WEBVTT 00:00:00.000 --> 00:00:01.494 align:middle line:90% [SQUEAKING] 00:00:01.494 --> 00:00:03.984 align:middle line:90% [RUSTLING] 00:00:03.984 --> 00:00:06.474 align:middle line:90% [CLICKING] 00:00:06.474 --> 00:00:11.153 align:middle line:90% 00:00:11.153 --> 00:00:12.570 align:middle line:84% DAVID KAISER: So today we're going 00:00:12.570 --> 00:00:16.200 align:middle line:84% to continue the story that we were looking 00:00:16.200 --> 00:00:19.980 align:middle line:84% at in on Monday's class, some of these early developments 00:00:19.980 --> 00:00:22.470 align:middle line:84% after the end of the Second World War 00:00:22.470 --> 00:00:26.250 align:middle line:84% to grapple with quantum field theory, 00:00:26.250 --> 00:00:29.850 align:middle line:84% trying to piece together a quantized treatment of things 00:00:29.850 --> 00:00:33.540 align:middle line:84% like the Maxwell field or electrons and positrons. 00:00:33.540 --> 00:00:36.750 align:middle line:84% And we saw last time there were a lot of puzzles, some of which 00:00:36.750 --> 00:00:39.780 align:middle line:84% had been identified as puzzles well before the war, 00:00:39.780 --> 00:00:42.270 align:middle line:84% going all the way back to the 1920s and '30s, 00:00:42.270 --> 00:00:45.210 align:middle line:84% like virtual particles that could borrow energy 00:00:45.210 --> 00:00:47.910 align:middle line:84% for temporary periods of time, which 00:00:47.910 --> 00:00:51.540 align:middle line:84% led to these infinite quantum corrections 00:00:51.540 --> 00:00:54.540 align:middle line:84% that when people tried to take into account quantitatively 00:00:54.540 --> 00:00:56.470 align:middle line:84% the impact of those virtual particles, 00:00:56.470 --> 00:00:57.720 align:middle line:90% their equations would blow up. 00:00:57.720 --> 00:01:00.300 align:middle line:84% They would encounter these divergences. 00:01:00.300 --> 00:01:06.555 align:middle line:84% And those were a big, big puzzle really for decades. 00:01:06.555 --> 00:01:09.180 align:middle line:84% And it was only very soon after the end of the Second World War 00:01:09.180 --> 00:01:11.140 align:middle line:84% when a newer generation of physicists 00:01:11.140 --> 00:01:13.000 align:middle line:84% came back to those older questions 00:01:13.000 --> 00:01:16.360 align:middle line:84% but now with some new skills, sometimes literally 00:01:16.360 --> 00:01:18.520 align:middle line:84% new instruments, and new ideas about how 00:01:18.520 --> 00:01:20.510 align:middle line:90% to organize their calculations. 00:01:20.510 --> 00:01:22.300 align:middle line:84% So near the end of last class, we 00:01:22.300 --> 00:01:25.480 align:middle line:84% looked at some of Julian Schwinger's efforts in that, 00:01:25.480 --> 00:01:29.710 align:middle line:84% and today we'll look at some efforts by his contemporary, 00:01:29.710 --> 00:01:32.180 align:middle line:84% Richard Feynman and Feynman's circle. 00:01:32.180 --> 00:01:38.540 align:middle line:84% So today's class draws on a book I wrote 15 years ago. 00:01:38.540 --> 00:01:42.230 align:middle line:84% It's actually hard to believe it's been out for 15 years. 00:01:42.230 --> 00:01:45.730 align:middle line:84% And so we'll talk about the book and how 00:01:45.730 --> 00:01:47.890 align:middle line:84% it fits into the kind of series of developments 00:01:47.890 --> 00:01:51.140 align:middle line:84% we've been talking about throughout the semester. 00:01:51.140 --> 00:01:55.550 align:middle line:84% And so as usual, the class has three main sections for today. 00:01:55.550 --> 00:01:59.050 align:middle line:84% The first is how did these new tools, in this case Feynman's 00:01:59.050 --> 00:02:02.200 align:middle line:84% particular approach to quantum field theory, 00:02:02.200 --> 00:02:05.170 align:middle line:84% how did these new tools enter into circulation? 00:02:05.170 --> 00:02:07.540 align:middle line:84% How do they become kind of second nature 00:02:07.540 --> 00:02:12.130 align:middle line:84% or a standard technique ultimately for essentially 00:02:12.130 --> 00:02:13.570 align:middle line:90% the entire profession? 00:02:13.570 --> 00:02:17.680 align:middle line:84% So how did these new tools begin to get picked up by people 00:02:17.680 --> 00:02:20.320 align:middle line:90% other than Feynman himself? 00:02:20.320 --> 00:02:23.180 align:middle line:84% And we'll spend a good chunk of time on that today. 00:02:23.180 --> 00:02:25.600 align:middle line:84% And then we'll see that once some people did start 00:02:25.600 --> 00:02:28.210 align:middle line:84% using them, they would often deploy 00:02:28.210 --> 00:02:31.510 align:middle line:84% these new tools, these paper techniques, pencil 00:02:31.510 --> 00:02:34.660 align:middle line:84% and paper techniques often in quite different ways than what 00:02:34.660 --> 00:02:36.667 align:middle line:90% Feynman himself had had in mind. 00:02:36.667 --> 00:02:39.250 align:middle line:84% So it's not just that new people had to start using the tools. 00:02:39.250 --> 00:02:41.590 align:middle line:84% New people began adapting the tools 00:02:41.590 --> 00:02:43.390 align:middle line:90% toward new or different ends. 00:02:43.390 --> 00:02:47.790 align:middle line:84% And what did that mean for the continuing conceptual puzzles 00:02:47.790 --> 00:02:49.990 align:middle line:84% they were wrestling with as they tried 00:02:49.990 --> 00:02:52.600 align:middle line:84% to continue to make sense of high-energy physics phenomena? 00:02:52.600 --> 00:02:56.230 align:middle line:84% And then finally, we'll ask just very briefly near the end 00:02:56.230 --> 00:02:59.440 align:middle line:84% why did this particular set of tools actually stick? 00:02:59.440 --> 00:03:04.060 align:middle line:84% Why was it that these tools really became the standard way 00:03:04.060 --> 00:03:07.420 align:middle line:84% to this day that physicists all around the world 00:03:07.420 --> 00:03:11.530 align:middle line:84% try to make sense of nature when it wasn't so clear they 00:03:11.530 --> 00:03:12.980 align:middle line:90% were going to take off at all? 00:03:12.980 --> 00:03:15.640 align:middle line:84% So why did this tool come to seem like such 00:03:15.640 --> 00:03:17.290 align:middle line:90% a natural or winning strategy? 00:03:17.290 --> 00:03:21.260 align:middle line:84% And that's our kind of three-part scope for today. 00:03:21.260 --> 00:03:23.420 align:middle line:84% So some of you, many of you, by now 00:03:23.420 --> 00:03:24.860 align:middle line:90% might recognize these things. 00:03:24.860 --> 00:03:26.860 align:middle line:84% You might have already had them in some classes. 00:03:26.860 --> 00:03:29.852 align:middle line:84% If not, you've probably seen them around, 00:03:29.852 --> 00:03:31.810 align:middle line:84% these things that we now call Feynman diagrams. 00:03:31.810 --> 00:03:33.550 align:middle line:84% They are really unavoidable today. 00:03:33.550 --> 00:03:35.800 align:middle line:90% They are literally ubiquitous. 00:03:35.800 --> 00:03:38.350 align:middle line:84% In fact, not only are they all over the place, 00:03:38.350 --> 00:03:40.870 align:middle line:84% they've become automatic or automated. 00:03:40.870 --> 00:03:43.450 align:middle line:84% So there are now computer routines 00:03:43.450 --> 00:03:46.630 align:middle line:84% that will both evaluate tens of thousands of them 00:03:46.630 --> 00:03:49.660 align:middle line:84% now even on not very fancy laptops. 00:03:49.660 --> 00:03:52.810 align:middle line:84% So you have these algorithms to compute very large numbers 00:03:52.810 --> 00:03:54.850 align:middle line:84% of Feynman diagrams quantitatively 00:03:54.850 --> 00:03:56.680 align:middle line:90% and also routines to draw them. 00:03:56.680 --> 00:03:58.840 align:middle line:84% They literally have-- the way they 00:03:58.840 --> 00:04:02.440 align:middle line:84% look has now become automated or subject to computer routine 00:04:02.440 --> 00:04:03.140 align:middle line:90% as well. 00:04:03.140 --> 00:04:06.130 align:middle line:84% They're all over the place in virtually every subfield 00:04:06.130 --> 00:04:08.890 align:middle line:84% of the discipline or many, many subfields anyway. 00:04:08.890 --> 00:04:10.690 align:middle line:84% And yet, of course, they have a history. 00:04:10.690 --> 00:04:12.010 align:middle line:90% It wasn't always that way. 00:04:12.010 --> 00:04:15.760 align:middle line:84% Our kind of present day saturation with these things 00:04:15.760 --> 00:04:18.339 align:middle line:90% is of relatively recent vintage. 00:04:18.339 --> 00:04:20.745 align:middle line:84% And when they were first introduced in the years 00:04:20.745 --> 00:04:22.370 align:middle line:84% through and after the Second World War, 00:04:22.370 --> 00:04:24.950 align:middle line:84% some people thought they didn't make any sense. 00:04:24.950 --> 00:04:26.810 align:middle line:84% Others thought they must be all wrong, 00:04:26.810 --> 00:04:29.600 align:middle line:84% and a small number of people began using a couple of them 00:04:29.600 --> 00:04:30.600 align:middle line:90% at a time. 00:04:30.600 --> 00:04:34.820 align:middle line:84% So it was a publishable feat to evaluate five of them 00:04:34.820 --> 00:04:37.460 align:middle line:84% by hand, not 10,000 on your laptop. 00:04:37.460 --> 00:04:39.470 align:middle line:84% You could get your PhD dissertation 00:04:39.470 --> 00:04:44.210 align:middle line:84% by evaluating a few dozen at most by hand 00:04:44.210 --> 00:04:46.333 align:middle line:90% into the early 1950s. 00:04:46.333 --> 00:04:47.750 align:middle line:84% So these things weren't these kind 00:04:47.750 --> 00:04:49.640 align:middle line:84% of automated tools from the beginning. 00:04:49.640 --> 00:04:51.920 align:middle line:84% In fact, they were kind of suspect, 00:04:51.920 --> 00:04:53.910 align:middle line:84% at least to some people, for quite a while. 00:04:53.910 --> 00:04:57.603 align:middle line:84% And as I mentioned already, they're kind of single-use. 00:04:57.603 --> 00:04:59.270 align:middle line:84% The fact that now you can train computer 00:04:59.270 --> 00:05:02.850 align:middle line:84% algorithms to evaluate these things unambiguously that, 00:05:02.850 --> 00:05:06.170 align:middle line:84% again, took quite a while to settle into place. 00:05:06.170 --> 00:05:09.530 align:middle line:84% And in fact, for two decades or more, 00:05:09.530 --> 00:05:12.180 align:middle line:84% even arguably about close to three decades, 00:05:12.180 --> 00:05:14.780 align:middle line:84% what the diagrams were used for, how 00:05:14.780 --> 00:05:17.780 align:middle line:84% they would be turned into elements of calculations 00:05:17.780 --> 00:05:21.110 align:middle line:84% and quantified, that was actually pretty malleable for, 00:05:21.110 --> 00:05:24.090 align:middle line:84% to me, what seemed at least to be a surprisingly long period 00:05:24.090 --> 00:05:24.590 align:middle line:90% of time. 00:05:24.590 --> 00:05:27.890 align:middle line:84% They were adapted as well as adopted. 00:05:27.890 --> 00:05:30.680 align:middle line:84% And so before I started working on this kind of series 00:05:30.680 --> 00:05:33.830 align:middle line:84% of puzzles, how the diagram spread, why did they 00:05:33.830 --> 00:05:36.367 align:middle line:84% come to be used, and so on, very little 00:05:36.367 --> 00:05:38.450 align:middle line:84% had been written about the spread of the diagrams. 00:05:38.450 --> 00:05:40.450 align:middle line:84% I used to tease that there had been more written 00:05:40.450 --> 00:05:43.310 align:middle line:84% at that point about the search for Richard Feynman's 00:05:43.310 --> 00:05:44.060 align:middle line:90% actual van. 00:05:44.060 --> 00:05:46.670 align:middle line:84% This is Feynman and his then very young children 00:05:46.670 --> 00:05:48.590 align:middle line:84% with his van that he used to drive 00:05:48.590 --> 00:05:51.380 align:middle line:84% around Southern California and with larger than life Feynman 00:05:51.380 --> 00:05:53.060 align:middle line:90% diagrams on the side. 00:05:53.060 --> 00:05:54.800 align:middle line:84% There was more written about his van 00:05:54.800 --> 00:05:58.160 align:middle line:84% than about the diagrams that bedecked the van. 00:05:58.160 --> 00:06:00.110 align:middle line:84% And so how was it that this was even 00:06:00.110 --> 00:06:02.340 align:middle line:84% something you'd paint on your van in the first place? 00:06:02.340 --> 00:06:03.860 align:middle line:84% Not only because it was the groovy '70s, 00:06:03.860 --> 00:06:04.910 align:middle line:90% and you're in California. 00:06:04.910 --> 00:06:07.100 align:middle line:84% Why would these become something to paint 00:06:07.100 --> 00:06:08.742 align:middle line:90% on your personal vehicle? 00:06:08.742 --> 00:06:10.700 align:middle line:84% And so that's what I was really kind of curious 00:06:10.700 --> 00:06:12.540 align:middle line:90% to try to learn more about. 00:06:12.540 --> 00:06:16.100 align:middle line:84% So to make sense of that, I wound up 00:06:16.100 --> 00:06:19.220 align:middle line:84% thinking a lot about this word dispersion. 00:06:19.220 --> 00:06:21.860 align:middle line:84% I think it's-- I still think it's helpful to organize 00:06:21.860 --> 00:06:24.320 align:middle line:84% the kind of different layers of this study. 00:06:24.320 --> 00:06:28.670 align:middle line:84% So disperse means many different things, the verb to disperse, 00:06:28.670 --> 00:06:31.610 align:middle line:84% where there are two main clusters of meanings. 00:06:31.610 --> 00:06:34.160 align:middle line:84% If you go look up, for example in the Oxford English 00:06:34.160 --> 00:06:36.800 align:middle line:84% Dictionary or your favorite Merriam-Webster 00:06:36.800 --> 00:06:38.450 align:middle line:84% or whatever you like, there are kind 00:06:38.450 --> 00:06:42.290 align:middle line:84% of two basic sets of meanings for the verb to disperse. 00:06:42.290 --> 00:06:44.270 align:middle line:84% One of them means to put into circulation. 00:06:44.270 --> 00:06:47.550 align:middle line:84% Think about dispersing things to people. 00:06:47.550 --> 00:06:49.730 align:middle line:84% And that's really the first part for today's class 00:06:49.730 --> 00:06:50.900 align:middle line:90% that we'll focus on. 00:06:50.900 --> 00:06:54.290 align:middle line:84% But disperse also means to cause to become basically 00:06:54.290 --> 00:06:55.380 align:middle line:90% more and more different. 00:06:55.380 --> 00:06:59.270 align:middle line:84% Think about optical dispersion, taking light and dispersing it 00:06:59.270 --> 00:07:01.400 align:middle line:84% into the distinct colors of the rainbow. 00:07:01.400 --> 00:07:04.760 align:middle line:84% And I think that also captures a lot of what was going on 00:07:04.760 --> 00:07:06.980 align:middle line:84% with these new theoretical tools, 00:07:06.980 --> 00:07:10.340 align:middle line:84% not just for a month or a year, but really over decades 00:07:10.340 --> 00:07:12.988 align:middle line:84% even after Feynman had introduced them. 00:07:12.988 --> 00:07:14.780 align:middle line:84% So that's what set up these three questions 00:07:14.780 --> 00:07:16.220 align:middle line:90% that I mentioned earlier. 00:07:16.220 --> 00:07:18.090 align:middle line:90% How do they spread so fast? 00:07:18.090 --> 00:07:20.030 align:middle line:84% What do people actually use them for? 00:07:20.030 --> 00:07:22.730 align:middle line:84% And then given that variety, why did they stick? 00:07:22.730 --> 00:07:25.548 align:middle line:84% So let's talk about how they start entering circulation 00:07:25.548 --> 00:07:26.340 align:middle line:90% in the first place. 00:07:26.340 --> 00:07:29.010 align:middle line:90% Let's dig into that a bit more. 00:07:29.010 --> 00:07:32.460 align:middle line:84% These were introduced at the second of this three 00:07:32.460 --> 00:07:35.070 align:middle line:84% sets of annual meetings that we talked a little bit 00:07:35.070 --> 00:07:36.700 align:middle line:90% about in the previous class. 00:07:36.700 --> 00:07:39.150 align:middle line:84% You might remember on Monday, I talked a bit 00:07:39.150 --> 00:07:42.403 align:middle line:84% about the June 1947 Shelter Island meeting. 00:07:42.403 --> 00:07:44.820 align:middle line:84% In fact, this photograph was from that Shelter Island one, 00:07:44.820 --> 00:07:48.780 align:middle line:84% from the first of them held just on a tiny island near Long 00:07:48.780 --> 00:07:50.733 align:middle line:90% Island at the Ram's Head Inn. 00:07:50.733 --> 00:07:51.650 align:middle line:90% I've never been there. 00:07:51.650 --> 00:07:52.710 align:middle line:90% I don't know if it still exists. 00:07:52.710 --> 00:07:54.060 align:middle line:84% You got to go to the actual bed and breakfast 00:07:54.060 --> 00:07:55.140 align:middle line:90% where they all stayed. 00:07:55.140 --> 00:07:57.300 align:middle line:84% And that was the meeting at which 00:07:57.300 --> 00:08:00.180 align:middle line:84% 24 kind of personally selected participants, 00:08:00.180 --> 00:08:03.360 align:middle line:84% selected by Robert Oppenheimer, got together for a week 00:08:03.360 --> 00:08:04.960 align:middle line:84% to talk about theoretical physics, 00:08:04.960 --> 00:08:07.350 align:middle line:84% including these puzzles of quantum field theory. 00:08:07.350 --> 00:08:11.452 align:middle line:84% That's where Willis Lamb first presented his results 00:08:11.452 --> 00:08:13.410 align:middle line:84% on what would come to be called the Lamb shift. 00:08:13.410 --> 00:08:16.950 align:middle line:84% Isidor Rabi talked about the new experimental measurements 00:08:16.950 --> 00:08:19.230 align:middle line:84% on the anomalous magnetic moment of the electron. 00:08:19.230 --> 00:08:22.770 align:middle line:84% And there were three in a row, so every annual meeting. 00:08:22.770 --> 00:08:26.010 align:middle line:84% The second of them was held not in Long Island 00:08:26.010 --> 00:08:29.500 align:middle line:84% but in the Pocono area, so due north of Philadelphia, 00:08:29.500 --> 00:08:33.850 align:middle line:84% due west of Manhattan, a short bus ride out of Manhattan, 00:08:33.850 --> 00:08:37.510 align:middle line:84% again, organized by Oppenheimer, very similar format, roughly 24 00:08:37.510 --> 00:08:40.360 align:middle line:84% or 25 kind of hand-selected participants, many of whom 00:08:40.360 --> 00:08:43.090 align:middle line:90% had come to the previous one. 00:08:43.090 --> 00:08:45.040 align:middle line:84% This is the first meeting of its kind 00:08:45.040 --> 00:08:48.160 align:middle line:84% after the experimental results for things 00:08:48.160 --> 00:08:50.230 align:middle line:84% that seemed to suggest at least to some people 00:08:50.230 --> 00:08:52.090 align:middle line:84% that virtual particles might actually 00:08:52.090 --> 00:08:53.680 align:middle line:90% have some heft to them. 00:08:53.680 --> 00:08:56.540 align:middle line:84% They might actually affect measurable quantities. 00:08:56.540 --> 00:08:58.810 align:middle line:84% So it was at this meeting, the second 00:08:58.810 --> 00:09:02.440 align:middle line:84% in the series, where Feynman introduced his new techniques. 00:09:02.440 --> 00:09:05.320 align:middle line:84% He was one of the informal speakers. 00:09:05.320 --> 00:09:08.032 align:middle line:84% This is actually from his first published example. 00:09:08.032 --> 00:09:09.490 align:middle line:84% We know from notes that were taken, 00:09:09.490 --> 00:09:12.040 align:middle line:84% he was scribbling very similar things on the blackboard, 00:09:12.040 --> 00:09:14.350 align:middle line:84% and he was trying to motivate for his colleagues 00:09:14.350 --> 00:09:17.980 align:middle line:84% how they could try to understand at a quantum mechanical level 00:09:17.980 --> 00:09:20.830 align:middle line:84% why it is that, for example, electrons repel each other. 00:09:20.830 --> 00:09:23.560 align:middle line:84% We all learned in high school that like charges repel 00:09:23.560 --> 00:09:25.390 align:middle line:90% and opposite charges attract. 00:09:25.390 --> 00:09:26.890 align:middle line:84% He said, well, why is it if we think 00:09:26.890 --> 00:09:29.410 align:middle line:84% at this quantum mechanical level that charges 00:09:29.410 --> 00:09:31.870 align:middle line:84% with the same sign of their electric charge 00:09:31.870 --> 00:09:34.970 align:middle line:84% would push each other apart, would repel each other? 00:09:34.970 --> 00:09:37.570 align:middle line:84% And so here's the kind of story that we 00:09:37.570 --> 00:09:39.250 align:middle line:90% could imagine unfolding. 00:09:39.250 --> 00:09:41.290 align:middle line:84% There would be some electron coming in here 00:09:41.290 --> 00:09:42.670 align:middle line:90% from the right hand side. 00:09:42.670 --> 00:09:45.610 align:middle line:84% It would have some likelihood to travel from here to here. 00:09:45.610 --> 00:09:48.940 align:middle line:84% It has some separate but calculable likelihood 00:09:48.940 --> 00:09:52.678 align:middle line:84% to emit a virtual photon at this point in space. 00:09:52.678 --> 00:09:53.470 align:middle line:90% You can't turn off. 00:09:53.470 --> 00:09:55.300 align:middle line:84% In certain principle, the vacuum is 00:09:55.300 --> 00:09:56.650 align:middle line:90% roiling with virtual particles. 00:09:56.650 --> 00:10:01.490 align:middle line:84% By this time, that had become kind of familiar set of ideas. 00:10:01.490 --> 00:10:04.510 align:middle line:84% So he wanted to have a way to calculate these effects. 00:10:04.510 --> 00:10:06.700 align:middle line:84% A little while later, that virtual photon 00:10:06.700 --> 00:10:09.100 align:middle line:84% would have zoomed across space, and it could 00:10:09.100 --> 00:10:10.720 align:middle line:90% smack into this other electron. 00:10:10.720 --> 00:10:13.510 align:middle line:84% The second electron, which had been otherwise traveling all 00:10:13.510 --> 00:10:17.980 align:middle line:84% by its lonesome unsuspected, going from, say, 0.1 to 0.5, 00:10:17.980 --> 00:10:20.020 align:middle line:84% all of a sudden it will get smacked 00:10:20.020 --> 00:10:22.300 align:middle line:84% by this virtual photon that is carrying 00:10:22.300 --> 00:10:25.900 align:middle line:90% some energy and some momentum. 00:10:25.900 --> 00:10:28.490 align:middle line:90% It's absorbing that momentum. 00:10:28.490 --> 00:10:31.180 align:middle line:84% So after it absorbs that virtual photon, 00:10:31.180 --> 00:10:32.680 align:middle line:84% it will be knocked off its course. 00:10:32.680 --> 00:10:35.028 align:middle line:84% Imagine getting hit with a dodgeball. 00:10:35.028 --> 00:10:37.570 align:middle line:84% Not that I want to trigger bad memories of elementary school, 00:10:37.570 --> 00:10:39.403 align:middle line:84% but anyway, you get knocked off your course. 00:10:39.403 --> 00:10:42.310 align:middle line:84% You get hit with some object carrying momentum. 00:10:42.310 --> 00:10:44.990 align:middle line:84% So its direction of travel will change. 00:10:44.990 --> 00:10:46.900 align:middle line:84% Meanwhile, the original electron has 00:10:46.900 --> 00:10:49.060 align:middle line:90% shot out that virtual photon. 00:10:49.060 --> 00:10:52.390 align:middle line:84% It recoils like a hunter firing a rifle. 00:10:52.390 --> 00:10:55.180 align:middle line:84% It's going to have some equal and opposite kickback, 00:10:55.180 --> 00:10:58.130 align:middle line:84% so its direction of travel will change as well. 00:10:58.130 --> 00:11:01.030 align:middle line:84% So Feynman says here's the kind of fundamental process 00:11:01.030 --> 00:11:03.910 align:middle line:84% or the reason quantum mechanically why 00:11:03.910 --> 00:11:05.800 align:middle line:84% like charges repel because they're 00:11:05.800 --> 00:11:09.340 align:middle line:84% trading back and forth these virtual force-carrying 00:11:09.340 --> 00:11:13.000 align:middle line:84% particles, in this case, the photon, the virtual photon. 00:11:13.000 --> 00:11:16.510 align:middle line:84% Now he could use this kind of map of that interaction 00:11:16.510 --> 00:11:19.450 align:middle line:84% and relate every single part of this little squiggle, 00:11:19.450 --> 00:11:24.170 align:middle line:84% this line drawing to particular parts of the integrals. 00:11:24.170 --> 00:11:26.590 align:middle line:84% And so he would map this, and he tried to explain this 00:11:26.590 --> 00:11:27.490 align:middle line:90% at the blackboard. 00:11:27.490 --> 00:11:29.560 align:middle line:84% The electron has some likelihood to travel 00:11:29.560 --> 00:11:32.030 align:middle line:90% unimpeded from 0.2 to 0.6. 00:11:32.030 --> 00:11:32.870 align:middle line:90% Here it is. 00:11:32.870 --> 00:11:35.390 align:middle line:84% The other electron, electron A, let's say, 00:11:35.390 --> 00:11:38.360 align:middle line:84% has some likelihood to travel from 0.1 to 0.5. 00:11:38.360 --> 00:11:40.280 align:middle line:84% They have a likelihood to both emit 00:11:40.280 --> 00:11:42.080 align:middle line:84% and absorb a photon, each of which 00:11:42.080 --> 00:11:44.300 align:middle line:84% is proportional to the charge of the electron. 00:11:44.300 --> 00:11:45.950 align:middle line:84% The photon itself has a likelihood 00:11:45.950 --> 00:11:47.900 align:middle line:90% to travel from 0.6 to 0.5. 00:11:47.900 --> 00:11:50.990 align:middle line:84% You just piece it all together kind of LEGO bricks. 00:11:50.990 --> 00:11:53.270 align:middle line:84% So now you have a kind of road map 00:11:53.270 --> 00:11:56.180 align:middle line:84% to the corresponding equations to map out 00:11:56.180 --> 00:11:59.450 align:middle line:84% this series of steps between electrons 00:11:59.450 --> 00:12:02.120 align:middle line:84% and their traded virtual particle. 00:12:02.120 --> 00:12:04.460 align:middle line:84% And Feynman said this is going to be important, not just 00:12:04.460 --> 00:12:07.140 align:middle line:84% because this is one thing that could happen, 00:12:07.140 --> 00:12:08.960 align:middle line:84% but because all kinds of things could 00:12:08.960 --> 00:12:12.230 align:middle line:84% happen when we start thinking about virtual particles. 00:12:12.230 --> 00:12:15.680 align:middle line:84% It had already become clear well before the Second World War 00:12:15.680 --> 00:12:17.150 align:middle line:84% that these virtual particles could 00:12:17.150 --> 00:12:20.000 align:middle line:84% borrow any amount of energy and momentum, 00:12:20.000 --> 00:12:24.200 align:middle line:84% consistent with paying it back sufficiently quickly given 00:12:24.200 --> 00:12:25.490 align:middle line:90% the uncertainty principle. 00:12:25.490 --> 00:12:27.740 align:middle line:84% But it was even more complicated. 00:12:27.740 --> 00:12:30.480 align:middle line:84% The electrons could trade more than one virtual particle. 00:12:30.480 --> 00:12:32.460 align:middle line:84% So instead of just saying the amount of energy 00:12:32.460 --> 00:12:35.820 align:middle line:84% that this one virtual particle borrowed was uncertain 00:12:35.820 --> 00:12:37.530 align:middle line:84% and in principle could be infinite, 00:12:37.530 --> 00:12:41.040 align:middle line:84% what if the electrons had traded two photons, two 00:12:41.040 --> 00:12:44.970 align:middle line:84% virtual photons, each of which had temporarily borrowed energy 00:12:44.970 --> 00:12:46.530 align:middle line:90% and momentum from the vacuum? 00:12:46.530 --> 00:12:48.840 align:middle line:84% Well, now it starts getting pretty tricky 00:12:48.840 --> 00:12:51.930 align:middle line:84% because there are actually several topologically distinct 00:12:51.930 --> 00:12:55.350 align:middle line:84% ways in which two incoming electrons could 00:12:55.350 --> 00:12:58.990 align:middle line:84% trade two photons and leave only two electrons coming out. 00:12:58.990 --> 00:13:01.860 align:middle line:84% So instead of only one storyline that you 00:13:01.860 --> 00:13:04.540 align:middle line:84% have to map into a line of algebra, 00:13:04.540 --> 00:13:07.410 align:middle line:84% you actually have all these different ways 00:13:07.410 --> 00:13:10.350 align:middle line:84% in which two electrons come in, two electrons go out, 00:13:10.350 --> 00:13:13.060 align:middle line:84% and in between, they've traded two virtual photons. 00:13:13.060 --> 00:13:15.180 align:middle line:84% And so the diagrams were literally 00:13:15.180 --> 00:13:16.410 align:middle line:90% a form of bookkeeping. 00:13:16.410 --> 00:13:18.510 align:middle line:84% And again, you could walk through the same series 00:13:18.510 --> 00:13:21.750 align:middle line:84% of steps to map every element of these slightly more 00:13:21.750 --> 00:13:26.700 align:middle line:84% complicated Feynman diagrams to the corresponding algebra. 00:13:26.700 --> 00:13:29.950 align:middle line:84% And you can do the same with three virtual photons or four. 00:13:29.950 --> 00:13:32.350 align:middle line:84% In principle, there could be an infinite number 00:13:32.350 --> 00:13:34.210 align:middle line:84% of virtual photons, each of which 00:13:34.210 --> 00:13:37.300 align:middle line:84% could carry, in principle, an infinite, albeit 00:13:37.300 --> 00:13:38.960 align:middle line:90% short-lived energy momentum. 00:13:38.960 --> 00:13:41.480 align:middle line:84% So you see the bookkeeping becomes like mind boggling, 00:13:41.480 --> 00:13:41.980 align:middle line:90% right? 00:13:41.980 --> 00:13:43.630 align:middle line:84% So this is a kind of way to march 00:13:43.630 --> 00:13:45.560 align:middle line:84% through the corresponding equations. 00:13:45.560 --> 00:13:47.650 align:middle line:84% Make sure you don't omit any terms. 00:13:47.650 --> 00:13:50.350 align:middle line:84% Make sure you don't double count certain terms, which 00:13:50.350 --> 00:13:52.060 align:middle line:84% have been bedeviling these calculations 00:13:52.060 --> 00:13:53.685 align:middle line:90% throughout the '30s. 00:13:53.685 --> 00:13:55.060 align:middle line:84% And so now you have a map to make 00:13:55.060 --> 00:13:57.268 align:middle line:84% sure you at least have the equations, the correct set 00:13:57.268 --> 00:13:58.880 align:middle line:90% of equations to worry about. 00:13:58.880 --> 00:14:04.150 align:middle line:84% And then by this point in late spring or early summer of 1948, 00:14:04.150 --> 00:14:06.700 align:middle line:84% Feynman could show that if you have the right bookkeeping, 00:14:06.700 --> 00:14:09.220 align:middle line:84% you see some of these infinities actually exactly cancel 00:14:09.220 --> 00:14:09.920 align:middle line:90% each other. 00:14:09.920 --> 00:14:13.060 align:middle line:84% So some of the infinities that had cropped up in these earlier 00:14:13.060 --> 00:14:16.630 align:middle line:84% calculations, not all, but some of them would exactly cancel, 00:14:16.630 --> 00:14:19.185 align:middle line:84% even before you got fancy with renormalization 00:14:19.185 --> 00:14:20.560 align:middle line:84% just because you have to remember 00:14:20.560 --> 00:14:22.540 align:middle line:84% that for every diagram like this, 00:14:22.540 --> 00:14:24.740 align:middle line:84% there's a corresponding one like that and so on. 00:14:24.740 --> 00:14:26.980 align:middle line:84% And some of these have exact cancellations. 00:14:26.980 --> 00:14:29.590 align:middle line:84% So the challenge of taming those infinities 00:14:29.590 --> 00:14:31.925 align:middle line:84% would become a bit more manageable 00:14:31.925 --> 00:14:34.300 align:middle line:84% if you could make sure you had the right set of equations 00:14:34.300 --> 00:14:36.500 align:middle line:90% to work with from the start. 00:14:36.500 --> 00:14:37.760 align:middle line:90% So how did that go? 00:14:37.760 --> 00:14:38.780 align:middle line:90% That sounds awesome. 00:14:38.780 --> 00:14:41.480 align:middle line:84% You have this amazing, kind of intuitive, very simple 00:14:41.480 --> 00:14:43.370 align:middle line:90% looking technique. 00:14:43.370 --> 00:14:47.990 align:middle line:84% This used to occupy literally 30 and 40-page journal articles. 00:14:47.990 --> 00:14:50.150 align:middle line:84% When people tried to do this without the diagrams 00:14:50.150 --> 00:14:52.820 align:middle line:84% throughout the 1930s, they'd always find these infinities. 00:14:52.820 --> 00:14:54.770 align:middle line:84% You think, oh, our hero's in town. 00:14:54.770 --> 00:14:56.450 align:middle line:90% Finally, help us on the way. 00:14:56.450 --> 00:14:59.870 align:middle line:84% It didn't play out that way for our poor MIT alumnus Richard 00:14:59.870 --> 00:15:00.380 align:middle line:90% Feynman. 00:15:00.380 --> 00:15:02.030 align:middle line:84% The first thing to keep in mind is 00:15:02.030 --> 00:15:05.450 align:middle line:84% that his presentation followed an eight-hour lecture 00:15:05.450 --> 00:15:06.500 align:middle line:90% by Julian Schwinger. 00:15:06.500 --> 00:15:08.390 align:middle line:84% I want to let that settle in for a second, 00:15:08.390 --> 00:15:10.550 align:middle line:90% an eight-hour lecture. 00:15:10.550 --> 00:15:13.310 align:middle line:84% That's like unlawful imprisonment. 00:15:13.310 --> 00:15:16.250 align:middle line:84% Now, I often run along with my lectures here, and I feel bad. 00:15:16.250 --> 00:15:19.040 align:middle line:84% I go like three minutes late, and you're all busy. 00:15:19.040 --> 00:15:21.240 align:middle line:84% But you know, anyway, there are limits. 00:15:21.240 --> 00:15:24.350 align:middle line:84% So why was Schwinger given so much space? 00:15:24.350 --> 00:15:27.110 align:middle line:84% In between the Shelter Island meeting and this 00:15:27.110 --> 00:15:30.560 align:middle line:84% follow up one in Pocono, it was Schwinger 00:15:30.560 --> 00:15:33.830 align:middle line:84% who had first found a way to tame these infinities. 00:15:33.830 --> 00:15:36.150 align:middle line:84% He first calculated with his new techniques 00:15:36.150 --> 00:15:38.700 align:middle line:84% that did not involve any of these diagrammatic methods. 00:15:38.700 --> 00:15:40.920 align:middle line:84% He not only found a way in principle 00:15:40.920 --> 00:15:42.780 align:middle line:84% to respect the symmetries of relativity 00:15:42.780 --> 00:15:46.110 align:middle line:84% and find finite answers with his renormalization program, 00:15:46.110 --> 00:15:48.270 align:middle line:84% he'd also found right in between, 00:15:48.270 --> 00:15:50.730 align:middle line:84% six months between these meetings. 00:15:50.730 --> 00:15:53.970 align:middle line:84% In December '47, he published the first kind 00:15:53.970 --> 00:15:57.630 align:middle line:84% of successful demonstration that renormalization 00:15:57.630 --> 00:16:00.750 align:middle line:84% could yield finite results that actually match unbelievably 00:16:00.750 --> 00:16:03.870 align:middle line:84% closely to these latest high precision experiments. 00:16:03.870 --> 00:16:06.660 align:middle line:84% Schwinger was the person of the hour, or rather, 00:16:06.660 --> 00:16:07.690 align:middle line:90% the eight hours. 00:16:07.690 --> 00:16:10.355 align:middle line:84% So it was after that they had a brief break for lunch, 00:16:10.355 --> 00:16:11.730 align:middle line:84% and they came back, and Schwinger 00:16:11.730 --> 00:16:13.620 align:middle line:84% talked for another four hours afterwards. 00:16:13.620 --> 00:16:15.690 align:middle line:84% And then Feynman had 30 minutes at the blackboard 00:16:15.690 --> 00:16:16.648 align:middle line:90% at the end of that day. 00:16:16.648 --> 00:16:18.930 align:middle line:84% All right, so it's not like great setup. 00:16:18.930 --> 00:16:21.420 align:middle line:84% Moreover, he was completely unprepared. 00:16:21.420 --> 00:16:24.810 align:middle line:84% He did not have a well-polished presentation in hand. 00:16:24.810 --> 00:16:27.600 align:middle line:84% He just wanted to wing it, which is not a good thing 00:16:27.600 --> 00:16:30.130 align:middle line:90% to do at the end of a busy day. 00:16:30.130 --> 00:16:32.640 align:middle line:84% It was so-- it seemed at least to some of his listeners 00:16:32.640 --> 00:16:35.970 align:middle line:84% to be so scattershot and so disorganized, 00:16:35.970 --> 00:16:38.250 align:middle line:84% that not only was he repeated all the time. 00:16:38.250 --> 00:16:40.320 align:middle line:84% At one point, Niels Bohr, who had 00:16:40.320 --> 00:16:43.200 align:middle line:84% been invited to participate, one of the few older European 00:16:43.200 --> 00:16:45.810 align:middle line:84% physicists, Bohr got out of his chair, 00:16:45.810 --> 00:16:48.030 align:middle line:84% walked up to the blackboard and took the chalk out 00:16:48.030 --> 00:16:49.530 align:middle line:84% of Feynman's hand and said you don't 00:16:49.530 --> 00:16:50.910 align:middle line:90% understand quantum physics. 00:16:50.910 --> 00:16:52.290 align:middle line:90% Not great. 00:16:52.290 --> 00:16:54.220 align:middle line:84% God, I wish I'd been able to see that. 00:16:54.220 --> 00:16:56.160 align:middle line:84% So Bohr says not just this is like 00:16:56.160 --> 00:16:57.660 align:middle line:90% a disorganized presentation. 00:16:57.660 --> 00:17:00.690 align:middle line:84% He says your whole framework violates the uncertainty 00:17:00.690 --> 00:17:01.360 align:middle line:90% principle. 00:17:01.360 --> 00:17:03.780 align:middle line:84% What does it mean to draw a picture of an electron moving 00:17:03.780 --> 00:17:05.069 align:middle line:90% from here to here? 00:17:05.069 --> 00:17:08.339 align:middle line:84% Bohr says, in effect, you've assumed that the electron has 00:17:08.339 --> 00:17:10.410 align:middle line:90% a well-defined trajectory. 00:17:10.410 --> 00:17:13.319 align:middle line:84% But no quantum object has a well-defined trajectory 00:17:13.319 --> 00:17:16.170 align:middle line:84% because to do so, it would need to have arbitrarily 00:17:16.170 --> 00:17:18.508 align:middle line:84% precise position and momentum at the same time. 00:17:18.508 --> 00:17:20.550 align:middle line:84% But we can't have that because it's [INAUDIBLE].. 00:17:20.550 --> 00:17:23.842 align:middle line:84% Bohr is like this is a nonstarter from the beginning. 00:17:23.842 --> 00:17:25.050 align:middle line:90% Feynman's a little flustered. 00:17:25.050 --> 00:17:26.369 align:middle line:90% It's not literally trajectory. 00:17:26.369 --> 00:17:27.869 align:middle line:90% Oh, let me go on. 00:17:27.869 --> 00:17:28.530 align:middle line:90% OK. 00:17:28.530 --> 00:17:30.210 align:middle line:90% Paul Dirac was there. 00:17:30.210 --> 00:17:33.180 align:middle line:84% Dirac says, well, when you calculate the probabilities 00:17:33.180 --> 00:17:36.450 align:middle line:84% with these new diagrams, do they obey unitarity? 00:17:36.450 --> 00:17:39.690 align:middle line:84% To which Feynman's response was, what's unitarity? 00:17:39.690 --> 00:17:41.350 align:middle line:90% Not good. 00:17:41.350 --> 00:17:45.300 align:middle line:84% OK, this was not a great presentation for Feynman. 00:17:45.300 --> 00:17:47.420 align:middle line:84% Unitarity is, again, some of you might know, 00:17:47.420 --> 00:17:49.440 align:middle line:84% you might have found in other classes, 00:17:49.440 --> 00:17:51.370 align:middle line:84% it's really a fancy way of asking, 00:17:51.370 --> 00:17:55.050 align:middle line:84% does the sum of all these probabilities add up to 1. 00:17:55.050 --> 00:17:58.020 align:middle line:84% There's a 100% chance that something will happen, 00:17:58.020 --> 00:18:01.650 align:middle line:84% and it might be 35% chance of that and 42% chance of that. 00:18:01.650 --> 00:18:03.330 align:middle line:90% Do you have to add all these up? 00:18:03.330 --> 00:18:05.820 align:middle line:84% Does the sum of all these probabilities 00:18:05.820 --> 00:18:07.710 align:middle line:84% obey the conservation of probability? 00:18:07.710 --> 00:18:08.670 align:middle line:90% Does it add up to 1? 00:18:08.670 --> 00:18:11.850 align:middle line:84% That's the fancy way that's the simple version of what 00:18:11.850 --> 00:18:12.660 align:middle line:90% Dirac was asking. 00:18:12.660 --> 00:18:15.540 align:middle line:84% And Feynman hadn't even thought about the question. 00:18:15.540 --> 00:18:17.550 align:middle line:84% He certainly had no answer ready yet. 00:18:17.550 --> 00:18:18.990 align:middle line:90% Edward Teller was there. 00:18:18.990 --> 00:18:21.870 align:middle line:84% He says what about when you have a pair of electrons 00:18:21.870 --> 00:18:23.490 align:middle line:90% in these intermediate states? 00:18:23.490 --> 00:18:26.190 align:middle line:84% Two virtual electrons, let's say, 00:18:26.190 --> 00:18:28.860 align:middle line:84% do they obey the Pauli exclusion principle? 00:18:28.860 --> 00:18:30.930 align:middle line:84% Another kind of cornerstone of quantum physics. 00:18:30.930 --> 00:18:33.000 align:middle line:84% And Feynman's response was that's a really interesting 00:18:33.000 --> 00:18:33.400 align:middle line:90% question. 00:18:33.400 --> 00:18:34.358 align:middle line:90% I'll go think about it. 00:18:34.358 --> 00:18:35.620 align:middle line:90% Again, he had no answer. 00:18:35.620 --> 00:18:38.790 align:middle line:84% So in general, what this very esteemed but small kind 00:18:38.790 --> 00:18:41.340 align:middle line:84% of elite audience kept asking during 00:18:41.340 --> 00:18:44.040 align:middle line:84% this scattered presentation of Feynman's was 00:18:44.040 --> 00:18:46.078 align:middle line:90% what rules govern their use. 00:18:46.078 --> 00:18:48.120 align:middle line:84% It really looked like he was kind of making it up 00:18:48.120 --> 00:18:51.570 align:middle line:84% as it went along, and he was not able, at least at that moment, 00:18:51.570 --> 00:18:54.600 align:middle line:84% to articulate the kind of rule-bound techniques 00:18:54.600 --> 00:18:59.220 align:middle line:84% that would perhaps yield as a comparable set of calculating 00:18:59.220 --> 00:19:02.520 align:middle line:84% techniques to Schwinger's very pristine, very 00:19:02.520 --> 00:19:04.990 align:middle line:90% precise algebraic approach. 00:19:04.990 --> 00:19:06.900 align:middle line:84% So by many, many accounts, Feynman 00:19:06.900 --> 00:19:10.110 align:middle line:84% left this meeting disappointed, maybe even depressed. 00:19:10.110 --> 00:19:13.140 align:middle line:84% He really-- was not a great start for these new techniques, 00:19:13.140 --> 00:19:15.650 align:middle line:90% and he was really down. 00:19:15.650 --> 00:19:17.840 align:middle line:84% Now, one might have thought that all he had to do 00:19:17.840 --> 00:19:22.100 align:middle line:84% was kind of collect himself, write up some clear articles. 00:19:22.100 --> 00:19:24.980 align:middle line:84% Just say point by point first do this, then do that. 00:19:24.980 --> 00:19:27.140 align:middle line:84% Here's where this comes from, give a derivation, 00:19:27.140 --> 00:19:28.340 align:middle line:90% give a demonstration. 00:19:28.340 --> 00:19:29.780 align:middle line:84% He could have cleared this up, one 00:19:29.780 --> 00:19:33.560 align:middle line:84% might have thought, by writing some kind of clear articles. 00:19:33.560 --> 00:19:35.390 align:middle line:84% Well, he did write some clear articles, 00:19:35.390 --> 00:19:37.190 align:middle line:84% and yet what, again, I found really 00:19:37.190 --> 00:19:40.670 align:middle line:84% fascinating was that kind of confusion about the diagrams 00:19:40.670 --> 00:19:44.130 align:middle line:84% lingered for years afterwards, not just for days, weeks, 00:19:44.130 --> 00:19:48.152 align:middle line:84% or months, even years after his articles had been in print. 00:19:48.152 --> 00:19:50.360 align:middle line:84% And so I won't go through all of these examples, just 00:19:50.360 --> 00:19:53.190 align:middle line:84% some examples I write about in more detail in the book. 00:19:53.190 --> 00:19:55.430 align:middle line:84% But you have people either writing directly 00:19:55.430 --> 00:19:58.070 align:middle line:84% to Feynman saying, I can't do this calculation. 00:19:58.070 --> 00:20:01.072 align:middle line:84% Will you do it for me with your trick and tell me what you get? 00:20:01.072 --> 00:20:03.030 align:middle line:84% And then they thank him in the acknowledgments. 00:20:03.030 --> 00:20:05.390 align:middle line:84% There's some interesting correspondence circles 00:20:05.390 --> 00:20:07.310 align:middle line:84% with people not including Feynman 00:20:07.310 --> 00:20:10.970 align:middle line:84% from very, very elite, very well-trained experts 00:20:10.970 --> 00:20:14.030 align:middle line:84% in the field who three of them try 00:20:14.030 --> 00:20:16.817 align:middle line:84% to do the same calculation with the same diagrams, 00:20:16.817 --> 00:20:19.150 align:middle line:84% and they keep getting different answers from each other. 00:20:19.150 --> 00:20:20.983 align:middle line:84% So you have this wonderful series of letters 00:20:20.983 --> 00:20:23.192 align:middle line:84% because it was pre-email, and they were, in fact, 00:20:23.192 --> 00:20:24.150 align:middle line:90% in different countries. 00:20:24.150 --> 00:20:27.160 align:middle line:84% They weren't going to make long distance telephone calls. 00:20:27.160 --> 00:20:29.670 align:middle line:84% So you have these letters of them trying to figure out 00:20:29.670 --> 00:20:31.710 align:middle line:84% what keeps going wrong when they each try 00:20:31.710 --> 00:20:33.210 align:middle line:90% to do the same calculation. 00:20:33.210 --> 00:20:36.210 align:middle line:90% That's as late as 1950. 00:20:36.210 --> 00:20:38.250 align:middle line:84% A few years later, my favorite example actually 00:20:38.250 --> 00:20:40.350 align:middle line:84% comes from a letter of recommendation 00:20:40.350 --> 00:20:43.950 align:middle line:84% for young physicists who was finishing his PhD at Stanford, 00:20:43.950 --> 00:20:46.320 align:middle line:84% and the student's advisor, Leonard Schiff, 00:20:46.320 --> 00:20:48.570 align:middle line:84% wrote to recommend the students, saying 00:20:48.570 --> 00:20:51.030 align:middle line:84% you should hire my student for the new professorship 00:20:51.030 --> 00:20:53.460 align:middle line:84% because he actually does understand Feynman diagrams 00:20:53.460 --> 00:20:54.960 align:middle line:84% and actually use them in his thesis. 00:20:54.960 --> 00:20:58.680 align:middle line:84% That was five years after this Pocono conference, 00:20:58.680 --> 00:21:01.710 align:middle line:84% roughly four years after Feynman's attempt 00:21:01.710 --> 00:21:04.350 align:middle line:84% to clarify the techniques with his articles. 00:21:04.350 --> 00:21:06.570 align:middle line:84% So if four or five years later, your advisor 00:21:06.570 --> 00:21:10.080 align:middle line:84% says my student is unusual because he does understand 00:21:10.080 --> 00:21:13.320 align:middle line:84% them, that seems to suggest these were not universally 00:21:13.320 --> 00:21:14.460 align:middle line:90% clear to everyone. 00:21:14.460 --> 00:21:17.130 align:middle line:84% So they were clearly not so obvious or automatic, 00:21:17.130 --> 00:21:20.550 align:middle line:84% even after Feynman did have a chance to try to clarify. 00:21:20.550 --> 00:21:22.770 align:middle line:84% And yet, you can see evidence that they're 00:21:22.770 --> 00:21:24.630 align:middle line:90% taking off like gangbusters. 00:21:24.630 --> 00:21:26.760 align:middle line:84% If you go through the Physical Review, 00:21:26.760 --> 00:21:30.030 align:middle line:84% and in the book I talk about similar searches 00:21:30.030 --> 00:21:32.890 align:middle line:84% in other journals throughout many parts of the world, 00:21:32.890 --> 00:21:35.070 align:middle line:84% in fact, not just in the United States, 00:21:35.070 --> 00:21:38.820 align:middle line:84% you see an exponential rise that these diagram techniques 00:21:38.820 --> 00:21:40.148 align:middle line:90% are getting picked up. 00:21:40.148 --> 00:21:41.940 align:middle line:84% The doubling time I've forgotten, something 00:21:41.940 --> 00:21:43.690 align:middle line:84% like two and a half years, or three years, 00:21:43.690 --> 00:21:45.450 align:middle line:84% where they're really growing literally 00:21:45.450 --> 00:21:49.538 align:middle line:84% exponentially over the first half decade or so. 00:21:49.538 --> 00:21:51.580 align:middle line:84% So you have the one hand, you have people saying, 00:21:51.580 --> 00:21:52.205 align:middle line:90% I don't get it. 00:21:52.205 --> 00:21:52.950 align:middle line:90% I can't do it. 00:21:52.950 --> 00:21:54.870 align:middle line:84% And yet you find this growing evidence 00:21:54.870 --> 00:21:58.440 align:middle line:84% that at least some people have become early adopters 00:21:58.440 --> 00:22:00.060 align:middle line:90% of the techniques. 00:22:00.060 --> 00:22:02.760 align:middle line:84% You can then do the usual trick and not 00:22:02.760 --> 00:22:05.520 align:middle line:84% just say how many articles use the diagrams, 00:22:05.520 --> 00:22:06.990 align:middle line:90% but who wrote those articles? 00:22:06.990 --> 00:22:07.800 align:middle line:90% Where were they? 00:22:07.800 --> 00:22:08.790 align:middle line:90% What were they up to? 00:22:08.790 --> 00:22:11.820 align:middle line:84% And you start seeing some pretty interesting traits, 00:22:11.820 --> 00:22:14.220 align:middle line:84% some common features among the people 00:22:14.220 --> 00:22:18.740 align:middle line:84% who were beginning to use these techniques in their own papers. 00:22:18.740 --> 00:22:22.580 align:middle line:84% So first hand, they were all young in their careers, which 00:22:22.580 --> 00:22:26.720 align:middle line:84% is to say they were all either graduate students or postdocs, 00:22:26.720 --> 00:22:27.830 align:middle line:90% the vast majority. 00:22:27.830 --> 00:22:30.110 align:middle line:84% A few of them were kind of assistant professors. 00:22:30.110 --> 00:22:33.920 align:middle line:84% They were all still fairly early in their training or careers. 00:22:33.920 --> 00:22:35.900 align:middle line:84% They were all theoretical physicists 00:22:35.900 --> 00:22:37.670 align:middle line:90% in this early period. 00:22:37.670 --> 00:22:40.340 align:middle line:84% Nowadays, these diagrams are just 00:22:40.340 --> 00:22:43.100 align:middle line:84% as ubiquitous among experimental physicists as theorists. 00:22:43.100 --> 00:22:46.550 align:middle line:84% But in this early phase, this early kind of exponential rise, 00:22:46.550 --> 00:22:48.830 align:middle line:84% it was young theoretical physicists. 00:22:48.830 --> 00:22:51.740 align:middle line:84% And the last part was that they were really in contact 00:22:51.740 --> 00:22:52.460 align:middle line:90% with each other. 00:22:52.460 --> 00:22:55.790 align:middle line:84% You can do a network study and trace it 00:22:55.790 --> 00:22:58.040 align:middle line:84% through by co-authorship, by acknowledgments, 00:22:58.040 --> 00:23:01.070 align:middle line:84% by unpublished correspondence that I 00:23:01.070 --> 00:23:03.020 align:middle line:84% was able to find and piece together, 00:23:03.020 --> 00:23:04.200 align:middle line:90% that they knew each other. 00:23:04.200 --> 00:23:06.380 align:middle line:84% It was a network that had come together 00:23:06.380 --> 00:23:09.180 align:middle line:84% to learn these techniques, and then they began to spread out. 00:23:09.180 --> 00:23:12.080 align:middle line:84% So something pedagogical is going on. 00:23:12.080 --> 00:23:14.480 align:middle line:84% The majority of these early users 00:23:14.480 --> 00:23:17.700 align:middle line:84% were still in the formal phase of their training. 00:23:17.700 --> 00:23:20.490 align:middle line:84% They were literally still being taught to be physicists. 00:23:20.490 --> 00:23:23.250 align:middle line:84% And yet it wasn't a story of write a textbook, 00:23:23.250 --> 00:23:25.860 align:middle line:84% teach some classes, it'll spread. 00:23:25.860 --> 00:23:30.900 align:middle line:84% All of the data points shown on this early plot 00:23:30.900 --> 00:23:33.360 align:middle line:84% represent articles that came out before the very 00:23:33.360 --> 00:23:35.460 align:middle line:84% first English language textbooks had 00:23:35.460 --> 00:23:37.630 align:middle line:84% been published that incorporated the new techniques. 00:23:37.630 --> 00:23:39.870 align:middle line:84% So the first textbook treatments of how 00:23:39.870 --> 00:23:42.150 align:middle line:84% to calculate with these new Feynman diagrams 00:23:42.150 --> 00:23:45.100 align:middle line:84% weren't published until 1955, by which time, 00:23:45.100 --> 00:23:47.760 align:middle line:84% there was already evidence of this fast-growing exponential 00:23:47.760 --> 00:23:49.110 align:middle line:90% rise. 00:23:49.110 --> 00:23:50.830 align:middle line:90% So how does that happen? 00:23:50.830 --> 00:23:53.685 align:middle line:84% A lot of it comes down to this gentleman, Freeman Dyson. 00:23:53.685 --> 00:23:57.790 align:middle line:90% 00:23:57.790 --> 00:24:00.060 align:middle line:84% Dyson, you might know his name, he just 00:24:00.060 --> 00:24:04.270 align:middle line:84% passed away this past March, just before quarantine in fact. 00:24:04.270 --> 00:24:08.190 align:middle line:84% He died in very early March at the age of 96, quite 00:24:08.190 --> 00:24:10.890 align:middle line:90% a remarkable life and career. 00:24:10.890 --> 00:24:13.110 align:middle line:84% At this point, he was quite a young person. 00:24:13.110 --> 00:24:14.940 align:middle line:84% He was, in fact, still in graduate school. 00:24:14.940 --> 00:24:16.770 align:middle line:90% He was originally from Britain. 00:24:16.770 --> 00:24:18.720 align:middle line:84% He got a very competitive fellowship 00:24:18.720 --> 00:24:21.540 align:middle line:84% very soon after the end of the Second World War 00:24:21.540 --> 00:24:24.360 align:middle line:84% called a Commonwealth fellowship reserved at the time 00:24:24.360 --> 00:24:27.930 align:middle line:84% for British students to study abroad, 00:24:27.930 --> 00:24:29.730 align:middle line:84% mostly in Commonwealth countries, 00:24:29.730 --> 00:24:33.150 align:middle line:84% like Canada or Australia, but also the United States. 00:24:33.150 --> 00:24:34.230 align:middle line:90% So he got a fellowship. 00:24:34.230 --> 00:24:36.780 align:middle line:84% He came to Cornell University because he really 00:24:36.780 --> 00:24:40.380 align:middle line:84% wanted to study with Hans Bethe, whose work even in the '30s 00:24:40.380 --> 00:24:41.730 align:middle line:90% had seemed super exciting. 00:24:41.730 --> 00:24:44.520 align:middle line:84% And this young grad student said I want to go study with Bethe. 00:24:44.520 --> 00:24:47.220 align:middle line:84% So he gets the fellowship, comes to Cornell. 00:24:47.220 --> 00:24:49.020 align:middle line:84% He starts working with Bethe but also 00:24:49.020 --> 00:24:50.970 align:middle line:84% very quickly meets Feynman, who at this point 00:24:50.970 --> 00:24:53.280 align:middle line:84% was a very young professor whom Bethe 00:24:53.280 --> 00:24:57.460 align:middle line:84% had recruited as soon as they were 00:24:57.460 --> 00:24:59.110 align:middle line:90% done at Los Alamos for the war. 00:24:59.110 --> 00:25:01.990 align:middle line:84% So Bethe and Feynman had interacted at Los Alamos. 00:25:01.990 --> 00:25:05.080 align:middle line:84% Bethe as the senior theoretical physicist at Cornell 00:25:05.080 --> 00:25:06.220 align:middle line:90% hired Feynman. 00:25:06.220 --> 00:25:09.730 align:middle line:84% This even younger physicist Dyson meets Feynman there. 00:25:09.730 --> 00:25:12.040 align:middle line:84% The summer after his first year of grad school, 00:25:12.040 --> 00:25:16.060 align:middle line:84% Dyson and Feynman drive cross-country together. 00:25:16.060 --> 00:25:17.950 align:middle line:84% Dyson wanted to just see the country. 00:25:17.950 --> 00:25:18.820 align:middle line:90% He was from Britain. 00:25:18.820 --> 00:25:21.550 align:middle line:84% He was sending these really kind of delicious letters 00:25:21.550 --> 00:25:23.320 align:middle line:84% back to his family, often writing 00:25:23.320 --> 00:25:25.390 align:middle line:84% to his mother on a manual typewriter, 00:25:25.390 --> 00:25:27.370 align:middle line:84% a small portable manual typewriter, 00:25:27.370 --> 00:25:29.080 align:middle line:90% often more than once a week. 00:25:29.080 --> 00:25:30.910 align:middle line:84% And he just wanted to explore the country 00:25:30.910 --> 00:25:32.410 align:middle line:84% because no member of his immediate family 00:25:32.410 --> 00:25:33.868 align:middle line:84% had ever visited the United States. 00:25:33.868 --> 00:25:34.990 align:middle line:90% He was very curious. 00:25:34.990 --> 00:25:39.410 align:middle line:84% And Feynman wanted to go back to New Mexico. 00:25:39.410 --> 00:25:40.660 align:middle line:90% He had a girlfriend out there. 00:25:40.660 --> 00:25:42.952 align:middle line:84% He maybe was going to do some consulting at Los Alamos. 00:25:42.952 --> 00:25:45.610 align:middle line:84% So they basically drove cross country together that summer 00:25:45.610 --> 00:25:52.060 align:middle line:84% of '48, which is to say just weeks after the Pocono meeting. 00:25:52.060 --> 00:25:53.920 align:middle line:90% So Dyson had not been at Pocono. 00:25:53.920 --> 00:25:56.680 align:middle line:84% He'd been hearing about these things in Ithaca 00:25:56.680 --> 00:26:01.180 align:middle line:84% from his new friend, but now he had a several days long 00:26:01.180 --> 00:26:03.610 align:middle line:90% drive to just pick his brain. 00:26:03.610 --> 00:26:06.520 align:middle line:84% Meanwhile, once they get to New Mexico, 00:26:06.520 --> 00:26:09.430 align:middle line:84% then Dyson took the bus to go to Ann Arbor, Michigan. 00:26:09.430 --> 00:26:11.260 align:middle line:84% Again, he was like being a tourist. 00:26:11.260 --> 00:26:15.910 align:middle line:84% He then spent about six weeks at University of Michigan 00:26:15.910 --> 00:26:18.400 align:middle line:84% attending summer school lectures by none other than Julian 00:26:18.400 --> 00:26:20.775 align:middle line:84% Schwinger, where, again, he had a chance to talk directly 00:26:20.775 --> 00:26:23.080 align:middle line:84% with Schwinger at some length and some detail, 00:26:23.080 --> 00:26:25.390 align:middle line:84% where Schwinger was lecturing on his own approach 00:26:25.390 --> 00:26:28.300 align:middle line:84% to quantum field theory and renormalization. 00:26:28.300 --> 00:26:31.690 align:middle line:84% So at this point, by the end of the summer of 1948, 00:26:31.690 --> 00:26:33.640 align:middle line:84% Freeman Dyson was the only person 00:26:33.640 --> 00:26:37.720 align:middle line:84% in the universe who had spent extensive close 00:26:37.720 --> 00:26:41.877 align:middle line:84% informal personal time with both Richard Feynman and Julian 00:26:41.877 --> 00:26:43.960 align:middle line:84% Schwinger, just at the time they were each working 00:26:43.960 --> 00:26:46.660 align:middle line:84% on their separate and very different looking approaches 00:26:46.660 --> 00:26:49.090 align:middle line:84% to quantum field theory and renormalization. 00:26:49.090 --> 00:26:53.272 align:middle line:84% Then he takes this now famous bus ride back from Michigan, 00:26:53.272 --> 00:26:54.730 align:middle line:84% back to the East Coast where he was 00:26:54.730 --> 00:26:57.250 align:middle line:84% going to start for the second year of his fellowship 00:26:57.250 --> 00:27:00.550 align:middle line:84% at the Institute for Advanced Study in Princeton. 00:27:00.550 --> 00:27:02.440 align:middle line:84% By the way, he never finished his PhD. 00:27:02.440 --> 00:27:07.480 align:middle line:84% To the day that he died, he was Mr. Dyson. 00:27:07.480 --> 00:27:10.540 align:middle line:84% And he thought PhDs were a horrible waste of time. 00:27:10.540 --> 00:27:11.290 align:middle line:90% He might be right. 00:27:11.290 --> 00:27:11.870 align:middle line:90% I don't know. 00:27:11.870 --> 00:27:15.250 align:middle line:84% Anyway, so he spent one year as a grad student at Cornell 00:27:15.250 --> 00:27:17.237 align:middle line:84% and one year on fellowship at the institute 00:27:17.237 --> 00:27:18.820 align:middle line:84% and then was hired as a full professor 00:27:18.820 --> 00:27:21.190 align:middle line:84% at Cornell like four years later, this guy. 00:27:21.190 --> 00:27:25.270 align:middle line:84% Anyway, on the bus ride, he has this amazing epiphany 00:27:25.270 --> 00:27:28.420 align:middle line:84% that he starts seeing how the two very different looking 00:27:28.420 --> 00:27:31.840 align:middle line:84% approaches might fit together, Schwinger's very formal looking 00:27:31.840 --> 00:27:35.980 align:middle line:84% approach to a kind of algebraic, almost axiomatic approach 00:27:35.980 --> 00:27:39.190 align:middle line:84% to quantum field theory and renormalization and Feynman's 00:27:39.190 --> 00:27:43.180 align:middle line:84% diagram-based, bookkeeping, more pictorial, somewhat more 00:27:43.180 --> 00:27:44.402 align:middle line:90% intuitive approach. 00:27:44.402 --> 00:27:46.360 align:middle line:84% The two of them, meaning Feynman and Schwinger, 00:27:46.360 --> 00:27:49.390 align:middle line:84% couldn't understand what each other was doing yet. 00:27:49.390 --> 00:27:53.260 align:middle line:84% And so Dyson is the one who actually puts it together, 00:27:53.260 --> 00:27:57.130 align:middle line:84% a good chunk of it literally on the bus heading back east. 00:27:57.130 --> 00:28:00.070 align:middle line:84% Once he gets to the institute, he then submits two articles 00:28:00.070 --> 00:28:00.830 align:middle line:90% that autumn. 00:28:00.830 --> 00:28:03.010 align:middle line:84% He sends both of them to the Physical Review. 00:28:03.010 --> 00:28:05.470 align:middle line:84% These were published before Feynman's own articles 00:28:05.470 --> 00:28:06.100 align:middle line:90% had come out. 00:28:06.100 --> 00:28:08.475 align:middle line:84% Feynman was actually quite slow to write up his articles. 00:28:08.475 --> 00:28:11.090 align:middle line:84% They came out a little bit later, also in 1949. 00:28:11.090 --> 00:28:14.270 align:middle line:84% In the early years, Dyson's papers were cited more often 00:28:14.270 --> 00:28:15.020 align:middle line:90% than Feynman's. 00:28:15.020 --> 00:28:16.880 align:middle line:84% They were getting a lot of attention, 00:28:16.880 --> 00:28:20.060 align:middle line:84% in part because he was so methodical in laying out 00:28:20.060 --> 00:28:22.940 align:middle line:84% a kind of point by point almost recipe book, 00:28:22.940 --> 00:28:25.940 align:middle line:84% a rule book for how to use them, exactly the stuff that 00:28:25.940 --> 00:28:28.730 align:middle line:84% seemed to be missing from Feynman's presentation at least 00:28:28.730 --> 00:28:29.540 align:middle line:90% at Pocono. 00:28:29.540 --> 00:28:32.390 align:middle line:84% Dyson was able to ground the diagrams 00:28:32.390 --> 00:28:34.370 align:middle line:84% in more first principles derivations 00:28:34.370 --> 00:28:36.980 align:middle line:84% and really go through worked examples. 00:28:36.980 --> 00:28:40.160 align:middle line:84% And it was in these papers where Dyson demonstrates 00:28:40.160 --> 00:28:43.550 align:middle line:84% the mathematical equivalence of the three separate methods that 00:28:43.550 --> 00:28:46.790 align:middle line:84% by this point were on offer, those by Feynman, Schwinger, 00:28:46.790 --> 00:28:50.000 align:middle line:84% and then separately by Shin'ichiro Tomonaga, 00:28:50.000 --> 00:28:51.740 align:middle line:84% whom I mentioned briefly last time. 00:28:51.740 --> 00:28:54.090 align:middle line:90% Tomonaga was still in Tokyo. 00:28:54.090 --> 00:28:57.770 align:middle line:84% Japan was under US occupation after the war. 00:28:57.770 --> 00:29:01.160 align:middle line:84% Tomonaga had worked out a method remarkably similar to what 00:29:01.160 --> 00:29:02.810 align:middle line:90% Schwinger later came up with. 00:29:02.810 --> 00:29:05.030 align:middle line:84% They were working totally independent of each other, 00:29:05.030 --> 00:29:06.890 align:middle line:90% partly because of the war. 00:29:06.890 --> 00:29:09.290 align:middle line:84% Tomonaga had gotten there to many parts, 00:29:09.290 --> 00:29:10.940 align:middle line:84% not all the things Schwinger did, 00:29:10.940 --> 00:29:13.580 align:middle line:84% but very similar framework and many of the same insights 00:29:13.580 --> 00:29:14.570 align:middle line:90% along the way. 00:29:14.570 --> 00:29:18.360 align:middle line:84% Tomonaga had done this starting in 1943, 00:29:18.360 --> 00:29:20.810 align:middle line:84% but the results were not known outside of Japan, 00:29:20.810 --> 00:29:24.500 align:middle line:84% partly because of the Naval blockade and so on. 00:29:24.500 --> 00:29:28.340 align:middle line:84% One of the first packages sent overseas out of Japan 00:29:28.340 --> 00:29:30.380 align:middle line:84% after the end of the war was actually 00:29:30.380 --> 00:29:32.960 align:middle line:84% a package of manuscripts and reprints 00:29:32.960 --> 00:29:35.480 align:middle line:84% that Tomonaga sent to Robert Oppenheimer. 00:29:35.480 --> 00:29:40.100 align:middle line:84% And it was actually ferried in official kind of US delivery 00:29:40.100 --> 00:29:44.000 align:middle line:84% was from US occupied Tokyo back to the United States 00:29:44.000 --> 00:29:48.890 align:middle line:84% because Tomonaga had read in one of the new libraries 00:29:48.890 --> 00:29:51.380 align:middle line:84% in a new subscription to Newsweek 00:29:51.380 --> 00:29:55.040 align:middle line:84% magazine about the Lamb shift because the magazine had 00:29:55.040 --> 00:29:56.930 align:middle line:84% covered everything about Robert Oppenheimer. 00:29:56.930 --> 00:30:00.620 align:middle line:84% He was amazingly famous in the United States after the war. 00:30:00.620 --> 00:30:02.930 align:middle line:84% The fact that he was talking about the Shelter Island 00:30:02.930 --> 00:30:04.490 align:middle line:90% conference became newsworthy. 00:30:04.490 --> 00:30:05.930 align:middle line:90% He mentioned the Lamb shift. 00:30:05.930 --> 00:30:08.090 align:middle line:84% This gets all the way back to Tokyo 00:30:08.090 --> 00:30:12.190 align:middle line:84% through this kind of crazy convoluted system. 00:30:12.190 --> 00:30:13.880 align:middle line:84% Tomonaga reads about it and says, 00:30:13.880 --> 00:30:16.930 align:middle line:84% hey, wow, and digs back through some of his old wartime 00:30:16.930 --> 00:30:19.540 align:middle line:84% manuscripts and reprints and sends materials 00:30:19.540 --> 00:30:21.850 align:middle line:84% to Oppenheimer, who then had them effectively 00:30:21.850 --> 00:30:24.190 align:middle line:84% mimeographed and shared with all the participants 00:30:24.190 --> 00:30:25.420 align:middle line:90% who'd been at Shelter Island. 00:30:25.420 --> 00:30:28.720 align:middle line:84% So the US-based and some of the Western European physicists 00:30:28.720 --> 00:30:32.110 align:middle line:84% who had heard about the Lamb shift and Rabi's group's 00:30:32.110 --> 00:30:35.650 align:middle line:84% measurements and so on, they learned in the days 00:30:35.650 --> 00:30:38.502 align:middle line:84% after Shelter Island about some of Tomonaga's work. 00:30:38.502 --> 00:30:40.960 align:middle line:84% Then they helped arrange for English language publications. 00:30:40.960 --> 00:30:42.760 align:middle line:84% They were very, very eager in fact 00:30:42.760 --> 00:30:45.940 align:middle line:84% to try to get Tomonaga credit, partly because it 00:30:45.940 --> 00:30:48.580 align:middle line:84% was remarkable, partly, I think, because there was a sense 00:30:48.580 --> 00:30:50.770 align:middle line:84% that this was a dramatic development coming 00:30:50.770 --> 00:30:53.830 align:middle line:84% from the city that had just been subjected 00:30:53.830 --> 00:30:55.960 align:middle line:84% to relentless firebombing during the war. 00:30:55.960 --> 00:30:57.460 align:middle line:84% But nonetheless this work somehow 00:30:57.460 --> 00:30:59.630 align:middle line:84% got done in the midst of horrible conditions. 00:30:59.630 --> 00:31:02.770 align:middle line:84% So Oppenheimer worked hard to get Tomonaga's work 00:31:02.770 --> 00:31:04.160 align:middle line:90% into circulation. 00:31:04.160 --> 00:31:05.590 align:middle line:90% So Dyson learned of it. 00:31:05.590 --> 00:31:09.430 align:middle line:84% And Dyson was able to show in this pair of articles from 1949 00:31:09.430 --> 00:31:12.620 align:middle line:84% that these three distinct approaches to quantum 00:31:12.620 --> 00:31:15.840 align:middle line:84% electrodynamics were, in fact, mathematically equivalent very, 00:31:15.840 --> 00:31:18.710 align:middle line:84% very much like what had happened 20 years earlier 00:31:18.710 --> 00:31:20.450 align:middle line:84% between Heisenberg's and Schrodinger's 00:31:20.450 --> 00:31:23.990 align:middle line:90% approaches to quantum theory. 00:31:23.990 --> 00:31:25.960 align:middle line:84% So Oppenheimer at this point had become 00:31:25.960 --> 00:31:28.150 align:middle line:84% director of the Institute for Advanced Study. 00:31:28.150 --> 00:31:31.600 align:middle line:84% He was now basically, in effect, Dyson's supervisor 00:31:31.600 --> 00:31:33.670 align:middle line:84% for the second year of the fellowship. 00:31:33.670 --> 00:31:35.800 align:middle line:84% Oppenheimer was not that impressed with the Feynman 00:31:35.800 --> 00:31:36.910 align:middle line:90% diagrams at first. 00:31:36.910 --> 00:31:40.510 align:middle line:84% In fact, he used to come to Dyson's informal presentations 00:31:40.510 --> 00:31:44.500 align:middle line:84% and interrupt and basically show that he was still the smartest 00:31:44.500 --> 00:31:46.010 align:middle line:90% person in the room. 00:31:46.010 --> 00:31:48.580 align:middle line:84% So the postdocs at the institute asked 00:31:48.580 --> 00:31:52.180 align:middle line:84% Dyson to repeat each of his many hour seminars in private, 00:31:52.180 --> 00:31:53.920 align:middle line:84% and they just wouldn't tell Oppenheimer. 00:31:53.920 --> 00:31:57.010 align:middle line:84% So Dyson would give these announced seminars. 00:31:57.010 --> 00:31:59.590 align:middle line:84% Oppenheimer would come and essentially kind of heckle 00:31:59.590 --> 00:32:02.680 align:middle line:84% and disrupt, and they'd have Dyson give the exact same talk 00:32:02.680 --> 00:32:04.550 align:middle line:90% the next day in secret. 00:32:04.550 --> 00:32:07.480 align:middle line:84% And finally, after Hans Bethe intervened, 00:32:07.480 --> 00:32:09.373 align:middle line:84% Oppenheimer said, OK, OK, I relent. 00:32:09.373 --> 00:32:11.290 align:middle line:84% In fact, he literally wrote "nolo contendere," 00:32:11.290 --> 00:32:13.140 align:middle line:90% like I don't contest the charge. 00:32:13.140 --> 00:32:15.250 align:middle line:90% I give up. 00:32:15.250 --> 00:32:19.330 align:middle line:84% And by a few weeks into Dyson's fellowship and after that, 00:32:19.330 --> 00:32:22.630 align:middle line:84% the diagrams really began to take off at the institute. 00:32:22.630 --> 00:32:26.188 align:middle line:84% So to understand what's going on in this very specific setting 00:32:26.188 --> 00:32:27.980 align:middle line:84% at the Institute for Advanced Study and all 00:32:27.980 --> 00:32:30.710 align:middle line:84% these new postdocs, again, it's important to step back 00:32:30.710 --> 00:32:33.320 align:middle line:84% and understand this is happening in a very particular 00:32:33.320 --> 00:32:34.570 align:middle line:90% institutional setting. 00:32:34.570 --> 00:32:36.320 align:middle line:84% And again, I found this really kind of fun 00:32:36.320 --> 00:32:39.230 align:middle line:84% to dig into when I was working on the book. 00:32:39.230 --> 00:32:41.930 align:middle line:84% The idea that young scientists will typically 00:32:41.930 --> 00:32:44.630 align:middle line:84% do one or two or now, not infrequently, 00:32:44.630 --> 00:32:48.380 align:middle line:84% three separate postdoctoral appointments after their PhD, 00:32:48.380 --> 00:32:52.940 align:middle line:84% but before they take on either a faculty job or a research job 00:32:52.940 --> 00:32:55.160 align:middle line:84% in industry or anything else, that's now 00:32:55.160 --> 00:32:56.880 align:middle line:84% pretty routine today across the sciences, 00:32:56.880 --> 00:32:58.880 align:middle line:84% in fact, even in more and more of the humanities 00:32:58.880 --> 00:32:59.900 align:middle line:90% and social sciences. 00:32:59.900 --> 00:33:02.810 align:middle line:84% The postdoc stage is pretty kind of self-evident, 00:33:02.810 --> 00:33:05.840 align:middle line:84% or we've gotten used to it by and large. 00:33:05.840 --> 00:33:07.760 align:middle line:90% But again, that has a history. 00:33:07.760 --> 00:33:10.070 align:middle line:84% And it's not a very, very long history. 00:33:10.070 --> 00:33:12.500 align:middle line:84% The idea of the postdoctoral fellowship 00:33:12.500 --> 00:33:15.590 align:middle line:84% really dates to the early years of the 20th century, 00:33:15.590 --> 00:33:17.887 align:middle line:84% very soon after the end of the First World War, 00:33:17.887 --> 00:33:19.220 align:middle line:90% but they were still pretty rare. 00:33:19.220 --> 00:33:20.660 align:middle line:90% They were very elite. 00:33:20.660 --> 00:33:23.810 align:middle line:84% It was a big deal if you got this fancy postdoctoral 00:33:23.810 --> 00:33:26.120 align:middle line:84% fellowship after finishing a PhD. 00:33:26.120 --> 00:33:29.180 align:middle line:84% And in fact, even after the Second World War, 00:33:29.180 --> 00:33:34.250 align:middle line:84% only roughly 16% of the US-based PhDs actually did a postdoc, 00:33:34.250 --> 00:33:36.710 align:middle line:84% just did one postdoc, let alone two or three. 00:33:36.710 --> 00:33:39.920 align:middle line:84% But the numbers began to grow very rapidly after the war. 00:33:39.920 --> 00:33:42.140 align:middle line:84% They became more and more common. 00:33:42.140 --> 00:33:47.760 align:middle line:84% The idea going right back to the 1918 proposals and 1920s 00:33:47.760 --> 00:33:50.720 align:middle line:84% and so on was these postdoc positions 00:33:50.720 --> 00:33:53.900 align:middle line:84% were designed to foster a different kind of training 00:33:53.900 --> 00:33:54.980 align:middle line:90% compared to the PhD. 00:33:54.980 --> 00:33:59.180 align:middle line:84% That was the hope, the ambition that they should foster 00:33:59.180 --> 00:34:04.130 align:middle line:84% what historians and sociologists often call tacit knowledge, not 00:34:04.130 --> 00:34:07.130 align:middle line:84% explicit kind of book learning, but actually 00:34:07.130 --> 00:34:09.139 align:middle line:90% stuff that you know by doing. 00:34:09.139 --> 00:34:11.090 align:middle line:84% Even for theoretical physicists who 00:34:11.090 --> 00:34:13.280 align:middle line:84% aren't like building apparatus or glass blowing 00:34:13.280 --> 00:34:14.780 align:middle line:84% or eventually learning to solder, 00:34:14.780 --> 00:34:17.060 align:middle line:84% there's a kind of knowledge that comes 00:34:17.060 --> 00:34:19.739 align:middle line:84% at a kind of intuitive level by practice, 00:34:19.739 --> 00:34:22.610 align:middle line:84% which is why we work on problem sets 00:34:22.610 --> 00:34:27.199 align:middle line:84% all the time, rather than only reading textbooks and dealing 00:34:27.199 --> 00:34:32.250 align:middle line:84% with kind of formal levels or explicit levels of instruction. 00:34:32.250 --> 00:34:33.980 align:middle line:84% So the postdoc was meant to complement 00:34:33.980 --> 00:34:35.989 align:middle line:84% the kind of more formal, more book learning 00:34:35.989 --> 00:34:39.080 align:middle line:84% explicit training of the PhD with this more 00:34:39.080 --> 00:34:40.940 align:middle line:90% informal tacit knowledge. 00:34:40.940 --> 00:34:43.520 align:middle line:84% Moreover, especially in the United States, 00:34:43.520 --> 00:34:46.909 align:middle line:84% they were often funded by private foundations and, again, 00:34:46.909 --> 00:34:51.320 align:middle line:84% a kind of patriotic ambition to improve and build up 00:34:51.320 --> 00:34:56.389 align:middle line:84% US domestic scientific talent and to share the wealth. 00:34:56.389 --> 00:35:00.110 align:middle line:84% So you'd have these young people getting PhDs at one school. 00:35:00.110 --> 00:35:01.700 align:middle line:84% They would get a fellowship to become 00:35:01.700 --> 00:35:03.548 align:middle line:90% a postdoc at a second school. 00:35:03.548 --> 00:35:05.840 align:middle line:84% They could bring what they've learned to the new place. 00:35:05.840 --> 00:35:08.167 align:middle line:84% They'll learn new things at the new place themselves. 00:35:08.167 --> 00:35:10.250 align:middle line:84% Then they'll hopefully get a job at a third place. 00:35:10.250 --> 00:35:13.800 align:middle line:84% So you start building in an emphasis on circulation. 00:35:13.800 --> 00:35:16.130 align:middle line:84% So that it was hoped would help knit together 00:35:16.130 --> 00:35:18.560 align:middle line:84% the US scientific community even more tightly 00:35:18.560 --> 00:35:21.050 align:middle line:84% and build in this kind of sharing of skills, especially 00:35:21.050 --> 00:35:23.370 align:middle line:90% this tacit knowledge stuff. 00:35:23.370 --> 00:35:25.910 align:middle line:84% So after the Second World War, this 00:35:25.910 --> 00:35:29.240 align:middle line:84% became especially pertinent for training young physicists 00:35:29.240 --> 00:35:31.640 align:middle line:84% in theoretical physics in the United States, 00:35:31.640 --> 00:35:33.200 align:middle line:84% which it's still been, it was felt 00:35:33.200 --> 00:35:36.258 align:middle line:84% at the time, kind of lacking and not nearly so developed 00:35:36.258 --> 00:35:37.550 align:middle line:90% as in other parts of the world. 00:35:37.550 --> 00:35:40.380 align:middle line:84% Mostly they had their eyes on Western Europe. 00:35:40.380 --> 00:35:41.990 align:middle line:84% So the most important place where 00:35:41.990 --> 00:35:44.870 align:middle line:84% this begins to really change soon after the war 00:35:44.870 --> 00:35:47.240 align:middle line:84% is this place where Dyson had wound up, 00:35:47.240 --> 00:35:50.240 align:middle line:84% the Institute for Advanced Study in Princeton, New Jersey. 00:35:50.240 --> 00:35:52.070 align:middle line:84% It's near Princeton University, though it's 00:35:52.070 --> 00:35:54.200 align:middle line:90% independent from the university. 00:35:54.200 --> 00:35:57.800 align:middle line:84% Oppenheimer moved there just soon after the end of the war. 00:35:57.800 --> 00:36:01.850 align:middle line:84% He became the new director for the institute starting in 1947. 00:36:01.850 --> 00:36:04.160 align:middle line:84% Partly so he'd be closer to Washington DC, 00:36:04.160 --> 00:36:07.320 align:middle line:84% he was still doing a lot of consulting for the government 00:36:07.320 --> 00:36:08.160 align:middle line:90% and so on. 00:36:08.160 --> 00:36:10.700 align:middle line:84% So one of the first things he did when he moved 00:36:10.700 --> 00:36:15.770 align:middle line:84% was jack up the number of theory postdocs by 60% in one year. 00:36:15.770 --> 00:36:17.880 align:middle line:84% He really said I'm in charge now. 00:36:17.880 --> 00:36:19.483 align:middle line:84% And rather than support other things 00:36:19.483 --> 00:36:21.650 align:middle line:84% that he might have done with the institute's budget, 00:36:21.650 --> 00:36:23.108 align:middle line:84% he said the most important thing we 00:36:23.108 --> 00:36:24.960 align:middle line:84% can do for the scientific community 00:36:24.960 --> 00:36:29.280 align:middle line:84% is really kind of rapidly expand the number of slots 00:36:29.280 --> 00:36:31.740 align:middle line:84% for young postdocs in theoretical physics, 00:36:31.740 --> 00:36:34.645 align:middle line:84% not coincidentally his own field. 00:36:34.645 --> 00:36:37.020 align:middle line:84% A lot of people at the institute didn't like that at all. 00:36:37.020 --> 00:36:37.980 align:middle line:90% But that's what he did. 00:36:37.980 --> 00:36:40.960 align:middle line:90% 00:36:40.960 --> 00:36:42.940 align:middle line:90% And he did that year after year. 00:36:42.940 --> 00:36:44.260 align:middle line:90% And he was-- 00:36:44.260 --> 00:36:46.630 align:middle line:84% I love this letter he wrote to Wolfgang Pauli, who 00:36:46.630 --> 00:36:49.300 align:middle line:84% at this point was back in Europe. 00:36:49.300 --> 00:36:52.420 align:middle line:84% Pauli had spent a good chunk of the war years at the institute, 00:36:52.420 --> 00:36:55.180 align:middle line:84% in fact, visiting and avoiding some of the worst 00:36:55.180 --> 00:36:57.370 align:middle line:90% parts of fighting in Europe. 00:36:57.370 --> 00:36:59.063 align:middle line:84% By this point, he was back in Europe, 00:36:59.063 --> 00:37:01.480 align:middle line:84% and Oppenheimer explained that the institute by this point 00:37:01.480 --> 00:37:03.940 align:middle line:84% is not a school in the sense that even 00:37:03.940 --> 00:37:06.340 align:middle line:84% the younger people are not listening to lectures 00:37:06.340 --> 00:37:09.820 align:middle line:84% or working for doctor's degrees, but it is a school in the sense 00:37:09.820 --> 00:37:12.190 align:middle line:84% that everyone who comes learns parts of physics 00:37:12.190 --> 00:37:13.610 align:middle line:90% which are new to him. 00:37:13.610 --> 00:37:15.160 align:middle line:84% And it turns out that was especially 00:37:15.160 --> 00:37:18.280 align:middle line:84% happening once Dyson arrived among the very first 00:37:18.280 --> 00:37:20.770 align:middle line:84% of these new cohorts, the very first 00:37:20.770 --> 00:37:23.850 align:middle line:84% of these rapidly expanded groups of 8 to 10 00:37:23.850 --> 00:37:27.250 align:middle line:84% to 12 theory postdocs at a time, as opposed to only one or two 00:37:27.250 --> 00:37:28.400 align:middle line:90% as before. 00:37:28.400 --> 00:37:30.610 align:middle line:84% So by the time Dyson and his first cohort 00:37:30.610 --> 00:37:34.060 align:middle line:84% arrived as the new postdocs, although Dyson was actually not 00:37:34.060 --> 00:37:35.950 align:middle line:84% a postdoc, he never did a doc, but he 00:37:35.950 --> 00:37:38.680 align:middle line:90% was joining these postdocs. 00:37:38.680 --> 00:37:41.660 align:middle line:84% The new building that would house him 00:37:41.660 --> 00:37:43.280 align:middle line:84% actually was still under construction, 00:37:43.280 --> 00:37:44.680 align:middle line:90% so they all shared one office. 00:37:44.680 --> 00:37:46.430 align:middle line:84% In fact, they shared Oppenheimer's office. 00:37:46.430 --> 00:37:48.833 align:middle line:84% The director's office was big enough for 12 postdocs. 00:37:48.833 --> 00:37:50.000 align:middle line:90% So some things don't change. 00:37:50.000 --> 00:37:52.000 align:middle line:84% Oppenheimer was in Europe for much of that fall. 00:37:52.000 --> 00:37:54.260 align:middle line:84% So they were literally kind of sharing desk space. 00:37:54.260 --> 00:37:56.510 align:middle line:84% They were completely kind of elbow to elbow 00:37:56.510 --> 00:37:59.270 align:middle line:90% informally sharing space. 00:37:59.270 --> 00:38:01.160 align:middle line:84% And then the postdocs would circulate 00:38:01.160 --> 00:38:04.490 align:middle line:84% through what Oppenheimer loved to call his intellectual hotel. 00:38:04.490 --> 00:38:05.720 align:middle line:90% You don't move there. 00:38:05.720 --> 00:38:08.510 align:middle line:84% You stay there for a visit, and then you go somewhere else. 00:38:08.510 --> 00:38:11.000 align:middle line:84% They would tend to stay for two-year stays. 00:38:11.000 --> 00:38:13.070 align:middle line:84% And while they were there in these early years, 00:38:13.070 --> 00:38:16.220 align:middle line:84% Dyson would coordinate these kind of little teams or groups 00:38:16.220 --> 00:38:18.380 align:middle line:84% of calculations because he was coaching them 00:38:18.380 --> 00:38:20.810 align:middle line:84% in these new techniques for the Feynman diagrams. 00:38:20.810 --> 00:38:22.760 align:middle line:84% And again, the word of that began to spread, 00:38:22.760 --> 00:38:24.800 align:middle line:84% so Pauli writes back from Europe, 00:38:24.800 --> 00:38:27.645 align:middle line:84% what are Dyson and the rest of the Feynman school working on? 00:38:27.645 --> 00:38:29.270 align:middle line:84% It was already becoming clear that they 00:38:29.270 --> 00:38:30.930 align:middle line:90% were working very hard on that. 00:38:30.930 --> 00:38:33.710 align:middle line:84% So when you go back to that curve of these exponential rise 00:38:33.710 --> 00:38:35.453 align:middle line:84% of who's using the diagrams, it starts 00:38:35.453 --> 00:38:36.620 align:middle line:90% to make a little more sense. 00:38:36.620 --> 00:38:38.510 align:middle line:90% It really was a social network. 00:38:38.510 --> 00:38:41.540 align:middle line:84% The overwhelming majority of those early users 00:38:41.540 --> 00:38:45.470 align:middle line:84% were either direct members of these postdoc cohorts 00:38:45.470 --> 00:38:47.930 align:middle line:84% at the institute, who learned and practiced 00:38:47.930 --> 00:38:50.090 align:middle line:84% the techniques directly from Freeman Dyson, 00:38:50.090 --> 00:38:53.420 align:middle line:84% just as he was working them out himself, 00:38:53.420 --> 00:38:56.240 align:middle line:84% or they were students or immediate colleagues 00:38:56.240 --> 00:38:59.150 align:middle line:84% of those postdocs, once they took up their first teaching 00:38:59.150 --> 00:39:01.160 align:middle line:84% jobs and moved to other universities 00:39:01.160 --> 00:39:02.150 align:middle line:90% around the country. 00:39:02.150 --> 00:39:04.820 align:middle line:84% The remaining 20%, I mean, not much 00:39:04.820 --> 00:39:08.450 align:middle line:84% more than a rounding error of those early articles that 00:39:08.450 --> 00:39:10.550 align:middle line:84% used the diagrams had come from Feynman 00:39:10.550 --> 00:39:12.240 align:middle line:84% or from Feynman's immediate circle. 00:39:12.240 --> 00:39:14.600 align:middle line:84% So we really have kind of two lightly 00:39:14.600 --> 00:39:18.790 align:middle line:84% connected networks that dominate the early adopters. 00:39:18.790 --> 00:39:22.420 align:middle line:84% And so you get these airline flight maps. 00:39:22.420 --> 00:39:24.400 align:middle line:84% This is not literally the Feynman diagram case. 00:39:24.400 --> 00:39:25.817 align:middle line:84% I just took it from Google Images. 00:39:25.817 --> 00:39:28.210 align:middle line:84% It is a map of domestic air travel route. 00:39:28.210 --> 00:39:31.510 align:middle line:84% But it was very similar how the diagrams themselves spread out. 00:39:31.510 --> 00:39:34.600 align:middle line:84% You can trace through who's publishing with the diagrams. 00:39:34.600 --> 00:39:35.770 align:middle line:90% We have their articles. 00:39:35.770 --> 00:39:38.290 align:middle line:84% We can see where they were from their kind of byline. 00:39:38.290 --> 00:39:40.540 align:middle line:84% Then look up where were, when did they 00:39:40.540 --> 00:39:42.610 align:middle line:84% interact with, say, Freeman Dyson, 00:39:42.610 --> 00:39:45.640 align:middle line:84% when did they attend this lengthy set of summer school 00:39:45.640 --> 00:39:46.780 align:middle line:90% lectures, and so on. 00:39:46.780 --> 00:39:49.510 align:middle line:84% And you start getting this kind of connected graph of how 00:39:49.510 --> 00:39:52.120 align:middle line:84% the diagrams spread throughout the United States. 00:39:52.120 --> 00:39:54.850 align:middle line:84% Let me say a little bit more about the spread, 00:39:54.850 --> 00:39:58.190 align:middle line:84% and then we'll pause for some discussion. 00:39:58.190 --> 00:40:00.460 align:middle line:84% So that works-- I think that helps account 00:40:00.460 --> 00:40:04.360 align:middle line:84% for how these techniques spread so kind of anomalously quickly 00:40:04.360 --> 00:40:05.980 align:middle line:90% within the United States. 00:40:05.980 --> 00:40:07.540 align:middle line:90% Go to the Physical Review. 00:40:07.540 --> 00:40:10.540 align:middle line:84% At that point, most articles in the Physical Review 00:40:10.540 --> 00:40:12.850 align:middle line:84% were contributed by physicists in the United States. 00:40:12.850 --> 00:40:14.892 align:middle line:84% That's certainly not the case now, but back then, 00:40:14.892 --> 00:40:17.230 align:middle line:84% that was a pretty good reflection of US-based physics. 00:40:17.230 --> 00:40:20.720 align:middle line:84% We get a sense of how the US-based users of the diagrams 00:40:20.720 --> 00:40:22.010 align:middle line:90% began to fan out. 00:40:22.010 --> 00:40:25.520 align:middle line:84% But very quickly, the diagrams were showing up 00:40:25.520 --> 00:40:28.080 align:middle line:84% in the journals from other countries as well. 00:40:28.080 --> 00:40:30.170 align:middle line:84% So it turns out in the United Kingdom, 00:40:30.170 --> 00:40:33.290 align:middle line:84% we have a replay of the same story. 00:40:33.290 --> 00:40:35.270 align:middle line:84% The rules of that fellowship that 00:40:35.270 --> 00:40:38.420 align:middle line:84% had allowed Dyson to come over to Cornell and to Princeton 00:40:38.420 --> 00:40:41.990 align:middle line:84% and the institute required that the recipients 00:40:41.990 --> 00:40:44.175 align:middle line:84% return to Britain for a couple of years. 00:40:44.175 --> 00:40:46.550 align:middle line:84% So you could go for two or three years on the fellowship, 00:40:46.550 --> 00:40:47.950 align:middle line:84% but you had to return to Britain, 00:40:47.950 --> 00:40:50.200 align:middle line:84% and you had to stay in Britain for at least two years. 00:40:50.200 --> 00:40:51.510 align:middle line:90% Those were the rules. 00:40:51.510 --> 00:40:53.480 align:middle line:84% So when Dyson's fellowship expired, 00:40:53.480 --> 00:40:54.740 align:middle line:90% he went back to Britain. 00:40:54.740 --> 00:40:58.010 align:middle line:84% He began teaching first at Cambridge, then eventually 00:40:58.010 --> 00:40:59.990 align:middle line:90% at Birmingham, again, no PhD. 00:40:59.990 --> 00:41:01.970 align:middle line:90% He was a professor with no PhD. 00:41:01.970 --> 00:41:05.068 align:middle line:84% And when you look at who was using the diagrams in Britain, 00:41:05.068 --> 00:41:07.610 align:middle line:84% there were people who learned from Dyson once Dyson went back 00:41:07.610 --> 00:41:08.110 align:middle line:90% to Britain. 00:41:08.110 --> 00:41:09.230 align:middle line:90% So like no mystery there. 00:41:09.230 --> 00:41:10.860 align:middle line:90% It's kind of the same story. 00:41:10.860 --> 00:41:13.050 align:middle line:84% This next part I found really interesting. 00:41:13.050 --> 00:41:15.140 align:middle line:84% I didn't know about this until my friend Kenji 00:41:15.140 --> 00:41:18.440 align:middle line:84% Ito helped me a lot with this, because he's originally 00:41:18.440 --> 00:41:20.210 align:middle line:90% from Tokyo. 00:41:20.210 --> 00:41:21.710 align:middle line:84% He knows the language, and he's also 00:41:21.710 --> 00:41:23.543 align:middle line:84% an expert in the history of quantum physics. 00:41:23.543 --> 00:41:26.870 align:middle line:84% We read some of Kenji's stuff I think for the paper 2 00:41:26.870 --> 00:41:27.440 align:middle line:90% assignment. 00:41:27.440 --> 00:41:28.940 align:middle line:84% So Kenji helped me a lot with this. 00:41:28.940 --> 00:41:30.380 align:middle line:84% I really learned working with him. 00:41:30.380 --> 00:41:33.155 align:middle line:84% So what happens with the spread of the diagrams in Japan 00:41:33.155 --> 00:41:34.280 align:middle line:90% after the Second World War? 00:41:34.280 --> 00:41:37.670 align:middle line:84% Here's Tomonaga, whose work I was describing earlier. 00:41:37.670 --> 00:41:39.530 align:middle line:84% It turns out Tomonaga was doing, I 00:41:39.530 --> 00:41:42.800 align:middle line:84% think, just extraordinary, kind of superhuman efforts, 00:41:42.800 --> 00:41:44.600 align:middle line:84% I think, superhuman efforts to try 00:41:44.600 --> 00:41:46.700 align:middle line:84% to rebuild the Japanese community 00:41:46.700 --> 00:41:48.560 align:middle line:84% in theoretical physics after the war. 00:41:48.560 --> 00:41:52.250 align:middle line:84% The university where he was hired had been leveled. 00:41:52.250 --> 00:41:54.890 align:middle line:84% Most of the buildings had been destroyed in the saturation 00:41:54.890 --> 00:41:56.390 align:middle line:90% firebombing of Tokyo. 00:41:56.390 --> 00:41:59.690 align:middle line:84% So he and his little group of students and advisees 00:41:59.690 --> 00:42:02.720 align:middle line:84% would meet in his home, but his home had been bombed out. 00:42:02.720 --> 00:42:04.670 align:middle line:84% So they were meeting in his Quonset hut. 00:42:04.670 --> 00:42:07.430 align:middle line:84% He literally had temporary shelter that was not 00:42:07.430 --> 00:42:08.960 align:middle line:90% meant to outlive the war. 00:42:08.960 --> 00:42:12.890 align:middle line:84% And soon after the war, amid shortages of food and paper 00:42:12.890 --> 00:42:15.650 align:middle line:84% and clothing and much else, he was 00:42:15.650 --> 00:42:18.590 align:middle line:84% working to get his own students back on track, 00:42:18.590 --> 00:42:21.260 align:middle line:84% and they would meet together in his residence, which 00:42:21.260 --> 00:42:24.525 align:middle line:84% itself was a temporary literally kind of a shell. 00:42:24.525 --> 00:42:26.900 align:middle line:84% And they returned to questions they'd been thinking about 00:42:26.900 --> 00:42:29.390 align:middle line:84% together, even during the war, things 00:42:29.390 --> 00:42:32.150 align:middle line:84% like quantum electrodynamics, virtual particles, 00:42:32.150 --> 00:42:34.070 align:middle line:90% and infinities. 00:42:34.070 --> 00:42:37.700 align:middle line:84% And they had developed soon after the war their own kinds 00:42:37.700 --> 00:42:40.670 align:middle line:84% of pencil and paper diagram bookkeepers, 00:42:40.670 --> 00:42:43.970 align:middle line:84% which Kenji found for me, and we wrote about them together, 00:42:43.970 --> 00:42:45.890 align:middle line:84% that these were in some of the kind 00:42:45.890 --> 00:42:50.450 align:middle line:84% of mimeographed early postwar publications that 00:42:50.450 --> 00:42:52.850 align:middle line:90% circulated in Japan. 00:42:52.850 --> 00:42:54.860 align:middle line:84% And these were in momentum space. 00:42:54.860 --> 00:42:56.720 align:middle line:84% They weren't space time diagrams. 00:42:56.720 --> 00:42:58.553 align:middle line:84% But they were trying to do similar things. 00:42:58.553 --> 00:43:00.470 align:middle line:84% You have all these ways that virtual particles 00:43:00.470 --> 00:43:01.580 align:middle line:90% could be involved. 00:43:01.580 --> 00:43:04.670 align:middle line:84% Here are examples of a single electron 00:43:04.670 --> 00:43:07.880 align:middle line:84% that's interacting with two separate virtual photons. 00:43:07.880 --> 00:43:09.120 align:middle line:90% How do you keep track of it? 00:43:09.120 --> 00:43:12.860 align:middle line:84% So Tomonaga and his group had invented their own techniques. 00:43:12.860 --> 00:43:15.500 align:middle line:84% Then they began getting news back from the United 00:43:15.500 --> 00:43:19.130 align:middle line:84% States after the war about Dyson's new work, 00:43:19.130 --> 00:43:24.520 align:middle line:84% not only from reading Newsweek magazine in the new occupation 00:43:24.520 --> 00:43:27.220 align:middle line:84% libraries but also because the more senior 00:43:27.220 --> 00:43:29.290 align:middle line:84% Japanese physicists, Hideki Yukawa, 00:43:29.290 --> 00:43:32.980 align:middle line:84% was actually invited to spend two years at the Institute 00:43:32.980 --> 00:43:35.620 align:middle line:84% for Advanced Study invited at the personal invitation 00:43:35.620 --> 00:43:37.030 align:middle line:90% of Robert Oppenheimer. 00:43:37.030 --> 00:43:39.790 align:middle line:84% While Yukawa was visiting is when he won the Nobel Prize 00:43:39.790 --> 00:43:42.100 align:middle line:84% for his work on nuclear physics, and he 00:43:42.100 --> 00:43:45.130 align:middle line:84% was unable to send preprints and news back to his younger 00:43:45.130 --> 00:43:46.600 align:middle line:90% colleagues in Japan. 00:43:46.600 --> 00:43:49.372 align:middle line:84% So Yukawa was learning-- he was among the people who 00:43:49.372 --> 00:43:51.580 align:middle line:84% could learn directly from Freeman Dyson and this very 00:43:51.580 --> 00:43:54.880 align:middle line:84% active group at the institute and is able to share news back 00:43:54.880 --> 00:43:57.760 align:middle line:84% with this incredible, tight knit, but somewhat separated 00:43:57.760 --> 00:43:59.320 align:middle line:90% group in Tokyo. 00:43:59.320 --> 00:44:02.440 align:middle line:84% And they basically, after a few months, 00:44:02.440 --> 00:44:06.430 align:middle line:84% kind of ditched their own momentum space diagrams 00:44:06.430 --> 00:44:09.410 align:middle line:84% and began adopting the Feynman diagrams because they were 00:44:09.410 --> 00:44:10.660 align:middle line:90% already kind of primed for it. 00:44:10.660 --> 00:44:12.970 align:middle line:84% They were already immersed in a lot of these details. 00:44:12.970 --> 00:44:15.160 align:middle line:84% They already recognized that some kind 00:44:15.160 --> 00:44:17.540 align:middle line:84% of diagrammatic bookkeeping would be important, 00:44:17.540 --> 00:44:20.980 align:middle line:84% and then they were kind of quick to go. 00:44:20.980 --> 00:44:22.890 align:middle line:84% So now you have a group in Tokyo that's 00:44:22.890 --> 00:44:25.740 align:middle line:84% really getting very intensively into this stuff. 00:44:25.740 --> 00:44:27.840 align:middle line:84% How do you spread it throughout the rest of Japan? 00:44:27.840 --> 00:44:30.480 align:middle line:84% Again, remarkable kind of coincidence. 00:44:30.480 --> 00:44:34.030 align:middle line:84% Under US occupation, the general headquarters, 00:44:34.030 --> 00:44:37.050 align:middle line:84% which is what the occupying force was called, 00:44:37.050 --> 00:44:39.780 align:middle line:84% they issued a decree right at this time 00:44:39.780 --> 00:44:42.450 align:middle line:84% to try to weaken the hold of the traditional, 00:44:42.450 --> 00:44:44.850 align:middle line:84% the so-called imperial university system 00:44:44.850 --> 00:44:46.020 align:middle line:90% throughout Japan. 00:44:46.020 --> 00:44:53.670 align:middle line:84% So the US ally occupying authorities kind of by Fiat 00:44:53.670 --> 00:44:55.920 align:middle line:84% said that every prefect, kind of like roughly speaking 00:44:55.920 --> 00:44:57.930 align:middle line:84% every state within Japan will have 00:44:57.930 --> 00:45:00.870 align:middle line:90% at least one new university. 00:45:00.870 --> 00:45:03.420 align:middle line:84% Much like in the United States, most states 00:45:03.420 --> 00:45:06.258 align:middle line:84% have at least two public universities, Michigan State 00:45:06.258 --> 00:45:07.800 align:middle line:84% and University of Michigan and so on. 00:45:07.800 --> 00:45:09.720 align:middle line:84% They wanted to do a similar thing in Japan 00:45:09.720 --> 00:45:12.360 align:middle line:84% partly to help rebuild the country 00:45:12.360 --> 00:45:14.070 align:middle line:84% and expand higher education, partly 00:45:14.070 --> 00:45:17.070 align:middle line:84% as a kind of political move to break the hold of the elites 00:45:17.070 --> 00:45:18.570 align:middle line:90% at these imperial universities. 00:45:18.570 --> 00:45:21.750 align:middle line:84% So suddenly, you have a tenfold increase 00:45:21.750 --> 00:45:23.280 align:middle line:84% in the number of universities that 00:45:23.280 --> 00:45:25.405 align:middle line:84% need to hire young physicists because they suddenly 00:45:25.405 --> 00:45:27.000 align:middle line:84% have to teach young students physics. 00:45:27.000 --> 00:45:28.923 align:middle line:84% So basically, Tomonaga's students 00:45:28.923 --> 00:45:30.840 align:middle line:84% disperse all through Japan because they're now 00:45:30.840 --> 00:45:33.840 align:middle line:84% getting hired in these newly created physics professorships. 00:45:33.840 --> 00:45:37.200 align:middle line:84% And again, you can chart when do the diagrams show up in Osaka. 00:45:37.200 --> 00:45:39.930 align:middle line:84% Oh, that's because this person just moved from Tokyo 00:45:39.930 --> 00:45:43.140 align:middle line:90% to Osaka or Kyoto and so on. 00:45:43.140 --> 00:45:44.190 align:middle line:90% Last example. 00:45:44.190 --> 00:45:46.080 align:middle line:90% What about in the Soviet Union? 00:45:46.080 --> 00:45:47.280 align:middle line:90% This is now the-- 00:45:47.280 --> 00:45:49.320 align:middle line:84% Feynman introduces these diagrams, 00:45:49.320 --> 00:45:52.630 align:middle line:84% and Dyson really helps make sense of them 00:45:52.630 --> 00:45:56.230 align:middle line:84% exactly the time that the kind of broader Cold War rivalry 00:45:56.230 --> 00:46:01.060 align:middle line:84% begins to really harden into a kind of standoff that 00:46:01.060 --> 00:46:04.420 align:middle line:84% would come to dominate the next roughly 20 years or more. 00:46:04.420 --> 00:46:06.410 align:middle line:90% So this is exactly the time. 00:46:06.410 --> 00:46:09.070 align:middle line:84% In other words, when it was very hard for journals 00:46:09.070 --> 00:46:11.590 align:middle line:84% to get back and forth and even much more difficult 00:46:11.590 --> 00:46:14.180 align:middle line:84% for individuals to travel back and forth. 00:46:14.180 --> 00:46:17.230 align:middle line:84% In fact, in this earliest period between 1948 00:46:17.230 --> 00:46:19.390 align:middle line:90% until the death of Stalin-- 00:46:19.390 --> 00:46:22.780 align:middle line:84% he died in March of '53, and about a year later, there 00:46:22.780 --> 00:46:25.660 align:middle line:84% was the first kind of tentative person 00:46:25.660 --> 00:46:27.940 align:middle line:84% to person exchanges again between scientists. 00:46:27.940 --> 00:46:31.150 align:middle line:84% There was no possibility for the kinds of personal contact 00:46:31.150 --> 00:46:33.040 align:middle line:84% that had been so important for spreading 00:46:33.040 --> 00:46:36.760 align:middle line:84% the diagrams in the United States and Britain. 00:46:36.760 --> 00:46:40.180 align:middle line:84% And maybe therefore, it helps us make sense of the fact 00:46:40.180 --> 00:46:42.880 align:middle line:84% that no diagrams were published in any of the Soviet physics 00:46:42.880 --> 00:46:45.280 align:middle line:90% journals for several years. 00:46:45.280 --> 00:46:48.410 align:middle line:84% There was a few months delay in Japan, which makes sense. 00:46:48.410 --> 00:46:52.570 align:middle line:84% And we saw how that was kind of overcome or what changed. 00:46:52.570 --> 00:46:55.210 align:middle line:84% It was actually multiple years in the case of the Soviet 00:46:55.210 --> 00:46:56.633 align:middle line:90% Union. 00:46:56.633 --> 00:46:59.050 align:middle line:84% When they did start showing up, there were just a trickle. 00:46:59.050 --> 00:47:02.560 align:middle line:84% There were literally 12 articles over the span of two years 00:47:02.560 --> 00:47:06.160 align:middle line:84% at the time when there were more than 100 in the US journal. 00:47:06.160 --> 00:47:08.290 align:middle line:84% And it turns out six of those 12 were 00:47:08.290 --> 00:47:09.610 align:middle line:90% submitted by one physicist. 00:47:09.610 --> 00:47:13.210 align:middle line:84% This was not an exponential rise in the same way 00:47:13.210 --> 00:47:14.410 align:middle line:90% at the same time. 00:47:14.410 --> 00:47:17.320 align:middle line:84% That one person who did submit them, Aleksei Galanin, 00:47:17.320 --> 00:47:19.840 align:middle line:84% had very particular reasons to learn 00:47:19.840 --> 00:47:22.125 align:middle line:84% how to calculate radiative corrections to Compton 00:47:22.125 --> 00:47:23.500 align:middle line:84% scattering because he was working 00:47:23.500 --> 00:47:25.750 align:middle line:84% on the top secret H-bomb project and had 00:47:25.750 --> 00:47:28.840 align:middle line:84% to worry about shielding for that high radiation 00:47:28.840 --> 00:47:31.990 align:middle line:84% pressure inside various H-bomb designs. 00:47:31.990 --> 00:47:35.830 align:middle line:84% He had, let's just say, special incentive 00:47:35.830 --> 00:47:38.020 align:middle line:90% to learn from Dyson's articles. 00:47:38.020 --> 00:47:40.990 align:middle line:84% When he did-- here's an example of one of Galanin's his early 00:47:40.990 --> 00:47:44.860 align:middle line:84% papers he stuck and this is not to fault him he did exactly 00:47:44.860 --> 00:47:47.620 align:middle line:84% what Dyson's articles had prepped him to do, 00:47:47.620 --> 00:47:49.660 align:middle line:90% but he didn't do any of the-- 00:47:49.660 --> 00:47:52.810 align:middle line:84% neither Galanin nor any of his immediate colleagues 00:47:52.810 --> 00:47:56.500 align:middle line:84% in the Soviet Union did any of the kind of broader more, 00:47:56.500 --> 00:48:00.730 align:middle line:84% let's just say, improvisational or more adaptive uses 00:48:00.730 --> 00:48:02.380 align:middle line:84% of the diagrams that were already 00:48:02.380 --> 00:48:04.270 align:middle line:84% becoming quite common in the United States, 00:48:04.270 --> 00:48:06.010 align:middle line:90% in Britain, and even in Japan. 00:48:06.010 --> 00:48:08.950 align:middle line:84% So you have a kind of transmission by text, 00:48:08.950 --> 00:48:12.340 align:middle line:84% it takes a lot longer, and then and the range of applications 00:48:12.340 --> 00:48:14.230 align:middle line:90% remains rather narrow. 00:48:14.230 --> 00:48:15.060 align:middle line:90% OK, let me pause. 00:48:15.060 --> 00:48:18.440 align:middle line:84% It was a long chunk, but let me pause there. 00:48:18.440 --> 00:48:21.128 align:middle line:84% I see some questions popping up in the chat. 00:48:21.128 --> 00:48:23.420 align:middle line:84% Lucas tells me the Ram's Head Inn is still in business. 00:48:23.420 --> 00:48:25.390 align:middle line:84% So once any of us can travel, we should all 00:48:25.390 --> 00:48:26.350 align:middle line:90% arrange a field trip. 00:48:26.350 --> 00:48:28.183 align:middle line:84% I'd love to see that place with my own eyes. 00:48:28.183 --> 00:48:29.932 align:middle line:84% Thank you, Lucas, for confirming. 00:48:29.932 --> 00:48:32.140 align:middle line:84% Alex says, "It's like when you get a speeding ticket, 00:48:32.140 --> 00:48:33.820 align:middle line:90% and you have to take the class." 00:48:33.820 --> 00:48:38.080 align:middle line:84% I'm not sure what that was about, but yes. 00:48:38.080 --> 00:48:40.930 align:middle line:84% Fisher says, I'd finally received [INAUDIBLE].. 00:48:40.930 --> 00:48:41.660 align:middle line:90% Oh, very good. 00:48:41.660 --> 00:48:45.130 align:middle line:84% So Feynman was, indeed, you know, [INAUDIBLE].. 00:48:45.130 --> 00:48:48.580 align:middle line:84% So Feynman was a professor at Cornell. 00:48:48.580 --> 00:48:51.722 align:middle line:90% He had finished his PhD. 00:48:51.722 --> 00:48:52.930 align:middle line:90% It's actually a little funny. 00:48:52.930 --> 00:48:56.770 align:middle line:84% He had finished the work for his PhD before leaving Princeton. 00:48:56.770 --> 00:48:58.690 align:middle line:84% He was in grad school at Princeton 00:48:58.690 --> 00:49:01.000 align:middle line:84% before leaving for Los Alamos before the war, 00:49:01.000 --> 00:49:03.220 align:middle line:84% but he hadn't formally written up his thesis yet. 00:49:03.220 --> 00:49:06.370 align:middle line:84% And then he got really busy working in the theory group 00:49:06.370 --> 00:49:07.270 align:middle line:90% at Los Alamos. 00:49:07.270 --> 00:49:10.282 align:middle line:84% So he didn't formally file his PhD dissertation 00:49:10.282 --> 00:49:12.490 align:middle line:84% until basically a few weeks after the end of the war, 00:49:12.490 --> 00:49:13.520 align:middle line:90% very soon afterwards. 00:49:13.520 --> 00:49:15.850 align:middle line:84% So he officially got his PhD, but everyone 00:49:15.850 --> 00:49:17.680 align:middle line:90% knew it was all but done. 00:49:17.680 --> 00:49:19.840 align:middle line:84% Remember, postdoc stages were not all that common. 00:49:19.840 --> 00:49:23.200 align:middle line:84% It was not that unusual to be hired straight into a faculty 00:49:23.200 --> 00:49:25.060 align:middle line:90% position from one's PhD. 00:49:25.060 --> 00:49:27.400 align:middle line:84% And everyone knew at that point that Feynman's PhD 00:49:27.400 --> 00:49:29.590 align:middle line:90% was essentially done. 00:49:29.590 --> 00:49:31.300 align:middle line:84% Moreover, he had really impressed 00:49:31.300 --> 00:49:34.240 align:middle line:84% people like Hans Bethe and Robert Oppenheimer 00:49:34.240 --> 00:49:35.320 align:middle line:90% during the war. 00:49:35.320 --> 00:49:37.750 align:middle line:84% And so he was actually being multiply recruited. 00:49:37.750 --> 00:49:41.800 align:middle line:84% I found letters-- he was made multiple faculty offers. 00:49:41.800 --> 00:49:43.690 align:middle line:84% So Oppenheimer first went back to Berkeley. 00:49:43.690 --> 00:49:45.190 align:middle line:90% He tried to hire Feynman. 00:49:45.190 --> 00:49:47.180 align:middle line:90% Bethe basically a better offer. 00:49:47.180 --> 00:49:48.850 align:middle line:84% So he was in high demand as many, many 00:49:48.850 --> 00:49:50.410 align:middle line:90% of these young physicists were. 00:49:50.410 --> 00:49:54.230 align:middle line:84% So he was starting a formally as a member of the faculty. 00:49:54.230 --> 00:49:55.570 align:middle line:90% He was still rather young. 00:49:55.570 --> 00:49:58.720 align:middle line:84% And he was relatively close in age to Freeman Dyson 00:49:58.720 --> 00:50:01.000 align:middle line:84% because Dyson had also had his studies 00:50:01.000 --> 00:50:02.320 align:middle line:90% kind of interrupted by the war. 00:50:02.320 --> 00:50:04.090 align:middle line:84% He'd worked for a couple of years 00:50:04.090 --> 00:50:10.120 align:middle line:84% in the British kind of military, basically part of the Royal Air 00:50:10.120 --> 00:50:13.630 align:middle line:84% Force doing statistical analysis of bombing runs. 00:50:13.630 --> 00:50:15.340 align:middle line:84% So they hired a lot of mathematically 00:50:15.340 --> 00:50:18.220 align:middle line:84% gifted young people to say what's the most effective way 00:50:18.220 --> 00:50:22.070 align:middle line:84% to use bombers, what's the highest kind of kill ratio, 00:50:22.070 --> 00:50:25.210 align:middle line:84% so to speak, and what yields the least 00:50:25.210 --> 00:50:27.070 align:middle line:90% losses to the British planes. 00:50:27.070 --> 00:50:29.080 align:middle line:84% So Dyson was doing a lot of statistical stuff 00:50:29.080 --> 00:50:30.130 align:middle line:90% during the war. 00:50:30.130 --> 00:50:31.760 align:middle line:90% So his own studies were delayed. 00:50:31.760 --> 00:50:33.605 align:middle line:84% So they were pretty close in age, 00:50:33.605 --> 00:50:35.980 align:middle line:84% even though they were at kind of different career stages. 00:50:35.980 --> 00:50:39.773 align:middle line:84% And Alex confirms that you have to take a class-- 00:50:39.773 --> 00:50:42.190 align:middle line:84% would be like having to sit through Schwinger's eight hour 00:50:42.190 --> 00:50:42.690 align:middle line:90% lecture. 00:50:42.690 --> 00:50:43.540 align:middle line:90% That's right. 00:50:43.540 --> 00:50:45.820 align:middle line:84% I've seen the lecture notes that I 00:50:45.820 --> 00:50:48.820 align:middle line:84% think it was John Wheeler took on Schwinger's lecture there, 00:50:48.820 --> 00:50:50.530 align:middle line:90% and they really they were-- 00:50:50.530 --> 00:50:52.043 align:middle line:90% they were beautiful, polished. 00:50:52.043 --> 00:50:53.710 align:middle line:84% Like Schwinger had thought this through. 00:50:53.710 --> 00:50:55.850 align:middle line:84% He wasn't hemming and hawing for eight hours. 00:50:55.850 --> 00:50:57.430 align:middle line:84% So the contrast with Feynman just 00:50:57.430 --> 00:50:59.410 align:middle line:84% like winging it for 30 minutes was, 00:50:59.410 --> 00:51:01.360 align:middle line:90% I think, all the more stark. 00:51:01.360 --> 00:51:03.360 align:middle line:84% But any other questions on any of that material, 00:51:03.360 --> 00:51:06.660 align:middle line:84% the early postdoc cascade or anything like that? 00:51:06.660 --> 00:51:12.070 align:middle line:90% 00:51:12.070 --> 00:51:13.870 align:middle line:90% OK, I will press on. 00:51:13.870 --> 00:51:18.870 align:middle line:84% But as usual, please jump in if other questions come up. 00:51:18.870 --> 00:51:21.370 align:middle line:84% I'm going to talk next about what were people actually doing 00:51:21.370 --> 00:51:22.930 align:middle line:84% with these diagrams, and this will 00:51:22.930 --> 00:51:24.670 align:middle line:84% connect with one of the articles that I 00:51:24.670 --> 00:51:26.900 align:middle line:90% assigned for today's reading. 00:51:26.900 --> 00:51:29.110 align:middle line:84% So remember that second meaning of dispersion 00:51:29.110 --> 00:51:31.810 align:middle line:84% is to get more and more distinct from each other, 00:51:31.810 --> 00:51:34.570 align:middle line:84% like the single beam of light separating 00:51:34.570 --> 00:51:37.570 align:middle line:84% into the distinct colors of the rainbow. 00:51:37.570 --> 00:51:40.030 align:middle line:84% So this picture of how they spread 00:51:40.030 --> 00:51:42.480 align:middle line:84% doesn't really capture what people were doing with them. 00:51:42.480 --> 00:51:45.190 align:middle line:84% And in fact, as we'll talk about in this part, 00:51:45.190 --> 00:51:48.820 align:middle line:84% people got actually pretty creative in putting 00:51:48.820 --> 00:51:52.250 align:middle line:84% the diagrams to a range of different uses. 00:51:52.250 --> 00:51:54.730 align:middle line:84% And so that had a few different seeds, 00:51:54.730 --> 00:51:57.302 align:middle line:84% what was driving the kind of distinctiveness of what 00:51:57.302 --> 00:51:58.510 align:middle line:90% people did with the diagrams. 00:51:58.510 --> 00:52:00.490 align:middle line:90% There were a couple ingredients. 00:52:00.490 --> 00:52:03.670 align:middle line:84% One of them was that Feynman and Dyson themselves actually held 00:52:03.670 --> 00:52:06.490 align:middle line:84% pretty different ideas about what the diagrams really 00:52:06.490 --> 00:52:10.100 align:middle line:84% represented or how they should properly be interpreted. 00:52:10.100 --> 00:52:13.430 align:middle line:84% So Feynman always talked about them as intuitive pictures, 00:52:13.430 --> 00:52:14.690 align:middle line:90% and I think that's fair. 00:52:14.690 --> 00:52:16.380 align:middle line:84% We can see where it's coming from. 00:52:16.380 --> 00:52:18.530 align:middle line:84% This is a story that he would often 00:52:18.530 --> 00:52:21.440 align:middle line:84% act out as I tried to do in my little Zoom share. 00:52:21.440 --> 00:52:23.930 align:middle line:90% The electron spits out a photon. 00:52:23.930 --> 00:52:24.830 align:middle line:90% It recoils here. 00:52:24.830 --> 00:52:29.120 align:middle line:84% They were very kind of animated tales of things unfolding 00:52:29.120 --> 00:52:30.770 align:middle line:90% through space and time. 00:52:30.770 --> 00:52:33.320 align:middle line:84% Dyson, whose original training was actually 00:52:33.320 --> 00:52:35.270 align:middle line:84% in pure mathematics, not in physics, 00:52:35.270 --> 00:52:38.690 align:middle line:84% and throughout his career was always much more formal, much 00:52:38.690 --> 00:52:42.350 align:middle line:84% more a mathematical physicist than Feynman, Dyson 00:52:42.350 --> 00:52:45.650 align:middle line:84% cautions in his very first article on the new techniques, 00:52:45.650 --> 00:52:47.537 align:middle line:84% that these are merely graphs on paper. 00:52:47.537 --> 00:52:48.620 align:middle line:90% That's the phrase he uses. 00:52:48.620 --> 00:52:49.970 align:middle line:90% These are not pictures. 00:52:49.970 --> 00:52:51.770 align:middle line:90% They're not Minkowski diagrams. 00:52:51.770 --> 00:52:53.870 align:middle line:84% These are not literal depictions of events 00:52:53.870 --> 00:52:56.000 align:middle line:90% unfolding in space and time. 00:52:56.000 --> 00:52:58.550 align:middle line:84% What's relevant is their kind of topology 00:52:58.550 --> 00:53:01.310 align:middle line:84% that some two lines connect here in a vertex. 00:53:01.310 --> 00:53:02.960 align:middle line:84% Two other lines connect over here, 00:53:02.960 --> 00:53:05.840 align:middle line:84% and there are only so many ways to arrange various lines 00:53:05.840 --> 00:53:06.680 align:middle line:90% and vertices. 00:53:06.680 --> 00:53:09.530 align:middle line:84% It was for him more like a kind of mathematician's graph 00:53:09.530 --> 00:53:10.110 align:middle line:90% theory. 00:53:10.110 --> 00:53:12.568 align:middle line:84% So from the beginning, you're getting kind of mixed signals 00:53:12.568 --> 00:53:14.480 align:middle line:84% about what these diagrams are all about. 00:53:14.480 --> 00:53:16.980 align:middle line:84% Even more important-- and this is what we'll talk more about 00:53:16.980 --> 00:53:19.423 align:middle line:90% in this next part-- 00:53:19.423 --> 00:53:20.840 align:middle line:84% was that the questions that seemed 00:53:20.840 --> 00:53:24.140 align:middle line:84% most pressing toward which many, many people tried 00:53:24.140 --> 00:53:26.720 align:middle line:84% to put these diagrams for use actually 00:53:26.720 --> 00:53:29.210 align:middle line:84% were not the problem area for which they'd first 00:53:29.210 --> 00:53:30.320 align:middle line:90% been introduced. 00:53:30.320 --> 00:53:32.540 align:middle line:84% So these were introduced in the context 00:53:32.540 --> 00:53:36.080 align:middle line:84% of quantum electrodynamics, meaning electrons, positrons, 00:53:36.080 --> 00:53:38.840 align:middle line:84% photons, every interaction of which 00:53:38.840 --> 00:53:40.980 align:middle line:84% is governed by the electric charge. 00:53:40.980 --> 00:53:43.580 align:middle line:84% When I say that the electron has a certain likelihood 00:53:43.580 --> 00:53:47.630 align:middle line:84% to emit a virtual photon, that likelihood quantitatively 00:53:47.630 --> 00:53:50.570 align:middle line:84% is governed by what we call its coupling constant, which 00:53:50.570 --> 00:53:52.470 align:middle line:84% is just to say its electric charge. 00:53:52.470 --> 00:53:54.860 align:middle line:84% So what that means pictorially is 00:53:54.860 --> 00:53:58.010 align:middle line:84% every one of these red dots where, say, electron lines meet 00:53:58.010 --> 00:54:00.410 align:middle line:84% a photon line, every time these lines literally connect 00:54:00.410 --> 00:54:04.580 align:middle line:84% in a vertex, the corresponding algebraic expression is 00:54:04.580 --> 00:54:08.630 align:middle line:84% multiplied by one factor of that coefficient, 00:54:08.630 --> 00:54:09.800 align:middle line:90% the electric charge. 00:54:09.800 --> 00:54:11.505 align:middle line:84% And then the lines meet again here. 00:54:11.505 --> 00:54:12.630 align:middle line:90% So there's a second factor. 00:54:12.630 --> 00:54:16.310 align:middle line:84% This is in e squared diagram, we say our second order diagram. 00:54:16.310 --> 00:54:18.350 align:middle line:84% This one is a more complicated diagram. 00:54:18.350 --> 00:54:21.170 align:middle line:84% There are four spots where electron lines 00:54:21.170 --> 00:54:24.230 align:middle line:84% hit photon lines, or vice versa, four red circles. 00:54:24.230 --> 00:54:26.000 align:middle line:84% That's an e to the fourth diagram. 00:54:26.000 --> 00:54:28.882 align:middle line:84% The algebra in front of the long-- 00:54:28.882 --> 00:54:30.590 align:middle line:84% excuse me, the coefficient, I should say, 00:54:30.590 --> 00:54:33.560 align:middle line:84% in front of the long algebra would have four factors 00:54:33.560 --> 00:54:35.600 align:middle line:90% of this constant number e. 00:54:35.600 --> 00:54:37.490 align:middle line:84% Here is an example of a tenth order 00:54:37.490 --> 00:54:39.920 align:middle line:84% diagram, where you're trading five virtual photons 00:54:39.920 --> 00:54:41.300 align:middle line:90% as an e to the 10th. 00:54:41.300 --> 00:54:44.990 align:middle line:84% Now, it turns out that in natural units, 00:54:44.990 --> 00:54:47.630 align:middle line:84% the charge of the electron is small. 00:54:47.630 --> 00:54:51.170 align:middle line:84% Electricity is a weakly coupled force. 00:54:51.170 --> 00:54:54.850 align:middle line:84% In particular, e squared is about 1 over 137 00:54:54.850 --> 00:54:57.320 align:middle line:90% in these kind of natural units. 00:54:57.320 --> 00:55:02.210 align:middle line:90% So it's smaller than 1 over 100. 00:55:02.210 --> 00:55:05.570 align:middle line:84% So this diagram is multiplied by a number 00:55:05.570 --> 00:55:08.600 align:middle line:84% that's 100 times smaller than this diagram. 00:55:08.600 --> 00:55:11.300 align:middle line:84% No matter what the algebra is, its coefficient 00:55:11.300 --> 00:55:14.960 align:middle line:84% is parametrically smaller, which means this diagram is 00:55:14.960 --> 00:55:16.910 align:middle line:90% exponentially smaller still. 00:55:16.910 --> 00:55:20.360 align:middle line:84% So that's why these things became so useful in QED. 00:55:20.360 --> 00:55:22.880 align:middle line:84% You didn't have to calculate to infinity. 00:55:22.880 --> 00:55:25.700 align:middle line:84% These two electrons could have traded an infinite number 00:55:25.700 --> 00:55:28.430 align:middle line:84% of virtual particles, but the more complicated 00:55:28.430 --> 00:55:32.780 align:middle line:84% the interaction, the more places where blue electron lines would 00:55:32.780 --> 00:55:36.110 align:middle line:84% connect with these kind of neon green photon lines, 00:55:36.110 --> 00:55:39.450 align:middle line:84% the more powers of that small number would come out in front. 00:55:39.450 --> 00:55:41.360 align:middle line:84% So as a practical matter, you could stop. 00:55:41.360 --> 00:55:44.670 align:middle line:84% This is a perturbation theory calculation, 00:55:44.670 --> 00:55:47.600 align:middle line:84% kind of tailor expanding, and each additional contribution 00:55:47.600 --> 00:55:49.190 align:middle line:90% weighs less quantitatively. 00:55:49.190 --> 00:55:50.420 align:middle line:90% OK, so that's great. 00:55:50.420 --> 00:55:51.530 align:middle line:90% It's a great bookkeeper. 00:55:51.530 --> 00:55:53.270 align:middle line:90% None of that works. 00:55:53.270 --> 00:55:55.670 align:middle line:84% None of that works when you apply these 00:55:55.670 --> 00:55:57.770 align:middle line:84% to strongly interacting particles. 00:55:57.770 --> 00:56:00.260 align:middle line:84% And guess what most physicists in the United States 00:56:00.260 --> 00:56:01.190 align:middle line:90% applied them to. 00:56:01.190 --> 00:56:02.900 align:middle line:90% Strongly interacting particles. 00:56:02.900 --> 00:56:04.520 align:middle line:90% It makes no sense at all. 00:56:04.520 --> 00:56:07.400 align:middle line:84% They applied it to the scattering of, say, protons off 00:56:07.400 --> 00:56:11.420 align:middle line:84% of pi mesons or neutrons off of other particles coming out 00:56:11.420 --> 00:56:13.010 align:middle line:90% of the new accelerators. 00:56:13.010 --> 00:56:16.130 align:middle line:84% The equivalent, the analog of the electric charge 00:56:16.130 --> 00:56:18.590 align:middle line:84% for those nuclear forces was strong 00:56:18.590 --> 00:56:20.510 align:middle line:90% in the same natural units. 00:56:20.510 --> 00:56:22.730 align:middle line:84% In fact, it's larger than 10, which 00:56:22.730 --> 00:56:24.830 align:middle line:84% means that this diagram counts exponentially 00:56:24.830 --> 00:56:26.930 align:middle line:84% more than this diagram, and there's 00:56:26.930 --> 00:56:28.100 align:middle line:90% an infinite number of them. 00:56:28.100 --> 00:56:30.428 align:middle line:84% So they're not doing perturbation theory. 00:56:30.428 --> 00:56:31.970 align:middle line:84% And yet they're still using diagrams. 00:56:31.970 --> 00:56:33.650 align:middle line:90% That is pretty strange. 00:56:33.650 --> 00:56:38.330 align:middle line:84% So that leads to this kind of real kind of explosion 00:56:38.330 --> 00:56:41.120 align:middle line:84% in how people adapted the diagrams, often even just 00:56:41.120 --> 00:56:44.000 align:middle line:84% the pictorial form of the diagrams themselves 00:56:44.000 --> 00:56:46.400 align:middle line:84% because they weren't just doing one cookie cutter thing. 00:56:46.400 --> 00:56:49.340 align:middle line:84% They weren't all doing Feynman-Dyson perturbation 00:56:49.340 --> 00:56:51.710 align:middle line:90% theory for electromagnetism. 00:56:51.710 --> 00:56:54.110 align:middle line:84% They were mostly applying it to nuclear forces. 00:56:54.110 --> 00:56:57.050 align:middle line:84% You can't just do the same trick for nuclear forces 00:56:57.050 --> 00:56:59.240 align:middle line:84% because the coupling constant is so large, 00:56:59.240 --> 00:57:01.920 align:middle line:84% but people still found useful things. 00:57:01.920 --> 00:57:03.835 align:middle line:84% So the diagrams are taking off exponentially, 00:57:03.835 --> 00:57:05.210 align:middle line:84% even though they're applying them 00:57:05.210 --> 00:57:07.680 align:middle line:84% to new and different kinds of applications. 00:57:07.680 --> 00:57:09.260 align:middle line:84% So this looks kind of scattershot. 00:57:09.260 --> 00:57:11.000 align:middle line:90% It's meant to be scattershot. 00:57:11.000 --> 00:57:13.850 align:middle line:84% We begin to get some order once we come back 00:57:13.850 --> 00:57:15.380 align:middle line:90% to asking about who knew whom. 00:57:15.380 --> 00:57:18.050 align:middle line:84% In particular, who was learning from whom? 00:57:18.050 --> 00:57:19.560 align:middle line:90% Who was studying with whom? 00:57:19.560 --> 00:57:22.790 align:middle line:84% So I call these kind of family resemblances. 00:57:22.790 --> 00:57:26.810 align:middle line:84% In each of these colored rectangles, 00:57:26.810 --> 00:57:30.380 align:middle line:84% the diagram that's a little elevated on the left 00:57:30.380 --> 00:57:33.080 align:middle line:84% comes from the PhD advisor of the person whose 00:57:33.080 --> 00:57:34.310 align:middle line:90% diagram appears on the right. 00:57:34.310 --> 00:57:36.770 align:middle line:84% These are literally mentor-student relationships. 00:57:36.770 --> 00:57:39.590 align:middle line:84% I used to try to play this kind of parlor game 00:57:39.590 --> 00:57:43.850 align:middle line:84% when I could go to parlors, like choose any random Feynman 00:57:43.850 --> 00:57:45.470 align:middle line:84% diagram from the Physical Review, 00:57:45.470 --> 00:57:47.330 align:middle line:84% at least up through the mid '50s. 00:57:47.330 --> 00:57:50.090 align:middle line:84% And with reasonable accuracy I at least would claim 00:57:50.090 --> 00:57:52.340 align:middle line:84% I could tell you who drew it or at least what 00:57:52.340 --> 00:57:54.200 align:middle line:90% PhD program they came from. 00:57:54.200 --> 00:57:55.100 align:middle line:90% It was pretty good. 00:57:55.100 --> 00:57:58.130 align:middle line:84% Now, there may be more useful life skills to train oneself 00:57:58.130 --> 00:57:59.570 align:middle line:84% on, but that was my way into this. 00:57:59.570 --> 00:58:02.150 align:middle line:84% So you could literally see oh, that's 00:58:02.150 --> 00:58:07.400 align:middle line:84% a Richard Feynman student, but this over here, that's actually 00:58:07.400 --> 00:58:09.620 align:middle line:84% a Norman Crowell student, or this one over here, 00:58:09.620 --> 00:58:12.840 align:middle line:84% that person was trained by Robert Marshak and so on. 00:58:12.840 --> 00:58:15.390 align:middle line:84% You can see these local adaptations 00:58:15.390 --> 00:58:17.430 align:middle line:84% because these different departments or members 00:58:17.430 --> 00:58:19.320 align:middle line:84% of these different departments were actually 00:58:19.320 --> 00:58:21.630 align:middle line:84% doing different things with the diagrams, often set 00:58:21.630 --> 00:58:24.730 align:middle line:90% by local demands or priorities. 00:58:24.730 --> 00:58:28.440 align:middle line:84% So for example, at Rochester in upstate New York, not too, 00:58:28.440 --> 00:58:30.930 align:middle line:84% too far from Ithaca, but far enough, 00:58:30.930 --> 00:58:34.110 align:middle line:84% they had just received, much like MIT had done, 00:58:34.110 --> 00:58:37.560 align:middle line:84% funding to build their own small particle accelerator, much 00:58:37.560 --> 00:58:39.540 align:middle line:90% like MIT synchrotron. 00:58:39.540 --> 00:58:43.020 align:middle line:84% So the theorists there, their main task 00:58:43.020 --> 00:58:45.990 align:middle line:84% was to help make sense of all the new kinds of particles 00:58:45.990 --> 00:58:47.490 align:middle line:84% that kept shooting out every time 00:58:47.490 --> 00:58:48.840 align:middle line:90% they turned that machine on. 00:58:48.840 --> 00:58:51.180 align:middle line:84% They weren't worrying about these very fancy 00:58:51.180 --> 00:58:52.650 align:middle line:90% virtual particle corrections. 00:58:52.650 --> 00:58:54.930 align:middle line:84% There were no single virtual particle or not 00:58:54.930 --> 00:58:58.030 align:middle line:84% these so-called loop corrections that led to all the trouble. 00:58:58.030 --> 00:58:59.820 align:middle line:84% It was really a way of classifying 00:58:59.820 --> 00:59:01.078 align:middle line:90% what goes with what. 00:59:01.078 --> 00:59:03.120 align:middle line:84% When these two things smash into each other, what 00:59:03.120 --> 00:59:04.680 align:middle line:90% kinds of detritus comes out? 00:59:04.680 --> 00:59:08.790 align:middle line:84% It's classification, rather than kind of dynamics. 00:59:08.790 --> 00:59:10.800 align:middle line:84% These people were applying the diagrams 00:59:10.800 --> 00:59:14.820 align:middle line:84% not to high energy physics but actually to many body theory 00:59:14.820 --> 00:59:17.250 align:middle line:84% and what would become known as condensed matter physics. 00:59:17.250 --> 00:59:19.630 align:middle line:84% What happens when two things are near each other 00:59:19.630 --> 00:59:23.430 align:middle line:84% and the same two particles keep trading force carrying 00:59:23.430 --> 00:59:24.690 align:middle line:90% particles over and over again? 00:59:24.690 --> 00:59:26.640 align:middle line:90% How do you add up that effect? 00:59:26.640 --> 00:59:29.040 align:middle line:84% That might be something like a kind of bound state 00:59:29.040 --> 00:59:31.560 align:middle line:84% or some stable system, different kind of challenge 00:59:31.560 --> 00:59:32.680 align:middle line:90% they were working toward. 00:59:32.680 --> 00:59:35.940 align:middle line:84% So you can start seeing the kind of local variation 00:59:35.940 --> 00:59:38.148 align:middle line:84% in who's using the diagrams toward what ends. 00:59:38.148 --> 00:59:39.690 align:middle line:84% And now let me talk briefly about one 00:59:39.690 --> 00:59:41.910 align:middle line:84% of the even further kind of excursions 00:59:41.910 --> 00:59:44.460 align:middle line:84% or even more creative reinterpretations 00:59:44.460 --> 00:59:48.150 align:middle line:84% that I wrote about in one of the articles for today 00:59:48.150 --> 00:59:50.490 align:middle line:90% a little bit later in time. 00:59:50.490 --> 00:59:53.120 align:middle line:84% And this focuses on the work from Geoffrey Chew. 00:59:53.120 --> 00:59:54.870 align:middle line:84% He's the one shown here at the blackboard. 00:59:54.870 --> 00:59:58.770 align:middle line:84% He was the kind of main theoretical high-energy 00:59:58.770 --> 01:00:00.750 align:middle line:84% physicist at the University of California 01:00:00.750 --> 01:00:06.960 align:middle line:84% Berkeley over the '50s and into the '60s, most of the '60s. 01:00:06.960 --> 01:00:09.960 align:middle line:84% So he was, like many of his colleagues, 01:00:09.960 --> 01:00:13.080 align:middle line:84% really interested in nuclear forces, not electrodynamics, 01:00:13.080 --> 01:00:15.010 align:middle line:84% but all these many particles coming out 01:00:15.010 --> 01:00:17.010 align:middle line:84% of these big accelerators and all different ways 01:00:17.010 --> 01:00:19.020 align:middle line:84% they could interact with each other. 01:00:19.020 --> 01:00:20.910 align:middle line:84% He knew as well as all of them did 01:00:20.910 --> 01:00:23.040 align:middle line:84% that faced with a large coupling constant, 01:00:23.040 --> 01:00:26.020 align:middle line:84% you can't do this kind of perturbation theory. 01:00:26.020 --> 01:00:27.960 align:middle line:84% And yet there's all this other things 01:00:27.960 --> 01:00:29.940 align:middle line:84% that one might try to do to make sense 01:00:29.940 --> 01:00:34.710 align:middle line:84% of all the new empirical riches coming from the new machines. 01:00:34.710 --> 01:00:38.160 align:middle line:84% So he actually becomes so frustrated with quantum field 01:00:38.160 --> 01:00:40.740 align:middle line:84% theory, precisely because it seems not up 01:00:40.740 --> 01:00:43.770 align:middle line:84% to the task of handling these strong nuclear forces. 01:00:43.770 --> 01:00:45.840 align:middle line:84% He says quantum field theory is dead. 01:00:45.840 --> 01:00:48.810 align:middle line:84% In fact, he says, it's sterile and destined not to die 01:00:48.810 --> 01:00:50.340 align:middle line:90% but just to fade away. 01:00:50.340 --> 01:00:52.440 align:middle line:84% And yet the diagrams, he says, hold 01:00:52.440 --> 01:00:54.010 align:middle line:90% a real key to moving forward. 01:00:54.010 --> 01:00:57.480 align:middle line:84% So he tries to lift the diagrams out of quantum field theory 01:00:57.480 --> 01:01:00.570 align:middle line:84% and toss away what had been used actually to derive them 01:01:00.570 --> 01:01:02.075 align:middle line:90% in the first place. 01:01:02.075 --> 01:01:03.450 align:middle line:84% That's a pretty interesting move. 01:01:03.450 --> 01:01:07.170 align:middle line:90% 01:01:07.170 --> 01:01:10.500 align:middle line:84% In its place, he starts talking about something he called-- he 01:01:10.500 --> 01:01:12.960 align:middle line:84% and his students called a nuclear democracy 01:01:12.960 --> 01:01:14.293 align:middle line:90% and eventually the bootstrap. 01:01:14.293 --> 01:01:16.710 align:middle line:84% And the idea was to treat all of these nuclear particles-- 01:01:16.710 --> 01:01:20.130 align:middle line:84% by this point, more than 100 of them have been identified-- 01:01:20.130 --> 01:01:22.710 align:middle line:84% treat them all as being on an equal footing. 01:01:22.710 --> 01:01:24.240 align:middle line:90% Why was that so radical? 01:01:24.240 --> 01:01:26.790 align:middle line:84% According to ordinary quantum field theory, 01:01:26.790 --> 01:01:28.710 align:middle line:84% you start out with a very different picture. 01:01:28.710 --> 01:01:31.320 align:middle line:84% You have certain so-called elementary particles, 01:01:31.320 --> 01:01:34.170 align:middle line:84% and some of them might stick together and make bound states 01:01:34.170 --> 01:01:35.370 align:middle line:90% or composites. 01:01:35.370 --> 01:01:38.220 align:middle line:84% But some are more special than others. 01:01:38.220 --> 01:01:39.990 align:middle line:84% He actually called that an aristocracy 01:01:39.990 --> 01:01:42.300 align:middle line:84% or a kind of elitism or hierarchy. 01:01:42.300 --> 01:01:45.820 align:middle line:84% And he said maybe with 100 plus nuclear particles, 01:01:45.820 --> 01:01:48.340 align:middle line:84% let's not try to them into which ones are really special 01:01:48.340 --> 01:01:49.257 align:middle line:90% and which ones aren't. 01:01:49.257 --> 01:01:50.830 align:middle line:84% They all seem to fly out together. 01:01:50.830 --> 01:01:52.800 align:middle line:84% Let's assume they're all equally special, 01:01:52.800 --> 01:01:56.010 align:middle line:84% treat them all on the same footing, a democracy. 01:01:56.010 --> 01:02:00.350 align:middle line:84% Now, this was unfolding, as I wrote about in the essay, 01:02:00.350 --> 01:02:02.100 align:middle line:84% at a time when he was very concerned about 01:02:02.100 --> 01:02:04.890 align:middle line:84% if other forms of democracy, a slightly more literal form 01:02:04.890 --> 01:02:08.200 align:middle line:84% involving people and fair treatment of people, 01:02:08.200 --> 01:02:11.418 align:middle line:84% amid the early stages of domestic anticommunism, 01:02:11.418 --> 01:02:13.460 align:middle line:84% the so-called McCarthy era, which we talked about 01:02:13.460 --> 01:02:15.040 align:middle line:90% some weeks ago in this class. 01:02:15.040 --> 01:02:17.228 align:middle line:84% In fact, he was the first professor 01:02:17.228 --> 01:02:19.270 align:middle line:84% to resign from the physics department and perhaps 01:02:19.270 --> 01:02:22.210 align:middle line:84% the first one from the entire University of California 01:02:22.210 --> 01:02:27.010 align:middle line:84% Berkeley campus to resign in 1949 over a kind of loyalty 01:02:27.010 --> 01:02:29.510 align:middle line:90% oath controversy. 01:02:29.510 --> 01:02:32.170 align:middle line:90% 01:02:32.170 --> 01:02:34.635 align:middle line:90% He got clearance during the war. 01:02:34.635 --> 01:02:36.010 align:middle line:84% There was no question that he had 01:02:36.010 --> 01:02:39.100 align:middle line:84% any kind of communist association in his past, 01:02:39.100 --> 01:02:41.980 align:middle line:84% but he thought on principle, it was simply un-American 01:02:41.980 --> 01:02:44.870 align:middle line:84% in his estimation to demand that people swear 01:02:44.870 --> 01:02:46.600 align:middle line:90% a kind of political allegiance. 01:02:46.600 --> 01:02:50.170 align:middle line:84% That was a violation of people's free political consciences. 01:02:50.170 --> 01:02:53.050 align:middle line:84% So he resigned because the university started 01:02:53.050 --> 01:02:56.802 align:middle line:84% requiring these anti-communist loyalty oaths, 01:02:56.802 --> 01:02:57.760 align:middle line:90% and he said, forget it. 01:02:57.760 --> 01:02:59.510 align:middle line:84% He was immediately hired at the University 01:02:59.510 --> 01:03:02.770 align:middle line:84% of Urbana-Champaign, University of Illinois, Urbana-Champaign. 01:03:02.770 --> 01:03:04.270 align:middle line:84% And he got more and more involved 01:03:04.270 --> 01:03:07.630 align:middle line:84% with political efforts on behalf of similar physics groups. 01:03:07.630 --> 01:03:10.102 align:middle line:84% He testified before the US Congress and so on. 01:03:10.102 --> 01:03:11.560 align:middle line:84% And what's interesting is if you go 01:03:11.560 --> 01:03:13.390 align:middle line:84% through his testimony and his op eds 01:03:13.390 --> 01:03:15.670 align:middle line:84% and his other publications from this period, 01:03:15.670 --> 01:03:18.940 align:middle line:84% you see that same language recur about a kind 01:03:18.940 --> 01:03:20.260 align:middle line:90% of Democratic treatment. 01:03:20.260 --> 01:03:23.860 align:middle line:84% No one and no nuclear particle deserves special status. 01:03:23.860 --> 01:03:26.752 align:middle line:84% They should all be treated as equal partners under the law. 01:03:26.752 --> 01:03:28.460 align:middle line:84% And I write more about that in the essay, 01:03:28.460 --> 01:03:29.740 align:middle line:90% but that's the kind of gist. 01:03:29.740 --> 01:03:31.540 align:middle line:84% He's using this language of treat everyone 01:03:31.540 --> 01:03:34.730 align:middle line:84% the same in a lot of domains around the same time. 01:03:34.730 --> 01:03:36.670 align:middle line:84% So why does he think these Feynman diagrams 01:03:36.670 --> 01:03:37.780 align:middle line:90% might be the way forward? 01:03:37.780 --> 01:03:39.863 align:middle line:84% What does he want to do with them in this new kind 01:03:39.863 --> 01:03:41.890 align:middle line:90% of so-called democracy? 01:03:41.890 --> 01:03:44.770 align:middle line:84% Well, he says that the diagrams seem 01:03:44.770 --> 01:03:47.860 align:middle line:84% to hold more content than quantum field theory. 01:03:47.860 --> 01:03:50.710 align:middle line:84% So let's see where the diagrams themselves will lead us. 01:03:50.710 --> 01:03:54.370 align:middle line:84% In this orientation of a simple-looking Feynman diagram, 01:03:54.370 --> 01:03:56.110 align:middle line:84% this rho meson, which had actually 01:03:56.110 --> 01:03:59.320 align:middle line:84% just been identified by some of his experimentalist colleagues 01:03:59.320 --> 01:04:05.360 align:middle line:84% not long before, this shows two pions exchanging aromas on. 01:04:05.360 --> 01:04:07.210 align:middle line:84% So the rho is a kind of force carrier, 01:04:07.210 --> 01:04:09.340 align:middle line:84% much like say a virtual photon would be a force 01:04:09.340 --> 01:04:11.830 align:middle line:90% carrier in a QED diagram. 01:04:11.830 --> 01:04:13.780 align:middle line:84% But if you just rotate that diagram, 01:04:13.780 --> 01:04:16.420 align:middle line:84% literally turn it on its side, then 01:04:16.420 --> 01:04:17.980 align:middle line:90% you tell a very different story. 01:04:17.980 --> 01:04:20.890 align:middle line:84% You see two pi mesons brought together. 01:04:20.890 --> 01:04:23.590 align:middle line:84% They were attracted because they felt a force. 01:04:23.590 --> 01:04:25.510 align:middle line:84% Once they approached each other, they actually 01:04:25.510 --> 01:04:28.810 align:middle line:84% can create a temporary bound state of the rho meson. 01:04:28.810 --> 01:04:33.490 align:middle line:84% It's an unstable particle, so the rho meson later will then 01:04:33.490 --> 01:04:35.380 align:middle line:90% decay into a pair of pions. 01:04:35.380 --> 01:04:37.870 align:middle line:84% And that just comes from rotating the same diagram. 01:04:37.870 --> 01:04:40.810 align:middle line:84% Meanwhile, once you create some rho mesons this way, 01:04:40.810 --> 01:04:43.420 align:middle line:84% they can be involved in all kinds of other interactions 01:04:43.420 --> 01:04:46.240 align:middle line:84% where they would appear as a so-called elementary particle. 01:04:46.240 --> 01:04:48.790 align:middle line:84% So the status of the particle type 01:04:48.790 --> 01:04:51.640 align:middle line:84% seems to have changed just by rotating these very 01:04:51.640 --> 01:04:53.530 align:middle line:90% simple looking line drawings. 01:04:53.530 --> 01:04:55.090 align:middle line:84% And so Geoffrey Chew said basically 01:04:55.090 --> 01:04:57.130 align:middle line:84% let's take the diagrams at face value. 01:04:57.130 --> 01:05:00.100 align:middle line:84% If they make no distinction between these different kinds 01:05:00.100 --> 01:05:02.350 align:middle line:84% of roles or hierarchies, what's truly 01:05:02.350 --> 01:05:06.110 align:middle line:84% elementary versus composite, then why should our equations? 01:05:06.110 --> 01:05:07.930 align:middle line:84% So he wanted to build a new approach 01:05:07.930 --> 01:05:12.670 align:middle line:84% to a quantitative approach to the nuclear forces following 01:05:12.670 --> 01:05:14.470 align:middle line:84% these kind of diagram-based symmetries, 01:05:14.470 --> 01:05:16.120 align:middle line:84% rather than quantum field theory. 01:05:16.120 --> 01:05:18.250 align:middle line:84% And they went even further, saying what 01:05:18.250 --> 01:05:22.120 align:middle line:84% if every single particle was a kind of self-consistent state? 01:05:22.120 --> 01:05:25.600 align:middle line:84% They would each pull itself up by its own bootstraps, 01:05:25.600 --> 01:05:30.730 align:middle line:84% using a well known kind of American idiomatic expression. 01:05:30.730 --> 01:05:34.300 align:middle line:84% They would all be kind of self-made people. 01:05:34.300 --> 01:05:37.120 align:middle line:84% No one was born being more elementary or more elitist 01:05:37.120 --> 01:05:38.810 align:middle line:90% than others was the idea. 01:05:38.810 --> 01:05:41.230 align:middle line:84% So what if every particle like that rho meson 01:05:41.230 --> 01:05:43.600 align:middle line:84% would generate the forces that would give rise 01:05:43.600 --> 01:05:45.400 align:middle line:90% to its own production? 01:05:45.400 --> 01:05:46.720 align:middle line:90% That's pretty cool. 01:05:46.720 --> 01:05:49.540 align:middle line:84% Could there be one unique self-consistent solution 01:05:49.540 --> 01:05:51.010 align:middle line:90% to all these equations? 01:05:51.010 --> 01:05:53.470 align:middle line:84% Going back to those kind of rotated diagrams, 01:05:53.470 --> 01:05:55.690 align:middle line:84% in this example, you have some expression, 01:05:55.690 --> 01:05:59.110 align:middle line:84% some quantitative expression for the force that this rho 01:05:59.110 --> 01:06:03.280 align:middle line:84% meson exerts, an attractive force between these pi mesons. 01:06:03.280 --> 01:06:06.130 align:middle line:84% That expression will depend on the mass of the particle that's 01:06:06.130 --> 01:06:08.890 align:middle line:84% exchanged and this coupling constant, the factor that 01:06:08.890 --> 01:06:10.990 align:middle line:90% appears at every vertex. 01:06:10.990 --> 01:06:14.450 align:middle line:84% Rotate your piece of paper by 90 degrees. 01:06:14.450 --> 01:06:17.200 align:middle line:84% Now you see that once these two pions have attracted 01:06:17.200 --> 01:06:19.960 align:middle line:84% each other, thanks to that rho meson, 01:06:19.960 --> 01:06:22.060 align:middle line:90% they've formed this bound state. 01:06:22.060 --> 01:06:25.690 align:middle line:84% The odds for that to happen also has some distinct expression 01:06:25.690 --> 01:06:27.640 align:middle line:84% still only depends on two quantities, 01:06:27.640 --> 01:06:29.680 align:middle line:84% the mass of the bound state they produce 01:06:29.680 --> 01:06:31.220 align:middle line:90% and this coupling constant. 01:06:31.220 --> 01:06:34.130 align:middle line:84% So now you have two equations for two unknowns. 01:06:34.130 --> 01:06:36.748 align:middle line:84% So you can look for self-consistent solutions. 01:06:36.748 --> 01:06:38.290 align:middle line:84% And in fact, he and his students were 01:06:38.290 --> 01:06:43.000 align:middle line:84% able to publish the first compelling theoretical account 01:06:43.000 --> 01:06:46.180 align:middle line:84% of why these nuclear particles had the quantitative properties 01:06:46.180 --> 01:06:49.030 align:middle line:84% they did at a time when no one else could come even close. 01:06:49.030 --> 01:06:52.760 align:middle line:84% This is far outside the regime of perturbation theory, 01:06:52.760 --> 01:06:56.530 align:middle line:84% and here was this kind of very clever self-consistent way 01:06:56.530 --> 01:06:59.080 align:middle line:84% of using their so-called bootstrap to try 01:06:59.080 --> 01:07:02.980 align:middle line:84% to account for why the rho meson was particularly heavy 01:07:02.980 --> 01:07:05.440 align:middle line:84% and why it had this particular interaction 01:07:05.440 --> 01:07:08.150 align:middle line:90% strength with pions. 01:07:08.150 --> 01:07:09.513 align:middle line:90% So let me pause there. 01:07:09.513 --> 01:07:10.430 align:middle line:90% Any questions on that? 01:07:10.430 --> 01:07:24.930 align:middle line:90% 01:07:24.930 --> 01:07:26.070 align:middle line:90% It's just too awesome. 01:07:26.070 --> 01:07:27.515 align:middle line:90% You're stunned. 01:07:27.515 --> 01:07:28.890 align:middle line:84% You're just shocked into silence. 01:07:28.890 --> 01:07:30.057 align:middle line:90% I mean, I get that way, too. 01:07:30.057 --> 01:07:31.870 align:middle line:90% It's OK. 01:07:31.870 --> 01:07:33.870 align:middle line:84% What I mostly want to emphasize with that part-- 01:07:33.870 --> 01:07:35.130 align:middle line:90% hopefully it was clear-- 01:07:35.130 --> 01:07:40.860 align:middle line:84% was that even after Dyson did such a kind of celebrated job 01:07:40.860 --> 01:07:44.280 align:middle line:84% of clarifying exactly what Feynman diagrams should mean, 01:07:44.280 --> 01:07:47.070 align:middle line:84% exactly how they should be used in a calculation, 01:07:47.070 --> 01:07:50.580 align:middle line:84% in the years after that, that led to more different uses, 01:07:50.580 --> 01:07:52.530 align:middle line:84% rather than collapsing to only one. 01:07:52.530 --> 01:07:55.398 align:middle line:84% I found that really pretty cool actually, pretty neat. 01:07:55.398 --> 01:07:57.690 align:middle line:84% And then some people got even more ambitious with them, 01:07:57.690 --> 01:08:00.480 align:middle line:84% like the more extreme example from the Berkeley group. 01:08:00.480 --> 01:08:05.910 align:middle line:84% But even at Rochester or Urbana or in Cambridge, England, 01:08:05.910 --> 01:08:07.950 align:middle line:84% people were being very kind of-- they 01:08:07.950 --> 01:08:11.070 align:middle line:84% treated the diagrams as pretty malleable for a long time. 01:08:11.070 --> 01:08:13.380 align:middle line:90% And that was neat. 01:08:13.380 --> 01:08:15.060 align:middle line:84% It's hard to get computers to do that. 01:08:15.060 --> 01:08:17.160 align:middle line:84% Computers do one thing with these diagrams now. 01:08:17.160 --> 01:08:19.470 align:middle line:84% But for much of their history, the diagrams 01:08:19.470 --> 01:08:21.270 align:middle line:84% meant a variety of things that could 01:08:21.270 --> 01:08:22.605 align:middle line:90% be used in a variety of ways. 01:08:22.605 --> 01:08:26.540 align:middle line:90% 01:08:26.540 --> 01:08:27.823 align:middle line:90% Yeah, good, Fisher. 01:08:27.823 --> 01:08:29.990 align:middle line:84% So Fisher asks when we're talking about perturbation 01:08:29.990 --> 01:08:31.670 align:middle line:84% theory, they're referring to everything 01:08:31.670 --> 01:08:34.740 align:middle line:84% beyond the second order, beyond e squared, or everything 01:08:34.740 --> 01:08:37.010 align:middle line:90% including e squared. 01:08:37.010 --> 01:08:39.740 align:middle line:84% I guess technically, we would even include the e squared. 01:08:39.740 --> 01:08:44.000 align:middle line:84% The first term would be one, which is that nothing happens, 01:08:44.000 --> 01:08:45.750 align:middle line:90% or I should say nothing changes. 01:08:45.750 --> 01:08:48.710 align:middle line:84% So your first term in what's called the s-matrix expansion 01:08:48.710 --> 01:08:50.670 align:middle line:90% is 1 plus everything else. 01:08:50.670 --> 01:08:54.020 align:middle line:84% And so the next term, the first term to enter 01:08:54.020 --> 01:08:55.208 align:middle line:90% would then be e squared. 01:08:55.208 --> 01:08:57.500 align:middle line:84% That would be the first correction to nothing happening 01:08:57.500 --> 01:08:59.540 align:middle line:84% is you could add two electrons scatter. 01:08:59.540 --> 01:09:01.920 align:middle line:84% Then they could have scattered in more complicated ways. 01:09:01.920 --> 01:09:03.680 align:middle line:90% So it is really like Taylor-- 01:09:03.680 --> 01:09:06.240 align:middle line:84% you can think of it like Taylor expanding. 01:09:06.240 --> 01:09:11.767 align:middle line:84% And it is remarkable because it works because you 01:09:11.767 --> 01:09:13.410 align:middle line:90% have a controlled parameter. 01:09:13.410 --> 01:09:16.330 align:middle line:84% You can really do a controlled perturbation expansion. 01:09:16.330 --> 01:09:19.620 align:middle line:84% So even without calculating an arbitrarily complicated 01:09:19.620 --> 01:09:22.200 align:middle line:84% diagram, you can estimate how much would that matter 01:09:22.200 --> 01:09:23.220 align:middle line:90% quantitatively. 01:09:23.220 --> 01:09:25.359 align:middle line:84% What would be your error budget if you left it out, 01:09:25.359 --> 01:09:26.160 align:middle line:90% so to speak. 01:09:26.160 --> 01:09:28.470 align:middle line:84% And you can't do any of that using these techniques 01:09:28.470 --> 01:09:30.555 align:middle line:90% for the nuclear force. 01:09:30.555 --> 01:09:31.680 align:middle line:90% All right, let me press on. 01:09:31.680 --> 01:09:32.760 align:middle line:90% I'll talk about this last part. 01:09:32.760 --> 01:09:33.689 align:middle line:90% It'll be pretty quick. 01:09:33.689 --> 01:09:35.819 align:middle line:84% I'll try not to go for eight hours. 01:09:35.819 --> 01:09:36.660 align:middle line:90% No promises. 01:09:36.660 --> 01:09:38.700 align:middle line:84% But this last part is so why do they stick. 01:09:38.700 --> 01:09:41.439 align:middle line:84% If they're being used in so many different ways, 01:09:41.439 --> 01:09:43.680 align:middle line:84% why do people stick with them instead of design 01:09:43.680 --> 01:09:46.149 align:middle line:90% other techniques along the way? 01:09:46.149 --> 01:09:47.880 align:middle line:84% So within perturbation theory, when 01:09:47.880 --> 01:09:50.279 align:middle line:84% doing these electrodynamic calculations, 01:09:50.279 --> 01:09:52.890 align:middle line:84% I think it's pretty clear, and people spoke of it even 01:09:52.890 --> 01:09:58.860 align:middle line:84% at the time that these were just an extraordinarily useful tool. 01:09:58.860 --> 01:10:02.010 align:middle line:84% Dyson remarked years later, the calculation 01:10:02.010 --> 01:10:04.440 align:middle line:84% he first did for Hans Bethe as a grad student 01:10:04.440 --> 01:10:06.640 align:middle line:84% before learning about the diagrams 01:10:06.640 --> 01:10:09.580 align:middle line:84% took him several months of work and several hundred sheets 01:10:09.580 --> 01:10:10.323 align:middle line:90% of paper. 01:10:10.323 --> 01:10:10.990 align:middle line:90% I've been there. 01:10:10.990 --> 01:10:13.000 align:middle line:84% Dick Feynman, Richard Feynman could 01:10:13.000 --> 01:10:15.555 align:middle line:84% get the same answer calculated on the blackboard in half 01:10:15.555 --> 01:10:16.930 align:middle line:84% an hour, and that was indeed what 01:10:16.930 --> 01:10:18.520 align:middle line:90% became more and more common. 01:10:18.520 --> 01:10:23.200 align:middle line:84% Julian Schwinger said a bit more snarkily-- 01:10:23.200 --> 01:10:25.900 align:middle line:84% Schwinger and Feynman were kind of like frenemies. 01:10:25.900 --> 01:10:28.150 align:middle line:84% He said Feynman diagrams brought computation 01:10:28.150 --> 01:10:31.210 align:middle line:84% to the masses, which you could almost see Schwinger sniffing, 01:10:31.210 --> 01:10:34.190 align:middle line:84% like my students learn really how to calculate. 01:10:34.190 --> 01:10:37.155 align:middle line:84% But any old slob could calculate using Feynman's techniques. 01:10:37.155 --> 01:10:38.530 align:middle line:84% That's the spirit in which I take 01:10:38.530 --> 01:10:40.840 align:middle line:84% that remark, that these really were effective, 01:10:40.840 --> 01:10:42.940 align:middle line:84% and many, many people could calculate, 01:10:42.940 --> 01:10:45.220 align:middle line:84% even people who weren't blessed to have had Julian 01:10:45.220 --> 01:10:47.650 align:middle line:90% Schwinger as their PhD advisor. 01:10:47.650 --> 01:10:50.080 align:middle line:84% This cartoon here ran in Physics Today 01:10:50.080 --> 01:10:52.510 align:middle line:84% many years ago, basically saying if you're 01:10:52.510 --> 01:10:54.370 align:middle line:84% going to go through these dangerous thickets 01:10:54.370 --> 01:10:56.620 align:middle line:84% of perturbation theory as if you were 01:10:56.620 --> 01:10:59.020 align:middle line:84% a kind of an explorer in the Amazonian jungle, 01:10:59.020 --> 01:11:00.610 align:middle line:90% it helps to have a reliable map. 01:11:00.610 --> 01:11:02.980 align:middle line:84% And so the Feynman diagrams would be a reliable map 01:11:02.980 --> 01:11:05.380 align:middle line:84% to this complicated, seemingly dangerous, 01:11:05.380 --> 01:11:06.428 align:middle line:90% or forbidding terrain. 01:11:06.428 --> 01:11:08.470 align:middle line:84% So I think that makes sense, except as I was just 01:11:08.470 --> 01:11:12.580 align:middle line:84% emphasizing, that can't hardly be the whole story because most 01:11:12.580 --> 01:11:15.430 align:middle line:84% physicists weren't using them in the early days for what they 01:11:15.430 --> 01:11:17.530 align:middle line:84% were most good at, for what the diagrams were 01:11:17.530 --> 01:11:18.850 align:middle line:90% most efficacious for. 01:11:18.850 --> 01:11:21.040 align:middle line:84% So sure, that would explain why people use them 01:11:21.040 --> 01:11:23.500 align:middle line:84% in weakly coupled situations, but what about all 01:11:23.500 --> 01:11:24.972 align:middle line:90% these other applications? 01:11:24.972 --> 01:11:27.430 align:middle line:84% So to make sense of that, I found it very helpful actually, 01:11:27.430 --> 01:11:31.870 align:middle line:84% very fun, to go back to some classic studies in art history. 01:11:31.870 --> 01:11:35.320 align:middle line:84% These are, after all, a kind of visual representation scheme, 01:11:35.320 --> 01:11:36.850 align:middle line:84% and art historians have been arguing 01:11:36.850 --> 01:11:39.790 align:middle line:84% for a long, long, long time about why 01:11:39.790 --> 01:11:42.730 align:middle line:84% various styles in art, modes of depiction 01:11:42.730 --> 01:11:45.760 align:middle line:84% have come to seem natural or have a kind of staying power 01:11:45.760 --> 01:11:48.160 align:middle line:84% and what happens when they change. 01:11:48.160 --> 01:11:49.990 align:middle line:84% So the art historian Ernst Gombrich 01:11:49.990 --> 01:11:52.000 align:middle line:84% wrote this really lovely, very influential book 01:11:52.000 --> 01:11:56.080 align:middle line:84% many years ago, where he says that basically, his catch 01:11:56.080 --> 01:11:58.870 align:middle line:90% phrase was that painters-- 01:11:58.870 --> 01:11:59.620 align:middle line:90% how does it go? 01:11:59.620 --> 01:12:01.990 align:middle line:90% They see what they paint. 01:12:01.990 --> 01:12:03.580 align:middle line:90% They don't paint what they see. 01:12:03.580 --> 01:12:06.100 align:middle line:84% They have an idea of what they want to convey, 01:12:06.100 --> 01:12:08.800 align:middle line:84% and that structure is how they even take in the world. 01:12:08.800 --> 01:12:10.252 align:middle line:90% He kind of flips the story. 01:12:10.252 --> 01:12:11.710 align:middle line:84% You don't just look out your window 01:12:11.710 --> 01:12:13.210 align:middle line:84% and say, oh, I'll paint a landscape. 01:12:13.210 --> 01:12:15.790 align:middle line:84% You learn techniques, and then you 01:12:15.790 --> 01:12:18.670 align:middle line:84% come to see the world through the lens of those techniques, 01:12:18.670 --> 01:12:21.130 align:middle line:84% not unlike what, say, the historian of science 01:12:21.130 --> 01:12:23.030 align:middle line:84% Thomas Kuhn had argued around the same time. 01:12:23.030 --> 01:12:24.863 align:middle line:84% So these are examples of the kinds of things 01:12:24.863 --> 01:12:26.260 align:middle line:90% that Gombrich talks about. 01:12:26.260 --> 01:12:30.520 align:middle line:84% These were from training manuals in the early modern period 01:12:30.520 --> 01:12:33.160 align:middle line:84% to learn how to draw a human face. 01:12:33.160 --> 01:12:34.750 align:middle line:84% You break it down, and you literally 01:12:34.750 --> 01:12:36.940 align:middle line:84% practice drawing an eyeball over and over 01:12:36.940 --> 01:12:40.570 align:middle line:84% and over again until you see actual people through this kind 01:12:40.570 --> 01:12:43.390 align:middle line:84% of schema of how you draw an eyeball, 01:12:43.390 --> 01:12:46.030 align:middle line:84% or if you're employed by the local church, which 01:12:46.030 --> 01:12:47.590 align:middle line:84% most of them were, here's how you 01:12:47.590 --> 01:12:50.920 align:middle line:84% draw the adorable little cherubs and little baby angels. 01:12:50.920 --> 01:12:53.920 align:middle line:84% You practice drawing these chubby-cheeked faces, 01:12:53.920 --> 01:12:56.320 align:middle line:84% and you break it down and you practice and practice, 01:12:56.320 --> 01:12:58.300 align:middle line:84% like doing problem sets before you 01:12:58.300 --> 01:13:00.880 align:middle line:84% go paint the kind of latest picture 01:13:00.880 --> 01:13:04.660 align:middle line:90% to decorate the local church. 01:13:04.660 --> 01:13:06.850 align:middle line:84% And so it seemed a similar thing was happening 01:13:06.850 --> 01:13:09.370 align:middle line:84% with these scientific images, that the physicists' 01:13:09.370 --> 01:13:14.350 align:middle line:84% kind of prior habits helped them see in a new way 01:13:14.350 --> 01:13:17.860 align:middle line:84% just as if you stare-- if you practice this technique over 01:13:17.860 --> 01:13:21.160 align:middle line:84% and over again, you structure your newer experiences 01:13:21.160 --> 01:13:22.930 align:middle line:84% with a kind of scheme that you've already 01:13:22.930 --> 01:13:24.920 align:middle line:90% worked hard to master. 01:13:24.920 --> 01:13:26.920 align:middle line:84% And so these pictorial conventions 01:13:26.920 --> 01:13:30.280 align:middle line:84% can actually help us map a kind of pedagogical lineage, not 01:13:30.280 --> 01:13:31.990 align:middle line:90% necessarily a conceptual one. 01:13:31.990 --> 01:13:35.500 align:middle line:84% They were often kind of irrelevant to the new uses, 01:13:35.500 --> 01:13:38.322 align:middle line:84% but they were more a kind of social or pedagogical value. 01:13:38.322 --> 01:13:40.030 align:middle line:84% They helped you get up to speed or helped 01:13:40.030 --> 01:13:43.820 align:middle line:84% you make sense of the newer things you then wanted to do. 01:13:43.820 --> 01:13:46.880 align:middle line:84% The most significant, at least as it makes sense to me, 01:13:46.880 --> 01:13:49.070 align:middle line:84% was that people were slotting these things 01:13:49.070 --> 01:13:51.788 align:middle line:84% into a very well established tradition by that point 01:13:51.788 --> 01:13:54.080 align:middle line:84% these Minkowski diagrams, which, of course, many of you 01:13:54.080 --> 01:13:56.030 align:middle line:84% had already seen probably before this term. 01:13:56.030 --> 01:13:58.610 align:middle line:84% We spent some time looking at them together early 01:13:58.610 --> 01:14:01.730 align:middle line:84% in this semester, and we talked about special relativity, 01:14:01.730 --> 01:14:03.980 align:middle line:90% literally space time diagrams. 01:14:03.980 --> 01:14:06.290 align:middle line:84% Feynman was not shy about adopting 01:14:06.290 --> 01:14:08.570 align:middle line:84% the exact same conventions when he 01:14:08.570 --> 01:14:11.960 align:middle line:84% began he began drawing his little doodles at first kind 01:14:11.960 --> 01:14:14.150 align:middle line:84% of private sketches, not just that you 01:14:14.150 --> 01:14:16.700 align:middle line:84% have one dimension of space and one of time. 01:14:16.700 --> 01:14:18.710 align:middle line:84% He oriented space along the horizontal. 01:14:18.710 --> 01:14:20.610 align:middle line:84% There's no law that says you have to do that. 01:14:20.610 --> 01:14:23.480 align:middle line:84% He tacitly starts scaling the speed of light 01:14:23.480 --> 01:14:27.440 align:middle line:84% to be 1, so that light travels along 45 degree diagonals. 01:14:27.440 --> 01:14:30.020 align:middle line:84% He's not literally drawing space time diagrams. 01:14:30.020 --> 01:14:34.100 align:middle line:84% These have been completely kind of pedagogical second nature 01:14:34.100 --> 01:14:37.290 align:middle line:84% for generations of physicists in many, many parts of the world, 01:14:37.290 --> 01:14:40.460 align:middle line:84% not just the United States before Feynman and Dyson 01:14:40.460 --> 01:14:41.940 align:middle line:90% introduced their work. 01:14:41.940 --> 01:14:45.060 align:middle line:84% This was a kind of context in which students could then 01:14:45.060 --> 01:14:46.590 align:middle line:90% encounter Feynman diagrams. 01:14:46.590 --> 01:14:49.950 align:middle line:84% These are examples from Feynman's own work. 01:14:49.950 --> 01:14:52.710 align:middle line:84% This one and this one from his early publications, 01:14:52.710 --> 01:14:53.820 align:middle line:90% this is my favorite. 01:14:53.820 --> 01:14:56.670 align:middle line:84% This comes from one of his lecture notes at Cornell 01:14:56.670 --> 01:15:01.343 align:middle line:84% when he was lecturing in 1949 in the department. 01:15:01.343 --> 01:15:03.510 align:middle line:84% What I love is that he actually gets his own Feynman 01:15:03.510 --> 01:15:04.380 align:middle line:90% diagrams wrong. 01:15:04.380 --> 01:15:08.010 align:middle line:84% He's so enamored of this kind of storytelling space time 01:15:08.010 --> 01:15:11.010 align:middle line:84% structure that he draws diagrams that literally could not 01:15:11.010 --> 01:15:12.750 align:middle line:90% be calculated in QED. 01:15:12.750 --> 01:15:15.510 align:middle line:84% They have the wrong number of legs entering each vertex, 01:15:15.510 --> 01:15:18.720 align:middle line:84% but he got caught up trying to tell his students about how you 01:15:18.720 --> 01:15:21.300 align:middle line:84% could have pair production in QED 01:15:21.300 --> 01:15:24.150 align:middle line:84% and trying to narrate that story through space and time, 01:15:24.150 --> 01:15:25.963 align:middle line:84% and we can forgive him for forgetting 01:15:25.963 --> 01:15:28.380 align:middle line:84% that in the theory for which he'd eventually win the Nobel 01:15:28.380 --> 01:15:32.400 align:middle line:84% Prize, only two straight legs and one curvy leg 01:15:32.400 --> 01:15:33.660 align:middle line:90% can meet at each point. 01:15:33.660 --> 01:15:36.060 align:middle line:84% Oops, because there's so much bound up, 01:15:36.060 --> 01:15:40.335 align:middle line:84% I think, for Feynman in this kind of space time narrative 01:15:40.335 --> 01:15:42.960 align:middle line:84% and the trajectories of thinking moving through space and time. 01:15:42.960 --> 01:15:44.190 align:middle line:90% It wasn't only Feynman. 01:15:44.190 --> 01:15:46.140 align:middle line:84% If you look at the earliest textbooks, 01:15:46.140 --> 01:15:49.020 align:middle line:84% they keep repeating the same scheme even when 01:15:49.020 --> 01:15:51.570 align:middle line:84% they move into momentum space for which there's absolutely 01:15:51.570 --> 01:15:54.420 align:middle line:84% no meaning, no relevance whatsoever to the kind 01:15:54.420 --> 01:15:56.280 align:middle line:90% of 45-degree diagonal. 01:15:56.280 --> 01:15:59.130 align:middle line:84% That only means something if you're actually 01:15:59.130 --> 01:16:01.560 align:middle line:84% working in space time and scaling the speed of light 01:16:01.560 --> 01:16:02.370 align:middle line:90% to be one. 01:16:02.370 --> 01:16:05.580 align:middle line:84% It means nothing if you're in momentum space, 01:16:05.580 --> 01:16:08.280 align:middle line:84% and yet in these examples and many of these, 01:16:08.280 --> 01:16:12.000 align:middle line:84% physicists working explicitly in momentum space nonetheless kept 01:16:12.000 --> 01:16:14.970 align:middle line:84% using the space time Minkowski conventions. 01:16:14.970 --> 01:16:17.440 align:middle line:84% And I argue that was kind of what they were used to, 01:16:17.440 --> 01:16:19.440 align:middle line:84% and it also probably helped some of the students 01:16:19.440 --> 01:16:22.230 align:middle line:84% get kind of comfortable with them as well. 01:16:22.230 --> 01:16:24.210 align:middle line:84% There was another visual feature that, again, 01:16:24.210 --> 01:16:26.820 align:middle line:84% in terms of which these physicists were immersed 01:16:26.820 --> 01:16:30.180 align:middle line:84% at the time, and that comes from this explosion 01:16:30.180 --> 01:16:34.170 align:middle line:84% of a very large and rapid production of particle 01:16:34.170 --> 01:16:37.230 align:middle line:84% accelerators after the war funded by the Atomic Energy 01:16:37.230 --> 01:16:40.080 align:middle line:84% Commission, where many, many universities, like MIT, 01:16:40.080 --> 01:16:42.750 align:middle line:84% had their own local atom smasher. 01:16:42.750 --> 01:16:44.370 align:middle line:84% So what became common was to draw 01:16:44.370 --> 01:16:47.850 align:middle line:84% these freehand reconstructions based on the bubble chamber 01:16:47.850 --> 01:16:48.450 align:middle line:90% photographs. 01:16:48.450 --> 01:16:50.520 align:middle line:84% This was not meant to be a Feynman diagram, 01:16:50.520 --> 01:16:52.320 align:middle line:84% but it became clear because it was actually 01:16:52.320 --> 01:16:55.560 align:middle line:84% fairly expensive to keep trying to reprint the photographs. 01:16:55.560 --> 01:16:57.870 align:middle line:84% You would just reprint these often hand 01:16:57.870 --> 01:17:02.070 align:middle line:84% drawn line sketch reconstructions, which consist, 01:17:02.070 --> 01:17:05.970 align:middle line:84% like these Feynman diagrams, of propagation lines and vertices. 01:17:05.970 --> 01:17:08.700 align:middle line:84% So there was, in some sense, a kind of reinforcement 01:17:08.700 --> 01:17:11.190 align:middle line:84% of a kind of realism that had nothing 01:17:11.190 --> 01:17:15.160 align:middle line:84% to do with Freeman Dyson's very careful kind of derivation 01:17:15.160 --> 01:17:17.380 align:middle line:84% or anything about perturbation theory. 01:17:17.380 --> 01:17:18.722 align:middle line:90% So there was a kind of realism. 01:17:18.722 --> 01:17:20.680 align:middle line:84% And you see that in this quotation for example, 01:17:20.680 --> 01:17:23.490 align:middle line:84% some years later in a very influential textbook 01:17:23.490 --> 01:17:25.560 align:middle line:84% that these Feynman diagrams, Richard Mattuck 01:17:25.560 --> 01:17:28.500 align:middle line:84% wrote, are so vividly physical looking, 01:17:28.500 --> 01:17:31.290 align:middle line:84% that it seems a bit extreme to completely reject 01:17:31.290 --> 01:17:33.670 align:middle line:84% any physical interpretation whatsoever. 01:17:33.670 --> 01:17:36.750 align:middle line:84% So he does this funny kind of cheat. 01:17:36.750 --> 01:17:39.120 align:middle line:84% We will therefore talk about the diagrams 01:17:39.120 --> 01:17:42.030 align:middle line:84% as if they were physical, but remember they're not. 01:17:42.030 --> 01:17:44.460 align:middle line:84% So he can't help himself but describe them 01:17:44.460 --> 01:17:46.530 align:middle line:84% as real things moving through space and time. 01:17:46.530 --> 01:17:49.530 align:middle line:84% Other textbooks at the time reinforced that visually. 01:17:49.530 --> 01:17:52.320 align:middle line:84% If we could look, if we could really kind of zoom in 01:17:52.320 --> 01:17:55.290 align:middle line:84% with our own eye and watch these elementary processes, 01:17:55.290 --> 01:17:57.060 align:middle line:90% we would see Feynman diagrams. 01:17:57.060 --> 01:18:01.740 align:middle line:84% We wouldn't see cathode rays scattering on a scintillation 01:18:01.740 --> 01:18:02.250 align:middle line:90% screen. 01:18:02.250 --> 01:18:04.590 align:middle line:84% We would literally see nature as Feynman diagrams 01:18:04.590 --> 01:18:06.750 align:middle line:90% if we had a big microscope. 01:18:06.750 --> 01:18:08.310 align:middle line:90% OK, so let me wrap up. 01:18:08.310 --> 01:18:12.000 align:middle line:84% So scientists then and as now always 01:18:12.000 --> 01:18:14.250 align:middle line:84% have to practice using their tools. 01:18:14.250 --> 01:18:15.877 align:middle line:90% Our tools don't come for free. 01:18:15.877 --> 01:18:18.210 align:middle line:84% That's why it takes many years of training, many problem 01:18:18.210 --> 01:18:20.580 align:middle line:84% sets, many late nights, many lab reports. 01:18:20.580 --> 01:18:22.860 align:middle line:90% And the tools aren't automatic. 01:18:22.860 --> 01:18:26.670 align:middle line:84% The tools themselves can change and can be put to new uses. 01:18:26.670 --> 01:18:29.520 align:middle line:84% How do they spread, how these new techniques spread, 01:18:29.520 --> 01:18:32.010 align:middle line:84% writing a really great textbook or nowadays 01:18:32.010 --> 01:18:33.900 align:middle line:84% maybe making a great viral YouTube 01:18:33.900 --> 01:18:35.670 align:middle line:90% video, that can certainly help. 01:18:35.670 --> 01:18:37.140 align:middle line:84% But at least in these early days, 01:18:37.140 --> 01:18:41.580 align:middle line:84% it took much more than only kind of text-based means 01:18:41.580 --> 01:18:42.690 align:middle line:90% of propagation. 01:18:42.690 --> 01:18:46.180 align:middle line:84% It really took very specific social institutions, 01:18:46.180 --> 01:18:48.400 align:middle line:84% like postdocs and their dispersal, 01:18:48.400 --> 01:18:51.130 align:middle line:84% to help move these techniques around. 01:18:51.130 --> 01:18:54.220 align:middle line:84% Moreover, even the kind of fanciest new techniques 01:18:54.220 --> 01:18:56.830 align:middle line:84% will be incorporated, will be made sense 01:18:56.830 --> 01:18:59.740 align:middle line:84% of in the context of what generations had already 01:18:59.740 --> 01:19:01.400 align:middle line:90% become comfortable with. 01:19:01.400 --> 01:19:04.030 align:middle line:84% So I think we can make sense of the particular rhythms 01:19:04.030 --> 01:19:07.240 align:middle line:84% of the history of these diagrams by thinking about pedagogically 01:19:07.240 --> 01:19:10.215 align:middle line:84% what had previous generations already become used to. 01:19:10.215 --> 01:19:11.590 align:middle line:84% And so in that sense, you can see 01:19:11.590 --> 01:19:15.100 align:middle line:84% the diagrams and their users kind of being forged together, 01:19:15.100 --> 01:19:17.110 align:middle line:84% that the early users of the techniques 01:19:17.110 --> 01:19:20.770 align:middle line:84% were themselves being molded in these formal training 01:19:20.770 --> 01:19:23.110 align:middle line:84% stages of their career, and they're often molding 01:19:23.110 --> 01:19:25.100 align:middle line:90% the diagrams at the same time. 01:19:25.100 --> 01:19:27.570 align:middle line:90% So I will stop there. 01:19:27.570 --> 01:19:40.000 align:middle line:90%