Lecture 1: Introduction to Superposition

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Quantam mechanics Is my daily language.

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Quantum mechanics is my old friend.

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I met quantum mechanics 20 years ago.

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I just realized that last night.

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It was kind of depressing.

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So, old friend.

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It's also my most powerful tool.

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So I'm pretty psyched about it.

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Our recitation instructors are Barton Zwiebach, yea!

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And Matt Evans-- yea!

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

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Hi.

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So he just started his faculty position,

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which is pretty awesome.

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And our TA is Paolo Glorioso.

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Paolo, are you here?

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Yea!

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There you go.

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

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

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Awesome.

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

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Solid.

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6?

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Excellent.

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9?

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No one?

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

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That's a shame.

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Last year one of the best students

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was a Course 9 student.

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So two practical things to know.

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The first thing is everything that we put out

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will be on the Stellar website.

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Lecture notes, homeworks, exams, everything

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

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The second thing is that as you may

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notice there are rather more lights than usual.

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I'm wearing a mic.

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And there are these signs up.

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We're going to be videotaping this course

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for the lectures for OCW.

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And if you're happy with that, cool.

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If not, just sit on the sides and you

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won't appear anywhere on video.

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Sadly, I can't do that.

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But you're welcome to if you like.

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But hopefully that should not play a meaningful role

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in any of the lectures.

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

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And by learn quantum mechanics, I

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don't mean to learn how to do calculations,

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although that's an important and critical thing.

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I mean learn some intuition.

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I want you to develop some intuition

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for quantum phenomena.

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Now, quantam mechanics is not hard.

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It has a reputation for being a hard topic.

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It is not a super hard topic.

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So in particular, everyone in this room,

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I'm totally positive, can learn quantum mechanics.

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It does require concerted effort.

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It's not a trivial topic.

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And in order to really develop a good intuition,

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the essential thing is to solve problems.

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So the way you develop a new intuition

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is by solving problems and by dealing

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with new situations, new context, new regimes, which

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is what we're going to do in 804.

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

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

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

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that the most interesting thing you could possibly

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do when you leave is the problem set.

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So you decide who has the harder job.

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So the workload is not so bad.

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So we have problem sets due, they're

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

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by 11 AM sharp on Tuesdays every week.

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Late work, no, not so much.

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But we will drop one problem set to make up

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for unanticipated events.

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We'll return the graded problem sets

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a week later in recitation.

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Should be easy.

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I strongly, strongly encourage you

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to collaborate with other students on your problem sets.

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You will learn more, they will learn more,

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it will be more efficient.

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Work together.

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However, write your problem sets yourself.

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

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your understanding.

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There will be two midterms, dates to be announced,

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and one final.

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I guess we could have multiple, but that

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would be a little exciting.

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

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We're not going to take attendance,

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but they will give a small contribution

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to your overall grade.

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And we'll use them most importantly

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for non-graded but just participation concept questions

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and the occasional in class quiz to probe your knowledge.

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This is mostly so that you have a real time

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measure of your own conceptual understanding of the material.

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This has been enormously valuable.

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And something I want to say just right off

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is that the way I've organized this class

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

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It's based to the degree possible on empirical lessons

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about what works in teaching, what

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actually makes you learn better.

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And clickers are an excellent example of that.

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So this is mostly a standard lecture course,

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but there will be clickers used.

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

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

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I haven't chosen a specific textbook.

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And this is discussed on the Stellar web page.

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

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

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The reason for this is twofold.

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First off, there are two languages

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that are canonically used for quantum mechanics.

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One is called wave mechanics, and the language,

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the mathematical language is partial differential equations.

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The other is a matrix mechanics.

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They have big names.

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And the language there is linear algebra.

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And different books emphasize different aspects

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and use different languages.

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And they also try to aim at different problems.

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Some books are aimed towards people

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who are interested in materials science, some books that

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are aimed towards people interested in philosophy.

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And depending on what you want, get

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the book that's suited to you.

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

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from each of the recommended texts.

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

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to work with every week, and make sure

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

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This'll give you as much access to the texts

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as possible without forcing you to buy four books, which

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I would discourage you from doing.

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So finally I guess the last thing to say

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is if this stuff were totally trivial,

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you wouldn't need to be here.

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So ask questions.

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If you're confused about something,

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lots of other people in the class

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are also going to be confused.

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

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then no one's getting the point, right?

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So ask questions.

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Don't hesitate to interrupt.

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

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And this is true for both in lecture,

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also go to office hours and recitations.

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Ask questions.

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

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Someone else will also be confused.

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

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So before I get going on the actual physics

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

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Yeah.

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AUDIENCE: You said there was a lateness policy.

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ALLAN ADAMS: Lateness policy.

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No late work is accepted whatsoever.

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

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you know, you'll be walking to school

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and your leg is going to fall off,

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

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next to you, whatever.

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Things happen.

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So we will drop your lowest problem set score

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without any questions.

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At the end of the semester, we'll

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just dropped your lowest score.

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And if you turn them all in, great,

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whatever your lowest score was, fine.

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If you missed one, then gone.

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

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going to be attacked by a rabid squirrel,

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

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want to have to worry about my problem set.

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Could we work this out?

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

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But you need to do that well ahead of time.

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The night before doesn't count.

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OK?

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Yeah.

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AUDIENCE: Will we be able to watch the videos?

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

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I don't know.

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I don't think so.

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

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Yeah.

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OK.

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

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Other questions.

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Yeah.

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AUDIENCE: Are there any other videos

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

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ALLAN ADAMS: Oh.

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That's an interesting question.

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

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I'll pursue it.

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Because I do know several other lecture series

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that I like very much, but I don't

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know if they're available on YouTube or publicly.

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So send me an email and I'll check.

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Yeah.

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AUDIENCE: So how about the reading assignments?

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ALLAN ADAMS: Reading assignments on the problem set every week

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will be listed.

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There will be equivalent reading from every textbook.

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And if there is something missing,

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like if no textbook covers something,

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I'll post a separate reading.

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

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and they'll be available on the Stellar website.

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

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will be available immediately after lecture

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on the Stellar website.

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

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and they are posted on the Stellar website

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and linked from the problem set.

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Others?

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OK.

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So the first lecture.

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The content of the physics of the first lecture

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is relatively standalone.

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

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going to haunt, plague, and charm us

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through the rest of the semester.

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The logic of this lecture is based

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on a very beautiful discussion in the first few chapters

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of a book by David Albert called Quantum Mechanics

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and Experience.

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It's a book for philosophers.

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But the first few chapters, a really lovely introduction

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at a non-technical level.

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And I encourage you to take a look at them,

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because they're very lovely.

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But it's to be sure straight up physics.

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Ready?

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I love this stuff.

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today I want to describe to you a particular set

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of experiments.

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

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ever done.

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These experiments involve electrons.

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They have been performed, and the results

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as I will describe them are true.

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

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I will call them color and hardness.

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And these are not the technical names.

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We'll learn the technical names for these properties

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later on in the semester.

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But to avoid distracting you by preconceived notions of what

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

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and hardness.

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And the empirical fact is that every electron, every electron

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that's ever been observed is either black or white

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and no other color.

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We've never seen a blue electron.

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There are no green electrons.

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No one has ever found a fluorescent electron.

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They're either black, or they are white.

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It is a binary property.

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Secondly, their hardness is either hard or soft.

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They're never squishy.

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No one's ever found one that dribbles.

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They are either hard, or they are soft.

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Binary properties.

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OK?

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Now, what I mean by this is that it

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is possible to build a device which

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measures the color and the hardness.

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In particular, it is possible to build

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

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And the way it works is this.

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It has three apertures, an in port and two out

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ports, one which sends out black electrons

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and one which sends out white electrons.

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And the utility of this box is that the color

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can be inferred from the position.

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If you find the particle, the electron over here,

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it is a white electron.

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

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Cool?

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Similarly, we can build a hardness box,

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which again has three apertures, an in port.

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And hard electrons come out this port,

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and soft electrons come out this port.

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

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built by putting a monkey inside.

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And you send in an electron, and the monkey,

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

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

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

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The workings inside do not matter.

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And in particular, later in the semester

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I will describe in considerable detail

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the workings inside this apparatus.

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

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It can be built in principle using monkeys,

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hyper intelligent monkeys that can see electrons.

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It could also be built using magnets and silver atoms.

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It could be done with neutrons.

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It could be done with all sorts of different technologies.

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And they all give precisely the same results

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as I'm about to describe.

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They all give precisely the same results.

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So it does not matter what's inside.

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But if you want a little idea, you

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could imagine putting a monkey inside, a hyper intelligent

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monkey.

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I know, it sounds good.

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So a key property of these hardness boxes and color boxes

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is that they are repeatable.

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And here's what I mean by that.

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

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

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then if I send it into another color box,

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it comes out black again.

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So in diagrams, if I send in some random electron

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

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the white aperture.

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

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

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

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coming out of the white port incident on the color box

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will come out the white aperture again.

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

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So this is a persistent property.

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You notice that it's white.

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You measure it again, it's still white.

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

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OK?

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It's a persistent property.

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Ditto the hardness.

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

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here is an important thing.

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Well, send them into a hardness box,

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and I take out the ones that come out soft.

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And I send them again into a hardness box,

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and they come out soft.

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They will come out soft with 100%

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confidence, 100% of the time.

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Never do they come out the hard aperture.

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Any questions at this point?

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So here's a natural question.

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

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And more precisely, might they be correlated?

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Might knowing the color infer something about the hardness?

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So for example, so being male and being a bachelor

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are correlated properties, because if you're male,

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

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

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That's the definition of the word.

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So is it possible that color and hardness

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are similarly correlated?

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

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like wearing a red shirt and beaming down to the surface

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and making it back to the Enterprise

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later after the away team returns.

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Correlated, right?

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Negatively, but correlated.

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

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suppose we know that an electron is white.

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Does that determine the hardness?

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So we can answer this question by using our boxes.

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So here's what I'm going to do.

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

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That's not random.

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Random.

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

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And I'm going to take the electrons that

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come out the white aperture.

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And here's a useful fact.

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

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I take some piece of material, I scrape it,

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I pull off some electrons, and they're totally

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randomly chosen from the material.

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And I send them in.

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

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

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It's just some random assortment.

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

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Suppose I send some random collection of electrons

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into a color box.

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And I take those which come out the white aperture.

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And I want to know, does white determine hardness.

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

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into a hardness box and seeing what comes out.

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Hard, soft.

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

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

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OK?

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And ditto if we reverse this.

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

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

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So if you take a white electron, you send it

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

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you're at chance as to whether it's

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going to come out hard or soft.

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And similarly, if you send a soft electron

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into a color box, even odds it's going

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to come out black or white.

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So knowing the hardness does not give you

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any information about the color, and knowing the color

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does not give you any information about the hardness.

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cool?

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These are independent facts, independent properties.

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They're not correlated in this sense,

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in precisely this operational sense.

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Cool?

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Questions?

19:20

OK.

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So measuring the color give zero predictive power

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for the hardness, and measuring the hardness

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gives zero predictive power for the color.

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And from that, I will say that these properties

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are correlated.

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

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So using these properties of the color and hardness boxes,

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I want to run a few more experiment's.

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I want to probe these properties of color and hardness

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a little more.

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And in particular, knowing these results

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allows us to make predictions, to predict the results

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for set a very simple experiments.

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

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we're going to run some simple experiments.

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And we're going to make predictions.

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And then those simple experiments

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are going to lead us to more complicated experiments.

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But let's make sure we understand the simple ones

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first.

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

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

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One more monkey.

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So color in, and we take those that

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come out the white aperture.

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And we send them into a hardness box.

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Hard, soft.

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And we take those electrons which

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come out the soft aperture.

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

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So it's easy to see what to predict.

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Black, white.

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

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

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

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And you send it into the color box,

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and what do you expect to happen?

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Well, let's think about the logic here.

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Anything reaching the hardness box

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must have been measured to be white.

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And we just did the experiment that if you

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send a white electron into a hardness box,

21:29

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

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of the time it comes out the soft aperture.

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So now we take that 50% of electrons

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that comes out the soft aperture, which had previously

21:38

been observed to be white and soft.

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

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Well, since colors are repeatable,

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

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So our prediction, our natural prediction

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

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

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

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that we're all agreeing.

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So let's vote.

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How many people think this is probably correct?

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OK, good.

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How many people think this probably wrong?

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OK, good.

22:26

That's reassuring.

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Except you're all wrong.

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Right?

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In fact, what happens is half of these electrons exit

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white, 50%.

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And 50% percent exit black.

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

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This is really kind of troubling.

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We've said already that knowing the color

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doesn't predict the hardness.

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And yet, this electron, which was previously

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measured to be white, now when subsequently measured sometimes

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it comes out white, sometimes it comes out

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black, 50-50% of the time.

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So that's surprising.

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

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

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You can't, because apparently that black and soft

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isn't a persistent thing, although it's

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persistent in the sense that once it's black,

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it stays black.

23:19

So what's going on here?

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Now, I should emphasize that the same thing happens

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if I had changed this to taking the black electrons

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and throwing in a hardness and picking soft and then measuring

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

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Any of those combinations, any of these ports

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would have given the same results, 50-50.

23:39

Is not persistent in this sense.

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Apparently the presence of the hardness box

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tampers with the color somehow.

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

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Something else is going on here.

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So this is suspicious.

23:56

So here's the first natural move.

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The first natural move is, oh, look, surely

24:01

there's some additional property of the electron

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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.

1:00:00

Very long.

1:00:04

Now, imagine an electron that enters

1:00:06

this, an initially white electron.

1:00:07

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

1:00:11

what do we get?

1:00:14

100% white, right?

1:00:15

We just did this experiment, to our surprise.

1:00:17

So if we did this, we get 100%.

1:00:18

And that means an electron, any electron,

1:00:20

going along the soft path comes out white.

1:00:21

Any electron going along the hard path goes out white.

1:00:24

They all come out white.

1:00:27

So now, imagine I do this.

1:00:29

Imagine we put a barrier in here 2 million miles away

1:00:33

from this path.

1:00:36

How does a hard electron along this path

1:00:37

know that I put the barrier there?

1:00:39

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

1:00:41

I'm going to insert the barrier along the path

1:00:44

after I launched the electron into the apparatus.

1:00:49

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

1:00:53

nor will the electron know, because, you

1:00:55

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

1:00:58

in place.

1:00:58

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

1:01:02

So an electron out here can't know.

1:01:05

It hasn't been there.

1:01:06

It just hasn't been there.

1:01:07

It can't know.

1:01:08

But we know that when we ran this apparatus

1:01:10

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

1:01:14

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

1:01:16

there or not, right?

1:01:18

It's over here.

1:01:22

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

1:01:25

to be down by 50%.

1:01:26

But all the electrons that do make

1:01:30

it through must come out white, because they

1:01:33

didn't know that there was a barrier there.

1:01:35

They didn't go along that path.

1:01:40

Yeah.

1:01:40

AUDIENCE: Not trying to be wise, but why

1:01:42

are you using the word know?

1:01:43

ALLAN ADAMS: Oh, sorry, thank you.

1:01:46

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

1:01:48

I was making fun of the electron.

1:01:50

So in that particular case, I was not

1:01:53

referring to my or your knowledge.

1:01:55

I was referring to the electron's

1:01:56

tragically impoverished knowledge.

1:02:01

Yeah.

1:02:02

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

1:02:04

then wouldn't we know then with certainty

1:02:06

that that electron is both hard and white,

1:02:09

which is like a violation?

1:02:11

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

1:02:14

Imagine it didn't come out 100% white.

1:02:17

Then the electron would have demonstrably not

1:02:20

go along the soft path.

1:02:22

It would have demonstrably gone through the hard path,

1:02:25

because that's the only path available to it.

1:02:27

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

1:02:29

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

1:02:31

So which one's more upsetting to you?

1:02:36

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

1:02:40

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

1:02:43

because a half of them get eaten.

1:02:44

But they should all come out white,

1:02:46

because those that didn't get eaten

1:02:47

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

1:02:50

millions of miles away.

1:02:53

So we run this experiment.

1:02:55

And here's the experimental result.

1:02:57

In fact, the experimental result is yes, the output

1:02:59

is down by 50%.

1:03:00

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

1:03:07

50% white.

1:03:11

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

1:03:14

If we put the barrier in the hardness path,

1:03:16

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

1:03:23

How could the electron know?

1:03:25

I'm making fun of it.

1:03:26

Yeah.

1:03:27

AUDIENCE: So I guess my question is

1:03:29

before we ask how it knows that there's

1:03:31

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

1:03:34

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

1:03:37

ALLAN ADAMS: Excellent.

1:03:38

Exactly.

1:03:38

So actually, this problem was there already

1:03:40

in the experiment we did.

1:03:41

All we've done here is tease out something

1:03:43

that was existing in the experiment, something

1:03:44

that was disturbing.

1:03:45

The presence of those mirrors, and the option

1:03:48

of taking two paths, somehow changed

1:03:51

the way the electron behaved.

1:03:53

How is that possible?

1:03:54

And here, we're seeing that very sharply.

1:03:56

Thank you for that excellent observation.

1:03:58

Yeah.

1:03:58

AUDIENCE: What if you replaced the two mirrors

1:04:00

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

1:04:07

ALLAN ADAMS: Yeah.

1:04:10

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

1:04:12

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

1:04:16

replacing these mirrors by color boxes.

1:04:18

So here's the thing I want to emphasize.

1:04:23

I strongly encourage you to think through that example.

1:04:25

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

1:04:28

hours, and ask me about it.

1:04:31

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

1:04:33

And different experiments are going

1:04:34

to have different results.

1:04:36

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

1:04:37

by case basis.

1:04:38

It's an interesting example, but it's

1:04:38

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

1:04:41

But after we get to the punchline from this,

1:04:43

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

1:04:46

Yeah.

1:04:47

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

1:04:51

and we got 50-50, like random.

1:04:53

How do you know the boxes work?

1:04:55

ALLAN ADAMS: How do I know the boxes work?

1:04:56

These are the same boxes we used from the beginning.

1:04:58

We tested them over and over.

1:04:59

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

1:05:01

[INAUDIBLE]

1:05:03

ALLAN ADAMS: How to say-- there's

1:05:04

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

1:05:07

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

1:05:10

again, and the mirrors behave this way.

1:05:13

Any box that does those first set of things, which

1:05:15

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

1:05:17

There's no other way to do it.

1:05:19

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

1:05:21

AUDIENCE: Because you can't actually check it,

1:05:23

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

1:05:26

ALLAN ADAMS: Oh, sure, you can.

1:05:27

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

1:05:29

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

1:05:30

AUDIENCE: [INAUDIBLE]

1:05:31

ALLAN ADAMS: But that's what it means

1:05:32

to say the electron is white.

1:05:34

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

1:05:35

You say, Allan, and I go, what?

1:05:37

Right?

1:05:37

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

1:05:40

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

1:05:41

That's how you test.

1:05:42

What's your name?

1:05:43

I'm Allan.

1:05:43

Oh, great, that's your name.

1:05:44

So that's what I mean by white.

1:05:46

Now you might quibble that that's a stupid thing

1:05:48

to call an electron.

1:05:49

And I grant you that.

1:05:50

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

1:05:53

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

1:05:55

from the people on the right.

1:05:57

Yeah.

1:05:57

AUDIENCE: Is it important whether the experimenter

1:05:59

knows if the wall is there or not?

1:06:02

ALLAN ADAMS: No.

1:06:03

This experiment has been done again by some French guys.

1:06:06

The French, look, dude.

1:06:08

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

1:06:12

great experimentalist, great physicist.

1:06:14

And he's done lots of beautiful experiments

1:06:16

on exactly this topic.

1:06:17

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

1:06:20

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

1:06:23

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

1:06:25

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

1:06:29

So what I want to do now is I want

1:06:30

to take the lesson of this experiment and the observation

1:06:32

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

1:06:35

present when we ran this experiment and go 100%.

1:06:37

We should have been freaked out already.

1:06:39

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

1:06:41

about the electron, the single electron,

1:06:43

as it transits the apparatus.

1:06:52

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

1:06:56

And here's the reason.

1:06:58

Consider a single electron inside the apparatus.

1:07:02

And I want to think about the electron inside the apparatus

1:07:05

while all walls are out.

1:07:06

So it's this experiment.

1:07:09

Consider the single electron.

1:07:11

We know, with total confidence, with complete reliability,

1:07:15

that every electron will exit this color box

1:07:17

out the white aperture.

1:07:18

We've done this experiment.

1:07:19

We know it will come out white.

1:07:20

Yes?

1:07:23

Here's my question.

1:07:26

Which route did it take?

1:07:34

AUDIENCE: Spoiler.

1:07:37

ALLAN ADAMS: Not a spoiler.

1:07:39

Which route did it take?

1:07:41

AUDIENCE: Why do we care what route?

1:07:43

ALLAN ADAMS: I'm asking you the question.

1:07:44

That's why you care.

1:07:46

I'm the professor here.

1:07:47

What is this?

1:07:49

Come on.

1:07:51

Which route did it take?

1:07:56

OK, let's think through the possibilities.

1:07:58

Grapple with this question in your belly.

1:08:00

Let's think through the possibilities.

1:08:02

First off, did it take the hardness path?

1:08:05

So as it transits through, the single electron

1:08:07

transiting through this apparatus,

1:08:08

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

1:08:10

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

1:08:13

This is not a ridiculous question.

1:08:15

Did it go millions of miles in that direction,

1:08:17

or millions of miles in that direction?

1:08:19

Did it take the hardness path?

1:08:22

Ladies and gentlemen, did it take the hard path?

1:08:25

AUDIENCE: Yes.

1:08:29

ALLAN ADAMS: Well, we ran this experiment

1:08:31

by putting a wall in the soft path.

1:08:33

And if we put a wall in the soft path,

1:08:35

then we know it took the hard path,

1:08:37

because no other electrons come out

1:08:38

except those that went through the hard path.

1:08:40

Correct?

1:08:40

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

1:08:43

it would come out 50% of the time white

1:08:46

and 50% of the time black.

1:08:48

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

1:08:52

It cannot have taken the hard path.

1:08:55

No.

1:08:59

Did it take the soft path?

1:09:05

Same argument, different side, right?

1:09:08

No.

1:09:10

Well, this is not looking good.

1:09:12

Well, look, this was suggested.

1:09:16

Maybe it took both.

1:09:19

Maybe electrons are sneaky little devils

1:09:21

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

1:09:24

goes the other.

1:09:27

Maybe it took both paths.

1:09:29

So this is easy.

1:09:30

We can test this one.

1:09:31

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

1:09:35

Oh, sorry.

1:09:37

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

1:09:39

So we can test this one.

1:09:40

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

1:09:43

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

1:09:46

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

1:09:48

got half an electron on one side and half an electron

1:09:50

on the other, or maybe two electrons,

1:09:51

one on each side and one on the other.

1:09:53

So this is the thing that you'd predict

1:09:54

if you said it went both.

1:09:55

So here's what we'll do.

1:09:56

We will take detectors.

1:09:57

We will put one along the hard path and one

1:09:59

along the soft path.

1:10:00

We will run the experiment and then observe

1:10:02

whether, and ask whether, we see two electrons,

1:10:05

we see half and half, what do we see.

1:10:06

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

1:10:10

of the paths.

1:10:12

You never see half an electron.

1:10:14

You never see a squishy electron.

1:10:15

You see one electron on one path, period.

1:10:18

It did not take both.

1:10:20

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

1:10:25

No.

1:10:28

Well, it didn't take the hard path,

1:10:30

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

1:10:33

There's one option left.

1:10:35

Neither.

1:10:36

Well, I say neither.

1:10:36

But what about neither?

1:10:40

And that's easy.

1:10:41

Let's put a barrier in both paths.

1:10:44

And then what happens?

1:10:46

Nothing comes out.

1:10:48

So no.

1:10:55

So now, to repeat an earlier prescient remark

1:10:58

from one of the students, what the hell?

1:11:01

So here's the world we're facing.

1:11:03

I want you to think about this.

1:11:04

Take this seriously.

1:11:05

Here's the world we're facing.

1:11:05

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

1:11:07

I don't mean just these experiments.

1:11:09

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

1:11:14

here is what they do.

1:11:15

When you send them through an apparatus like this,

1:11:19

every single object that goes through this apparatus

1:11:22

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

1:11:25

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

1:11:29

And that pretty much exhausts the set

1:11:31

of logical possibilities.

1:11:34

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

1:11:40

How do you describe that electron inside the apparatus?

1:11:43

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

1:11:44

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

1:11:46

and it's not on neither.

1:11:47

What is it doing halfway through this experiment?

1:11:51

So if our experiments are accurate,

1:11:52

and to the best of our ability to determine,

1:11:54

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

1:12:00

then they're doing something, these electrons

1:12:02

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

1:12:05

something we've never dreamt of before,

1:12:06

something for which we don't really

1:12:08

have good words in the English language.

1:12:11

Apparently, empirically, electrons have a way of moving,

1:12:16

electrons have a way of being which is unlike anything

1:12:19

that we're used to thinking about.

1:12:22

And so do molecules.

1:12:23

And so do bacteria.

1:12:25

So does chalk.

1:12:28

It's just harder to detect in those objects.

1:12:32

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

1:12:35

And we call it superposition.

1:12:39

Now, at the moment, superposition

1:12:42

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

1:12:48

Usage of the word superposition would go something like this.

1:12:51

An initially white electron inside this apparatus

1:12:55

with the walls out is neither hard, nor soft,

1:12:59

nor both, nor neither.

1:13:01

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

1:13:04

and of being soft.

1:13:07

This is why we can't meaningfully

1:13:09

say this electron is some color and some hardness.

1:13:13

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

1:13:16

though our boxes are crude and we are ignorant.

1:13:20

It's deeper.

1:13:21

Having a definite color means not having a definite hardness,

1:13:25

but rather being in a superposition of being hard

1:13:28

and being soft.

1:13:31

Every electron exits a hardness box either hard or soft.

1:13:40

But not every electron is hard or soft.

1:13:43

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

1:13:48

The probability that we subsequently

1:13:51

measure it to be hard or soft depends

1:13:54

on precisely what superposition it is.

1:13:59

For example, we know that if an electron is

1:14:01

in the superposition corresponding to being white

1:14:05

then there are even odds of it being subsequently

1:14:08

measured be hard or to be soft.

1:14:13

So to build a better definition of superposition

1:14:18

than I have no idea what's going on

1:14:22

is going to require a new language.

1:14:23

And that language is quantum mechanics.

1:14:26

And the underpinnings of this language

1:14:28

are the topic of the course.

1:14:29

And developing a better understanding

1:14:31

of this idea of superposition is what

1:14:35

you have to do over the next three months.

1:14:38

Now, if all of this troubles your intuition,

1:14:42

well, that shouldn't be too surprising.

1:14:44

Your intuition was developed by throwing spears, and running

1:14:49

from tigers, and catching toast as it jumps out

1:14:52

of the toaster, all of which involves things so big

1:14:58

and with so much energy that quantum effects are negligible.

1:15:04

As a friend of mine likes to say,

1:15:05

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

1:15:09

However, when we work in very different regimes, when

1:15:11

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

1:15:15

in the regime of very low energies and very

1:15:18

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

1:15:23

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

1:15:26

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

1:15:30

The electrons do what electrons do.

1:15:33

This is what they do.

1:15:34

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

1:15:37

The thing that's surprising is that lots of electrons

1:15:40

behave like this.

1:15:42

Lots of electrons behave like cheese and chalk.

1:15:47

And that's the goal of 804, to step

1:15:49

beyond your daily experience and your familiar intuition

1:15:52

and to develop an intuition for this idea of superposition.

1:15:57

And we'll start in the next lecture.

1:15:59

I'll see you on Thursday.

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