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  • ALLAN ADAMS: Hi everyone.

  • Welcome to 804 for spring 2013.

  • This is the fourth, and presumably final time

  • that I will be teaching this class.

  • So I'm pretty excited about it.

  • So my name is Allan Adams.

  • I'll be lecturing the course.

  • I'm an assistant professor in Course 8.

  • I study string theory and its applications

  • to gravity, quantum gravity, and condensed matter physics.

  • Quantum mechanics, this is a course in quantam mechanics.

  • Quantam mechanics Is my daily language.

  • Quantum mechanics is my old friend.

  • I met quantum mechanics 20 years ago.

  • I just realized that last night.

  • It was kind of depressing.

  • So, old friend.

  • It's also my most powerful tool.

  • So I'm pretty psyched about it.

  • Our recitation instructors are Barton Zwiebach, yea!

  • And Matt Evans-- yea!

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

  • Hi.

  • So he just started his faculty position,

  • which is pretty awesome.

  • And our TA is Paolo Glorioso.

  • Paolo, are you here?

  • Yea!

  • There you go.

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

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

  • Awesome.

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

  • Solid.

  • 6?

  • Excellent.

  • 9?

  • No one?

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

  • That's a shame.

  • Last year one of the best students

  • was a Course 9 student.

  • So two practical things to know.

  • The first thing is everything that we put out

  • will be on the Stellar website.

  • Lecture notes, homeworks, exams, everything

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

  • The second thing is that as you may

  • notice there are rather more lights than usual.

  • I'm wearing a mic.

  • And there are these signs up.

  • We're going to be videotaping this course

  • for the lectures for OCW.

  • And if you're happy with that, cool.

  • If not, just sit on the sides and you

  • won't appear anywhere on video.

  • Sadly, I can't do that.

  • But you're welcome to if you like.

  • But hopefully that should not play a meaningful role

  • in any of the lectures.

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

  • And by learn quantum mechanics, I

  • don't mean to learn how to do calculations,

  • although that's an important and critical thing.

  • I mean learn some intuition.

  • I want you to develop some intuition

  • for quantum phenomena.

  • Now, quantam mechanics is not hard.

  • It has a reputation for being a hard topic.

  • It is not a super hard topic.

  • So in particular, everyone in this room,

  • I'm totally positive, can learn quantum mechanics.

  • It does require concerted effort.

  • It's not a trivial topic.

  • And in order to really develop a good intuition,

  • the essential thing is to solve problems.

  • So the way you develop a new intuition

  • is by solving problems and by dealing

  • with new situations, new context, new regimes, which

  • is what we're going to do in 804.

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

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

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

  • that the most interesting thing you could possibly

  • do when you leave is the problem set.

  • So you decide who has the harder job.

  • So the workload is not so bad.

  • So we have problem sets due, they're

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

  • by 11 AM sharp on Tuesdays every week.

  • Late work, no, not so much.

  • But we will drop one problem set to make up

  • for unanticipated events.

  • We'll return the graded problem sets

  • a week later in recitation.

  • Should be easy.

  • I strongly, strongly encourage you

  • to collaborate with other students on your problem sets.

  • You will learn more, they will learn more,

  • it will be more efficient.

  • Work together.

  • However, write your problem sets yourself.

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

  • your understanding.

  • There will be two midterms, dates to be announced,

  • and one final.

  • I guess we could have multiple, but that

  • would be a little exciting.

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

  • We're not going to take attendance,

  • but they will give a small contribution

  • to your overall grade.

  • And we'll use them most importantly

  • for non-graded but just participation concept questions

  • and the occasional in class quiz to probe your knowledge.

  • This is mostly so that you have a real time

  • measure of your own conceptual understanding of the material.

  • This has been enormously valuable.

  • And something I want to say just right off

  • is that the way I've organized this class

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

  • It's based to the degree possible on empirical lessons

  • about what works in teaching, what

  • actually makes you learn better.

  • And clickers are an excellent example of that.

  • So this is mostly a standard lecture course,

  • but there will be clickers used.

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

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

  • I haven't chosen a specific textbook.

  • And this is discussed on the Stellar web page.

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

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

  • The reason for this is twofold.

  • First off, there are two languages

  • that are canonically used for quantum mechanics.

  • One is called wave mechanics, and the language,

  • the mathematical language is partial differential equations.

  • The other is a matrix mechanics.

  • They have big names.

  • And the language there is linear algebra.

  • And different books emphasize different aspects

  • and use different languages.

  • And they also try to aim at different problems.

  • Some books are aimed towards people

  • who are interested in materials science, some books that

  • are aimed towards people interested in philosophy.

  • And depending on what you want, get

  • the book that's suited to you.

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

  • from each of the recommended texts.

  • So what I really encourage you to do is find a group of people

  • to work with every week, and make sure

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

  • This'll give you as much access to the texts

  • as possible without forcing you to buy four books, which

  • I would discourage you from doing.

  • So finally I guess the last thing to say

  • is if this stuff were totally trivial,

  • you wouldn't need to be here.

  • So ask questions.

  • If you're confused about something,

  • lots of other people in the class

  • are also going to be confused.

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

  • then no one's getting the point, right?

  • So ask questions.

  • Don't hesitate to interrupt.

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

  • And this is true for both in lecture,

  • also go to office hours and recitations.

  • Ask questions.

  • I promise, there's no such thing as a terrible question.

  • Someone else will also be confused.

  • So it's a very valuable to me and everyone else.

  • So before I get going on the actual physics

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

  • Yeah.

  • AUDIENCE: You said there was a lateness policy.

  • ALLAN ADAMS: Lateness policy.

  • No late work is accepted whatsoever.

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

  • you know, you'll be walking to school

  • and your leg is going to fall off,

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

  • next to you, whatever.

  • Things happen.

  • So we will drop your lowest problem set score

  • without any questions.

  • At the end of the semester, we'll

  • just dropped your lowest score.

  • And if you turn them all in, great,

  • whatever your lowest score was, fine.

  • If you missed one, then gone.

  • On the other hand, if you know next week, I'm

  • going to be attacked by a rabid squirrel,

  • it's going to be horrible, I don't

  • want to have to worry about my problem set.

  • Could we work this out?

  • So if you know ahead of time, come to us.

  • But you need to do that well ahead of time.

  • The night before doesn't count.

  • OK?

  • Yeah.

  • AUDIENCE: Will we be able to watch the videos?

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

  • I don't know.

  • I don't think so.

  • I think it's going to happen at the end of the semester.

  • Yeah.

  • OK.

  • So no, you'll be able to watch them later on the OCW website.

  • Other questions.

  • Yeah.

  • AUDIENCE: Are there any other videos

  • that you'd recommend, just like other courses on YouTube?

  • ALLAN ADAMS: Oh.

  • That's an interesting question.

  • I don't off the top of my head, but if you send me an email,

  • I'll pursue it.

  • Because I do know several other lecture series

  • that I like very much, but I don't

  • know if they're available on YouTube or publicly.

  • So send me an email and I'll check.

  • Yeah.

  • AUDIENCE: So how about the reading assignments?

  • ALLAN ADAMS: Reading assignments on the problem set every week

  • will be listed.

  • There will be equivalent reading from every textbook.

  • And if there is something missing,

  • like if no textbook covers something,

  • I'll post a separate reading.

  • Every once in a while, I'll post auxiliary readings,

  • and they'll be available on the Stellar website.

  • So for example, in your problem set, first one was posted,

  • will be available immediately after lecture

  • on the Stellar website.

  • There are three papers that it refers to, or two,

  • and they are posted on the Stellar website

  • and linked from the problem set.

  • Others?

  • OK.

  • So the first lecture.

  • The content of the physics of the first lecture

  • is relatively standalone.

  • It's going to be an introduction to a basic idea then is

  • going to haunt, plague, and charm us

  • through the rest of the semester.

  • The logic of this lecture is based

  • on a very beautiful discussion in the first few chapters

  • of a book by David Albert called Quantum Mechanics

  • and Experience.

  • It's a book for philosophers.

  • But the first few chapters, a really lovely introduction

  • at a non-technical level.

  • And I encourage you to take a look at them,

  • because they're very lovely.

  • But it's to be sure straight up physics.

  • Ready?

  • I love this stuff.

  • today I want to describe to you a particular set

  • of experiments.

  • Now, to my mind, these are the most unsettling experiments

  • ever done.

  • These experiments involve electrons.

  • They have been performed, and the results

  • as I will describe them are true.

  • I'm going to focus on two properties of electrons.

  • I will call them color and hardness.

  • And these are not the technical names.

  • We'll learn the technical names for these properties

  • later on in the semester.

  • But to avoid distracting you by preconceived notions of what

  • these things mean, I'm going to use ambiguous labels, color

  • and hardness.

  • And the empirical fact is that every electron, every electron

  • that's ever been observed is either black or white

  • and no other color.

  • We've never seen a blue electron.

  • There are no green electrons.

  • No one has ever found a fluorescent electron.

  • They're either black, or they are white.

  • It is a binary property.

  • Secondly, their hardness is either hard or soft.

  • They're never squishy.

  • No one's ever found one that dribbles.

  • They are either hard, or they are soft.

  • Binary properties.

  • OK?

  • Now, what I mean by this is that it

  • is possible to build a device which

  • measures the color and the hardness.

  • In particular, it is possible to build

  • a box, which I will call a color box, that measures the color.

  • And the way it works is this.

  • It has three apertures, an in port and two out

  • ports, one which sends out black electrons

  • and one which sends out white electrons.

  • And the utility of this box is that the color

  • can be inferred from the position.

  • If you find the particle, the electron over here,

  • it is a white electron.

  • If you find the electron here, it is a black electron.

  • Cool?

  • Similarly, we can build a hardness box,

  • which again has three apertures, an in port.

  • And hard electrons come out this port,

  • and soft electrons come out this port.

  • Now, if you want, you're free to imagine that these boxes are

  • built by putting a monkey inside.

  • And you send in an electron, and the monkey,

  • you know, with the ears, looks at the electron,

  • and says it's a hard electron, it sends it out one way,

  • or it's a soft electron, it sends it out the other.

  • The workings inside do not matter.

  • And in particular, later in the semester

  • I will describe in considerable detail

  • the workings inside this apparatus.

  • And here's something I want to emphasize to you.

  • It can be built in principle using monkeys,

  • hyper intelligent monkeys that can see electrons.

  • It could also be built using magnets and silver atoms.

  • It could be done with neutrons.

  • It could be done with all sorts of different technologies.

  • And they all give precisely the same results

  • as I'm about to describe.

  • They all give precisely the same results.

  • So it does not matter what's inside.

  • But if you want a little idea, you

  • could imagine putting a monkey inside, a hyper intelligent

  • monkey.

  • I know, it sounds good.

  • So a key property of these hardness boxes and color boxes

  • is that they are repeatable.

  • And here's what I mean by that.

  • If I send in an electron, and I find that it comes out

  • of a color box black, and then I send it in again,

  • then if I send it into another color box,

  • it comes out black again.

  • So in diagrams, if I send in some random electron

  • to a color box, and I discover that it comes out, let's say,

  • the white aperture.

  • And so here's dot dot dot, and I take the ones that come out

  • the white aperture, and I send them into a color box again.

  • Then with 100% confidence, 100% of the time, the electron

  • coming out of the white port incident on the color box

  • will come out the white aperture again.

  • And 0% of the time will it come out the black aperture.

  • So this is a persistent property.

  • You notice that it's white.

  • You measure it again, it's still white.

  • Do a little bit later, it's still white.

  • OK?

  • It's a persistent property.

  • Ditto the hardness.

  • If I send in a bunch of electrons in to a hardness box,

  • here is an important thing.

  • Well, send them into a hardness box,

  • and I take out the ones that come out soft.

  • And I send them again into a hardness box,

  • and they come out soft.

  • They will come out soft with 100%

  • confidence, 100% of the time.

  • Never do they come out the hard aperture.

  • Any questions at this point?

  • So here's a natural question.

  • Might the color and the hardness of an electron be related?

  • And more precisely, might they be correlated?

  • Might knowing the color infer something about the hardness?

  • So for example, so being male and being a bachelor

  • are correlated properties, because if you're male,

  • you don't know if you're a bachelor or not,

  • but if you're a bachelor, you're male.

  • That's the definition of the word.

  • So is it possible that color and hardness

  • are similarly correlated?

  • So, I don't know, there are lots of good examples,

  • like wearing a red shirt and beaming down to the surface

  • and making it back to the Enterprise

  • later after the away team returns.

  • Correlated, right?

  • Negatively, but correlated.

  • So the question is, suppose, e.g.,

  • suppose we know that an electron is white.

  • Does that determine the hardness?

  • So we can answer this question by using our boxes.

  • So here's what I'm going to do.

  • I'm going to take some random set of electrons.

  • That's not random.

  • Random.

  • And I'm going to send them in to a color box.

  • And I'm going to take the electrons that

  • come out the white aperture.

  • And here's a useful fact.

  • When I say random, here's operationally what I mean.

  • I take some piece of material, I scrape it,

  • I pull off some electrons, and they're totally

  • randomly chosen from the material.

  • And I send them in.

  • If I send a random pile of electrons into a color box,

  • useful thing to know, they come out about half and half.

  • It's just some random assortment.

  • Some of them are white, some of them come out black.

  • Suppose I send some random collection of electrons

  • into a color box.

  • And I take those which come out the white aperture.

  • And I want to know, does white determine hardness.

  • So I can do that, check, by then sending these white electrons

  • into a hardness box and seeing what comes out.

  • Hard, soft.

  • And what we find is that 50% of those electrons incident

  • on the hardness box come out hard, and 50% come out soft.

  • OK?

  • And ditto if we reverse this.

  • If we take hardness, and take, for example, a soft electron

  • and send it into a color box, we again get 50-50.

  • So if you take a white electron, you send it

  • into a hardness box, you're at even odds,

  • you're at chance as to whether it's

  • going to come out hard or soft.

  • And similarly, if you send a soft electron

  • into a color box, even odds it's going

  • to come out black or white.

  • So knowing the hardness does not give you

  • any information about the color, and knowing the color

  • does not give you any information about the hardness.

  • cool?

  • These are independent facts, independent properties.

  • They're not correlated in this sense,

  • in precisely this operational sense.

  • Cool?

  • Questions?

  • OK.

  • So measuring the color give zero predictive power

  • for the hardness, and measuring the hardness

  • gives zero predictive power for the color.

  • And from that, I will say that these properties

  • are correlated.

  • So H, hardness, and color are in this sense uncorrelated.

  • So using these properties of the color and hardness boxes,

  • I want to run a few more experiment's.

  • I want to probe these properties of color and hardness

  • a little more.

  • And in particular, knowing these results

  • allows us to make predictions, to predict the results

  • for set a very simple experiments.

  • Now, what we're going to do for the next bit is

  • we're going to run some simple experiments.

  • And we're going to make predictions.

  • And then those simple experiments

  • are going to lead us to more complicated experiments.

  • But let's make sure we understand the simple ones

  • first.

  • So for example, let's take this last experiment, color

  • and hardness, and let's add a color box.

  • One more monkey.

  • So color in, and we take those that

  • come out the white aperture.

  • And we send them into a hardness box.

  • Hard, soft.

  • And we take those electrons which

  • come out the soft aperture.

  • And now let's send these again into a color box.

  • So it's easy to see what to predict.

  • Black, white.

  • So you can imagine a monkey inside this, going, aha.

  • You look at it, you inspect, it comes out white.

  • Here you look at it and inspect, it comes out soft.

  • And you send it into the color box,

  • and what do you expect to happen?

  • Well, let's think about the logic here.

  • Anything reaching the hardness box

  • must have been measured to be white.

  • And we just did the experiment that if you

  • send a white electron into a hardness box,

  • 50% of the time it comes out a hard aperture and 50%

  • of the time it comes out the soft aperture.

  • So now we take that 50% of electrons

  • that comes out the soft aperture, which had previously

  • been observed to be white and soft.

  • And then we send them into a color box, and what happens?

  • Well, since colors are repeatable,

  • the natural expectation is that, of course, it comes out white.

  • So our prediction, our natural prediction

  • here is that of those electrons that are incident on this color

  • box, 100% should come out white, and 0% should come out black.

  • That seem like a reasonable-- let's just make sure

  • that we're all agreeing.

  • So let's vote.

  • How many people think this is probably correct?

  • OK, good.

  • How many people think this probably wrong?

  • OK, good.

  • That's reassuring.

  • Except you're all wrong.

  • Right?

  • In fact, what happens is half of these electrons exit

  • white, 50%.

  • And 50% percent exit black.

  • So let's think about what's going on here.

  • This is really kind of troubling.

  • We've said already that knowing the color

  • doesn't predict the hardness.

  • And yet, this electron, which was previously

  • measured to be white, now when subsequently measured sometimes

  • it comes out white, sometimes it comes out

  • black, 50-50% of the time.

  • So that's surprising.

  • What that tells you is you can't think of the electron

  • as a little ball that has black and soft written on it, right?

  • You can't, because apparently that black and soft

  • isn't a persistent thing, although it's

  • persistent in the sense that once it's black,

  • it stays black.

  • So what's going on here?

  • Now, I should emphasize that the same thing happens

  • if I had changed this to taking the black electrons

  • and throwing in a hardness and picking soft and then measuring

  • the color, or if I had used the hard electrons.

  • Any of those combinations, any of these ports

  • would have given the same results, 50-50.

  • Is not persistent in this sense.

  • Apparently the presence of the hardness box

  • tampers with the color somehow.

  • So it's not quite as trivial is that hyper intelligent monkey.

  • Something else is going on here.

  • So this is suspicious.

  • So here's the first natural move.

  • The first natural move is, oh, look, surely

  • there's some additional property of the electron

  • that we just haven't measured yet

  • that determines whether it comes out the second color

  • box black or white.

  • There's got be some property that determines this.

  • And so people have spent a tremendous amount

  • of time and energy looking at these initial electrons

  • and looking with great care to see whether there's

  • any sort of feature of these incident electrons

  • which determines which port they come out of.

  • And the shocker is no one's ever found such a property.

  • No one has ever found a property which

  • determines which port it comes out of.

  • As far as we can tell, it is completely random.

  • Those that flip and those that don't are

  • indistinguishable at beginning.

  • And let me just emphasize, if anyone found such a-- it's not

  • like we're not looking, right?

  • If anyone found such a property, fame, notoriety,

  • subverting quantum mechanics, Nobel Prize.

  • People have looked.

  • And there is none that anyone's been able to find.

  • And as we'll see later on, using Bell's inequality,

  • we can more or less nail that such things don't exist,

  • such a fact doesn't exist.

  • But this tells us something really disturbing.

  • This tells us, and this is the first real shocker,

  • that there is something intrinsically unpredictable,

  • non-deterministic, and random about physical processes

  • that we observe in a laboratory.

  • There's no way to determine a priori whether it

  • will come out black or white from the second box.

  • Probability in this experiment, it's

  • forced upon us by observations.

  • OK, well, there's another way to come at this.

  • You could say, look, you ran this experiment, that's fine.

  • But look, I've met the guy who built these boxes,

  • and look, he's just some guy, right?

  • And he just didn't do a very good job.

  • The boxes are just badly built.

  • So here's the way to defeat that argument.

  • No, we've built these things out of different materials,

  • using different technologies, using electrons, using

  • neutrons, using bucky-balls, C60, seriously, it's been done.

  • We've done this experiment, and this property does not change.

  • It is persistent.

  • And the thing that's most upsetting to me is that not

  • only do we get the same results independent of what objects we

  • use to run the experiment, we cannot change the probability

  • away from 50-50 at all.

  • Within experimental tolerances, we cannot change,

  • no matter how we build the boxes,

  • we cannot change the probability by part in 100.

  • 50-50.

  • And to anyone who grew up with determinism from Newton,

  • this should hurt.

  • This should feel wrong.

  • But it's a property of the real world.

  • And our job is going to be to deal with it.

  • Rather, your job is going to be to deal with it, because I

  • went through this already.

  • So here's a curious consequence-- oh,

  • any questions before I cruise?

  • OK.

  • So here's a curious consequence of this series of experiments.

  • Here's something you can't do.

  • Are you guys old enough for you can't do this on television?

  • This is so sad.

  • OK, so here's something you can't do.

  • We cannot build, it is impossible to build,

  • a reliable color and hardness box.

  • We've built a box that tells you what color it is.

  • We've built a box that tells you what hardness it is.

  • But you cannot build a meaningful box that tells you

  • what color and hardness an electron is.

  • So in particular, what would this magical box be?

  • It would have four ports.

  • And its ports would say, well, one is white and hard,

  • and one is white and soft, one is black and hard,

  • and one is black and soft.

  • So you can imagine how you might try

  • to build a color and hardness box.

  • So for example, here's something you might imagine.

  • Take your incident electrons, and first

  • send them into a color box.

  • And take those white electrons, and send them

  • into a hardness box.

  • And take those electrons, and this

  • is going to be white and hard, and this

  • is going to be white and soft.

  • And similarly, send these black electrons

  • into the hardness box, and here's hard and black,

  • and here's soft and back.

  • Everybody cool with that?

  • So this seems to do the thing I wanted.

  • It measures both the hardness and the color.

  • What's the problem with it?

  • AUDIENCE: [INAUDIBLE]

  • ALLAN ADAMS: Yeah, exactly.

  • So the color is not persistent.

  • So you tell me this is a soft and black electron, right?

  • That's what you told me.

  • Here's the box.

  • But if I put a color box here, that's

  • the experiment we just ran.

  • And what happens?

  • Does this come out black?

  • No, this is a crappy source of black electrons.

  • It's 50/50 black and white.

  • So this box can't be built.

  • And the reason, and I want to emphasize this,

  • the reason we cannot build this box is not

  • because our experiments are crude.

  • And it's not because I can't build things,

  • although that's true.

  • I was banned from a lab one day after joining it, actually.

  • So I really can't build, but other people can.

  • And that's not why.

  • We can't because of something much more fundamental,

  • something deeper, something in principle,

  • which is encoded in this awesome experiment.

  • This can be done.

  • It does not mean anything, as a consequence.

  • It does not mean anything to say this electron is

  • white and hard, because if you tell me it's white and hard,

  • and I measure the white, well, I know if it's hard,

  • it's going to come out 50-50.

  • It does not mean anything.

  • So this is an important idea.

  • This is an idea which is enshrined in physics

  • with a term which comes with capital

  • letters, the Uncertainty Principle.

  • And the Uncertainty Principle says basically that, look,

  • there's some observable, measurable properties

  • of a system which are incompatible

  • with each other in precisely this way,

  • incompatible with each other in the sense

  • not that you can't know, because you can't know whether it's

  • hard and soft simultaneously, deeper.

  • It is not hard and white simultaneously.

  • It cannot be.

  • It does not mean anything to say it

  • is hard and white simultaneously.

  • That is uncertainty.

  • And again, uncertainty is an idea

  • we're going to come back to over and over in the class.

  • But every time you think about it,

  • this should be the first place you

  • start for the next few weeks.

  • Yeah.

  • Questions.

  • No questions?

  • OK.

  • So at this point, it's really tempting

  • to think yeah, OK, this is just about the hardness

  • and the color of electrons.

  • It's just a weird thing about electrons.

  • It's not a weird thing about the rest of the world.

  • The rest of the world's completely reasonable.

  • And no, that's absolutely wrong.

  • Every object in the world has the same properties.

  • If you take bucky-balls, and you send them

  • through the analogous experiment--

  • and I will show you the data, I think tomorrow,

  • but soon, I will show you the data.

  • When you take bucky-balls and run it

  • through a similar experiment, you get the same effect.

  • Now, bucky-balls are huge, right, 60 carbon atoms.

  • But, OK, OK, at that point, you're

  • saying, dude, come on, huge, 60 carbon atoms.

  • So there is a pendulum, depending

  • on how you define building, in this building, a pendulum which

  • is used, in principle which is used to improve detectors

  • to detect gravitational waves.

  • There's a pendulum with a, I think it's 20 kilo mirror.

  • And that pendulum exhibits the same sort of effects here.

  • We can see these quantum mechanical effects

  • in those mirrors.

  • And this is in breathtakingly awesome experiments

  • done by Nergis Malvalvala, whose name I can never pronounce,

  • but who is totally awesome.

  • She's an amazing physicist.

  • And she can get these kind of quantum effects out of a 20

  • kilo mirror.

  • So before you say something silly, like, oh, it's

  • just electrons, it's 20 kilo mirrors.

  • And if I could put you on a pendulum that accurate,

  • it would be you.

  • OK?

  • These are properties of everything around you.

  • The miracle is not that electrons behave oddly.

  • The miracle is that when you take 10 to the 27 electrons,

  • they behave like cheese.

  • That's the miracle.

  • This is the underlying correct thing.

  • OK, so this is so far so good.

  • But let's go deeper.

  • Let's push it.

  • And to push it, I want to design for you

  • a slightly more elaborate apparatus, a slightly more

  • elaborate experimental apparatus.

  • And for this, I want you to consider the following device.

  • I'm going to need to introduce a couple of new features for you.

  • Here's a hardness box.

  • And it has an in port.

  • And the hardness box has a hard aperture,

  • and it has a soft aperture.

  • And now, in addition to this hardness box,

  • I'm going to introduce two elements.

  • First, mirrors.

  • And what these mirrors do is they take the incident

  • electrons and, nothing else, they

  • change the direction of motion, change the direction of motion.

  • And here's what I mean by doing nothing else.

  • If I take one of these mirrors, and I take,

  • for example, a color box.

  • And I take the white electrons that come out,

  • and I bounce it off the mirror, and then

  • I send these into a color box, then

  • they come out white 100% of the time.

  • It does not change the observable color.

  • Cool?

  • All it does is change the direction.

  • Similarly, with the hardness box,

  • it doesn't change the hardness.

  • It just changes the direction of motion.

  • And every experiment we've ever done on these, guys,

  • changes in no way whatsoever the color

  • or the hardness by subsequent measurement.

  • Cool?

  • Just changes the direction of motion.

  • And then I'm going to add another mirror.

  • It's actually a slightly fancy set of mirrors.

  • All they do is they join these beams together

  • into a single beam.

  • And again, this doesn't change the color.

  • You send in a white electron, you get out,

  • and you measure the color on the other side,

  • you get a white electron.

  • You send in a black electron from here,

  • and you measure the color, you get a black electron again out.

  • Cool?

  • So here's my apparatus.

  • And I'm going to put this inside a big box.

  • And I want to run some experiments

  • with this apparatus.

  • Everyone cool with the basic design?

  • Any questions before I cruise on?

  • This part's fun.

  • So what I want to do now is I want

  • to run some simple experiments before we get to fancy stuff.

  • And the simple experiments are just going to warm you up.

  • They're going to prepare you to make

  • some predictions and some calculations.

  • And eventually we'd like to lead back to this guy.

  • So the first experiment, I'm going

  • to send in white electrons.

  • Whoops.

  • Im.

  • I'm going to send in white electrons.

  • And I'm going to measure at the end,

  • and in particular at the output, the hardness.

  • So I'm going to send in white electrons.

  • And I'm going to measure the hardness.

  • So this is my apparatus.

  • I'm going to measure the hardness at the output.

  • And what I mean by measure the hardness

  • is I throw these electrons into a hardness box

  • and see what comes out.

  • So this is experiment 1.

  • And let me draw this, let me biggen the diagram.

  • So you send white into-- so the mechanism is a hardness box.

  • Mirror, mirror, mirrors, and now we're

  • measuring the hardness out.

  • And the question I want to ask is how many electrons come out

  • the hard aperture, and how many electrons come out

  • the soft aperture of this final hardness box.

  • So I'd like to know what fraction come out hard,

  • and what fraction come out soft.

  • I send an initial white electron,

  • for example I took a color box and took the white output,

  • send them into the hardness box, mirror, mirror,

  • hard, hard, soft.

  • And what fraction come out hard, and what fraction

  • come out soft.

  • So just think about it for a minute.

  • And when you have a prediction in your head, raise your hand.

  • All right, good.

  • Walk me through your prediction.

  • AUDIENCE: I think it should be 50-50.

  • ALLAN ADAMS: 50-50.

  • How come?

  • AUDIENCE: [INAUDIBLE] color doesn't

  • have any bearing on hardness.

  • [INAUDIBLE]

  • ALLAN ADAMS: Awesome.

  • So let me say that again.

  • So we've done the experiment, you send a white electron

  • into the hardness box, and we know

  • that it's non-predictive, 50-50.

  • So if you take a white electron and you send it

  • into the hardness box, 50% of the time

  • it will come out the hard aperture, and 50% of the time

  • it will come out the soft aperture.

  • Now if you take the one that comes out the hard aperture,

  • then you send it up here or send it up here,

  • we know that these mirrors do nothing

  • to the hardness of the electron except

  • change the direction of motion.

  • We've already done that experiment.

  • So you measure the hardness at the output, what do you get?

  • Hard, because it came out hard, mirror, mirror, hardness, hard.

  • But it only came out hard 50% of the time

  • because we sent in initially white electron.

  • Yeah?

  • What about the other 50%?

  • Well, the other 50% of the time, it comes out the soft aperture

  • and follows what I'll call the soft path

  • to the mirror, mirror, hardness.

  • And with soft, mirror, mirror, hardness,

  • you know it comes out soft.

  • 50% of the time it comes out this way,

  • and then it will come out hard.

  • 50% it follows the soft path, and then it will come out soft.

  • Was this the logic?

  • Good.

  • How many people agree with this?

  • Solid.

  • How many people disagree?

  • No abstention.

  • OK.

  • So here's a prediction.

  • Oh, yep.

  • AUDIENCE: Just a question.

  • Could you justify that prediction

  • without talking about oh, well, half the electrons were

  • initially measured to be hard, and half were initially

  • measured to be soft, by just saying, well,

  • we have a hardness box, and then we joined these electrons

  • together again, so we don't know anything about it.

  • So it's just like sending white electrons

  • into one hardness box instead of two.

  • ALLAN ADAMS: Yeah, that's a really tempting argument,

  • isn't it?

  • So let's see.

  • We're going to see in a few minutes

  • whether that kind of an argument is reliable or not.

  • But so far we've been given two different arguments that lead

  • to the same prediction, 50-50.

  • Yeah?

  • Question.

  • AUDIENCE: Are the electrons interacting between themselves?

  • Like when you get them to where--

  • ALLAN ADAMS: Yeah.

  • This is a very good question.

  • So here's a question look you're sending a bunch of electrons

  • into this apparatus.

  • But if I take-- look, I took 802.

  • You take two electrons and you put

  • them close to each other, what do they do?

  • Pyewww.

  • Right?

  • They interact with each other through a potential, right?

  • So yeah, we're being a little bold here, throwing

  • a bunch of electrons in and saying,

  • oh, they're independent.

  • So I'm going to do one better.

  • I will send them in one at a time.

  • One electron through the apparatus.

  • And then I will wait for six weeks.

  • [LAUGHTER]

  • See, you guys laugh, you think that's funny.

  • But there's a famous story about a guy

  • who did a similar experiment with photons, French guy.

  • And, I mean, the French, they know what they're doing.

  • So he wanted to do the same experiment with photons.

  • But the problem is if you take a laser

  • and you shined it into your apparatus,

  • there there are like, 10 to the 18 photons in there

  • at any given moment.

  • And the photons, who knows what they're doing with each other,

  • right?

  • So I want to send in one photon, but the problem

  • is, it's very hard to get a single photon, very hard.

  • So what he did, I kid you not, he took an opaque barrier,

  • I don't remember what it was, it was some sort of film

  • on top of glass, I think it was some sort of oil-tar film.

  • Barton, do you remember what he used?

  • So he takes a film, and it has this opaque property,

  • such that the photons that are incident upon it get absorbed.

  • Once in a blue moon a photon manages

  • to make its way through.

  • Literally, like once every couple of days,

  • or a couple of hours, I think.

  • So it's going to take a long time

  • to get any sort of statistics.

  • But he this advantage, that once every couple of hours

  • or whatever a photon makes its way through.

  • That means inside the apparatus, if it

  • takes a pico-second to cross, triumph, right?

  • That's the week I was talking about.

  • So he does this experiment.

  • But as you can tell, you start the experiment, you press go,

  • and then you wait for six months.

  • Side note on this guy, liked boats, really liked yachts.

  • So he had six months to wait before doing

  • a beautiful experiment and having the results.

  • So what did he do?

  • Went on a world tour in his yacht.

  • Comes back, collects the data, and declares victory,

  • because indeed, he saw the effect he wanted.

  • So I was not kidding.

  • We really do wait.

  • So I will take your challenge.

  • And single electron, throw it in,

  • let it go through the apparatus, takes mere moments.

  • Wait for a week, send in another electron.

  • No electrons are interacting with each other.

  • Just a single electron at a time going through this apparatus.

  • Other complaints?

  • AUDIENCE: More stories?

  • ALLAN ADAMS: Sorry?

  • AUDIENCE: More stories?

  • ALLAN ADAMS: Oh, you'll get them.

  • I have a hard time resisting.

  • So here's a prediction, 50-50.

  • We now have two arguments for this.

  • So again, let's vote after the second argument.

  • 50-50, how many people?

  • You sure?

  • Positive?

  • How many people don't think so?

  • Very small dust.

  • OK.

  • It's correct.

  • Yea.

  • So, good.

  • I like messing with you guys.

  • So remember, we're going to go through a few experiments

  • first where it's going to be very

  • easy to predict the results.

  • We've got four experiments like this to do.

  • And then we'll go on to the interesting examples.

  • But we need to go through them so we know what happens,

  • so we can make an empirical argument rather than an in

  • principle argument.

  • So there's the first experiment.

  • Now, I want to run the second experiment.

  • And the second experiment, same as the first,

  • a little bit louder, a little bit worse.

  • Sorry.

  • The second experiment, we're going

  • to send in hard electrons, and we're

  • going to measure color at out.

  • So again, let's look at the apparatus.

  • We send in hard electrons.

  • And our apparatus is hardness box

  • with a hard and a soft aperture.

  • And now we're going to measure the color at the output.

  • Color, what have I been doing?

  • And now I want to know what fraction come out black,

  • and what fraction come out white.

  • We're using lots of monkeys in this process.

  • OK, so this is not rocket science.

  • Rocket science isn't that complicated.

  • Neuroscience is much harder.

  • This is not neuroscience.

  • So let's figure out what this is.

  • Predictions.

  • So again, think about your prediction

  • your head, come to a conclusion, raise

  • your hand when you have an idea.

  • And just because you don't raise your hand

  • doesn't mean I won't call on you.

  • AUDIENCE: 50-50 black and white.

  • ALLAN ADAMS: 50-50 black and white.

  • I like it.

  • Tell me why.

  • AUDIENCE: It's gone through a hardness box, which

  • scrambled the color, and therefore has to be [INAUDIBLE]

  • ALLAN ADAMS: Great.

  • So the statement, I'm going to say that slightly more slowly.

  • That was an excellent argument.

  • We have a hard electron.

  • We know that hardness boxes are persistent.

  • If you send a hard electron in, it comes out hard.

  • So every electron incident upon our apparatus

  • will transit across the hard trajectory.

  • It will bounce, it will bounce, but it is still hard,

  • because we've already done that experiment.

  • The mirrors do nothing to the hardness.

  • So we send a hard electron into the color box,

  • and what comes out?

  • Well, we've done that experiment, too.

  • Hard into color, 50-50.

  • So the prediction is 50-50.

  • This is your prediction.

  • Is that correct?

  • Awesome.

  • OK, let us vote.

  • How many people think this is correct?

  • Gusto, I like it.

  • How many people think it's not?

  • All right.

  • Yay, this is correct.

  • Third experiment, slightly more complicated.

  • But we have to go through these to get to the good stuff,

  • so humor me for a moment.

  • Third, let's send in white electrons,

  • and then measure the color at the output port.

  • So now we send in white electrons, same beast.

  • And our apparatus is a hardness box

  • with a hard path and a soft path.

  • Do-do-do, mirror, do-do-do, mirror, box,

  • join together into our out.

  • And now we send those out electrons into a color box.

  • And our color box, black and white.

  • And now the question is how many come out black,

  • and how many come out white.

  • Again, think through the logic, follow the electrons,

  • come up with a prediction.

  • Raise your hand when you have a prediction.

  • AUDIENCE: Well, earlier we showed that [INAUDIBLE]

  • so it'll take those paths equally--

  • ALLAN ADAMS: With equal probability.

  • Good.

  • AUDIENCE: Yeah.

  • And then it'll go back into the color box.

  • But earlier when we did the same thing

  • without the weird path-changing, it came out 50-50 still.

  • So I would say still 50-50.

  • ALLAN ADAMS: Great.

  • So let me say that again, out loud.

  • And tell me if this is an accurate

  • extension of what you said.

  • I'm just going to use more words.

  • But it's, I think, the same logic.

  • We have a white electron, initially white electron.

  • We send it into a hardness box.

  • When we send a white electron into a hardness box,

  • we know what happens.

  • 50% of the time it comes out hard, the hard aperture,

  • 50% of the time it comes out the soft aperture.

  • Consider those electrons that came out the hard aperture.

  • Those electrons that came out the hard aperture

  • will then transit across the system,

  • preserving their hardness by virtue of the fact

  • that these mirrors preserve hardness, and end up

  • at a color box.

  • When they end at the color box, when

  • that electron, the single electron in the system

  • ends at this color box, then we know

  • that a hard electron entering a color box

  • comes out black or white 50% of the time.

  • We've done that experiment, too.

  • So for those 50% that came out hard, we get 50/50.

  • Now consider the other 50%.

  • The other half of the time, the single electron in the system

  • will come out the soft aperture.

  • It will then proceed along the soft trajectory, bounce,

  • bounce, not changing its hardness,

  • and is then a soft electron incident on the color box.

  • But we've also done that experiment,

  • and we get 50-50 out, black and white.

  • So those electrons that came out hard come out 50-50,

  • and those electrons that come out soft come out 50/50.

  • And the logic then leads to 50-50, twice, 50-50.

  • Was that an accurate statement?

  • Good.

  • It's a pretty reasonable extension.

  • OK, let's vote.

  • How many people agree with this one?

  • OK, and how many people disagree?

  • Yeah, OK.

  • So vast majority agree.

  • And the answer is no, this is wrong.

  • In fact, all of these, 100% come out white and 0 come out black.

  • Never ever does an electron come out the black aperture.

  • I would like to quote what a student just

  • said, because it's actually the next line in my notes, which

  • is what the hell is going on?

  • So let's the series of follow up experiments

  • to tease out what's going on here.

  • So something very strange, let's just

  • all agree, something very strange just happened.

  • We sent a single electron in.

  • And that single electron comes out the hardness box,

  • well, it either came out the hard aperture

  • or the soft aperture.

  • And if it came out the hard, we know what happens,

  • if it came out the soft, we know what happens.

  • And it's not 50-50.

  • So we need to improve the situation.

  • Hold on a sec.

  • Hold on one sec.

  • Well, OK, go ahead.

  • AUDIENCE: Yeah, it's just a question about the setup.

  • So with the second hardness box, are we

  • collecting both the soft and hard outputs?

  • ALLAN ADAMS: The second, you mean the first hardness box?

  • AUDIENCE: The one-- are we getting-- no, the--

  • ALLAN ADAMS: Which one, sorry?

  • This guy?

  • Oh, that's a mirror, not a hardness box.

  • Oh, thanks for asking.

  • Yeah, sorry.

  • I wish I had a better notation for this, but I don't.

  • There's a classic-- well, I'm not going to go into it.

  • Remember that thing where I can't stop myself

  • from telling stories?

  • So all this does, it's just a set of mirrors.

  • It's a set of fancy mirrors.

  • And all it does is it takes an electron coming

  • this way or an electron coming this way, and both of them

  • get sent out in the same direction.

  • It's like a beam joiner, right?

  • It's like a y junction.

  • That's all it is.

  • So if you will, imagine the box is a box,

  • and you take, I don't know, Professor Zwiebach,

  • and you put him inside.

  • And every time an electron comes up this way,

  • he throws it out that way, and every time

  • it comes in this way, he throws it out that way.

  • And he'd be really ticked at you for putting him in a box,

  • but he'd do the job well.

  • Yeah.

  • AUDIENCE: And this also works if you go one electron at a time?

  • ALLAN ADAMS: This works if you go one electron at a time,

  • this works if you go 14 electrons at a time, it works.

  • It works reliably.

  • Yeah.

  • AUDIENCE: Just, maybe [INAUDIBLE]

  • but what's the difference between this experiment

  • and that one?

  • ALLAN ADAMS: Yeah, I know.

  • Right?

  • Right?

  • So the question was, what's the difference

  • between this experiment and the last one.

  • Yeah, good question.

  • So we're going to have to answer that.

  • Yeah.

  • AUDIENCE: Well, you're mixing again the hardness.

  • So it's like as you weren't measuring it at all, right?

  • ALLAN ADAMS: Apparently it's a lot we weren't measuring it,

  • right?

  • Because we send in the white electron, and at the end

  • we get out that it's still white.

  • So somehow this is like not doing anything.

  • But how does that work?

  • So that's an excellent observation.

  • And I'm going to build you now a couple of experiments that

  • tease out what's going on.

  • And you're not going to like the answer.

  • Yeah.

  • AUDIENCE: How were the white electrons

  • generated in this experiment?

  • ALLAN ADAMS: The white electrons were

  • generated in the following way.

  • I take a random source of electrons,

  • I rub a cat against a balloon and I charge up the balloon.

  • And so I take those random electrons,

  • and I send them into a color box.

  • And we have previously observed that if you

  • take random electrons and throw them into a color box

  • and pull out the electrons that come out the white aperture,

  • if you then send them into a color box

  • again, they're still white.

  • So that's how I've generated them.

  • I could have done it by rubbing the cat against glass,

  • or rubbing it against me, right, just stroke the cat.

  • Any randomly selected set of electrons

  • sent into a color box, and then from which

  • you take the white electrons.

  • AUDIENCE: So how is it different from the experiment up there?

  • ALLAN ADAMS: Yeah.

  • Uh-huh.

  • Exactly.

  • Yeah.

  • AUDIENCE: Is the difference that you never actually know

  • whether the electron's hard or soft?

  • ALLAN ADAMS: That's a really good question.

  • So here's something I'm going to be very careful not

  • to say in this class to the degree possible.

  • I'm not going to use the word to know.

  • AUDIENCE: Well, to measure. [INAUDIBLE]

  • ALLAN ADAMS: Good.

  • Measure is a very slippery word, too.

  • I've used it here because I couldn't really

  • get away with not using it.

  • But we'll talk about that in some detail

  • later on in the course.

  • For the moment, I want to emphasize

  • that it's tempting but dangerous at this point to talk about

  • whether you know or don't know, or whether someone knows

  • or doesn't know, for example, the monkey

  • inside knows or doesn't know.

  • So let's try to avoid that, and focus

  • on just operational questions of what are the things that go in,

  • what are the things that come out, and with what

  • probabilities.

  • And the reason that's so useful is

  • that it's something that you can just do.

  • There's no ambiguity about whether you've

  • caught a white electron in a particular spot.

  • Now in particular, the reason these boxes

  • are such a powerful tool is that you don't measure the electron,

  • you measure the position of the electron.

  • You get hit by the electron or you don't.

  • And by using these boxes we can infer from their position

  • the color or the hardness.

  • And that's the reason these boxes are so useful.

  • So we're inferring from the position, which

  • is easy to measure, you get beaned

  • or you don't, we're inferring the property

  • that we're interested in.

  • It's a really good question, though.

  • Keep it in the back of your mind.

  • And we'll talk about it on and off for the rest

  • of the semester.

  • Yeah.

  • AUDIENCE: So what happens if you have this setup,

  • and you just take away the bottom right mirror?

  • ALLAN ADAMS: Perfect question.

  • This leads me into the next experiment.

  • So here's the modification.

  • But thank you, that's a great question.

  • Here's the modification of this experiment.

  • So let's rig up a small-- hold on,

  • I want to go through the next series of experiments,

  • and then I'll come back to questions.

  • And these are great questions.

  • So I want to rig up a small movable wall, a small movable

  • barrier.

  • And here's what this movable barrier will do.

  • If I put the barrier in, so this would be in the soft path,

  • when I put the barrier in the soft path,

  • it absorbs all electrons incident upon it

  • and impedes them from proceeding.

  • So you put a barrier in here, put a barrier in the soft path,

  • no electrons continue through.

  • An electron incident cannot continue through.

  • When I say that the barrier is out, what I mean

  • is it's not in the way.

  • I've moved it out of the way.

  • Cool?

  • So I want to run the same experiment.

  • And I want to run this experiment using the barriers

  • to tease out how the electrons transit through our apparatus.

  • So experiment four.

  • Let's send in a white electron again.

  • I want to do the same experiment we just did.

  • And color at out, but now with the wall in the soft path.

  • Wall in soft.

  • So that's this experiment.

  • So we send in white electrons, and at the output

  • we measure the color as before.

  • And the question is what fraction come out black,

  • and what fraction come out white.

  • So again, everyone think through it for a second.

  • Just take a second.

  • And this one's a little sneaky.

  • So feel free to discuss it with the person sitting next to you.

  • [CHATTER]

  • ALLAN ADAMS: All right.

  • All right, now that everyone has had a quick second

  • to think through this one, let me just

  • talk through what I'd expect from the point

  • of these experiments.

  • And then we'll talk about whether this is reasonable.

  • So the first thing I expect is that, look,

  • if I send in a white electron and I put it

  • into a hardness pass, I know that 50% of the time it goes

  • out hard, and 50% of the time it goes out soft.

  • If it goes out the soft aperture,

  • it's going to get eaten by the barrier, right?

  • It's going to get eaten by the barrier.

  • So first thing I predict is that the output

  • should be down by 50%.

  • However, here's an important bit of physics.

  • And this comes to the idea of locality.

  • I didn't tell you this, but these

  • armlinks in the experiment I did, 3,000 kilometers long.

  • 3,000 kilometers long.

  • That's too minor.

  • 10 million kilometers long.

  • Really long.

  • Very long.

  • Now, imagine an electron that enters

  • this, an initially white electron.

  • If we had the barriers out, if the barrier was out,

  • what do we get?

  • 100% white, right?

  • We just did this experiment, to our surprise.

  • So if we did this, we get 100%.

  • And that means an electron, any electron,

  • going along the soft path comes out white.

  • Any electron going along the hard path goes out white.

  • They all come out white.

  • So now, imagine I do this.

  • Imagine we put a barrier in here 2 million miles away

  • from this path.

  • How does a hard electron along this path

  • know that I put the barrier there?

  • And I'm going to make it even more sneaky for you.

  • I'm going to insert the barrier along the path

  • after I launched the electron into the apparatus.

  • And when I send in the electron, I will not know at that moment,

  • nor will the electron know, because, you

  • know, they're not very smart, whether the barrier is

  • in place.

  • And this is going to be millions of miles away from this guy.

  • So an electron out here can't know.

  • It hasn't been there.

  • It just hasn't been there.

  • It can't know.

  • But we know that when we ran this apparatus

  • without the barrier in there, they came out 100% white.

  • But it can't possibly know whether the barrier's in

  • there or not, right?

  • It's over here.

  • So what this tells us is that we should expect the output

  • to be down by 50%.

  • But all the electrons that do make

  • it through must come out white, because they

  • didn't know that there was a barrier there.

  • They didn't go along that path.

  • Yeah.

  • AUDIENCE: Not trying to be wise, but why

  • are you using the word know?

  • ALLAN ADAMS: Oh, sorry, thank you.

  • Thank you, thank you, thank you, that was a slip of the tongue.

  • I was making fun of the electron.

  • So in that particular case, I was not

  • referring to my or your knowledge.

  • I was referring to the electron's

  • tragically impoverished knowledge.

  • Yeah.

  • AUDIENCE: But if they come out one at a time white,

  • then wouldn't we know then with certainty

  • that that electron is both hard and white,

  • which is like a violation?

  • ALLAN ADAMS: Well, here's the more troubling thing.

  • Imagine it didn't come out 100% white.

  • Then the electron would have demonstrably not

  • go along the soft path.

  • It would have demonstrably gone through the hard path,

  • because that's the only path available to it.

  • And yet, it would still have known that millions of miles

  • away, there's a barrier on a path it didn't take.

  • So which one's more upsetting to you?

  • And personally, I find this one the less upsetting of the two.

  • So the prediction is our output should down by 50%,

  • because a half of them get eaten.

  • But they should all come out white,

  • because those that didn't get eaten

  • can't possibly know that there was a barrier here,

  • millions of miles away.

  • So we run this experiment.

  • And here's the experimental result.

  • In fact, the experimental result is yes, the output

  • is down by 50%.

  • But no, not 100% white, 50% white.

  • 50% white.

  • The barrier, if we put the barrier in the hardness path.

  • If we put the barrier in the hardness path,

  • still down by 50%, and it's at odds, 50-50.

  • How could the electron know?

  • I'm making fun of it.

  • Yeah.

  • AUDIENCE: So I guess my question is

  • before we ask how it knows that there's

  • a block in one of the paths, how does it know, before,

  • over there, that there were two paths, and combine again?

  • ALLAN ADAMS: Excellent.

  • Exactly.

  • So actually, this problem was there already

  • in the experiment we did.

  • All we've done here is tease out something

  • that was existing in the experiment, something

  • that was disturbing.

  • The presence of those mirrors, and the option

  • of taking two paths, somehow changed

  • the way the electron behaved.

  • How is that possible?

  • And here, we're seeing that very sharply.

  • Thank you for that excellent observation.

  • Yeah.

  • AUDIENCE: What if you replaced the two mirrors

  • with color boxes, so that both color boxes [INAUDIBLE]

  • ALLAN ADAMS: Yeah.

  • So the question is basically, let's take this experiment,

  • and let's make it even more intricate by, for example,

  • replacing these mirrors by color boxes.

  • So here's the thing I want to emphasize.

  • I strongly encourage you to think through that example.

  • And in particular, think through that example, come to my office

  • hours, and ask me about it.

  • So that's going to be setting a different experiment.

  • And different experiments are going

  • to have different results.

  • So we're going to have to deal with that on a case

  • by case basis.

  • It's an interesting example, but it's

  • going to take us a bit afar from where we are right now.

  • But after we get to the punchline from this,

  • come to my office hours and ask me exactly that question.

  • Yeah.

  • AUDIENCE: So we had a color box, we put in white electrons

  • and we got 50-50, like random.

  • How do you know the boxes work?

  • ALLAN ADAMS: How do I know the boxes work?

  • These are the same boxes we used from the beginning.

  • We tested them over and over.

  • AUDIENCE: How did you first check that it was working?

  • [INAUDIBLE]

  • ALLAN ADAMS: How to say-- there's

  • no other way to build a box that does the properties that we

  • want, which is that you send in color and it comes out color

  • again, and the mirrors behave this way.

  • Any box that does those first set of things, which

  • is what I will call a color box, does this, too.

  • There's no other way to do it.

  • I don't mean just because like, no one's tested--

  • AUDIENCE: Because you can't actually check it,

  • you can't actually [INAUDIBLE] you know which one is white.

  • ALLAN ADAMS: Oh, sure, you can.

  • You take the electron that came out of the color box.

  • That's what we mean by saying it's white.

  • AUDIENCE: [INAUDIBLE]

  • ALLAN ADAMS: But that's what it means

  • to say the electron is white.

  • It's like, how do you know that my name is Allan?

  • You say, Allan, and I go, what?

  • Right?

  • But you're like, look that's not a test of whether I'm Allan.

  • It's like, well, what is the test?

  • That's how you test.

  • What's your name?

  • I'm Allan.

  • Oh, great, that's your name.

  • So that's what I mean by white.

  • Now you might quibble that that's a stupid thing

  • to call an electron.

  • And I grant you that.

  • But it is nonetheless a property that I can empirically engage.

  • OK, so I've been told that I never ask questions

  • from the people on the right.

  • Yeah.

  • AUDIENCE: Is it important whether the experimenter

  • knows if the wall is there or not?

  • ALLAN ADAMS: No.

  • This experiment has been done again by some French guys.

  • The French, look, dude.

  • So there's this guy, Alain Aspect, ahh,

  • great experimentalist, great physicist.

  • And he's done lots of beautiful experiments

  • on exactly this topic.

  • And send me an email, and I'll post some example papers

  • and reviews by him-- and he's a great writer-- on the web page.

  • So just send me an email to remind me of that.

  • OK, so we're lowish on time, so let me move on.

  • So what I want to do now is I want

  • to take the lesson of this experiment and the observation

  • that was made a minute ago, that in fact the same problem was

  • present when we ran this experiment and go 100%.

  • We should have been freaked out already.

  • And I want to think through what that's telling us

  • about the electron, the single electron,

  • as it transits the apparatus.

  • The thing is, at this point we're in real trouble.

  • And here's the reason.

  • Consider a single electron inside the apparatus.

  • And I want to think about the electron inside the apparatus

  • while all walls are out.

  • So it's this experiment.

  • Consider the single electron.

  • We know, with total confidence, with complete reliability,

  • that every electron will exit this color box

  • out the white aperture.

  • We've done this experiment.

  • We know it will come out white.

  • Yes?

  • Here's my question.

  • Which route did it take?

  • AUDIENCE: Spoiler.

  • ALLAN ADAMS: Not a spoiler.

  • Which route did it take?

  • AUDIENCE: Why do we care what route?

  • ALLAN ADAMS: I'm asking you the question.

  • That's why you care.

  • I'm the professor here.

  • What is this?

  • Come on.

  • Which route did it take?

  • OK, let's think through the possibilities.

  • Grapple with this question in your belly.

  • Let's think through the possibilities.

  • First off, did it take the hardness path?

  • So as it transits through, the single electron

  • transiting through this apparatus,

  • did it take the hard path or did it take the soft?

  • These are millions of miles long, millions of miles apart.

  • This is not a ridiculous question.

  • Did it go millions of miles in that direction,

  • or millions of miles in that direction?

  • Did it take the hardness path?

  • Ladies and gentlemen, did it take the hard path?

  • AUDIENCE: Yes.

  • ALLAN ADAMS: Well, we ran this experiment

  • by putting a wall in the soft path.

  • And if we put a wall in the soft path,

  • then we know it took the hard path,

  • because no other electrons come out

  • except those that went through the hard path.

  • Correct?

  • On the other hand, if it went through the hard path,

  • it would come out 50% of the time white

  • and 50% of the time black.

  • But in fact, in this apparatus it comes out always 100% white.

  • It cannot have taken the hard path.

  • No.

  • Did it take the soft path?

  • Same argument, different side, right?

  • No.

  • Well, this is not looking good.

  • Well, look, this was suggested.

  • Maybe it took both.

  • Maybe electrons are sneaky little devils

  • that split in two, and part of it goes one way and part of it

  • goes the other.

  • Maybe it took both paths.

  • So this is easy.

  • We can test this one.

  • And here is how I'm going to test this one.

  • Oh, sorry.

  • Actually, I'm not going to do that yet.

  • So we can test this one.

  • So if it took both paths, here's what you should be able to do.

  • You should be able to put a detector along each path,

  • and you'd be able to follow, if you've

  • got half an electron on one side and half an electron

  • on the other, or maybe two electrons,

  • one on each side and one on the other.

  • So this is the thing that you'd predict

  • if you said it went both.

  • So here's what we'll do.

  • We will take detectors.

  • We will put one along the hard path and one

  • along the soft path.

  • We will run the experiment and then observe

  • whether, and ask whether, we see two electrons,

  • we see half and half, what do we see.

  • The answer is you always, always see one electron on one

  • of the paths.

  • You never see half an electron.

  • You never see a squishy electron.

  • You see one electron on one path, period.

  • It did not take both.

  • You never see an electron split in two, divided, confused.

  • No.

  • Well, it didn't take the hard path,

  • didn't take the soft path, it didn't take both.

  • There's one option left.

  • Neither.

  • Well, I say neither.

  • But what about neither?

  • And that's easy.

  • Let's put a barrier in both paths.

  • And then what happens?

  • Nothing comes out.

  • So no.

  • So now, to repeat an earlier prescient remark

  • from one of the students, what the hell?

  • So here's the world we're facing.

  • I want you to think about this.

  • Take this seriously.

  • Here's the world we're facing.

  • And when I say, here's the world we're facing,

  • I don't mean just these experiments.

  • I mean the world around you, 20 kilo mirrors, bucky-balls,

  • here is what they do.

  • When you send them through an apparatus like this,

  • every single object that goes through this apparatus

  • does not take the hard path, it does not take the soft path,

  • it doesn't take both, and it does not take neither.

  • And that pretty much exhausts the set

  • of logical possibilities.

  • So what are electrons doing when they're inside the apparatus?

  • How do you describe that electron inside the apparatus?

  • You can't say it's on one path, you

  • can't say it's on the other, it's not on both,

  • and it's not on neither.

  • What is it doing halfway through this experiment?

  • So if our experiments are accurate,

  • and to the best of our ability to determine,

  • they are, and if our arguments are correct, and that's on me,

  • then they're doing something, these electrons

  • are doing something we've just never thought of before,

  • something we've never dreamt of before,

  • something for which we don't really

  • have good words in the English language.

  • Apparently, empirically, electrons have a way of moving,

  • electrons have a way of being which is unlike anything

  • that we're used to thinking about.

  • And so do molecules.

  • And so do bacteria.

  • So does chalk.

  • It's just harder to detect in those objects.

  • So physicists have a name for this new mode of being.

  • And we call it superposition.

  • Now, at the moment, superposition

  • is code for I have no idea what's going on.

  • Usage of the word superposition would go something like this.

  • An initially white electron inside this apparatus

  • with the walls out is neither hard, nor soft,

  • nor both, nor neither.

  • It is, in fact, in a superposition of being hard

  • and of being soft.

  • This is why we can't meaningfully

  • say this electron is some color and some hardness.

  • Not because our boxes are crude, and not because we're ignorant,

  • though our boxes are crude and we are ignorant.

  • It's deeper.

  • Having a definite color means not having a definite hardness,

  • but rather being in a superposition of being hard

  • and being soft.

  • Every electron exits a hardness box either hard or soft.

  • But not every electron is hard or soft.

  • It can also be a superposition of being hard or being soft.

  • The probability that we subsequently

  • measure it to be hard or soft depends

  • on precisely what superposition it is.

  • For example, we know that if an electron is

  • in the superposition corresponding to being white

  • then there are even odds of it being subsequently

  • measured be hard or to be soft.

  • So to build a better definition of superposition

  • than I have no idea what's going on

  • is going to require a new language.

  • And that language is quantum mechanics.

  • And the underpinnings of this language

  • are the topic of the course.

  • And developing a better understanding

  • of this idea of superposition is what

  • you have to do over the next three months.

  • Now, if all of this troubles your intuition,

  • well, that shouldn't be too surprising.

  • Your intuition was developed by throwing spears, and running

  • from tigers, and catching toast as it jumps out

  • of the toaster, all of which involves things so big

  • and with so much energy that quantum effects are negligible.

  • As a friend of mine likes to say,

  • you don't need to know quantum mechanics to make chicken soup.

  • However, when we work in very different regimes, when

  • we work with atoms, when we work with molecules, when we work

  • in the regime of very low energies and very

  • small objects, your intuition is just not a reasonable guide.

  • It's not that the electrons-- and I cannot emphasize this

  • strongly enough-- it is not that the electrons are weird.

  • The electrons do what electrons do.

  • This is what they do.

  • And it violates your intuition, but it's true.

  • The thing that's surprising is that lots of electrons

  • behave like this.

  • Lots of electrons behave like cheese and chalk.

  • And that's the goal of 804, to step

  • beyond your daily experience and your familiar intuition

  • and to develop an intuition for this idea of superposition.

  • And we'll start in the next lecture.

  • I'll see you on Thursday.

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