1 00:00:00,050 --> 00:00:01,670 The following content is provided 2 00:00:01,670 --> 00:00:03,800 under a Creative Commons license. 3 00:00:03,800 --> 00:00:06,530 Your support will help MIT OpenCourseWare continue 4 00:00:06,530 --> 00:00:10,110 to offer high quality educational resources for free. 5 00:00:10,110 --> 00:00:12,690 To make a donation or view additional materials 6 00:00:12,690 --> 00:00:16,600 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:16,600 --> 00:00:17,241 at ocw.mit.edu. 8 00:00:21,810 --> 00:00:24,270 ALLAN ADAMS: Hi everyone. 9 00:00:24,270 --> 00:00:27,100 Welcome to 804 for spring 2013. 10 00:00:27,100 --> 00:00:29,542 This is the fourth, and presumably final time 11 00:00:29,542 --> 00:00:31,000 that I will be teaching this class. 12 00:00:31,000 --> 00:00:33,070 So I'm pretty excited about it. 13 00:00:33,070 --> 00:00:34,470 So my name is Allan Adams. 14 00:00:34,470 --> 00:00:37,480 I'll be lecturing the course. 15 00:00:37,480 --> 00:00:40,470 I'm an assistant professor in Course 8. 16 00:00:40,470 --> 00:00:43,400 I study string theory and its applications 17 00:00:43,400 --> 00:00:48,290 to gravity, quantum gravity, and condensed matter physics. 18 00:00:48,290 --> 00:00:52,020 Quantum mechanics, this is a course in quantam mechanics. 19 00:00:52,020 --> 00:00:54,890 Quantam mechanics Is my daily language. 20 00:00:54,890 --> 00:00:57,700 Quantum mechanics is my old friend. 21 00:00:57,700 --> 00:00:59,560 I met quantum mechanics 20 years ago. 22 00:00:59,560 --> 00:01:00,500 I just realized that last night. 23 00:01:00,500 --> 00:01:01,583 It was kind of depressing. 24 00:01:01,583 --> 00:01:03,910 So, old friend. 25 00:01:03,910 --> 00:01:07,490 It's also my most powerful tool. 26 00:01:07,490 --> 00:01:10,860 So I'm pretty psyched about it. 27 00:01:10,860 --> 00:01:15,230 Our recitation instructors are Barton Zwiebach, yea! 28 00:01:15,230 --> 00:01:18,875 And Matt Evans-- yea! 29 00:01:18,875 --> 00:01:20,750 Matt's new to the department, so welcome him. 30 00:01:20,750 --> 00:01:23,384 Hi. 31 00:01:23,384 --> 00:01:25,050 So he just started his faculty position, 32 00:01:25,050 --> 00:01:26,840 which is pretty awesome. 33 00:01:26,840 --> 00:01:28,830 And our TA is Paolo Glorioso. 34 00:01:28,830 --> 00:01:29,851 Paolo, are you here? 35 00:01:29,851 --> 00:01:30,350 Yea! 36 00:01:30,350 --> 00:01:30,891 There you go. 37 00:01:30,891 --> 00:01:35,990 OK, so he's the person to send all complaints to. 38 00:01:35,990 --> 00:01:41,070 So just out of curiosity, how many of you all are Course 8? 39 00:01:41,070 --> 00:01:41,570 Awesome. 40 00:01:41,570 --> 00:01:45,350 How many of you all are, I don't know, 18? 41 00:01:45,350 --> 00:01:46,150 Solid. 42 00:01:46,150 --> 00:01:47,940 6? 43 00:01:47,940 --> 00:01:49,240 Excellent. 44 00:01:49,240 --> 00:01:51,170 9? 45 00:01:51,170 --> 00:01:52,420 No one? 46 00:01:52,420 --> 00:01:54,670 This is the first year we haven't had anyone Course 9. 47 00:01:54,670 --> 00:01:55,295 That's a shame. 48 00:01:57,254 --> 00:01:58,670 Last year one of the best students 49 00:01:58,670 --> 00:01:59,720 was a Course 9 student. 50 00:01:59,720 --> 00:02:01,820 So two practical things to know. 51 00:02:01,820 --> 00:02:04,020 The first thing is everything that we put out 52 00:02:04,020 --> 00:02:06,140 will be on the Stellar website. 53 00:02:06,140 --> 00:02:09,090 Lecture notes, homeworks, exams, everything 54 00:02:09,090 --> 00:02:12,690 is going to be done through Stellar, including your grades. 55 00:02:12,690 --> 00:02:14,930 The second thing is that as you may 56 00:02:14,930 --> 00:02:16,900 notice there are rather more lights than usual. 57 00:02:16,900 --> 00:02:17,830 I'm wearing a mic. 58 00:02:17,830 --> 00:02:19,130 And there are these signs up. 59 00:02:19,130 --> 00:02:21,040 We're going to be videotaping this course 60 00:02:21,040 --> 00:02:23,820 for the lectures for OCW. 61 00:02:23,820 --> 00:02:27,649 And if you're happy with that, cool. 62 00:02:27,649 --> 00:02:29,190 If not, just sit on the sides and you 63 00:02:29,190 --> 00:02:31,690 won't appear anywhere on video. 64 00:02:31,690 --> 00:02:33,375 Sadly, I can't do that. 65 00:02:33,375 --> 00:02:36,120 But you're welcome to if you like. 66 00:02:36,120 --> 00:02:39,630 But hopefully that should not play a meaningful role 67 00:02:39,630 --> 00:02:41,670 in any of the lectures. 68 00:02:47,480 --> 00:02:50,170 So the goal of 804 is for you to learn quantum mechanics. 69 00:02:50,170 --> 00:02:51,860 And by learn quantum mechanics, I 70 00:02:51,860 --> 00:02:54,340 don't mean to learn how to do calculations, 71 00:02:54,340 --> 00:02:56,384 although that's an important and critical thing. 72 00:02:56,384 --> 00:02:57,550 I mean learn some intuition. 73 00:02:57,550 --> 00:02:59,049 I want you to develop some intuition 74 00:02:59,049 --> 00:03:00,710 for quantum phenomena. 75 00:03:00,710 --> 00:03:03,400 Now, quantam mechanics is not hard. 76 00:03:03,400 --> 00:03:05,875 It has a reputation for being a hard topic. 77 00:03:05,875 --> 00:03:07,585 It is not a super hard topic. 78 00:03:10,460 --> 00:03:12,280 So in particular, everyone in this room, 79 00:03:12,280 --> 00:03:15,480 I'm totally positive, can learn quantum mechanics. 80 00:03:15,480 --> 00:03:17,880 It does require concerted effort. 81 00:03:17,880 --> 00:03:20,690 It's not a trivial topic. 82 00:03:20,690 --> 00:03:24,060 And in order to really develop a good intuition, 83 00:03:24,060 --> 00:03:26,390 the essential thing is to solve problems. 84 00:03:26,390 --> 00:03:28,960 So the way you develop a new intuition 85 00:03:28,960 --> 00:03:31,420 is by solving problems and by dealing 86 00:03:31,420 --> 00:03:34,930 with new situations, new context, new regimes, which 87 00:03:34,930 --> 00:03:36,410 is what we're going to do in 804. 88 00:03:36,410 --> 00:03:40,350 It's essential that you work hard on the problem sets. 89 00:03:40,350 --> 00:03:43,870 So your job is to devote yourself to the problem sets. 90 00:03:43,870 --> 00:03:47,660 My job is to convince you at the end of every lecture 91 00:03:47,660 --> 00:03:49,910 that the most interesting thing you could possibly 92 00:03:49,910 --> 00:03:53,600 do when you leave is the problem set. 93 00:03:53,600 --> 00:03:57,340 So you decide who has the harder job. 94 00:03:57,340 --> 00:04:00,100 So the workload is not so bad. 95 00:04:00,100 --> 00:04:02,390 So we have problem sets due, they're 96 00:04:02,390 --> 00:04:05,650 due in the physics box in the usual places, by lecture, 97 00:04:05,650 --> 00:04:10,820 by 11 AM sharp on Tuesdays every week. 98 00:04:10,820 --> 00:04:13,099 Late work, no, not so much. 99 00:04:13,099 --> 00:04:14,890 But we will drop one problem set to make up 100 00:04:14,890 --> 00:04:18,899 for unanticipated events. 101 00:04:18,899 --> 00:04:20,399 We'll return the graded problem sets 102 00:04:20,399 --> 00:04:22,079 a week later in recitation. 103 00:04:22,079 --> 00:04:23,360 Should be easy. 104 00:04:23,360 --> 00:04:26,340 I strongly, strongly encourage you 105 00:04:26,340 --> 00:04:28,950 to collaborate with other students on your problem sets. 106 00:04:28,950 --> 00:04:31,290 You will learn more, they will learn more, 107 00:04:31,290 --> 00:04:32,740 it will be more efficient. 108 00:04:32,740 --> 00:04:34,000 Work together. 109 00:04:34,000 --> 00:04:37,222 However, write your problem sets yourself. 110 00:04:37,222 --> 00:04:39,180 That's the best way for you to develop and test 111 00:04:39,180 --> 00:04:39,971 your understanding. 112 00:04:42,360 --> 00:04:45,280 There will be two midterms, dates to be announced, 113 00:04:45,280 --> 00:04:46,480 and one final. 114 00:04:46,480 --> 00:04:48,410 I guess we could have multiple, but that 115 00:04:48,410 --> 00:04:50,902 would be a little exciting. 116 00:04:50,902 --> 00:04:53,360 We're going to use clickers, and clickers will be required. 117 00:04:53,360 --> 00:04:54,818 We're not going to take attendance, 118 00:04:54,818 --> 00:04:56,530 but they will give a small contribution 119 00:04:56,530 --> 00:04:57,460 to your overall grade. 120 00:04:57,460 --> 00:04:59,260 And we'll use them most importantly 121 00:04:59,260 --> 00:05:02,770 for non-graded but just participation concept questions 122 00:05:02,770 --> 00:05:06,030 and the occasional in class quiz to probe your knowledge. 123 00:05:06,030 --> 00:05:08,340 This is mostly so that you have a real time 124 00:05:08,340 --> 00:05:13,240 measure of your own conceptual understanding of the material. 125 00:05:13,240 --> 00:05:15,000 This has been enormously valuable. 126 00:05:15,000 --> 00:05:16,750 And something I want to say just right off 127 00:05:16,750 --> 00:05:18,800 is that the way I've organized this class 128 00:05:18,800 --> 00:05:21,760 is not so much based on the classes I was taught. 129 00:05:21,760 --> 00:05:24,630 It's based to the degree possible on empirical lessons 130 00:05:24,630 --> 00:05:27,150 about what works in teaching, what 131 00:05:27,150 --> 00:05:29,000 actually makes you learn better. 132 00:05:29,000 --> 00:05:31,440 And clickers are an excellent example of that. 133 00:05:31,440 --> 00:05:34,440 So this is mostly a standard lecture course, 134 00:05:34,440 --> 00:05:36,520 but there will be clickers used. 135 00:05:36,520 --> 00:05:40,020 So by next week I need you all to have clickers, 136 00:05:40,020 --> 00:05:42,760 and I need you to register them on the TSG website. 137 00:05:49,040 --> 00:05:50,980 I haven't chosen a specific textbook. 138 00:05:50,980 --> 00:05:52,940 And this is discussed on the Stellar web page. 139 00:05:52,940 --> 00:05:55,440 There are a set of textbooks, four textbooks that I strongly 140 00:05:55,440 --> 00:05:58,020 recommend, and a set of others that are nice references. 141 00:05:58,020 --> 00:05:59,830 The reason for this is twofold. 142 00:05:59,830 --> 00:06:01,545 First off, there are two languages 143 00:06:01,545 --> 00:06:03,780 that are canonically used for quantum mechanics. 144 00:06:03,780 --> 00:06:07,460 One is called wave mechanics, and the language, 145 00:06:07,460 --> 00:06:09,980 the mathematical language is partial differential equations. 146 00:06:09,980 --> 00:06:11,500 The other is a matrix mechanics. 147 00:06:11,500 --> 00:06:13,210 They have big names. 148 00:06:13,210 --> 00:06:15,880 And the language there is linear algebra. 149 00:06:15,880 --> 00:06:18,420 And different books emphasize different aspects 150 00:06:18,420 --> 00:06:20,392 and use different languages. 151 00:06:20,392 --> 00:06:22,350 And they also try to aim at different problems. 152 00:06:22,350 --> 00:06:23,790 Some books are aimed towards people 153 00:06:23,790 --> 00:06:25,710 who are interested in materials science, some books that 154 00:06:25,710 --> 00:06:27,910 are aimed towards people interested in philosophy. 155 00:06:27,910 --> 00:06:29,550 And depending on what you want, get 156 00:06:29,550 --> 00:06:32,300 the book that's suited to you. 157 00:06:32,300 --> 00:06:35,540 And every week I'll be providing with your problem sets readings 158 00:06:35,540 --> 00:06:38,287 from each of the recommended texts. 159 00:06:38,287 --> 00:06:40,870 So what I really encourage you to do is find a group of people 160 00:06:40,870 --> 00:06:42,810 to work with every week, and make sure 161 00:06:42,810 --> 00:06:45,400 that you've got all the books covered between you. 162 00:06:45,400 --> 00:06:47,400 This'll give you as much access to the texts 163 00:06:47,400 --> 00:06:49,960 as possible without forcing you to buy four books, which 164 00:06:49,960 --> 00:06:51,746 I would discourage you from doing. 165 00:06:54,440 --> 00:06:56,640 So finally I guess the last thing to say 166 00:06:56,640 --> 00:06:59,610 is if this stuff were totally trivial, 167 00:06:59,610 --> 00:07:02,020 you wouldn't need to be here. 168 00:07:02,020 --> 00:07:04,120 So ask questions. 169 00:07:04,120 --> 00:07:06,005 If you're confused about something, 170 00:07:06,005 --> 00:07:07,380 lots of other people in the class 171 00:07:07,380 --> 00:07:08,680 are also going to be confused. 172 00:07:08,680 --> 00:07:11,096 And if I'm not answering your question without you asking, 173 00:07:11,096 --> 00:07:12,730 then no one's getting the point, right? 174 00:07:12,730 --> 00:07:13,794 So ask questions. 175 00:07:13,794 --> 00:07:14,960 Don't hesitate to interrupt. 176 00:07:14,960 --> 00:07:17,860 Just raise your hand, and I will do my best to call on you. 177 00:07:17,860 --> 00:07:19,660 And this is true for both in lecture, 178 00:07:19,660 --> 00:07:21,840 also go to office hours and recitations. 179 00:07:21,840 --> 00:07:23,400 Ask questions. 180 00:07:23,400 --> 00:07:25,970 I promise, there's no such thing as a terrible question. 181 00:07:25,970 --> 00:07:28,560 Someone else will also be confused. 182 00:07:28,560 --> 00:07:30,860 So it's a very valuable to me and everyone else. 183 00:07:34,180 --> 00:07:36,840 So before I get going on the actual physics 184 00:07:36,840 --> 00:07:42,770 content of the class, are there any other practical questions? 185 00:07:42,770 --> 00:07:43,272 Yeah. 186 00:07:43,272 --> 00:07:45,230 AUDIENCE: You said there was a lateness policy. 187 00:07:45,230 --> 00:07:45,930 ALLAN ADAMS: Lateness policy. 188 00:07:45,930 --> 00:07:47,429 No late work is accepted whatsoever. 189 00:07:49,970 --> 00:07:52,429 So the deal is given that every once in a while, 190 00:07:52,429 --> 00:07:53,970 you know, you'll be walking to school 191 00:07:53,970 --> 00:07:55,386 and your leg is going to fall off, 192 00:07:55,386 --> 00:07:58,800 or a dog's going to jump out and eat your person standing 193 00:07:58,800 --> 00:08:01,370 next to you, whatever. 194 00:08:01,370 --> 00:08:02,250 Things happen. 195 00:08:02,250 --> 00:08:04,960 So we will drop your lowest problem set score 196 00:08:04,960 --> 00:08:05,877 without any questions. 197 00:08:05,877 --> 00:08:07,251 At the end of the semester, we'll 198 00:08:07,251 --> 00:08:08,600 just dropped your lowest score. 199 00:08:08,600 --> 00:08:10,139 And if you turn them all in, great, 200 00:08:10,139 --> 00:08:11,680 whatever your lowest score was, fine. 201 00:08:11,680 --> 00:08:13,550 If you missed one, then gone. 202 00:08:13,550 --> 00:08:16,350 On the other hand, if you know next week, I'm 203 00:08:16,350 --> 00:08:18,160 going to be attacked by a rabid squirrel, 204 00:08:18,160 --> 00:08:19,200 it's going to be horrible, I don't 205 00:08:19,200 --> 00:08:20,992 want to have to worry about my problem set. 206 00:08:20,992 --> 00:08:21,950 Could we work this out? 207 00:08:21,950 --> 00:08:23,690 So if you know ahead of time, come to us. 208 00:08:23,690 --> 00:08:25,010 But you need to do that well ahead of time. 209 00:08:25,010 --> 00:08:26,510 The night before doesn't count. 210 00:08:26,510 --> 00:08:27,770 OK? 211 00:08:27,770 --> 00:08:28,330 Yeah. 212 00:08:28,330 --> 00:08:30,294 AUDIENCE: Will we be able to watch the videos? 213 00:08:30,294 --> 00:08:31,770 ALLAN ADAMS: You know, that's an excellent question. 214 00:08:31,770 --> 00:08:32,700 I don't know. 215 00:08:32,700 --> 00:08:34,780 I don't think so. 216 00:08:34,780 --> 00:08:37,179 I think it's going to happen at the end of the semester. 217 00:08:37,179 --> 00:08:37,419 Yeah. 218 00:08:37,419 --> 00:08:37,919 OK. 219 00:08:37,919 --> 00:08:41,370 So no, you'll be able to watch them later on the OCW website. 220 00:08:45,120 --> 00:08:47,020 Other questions. 221 00:08:47,020 --> 00:08:47,730 Yeah. 222 00:08:47,730 --> 00:08:48,697 AUDIENCE: Are there any other videos 223 00:08:48,697 --> 00:08:51,270 that you'd recommend, just like other courses on YouTube? 224 00:08:51,270 --> 00:08:51,950 ALLAN ADAMS: Oh. 225 00:08:51,950 --> 00:08:54,440 That's an interesting question. 226 00:08:54,440 --> 00:08:57,156 I don't off the top of my head, but if you send me an email, 227 00:08:57,156 --> 00:08:57,780 I'll pursue it. 228 00:08:57,780 --> 00:08:59,720 Because I do know several other lecture series 229 00:08:59,720 --> 00:09:01,030 that I like very much, but I don't 230 00:09:01,030 --> 00:09:03,090 know if they're available on YouTube or publicly. 231 00:09:03,090 --> 00:09:05,380 So send me an email and I'll check. 232 00:09:05,380 --> 00:09:05,910 Yeah. 233 00:09:05,910 --> 00:09:07,870 AUDIENCE: So how about the reading assignments? 234 00:09:07,870 --> 00:09:10,453 ALLAN ADAMS: Reading assignments on the problem set every week 235 00:09:10,453 --> 00:09:11,150 will be listed. 236 00:09:11,150 --> 00:09:13,750 There will be equivalent reading from every textbook. 237 00:09:13,750 --> 00:09:15,250 And if there is something missing, 238 00:09:15,250 --> 00:09:16,791 like if no textbook covers something, 239 00:09:16,791 --> 00:09:18,074 I'll post a separate reading. 240 00:09:18,074 --> 00:09:20,240 Every once in a while, I'll post auxiliary readings, 241 00:09:20,240 --> 00:09:22,430 and they'll be available on the Stellar website. 242 00:09:22,430 --> 00:09:25,209 So for example, in your problem set, first one was posted, 243 00:09:25,209 --> 00:09:27,000 will be available immediately after lecture 244 00:09:27,000 --> 00:09:28,300 on the Stellar website. 245 00:09:28,300 --> 00:09:32,230 There are three papers that it refers to, or two, 246 00:09:32,230 --> 00:09:34,880 and they are posted on the Stellar website 247 00:09:34,880 --> 00:09:38,070 and linked from the problem set. 248 00:09:38,070 --> 00:09:38,570 Others? 249 00:09:41,090 --> 00:09:41,750 OK. 250 00:09:41,750 --> 00:09:45,800 So the first lecture. 251 00:09:45,800 --> 00:09:48,590 The content of the physics of the first lecture 252 00:09:48,590 --> 00:09:51,040 is relatively standalone. 253 00:09:51,040 --> 00:09:53,550 It's going to be an introduction to a basic idea then is 254 00:09:53,550 --> 00:09:55,800 going to haunt, plague, and charm us 255 00:09:55,800 --> 00:09:57,175 through the rest of the semester. 256 00:10:00,580 --> 00:10:02,560 The logic of this lecture is based 257 00:10:02,560 --> 00:10:05,257 on a very beautiful discussion in the first few chapters 258 00:10:05,257 --> 00:10:07,340 of a book by David Albert called Quantum Mechanics 259 00:10:07,340 --> 00:10:09,200 and Experience. 260 00:10:09,200 --> 00:10:10,700 It's a book for philosophers. 261 00:10:10,700 --> 00:10:13,529 But the first few chapters, a really lovely introduction 262 00:10:13,529 --> 00:10:14,570 at a non-technical level. 263 00:10:14,570 --> 00:10:16,361 And I encourage you to take a look at them, 264 00:10:16,361 --> 00:10:19,460 because they're very lovely. 265 00:10:19,460 --> 00:10:21,710 But it's to be sure straight up physics. 266 00:10:25,390 --> 00:10:27,180 Ready? 267 00:10:27,180 --> 00:10:30,550 I love this stuff. 268 00:10:30,550 --> 00:10:34,290 today I want to describe to you a particular set 269 00:10:34,290 --> 00:10:35,860 of experiments. 270 00:10:35,860 --> 00:10:41,460 Now, to my mind, these are the most unsettling experiments 271 00:10:41,460 --> 00:10:43,370 ever done. 272 00:10:43,370 --> 00:10:46,900 These experiments involve electrons. 273 00:10:46,900 --> 00:10:49,230 They have been performed, and the results 274 00:10:49,230 --> 00:10:53,110 as I will describe them are true. 275 00:10:53,110 --> 00:10:56,890 I'm going to focus on two properties of electrons. 276 00:10:56,890 --> 00:11:00,570 I will call them color and hardness. 277 00:11:05,440 --> 00:11:07,054 And these are not the technical names. 278 00:11:07,054 --> 00:11:09,220 We'll learn the technical names for these properties 279 00:11:09,220 --> 00:11:10,380 later on in the semester. 280 00:11:10,380 --> 00:11:13,470 But to avoid distracting you by preconceived notions of what 281 00:11:13,470 --> 00:11:16,330 these things mean, I'm going to use ambiguous labels, color 282 00:11:16,330 --> 00:11:17,240 and hardness. 283 00:11:17,240 --> 00:11:27,320 And the empirical fact is that every electron, every electron 284 00:11:27,320 --> 00:11:34,450 that's ever been observed is either black or white 285 00:11:34,450 --> 00:11:35,670 and no other color. 286 00:11:35,670 --> 00:11:37,300 We've never seen a blue electron. 287 00:11:37,300 --> 00:11:38,970 There are no green electrons. 288 00:11:38,970 --> 00:11:40,950 No one has ever found a fluorescent electron. 289 00:11:40,950 --> 00:11:42,860 They're either black, or they are white. 290 00:11:42,860 --> 00:11:45,400 It is a binary property. 291 00:11:45,400 --> 00:11:50,150 Secondly, their hardness is either hard or soft. 292 00:11:50,150 --> 00:11:52,240 They're never squishy. 293 00:11:52,240 --> 00:11:54,570 No one's ever found one that dribbles. 294 00:11:54,570 --> 00:11:56,210 They are either hard, or they are soft. 295 00:11:56,210 --> 00:11:57,940 Binary properties. 296 00:11:57,940 --> 00:12:00,820 OK? 297 00:12:00,820 --> 00:12:04,170 Now, what I mean by this is that it 298 00:12:04,170 --> 00:12:07,620 is possible to build a device which 299 00:12:07,620 --> 00:12:09,580 measures the color and the hardness. 300 00:12:09,580 --> 00:12:11,500 In particular, it is possible to build 301 00:12:11,500 --> 00:12:16,652 a box, which I will call a color box, that measures the color. 302 00:12:16,652 --> 00:12:17,860 And the way it works is this. 303 00:12:17,860 --> 00:12:21,460 It has three apertures, an in port and two out 304 00:12:21,460 --> 00:12:25,734 ports, one which sends out black electrons 305 00:12:25,734 --> 00:12:27,400 and one which sends out white electrons. 306 00:12:32,430 --> 00:12:36,090 And the utility of this box is that the color 307 00:12:36,090 --> 00:12:38,260 can be inferred from the position. 308 00:12:38,260 --> 00:12:40,360 If you find the particle, the electron over here, 309 00:12:40,360 --> 00:12:41,670 it is a white electron. 310 00:12:41,670 --> 00:12:44,480 If you find the electron here, it is a black electron. 311 00:12:44,480 --> 00:12:46,360 Cool? 312 00:12:46,360 --> 00:12:50,460 Similarly, we can build a hardness box, 313 00:12:50,460 --> 00:12:52,700 which again has three apertures, an in port. 314 00:12:52,700 --> 00:12:59,050 And hard electrons come out this port, 315 00:12:59,050 --> 00:13:00,660 and soft electrons come out this port. 316 00:13:10,430 --> 00:13:14,460 Now, if you want, you're free to imagine that these boxes are 317 00:13:14,460 --> 00:13:20,440 built by putting a monkey inside. 318 00:13:20,440 --> 00:13:22,980 And you send in an electron, and the monkey, 319 00:13:22,980 --> 00:13:26,150 you know, with the ears, looks at the electron, 320 00:13:26,150 --> 00:13:28,996 and says it's a hard electron, it sends it out one way, 321 00:13:28,996 --> 00:13:31,120 or it's a soft electron, it sends it out the other. 322 00:13:31,120 --> 00:13:32,894 The workings inside do not matter. 323 00:13:32,894 --> 00:13:34,560 And in particular, later in the semester 324 00:13:34,560 --> 00:13:37,200 I will describe in considerable detail 325 00:13:37,200 --> 00:13:39,600 the workings inside this apparatus. 326 00:13:39,600 --> 00:13:41,630 And here's something I want to emphasize to you. 327 00:13:41,630 --> 00:13:44,569 It can be built in principle using monkeys, 328 00:13:44,569 --> 00:13:46,610 hyper intelligent monkeys that can see electrons. 329 00:13:46,610 --> 00:13:50,549 It could also be built using magnets and silver atoms. 330 00:13:50,549 --> 00:13:51,840 It could be done with neutrons. 331 00:13:51,840 --> 00:13:54,256 It could be done with all sorts of different technologies. 332 00:13:54,256 --> 00:13:56,680 And they all give precisely the same results 333 00:13:56,680 --> 00:13:59,990 as I'm about to describe. 334 00:13:59,990 --> 00:14:01,830 They all give precisely the same results. 335 00:14:01,830 --> 00:14:04,080 So it does not matter what's inside. 336 00:14:04,080 --> 00:14:05,640 But if you want a little idea, you 337 00:14:05,640 --> 00:14:08,350 could imagine putting a monkey inside, a hyper intelligent 338 00:14:08,350 --> 00:14:10,128 monkey. 339 00:14:10,128 --> 00:14:11,550 I know, it sounds good. 340 00:14:16,290 --> 00:14:21,930 So a key property of these hardness boxes and color boxes 341 00:14:21,930 --> 00:14:23,330 is that they are repeatable. 342 00:14:23,330 --> 00:14:25,460 And here's what I mean by that. 343 00:14:25,460 --> 00:14:29,040 If I send in an electron, and I find that it comes out 344 00:14:29,040 --> 00:14:32,702 of a color box black, and then I send it in again, 345 00:14:32,702 --> 00:14:34,410 then if I send it into another color box, 346 00:14:34,410 --> 00:14:35,605 it comes out black again. 347 00:14:38,810 --> 00:14:44,660 So in diagrams, if I send in some random electron 348 00:14:44,660 --> 00:14:48,120 to a color box, and I discover that it comes out, let's say, 349 00:14:48,120 --> 00:14:50,840 the white aperture. 350 00:14:50,840 --> 00:14:53,520 And so here's dot dot dot, and I take the ones that come out 351 00:14:53,520 --> 00:14:56,520 the white aperture, and I send them into a color box again. 352 00:14:56,520 --> 00:15:02,091 Then with 100% confidence, 100% of the time, the electron 353 00:15:02,091 --> 00:15:04,340 coming out of the white port incident on the color box 354 00:15:04,340 --> 00:15:05,980 will come out the white aperture again. 355 00:15:05,980 --> 00:15:09,760 And 0% of the time will it come out the black aperture. 356 00:15:09,760 --> 00:15:11,536 So this is a persistent property. 357 00:15:11,536 --> 00:15:12,660 You notice that it's white. 358 00:15:12,660 --> 00:15:14,814 You measure it again, it's still white. 359 00:15:14,814 --> 00:15:16,480 Do a little bit later, it's still white. 360 00:15:16,480 --> 00:15:17,370 OK? 361 00:15:17,370 --> 00:15:20,650 It's a persistent property. 362 00:15:20,650 --> 00:15:21,700 Ditto the hardness. 363 00:15:21,700 --> 00:15:25,856 If I send in a bunch of electrons in to a hardness box, 364 00:15:25,856 --> 00:15:26,980 here is an important thing. 365 00:15:26,980 --> 00:15:29,270 Well, send them into a hardness box, 366 00:15:29,270 --> 00:15:32,330 and I take out the ones that come out soft. 367 00:15:32,330 --> 00:15:34,280 And I send them again into a hardness box, 368 00:15:34,280 --> 00:15:36,180 and they come out soft. 369 00:15:36,180 --> 00:15:38,390 They will come out soft with 100% 370 00:15:38,390 --> 00:15:40,040 confidence, 100% of the time. 371 00:15:40,040 --> 00:15:42,940 Never do they come out the hard aperture. 372 00:15:52,844 --> 00:15:54,010 Any questions at this point? 373 00:15:59,802 --> 00:16:01,010 So here's a natural question. 374 00:16:07,070 --> 00:16:13,530 Might the color and the hardness of an electron be related? 375 00:16:13,530 --> 00:16:18,280 And more precisely, might they be correlated? 376 00:16:18,280 --> 00:16:21,460 Might knowing the color infer something about the hardness? 377 00:16:21,460 --> 00:16:26,530 So for example, so being male and being a bachelor 378 00:16:26,530 --> 00:16:28,749 are correlated properties, because if you're male, 379 00:16:28,749 --> 00:16:30,540 you don't know if you're a bachelor or not, 380 00:16:30,540 --> 00:16:32,123 but if you're a bachelor, you're male. 381 00:16:32,123 --> 00:16:34,870 That's the definition of the word. 382 00:16:34,870 --> 00:16:36,850 So is it possible that color and hardness 383 00:16:36,850 --> 00:16:39,110 are similarly correlated? 384 00:16:39,110 --> 00:16:41,970 So, I don't know, there are lots of good examples, 385 00:16:41,970 --> 00:16:44,651 like wearing a red shirt and beaming down to the surface 386 00:16:44,651 --> 00:16:46,150 and making it back to the Enterprise 387 00:16:46,150 --> 00:16:48,360 later after the away team returns. 388 00:16:48,360 --> 00:16:49,650 Correlated, right? 389 00:16:49,650 --> 00:16:52,540 Negatively, but correlated. 390 00:16:52,540 --> 00:16:55,790 So the question is, suppose, e.g., 391 00:16:55,790 --> 00:16:59,880 suppose we know that an electron is white. 392 00:17:02,990 --> 00:17:05,215 Does that determine the hardness? 393 00:17:10,760 --> 00:17:15,043 So we can answer this question by using our boxes. 394 00:17:15,043 --> 00:17:16,334 So here's what I'm going to do. 395 00:17:16,334 --> 00:17:19,030 I'm going to take some random set of electrons. 396 00:17:19,030 --> 00:17:20,790 That's not random. 397 00:17:20,790 --> 00:17:22,069 Random. 398 00:17:22,069 --> 00:17:24,814 And I'm going to send them in to a color box. 399 00:17:24,814 --> 00:17:26,480 And I'm going to take the electrons that 400 00:17:26,480 --> 00:17:27,740 come out the white aperture. 401 00:17:27,740 --> 00:17:28,850 And here's a useful fact. 402 00:17:28,850 --> 00:17:31,016 When I say random, here's operationally what I mean. 403 00:17:31,016 --> 00:17:33,580 I take some piece of material, I scrape it, 404 00:17:33,580 --> 00:17:36,330 I pull off some electrons, and they're totally 405 00:17:36,330 --> 00:17:37,789 randomly chosen from the material. 406 00:17:37,789 --> 00:17:38,580 And I send them in. 407 00:17:38,580 --> 00:17:41,180 If I send a random pile of electrons into a color box, 408 00:17:41,180 --> 00:17:44,436 useful thing to know, they come out about half and half. 409 00:17:44,436 --> 00:17:45,810 It's just some random assortment. 410 00:17:45,810 --> 00:17:49,200 Some of them are white, some of them come out black. 411 00:17:49,200 --> 00:17:51,900 Suppose I send some random collection of electrons 412 00:17:51,900 --> 00:17:52,880 into a color box. 413 00:17:52,880 --> 00:17:55,007 And I take those which come out the white aperture. 414 00:17:55,007 --> 00:17:57,090 And I want to know, does white determine hardness. 415 00:17:57,090 --> 00:18:01,140 So I can do that, check, by then sending these white electrons 416 00:18:01,140 --> 00:18:03,990 into a hardness box and seeing what comes out. 417 00:18:09,100 --> 00:18:11,690 Hard, soft. 418 00:18:11,690 --> 00:18:17,860 And what we find is that 50% of those electrons incident 419 00:18:17,860 --> 00:18:26,060 on the hardness box come out hard, and 50% come out soft. 420 00:18:26,060 --> 00:18:27,600 OK? 421 00:18:27,600 --> 00:18:28,850 And ditto if we reverse this. 422 00:18:28,850 --> 00:18:32,560 If we take hardness, and take, for example, a soft electron 423 00:18:32,560 --> 00:18:40,265 and send it into a color box, we again get 50-50. 424 00:18:45,067 --> 00:18:46,900 So if you take a white electron, you send it 425 00:18:46,900 --> 00:18:49,232 into a hardness box, you're at even odds, 426 00:18:49,232 --> 00:18:50,690 you're at chance as to whether it's 427 00:18:50,690 --> 00:18:52,050 going to come out hard or soft. 428 00:18:52,050 --> 00:18:54,340 And similarly, if you send a soft electron 429 00:18:54,340 --> 00:18:56,310 into a color box, even odds it's going 430 00:18:56,310 --> 00:18:58,190 to come out black or white. 431 00:18:58,190 --> 00:18:59,980 So knowing the hardness does not give you 432 00:18:59,980 --> 00:19:02,570 any information about the color, and knowing the color 433 00:19:02,570 --> 00:19:05,220 does not give you any information about the hardness. 434 00:19:05,220 --> 00:19:06,000 cool? 435 00:19:06,000 --> 00:19:08,910 These are independent facts, independent properties. 436 00:19:08,910 --> 00:19:11,590 They're not correlated in this sense, 437 00:19:11,590 --> 00:19:15,950 in precisely this operational sense. 438 00:19:15,950 --> 00:19:18,100 Cool? 439 00:19:18,100 --> 00:19:20,135 Questions? 440 00:19:20,135 --> 00:19:20,635 OK. 441 00:19:24,280 --> 00:19:26,720 So measuring the color give zero predictive power 442 00:19:26,720 --> 00:19:28,553 for the hardness, and measuring the hardness 443 00:19:28,553 --> 00:19:31,280 gives zero predictive power for the color. 444 00:19:34,120 --> 00:19:36,080 And from that, I will say that these properties 445 00:19:36,080 --> 00:19:37,662 are correlated. 446 00:19:37,662 --> 00:19:45,800 So H, hardness, and color are in this sense uncorrelated. 447 00:19:55,130 --> 00:19:59,237 So using these properties of the color and hardness boxes, 448 00:19:59,237 --> 00:20:00,820 I want to run a few more experiment's. 449 00:20:00,820 --> 00:20:03,069 I want to probe these properties of color and hardness 450 00:20:03,069 --> 00:20:04,310 a little more. 451 00:20:04,310 --> 00:20:06,350 And in particular, knowing these results 452 00:20:06,350 --> 00:20:09,110 allows us to make predictions, to predict the results 453 00:20:09,110 --> 00:20:10,550 for set a very simple experiments. 454 00:20:10,550 --> 00:20:12,508 Now, what we're going to do for the next bit is 455 00:20:12,508 --> 00:20:15,111 we're going to run some simple experiments. 456 00:20:15,111 --> 00:20:16,610 And we're going to make predictions. 457 00:20:16,610 --> 00:20:18,110 And then those simple experiments 458 00:20:18,110 --> 00:20:20,549 are going to lead us to more complicated experiments. 459 00:20:20,549 --> 00:20:22,590 But let's make sure we understand the simple ones 460 00:20:22,590 --> 00:20:23,090 first. 461 00:20:26,580 --> 00:20:30,980 So for example, let's take this last experiment, color 462 00:20:30,980 --> 00:20:33,750 and hardness, and let's add a color box. 463 00:20:33,750 --> 00:20:36,090 One more monkey. 464 00:20:36,090 --> 00:20:41,360 So color in, and we take those that 465 00:20:41,360 --> 00:20:44,550 come out the white aperture. 466 00:20:44,550 --> 00:20:47,670 And we send them into a hardness box. 467 00:20:47,670 --> 00:20:49,095 Hard, soft. 468 00:20:49,095 --> 00:20:50,470 And we take those electrons which 469 00:20:50,470 --> 00:20:53,260 come out the soft aperture. 470 00:20:53,260 --> 00:20:55,830 And now let's send these again into a color box. 471 00:20:55,830 --> 00:20:59,220 So it's easy to see what to predict. 472 00:20:59,220 --> 00:21:00,420 Black, white. 473 00:21:02,814 --> 00:21:04,980 So you can imagine a monkey inside this, going, aha. 474 00:21:08,830 --> 00:21:11,450 You look at it, you inspect, it comes out white. 475 00:21:11,450 --> 00:21:13,670 Here you look at it and inspect, it comes out soft. 476 00:21:13,670 --> 00:21:15,260 And you send it into the color box, 477 00:21:15,260 --> 00:21:17,480 and what do you expect to happen? 478 00:21:17,480 --> 00:21:21,310 Well, let's think about the logic here. 479 00:21:21,310 --> 00:21:22,880 Anything reaching the hardness box 480 00:21:22,880 --> 00:21:25,851 must have been measured to be white. 481 00:21:25,851 --> 00:21:27,600 And we just did the experiment that if you 482 00:21:27,600 --> 00:21:29,350 send a white electron into a hardness box, 483 00:21:29,350 --> 00:21:31,680 50% of the time it comes out a hard aperture and 50% 484 00:21:31,680 --> 00:21:33,910 of the time it comes out the soft aperture. 485 00:21:33,910 --> 00:21:35,770 So now we take that 50% of electrons 486 00:21:35,770 --> 00:21:38,019 that comes out the soft aperture, which had previously 487 00:21:38,019 --> 00:21:40,280 been observed to be white and soft. 488 00:21:40,280 --> 00:21:42,655 And then we send them into a color box, and what happens? 489 00:21:44,990 --> 00:21:46,976 Well, since colors are repeatable, 490 00:21:46,976 --> 00:21:49,600 the natural expectation is that, of course, it comes out white. 491 00:21:49,600 --> 00:21:53,550 So our prediction, our natural prediction 492 00:21:53,550 --> 00:21:58,970 here is that of those electrons that are incident on this color 493 00:21:58,970 --> 00:22:09,920 box, 100% should come out white, and 0% should come out black. 494 00:22:14,620 --> 00:22:17,340 That seem like a reasonable-- let's just make sure 495 00:22:17,340 --> 00:22:18,467 that we're all agreeing. 496 00:22:18,467 --> 00:22:19,050 So let's vote. 497 00:22:19,050 --> 00:22:21,008 How many people think this is probably correct? 498 00:22:23,130 --> 00:22:23,630 OK, good. 499 00:22:23,630 --> 00:22:26,300 How many people think this probably wrong? 500 00:22:26,300 --> 00:22:26,800 OK, good. 501 00:22:26,800 --> 00:22:29,480 That's reassuring. 502 00:22:29,480 --> 00:22:31,330 Except you're all wrong. 503 00:22:31,330 --> 00:22:32,310 Right? 504 00:22:32,310 --> 00:22:36,900 In fact, what happens is half of these electrons exit 505 00:22:36,900 --> 00:22:39,060 white, 50%. 506 00:22:39,060 --> 00:22:41,920 And 50% percent exit black. 507 00:22:45,600 --> 00:22:47,350 So let's think about what's going on here. 508 00:22:47,350 --> 00:22:48,725 This is really kind of troubling. 509 00:22:48,725 --> 00:22:50,450 We've said already that knowing the color 510 00:22:50,450 --> 00:22:51,990 doesn't predict the hardness. 511 00:22:51,990 --> 00:22:54,250 And yet, this electron, which was previously 512 00:22:54,250 --> 00:22:57,770 measured to be white, now when subsequently measured sometimes 513 00:22:57,770 --> 00:23:00,240 it comes out white, sometimes it comes out 514 00:23:00,240 --> 00:23:04,450 black, 50-50% of the time. 515 00:23:04,450 --> 00:23:05,510 So that's surprising. 516 00:23:05,510 --> 00:23:07,760 What that tells you is you can't think of the electron 517 00:23:07,760 --> 00:23:11,630 as a little ball that has black and soft written on it, right? 518 00:23:11,630 --> 00:23:14,216 You can't, because apparently that black and soft 519 00:23:14,216 --> 00:23:15,840 isn't a persistent thing, although it's 520 00:23:15,840 --> 00:23:17,714 persistent in the sense that once it's black, 521 00:23:17,714 --> 00:23:19,650 it stays black. 522 00:23:19,650 --> 00:23:22,090 So what's going on here? 523 00:23:22,090 --> 00:23:25,310 Now, I should emphasize that the same thing happens 524 00:23:25,310 --> 00:23:30,570 if I had changed this to taking the black electrons 525 00:23:30,570 --> 00:23:33,570 and throwing in a hardness and picking soft and then measuring 526 00:23:33,570 --> 00:23:35,865 the color, or if I had used the hard electrons. 527 00:23:35,865 --> 00:23:37,740 Any of those combinations, any of these ports 528 00:23:37,740 --> 00:23:39,448 would have given the same results, 50-50. 529 00:23:39,448 --> 00:23:43,190 Is not persistent in this sense. 530 00:23:43,190 --> 00:23:45,910 Apparently the presence of the hardness box 531 00:23:45,910 --> 00:23:48,910 tampers with the color somehow. 532 00:23:48,910 --> 00:23:52,390 So it's not quite as trivial is that hyper intelligent monkey. 533 00:23:52,390 --> 00:23:54,480 Something else is going on here. 534 00:23:54,480 --> 00:23:56,110 So this is suspicious. 535 00:23:56,110 --> 00:23:57,750 So here's the first natural move. 536 00:23:57,750 --> 00:24:01,120 The first natural move is, oh, look, surely 537 00:24:01,120 --> 00:24:04,070 there's some additional property of the electron 538 00:24:04,070 --> 00:24:05,830 that we just haven't measured yet 539 00:24:05,830 --> 00:24:08,530 that determines whether it comes out the second color 540 00:24:08,530 --> 00:24:10,520 box black or white. 541 00:24:10,520 --> 00:24:15,520 There's got be some property that determines this. 542 00:24:15,520 --> 00:24:17,990 And so people have spent a tremendous amount 543 00:24:17,990 --> 00:24:20,930 of time and energy looking at these initial electrons 544 00:24:20,930 --> 00:24:24,040 and looking with great care to see whether there's 545 00:24:24,040 --> 00:24:28,480 any sort of feature of these incident electrons 546 00:24:28,480 --> 00:24:30,960 which determines which port they come out of. 547 00:24:30,960 --> 00:24:35,170 And the shocker is no one's ever found such a property. 548 00:24:35,170 --> 00:24:36,760 No one has ever found a property which 549 00:24:36,760 --> 00:24:38,820 determines which port it comes out of. 550 00:24:38,820 --> 00:24:41,815 As far as we can tell, it is completely random. 551 00:24:45,750 --> 00:24:48,219 Those that flip and those that don't are 552 00:24:48,219 --> 00:24:49,510 indistinguishable at beginning. 553 00:24:49,510 --> 00:24:52,730 And let me just emphasize, if anyone found such a-- it's not 554 00:24:52,730 --> 00:24:53,980 like we're not looking, right? 555 00:24:53,980 --> 00:24:56,850 If anyone found such a property, fame, notoriety, 556 00:24:56,850 --> 00:24:59,000 subverting quantum mechanics, Nobel Prize. 557 00:24:59,000 --> 00:24:59,930 People have looked. 558 00:24:59,930 --> 00:25:03,360 And there is none that anyone's been able to find. 559 00:25:03,360 --> 00:25:05,830 And as we'll see later on, using Bell's inequality, 560 00:25:05,830 --> 00:25:08,800 we can more or less nail that such things don't exist, 561 00:25:08,800 --> 00:25:10,134 such a fact doesn't exist. 562 00:25:10,134 --> 00:25:12,050 But this tells us something really disturbing. 563 00:25:12,050 --> 00:25:14,770 This tells us, and this is the first real shocker, 564 00:25:14,770 --> 00:25:20,030 that there is something intrinsically unpredictable, 565 00:25:20,030 --> 00:25:24,190 non-deterministic, and random about physical processes 566 00:25:24,190 --> 00:25:27,100 that we observe in a laboratory. 567 00:25:27,100 --> 00:25:29,300 There's no way to determine a priori whether it 568 00:25:29,300 --> 00:25:32,900 will come out black or white from the second box. 569 00:25:32,900 --> 00:25:35,160 Probability in this experiment, it's 570 00:25:35,160 --> 00:25:37,080 forced upon us by observations. 571 00:25:42,190 --> 00:25:45,010 OK, well, there's another way to come at this. 572 00:25:45,010 --> 00:25:48,430 You could say, look, you ran this experiment, that's fine. 573 00:25:48,430 --> 00:25:52,050 But look, I've met the guy who built these boxes, 574 00:25:52,050 --> 00:25:54,200 and look, he's just some guy, right? 575 00:25:54,200 --> 00:25:57,080 And he just didn't do a very good job. 576 00:25:57,080 --> 00:26:00,520 The boxes are just badly built. 577 00:26:00,520 --> 00:26:03,270 So here's the way to defeat that argument. 578 00:26:03,270 --> 00:26:05,990 No, we've built these things out of different materials, 579 00:26:05,990 --> 00:26:09,310 using different technologies, using electrons, using 580 00:26:09,310 --> 00:26:14,320 neutrons, using bucky-balls, C60, seriously, it's been done. 581 00:26:14,320 --> 00:26:18,962 We've done this experiment, and this property does not change. 582 00:26:18,962 --> 00:26:19,670 It is persistent. 583 00:26:19,670 --> 00:26:22,240 And the thing that's most upsetting to me is that not 584 00:26:22,240 --> 00:26:25,890 only do we get the same results independent of what objects we 585 00:26:25,890 --> 00:26:29,450 use to run the experiment, we cannot change the probability 586 00:26:29,450 --> 00:26:31,970 away from 50-50 at all. 587 00:26:31,970 --> 00:26:34,920 Within experimental tolerances, we cannot change, 588 00:26:34,920 --> 00:26:36,990 no matter how we build the boxes, 589 00:26:36,990 --> 00:26:41,441 we cannot change the probability by part in 100. 590 00:26:41,441 --> 00:26:41,940 50-50. 591 00:26:45,880 --> 00:26:49,400 And to anyone who grew up with determinism from Newton, 592 00:26:49,400 --> 00:26:52,330 this should hurt. 593 00:26:52,330 --> 00:26:54,580 This should feel wrong. 594 00:26:54,580 --> 00:26:56,460 But it's a property of the real world. 595 00:26:56,460 --> 00:27:00,084 And our job is going to be to deal with it. 596 00:27:00,084 --> 00:27:02,500 Rather, your job is going to be to deal with it, because I 597 00:27:02,500 --> 00:27:03,583 went through this already. 598 00:27:06,940 --> 00:27:08,790 So here's a curious consequence-- oh, 599 00:27:08,790 --> 00:27:10,910 any questions before I cruise? 600 00:27:10,910 --> 00:27:11,470 OK. 601 00:27:11,470 --> 00:27:15,630 So here's a curious consequence of this series of experiments. 602 00:27:15,630 --> 00:27:17,550 Here's something you can't do. 603 00:27:17,550 --> 00:27:20,050 Are you guys old enough for you can't do this on television? 604 00:27:22,830 --> 00:27:24,270 This is so sad. 605 00:27:24,270 --> 00:27:28,000 OK, so here's something you can't do. 606 00:27:28,000 --> 00:27:30,680 We cannot build, it is impossible to build, 607 00:27:30,680 --> 00:27:33,717 a reliable color and hardness box. 608 00:27:33,717 --> 00:27:35,800 We've built a box that tells you what color it is. 609 00:27:35,800 --> 00:27:38,405 We've built a box that tells you what hardness it is. 610 00:27:38,405 --> 00:27:42,850 But you cannot build a meaningful box that tells you 611 00:27:42,850 --> 00:27:46,720 what color and hardness an electron is. 612 00:27:46,720 --> 00:27:49,410 So in particular, what would this magical box be? 613 00:27:49,410 --> 00:27:51,700 It would have four ports. 614 00:27:51,700 --> 00:27:54,840 And its ports would say, well, one is white and hard, 615 00:27:54,840 --> 00:27:58,330 and one is white and soft, one is black and hard, 616 00:27:58,330 --> 00:28:00,410 and one is black and soft. 617 00:28:00,410 --> 00:28:02,310 So you can imagine how you might try 618 00:28:02,310 --> 00:28:05,610 to build a color and hardness box. 619 00:28:05,610 --> 00:28:08,430 So for example, here's something you might imagine. 620 00:28:08,430 --> 00:28:12,510 Take your incident electrons, and first 621 00:28:12,510 --> 00:28:16,060 send them into a color box. 622 00:28:16,060 --> 00:28:22,460 And take those white electrons, and send them 623 00:28:22,460 --> 00:28:24,780 into a hardness box. 624 00:28:24,780 --> 00:28:26,580 And take those electrons, and this 625 00:28:26,580 --> 00:28:29,090 is going to be white and hard, and this 626 00:28:29,090 --> 00:28:31,740 is going to be white and soft. 627 00:28:31,740 --> 00:28:33,610 And similarly, send these black electrons 628 00:28:33,610 --> 00:28:37,780 into the hardness box, and here's hard and black, 629 00:28:37,780 --> 00:28:40,340 and here's soft and back. 630 00:28:45,514 --> 00:28:46,580 Everybody cool with that? 631 00:28:46,580 --> 00:28:48,267 So this seems to do the thing I wanted. 632 00:28:48,267 --> 00:28:50,100 It measures both the hardness and the color. 633 00:28:50,100 --> 00:28:53,003 What's the problem with it? 634 00:28:53,003 --> 00:28:53,878 AUDIENCE: [INAUDIBLE] 635 00:28:56,716 --> 00:28:58,030 ALLAN ADAMS: Yeah, exactly. 636 00:28:58,030 --> 00:29:00,020 So the color is not persistent. 637 00:29:00,020 --> 00:29:03,750 So you tell me this is a soft and black electron, right? 638 00:29:03,750 --> 00:29:05,120 That's what you told me. 639 00:29:05,120 --> 00:29:06,100 Here's the box. 640 00:29:06,100 --> 00:29:10,160 But if I put a color box here, that's 641 00:29:10,160 --> 00:29:12,250 the experiment we just ran. 642 00:29:12,250 --> 00:29:13,120 And what happens? 643 00:29:13,120 --> 00:29:15,290 Does this come out black? 644 00:29:15,290 --> 00:29:17,440 No, this is a crappy source of black electrons. 645 00:29:17,440 --> 00:29:19,570 It's 50/50 black and white. 646 00:29:19,570 --> 00:29:21,706 So this box can't be built. 647 00:29:21,706 --> 00:29:23,580 And the reason, and I want to emphasize this, 648 00:29:23,580 --> 00:29:25,970 the reason we cannot build this box is not 649 00:29:25,970 --> 00:29:28,130 because our experiments are crude. 650 00:29:28,130 --> 00:29:30,590 And it's not because I can't build things, 651 00:29:30,590 --> 00:29:32,190 although that's true. 652 00:29:32,190 --> 00:29:36,590 I was banned from a lab one day after joining it, actually. 653 00:29:36,590 --> 00:29:40,310 So I really can't build, but other people can. 654 00:29:40,310 --> 00:29:41,230 And that's not why. 655 00:29:41,230 --> 00:29:43,490 We can't because of something much more fundamental, 656 00:29:43,490 --> 00:29:45,610 something deeper, something in principle, 657 00:29:45,610 --> 00:29:50,170 which is encoded in this awesome experiment. 658 00:29:50,170 --> 00:29:51,580 This can be done. 659 00:29:51,580 --> 00:29:55,030 It does not mean anything, as a consequence. 660 00:29:55,030 --> 00:29:57,900 It does not mean anything to say this electron is 661 00:29:57,900 --> 00:30:04,376 white and hard, because if you tell me it's white and hard, 662 00:30:04,376 --> 00:30:06,500 and I measure the white, well, I know if it's hard, 663 00:30:06,500 --> 00:30:09,130 it's going to come out 50-50. 664 00:30:09,130 --> 00:30:11,490 It does not mean anything. 665 00:30:11,490 --> 00:30:13,310 So this is an important idea. 666 00:30:13,310 --> 00:30:16,670 This is an idea which is enshrined in physics 667 00:30:16,670 --> 00:30:19,420 with a term which comes with capital 668 00:30:19,420 --> 00:30:21,510 letters, the Uncertainty Principle. 669 00:30:21,510 --> 00:30:24,620 And the Uncertainty Principle says basically that, look, 670 00:30:24,620 --> 00:30:27,430 there's some observable, measurable properties 671 00:30:27,430 --> 00:30:31,160 of a system which are incompatible 672 00:30:31,160 --> 00:30:34,240 with each other in precisely this way, 673 00:30:34,240 --> 00:30:36,000 incompatible with each other in the sense 674 00:30:36,000 --> 00:30:41,170 not that you can't know, because you can't know whether it's 675 00:30:41,170 --> 00:30:43,450 hard and soft simultaneously, deeper. 676 00:30:43,450 --> 00:30:47,690 It is not hard and white simultaneously. 677 00:30:47,690 --> 00:30:48,600 It cannot be. 678 00:30:48,600 --> 00:30:50,580 It does not mean anything to say it 679 00:30:50,580 --> 00:30:54,770 is hard and white simultaneously. 680 00:30:54,770 --> 00:30:56,270 That is uncertainty. 681 00:30:56,270 --> 00:30:58,290 And again, uncertainty is an idea 682 00:30:58,290 --> 00:31:01,290 we're going to come back to over and over in the class. 683 00:31:01,290 --> 00:31:02,790 But every time you think about it, 684 00:31:02,790 --> 00:31:04,870 this should be the first place you 685 00:31:04,870 --> 00:31:06,680 start for the next few weeks. 686 00:31:09,680 --> 00:31:11,700 Yeah. 687 00:31:11,700 --> 00:31:14,190 Questions. 688 00:31:14,190 --> 00:31:16,241 No questions? 689 00:31:16,241 --> 00:31:16,740 OK. 690 00:31:16,740 --> 00:31:19,520 So at this point, it's really tempting 691 00:31:19,520 --> 00:31:24,325 to think yeah, OK, this is just about the hardness 692 00:31:24,325 --> 00:31:25,450 and the color of electrons. 693 00:31:28,290 --> 00:31:30,620 It's just a weird thing about electrons. 694 00:31:30,620 --> 00:31:31,800 It's not a weird thing about the rest of the world. 695 00:31:31,800 --> 00:31:33,090 The rest of the world's completely reasonable. 696 00:31:33,090 --> 00:31:34,850 And no, that's absolutely wrong. 697 00:31:34,850 --> 00:31:39,640 Every object in the world has the same properties. 698 00:31:39,640 --> 00:31:42,430 If you take bucky-balls, and you send them 699 00:31:42,430 --> 00:31:44,180 through the analogous experiment-- 700 00:31:44,180 --> 00:31:46,340 and I will show you the data, I think tomorrow, 701 00:31:46,340 --> 00:31:48,030 but soon, I will show you the data. 702 00:31:48,030 --> 00:31:49,530 When you take bucky-balls and run it 703 00:31:49,530 --> 00:31:51,980 through a similar experiment, you get the same effect. 704 00:31:51,980 --> 00:31:56,870 Now, bucky-balls are huge, right, 60 carbon atoms. 705 00:31:56,870 --> 00:31:58,700 But, OK, OK, at that point, you're 706 00:31:58,700 --> 00:32:01,430 saying, dude, come on, huge, 60 carbon atoms. 707 00:32:01,430 --> 00:32:06,240 So there is a pendulum, depending 708 00:32:06,240 --> 00:32:10,870 on how you define building, in this building, a pendulum which 709 00:32:10,870 --> 00:32:13,950 is used, in principle which is used to improve detectors 710 00:32:13,950 --> 00:32:15,970 to detect gravitational waves. 711 00:32:15,970 --> 00:32:18,930 There's a pendulum with a, I think it's 20 kilo mirror. 712 00:32:21,570 --> 00:32:27,380 And that pendulum exhibits the same sort of effects here. 713 00:32:27,380 --> 00:32:29,482 We can see these quantum mechanical effects 714 00:32:29,482 --> 00:32:30,190 in those mirrors. 715 00:32:30,190 --> 00:32:32,260 And this is in breathtakingly awesome experiments 716 00:32:32,260 --> 00:32:35,930 done by Nergis Malvalvala, whose name I can never pronounce, 717 00:32:35,930 --> 00:32:38,230 but who is totally awesome. 718 00:32:38,230 --> 00:32:40,015 She's an amazing physicist. 719 00:32:40,015 --> 00:32:42,390 And she can get these kind of quantum effects out of a 20 720 00:32:42,390 --> 00:32:43,720 kilo mirror. 721 00:32:43,720 --> 00:32:46,260 So before you say something silly, like, oh, it's 722 00:32:46,260 --> 00:32:48,400 just electrons, it's 20 kilo mirrors. 723 00:32:48,400 --> 00:32:50,760 And if I could put you on a pendulum that accurate, 724 00:32:50,760 --> 00:32:52,014 it would be you. 725 00:32:52,014 --> 00:32:53,210 OK? 726 00:32:53,210 --> 00:32:56,800 These are properties of everything around you. 727 00:32:56,800 --> 00:32:59,860 The miracle is not that electrons behave oddly. 728 00:32:59,860 --> 00:33:03,190 The miracle is that when you take 10 to the 27 electrons, 729 00:33:03,190 --> 00:33:06,570 they behave like cheese. 730 00:33:06,570 --> 00:33:08,050 That's the miracle. 731 00:33:08,050 --> 00:33:10,040 This is the underlying correct thing. 732 00:33:13,200 --> 00:33:16,490 OK, so this is so far so good. 733 00:33:16,490 --> 00:33:18,210 But let's go deeper. 734 00:33:18,210 --> 00:33:21,110 Let's push it. 735 00:33:21,110 --> 00:33:23,080 And to push it, I want to design for you 736 00:33:23,080 --> 00:33:26,960 a slightly more elaborate apparatus, a slightly more 737 00:33:26,960 --> 00:33:29,290 elaborate experimental apparatus. 738 00:33:29,290 --> 00:33:32,600 And for this, I want you to consider the following device. 739 00:33:32,600 --> 00:33:35,490 I'm going to need to introduce a couple of new features for you. 740 00:33:35,490 --> 00:33:36,910 Here's a hardness box. 741 00:33:36,910 --> 00:33:38,740 And it has an in port. 742 00:33:38,740 --> 00:33:41,250 And the hardness box has a hard aperture, 743 00:33:41,250 --> 00:33:43,601 and it has a soft aperture. 744 00:33:43,601 --> 00:33:45,350 And now, in addition to this hardness box, 745 00:33:45,350 --> 00:33:46,850 I'm going to introduce two elements. 746 00:33:46,850 --> 00:33:49,675 First, mirrors. 747 00:33:49,675 --> 00:33:51,800 And what these mirrors do is they take the incident 748 00:33:51,800 --> 00:33:53,880 electrons and, nothing else, they 749 00:33:53,880 --> 00:33:57,715 change the direction of motion, change the direction of motion. 750 00:33:57,715 --> 00:33:59,590 And here's what I mean by doing nothing else. 751 00:33:59,590 --> 00:34:02,250 If I take one of these mirrors, and I take, 752 00:34:02,250 --> 00:34:03,565 for example, a color box. 753 00:34:03,565 --> 00:34:05,440 And I take the white electrons that come out, 754 00:34:05,440 --> 00:34:08,270 and I bounce it off the mirror, and then 755 00:34:08,270 --> 00:34:13,469 I send these into a color box, then 756 00:34:13,469 --> 00:34:17,270 they come out white 100% of the time. 757 00:34:17,270 --> 00:34:19,699 It does not change the observable color. 758 00:34:19,699 --> 00:34:20,199 Cool? 759 00:34:20,199 --> 00:34:21,639 All it does is change the direction. 760 00:34:21,639 --> 00:34:22,960 Similarly, with the hardness box, 761 00:34:22,960 --> 00:34:24,251 it doesn't change the hardness. 762 00:34:24,251 --> 00:34:26,780 It just changes the direction of motion. 763 00:34:26,780 --> 00:34:29,340 And every experiment we've ever done on these, guys, 764 00:34:29,340 --> 00:34:31,860 changes in no way whatsoever the color 765 00:34:31,860 --> 00:34:34,540 or the hardness by subsequent measurement. 766 00:34:34,540 --> 00:34:35,370 Cool? 767 00:34:35,370 --> 00:34:37,860 Just changes the direction of motion. 768 00:34:37,860 --> 00:34:40,110 And then I'm going to add another mirror. 769 00:34:40,110 --> 00:34:43,310 It's actually a slightly fancy set of mirrors. 770 00:34:43,310 --> 00:34:45,989 All they do is they join these beams together 771 00:34:45,989 --> 00:34:47,001 into a single beam. 772 00:34:50,689 --> 00:34:52,580 And again, this doesn't change the color. 773 00:34:52,580 --> 00:34:53,920 You send in a white electron, you get out, 774 00:34:53,920 --> 00:34:55,909 and you measure the color on the other side, 775 00:34:55,909 --> 00:34:56,530 you get a white electron. 776 00:34:56,530 --> 00:34:57,830 You send in a black electron from here, 777 00:34:57,830 --> 00:35:00,413 and you measure the color, you get a black electron again out. 778 00:35:00,413 --> 00:35:02,137 Cool? 779 00:35:02,137 --> 00:35:03,095 So here's my apparatus. 780 00:35:05,509 --> 00:35:07,300 And I'm going to put this inside a big box. 781 00:35:09,890 --> 00:35:11,417 And I want to run some experiments 782 00:35:11,417 --> 00:35:12,250 with this apparatus. 783 00:35:22,040 --> 00:35:24,030 Everyone cool with the basic design? 784 00:35:24,030 --> 00:35:25,820 Any questions before I cruise on? 785 00:35:30,144 --> 00:35:30,810 This part's fun. 786 00:35:34,724 --> 00:35:36,140 So what I want to do now is I want 787 00:35:36,140 --> 00:35:39,440 to run some simple experiments before we get to fancy stuff. 788 00:35:39,440 --> 00:35:42,090 And the simple experiments are just going to warm you up. 789 00:35:42,090 --> 00:35:43,590 They're going to prepare you to make 790 00:35:43,590 --> 00:35:45,430 some predictions and some calculations. 791 00:35:45,430 --> 00:35:48,900 And eventually we'd like to lead back to this guy. 792 00:35:48,900 --> 00:35:51,690 So the first experiment, I'm going 793 00:35:51,690 --> 00:35:53,870 to send in white electrons. 794 00:35:53,870 --> 00:35:54,406 Whoops. 795 00:35:54,406 --> 00:35:56,540 Im. 796 00:35:56,540 --> 00:36:00,320 I'm going to send in white electrons. 797 00:36:00,320 --> 00:36:03,620 And I'm going to measure at the end, 798 00:36:03,620 --> 00:36:07,870 and in particular at the output, the hardness. 799 00:36:15,439 --> 00:36:17,105 So I'm going to send in white electrons. 800 00:36:23,367 --> 00:36:24,950 And I'm going to measure the hardness. 801 00:36:24,950 --> 00:36:27,501 So this is my apparatus. 802 00:36:27,501 --> 00:36:29,500 I'm going to measure the hardness at the output. 803 00:36:29,500 --> 00:36:30,370 And what I mean by measure the hardness 804 00:36:30,370 --> 00:36:32,780 is I throw these electrons into a hardness box 805 00:36:32,780 --> 00:36:34,720 and see what comes out. 806 00:36:34,720 --> 00:36:37,932 So this is experiment 1. 807 00:36:37,932 --> 00:36:41,890 And let me draw this, let me biggen the diagram. 808 00:36:41,890 --> 00:36:49,110 So you send white into-- so the mechanism is a hardness box. 809 00:36:49,110 --> 00:36:58,070 Mirror, mirror, mirrors, and now we're 810 00:36:58,070 --> 00:36:59,520 measuring the hardness out. 811 00:37:05,840 --> 00:37:10,950 And the question I want to ask is how many electrons come out 812 00:37:10,950 --> 00:37:14,020 the hard aperture, and how many electrons come out 813 00:37:14,020 --> 00:37:18,130 the soft aperture of this final hardness box. 814 00:37:18,130 --> 00:37:20,220 So I'd like to know what fraction come out hard, 815 00:37:20,220 --> 00:37:21,730 and what fraction come out soft. 816 00:37:21,730 --> 00:37:23,246 I send an initial white electron, 817 00:37:23,246 --> 00:37:25,620 for example I took a color box and took the white output, 818 00:37:25,620 --> 00:37:28,770 send them into the hardness box, mirror, mirror, 819 00:37:28,770 --> 00:37:30,710 hard, hard, soft. 820 00:37:30,710 --> 00:37:33,030 And what fraction come out hard, and what fraction 821 00:37:33,030 --> 00:37:33,680 come out soft. 822 00:37:38,370 --> 00:37:39,893 So just think about it for a minute. 823 00:37:44,530 --> 00:37:47,990 And when you have a prediction in your head, raise your hand. 824 00:37:56,630 --> 00:37:57,897 All right, good. 825 00:37:57,897 --> 00:37:59,230 Walk me through your prediction. 826 00:38:01,820 --> 00:38:04,390 AUDIENCE: I think it should be 50-50. 827 00:38:04,390 --> 00:38:06,980 ALLAN ADAMS: 50-50. 828 00:38:06,980 --> 00:38:08,296 How come? 829 00:38:08,296 --> 00:38:10,248 AUDIENCE: [INAUDIBLE] color doesn't 830 00:38:10,248 --> 00:38:13,626 have any bearing on hardness. 831 00:38:13,626 --> 00:38:14,126 [INAUDIBLE] 832 00:38:20,600 --> 00:38:21,520 ALLAN ADAMS: Awesome. 833 00:38:21,520 --> 00:38:22,170 So let me say that again. 834 00:38:22,170 --> 00:38:24,530 So we've done the experiment, you send a white electron 835 00:38:24,530 --> 00:38:25,946 into the hardness box, and we know 836 00:38:25,946 --> 00:38:27,930 that it's non-predictive, 50-50. 837 00:38:27,930 --> 00:38:30,905 So if you take a white electron and you send it 838 00:38:30,905 --> 00:38:33,879 into the hardness box, 50% of the time 839 00:38:33,879 --> 00:38:36,170 it will come out the hard aperture, and 50% of the time 840 00:38:36,170 --> 00:38:37,750 it will come out the soft aperture. 841 00:38:37,750 --> 00:38:40,727 Now if you take the one that comes out the hard aperture, 842 00:38:40,727 --> 00:38:42,560 then you send it up here or send it up here, 843 00:38:42,560 --> 00:38:44,930 we know that these mirrors do nothing 844 00:38:44,930 --> 00:38:46,720 to the hardness of the electron except 845 00:38:46,720 --> 00:38:48,062 change the direction of motion. 846 00:38:48,062 --> 00:38:49,520 We've already done that experiment. 847 00:38:49,520 --> 00:38:52,540 So you measure the hardness at the output, what do you get? 848 00:38:52,540 --> 00:38:56,050 Hard, because it came out hard, mirror, mirror, hardness, hard. 849 00:38:56,050 --> 00:38:58,060 But it only came out hard 50% of the time 850 00:38:58,060 --> 00:39:00,270 because we sent in initially white electron. 851 00:39:00,270 --> 00:39:00,870 Yeah? 852 00:39:00,870 --> 00:39:01,911 What about the other 50%? 853 00:39:01,911 --> 00:39:04,680 Well, the other 50% of the time, it comes out the soft aperture 854 00:39:04,680 --> 00:39:07,212 and follows what I'll call the soft path 855 00:39:07,212 --> 00:39:08,849 to the mirror, mirror, hardness. 856 00:39:08,849 --> 00:39:10,515 And with soft, mirror, mirror, hardness, 857 00:39:10,515 --> 00:39:12,097 you know it comes out soft. 858 00:39:12,097 --> 00:39:13,680 50% of the time it comes out this way, 859 00:39:13,680 --> 00:39:14,525 and then it will come out hard. 860 00:39:14,525 --> 00:39:17,290 50% it follows the soft path, and then it will come out soft. 861 00:39:17,290 --> 00:39:18,810 Was this the logic? 862 00:39:18,810 --> 00:39:20,130 Good. 863 00:39:20,130 --> 00:39:23,870 How many people agree with this? 864 00:39:23,870 --> 00:39:24,490 Solid. 865 00:39:24,490 --> 00:39:27,810 How many people disagree? 866 00:39:27,810 --> 00:39:29,630 No abstention. 867 00:39:29,630 --> 00:39:30,280 OK. 868 00:39:30,280 --> 00:39:35,120 So here's a prediction. 869 00:39:35,120 --> 00:39:35,840 Oh, yep. 870 00:39:35,840 --> 00:39:38,220 AUDIENCE: Just a question. 871 00:39:38,220 --> 00:39:40,600 Could you justify that prediction 872 00:39:40,600 --> 00:39:44,412 without talking about oh, well, half the electrons were 873 00:39:44,412 --> 00:39:47,000 initially measured to be hard, and half were initially 874 00:39:47,000 --> 00:39:48,860 measured to be soft, by just saying, well, 875 00:39:48,860 --> 00:39:54,120 we have a hardness box, and then we joined these electrons 876 00:39:54,120 --> 00:39:57,045 together again, so we don't know anything about it. 877 00:39:57,045 --> 00:40:00,171 So it's just like sending white electrons 878 00:40:00,171 --> 00:40:01,802 into one hardness box instead of two. 879 00:40:01,802 --> 00:40:04,010 ALLAN ADAMS: Yeah, that's a really tempting argument, 880 00:40:04,010 --> 00:40:04,690 isn't it? 881 00:40:04,690 --> 00:40:05,292 So let's see. 882 00:40:05,292 --> 00:40:06,750 We're going to see in a few minutes 883 00:40:06,750 --> 00:40:09,400 whether that kind of an argument is reliable or not. 884 00:40:09,400 --> 00:40:12,390 But so far we've been given two different arguments that lead 885 00:40:12,390 --> 00:40:14,760 to the same prediction, 50-50. 886 00:40:14,760 --> 00:40:15,981 Yeah? 887 00:40:15,981 --> 00:40:16,480 Question. 888 00:40:20,415 --> 00:40:23,140 AUDIENCE: Are the electrons interacting between themselves? 889 00:40:23,140 --> 00:40:25,933 Like when you get them to where-- 890 00:40:25,933 --> 00:40:27,642 ALLAN ADAMS: Yeah. 891 00:40:27,642 --> 00:40:28,850 This is a very good question. 892 00:40:28,850 --> 00:40:31,900 So here's a question look you're sending a bunch of electrons 893 00:40:31,900 --> 00:40:33,520 into this apparatus. 894 00:40:33,520 --> 00:40:35,814 But if I take-- look, I took 802. 895 00:40:35,814 --> 00:40:37,230 You take two electrons and you put 896 00:40:37,230 --> 00:40:38,770 them close to each other, what do they do? 897 00:40:38,770 --> 00:40:39,290 Pyewww. 898 00:40:39,290 --> 00:40:39,630 Right? 899 00:40:39,630 --> 00:40:42,140 They interact with each other through a potential, right? 900 00:40:42,140 --> 00:40:44,320 So yeah, we're being a little bold here, throwing 901 00:40:44,320 --> 00:40:45,080 a bunch of electrons in and saying, 902 00:40:45,080 --> 00:40:46,270 oh, they're independent. 903 00:40:46,270 --> 00:40:47,650 So I'm going to do one better. 904 00:40:47,650 --> 00:40:49,670 I will send them in one at a time. 905 00:40:49,670 --> 00:40:51,950 One electron through the apparatus. 906 00:40:51,950 --> 00:40:54,140 And then I will wait for six weeks. 907 00:40:54,140 --> 00:40:57,440 [LAUGHTER] 908 00:40:57,440 --> 00:40:59,280 See, you guys laugh, you think that's funny. 909 00:40:59,280 --> 00:41:01,250 But there's a famous story about a guy 910 00:41:01,250 --> 00:41:05,190 who did a similar experiment with photons, French guy. 911 00:41:05,190 --> 00:41:07,440 And, I mean, the French, they know what they're doing. 912 00:41:07,440 --> 00:41:11,720 So he wanted to do the same experiment with photons. 913 00:41:11,720 --> 00:41:13,560 But the problem is if you take a laser 914 00:41:13,560 --> 00:41:15,220 and you shined it into your apparatus, 915 00:41:15,220 --> 00:41:18,190 there there are like, 10 to the 18 photons in there 916 00:41:18,190 --> 00:41:19,050 at any given moment. 917 00:41:19,050 --> 00:41:21,633 And the photons, who knows what they're doing with each other, 918 00:41:21,633 --> 00:41:23,460 right? 919 00:41:23,460 --> 00:41:25,925 So I want to send in one photon, but the problem 920 00:41:25,925 --> 00:41:28,580 is, it's very hard to get a single photon, very hard. 921 00:41:28,580 --> 00:41:31,851 So what he did, I kid you not, he took an opaque barrier, 922 00:41:31,851 --> 00:41:34,100 I don't remember what it was, it was some sort of film 923 00:41:34,100 --> 00:41:37,620 on top of glass, I think it was some sort of oil-tar film. 924 00:41:37,620 --> 00:41:39,390 Barton, do you remember what he used? 925 00:41:39,390 --> 00:41:44,650 So he takes a film, and it has this opaque property, 926 00:41:44,650 --> 00:41:49,850 such that the photons that are incident upon it get absorbed. 927 00:41:49,850 --> 00:41:52,720 Once in a blue moon a photon manages 928 00:41:52,720 --> 00:41:53,720 to make its way through. 929 00:41:53,720 --> 00:41:56,820 Literally, like once every couple of days, 930 00:41:56,820 --> 00:41:58,070 or a couple of hours, I think. 931 00:41:58,070 --> 00:42:01,280 So it's going to take a long time 932 00:42:01,280 --> 00:42:02,900 to get any sort of statistics. 933 00:42:02,900 --> 00:42:05,580 But he this advantage, that once every couple of hours 934 00:42:05,580 --> 00:42:07,690 or whatever a photon makes its way through. 935 00:42:07,690 --> 00:42:09,273 That means inside the apparatus, if it 936 00:42:09,273 --> 00:42:12,280 takes a pico-second to cross, triumph, right? 937 00:42:12,280 --> 00:42:13,780 That's the week I was talking about. 938 00:42:13,780 --> 00:42:15,850 So he does this experiment. 939 00:42:15,850 --> 00:42:18,600 But as you can tell, you start the experiment, you press go, 940 00:42:18,600 --> 00:42:21,510 and then you wait for six months. 941 00:42:21,510 --> 00:42:26,890 Side note on this guy, liked boats, really liked yachts. 942 00:42:26,890 --> 00:42:29,254 So he had six months to wait before doing 943 00:42:29,254 --> 00:42:31,170 a beautiful experiment and having the results. 944 00:42:31,170 --> 00:42:32,650 So what did he do? 945 00:42:32,650 --> 00:42:35,380 Went on a world tour in his yacht. 946 00:42:35,380 --> 00:42:37,990 Comes back, collects the data, and declares victory, 947 00:42:37,990 --> 00:42:40,350 because indeed, he saw the effect he wanted. 948 00:42:40,350 --> 00:42:41,515 So I was not kidding. 949 00:42:44,650 --> 00:42:46,390 We really do wait. 950 00:42:46,390 --> 00:42:49,730 So I will take your challenge. 951 00:42:49,730 --> 00:42:53,500 And single electron, throw it in, 952 00:42:53,500 --> 00:42:56,050 let it go through the apparatus, takes mere moments. 953 00:42:56,050 --> 00:42:59,110 Wait for a week, send in another electron. 954 00:42:59,110 --> 00:43:02,950 No electrons are interacting with each other. 955 00:43:02,950 --> 00:43:07,317 Just a single electron at a time going through this apparatus. 956 00:43:07,317 --> 00:43:08,025 Other complaints? 957 00:43:11,076 --> 00:43:12,579 AUDIENCE: More stories? 958 00:43:12,579 --> 00:43:13,370 ALLAN ADAMS: Sorry? 959 00:43:13,370 --> 00:43:14,328 AUDIENCE: More stories? 960 00:43:14,328 --> 00:43:16,092 ALLAN ADAMS: Oh, you'll get them. 961 00:43:16,092 --> 00:43:17,300 I have a hard time resisting. 962 00:43:17,300 --> 00:43:21,870 So here's a prediction, 50-50. 963 00:43:21,870 --> 00:43:24,570 We now have two arguments for this. 964 00:43:24,570 --> 00:43:26,880 So again, let's vote after the second argument. 965 00:43:26,880 --> 00:43:29,710 50-50, how many people? 966 00:43:29,710 --> 00:43:30,960 You sure? 967 00:43:30,960 --> 00:43:31,669 Positive? 968 00:43:31,669 --> 00:43:32,960 How many people don't think so? 969 00:43:35,670 --> 00:43:37,330 Very small dust. 970 00:43:37,330 --> 00:43:37,830 OK. 971 00:43:37,830 --> 00:43:38,950 It's correct. 972 00:43:38,950 --> 00:43:41,150 Yea. 973 00:43:41,150 --> 00:43:41,700 So, good. 974 00:43:46,710 --> 00:43:50,100 I like messing with you guys. 975 00:43:50,100 --> 00:43:53,346 So remember, we're going to go through a few experiments 976 00:43:53,346 --> 00:43:54,720 first where it's going to be very 977 00:43:54,720 --> 00:43:55,810 easy to predict the results. 978 00:43:55,810 --> 00:43:57,510 We've got four experiments like this to do. 979 00:43:57,510 --> 00:43:58,890 And then we'll go on to the interesting examples. 980 00:43:58,890 --> 00:44:00,900 But we need to go through them so we know what happens, 981 00:44:00,900 --> 00:44:03,149 so we can make an empirical argument rather than an in 982 00:44:03,149 --> 00:44:03,941 principle argument. 983 00:44:03,941 --> 00:44:05,273 So there's the first experiment. 984 00:44:05,273 --> 00:44:07,020 Now, I want to run the second experiment. 985 00:44:09,970 --> 00:44:12,480 And the second experiment, same as the first, 986 00:44:12,480 --> 00:44:15,200 a little bit louder, a little bit worse. 987 00:44:15,200 --> 00:44:16,770 Sorry. 988 00:44:16,770 --> 00:44:18,960 The second experiment, we're going 989 00:44:18,960 --> 00:44:23,590 to send in hard electrons, and we're 990 00:44:23,590 --> 00:44:27,900 going to measure color at out. 991 00:44:31,300 --> 00:44:32,930 So again, let's look at the apparatus. 992 00:44:32,930 --> 00:44:34,560 We send in hard electrons. 993 00:44:34,560 --> 00:44:39,060 And our apparatus is hardness box 994 00:44:39,060 --> 00:44:40,705 with a hard and a soft aperture. 995 00:44:47,729 --> 00:44:50,020 And now we're going to measure the color at the output. 996 00:44:53,390 --> 00:44:56,500 Color, what have I been doing? 997 00:44:58,984 --> 00:45:01,150 And now I want to know what fraction come out black, 998 00:45:01,150 --> 00:45:02,525 and what fraction come out white. 999 00:45:07,130 --> 00:45:10,270 We're using lots of monkeys in this process. 1000 00:45:10,270 --> 00:45:11,880 OK, so this is not rocket science. 1001 00:45:16,030 --> 00:45:17,620 Rocket science isn't that complicated. 1002 00:45:17,620 --> 00:45:18,786 Neuroscience is much harder. 1003 00:45:18,786 --> 00:45:20,540 This is not neuroscience. 1004 00:45:20,540 --> 00:45:23,710 So let's figure out what this is. 1005 00:45:23,710 --> 00:45:24,380 Predictions. 1006 00:45:24,380 --> 00:45:25,921 So again, think about your prediction 1007 00:45:25,921 --> 00:45:27,870 your head, come to a conclusion, raise 1008 00:45:27,870 --> 00:45:29,203 your hand when you have an idea. 1009 00:45:31,591 --> 00:45:33,340 And just because you don't raise your hand 1010 00:45:33,340 --> 00:45:34,841 doesn't mean I won't call on you. 1011 00:45:47,267 --> 00:45:48,600 AUDIENCE: 50-50 black and white. 1012 00:45:48,600 --> 00:45:49,780 ALLAN ADAMS: 50-50 black and white. 1013 00:45:49,780 --> 00:45:50,365 I like it. 1014 00:45:50,365 --> 00:45:51,662 Tell me why. 1015 00:45:51,662 --> 00:45:53,703 AUDIENCE: It's gone through a hardness box, which 1016 00:45:53,703 --> 00:45:56,270 scrambled the color, and therefore has to be [INAUDIBLE] 1017 00:45:56,270 --> 00:45:56,570 ALLAN ADAMS: Great. 1018 00:45:56,570 --> 00:45:59,111 So the statement, I'm going to say that slightly more slowly. 1019 00:45:59,111 --> 00:46:01,630 That was an excellent argument. 1020 00:46:01,630 --> 00:46:02,630 We have a hard electron. 1021 00:46:02,630 --> 00:46:05,097 We know that hardness boxes are persistent. 1022 00:46:05,097 --> 00:46:07,180 If you send a hard electron in, it comes out hard. 1023 00:46:07,180 --> 00:46:09,860 So every electron incident upon our apparatus 1024 00:46:09,860 --> 00:46:13,880 will transit across the hard trajectory. 1025 00:46:13,880 --> 00:46:16,090 It will bounce, it will bounce, but it is still hard, 1026 00:46:16,090 --> 00:46:17,310 because we've already done that experiment. 1027 00:46:17,310 --> 00:46:18,710 The mirrors do nothing to the hardness. 1028 00:46:18,710 --> 00:46:20,460 So we send a hard electron into the color box, 1029 00:46:20,460 --> 00:46:21,030 and what comes out? 1030 00:46:21,030 --> 00:46:22,613 Well, we've done that experiment, too. 1031 00:46:22,613 --> 00:46:24,255 Hard into color, 50-50. 1032 00:46:24,255 --> 00:46:25,640 So the prediction is 50-50. 1033 00:46:25,640 --> 00:46:27,500 This is your prediction. 1034 00:46:27,500 --> 00:46:28,490 Is that correct? 1035 00:46:28,490 --> 00:46:29,090 Awesome. 1036 00:46:29,090 --> 00:46:33,140 OK, let us vote. 1037 00:46:33,140 --> 00:46:36,520 How many people think this is correct? 1038 00:46:36,520 --> 00:46:37,570 Gusto, I like it. 1039 00:46:37,570 --> 00:46:40,810 How many people think it's not? 1040 00:46:40,810 --> 00:46:41,540 All right. 1041 00:46:41,540 --> 00:46:45,217 Yay, this is correct. 1042 00:46:45,217 --> 00:46:47,050 Third experiment, slightly more complicated. 1043 00:46:50,410 --> 00:46:54,200 But we have to go through these to get to the good stuff, 1044 00:46:54,200 --> 00:46:56,220 so humor me for a moment. 1045 00:46:56,220 --> 00:47:02,880 Third, let's send in white electrons, 1046 00:47:02,880 --> 00:47:10,630 and then measure the color at the output port. 1047 00:47:10,630 --> 00:47:14,640 So now we send in white electrons, same beast. 1048 00:47:14,640 --> 00:47:17,520 And our apparatus is a hardness box 1049 00:47:17,520 --> 00:47:20,606 with a hard path and a soft path. 1050 00:47:20,606 --> 00:47:26,736 Do-do-do, mirror, do-do-do, mirror, box, 1051 00:47:26,736 --> 00:47:27,860 join together into our out. 1052 00:47:27,860 --> 00:47:30,720 And now we send those out electrons into a color box. 1053 00:47:34,960 --> 00:47:39,120 And our color box, black and white. 1054 00:47:39,120 --> 00:47:41,140 And now the question is how many come out black, 1055 00:47:41,140 --> 00:47:42,306 and how many come out white. 1056 00:47:44,180 --> 00:47:48,310 Again, think through the logic, follow the electrons, 1057 00:47:48,310 --> 00:47:49,690 come up with a prediction. 1058 00:47:49,690 --> 00:47:51,481 Raise your hand when you have a prediction. 1059 00:48:09,958 --> 00:48:18,305 AUDIENCE: Well, earlier we showed that [INAUDIBLE] 1060 00:48:18,305 --> 00:48:20,099 so it'll take those paths equally-- 1061 00:48:20,099 --> 00:48:21,598 ALLAN ADAMS: With equal probability. 1062 00:48:21,598 --> 00:48:22,098 Good. 1063 00:48:22,098 --> 00:48:23,032 AUDIENCE: Yeah. 1064 00:48:23,032 --> 00:48:24,795 And then it'll go back into the color box. 1065 00:48:24,795 --> 00:48:26,378 But earlier when we did the same thing 1066 00:48:26,378 --> 00:48:29,246 without the weird path-changing, it came out 50-50 still. 1067 00:48:29,246 --> 00:48:30,372 So I would say still 50-50. 1068 00:48:30,372 --> 00:48:31,162 ALLAN ADAMS: Great. 1069 00:48:31,162 --> 00:48:32,860 So let me say that again, out loud. 1070 00:48:32,860 --> 00:48:35,980 And tell me if this is an accurate 1071 00:48:35,980 --> 00:48:37,435 extension of what you said. 1072 00:48:37,435 --> 00:48:38,810 I'm just going to use more words. 1073 00:48:38,810 --> 00:48:40,410 But it's, I think, the same logic. 1074 00:48:40,410 --> 00:48:42,540 We have a white electron, initially white electron. 1075 00:48:42,540 --> 00:48:43,740 We send it into a hardness box. 1076 00:48:43,740 --> 00:48:45,580 When we send a white electron into a hardness box, 1077 00:48:45,580 --> 00:48:46,580 we know what happens. 1078 00:48:46,580 --> 00:48:49,372 50% of the time it comes out hard, the hard aperture, 1079 00:48:49,372 --> 00:48:51,330 50% of the time it comes out the soft aperture. 1080 00:48:51,330 --> 00:48:53,640 Consider those electrons that came out the hard aperture. 1081 00:48:53,640 --> 00:48:55,030 Those electrons that came out the hard aperture 1082 00:48:55,030 --> 00:48:56,942 will then transit across the system, 1083 00:48:56,942 --> 00:48:58,900 preserving their hardness by virtue of the fact 1084 00:48:58,900 --> 00:49:01,000 that these mirrors preserve hardness, and end up 1085 00:49:01,000 --> 00:49:01,950 at a color box. 1086 00:49:01,950 --> 00:49:03,860 When they end at the color box, when 1087 00:49:03,860 --> 00:49:05,860 that electron, the single electron in the system 1088 00:49:05,860 --> 00:49:07,360 ends at this color box, then we know 1089 00:49:07,360 --> 00:49:09,450 that a hard electron entering a color box 1090 00:49:09,450 --> 00:49:11,720 comes out black or white 50% of the time. 1091 00:49:11,720 --> 00:49:13,920 We've done that experiment, too. 1092 00:49:13,920 --> 00:49:17,320 So for those 50% that came out hard, we get 50/50. 1093 00:49:17,320 --> 00:49:18,739 Now consider the other 50%. 1094 00:49:18,739 --> 00:49:21,280 The other half of the time, the single electron in the system 1095 00:49:21,280 --> 00:49:24,059 will come out the soft aperture. 1096 00:49:24,059 --> 00:49:26,350 It will then proceed along the soft trajectory, bounce, 1097 00:49:26,350 --> 00:49:28,420 bounce, not changing its hardness, 1098 00:49:28,420 --> 00:49:30,880 and is then a soft electron incident on the color box. 1099 00:49:30,880 --> 00:49:32,380 But we've also done that experiment, 1100 00:49:32,380 --> 00:49:34,640 and we get 50-50 out, black and white. 1101 00:49:34,640 --> 00:49:37,470 So those electrons that came out hard come out 50-50, 1102 00:49:37,470 --> 00:49:40,020 and those electrons that come out soft come out 50/50. 1103 00:49:40,020 --> 00:49:43,690 And the logic then leads to 50-50, twice, 50-50. 1104 00:49:46,909 --> 00:49:48,200 Was that an accurate statement? 1105 00:49:48,200 --> 00:49:48,980 Good. 1106 00:49:48,980 --> 00:49:50,580 It's a pretty reasonable extension. 1107 00:49:50,580 --> 00:49:51,590 OK, let's vote. 1108 00:49:51,590 --> 00:49:54,850 How many people agree with this one? 1109 00:49:54,850 --> 00:49:58,400 OK, and how many people disagree? 1110 00:49:58,400 --> 00:49:59,110 Yeah, OK. 1111 00:49:59,110 --> 00:50:01,620 So vast majority agree. 1112 00:50:01,620 --> 00:50:04,500 And the answer is no, this is wrong. 1113 00:50:04,500 --> 00:50:11,620 In fact, all of these, 100% come out white and 0 come out black. 1114 00:50:11,620 --> 00:50:15,660 Never ever does an electron come out the black aperture. 1115 00:50:28,940 --> 00:50:33,160 I would like to quote what a student just 1116 00:50:33,160 --> 00:50:36,720 said, because it's actually the next line in my notes, which 1117 00:50:36,720 --> 00:50:38,630 is what the hell is going on? 1118 00:50:42,170 --> 00:50:46,340 So let's the series of follow up experiments 1119 00:50:46,340 --> 00:50:49,790 to tease out what's going on here. 1120 00:50:49,790 --> 00:50:51,720 So something very strange, let's just 1121 00:50:51,720 --> 00:50:55,000 all agree, something very strange just happened. 1122 00:50:55,000 --> 00:50:57,750 We sent a single electron in. 1123 00:50:57,750 --> 00:50:59,970 And that single electron comes out the hardness box, 1124 00:50:59,970 --> 00:51:03,865 well, it either came out the hard aperture 1125 00:51:03,865 --> 00:51:05,110 or the soft aperture. 1126 00:51:05,110 --> 00:51:06,330 And if it came out the hard, we know what happens, 1127 00:51:06,330 --> 00:51:08,246 if it came out the soft, we know what happens. 1128 00:51:08,246 --> 00:51:10,930 And it's not 50-50. 1129 00:51:10,930 --> 00:51:16,530 So we need to improve the situation. 1130 00:51:16,530 --> 00:51:17,846 Hold on a sec. 1131 00:51:17,846 --> 00:51:18,620 Hold on one sec. 1132 00:51:21,192 --> 00:51:22,572 Well, OK, go ahead. 1133 00:51:22,572 --> 00:51:24,780 AUDIENCE: Yeah, it's just a question about the setup. 1134 00:51:24,780 --> 00:51:27,708 So with the second hardness box, are we 1135 00:51:27,708 --> 00:51:30,940 collecting both the soft and hard outputs? 1136 00:51:30,940 --> 00:51:33,816 ALLAN ADAMS: The second, you mean the first hardness box? 1137 00:51:33,816 --> 00:51:39,020 AUDIENCE: The one-- are we getting-- no, the-- 1138 00:51:39,020 --> 00:51:41,288 ALLAN ADAMS: Which one, sorry? 1139 00:51:41,288 --> 00:51:42,630 This guy? 1140 00:51:42,630 --> 00:51:45,300 Oh, that's a mirror, not a hardness box. 1141 00:51:45,300 --> 00:51:46,410 Oh, thanks for asking. 1142 00:51:46,410 --> 00:51:47,330 Yeah, sorry. 1143 00:51:47,330 --> 00:51:50,200 I wish I had a better notation for this, but I don't. 1144 00:51:50,200 --> 00:51:53,910 There's a classic-- well, I'm not going to go into it. 1145 00:51:53,910 --> 00:51:55,785 Remember that thing where I can't stop myself 1146 00:51:55,785 --> 00:51:57,840 from telling stories? 1147 00:51:57,840 --> 00:51:59,790 So all this does, it's just a set of mirrors. 1148 00:51:59,790 --> 00:52:00,956 It's a set of fancy mirrors. 1149 00:52:00,956 --> 00:52:03,020 And all it does is it takes an electron coming 1150 00:52:03,020 --> 00:52:05,530 this way or an electron coming this way, and both of them 1151 00:52:05,530 --> 00:52:06,988 get sent out in the same direction. 1152 00:52:06,988 --> 00:52:08,600 It's like a beam joiner, right? 1153 00:52:08,600 --> 00:52:10,240 It's like a y junction. 1154 00:52:10,240 --> 00:52:11,090 That's all it is. 1155 00:52:11,090 --> 00:52:14,050 So if you will, imagine the box is a box, 1156 00:52:14,050 --> 00:52:16,830 and you take, I don't know, Professor Zwiebach, 1157 00:52:16,830 --> 00:52:17,860 and you put him inside. 1158 00:52:17,860 --> 00:52:19,060 And every time an electron comes up this way, 1159 00:52:19,060 --> 00:52:19,800 he throws it out that way, and every time 1160 00:52:19,800 --> 00:52:21,440 it comes in this way, he throws it out that way. 1161 00:52:21,440 --> 00:52:23,856 And he'd be really ticked at you for putting him in a box, 1162 00:52:23,856 --> 00:52:24,980 but he'd do the job well. 1163 00:52:24,980 --> 00:52:25,480 Yeah. 1164 00:52:25,480 --> 00:52:27,930 AUDIENCE: And this also works if you go one electron at a time? 1165 00:52:27,930 --> 00:52:30,305 ALLAN ADAMS: This works if you go one electron at a time, 1166 00:52:30,305 --> 00:52:33,190 this works if you go 14 electrons at a time, it works. 1167 00:52:33,190 --> 00:52:33,940 It works reliably. 1168 00:52:33,940 --> 00:52:34,805 Yeah. 1169 00:52:34,805 --> 00:52:36,705 AUDIENCE: Just, maybe [INAUDIBLE] 1170 00:52:36,705 --> 00:52:39,019 but what's the difference between this experiment 1171 00:52:39,019 --> 00:52:39,560 and that one? 1172 00:52:39,560 --> 00:52:41,120 ALLAN ADAMS: Yeah, I know. 1173 00:52:41,120 --> 00:52:41,910 Right? 1174 00:52:41,910 --> 00:52:43,811 Right? 1175 00:52:43,811 --> 00:52:45,560 So the question was, what's the difference 1176 00:52:45,560 --> 00:52:48,137 between this experiment and the last one. 1177 00:52:48,137 --> 00:52:48,970 Yeah, good question. 1178 00:52:48,970 --> 00:52:49,970 So we're going to have to answer that. 1179 00:52:49,970 --> 00:52:50,861 Yeah. 1180 00:52:50,861 --> 00:52:54,789 AUDIENCE: Well, you're mixing again the hardness. 1181 00:52:54,789 --> 00:52:58,852 So it's like as you weren't measuring it at all, right? 1182 00:52:58,852 --> 00:53:01,310 ALLAN ADAMS: Apparently it's a lot we weren't measuring it, 1183 00:53:01,310 --> 00:53:01,810 right? 1184 00:53:01,810 --> 00:53:05,150 Because we send in the white electron, and at the end 1185 00:53:05,150 --> 00:53:06,870 we get out that it's still white. 1186 00:53:06,870 --> 00:53:09,640 So somehow this is like not doing anything. 1187 00:53:09,640 --> 00:53:11,870 But how does that work? 1188 00:53:11,870 --> 00:53:13,330 So that's an excellent observation. 1189 00:53:13,330 --> 00:53:15,788 And I'm going to build you now a couple of experiments that 1190 00:53:15,788 --> 00:53:18,630 tease out what's going on. 1191 00:53:18,630 --> 00:53:20,500 And you're not going to like the answer. 1192 00:53:20,500 --> 00:53:21,001 Yeah. 1193 00:53:21,001 --> 00:53:22,583 AUDIENCE: How were the white electrons 1194 00:53:22,583 --> 00:53:23,970 generated in this experiment? 1195 00:53:23,970 --> 00:53:24,770 ALLAN ADAMS: The white electrons were 1196 00:53:24,770 --> 00:53:26,070 generated in the following way. 1197 00:53:26,070 --> 00:53:27,570 I take a random source of electrons, 1198 00:53:27,570 --> 00:53:31,230 I rub a cat against a balloon and I charge up the balloon. 1199 00:53:31,230 --> 00:53:33,120 And so I take those random electrons, 1200 00:53:33,120 --> 00:53:34,520 and I send them into a color box. 1201 00:53:34,520 --> 00:53:36,275 And we have previously observed that if you 1202 00:53:36,275 --> 00:53:38,200 take random electrons and throw them into a color box 1203 00:53:38,200 --> 00:53:40,400 and pull out the electrons that come out the white aperture, 1204 00:53:40,400 --> 00:53:41,730 if you then send them into a color box 1205 00:53:41,730 --> 00:53:43,020 again, they're still white. 1206 00:53:43,020 --> 00:53:45,000 So that's how I've generated them. 1207 00:53:45,000 --> 00:53:47,540 I could have done it by rubbing the cat against glass, 1208 00:53:47,540 --> 00:53:53,300 or rubbing it against me, right, just stroke the cat. 1209 00:53:53,300 --> 00:53:55,510 Any randomly selected set of electrons 1210 00:53:55,510 --> 00:53:57,760 sent into a color box, and then from which 1211 00:53:57,760 --> 00:53:59,040 you take the white electrons. 1212 00:53:59,040 --> 00:54:01,040 AUDIENCE: So how is it different from the experiment up there? 1213 00:54:01,040 --> 00:54:01,435 ALLAN ADAMS: Yeah. 1214 00:54:01,435 --> 00:54:02,290 Uh-huh. 1215 00:54:02,290 --> 00:54:03,470 Exactly. 1216 00:54:03,470 --> 00:54:04,257 Yeah. 1217 00:54:04,257 --> 00:54:06,590 AUDIENCE: Is the difference that you never actually know 1218 00:54:06,590 --> 00:54:07,790 whether the electron's hard or soft? 1219 00:54:07,790 --> 00:54:09,581 ALLAN ADAMS: That's a really good question. 1220 00:54:09,581 --> 00:54:12,180 So here's something I'm going to be very careful not 1221 00:54:12,180 --> 00:54:14,890 to say in this class to the degree possible. 1222 00:54:14,890 --> 00:54:17,270 I'm not going to use the word to know. 1223 00:54:17,270 --> 00:54:18,895 AUDIENCE: Well, to measure. [INAUDIBLE] 1224 00:54:18,895 --> 00:54:19,644 ALLAN ADAMS: Good. 1225 00:54:19,644 --> 00:54:21,290 Measure is a very slippery word, too. 1226 00:54:21,290 --> 00:54:23,320 I've used it here because I couldn't really 1227 00:54:23,320 --> 00:54:24,880 get away with not using it. 1228 00:54:24,880 --> 00:54:27,880 But we'll talk about that in some detail 1229 00:54:27,880 --> 00:54:28,990 later on in the course. 1230 00:54:28,990 --> 00:54:30,448 For the moment, I want to emphasize 1231 00:54:30,448 --> 00:54:34,410 that it's tempting but dangerous at this point to talk about 1232 00:54:34,410 --> 00:54:37,070 whether you know or don't know, or whether someone knows 1233 00:54:37,070 --> 00:54:38,736 or doesn't know, for example, the monkey 1234 00:54:38,736 --> 00:54:40,250 inside knows or doesn't know. 1235 00:54:40,250 --> 00:54:42,170 So let's try to avoid that, and focus 1236 00:54:42,170 --> 00:54:44,837 on just operational questions of what are the things that go in, 1237 00:54:44,837 --> 00:54:46,836 what are the things that come out, and with what 1238 00:54:46,836 --> 00:54:47,630 probabilities. 1239 00:54:47,630 --> 00:54:49,600 And the reason that's so useful is 1240 00:54:49,600 --> 00:54:51,890 that it's something that you can just do. 1241 00:54:51,890 --> 00:54:53,640 There's no ambiguity about whether you've 1242 00:54:53,640 --> 00:54:55,590 caught a white electron in a particular spot. 1243 00:54:55,590 --> 00:54:57,374 Now in particular, the reason these boxes 1244 00:54:57,374 --> 00:55:00,040 are such a powerful tool is that you don't measure the electron, 1245 00:55:00,040 --> 00:55:01,748 you measure the position of the electron. 1246 00:55:01,748 --> 00:55:03,990 You get hit by the electron or you don't. 1247 00:55:03,990 --> 00:55:07,590 And by using these boxes we can infer from their position 1248 00:55:07,590 --> 00:55:09,690 the color or the hardness. 1249 00:55:09,690 --> 00:55:12,270 And that's the reason these boxes are so useful. 1250 00:55:12,270 --> 00:55:14,064 So we're inferring from the position, which 1251 00:55:14,064 --> 00:55:15,480 is easy to measure, you get beaned 1252 00:55:15,480 --> 00:55:18,130 or you don't, we're inferring the property 1253 00:55:18,130 --> 00:55:20,300 that we're interested in. 1254 00:55:20,300 --> 00:55:21,800 It's a really good question, though. 1255 00:55:21,800 --> 00:55:23,230 Keep it in the back of your mind. 1256 00:55:23,230 --> 00:55:25,188 And we'll talk about it on and off for the rest 1257 00:55:25,188 --> 00:55:26,810 of the semester. 1258 00:55:26,810 --> 00:55:27,649 Yeah. 1259 00:55:27,649 --> 00:55:29,690 AUDIENCE: So what happens if you have this setup, 1260 00:55:29,690 --> 00:55:32,510 and you just take away the bottom right mirror? 1261 00:55:32,510 --> 00:55:33,760 ALLAN ADAMS: Perfect question. 1262 00:55:33,760 --> 00:55:35,385 This leads me into the next experiment. 1263 00:55:35,385 --> 00:55:36,516 So here's the modification. 1264 00:55:36,516 --> 00:55:38,140 But thank you, that's a great question. 1265 00:55:38,140 --> 00:55:40,950 Here's the modification of this experiment. 1266 00:55:40,950 --> 00:55:44,574 So let's rig up a small-- hold on, 1267 00:55:44,574 --> 00:55:46,740 I want to go through the next series of experiments, 1268 00:55:46,740 --> 00:55:47,830 and then I'll come back to questions. 1269 00:55:47,830 --> 00:55:49,080 And these are great questions. 1270 00:55:49,080 --> 00:55:53,360 So I want to rig up a small movable wall, a small movable 1271 00:55:53,360 --> 00:55:53,910 barrier. 1272 00:55:53,910 --> 00:55:56,050 And here's what this movable barrier will do. 1273 00:56:00,710 --> 00:56:07,234 If I put the barrier in, so this would be in the soft path, 1274 00:56:07,234 --> 00:56:08,900 when I put the barrier in the soft path, 1275 00:56:08,900 --> 00:56:12,590 it absorbs all electrons incident upon it 1276 00:56:12,590 --> 00:56:15,400 and impedes them from proceeding. 1277 00:56:15,400 --> 00:56:19,520 So you put a barrier in here, put a barrier in the soft path, 1278 00:56:19,520 --> 00:56:20,930 no electrons continue through. 1279 00:56:20,930 --> 00:56:24,110 An electron incident cannot continue through. 1280 00:56:24,110 --> 00:56:27,042 When I say that the barrier is out, what I mean 1281 00:56:27,042 --> 00:56:28,000 is it's not in the way. 1282 00:56:28,000 --> 00:56:29,740 I've moved it out of the way. 1283 00:56:29,740 --> 00:56:31,160 Cool? 1284 00:56:31,160 --> 00:56:34,450 So I want to run the same experiment. 1285 00:56:34,450 --> 00:56:38,740 And I want to run this experiment using the barriers 1286 00:56:38,740 --> 00:56:42,785 to tease out how the electrons transit through our apparatus. 1287 00:56:47,280 --> 00:56:48,940 So experiment four. 1288 00:56:52,340 --> 00:56:55,520 Let's send in a white electron again. 1289 00:56:55,520 --> 00:56:57,850 I want to do the same experiment we just did. 1290 00:56:57,850 --> 00:57:06,900 And color at out, but now with the wall in the soft path. 1291 00:57:06,900 --> 00:57:10,350 Wall in soft. 1292 00:57:10,350 --> 00:57:13,500 So that's this experiment. 1293 00:57:13,500 --> 00:57:19,670 So we send in white electrons, and at the output 1294 00:57:19,670 --> 00:57:25,550 we measure the color as before. 1295 00:57:25,550 --> 00:57:33,185 And the question is what fraction come out black, 1296 00:57:33,185 --> 00:57:34,560 and what fraction come out white. 1297 00:57:40,029 --> 00:57:42,070 So again, everyone think through it for a second. 1298 00:57:42,070 --> 00:57:42,861 Just take a second. 1299 00:57:44,759 --> 00:57:46,050 And this one's a little sneaky. 1300 00:57:46,050 --> 00:57:50,267 So feel free to discuss it with the person sitting next to you. 1301 00:57:50,267 --> 00:57:53,760 [CHATTER] 1302 00:59:00,782 --> 00:59:01,740 ALLAN ADAMS: All right. 1303 00:59:04,380 --> 00:59:06,880 All right, now that everyone has had a quick second 1304 00:59:06,880 --> 00:59:08,680 to think through this one, let me just 1305 00:59:08,680 --> 00:59:10,945 talk through what I'd expect from the point 1306 00:59:10,945 --> 00:59:11,820 of these experiments. 1307 00:59:11,820 --> 00:59:14,950 And then we'll talk about whether this is reasonable. 1308 00:59:14,950 --> 00:59:16,871 So the first thing I expect is that, look, 1309 00:59:16,871 --> 00:59:18,620 if I send in a white electron and I put it 1310 00:59:18,620 --> 00:59:20,994 into a hardness pass, I know that 50% of the time it goes 1311 00:59:20,994 --> 00:59:22,980 out hard, and 50% of the time it goes out soft. 1312 00:59:22,980 --> 00:59:24,870 If it goes out the soft aperture, 1313 00:59:24,870 --> 00:59:27,966 it's going to get eaten by the barrier, right? 1314 00:59:27,966 --> 00:59:29,590 It's going to get eaten by the barrier. 1315 00:59:29,590 --> 00:59:31,730 So first thing I predict is that the output 1316 00:59:31,730 --> 00:59:34,210 should be down by 50%. 1317 00:59:37,170 --> 00:59:39,390 However, here's an important bit of physics. 1318 00:59:39,390 --> 00:59:41,015 And this comes to the idea of locality. 1319 00:59:44,110 --> 00:59:47,080 I didn't tell you this, but these 1320 00:59:47,080 --> 00:59:52,860 armlinks in the experiment I did, 3,000 kilometers long. 1321 00:59:52,860 --> 00:59:56,000 3,000 kilometers long. 1322 00:59:56,000 --> 00:59:57,380 That's too minor. 1323 00:59:57,380 --> 00:59:59,350 10 million kilometers long. 1324 00:59:59,350 --> 01:00:00,970 Really long. 1325 01:00:00,970 --> 01:00:01,470 Very long. 1326 01:00:04,190 --> 01:00:06,464 Now, imagine an electron that enters 1327 01:00:06,464 --> 01:00:07,880 this, an initially white electron. 1328 01:00:07,880 --> 01:00:11,090 If we had the barriers out, if the barrier was out, 1329 01:00:11,090 --> 01:00:12,015 what do we get? 1330 01:00:14,690 --> 01:00:15,600 100% white, right? 1331 01:00:15,600 --> 01:00:17,640 We just did this experiment, to our surprise. 1332 01:00:17,640 --> 01:00:18,630 So if we did this, we get 100%. 1333 01:00:18,630 --> 01:00:20,030 And that means an electron, any electron, 1334 01:00:20,030 --> 01:00:21,780 going along the soft path comes out white. 1335 01:00:21,780 --> 01:00:24,430 Any electron going along the hard path goes out white. 1336 01:00:24,430 --> 01:00:27,270 They all come out white. 1337 01:00:27,270 --> 01:00:29,550 So now, imagine I do this. 1338 01:00:29,550 --> 01:00:33,140 Imagine we put a barrier in here 2 million miles away 1339 01:00:33,140 --> 01:00:36,020 from this path. 1340 01:00:36,020 --> 01:00:37,844 How does a hard electron along this path 1341 01:00:37,844 --> 01:00:39,260 know that I put the barrier there? 1342 01:00:39,260 --> 01:00:41,710 And I'm going to make it even more sneaky for you. 1343 01:00:41,710 --> 01:00:44,500 I'm going to insert the barrier along the path 1344 01:00:44,500 --> 01:00:49,060 after I launched the electron into the apparatus. 1345 01:00:49,060 --> 01:00:53,470 And when I send in the electron, I will not know at that moment, 1346 01:00:53,470 --> 01:00:55,520 nor will the electron know, because, you 1347 01:00:55,520 --> 01:00:58,070 know, they're not very smart, whether the barrier is 1348 01:00:58,070 --> 01:00:58,810 in place. 1349 01:00:58,810 --> 01:01:02,330 And this is going to be millions of miles away from this guy. 1350 01:01:02,330 --> 01:01:05,150 So an electron out here can't know. 1351 01:01:05,150 --> 01:01:06,220 It hasn't been there. 1352 01:01:06,220 --> 01:01:07,890 It just hasn't been there. 1353 01:01:07,890 --> 01:01:08,820 It can't know. 1354 01:01:08,820 --> 01:01:10,820 But we know that when we ran this apparatus 1355 01:01:10,820 --> 01:01:14,575 without the barrier in there, they came out 100% white. 1356 01:01:14,575 --> 01:01:16,700 But it can't possibly know whether the barrier's in 1357 01:01:16,700 --> 01:01:18,460 there or not, right? 1358 01:01:18,460 --> 01:01:19,340 It's over here. 1359 01:01:22,320 --> 01:01:25,310 So what this tells us is that we should expect the output 1360 01:01:25,310 --> 01:01:26,950 to be down by 50%. 1361 01:01:26,950 --> 01:01:30,980 But all the electrons that do make 1362 01:01:30,980 --> 01:01:33,319 it through must come out white, because they 1363 01:01:33,319 --> 01:01:35,110 didn't know that there was a barrier there. 1364 01:01:35,110 --> 01:01:36,694 They didn't go along that path. 1365 01:01:40,010 --> 01:01:40,510 Yeah. 1366 01:01:40,510 --> 01:01:42,259 AUDIENCE: Not trying to be wise, but why 1367 01:01:42,259 --> 01:01:43,860 are you using the word know? 1368 01:01:43,860 --> 01:01:46,035 ALLAN ADAMS: Oh, sorry, thank you. 1369 01:01:46,035 --> 01:01:48,660 Thank you, thank you, thank you, that was a slip of the tongue. 1370 01:01:48,660 --> 01:01:50,300 I was making fun of the electron. 1371 01:01:50,300 --> 01:01:53,810 So in that particular case, I was not 1372 01:01:53,810 --> 01:01:55,510 referring to my or your knowledge. 1373 01:01:55,510 --> 01:01:56,884 I was referring to the electron's 1374 01:01:56,884 --> 01:01:58,630 tragically impoverished knowledge. 1375 01:02:01,370 --> 01:02:02,178 Yeah. 1376 01:02:02,178 --> 01:02:04,568 AUDIENCE: But if they come out one at a time white, 1377 01:02:04,568 --> 01:02:06,320 then wouldn't we know then with certainty 1378 01:02:06,320 --> 01:02:09,826 that that electron is both hard and white, 1379 01:02:09,826 --> 01:02:11,996 which is like a violation? 1380 01:02:11,996 --> 01:02:14,120 ALLAN ADAMS: Well, here's the more troubling thing. 1381 01:02:14,120 --> 01:02:17,070 Imagine it didn't come out 100% white. 1382 01:02:17,070 --> 01:02:20,170 Then the electron would have demonstrably not 1383 01:02:20,170 --> 01:02:22,990 go along the soft path. 1384 01:02:22,990 --> 01:02:25,240 It would have demonstrably gone through the hard path, 1385 01:02:25,240 --> 01:02:27,115 because that's the only path available to it. 1386 01:02:27,115 --> 01:02:29,520 And yet, it would still have known that millions of miles 1387 01:02:29,520 --> 01:02:31,860 away, there's a barrier on a path it didn't take. 1388 01:02:31,860 --> 01:02:34,100 So which one's more upsetting to you? 1389 01:02:36,720 --> 01:02:40,870 And personally, I find this one the less upsetting of the two. 1390 01:02:40,870 --> 01:02:43,370 So the prediction is our output should down by 50%, 1391 01:02:43,370 --> 01:02:44,952 because a half of them get eaten. 1392 01:02:44,952 --> 01:02:46,410 But they should all come out white, 1393 01:02:46,410 --> 01:02:47,868 because those that didn't get eaten 1394 01:02:47,868 --> 01:02:50,470 can't possibly know that there was a barrier here, 1395 01:02:50,470 --> 01:02:53,480 millions of miles away. 1396 01:02:53,480 --> 01:02:55,622 So we run this experiment. 1397 01:02:55,622 --> 01:02:57,080 And here's the experimental result. 1398 01:02:57,080 --> 01:02:59,320 In fact, the experimental result is yes, the output 1399 01:02:59,320 --> 01:03:00,510 is down by 50%. 1400 01:03:00,510 --> 01:03:04,340 But no, not 100% white, 50% white. 1401 01:03:07,870 --> 01:03:08,800 50% white. 1402 01:03:11,850 --> 01:03:14,310 The barrier, if we put the barrier in the hardness path. 1403 01:03:14,310 --> 01:03:16,550 If we put the barrier in the hardness path, 1404 01:03:16,550 --> 01:03:20,170 still down by 50%, and it's at odds, 50-50. 1405 01:03:23,050 --> 01:03:25,295 How could the electron know? 1406 01:03:25,295 --> 01:03:26,170 I'm making fun of it. 1407 01:03:26,170 --> 01:03:27,095 Yeah. 1408 01:03:27,095 --> 01:03:29,310 AUDIENCE: So I guess my question is 1409 01:03:29,310 --> 01:03:31,110 before we ask how it knows that there's 1410 01:03:31,110 --> 01:03:34,310 a block in one of the paths, how does it know, before, 1411 01:03:34,310 --> 01:03:37,072 over there, that there were two paths, and combine again? 1412 01:03:37,072 --> 01:03:38,030 ALLAN ADAMS: Excellent. 1413 01:03:38,030 --> 01:03:38,630 Exactly. 1414 01:03:38,630 --> 01:03:40,650 So actually, this problem was there already 1415 01:03:40,650 --> 01:03:41,730 in the experiment we did. 1416 01:03:41,730 --> 01:03:43,480 All we've done here is tease out something 1417 01:03:43,480 --> 01:03:44,870 that was existing in the experiment, something 1418 01:03:44,870 --> 01:03:45,890 that was disturbing. 1419 01:03:45,890 --> 01:03:48,620 The presence of those mirrors, and the option 1420 01:03:48,620 --> 01:03:51,320 of taking two paths, somehow changed 1421 01:03:51,320 --> 01:03:53,370 the way the electron behaved. 1422 01:03:53,370 --> 01:03:54,830 How is that possible? 1423 01:03:54,830 --> 01:03:56,550 And here, we're seeing that very sharply. 1424 01:03:56,550 --> 01:03:58,140 Thank you for that excellent observation. 1425 01:03:58,140 --> 01:03:58,420 Yeah. 1426 01:03:58,420 --> 01:04:00,340 AUDIENCE: What if you replaced the two mirrors 1427 01:04:00,340 --> 01:04:04,660 with color boxes, so that both color boxes [INAUDIBLE] 1428 01:04:07,540 --> 01:04:10,040 ALLAN ADAMS: Yeah. 1429 01:04:10,040 --> 01:04:12,910 So the question is basically, let's take this experiment, 1430 01:04:12,910 --> 01:04:16,000 and let's make it even more intricate by, for example, 1431 01:04:16,000 --> 01:04:18,430 replacing these mirrors by color boxes. 1432 01:04:18,430 --> 01:04:20,690 So here's the thing I want to emphasize. 1433 01:04:23,440 --> 01:04:25,894 I strongly encourage you to think through that example. 1434 01:04:25,894 --> 01:04:28,560 And in particular, think through that example, come to my office 1435 01:04:28,560 --> 01:04:31,600 hours, and ask me about it. 1436 01:04:31,600 --> 01:04:33,950 So that's going to be setting a different experiment. 1437 01:04:33,950 --> 01:04:34,890 And different experiments are going 1438 01:04:34,890 --> 01:04:36,230 to have different results. 1439 01:04:36,230 --> 01:04:37,340 So we're going to have to deal with that on a case 1440 01:04:37,340 --> 01:04:38,090 by case basis. 1441 01:04:38,090 --> 01:04:38,994 It's an interesting example, but it's 1442 01:04:38,994 --> 01:04:41,440 going to take us a bit afar from where we are right now. 1443 01:04:41,440 --> 01:04:43,870 But after we get to the punchline from this, 1444 01:04:43,870 --> 01:04:46,620 come to my office hours and ask me exactly that question. 1445 01:04:46,620 --> 01:04:47,720 Yeah. 1446 01:04:47,720 --> 01:04:51,210 AUDIENCE: So we had a color box, we put in white electrons 1447 01:04:51,210 --> 01:04:53,470 and we got 50-50, like random. 1448 01:04:53,470 --> 01:04:55,160 How do you know the boxes work? 1449 01:04:55,160 --> 01:04:56,910 ALLAN ADAMS: How do I know the boxes work? 1450 01:04:56,910 --> 01:04:58,310 These are the same boxes we used from the beginning. 1451 01:04:58,310 --> 01:04:59,350 We tested them over and over. 1452 01:04:59,350 --> 01:05:01,600 AUDIENCE: How did you first check that it was working? 1453 01:05:01,600 --> 01:05:03,595 [INAUDIBLE] 1454 01:05:03,595 --> 01:05:04,970 ALLAN ADAMS: How to say-- there's 1455 01:05:04,970 --> 01:05:07,760 no other way to build a box that does the properties that we 1456 01:05:07,760 --> 01:05:10,260 want, which is that you send in color and it comes out color 1457 01:05:10,260 --> 01:05:13,207 again, and the mirrors behave this way. 1458 01:05:13,207 --> 01:05:15,290 Any box that does those first set of things, which 1459 01:05:15,290 --> 01:05:17,870 is what I will call a color box, does this, too. 1460 01:05:17,870 --> 01:05:19,280 There's no other way to do it. 1461 01:05:19,280 --> 01:05:21,484 I don't mean just because like, no one's tested-- 1462 01:05:21,484 --> 01:05:23,400 AUDIENCE: Because you can't actually check it, 1463 01:05:23,400 --> 01:05:26,499 you can't actually [INAUDIBLE] you know which one is white. 1464 01:05:26,499 --> 01:05:27,790 ALLAN ADAMS: Oh, sure, you can. 1465 01:05:27,790 --> 01:05:29,170 You take the electron that came out of the color box. 1466 01:05:29,170 --> 01:05:30,650 That's what we mean by saying it's white. 1467 01:05:30,650 --> 01:05:31,370 AUDIENCE: [INAUDIBLE] 1468 01:05:31,370 --> 01:05:32,911 ALLAN ADAMS: But that's what it means 1469 01:05:32,911 --> 01:05:34,580 to say the electron is white. 1470 01:05:34,580 --> 01:05:35,820 It's like, how do you know that my name is Allan? 1471 01:05:35,820 --> 01:05:37,220 You say, Allan, and I go, what? 1472 01:05:37,220 --> 01:05:37,590 Right? 1473 01:05:37,590 --> 01:05:40,131 But you're like, look that's not a test of whether I'm Allan. 1474 01:05:40,131 --> 01:05:41,917 It's like, well, what is the test? 1475 01:05:41,917 --> 01:05:42,750 That's how you test. 1476 01:05:42,750 --> 01:05:43,230 What's your name? 1477 01:05:43,230 --> 01:05:43,450 I'm Allan. 1478 01:05:43,450 --> 01:05:44,740 Oh, great, that's your name. 1479 01:05:44,740 --> 01:05:46,110 So that's what I mean by white. 1480 01:05:46,110 --> 01:05:48,110 Now you might quibble that that's a stupid thing 1481 01:05:48,110 --> 01:05:49,070 to call an electron. 1482 01:05:49,070 --> 01:05:50,460 And I grant you that. 1483 01:05:50,460 --> 01:05:53,710 But it is nonetheless a property that I can empirically engage. 1484 01:05:53,710 --> 01:05:55,932 OK, so I've been told that I never ask questions 1485 01:05:55,932 --> 01:05:57,140 from the people on the right. 1486 01:05:57,140 --> 01:05:57,633 Yeah. 1487 01:05:57,633 --> 01:05:59,716 AUDIENCE: Is it important whether the experimenter 1488 01:05:59,716 --> 01:06:02,070 knows if the wall is there or not? 1489 01:06:02,070 --> 01:06:03,140 ALLAN ADAMS: No. 1490 01:06:03,140 --> 01:06:06,930 This experiment has been done again by some French guys. 1491 01:06:06,930 --> 01:06:08,850 The French, look, dude. 1492 01:06:08,850 --> 01:06:12,860 So there's this guy, Alain Aspect, ahh, 1493 01:06:12,860 --> 01:06:14,719 great experimentalist, great physicist. 1494 01:06:14,719 --> 01:06:16,510 And he's done lots of beautiful experiments 1495 01:06:16,510 --> 01:06:17,590 on exactly this topic. 1496 01:06:17,590 --> 01:06:20,500 And send me an email, and I'll post some example papers 1497 01:06:20,500 --> 01:06:23,640 and reviews by him-- and he's a great writer-- on the web page. 1498 01:06:23,640 --> 01:06:25,960 So just send me an email to remind me of that. 1499 01:06:25,960 --> 01:06:29,554 OK, so we're lowish on time, so let me move on. 1500 01:06:29,554 --> 01:06:30,970 So what I want to do now is I want 1501 01:06:30,970 --> 01:06:32,720 to take the lesson of this experiment and the observation 1502 01:06:32,720 --> 01:06:35,390 that was made a minute ago, that in fact the same problem was 1503 01:06:35,390 --> 01:06:37,604 present when we ran this experiment and go 100%. 1504 01:06:37,604 --> 01:06:39,270 We should have been freaked out already. 1505 01:06:39,270 --> 01:06:41,353 And I want to think through what that's telling us 1506 01:06:41,353 --> 01:06:43,580 about the electron, the single electron, 1507 01:06:43,580 --> 01:06:45,325 as it transits the apparatus. 1508 01:06:52,060 --> 01:06:56,970 The thing is, at this point we're in real trouble. 1509 01:06:56,970 --> 01:06:58,150 And here's the reason. 1510 01:06:58,150 --> 01:07:02,542 Consider a single electron inside the apparatus. 1511 01:07:02,542 --> 01:07:05,000 And I want to think about the electron inside the apparatus 1512 01:07:05,000 --> 01:07:06,840 while all walls are out. 1513 01:07:06,840 --> 01:07:09,430 So it's this experiment. 1514 01:07:09,430 --> 01:07:11,890 Consider the single electron. 1515 01:07:11,890 --> 01:07:15,630 We know, with total confidence, with complete reliability, 1516 01:07:15,630 --> 01:07:17,552 that every electron will exit this color box 1517 01:07:17,552 --> 01:07:18,510 out the white aperture. 1518 01:07:18,510 --> 01:07:19,380 We've done this experiment. 1519 01:07:19,380 --> 01:07:20,830 We know it will come out white. 1520 01:07:20,830 --> 01:07:21,330 Yes? 1521 01:07:23,922 --> 01:07:26,321 Here's my question. 1522 01:07:26,321 --> 01:07:27,320 Which route did it take? 1523 01:07:34,580 --> 01:07:37,220 AUDIENCE: Spoiler. 1524 01:07:37,220 --> 01:07:39,620 ALLAN ADAMS: Not a spoiler. 1525 01:07:39,620 --> 01:07:41,350 Which route did it take? 1526 01:07:41,350 --> 01:07:43,230 AUDIENCE: Why do we care what route? 1527 01:07:43,230 --> 01:07:44,938 ALLAN ADAMS: I'm asking you the question. 1528 01:07:44,938 --> 01:07:46,370 That's why you care. 1529 01:07:46,370 --> 01:07:47,750 I'm the professor here. 1530 01:07:47,750 --> 01:07:49,210 What is this? 1531 01:07:49,210 --> 01:07:51,445 Come on. 1532 01:07:51,445 --> 01:07:52,445 Which route did it take? 1533 01:07:56,220 --> 01:07:58,910 OK, let's think through the possibilities. 1534 01:07:58,910 --> 01:08:00,837 Grapple with this question in your belly. 1535 01:08:00,837 --> 01:08:02,420 Let's think through the possibilities. 1536 01:08:02,420 --> 01:08:05,100 First off, did it take the hardness path? 1537 01:08:05,100 --> 01:08:07,414 So as it transits through, the single electron 1538 01:08:07,414 --> 01:08:08,830 transiting through this apparatus, 1539 01:08:08,830 --> 01:08:10,913 did it take the hard path or did it take the soft? 1540 01:08:10,913 --> 01:08:13,800 These are millions of miles long, millions of miles apart. 1541 01:08:13,800 --> 01:08:15,733 This is not a ridiculous question. 1542 01:08:15,733 --> 01:08:17,649 Did it go millions of miles in that direction, 1543 01:08:17,649 --> 01:08:19,620 or millions of miles in that direction? 1544 01:08:19,620 --> 01:08:22,630 Did it take the hardness path? 1545 01:08:22,630 --> 01:08:25,688 Ladies and gentlemen, did it take the hard path? 1546 01:08:25,688 --> 01:08:26,271 AUDIENCE: Yes. 1547 01:08:29,250 --> 01:08:31,029 ALLAN ADAMS: Well, we ran this experiment 1548 01:08:31,029 --> 01:08:33,000 by putting a wall in the soft path. 1549 01:08:33,000 --> 01:08:35,682 And if we put a wall in the soft path, 1550 01:08:35,682 --> 01:08:37,140 then we know it took the hard path, 1551 01:08:37,140 --> 01:08:38,540 because no other electrons come out 1552 01:08:38,540 --> 01:08:40,415 except those that went through the hard path. 1553 01:08:40,415 --> 01:08:40,979 Correct? 1554 01:08:40,979 --> 01:08:43,850 On the other hand, if it went through the hard path, 1555 01:08:43,850 --> 01:08:46,189 it would come out 50% of the time white 1556 01:08:46,189 --> 01:08:48,390 and 50% of the time black. 1557 01:08:48,390 --> 01:08:52,069 But in fact, in this apparatus it comes out always 100% white. 1558 01:08:52,069 --> 01:08:55,221 It cannot have taken the hard path. 1559 01:08:55,221 --> 01:08:55,720 No. 1560 01:08:59,400 --> 01:09:01,388 Did it take the soft path? 1561 01:09:05,140 --> 01:09:08,580 Same argument, different side, right? 1562 01:09:08,580 --> 01:09:10,220 No. 1563 01:09:10,220 --> 01:09:12,729 Well, this is not looking good. 1564 01:09:12,729 --> 01:09:16,550 Well, look, this was suggested. 1565 01:09:16,550 --> 01:09:19,260 Maybe it took both. 1566 01:09:19,260 --> 01:09:21,760 Maybe electrons are sneaky little devils 1567 01:09:21,760 --> 01:09:24,729 that split in two, and part of it goes one way and part of it 1568 01:09:24,729 --> 01:09:27,540 goes the other. 1569 01:09:27,540 --> 01:09:29,729 Maybe it took both paths. 1570 01:09:29,729 --> 01:09:30,729 So this is easy. 1571 01:09:30,729 --> 01:09:31,609 We can test this one. 1572 01:09:31,609 --> 01:09:35,970 And here is how I'm going to test this one. 1573 01:09:35,970 --> 01:09:37,220 Oh, sorry. 1574 01:09:37,220 --> 01:09:39,000 Actually, I'm not going to do that yet. 1575 01:09:39,000 --> 01:09:40,404 So we can test this one. 1576 01:09:40,404 --> 01:09:43,029 So if it took both paths, here's what you should be able to do. 1577 01:09:43,029 --> 01:09:46,729 You should be able to put a detector along each path, 1578 01:09:46,729 --> 01:09:48,464 and you'd be able to follow, if you've 1579 01:09:48,464 --> 01:09:50,029 got half an electron on one side and half an electron 1580 01:09:50,029 --> 01:09:51,609 on the other, or maybe two electrons, 1581 01:09:51,609 --> 01:09:53,569 one on each side and one on the other. 1582 01:09:53,569 --> 01:09:54,770 So this is the thing that you'd predict 1583 01:09:54,770 --> 01:09:55,720 if you said it went both. 1584 01:09:55,720 --> 01:09:56,720 So here's what we'll do. 1585 01:09:56,720 --> 01:09:57,690 We will take detectors. 1586 01:09:57,690 --> 01:09:59,410 We will put one along the hard path and one 1587 01:09:59,410 --> 01:10:00,243 along the soft path. 1588 01:10:00,243 --> 01:10:02,620 We will run the experiment and then observe 1589 01:10:02,620 --> 01:10:05,349 whether, and ask whether, we see two electrons, 1590 01:10:05,349 --> 01:10:06,890 we see half and half, what do we see. 1591 01:10:06,890 --> 01:10:10,990 The answer is you always, always see one electron on one 1592 01:10:10,990 --> 01:10:12,140 of the paths. 1593 01:10:12,140 --> 01:10:14,320 You never see half an electron. 1594 01:10:14,320 --> 01:10:15,750 You never see a squishy electron. 1595 01:10:15,750 --> 01:10:18,950 You see one electron on one path, period. 1596 01:10:18,950 --> 01:10:20,540 It did not take both. 1597 01:10:20,540 --> 01:10:25,720 You never see an electron split in two, divided, confused. 1598 01:10:25,720 --> 01:10:28,275 No. 1599 01:10:28,275 --> 01:10:30,480 Well, it didn't take the hard path, 1600 01:10:30,480 --> 01:10:33,730 didn't take the soft path, it didn't take both. 1601 01:10:33,730 --> 01:10:35,580 There's one option left. 1602 01:10:35,580 --> 01:10:36,157 Neither. 1603 01:10:36,157 --> 01:10:36,990 Well, I say neither. 1604 01:10:36,990 --> 01:10:40,724 But what about neither? 1605 01:10:40,724 --> 01:10:41,390 And that's easy. 1606 01:10:41,390 --> 01:10:44,870 Let's put a barrier in both paths. 1607 01:10:44,870 --> 01:10:46,490 And then what happens? 1608 01:10:46,490 --> 01:10:48,740 Nothing comes out. 1609 01:10:48,740 --> 01:10:49,370 So no. 1610 01:10:55,050 --> 01:10:58,650 So now, to repeat an earlier prescient remark 1611 01:10:58,650 --> 01:11:01,760 from one of the students, what the hell? 1612 01:11:01,760 --> 01:11:03,220 So here's the world we're facing. 1613 01:11:03,220 --> 01:11:04,100 I want you to think about this. 1614 01:11:04,100 --> 01:11:05,020 Take this seriously. 1615 01:11:05,020 --> 01:11:05,930 Here's the world we're facing. 1616 01:11:05,930 --> 01:11:07,846 And when I say, here's the world we're facing, 1617 01:11:07,846 --> 01:11:09,380 I don't mean just these experiments. 1618 01:11:09,380 --> 01:11:14,250 I mean the world around you, 20 kilo mirrors, bucky-balls, 1619 01:11:14,250 --> 01:11:15,900 here is what they do. 1620 01:11:15,900 --> 01:11:19,940 When you send them through an apparatus like this, 1621 01:11:19,940 --> 01:11:22,680 every single object that goes through this apparatus 1622 01:11:22,680 --> 01:11:25,960 does not take the hard path, it does not take the soft path, 1623 01:11:25,960 --> 01:11:29,790 it doesn't take both, and it does not take neither. 1624 01:11:29,790 --> 01:11:31,450 And that pretty much exhausts the set 1625 01:11:31,450 --> 01:11:34,840 of logical possibilities. 1626 01:11:34,840 --> 01:11:40,300 So what are electrons doing when they're inside the apparatus? 1627 01:11:40,300 --> 01:11:43,250 How do you describe that electron inside the apparatus? 1628 01:11:43,250 --> 01:11:44,720 You can't say it's on one path, you 1629 01:11:44,720 --> 01:11:46,040 can't say it's on the other, it's not on both, 1630 01:11:46,040 --> 01:11:47,040 and it's not on neither. 1631 01:11:47,040 --> 01:11:51,270 What is it doing halfway through this experiment? 1632 01:11:51,270 --> 01:11:52,967 So if our experiments are accurate, 1633 01:11:52,967 --> 01:11:54,800 and to the best of our ability to determine, 1634 01:11:54,800 --> 01:12:00,890 they are, and if our arguments are correct, and that's on me, 1635 01:12:00,890 --> 01:12:02,930 then they're doing something, these electrons 1636 01:12:02,930 --> 01:12:05,300 are doing something we've just never thought of before, 1637 01:12:05,300 --> 01:12:06,932 something we've never dreamt of before, 1638 01:12:06,932 --> 01:12:08,390 something for which we don't really 1639 01:12:08,390 --> 01:12:11,760 have good words in the English language. 1640 01:12:11,760 --> 01:12:16,710 Apparently, empirically, electrons have a way of moving, 1641 01:12:16,710 --> 01:12:19,970 electrons have a way of being which is unlike anything 1642 01:12:19,970 --> 01:12:22,130 that we're used to thinking about. 1643 01:12:22,130 --> 01:12:23,930 And so do molecules. 1644 01:12:23,930 --> 01:12:25,630 And so do bacteria. 1645 01:12:25,630 --> 01:12:28,170 So does chalk. 1646 01:12:28,170 --> 01:12:32,390 It's just harder to detect in those objects. 1647 01:12:32,390 --> 01:12:35,430 So physicists have a name for this new mode of being. 1648 01:12:35,430 --> 01:12:36,683 And we call it superposition. 1649 01:12:39,830 --> 01:12:42,250 Now, at the moment, superposition 1650 01:12:42,250 --> 01:12:45,650 is code for I have no idea what's going on. 1651 01:12:48,720 --> 01:12:51,370 Usage of the word superposition would go something like this. 1652 01:12:51,370 --> 01:12:55,170 An initially white electron inside this apparatus 1653 01:12:55,170 --> 01:12:59,960 with the walls out is neither hard, nor soft, 1654 01:12:59,960 --> 01:13:01,030 nor both, nor neither. 1655 01:13:01,030 --> 01:13:04,950 It is, in fact, in a superposition of being hard 1656 01:13:04,950 --> 01:13:07,930 and of being soft. 1657 01:13:07,930 --> 01:13:09,600 This is why we can't meaningfully 1658 01:13:09,600 --> 01:13:13,530 say this electron is some color and some hardness. 1659 01:13:13,530 --> 01:13:16,680 Not because our boxes are crude, and not because we're ignorant, 1660 01:13:16,680 --> 01:13:20,220 though our boxes are crude and we are ignorant. 1661 01:13:20,220 --> 01:13:21,240 It's deeper. 1662 01:13:21,240 --> 01:13:25,950 Having a definite color means not having a definite hardness, 1663 01:13:25,950 --> 01:13:28,850 but rather being in a superposition of being hard 1664 01:13:28,850 --> 01:13:31,550 and being soft. 1665 01:13:31,550 --> 01:13:40,300 Every electron exits a hardness box either hard or soft. 1666 01:13:40,300 --> 01:13:43,630 But not every electron is hard or soft. 1667 01:13:43,630 --> 01:13:48,620 It can also be a superposition of being hard or being soft. 1668 01:13:48,620 --> 01:13:51,240 The probability that we subsequently 1669 01:13:51,240 --> 01:13:54,700 measure it to be hard or soft depends 1670 01:13:54,700 --> 01:13:59,430 on precisely what superposition it is. 1671 01:13:59,430 --> 01:14:01,900 For example, we know that if an electron is 1672 01:14:01,900 --> 01:14:05,730 in the superposition corresponding to being white 1673 01:14:05,730 --> 01:14:08,840 then there are even odds of it being subsequently 1674 01:14:08,840 --> 01:14:10,960 measured be hard or to be soft. 1675 01:14:13,800 --> 01:14:18,620 So to build a better definition of superposition 1676 01:14:18,620 --> 01:14:22,030 than I have no idea what's going on 1677 01:14:22,030 --> 01:14:23,580 is going to require a new language. 1678 01:14:23,580 --> 01:14:26,310 And that language is quantum mechanics. 1679 01:14:26,310 --> 01:14:28,630 And the underpinnings of this language 1680 01:14:28,630 --> 01:14:29,970 are the topic of the course. 1681 01:14:29,970 --> 01:14:31,780 And developing a better understanding 1682 01:14:31,780 --> 01:14:35,050 of this idea of superposition is what 1683 01:14:35,050 --> 01:14:38,330 you have to do over the next three months. 1684 01:14:38,330 --> 01:14:42,380 Now, if all of this troubles your intuition, 1685 01:14:42,380 --> 01:14:44,800 well, that shouldn't be too surprising. 1686 01:14:44,800 --> 01:14:49,630 Your intuition was developed by throwing spears, and running 1687 01:14:49,630 --> 01:14:52,910 from tigers, and catching toast as it jumps out 1688 01:14:52,910 --> 01:14:58,070 of the toaster, all of which involves things so big 1689 01:14:58,070 --> 01:15:01,410 and with so much energy that quantum effects are negligible. 1690 01:15:04,310 --> 01:15:05,920 As a friend of mine likes to say, 1691 01:15:05,920 --> 01:15:09,777 you don't need to know quantum mechanics to make chicken soup. 1692 01:15:09,777 --> 01:15:11,985 However, when we work in very different regimes, when 1693 01:15:11,985 --> 01:15:15,920 we work with atoms, when we work with molecules, when we work 1694 01:15:15,920 --> 01:15:18,010 in the regime of very low energies and very 1695 01:15:18,010 --> 01:15:23,870 small objects, your intuition is just not a reasonable guide. 1696 01:15:23,870 --> 01:15:26,320 It's not that the electrons-- and I cannot emphasize this 1697 01:15:26,320 --> 01:15:30,460 strongly enough-- it is not that the electrons are weird. 1698 01:15:30,460 --> 01:15:33,160 The electrons do what electrons do. 1699 01:15:33,160 --> 01:15:34,170 This is what they do. 1700 01:15:34,170 --> 01:15:37,430 And it violates your intuition, but it's true. 1701 01:15:37,430 --> 01:15:40,100 The thing that's surprising is that lots of electrons 1702 01:15:40,100 --> 01:15:42,420 behave like this. 1703 01:15:42,420 --> 01:15:47,090 Lots of electrons behave like cheese and chalk. 1704 01:15:47,090 --> 01:15:49,570 And that's the goal of 804, to step 1705 01:15:49,570 --> 01:15:52,685 beyond your daily experience and your familiar intuition 1706 01:15:52,685 --> 01:15:57,040 and to develop an intuition for this idea of superposition. 1707 01:15:57,040 --> 01:15:59,070 And we'll start in the next lecture. 1708 01:15:59,070 --> 01:16:01,740 I'll see you on Thursday.