[45:23] Predictions.
[45:24] So again, think
about your prediction
[45:25] your head, come to
a conclusion, raise
[45:27] your hand when you have an idea.
[45:31] And just because you
don't raise your hand
[45:33] doesn't mean I
won't call on you.
[45:47] AUDIENCE: 50-50 black and white.
[45:48] ALLAN ADAMS: 50-50
black and white.
[45:49] I like it.
[45:50] Tell me why.
[45:51] AUDIENCE: It's gone through
a hardness box, which
[45:53] scrambled the color, and
therefore has to be [INAUDIBLE]
[45:56] ALLAN ADAMS: Great.
[45:56] So the statement, I'm going to
say that slightly more slowly.
[45:59] That was an excellent argument.
[46:01] We have a hard electron.
[46:02] We know that hardness
boxes are persistent.
[46:05] If you send a hard electron
in, it comes out hard.
[46:07] So every electron incident
upon our apparatus
[46:09] will transit across
the hard trajectory.
[46:13] It will bounce, it will
bounce, but it is still hard,
[46:16] because we've already
done that experiment.
[46:17] The mirrors do nothing
to the hardness.
[46:18] So we send a hard electron
into the color box,
[46:20] and what comes out?
[46:21] Well, we've done
that experiment, too.
[46:22] Hard into color, 50-50.
[46:24] So the prediction is 50-50.
[46:25] This is your prediction.
[46:27] Is that correct?
[46:28] Awesome.
[46:29] OK, let us vote.
[46:33] How many people think
this is correct?
[46:36] Gusto, I like it.
[46:37] How many people think it's not?
[46:40] All right.
[46:41] Yay, this is correct.
[46:45] Third experiment,
slightly more complicated.
[46:50] But we have to go through
these to get to the good stuff,
[46:54] so humor me for a moment.
[46:56] Third, let's send
in white electrons,
[47:02] and then measure the
color at the output port.
[47:10] So now we send in white
electrons, same beast.
[47:14] And our apparatus
is a hardness box
[47:17] with a hard path
and a soft path.
[47:20] Do-do-do, mirror,
do-do-do, mirror, box,
[47:26] join together into our out.
[47:27] And now we send those out
electrons into a color box.
[47:34] And our color box,
black and white.
[47:39] And now the question is
how many come out black,
[47:41] and how many come out white.
[47:44] Again, think through the
logic, follow the electrons,
[47:48] come up with a prediction.
[47:49] Raise your hand when
you have a prediction.
[48:09] AUDIENCE: Well, earlier
we showed that [INAUDIBLE]
[48:18] so it'll take those
paths equally--
[48:20] ALLAN ADAMS: With
equal probability.
[48:21] Good.
[48:22] AUDIENCE: Yeah.
[48:23] And then it'll go back
into the color box.
[48:24] But earlier when we
did the same thing
[48:26] without the weird path-changing,
it came out 50-50 still.
[48:29] So I would say still 50-50.
[48:30] ALLAN ADAMS: Great.
[48:31] So let me say that
again, out loud.
[48:32] And tell me if
this is an accurate
[48:35] extension of what you said.
[48:37] I'm just going to
use more words.
[48:38] But it's, I think,
the same logic.
[48:40] We have a white electron,
initially white electron.
[48:42] We send it into a hardness box.
[48:43] When we send a white
electron into a hardness box,
[48:45] we know what happens.
[48:46] 50% of the time it comes
out hard, the hard aperture,
[48:49] 50% of the time it comes
out the soft aperture.
[48:51] Consider those electrons that
came out the hard aperture.
[48:53] Those electrons that came
out the hard aperture
[48:55] will then transit
across the system,
[48:56] preserving their hardness
by virtue of the fact
[48:58] that these mirrors preserve
hardness, and end up
[49:01] at a color box.
[49:01] When they end at
the color box, when
[49:03] that electron, the single
electron in the system
[49:05] ends at this color
box, then we know
[49:07] that a hard electron
entering a color box
[49:09] comes out black or
white 50% of the time.
[49:11] We've done that experiment, too.
[49:13] So for those 50% that came
out hard, we get 50/50.
[49:17] Now consider the other 50%.
[49:18] The other half of the time, the
single electron in the system
[49:21] will come out the soft aperture.
[49:24] It will then proceed along
the soft trajectory, bounce,
[49:26] bounce, not changing
its hardness,
[49:28] and is then a soft electron
incident on the color box.
[49:30] But we've also done
that experiment,
[49:32] and we get 50-50
out, black and white.
[49:34] So those electrons that came
out hard come out 50-50,
[49:37] and those electrons that
come out soft come out 50/50.
[49:40] And the logic then leads
to 50-50, twice, 50-50.
[49:46] Was that an accurate statement?
[49:48] Good.
[49:48] It's a pretty
reasonable extension.
[49:50] OK, let's vote.
[49:51] How many people
agree with this one?
[49:54] OK, and how many
people disagree?
[49:58] Yeah, OK.
[49:59] So vast majority agree.
[50:01] And the answer is
no, this is wrong.
[50:04] In fact, all of these, 100% come
out white and 0 come out black.
[50:11] Never ever does an electron
come out the black aperture.
[50:28] I would like to quote
what a student just
[50:33] said, because it's actually the
next line in my notes, which
[50:36] is what the hell is going on?
[50:42] So let's the series of
follow up experiments
[50:46] to tease out what's
going on here.
[50:49] So something very
strange, let's just
[50:51] all agree, something very
strange just happened.
[50:55] We sent a single electron in.
[50:57] And that single electron
comes out the hardness box,
[50:59] well, it either came
out the hard aperture
[51:03] or the soft aperture.
[51:05] And if it came out the
hard, we know what happens,
[51:06] if it came out the soft,
we know what happens.
[51:08] And it's not 50-50.
[51:10] So we need to improve
the situation.
[51:16] Hold on a sec.
[51:17] Hold on one sec.
[51:21] Well, OK, go ahead.
[51:22] AUDIENCE: Yeah, it's just
a question about the setup.
[51:24] So with the second
hardness box, are we
[51:27] collecting both the
soft and hard outputs?
[51:30] ALLAN ADAMS: The second, you
mean the first hardness box?
[51:33] AUDIENCE: The one-- are
we getting-- no, the--
[51:39] ALLAN ADAMS: Which one, sorry?
[51:41] This guy?
[51:42] Oh, that's a mirror,
not a hardness box.
[51:45] Oh, thanks for asking.
[51:46] Yeah, sorry.
[51:47] I wish I had a better notation
for this, but I don't.
[51:50] There's a classic-- well,
I'm not going to go into it.
[51:53] Remember that thing
where I can't stop myself
[51:55] from telling stories?
[51:57] So all this does, it's
just a set of mirrors.
[51:59] It's a set of fancy mirrors.
[52:00] And all it does is it
takes an electron coming
[52:03] this way or an electron coming
this way, and both of them
[52:05] get sent out in
the same direction.
[52:06] It's like a beam joiner, right?
[52:08] It's like a y junction.
[52:10] That's all it is.
[52:11] So if you will, imagine
the box is a box,
[52:14] and you take, I don't
know, Professor Zwiebach,
[52:16] and you put him inside.
[52:17] And every time an electron
comes up this way,
[52:19] he throws it out that
way, and every time
[52:19] it comes in this way, he
throws it out that way.
[52:21] And he'd be really ticked at
you for putting him in a box,
[52:23] but he'd do the job well.
[52:24] Yeah.
[52:25] AUDIENCE: And this also works if
you go one electron at a time?
[52:27] ALLAN ADAMS: This works if
you go one electron at a time,
[52:30] this works if you go 14
electrons at a time, it works.
[52:33] It works reliably.
[52:33] Yeah.
[52:34] AUDIENCE: Just,
maybe [INAUDIBLE]
[52:36] but what's the difference
between this experiment
[52:39] and that one?
[52:39] ALLAN ADAMS: Yeah, I know.
[52:41] Right?
[52:41] Right?
[52:43] So the question was,
what's the difference
[52:45] between this experiment
and the last one.
[52:48] Yeah, good question.
[52:48] So we're going to
have to answer that.
[52:49] Yeah.
[52:50] AUDIENCE: Well, you're
mixing again the hardness.
[52:54] So it's like as you weren't
measuring it at all, right?
[52:58] ALLAN ADAMS: Apparently it's
a lot we weren't measuring it,
[53:01] right?
[53:01] Because we send in the white
electron, and at the end
[53:05] we get out that
it's still white.
[53:06] So somehow this is like
not doing anything.
[53:09] But how does that work?
[53:11] So that's an
excellent observation.
[53:13] And I'm going to build you now
a couple of experiments that
[53:15] tease out what's going on.
[53:18] And you're not going
to like the answer.
[53:20] Yeah.
[53:21] AUDIENCE: How were
the white electrons
[53:22] generated in this experiment?
[53:23] ALLAN ADAMS: The
white electrons were
[53:24] generated in the following way.
[53:26] I take a random
source of electrons,
[53:27] I rub a cat against a balloon
and I charge up the balloon.
[53:31] And so I take those
random electrons,
[53:33] and I send them
into a color box.
[53:34] And we have previously
observed that if you
[53:36] take random electrons and
throw them into a color box
[53:38] and pull out the electrons that
come out the white aperture,
[53:40] if you then send
them into a color box
[53:41] again, they're still white.
[53:43] So that's how I've
generated them.
[53:45] I could have done it by
rubbing the cat against glass,
[53:47] or rubbing it against me,
right, just stroke the cat.
[53:53] Any randomly selected
set of electrons
[53:55] sent into a color box,
and then from which
[53:57] you take the white electrons.
[53:59] AUDIENCE: So how is it different
from the experiment up there?
[54:01] ALLAN ADAMS: Yeah.
[54:01] Uh-huh.
[54:02] Exactly.
[54:03] Yeah.
[54:04] AUDIENCE: Is the difference
that you never actually know
[54:06] whether the electron's
hard or soft?
[54:07] ALLAN ADAMS: That's a
really good question.
[54:09] So here's something I'm
going to be very careful not
[54:12] to say in this class
to the degree possible.
[54:14] I'm not going to use
the word to know.
[54:17] AUDIENCE: Well, to
measure. [INAUDIBLE]
[54:18] ALLAN ADAMS: Good.
[54:19] Measure is a very
slippery word, too.
[54:21] I've used it here
because I couldn't really
[54:23] get away with not using it.
[54:24] But we'll talk about
that in some detail
[54:27] later on in the course.
[54:28] For the moment, I
want to emphasize
[54:30] that it's tempting but dangerous
at this point to talk about
[54:34] whether you know or don't
know, or whether someone knows
[54:37] or doesn't know, for
example, the monkey
[54:38] inside knows or doesn't know.
[54:40] So let's try to
avoid that, and focus
[54:42] on just operational questions of
what are the things that go in,
[54:44] what are the things that
come out, and with what
[54:46] probabilities.
[54:47] And the reason
that's so useful is
[54:49] that it's something
that you can just do.
[54:51] There's no ambiguity
about whether you've
[54:53] caught a white electron
in a particular spot.
[54:55] Now in particular,
the reason these boxes
[54:57] are such a powerful tool is that
you don't measure the electron,
[55:00] you measure the position
of the electron.
[55:01] You get hit by the
electron or you don't.
[55:03] And by using these boxes we
can infer from their position
[55:07] the color or the hardness.
[55:09] And that's the reason
these boxes are so useful.
[55:12] So we're inferring from
the position, which
[55:14] is easy to measure,
you get beaned
[55:15] or you don't, we're
inferring the property
[55:18] that we're interested in.
[55:20] It's a really good
question, though.
[55:21] Keep it in the
back of your mind.
[55:23] And we'll talk about it
on and off for the rest
[55:25] of the semester.
[55:26] Yeah.
[55:27] AUDIENCE: So what happens
if you have this setup,
[55:29] and you just take away
the bottom right mirror?
[55:32] ALLAN ADAMS: Perfect question.
[55:33] This leads me into
the next experiment.
[55:35] So here's the modification.
[55:36] But thank you, that's
a great question.
[55:38] Here's the modification
of this experiment.
[55:40] So let's rig up a
small-- hold on,
[55:44] I want to go through the
next series of experiments,
[55:46] and then I'll come
back to questions.
[55:47] And these are great questions.
[55:49] So I want to rig up a small
movable wall, a small movable
[55:53] barrier.
[55:53] And here's what this
movable barrier will do.
[56:00] If I put the barrier in, so
this would be in the soft path,
[56:07] when I put the barrier
in the soft path,
[56:08] it absorbs all electrons
incident upon it
[56:12] and impedes them
from proceeding.
[56:15] So you put a barrier in here,
put a barrier in the soft path,
[56:19] no electrons continue through.
[56:20] An electron incident
cannot continue through.
[56:24] When I say that the
barrier is out, what I mean
[56:27] is it's not in the way.
[56:28] I've moved it out of the way.
[56:29] Cool?
[56:31] So I want to run
the same experiment.
[56:34] And I want to run this
experiment using the barriers
[56:38] to tease out how the electrons
transit through our apparatus.
[56:47] So experiment four.
[56:52] Let's send in a
white electron again.
[56:55] I want to do the same
experiment we just did.
[56:57] And color at out, but now with
the wall in the soft path.
[57:06] Wall in soft.
[57:10] So that's this experiment.
[57:13] So we send in white
electrons, and at the output
[57:19] we measure the color as before.
[57:25] And the question is what
fraction come out black,
[57:33] and what fraction
come out white.
[57:40] So again, everyone think
through it for a second.
[57:42] Just take a second.
[57:44] And this one's a little sneaky.
[57:46] So feel free to discuss it with
the person sitting next to you.
[57:50] [CHATTER]
[59:00] ALLAN ADAMS: All right.
[59:04] All right, now that everyone
has had a quick second
[59:06] to think through
this one, let me just
[59:08] talk through what I'd
expect from the point
[59:10] of these experiments.
[59:11] And then we'll talk about
whether this is reasonable.
[59:14] So the first thing I
expect is that, look,
[59:16] if I send in a white
electron and I put it
[59:18] into a hardness pass, I know
that 50% of the time it goes
[59:20] out hard, and 50% of the
time it goes out soft.
[59:22] If it goes out
the soft aperture,
[59:24] it's going to get eaten
by the barrier, right?
[59:27] It's going to get
eaten by the barrier.
[59:29] So first thing I predict
is that the output
[59:31] should be down by 50%.
[59:37] However, here's an
important bit of physics.
[59:39] And this comes to
the idea of locality.
[59:44] I didn't tell you
this, but these
[59:47] armlinks in the experiment I
did, 3,000 kilometers long.
[59:52] 3,000 kilometers long.
[59:56] That's too minor.
[59:57] 10 million kilometers long.
[59:59] Really long.
[01:00:00] Very long.
[01:00:04] Now, imagine an
electron that enters
[01:00:06] this, an initially
white electron.
[01:00:07] If we had the barriers out,
if the barrier was out,
[01:00:11] what do we get?
[01:00:14] 100% white, right?
[01:00:15] We just did this
experiment, to our surprise.
[01:00:17] So if we did this, we get 100%.
[01:00:18] And that means an
electron, any electron,
[01:00:20] going along the soft
path comes out white.
[01:00:21] Any electron going along the
hard path goes out white.
[01:00:24] They all come out white.
[01:00:27] So now, imagine I do this.
[01:00:29] Imagine we put a barrier in
here 2 million miles away
[01:00:33] from this path.
[01:00:36] How does a hard
electron along this path
[01:00:37] know that I put
the barrier there?
[01:00:39] And I'm going to make it
even more sneaky for you.
[01:00:41] I'm going to insert the
barrier along the path
[01:00:44] after I launched the
electron into the apparatus.
[01:00:49] And when I send in the electron,
I will not know at that moment,
[01:00:53] nor will the electron
know, because, you
[01:00:55] know, they're not very
smart, whether the barrier is
[01:00:58] in place.
[01:00:58] And this is going to be millions
of miles away from this guy.
[01:01:02] So an electron out
here can't know.
[01:01:05] It hasn't been there.
[01:01:06] It just hasn't been there.
[01:01:07] It can't know.
[01:01:08] But we know that when
we ran this apparatus
[01:01:10] without the barrier in there,
they came out 100% white.
[01:01:14] But it can't possibly know
whether the barrier's in
[01:01:16] there or not, right?
[01:01:18] It's over here.
[01:01:22] So what this tells us is that
we should expect the output
[01:01:25] to be down by 50%.
[01:01:26] But all the electrons
that do make
[01:01:30] it through must come
out white, because they
[01:01:33] didn't know that there
was a barrier there.
[01:01:35] They didn't go along that path.
[01:01:40] Yeah.
[01:01:40] AUDIENCE: Not trying
to be wise, but why
[01:01:42] are you using the word know?
[01:01:43] ALLAN ADAMS: Oh,
sorry, thank you.
[01:01:46] Thank you, thank you, thank you,
that was a slip of the tongue.
[01:01:48] I was making fun
of the electron.
[01:01:50] So in that particular
case, I was not
[01:01:53] referring to my
or your knowledge.
[01:01:55] I was referring
to the electron's
[01:01:56] tragically
impoverished knowledge.
[01:02:01] Yeah.
[01:02:02] AUDIENCE: But if they come
out one at a time white,
[01:02:04] then wouldn't we know
then with certainty
[01:02:06] that that electron is
both hard and white,
[01:02:09] which is like a violation?
[01:02:11] ALLAN ADAMS: Well, here's
the more troubling thing.
[01:02:14] Imagine it didn't
come out 100% white.
[01:02:17] Then the electron would
have demonstrably not
[01:02:20] go along the soft path.
[01:02:22] It would have demonstrably
gone through the hard path,
[01:02:25] because that's the only
path available to it.
[01:02:27] And yet, it would still have
known that millions of miles
[01:02:29] away, there's a barrier
on a path it didn't take.
[01:02:31] So which one's more
upsetting to you?
[01:02:36] And personally, I find this one
the less upsetting of the two.
[01:02:40] So the prediction is our
output should down by 50%,
[01:02:43] because a half of
them get eaten.
[01:02:44] But they should
all come out white,
[01:02:46] because those that
didn't get eaten
[01:02:47] can't possibly know that
there was a barrier here,
[01:02:50] millions of miles away.
[01:02:53] So we run this experiment.
[01:02:55] And here's the
experimental result.
[01:02:57] In fact, the experimental
result is yes, the output
[01:02:59] is down by 50%.
[01:03:00] But no, not 100%
white, 50% white.
[01:03:07] 50% white.
[01:03:11] The barrier, if we put the
barrier in the hardness path.
[01:03:14] If we put the barrier
in the hardness path,
[01:03:16] still down by 50%, and
it's at odds, 50-50.
[01:03:23] How could the electron know?
[01:03:25] I'm making fun of it.
[01:03:26] Yeah.
[01:03:27] AUDIENCE: So I
guess my question is
[01:03:29] before we ask how it
knows that there's
[01:03:31] a block in one of the paths,
how does it know, before,
[01:03:34] over there, that there were
two paths, and combine again?
[01:03:37] ALLAN ADAMS: Excellent.
[01:03:38] Exactly.
[01:03:38] So actually, this
problem was there already
[01:03:40] in the experiment we did.
[01:03:41] All we've done here
is tease out something
[01:03:43] that was existing in the
experiment, something
[01:03:44] that was disturbing.
[01:03:45] The presence of those
mirrors, and the option
[01:03:48] of taking two paths,
somehow changed
[01:03:51] the way the electron behaved.
[01:03:53] How is that possible?
[01:03:54] And here, we're seeing
that very sharply.
[01:03:56] Thank you for that
excellent observation.
[01:03:58] Yeah.
[01:03:58] AUDIENCE: What if you
replaced the two mirrors
[01:04:00] with color boxes, so that
both color boxes [INAUDIBLE]
[01:04:07] ALLAN ADAMS: Yeah.
[01:04:10] So the question is basically,
let's take this experiment,
[01:04:12] and let's make it even more
intricate by, for example,
[01:04:16] replacing these
mirrors by color boxes.
[01:04:18] So here's the thing
I want to emphasize.
[01:04:23] I strongly encourage you to
think through that example.
[01:04:25] And in particular, think through
that example, come to my office
[01:04:28] hours, and ask me about it.
[01:04:31] So that's going to be setting
a different experiment.
[01:04:33] And different
experiments are going
[01:04:34] to have different results.
[01:04:36] So we're going to have to
deal with that on a case
[01:04:37] by case basis.
[01:04:38] It's an interesting
example, but it's
[01:04:38] going to take us a bit afar
from where we are right now.
[01:04:41] But after we get to the
punchline from this,
[01:04:43] come to my office hours and
ask me exactly that question.
[01:04:46] Yeah.
[01:04:47] AUDIENCE: So we had a color
box, we put in white electrons
[01:04:51] and we got 50-50, like random.
[01:04:53] How do you know the boxes work?
[01:04:55] ALLAN ADAMS: How do I
know the boxes work?
[01:04:56] These are the same boxes
we used from the beginning.
[01:04:58] We tested them over and over.
[01:04:59] AUDIENCE: How did you first
check that it was working?
[01:05:01] [INAUDIBLE]
[01:05:03] ALLAN ADAMS: How
to say-- there's
[01:05:04] no other way to build a box
that does the properties that we
[01:05:07] want, which is that you send
in color and it comes out color
[01:05:10] again, and the mirrors
behave this way.
[01:05:13] Any box that does those
first set of things, which
[01:05:15] is what I will call a
color box, does this, too.
[01:05:17] There's no other way to do it.
[01:05:19] I don't mean just because
like, no one's tested--
[01:05:21] AUDIENCE: Because you
can't actually check it,
[01:05:23] you can't actually [INAUDIBLE]
you know which one is white.
[01:05:26] ALLAN ADAMS: Oh, sure, you can.
[01:05:27] You take the electron that
came out of the color box.
[01:05:29] That's what we mean
by saying it's white.
[01:05:30] AUDIENCE: [INAUDIBLE]
[01:05:31] ALLAN ADAMS: But
that's what it means
[01:05:32] to say the electron is white.
[01:05:34] It's like, how do you know
that my name is Allan?
[01:05:35] You say, Allan, and I go, what?
[01:05:37] Right?
[01:05:37] But you're like, look that's
not a test of whether I'm Allan.
[01:05:40] It's like, well,
what is the test?
[01:05:41] That's how you test.
[01:05:42] What's your name?
[01:05:43] I'm Allan.
[01:05:43] Oh, great, that's your name.
[01:05:44] So that's what I mean by white.
[01:05:46] Now you might quibble
that that's a stupid thing
[01:05:48] to call an electron.
[01:05:49] And I grant you that.
[01:05:50] But it is nonetheless a property
that I can empirically engage.
[01:05:53] OK, so I've been told
that I never ask questions
[01:05:55] from the people on the right.
[01:05:57] Yeah.
[01:05:57] AUDIENCE: Is it important
whether the experimenter
[01:05:59] knows if the wall
is there or not?
[01:06:02] ALLAN ADAMS: No.
[01:06:03] This experiment has been done
again by some French guys.
[01:06:06] The French, look, dude.
[01:06:08] So there's this guy,
Alain Aspect, ahh,
[01:06:12] great experimentalist,
great physicist.
[01:06:14] And he's done lots of
beautiful experiments
[01:06:16] on exactly this topic.
[01:06:17] And send me an email, and
I'll post some example papers
[01:06:20] and reviews by him-- and he's a
great writer-- on the web page.
[01:06:23] So just send me an email
to remind me of that.
[01:06:25] OK, so we're lowish on
time, so let me move on.
[01:06:29] So what I want to
do now is I want
[01:06:30] to take the lesson of this
experiment and the observation
[01:06:32] that was made a minute ago, that
in fact the same problem was
[01:06:35] present when we ran this
experiment and go 100%.
[01:06:37] We should have been
freaked out already.
[01:06:39] And I want to think through
what that's telling us
[01:06:41] about the electron,
the single electron,
[01:06:43] as it transits the apparatus.
[01:06:52] The thing is, at this point
we're in real trouble.
[01:06:56] And here's the reason.
[01:06:58] Consider a single electron
inside the apparatus.
[01:07:02] And I want to think about the
electron inside the apparatus
[01:07:05] while all walls are out.
[01:07:06] So it's this experiment.
[01:07:09] Consider the single electron.
[01:07:11] We know, with total confidence,
with complete reliability,
[01:07:15] that every electron
will exit this color box
[01:07:17] out the white aperture.
[01:07:18] We've done this experiment.
[01:07:19] We know it will come out white.
[01:07:20] Yes?
[01:07:23] Here's my question.
[01:07:26] Which route did it take?
[01:07:34] AUDIENCE: Spoiler.
[01:07:37] ALLAN ADAMS: Not a spoiler.
[01:07:39] Which route did it take?
[01:07:41] AUDIENCE: Why do
we care what route?
[01:07:43] ALLAN ADAMS: I'm asking
you the question.
[01:07:44] That's why you care.
[01:07:46] I'm the professor here.
[01:07:47] What is this?
[01:07:49] Come on.
[01:07:51] Which route did it take?
[01:07:56] OK, let's think through
the possibilities.
[01:07:58] Grapple with this
question in your belly.
[01:08:00] Let's think through
the possibilities.
[01:08:02] First off, did it take
the hardness path?
[01:08:05] So as it transits through,
the single electron
[01:08:07] transiting through
this apparatus,
[01:08:08] did it take the hard path
or did it take the soft?
[01:08:10] These are millions of miles
long, millions of miles apart.
[01:08:13] This is not a
ridiculous question.
[01:08:15] Did it go millions of
miles in that direction,
[01:08:17] or millions of miles
in that direction?
[01:08:19] Did it take the hardness path?
[01:08:22] Ladies and gentlemen, did
it take the hard path?
[01:08:25] AUDIENCE: Yes.
[01:08:29] ALLAN ADAMS: Well, we
ran this experiment
[01:08:31] by putting a wall
in the soft path.
[01:08:33] And if we put a wall
in the soft path,
[01:08:35] then we know it
took the hard path,
[01:08:37] because no other
electrons come out
[01:08:38] except those that went
through the hard path.
[01:08:40] Correct?
[01:08:40] On the other hand, if it
went through the hard path,
[01:08:43] it would come out
50% of the time white
[01:08:46] and 50% of the time black.
[01:08:48] But in fact, in this apparatus
it comes out always 100% white.
[01:08:52] It cannot have
taken the hard path.
[01:08:55] No.
[01:08:59] Did it take the soft path?
[01:09:05] Same argument,
different side, right?
[01:09:08] No.
[01:09:10] Well, this is not looking good.
[01:09:12] Well, look, this was suggested.
[01:09:16] Maybe it took both.
[01:09:19] Maybe electrons are
sneaky little devils
[01:09:21] that split in two, and part of
it goes one way and part of it
[01:09:24] goes the other.
[01:09:27] Maybe it took both paths.
[01:09:29] So this is easy.
[01:09:30] We can test this one.
[01:09:31] And here is how I'm
going to test this one.
[01:09:35] Oh, sorry.
[01:09:37] Actually, I'm not
going to do that yet.
[01:09:39] So we can test this one.
[01:09:40] So if it took both paths, here's
what you should be able to do.
[01:09:43] You should be able to put
a detector along each path,
[01:09:46] and you'd be able
to follow, if you've
[01:09:48] got half an electron on one
side and half an electron
[01:09:50] on the other, or
maybe two electrons,
[01:09:51] one on each side and
one on the other.
[01:09:53] So this is the thing
that you'd predict
[01:09:54] if you said it went both.
[01:09:55] So here's what we'll do.
[01:09:56] We will take detectors.
[01:09:57] We will put one along
the hard path and one
[01:09:59] along the soft path.
[01:10:00] We will run the experiment
and then observe
[01:10:02] whether, and ask whether,
we see two electrons,
[01:10:05] we see half and
half, what do we see.
[01:10:06] The answer is you always,
always see one electron on one
[01:10:10] of the paths.
[01:10:12] You never see half an electron.
[01:10:14] You never see a
squishy electron.
[01:10:15] You see one electron
on one path, period.
[01:10:18] It did not take both.
[01:10:20] You never see an electron split
in two, divided, confused.
[01:10:25] No.
[01:10:28] Well, it didn't
take the hard path,
[01:10:30] didn't take the soft
path, it didn't take both.
[01:10:33] There's one option left.
[01:10:35] Neither.
[01:10:36] Well, I say neither.
[01:10:36] But what about neither?
[01:10:40] And that's easy.
[01:10:41] Let's put a barrier
in both paths.
[01:10:44] And then what happens?
[01:10:46] Nothing comes out.
[01:10:48] So no.
[01:10:55] So now, to repeat an
earlier prescient remark
[01:10:58] from one of the
students, what the hell?
[01:11:01] So here's the
world we're facing.
[01:11:03] I want you to think about this.
[01:11:04] Take this seriously.
[01:11:05] Here's the world we're facing.
[01:11:05] And when I say, here's
the world we're facing,
[01:11:07] I don't mean just
these experiments.
[01:11:09] I mean the world around you,
20 kilo mirrors, bucky-balls,
[01:11:14] here is what they do.
[01:11:15] When you send them through
an apparatus like this,
[01:11:19] every single object that
goes through this apparatus
[01:11:22] does not take the hard path,
it does not take the soft path,
[01:11:25] it doesn't take both, and
it does not take neither.
[01:11:29] And that pretty much
exhausts the set
[01:11:31] of logical possibilities.
[01:11:34] So what are electrons doing when
they're inside the apparatus?
[01:11:40] How do you describe that
electron inside the apparatus?
[01:11:43] You can't say it's
on one path, you
[01:11:44] can't say it's on the
other, it's not on both,
[01:11:46] and it's not on neither.
[01:11:47] What is it doing halfway
through this experiment?
[01:11:51] So if our experiments
are accurate,
[01:11:52] and to the best of our
ability to determine,
[01:11:54] they are, and if our arguments
are correct, and that's on me,
[01:12:00] then they're doing
something, these electrons
[01:12:02] are doing something we've
just never thought of before,
[01:12:05] something we've never
dreamt of before,
[01:12:06] something for which
we don't really
[01:12:08] have good words in
the English language.
[01:12:11] Apparently, empirically,
electrons have a way of moving,
[01:12:16] electrons have a way of being
which is unlike anything
[01:12:19] that we're used
to thinking about.
[01:12:22] And so do molecules.
[01:12:23] And so do bacteria.
[01:12:25] So does chalk.
[01:12:28] It's just harder to
detect in those objects.
[01:12:32] So physicists have a name
for this new mode of being.
[01:12:35] And we call it superposition.
[01:12:39] Now, at the moment,
superposition
[01:12:42] is code for I have no
idea what's going on.
[01:12:48] Usage of the word superposition
would go something like this.
[01:12:51] An initially white electron
inside this apparatus
[01:12:55] with the walls out is
neither hard, nor soft,
[01:12:59] nor both, nor neither.
[01:13:01] It is, in fact, in a
superposition of being hard
[01:13:04] and of being soft.
[01:13:07] This is why we
can't meaningfully
[01:13:09] say this electron is some
color and some hardness.
[01:13:13] Not because our boxes are crude,
and not because we're ignorant,
[01:13:16] though our boxes are
crude and we are ignorant.
[01:13:20] It's deeper.
[01:13:21] Having a definite color means
not having a definite hardness,
[01:13:25] but rather being in a
superposition of being hard
[01:13:28] and being soft.
[01:13:31] Every electron exits a hardness
box either hard or soft.
[01:13:40] But not every electron
is hard or soft.
[01:13:43] It can also be a superposition
of being hard or being soft.
[01:13:48] The probability
that we subsequently
[01:13:51] measure it to be
hard or soft depends
[01:13:54] on precisely what
superposition it is.
[01:13:59] For example, we know
that if an electron is
[01:14:01] in the superposition
corresponding to being white
[01:14:05] then there are even odds
of it being subsequently
[01:14:08] measured be hard or to be soft.
[01:14:13] So to build a better
definition of superposition
[01:14:18] than I have no idea
what's going on
[01:14:22] is going to require
a new language.
[01:14:23] And that language is
quantum mechanics.
[01:14:26] And the underpinnings
of this language
[01:14:28] are the topic of the course.
[01:14:29] And developing a
better understanding
[01:14:31] of this idea of
superposition is what
[01:14:35] you have to do over
the next three months.
[01:14:38] Now, if all of this
troubles your intuition,
[01:14:42] well, that shouldn't
be too surprising.
[01:14:44] Your intuition was developed
by throwing spears, and running
[01:14:49] from tigers, and catching
toast as it jumps out
[01:14:52] of the toaster, all of
which involves things so big
[01:14:58] and with so much energy that
quantum effects are negligible.
[01:15:04] As a friend of
mine likes to say,
[01:15:05] you don't need to know quantum
mechanics to make chicken soup.
[01:15:09] However, when we work in
very different regimes, when
[01:15:11] we work with atoms, when we work
with molecules, when we work
[01:15:15] in the regime of very
low energies and very
[01:15:18] small objects, your intuition
is just not a reasonable guide.
[01:15:23] It's not that the electrons--
and I cannot emphasize this
[01:15:26] strongly enough-- it is not
that the electrons are weird.
[01:15:30] The electrons do
what electrons do.
[01:15:33] This is what they do.
[01:15:34] And it violates your
intuition, but it's true.
[01:15:37] The thing that's surprising
is that lots of electrons
[01:15:40] behave like this.
[01:15:42] Lots of electrons behave
like cheese and chalk.
[01:15:47] And that's the goal
of 804, to step
[01:15:49] beyond your daily experience
and your familiar intuition
[01:15:52] and to develop an intuition
for this idea of superposition.
[01:15:57] And we'll start in
the next lecture.
[01:15:59] I'll see you on Thursday.