WEBVTT 00:00:00.000 --> 00:00:01.972 align:middle line:90% [SQUEAKING] 00:00:01.972 --> 00:00:04.430 align:middle line:90% [RUSTLING] 00:00:04.430 --> 00:00:04.930 align:middle line:90% 00:00:04.930 --> 00:00:07.395 align:middle line:90% [CLICKING] 00:00:07.395 --> 00:00:10.850 align:middle line:90% 00:00:10.850 --> 00:00:13.250 align:middle line:84% DAVID KAISER: We're going to launch in today 00:00:13.250 --> 00:00:19.190 align:middle line:84% on the first part of our new kind of material, new set 00:00:19.190 --> 00:00:21.300 align:middle line:90% of material on quantum theory. 00:00:21.300 --> 00:00:25.400 align:middle line:84% So we talked a bit about the road toward relativity 00:00:25.400 --> 00:00:29.720 align:middle line:90% in the first few class sessions. 00:00:29.720 --> 00:00:31.400 align:middle line:84% We're going to pivot now and talk 00:00:31.400 --> 00:00:34.850 align:middle line:84% about this other amazing edifice of what becomes known 00:00:34.850 --> 00:00:37.400 align:middle line:84% as modern physics, quantum theory, 00:00:37.400 --> 00:00:40.910 align:middle line:84% as that was getting pieced together over the first quarter 00:00:40.910 --> 00:00:44.370 align:middle line:84% century or so of the 20th century. 00:00:44.370 --> 00:00:47.540 align:middle line:84% So for this material, we're going 00:00:47.540 --> 00:00:50.030 align:middle line:84% to spend this class session and the next one 00:00:50.030 --> 00:00:53.552 align:middle line:84% talking about what came to be known as old quantum theory. 00:00:53.552 --> 00:00:55.760 align:middle line:84% Of course, it only became known as old quantum theory 00:00:55.760 --> 00:00:57.500 align:middle line:84% once there was a new quantum theory that 00:00:57.500 --> 00:00:58.980 align:middle line:90% seemed to replace it. 00:00:58.980 --> 00:01:02.960 align:middle line:84% And so physicists themselves introduced the term old quantum 00:01:02.960 --> 00:01:07.020 align:middle line:84% theory within the time span that we'll be talking about. 00:01:07.020 --> 00:01:11.910 align:middle line:84% So in their own reckoning, by the mid to late 1920s, 00:01:11.910 --> 00:01:15.570 align:middle line:84% physicists began to refer by the term of old quantum theory 00:01:15.570 --> 00:01:17.970 align:middle line:84% to this collection of work that had unfolded really 00:01:17.970 --> 00:01:21.240 align:middle line:90% between around 1900 and 1924. 00:01:21.240 --> 00:01:24.060 align:middle line:84% That looked like the old period, once the new stuff 00:01:24.060 --> 00:01:27.970 align:middle line:84% had begun to coalesce in 1925, and '26, and so on. 00:01:27.970 --> 00:01:29.465 align:middle line:90% Now, here, I have an asterisk. 00:01:29.465 --> 00:01:30.960 align:middle line:90% I hope you can see that. 00:01:30.960 --> 00:01:32.462 align:middle line:90% These dates are approximate. 00:01:32.462 --> 00:01:34.170 align:middle line:84% One of the things we'll be really sitting 00:01:34.170 --> 00:01:37.830 align:middle line:84% with throughout these first few discussions about quantum 00:01:37.830 --> 00:01:41.220 align:middle line:84% theory is just how much in play these developments 00:01:41.220 --> 00:01:44.982 align:middle line:84% remained well after the nominal date at which they 00:01:44.982 --> 00:01:45.690 align:middle line:90% were put forward. 00:01:45.690 --> 00:01:47.550 align:middle line:84% Much like we saw with relativity, 00:01:47.550 --> 00:01:50.070 align:middle line:84% it wasn't that Einstein published his paper 00:01:50.070 --> 00:01:53.070 align:middle line:84% on the electrodynamics of moving bodies in 1905, 00:01:53.070 --> 00:01:55.230 align:middle line:84% and then the next day everyone woke up and was 00:01:55.230 --> 00:01:59.467 align:middle line:84% a devoted Einsteinian or a convinced relativist. 00:01:59.467 --> 00:02:01.050 align:middle line:84% Likewise, here with these developments 00:02:01.050 --> 00:02:04.800 align:middle line:84% on the early steps toward quantum mechanics, 00:02:04.800 --> 00:02:08.070 align:middle line:84% these ideas themselves were unfolding over time. 00:02:08.070 --> 00:02:11.850 align:middle line:84% They were subject to sometimes quite wide ranging debate 00:02:11.850 --> 00:02:14.028 align:middle line:90% and varying interpretation. 00:02:14.028 --> 00:02:15.570 align:middle line:84% So these dates are really meant to be 00:02:15.570 --> 00:02:17.100 align:middle line:84% approximate to help us understand 00:02:17.100 --> 00:02:22.304 align:middle line:84% the general flow of this body of work between roughly 1900 00:02:22.304 --> 00:02:23.820 align:middle line:90% and 1924. 00:02:23.820 --> 00:02:28.110 align:middle line:84% So I find it helpful to divide up that first period of roughly 00:02:28.110 --> 00:02:31.110 align:middle line:84% 25 years or so into a set of developments 00:02:31.110 --> 00:02:33.635 align:middle line:84% in which physicists began rethinking the nature of light. 00:02:33.635 --> 00:02:35.260 align:middle line:84% And that's what we'll talk about today. 00:02:35.260 --> 00:02:36.870 align:middle line:90% So today is rethinking light. 00:02:36.870 --> 00:02:39.870 align:middle line:84% And really interwoven with those developments, 00:02:39.870 --> 00:02:42.120 align:middle line:84% as we'll see in our next class session, 00:02:42.120 --> 00:02:46.290 align:middle line:84% were a series of equally surprising developments 00:02:46.290 --> 00:02:47.760 align:middle line:84% in which physicists were rethinking 00:02:47.760 --> 00:02:49.420 align:middle line:90% the nature of matter. 00:02:49.420 --> 00:02:52.480 align:middle line:84% They didn't always make that division so clear at the time. 00:02:52.480 --> 00:02:53.970 align:middle line:84% But again, with a bit of hindsight, 00:02:53.970 --> 00:02:56.460 align:middle line:84% once the newer work began to coalesce, 00:02:56.460 --> 00:02:58.170 align:middle line:84% what we now call quantum mechanics, 00:02:58.170 --> 00:03:01.800 align:middle line:84% this division of the strands within old quantum theory 00:03:01.800 --> 00:03:03.790 align:middle line:90% made a bit more sense. 00:03:03.790 --> 00:03:05.940 align:middle line:84% And again, just a reminder for today, it's 00:03:05.940 --> 00:03:07.493 align:middle line:90% thoroughly optional, as always. 00:03:07.493 --> 00:03:09.410 align:middle line:84% But for those who might be interested and have 00:03:09.410 --> 00:03:12.720 align:middle line:84% a bit more time, I did post some additional lecture notes 00:03:12.720 --> 00:03:14.220 align:middle line:84% on the Canvas site that are going 00:03:14.220 --> 00:03:17.910 align:middle line:84% to go into a little more detail about parts 1 and 3 for today's 00:03:17.910 --> 00:03:21.880 align:middle line:84% material in particular, both blackbody radiation and Compton 00:03:21.880 --> 00:03:22.380 align:middle line:90% scattering. 00:03:22.380 --> 00:03:24.930 align:middle line:84% So if some ideas go by really quickly 00:03:24.930 --> 00:03:27.930 align:middle line:84% or you have no idea where that particular equation came from, 00:03:27.930 --> 00:03:31.530 align:middle line:84% there is a bit more that you can delve into on the course site. 00:03:31.530 --> 00:03:32.880 align:middle line:90% OK. 00:03:32.880 --> 00:03:35.790 align:middle line:84% So before we even talk about who was rethinking light 00:03:35.790 --> 00:03:38.910 align:middle line:84% where and when, it's really helpful and very important 00:03:38.910 --> 00:03:41.520 align:middle line:84% to step back and remind ourselves again 00:03:41.520 --> 00:03:44.250 align:middle line:84% of where this is happening and why 00:03:44.250 --> 00:03:45.820 align:middle line:90% it was happening at that time. 00:03:45.820 --> 00:03:50.670 align:middle line:84% So a lot of the work that we're focusing on today's class 00:03:50.670 --> 00:03:52.860 align:middle line:84% in particular-- not all of it, but a lot of it 00:03:52.860 --> 00:03:57.120 align:middle line:84% was happening within this newly unified country called Germany. 00:03:57.120 --> 00:03:58.410 align:middle line:90% We saw this a few times. 00:03:58.410 --> 00:04:01.680 align:middle line:84% There was no country of Germany until 1871. 00:04:01.680 --> 00:04:03.990 align:middle line:84% There were German-speaking territories. 00:04:03.990 --> 00:04:07.200 align:middle line:84% But a single, unified, national country called Germany 00:04:07.200 --> 00:04:11.940 align:middle line:84% emerged really as one outcome of the Franco-Prussian War, 00:04:11.940 --> 00:04:16.200 align:middle line:84% the Prussian state war against the country of France 00:04:16.200 --> 00:04:18.779 align:middle line:84% not too long before Einstein himself was born. 00:04:18.779 --> 00:04:22.260 align:middle line:84% One of the things that the new country of Germany began to do 00:04:22.260 --> 00:04:25.630 align:middle line:84% was to invest very aggressively in a program 00:04:25.630 --> 00:04:27.330 align:middle line:90% of rapid industrialization. 00:04:27.330 --> 00:04:29.730 align:middle line:84% Once it became a single unified country, 00:04:29.730 --> 00:04:32.430 align:middle line:84% the new leaders of the country looked around 00:04:32.430 --> 00:04:35.880 align:middle line:84% and were concerned that they were falling 00:04:35.880 --> 00:04:38.670 align:middle line:84% far behind other European neighbors 00:04:38.670 --> 00:04:41.700 align:middle line:84% in basic industrial capacity, especially Britain. 00:04:41.700 --> 00:04:43.840 align:middle line:84% To some degree they worried about France, 00:04:43.840 --> 00:04:46.208 align:middle line:84% though they had prevailed in the recent war. 00:04:46.208 --> 00:04:48.000 align:middle line:84% So the country begins investing quite a lot 00:04:48.000 --> 00:04:49.230 align:middle line:90% in industrialization. 00:04:49.230 --> 00:04:52.230 align:middle line:84% And that often meant investing in science and technology, what 00:04:52.230 --> 00:04:54.420 align:middle line:84% we would now call science and engineering. 00:04:54.420 --> 00:04:58.680 align:middle line:84% So a few years into this new country's life, its existence, 00:04:58.680 --> 00:05:01.620 align:middle line:84% the leaders put together a new kind of institute-- 00:05:01.620 --> 00:05:05.260 align:middle line:84% not just new to Germany, kind of new even across Europe-- 00:05:05.260 --> 00:05:08.303 align:middle line:84% a specially designed, government-funded institute 00:05:08.303 --> 00:05:09.720 align:middle line:84% called the Physikalisch-Technische 00:05:09.720 --> 00:05:12.060 align:middle line:84% Reichsanstalt, which is fun to say-- 00:05:12.060 --> 00:05:14.880 align:middle line:84% we can just call it by its initials of PTR-- 00:05:14.880 --> 00:05:18.720 align:middle line:84% that really stood for the imperial or the German National 00:05:18.720 --> 00:05:22.110 align:middle line:84% Physical Technical Institute, the PTR. 00:05:22.110 --> 00:05:26.010 align:middle line:84% The idea was that this new kind of space, this new institution, 00:05:26.010 --> 00:05:28.380 align:middle line:84% should foster several kinds of research 00:05:28.380 --> 00:05:31.170 align:middle line:84% and try to get them talking together to really help 00:05:31.170 --> 00:05:33.480 align:middle line:84% jumpstart what the country's leaders hoped 00:05:33.480 --> 00:05:38.440 align:middle line:84% would be this very rapid pace of industrialization. 00:05:38.440 --> 00:05:41.430 align:middle line:84% So the PTR was designed on purpose 00:05:41.430 --> 00:05:43.980 align:middle line:84% to foster research into basic science, 00:05:43.980 --> 00:05:47.520 align:middle line:84% into curiosity-driven research in physics, and chemistry, 00:05:47.520 --> 00:05:51.450 align:middle line:84% and related areas, but also support work 00:05:51.450 --> 00:05:53.613 align:middle line:84% in applied research and industrial development. 00:05:53.613 --> 00:05:55.530 align:middle line:84% So it was pretty similar to what would soon be 00:05:55.530 --> 00:05:57.000 align:middle line:90% developed in the United States. 00:05:57.000 --> 00:05:59.430 align:middle line:84% It was originally called the US Bureau of Standards. 00:05:59.430 --> 00:06:02.580 align:middle line:84% Now, you might know it by the name the National Institute 00:06:02.580 --> 00:06:04.410 align:middle line:84% of Standards and Technology, or NIST, 00:06:04.410 --> 00:06:06.240 align:middle line:84% which has several National Laboratory 00:06:06.240 --> 00:06:07.380 align:middle line:90% sites throughout the US. 00:06:07.380 --> 00:06:09.240 align:middle line:90% The PTR was in that mold. 00:06:09.240 --> 00:06:11.380 align:middle line:84% It was really forming that mold-- 00:06:11.380 --> 00:06:14.710 align:middle line:84% government-sponsored to try to encourage 00:06:14.710 --> 00:06:17.110 align:middle line:84% certain kinds of research, both in basic sciences 00:06:17.110 --> 00:06:19.510 align:middle line:90% and industrial applications. 00:06:19.510 --> 00:06:21.850 align:middle line:84% One of the earliest pressing priorities 00:06:21.850 --> 00:06:26.410 align:middle line:84% for this new institute was to evaluate competing proposals 00:06:26.410 --> 00:06:30.500 align:middle line:84% for public works projects, like large scale electric street 00:06:30.500 --> 00:06:31.000 align:middle line:90% lighting. 00:06:31.000 --> 00:06:33.850 align:middle line:84% Some of you may know, the incandescent light bulb, 00:06:33.850 --> 00:06:36.360 align:middle line:84% the electric light bulbs were actually quite new. 00:06:36.360 --> 00:06:39.430 align:middle line:84% People think about people like Thomas Edison and others 00:06:39.430 --> 00:06:42.370 align:middle line:84% in the United States, similar work going on elsewhere. 00:06:42.370 --> 00:06:44.110 align:middle line:84% And one of the earliest efforts was 00:06:44.110 --> 00:06:46.090 align:middle line:84% to put this new kind of technology, 00:06:46.090 --> 00:06:48.850 align:middle line:84% an incandescent light bulb, an electric light bulb, 00:06:48.850 --> 00:06:51.400 align:middle line:90% into use in public spaces. 00:06:51.400 --> 00:06:55.780 align:middle line:84% Imagine the difference for city life, for commerce, 00:06:55.780 --> 00:07:00.460 align:middle line:84% for communities in general, if cities were pitch dark just as 00:07:00.460 --> 00:07:01.582 align:middle line:90% soon as the sun went down. 00:07:01.582 --> 00:07:03.790 align:middle line:84% Now, of course, there were many, many competing ideas 00:07:03.790 --> 00:07:05.900 align:middle line:84% about how to do that-- how to do it efficiently, 00:07:05.900 --> 00:07:08.950 align:middle line:84% how to make the right kinds of bulbs that could give out 00:07:08.950 --> 00:07:12.610 align:middle line:84% a lot of light with hopefully not too much power usage 00:07:12.610 --> 00:07:13.430 align:middle line:90% and so on. 00:07:13.430 --> 00:07:16.180 align:middle line:84% And so one of the first questions that this new PTR had 00:07:16.180 --> 00:07:19.510 align:middle line:84% to wrestle with was how to compare these competing 00:07:19.510 --> 00:07:22.792 align:middle line:84% proposals for things like electric street lighting. 00:07:22.792 --> 00:07:24.250 align:middle line:84% What they were asking about is, how 00:07:24.250 --> 00:07:25.720 align:middle line:84% can you measure the amount of light 00:07:25.720 --> 00:07:28.510 align:middle line:84% that comes out from these very hot filaments 00:07:28.510 --> 00:07:30.590 align:middle line:90% in these electric bulbs? 00:07:30.590 --> 00:07:34.310 align:middle line:84% Now people had known for a long, long, long time, a long 00:07:34.310 --> 00:07:35.900 align:middle line:90% before the PCR-- 00:07:35.900 --> 00:07:38.780 align:middle line:84% humans had known that when materials are heated up 00:07:38.780 --> 00:07:40.240 align:middle line:84% to a sufficiently high temperature, 00:07:40.240 --> 00:07:41.240 align:middle line:90% they will begin to glow. 00:07:41.240 --> 00:07:44.190 align:middle line:84% They'll give off some kind of radiation, some light. 00:07:44.190 --> 00:07:46.730 align:middle line:84% Think about very casual observations 00:07:46.730 --> 00:07:50.030 align:middle line:84% like embers glowing in a fireplace or charcoals 00:07:50.030 --> 00:07:53.330 align:middle line:84% on a grill or now, tragically, the photographs 00:07:53.330 --> 00:07:56.090 align:middle line:84% we see from these horrific forest 00:07:56.090 --> 00:07:59.060 align:middle line:84% fires out in California and up and down the West Coast. 00:07:59.060 --> 00:08:01.580 align:middle line:84% When you heat stuff up to a high enough temperature, 00:08:01.580 --> 00:08:02.720 align:middle line:90% it will give off light. 00:08:02.720 --> 00:08:04.400 align:middle line:90% It will glow. 00:08:04.400 --> 00:08:06.590 align:middle line:84% And in fact, the color of the emitted light 00:08:06.590 --> 00:08:08.645 align:middle line:84% shifts with the temperature to which 00:08:08.645 --> 00:08:09.770 align:middle line:90% the object has been heated. 00:08:09.770 --> 00:08:12.650 align:middle line:84% So the colors, the main frequencies of light 00:08:12.650 --> 00:08:16.190 align:middle line:84% that dominate that glow, will shift with temperature. 00:08:16.190 --> 00:08:18.530 align:middle line:84% And that was, again, something that was known casually 00:08:18.530 --> 00:08:20.600 align:middle line:90% long before there was a PTR. 00:08:20.600 --> 00:08:23.390 align:middle line:84% Well, that feeds into this very specific work 00:08:23.390 --> 00:08:26.990 align:middle line:84% at this new institute, the PTR, because one 00:08:26.990 --> 00:08:30.830 align:middle line:84% of the tasks of the new group was to figure out calibrations 00:08:30.830 --> 00:08:34.460 align:middle line:84% for these different kinds of electric light technologies, 00:08:34.460 --> 00:08:35.809 align:middle line:90% these proposals. 00:08:35.809 --> 00:08:38.252 align:middle line:84% And what the PTR researchers began to notice 00:08:38.252 --> 00:08:39.710 align:middle line:84% was it looked like there was a kind 00:08:39.710 --> 00:08:43.640 align:middle line:84% of universal or shared pattern in the kind of light, 00:08:43.640 --> 00:08:46.580 align:middle line:84% in the pattern of light that came out from various objects 00:08:46.580 --> 00:08:48.560 align:middle line:84% when they were heated to high temperatures. 00:08:48.560 --> 00:08:49.970 align:middle line:84% And they thought it was universal 00:08:49.970 --> 00:08:51.810 align:middle line:84% because it looked like the pattern of light, 00:08:51.810 --> 00:08:55.700 align:middle line:84% how much light came out at which particular colors, seemed 00:08:55.700 --> 00:08:58.503 align:middle line:84% to depend only on the temperature to which 00:08:58.503 --> 00:09:00.170 align:middle line:84% those materials had been heated, but not 00:09:00.170 --> 00:09:03.530 align:middle line:84% on the material, the chemical makeup 00:09:03.530 --> 00:09:04.790 align:middle line:90% of the materials themselves. 00:09:04.790 --> 00:09:07.050 align:middle line:84% Different kinds of filaments, for example, 00:09:07.050 --> 00:09:09.950 align:middle line:84% even if they were made up from entirely different atoms 00:09:09.950 --> 00:09:13.455 align:middle line:84% and molecules, would glow with the same kind of pattern 00:09:13.455 --> 00:09:15.830 align:middle line:84% once they were heated to a sufficiently high temperature. 00:09:15.830 --> 00:09:17.480 align:middle line:84% At least, it looked like that might 00:09:17.480 --> 00:09:19.850 align:middle line:84% be the case in these early tests to calibrate 00:09:19.850 --> 00:09:22.040 align:middle line:84% these different kinds of electric light fixtures 00:09:22.040 --> 00:09:23.160 align:middle line:90% and so on. 00:09:23.160 --> 00:09:26.180 align:middle line:84% So these researchers began to postulate that there was 00:09:26.180 --> 00:09:29.280 align:middle line:90% some ideal so-called blackbody. 00:09:29.280 --> 00:09:31.230 align:middle line:84% The idea was imagine an object that 00:09:31.230 --> 00:09:33.600 align:middle line:84% absorbed all the light that fell upon it 00:09:33.600 --> 00:09:35.010 align:middle line:90% and reflected none back. 00:09:35.010 --> 00:09:36.900 align:middle line:84% So it would appear to our eyes to be black. 00:09:36.900 --> 00:09:38.470 align:middle line:84% It would reflect no light at all. 00:09:38.470 --> 00:09:42.450 align:middle line:84% We'd see it as emitting or reflecting no light at all. 00:09:42.450 --> 00:09:46.320 align:middle line:84% So you want to remove any accidents of the kind of light 00:09:46.320 --> 00:09:49.110 align:middle line:84% that might have shown on it and concentrate on the light being 00:09:49.110 --> 00:09:52.050 align:middle line:84% emitted by this so-called blackbody when 00:09:52.050 --> 00:09:54.667 align:middle line:84% you heat that object up to a high temperature. 00:09:54.667 --> 00:09:57.000 align:middle line:84% And it shouldn't have mattered whether the blackbody was 00:09:57.000 --> 00:09:59.970 align:middle line:84% actually made of wood, or charcoal, or anything else. 00:09:59.970 --> 00:10:02.880 align:middle line:84% If it really is a universal glow that you 00:10:02.880 --> 00:10:06.630 align:middle line:84% can imagine as this idealized, otherwise unspecified kind 00:10:06.630 --> 00:10:08.610 align:middle line:90% of object, a blackbody. 00:10:08.610 --> 00:10:10.530 align:middle line:84% And therefore, when you heat this object, 00:10:10.530 --> 00:10:12.732 align:middle line:84% this mysterious or hypothetical object up 00:10:12.732 --> 00:10:14.190 align:middle line:84% to a sufficiently high temperature, 00:10:14.190 --> 00:10:16.980 align:middle line:84% the pattern of light that would be emitted 00:10:16.980 --> 00:10:20.190 align:middle line:84% should tell you something about universal properties, 00:10:20.190 --> 00:10:24.550 align:middle line:84% not the accidental features of this or that chemical material. 00:10:24.550 --> 00:10:26.950 align:middle line:84% So this universal blackbody spectrum, or at least 00:10:26.950 --> 00:10:29.920 align:middle line:84% the hypothesis that there might be this universal behavior, 00:10:29.920 --> 00:10:33.250 align:middle line:84% that seemed interesting for at least two reasons of exactly 00:10:33.250 --> 00:10:36.700 align:middle line:84% the kinds of things that this new PTR had been set up 00:10:36.700 --> 00:10:38.260 align:middle line:90% to foster. 00:10:38.260 --> 00:10:40.750 align:middle line:84% This could be really useful for calibrations 00:10:40.750 --> 00:10:42.220 align:middle line:90% and standardization. 00:10:42.220 --> 00:10:46.390 align:middle line:84% Take any new electric light fixture or similar device. 00:10:46.390 --> 00:10:48.850 align:middle line:84% You should now have a universal standard 00:10:48.850 --> 00:10:51.940 align:middle line:84% against which one could measure its own light output-- 00:10:51.940 --> 00:10:54.958 align:middle line:84% what pattern of light would come out from, say, 00:10:54.958 --> 00:10:56.500 align:middle line:84% this or that filament because now you 00:10:56.500 --> 00:10:59.770 align:middle line:84% have a universal standard with which to compare it. 00:10:59.770 --> 00:11:01.690 align:middle line:84% And it also suggested this might tell us 00:11:01.690 --> 00:11:04.510 align:middle line:84% something deeply fundamental and very basic 00:11:04.510 --> 00:11:06.663 align:middle line:84% about the interactions between light and matter. 00:11:06.663 --> 00:11:08.080 align:middle line:84% It shouldn't matter whether you're 00:11:08.080 --> 00:11:09.610 align:middle line:84% talking about this kind of material 00:11:09.610 --> 00:11:10.900 align:middle line:90% for a filament or that kind. 00:11:10.900 --> 00:11:14.410 align:middle line:84% This tells us perhaps something very universal about light 00:11:14.410 --> 00:11:17.180 align:middle line:90% and matter at their core. 00:11:17.180 --> 00:11:20.410 align:middle line:84% So these researchers at this newly generously funded 00:11:20.410 --> 00:11:22.990 align:middle line:84% Physikalisch-Technische Reichsanstalt, the PTR-- 00:11:22.990 --> 00:11:25.610 align:middle line:84% they began conducting more and more sensitive 00:11:25.610 --> 00:11:27.740 align:middle line:84% experiments on the pattern of light, 00:11:27.740 --> 00:11:30.080 align:middle line:84% what became known as the spectrum of light, that 00:11:30.080 --> 00:11:32.540 align:middle line:84% was emitted from these blackbodies over the course 00:11:32.540 --> 00:11:35.270 align:middle line:84% of the 1880s and 1890s, soon after the PTR 00:11:35.270 --> 00:11:36.870 align:middle line:90% itself had been founded. 00:11:36.870 --> 00:11:39.478 align:middle line:84% And they began finding curves that looked like this. 00:11:39.478 --> 00:11:42.020 align:middle line:84% Now, in the early data-- this is an example of real published 00:11:42.020 --> 00:11:45.620 align:middle line:84% data from the researchers, Lummer and Pringsheim-- 00:11:45.620 --> 00:11:48.320 align:middle line:84% they often would plot the spectrum, the amount of energy 00:11:48.320 --> 00:11:51.680 align:middle line:84% that came out as one varied the wavelength of light. 00:11:51.680 --> 00:11:53.837 align:middle line:84% Typically, these days, we tend to characterize it 00:11:53.837 --> 00:11:54.920 align:middle line:90% in terms of the frequency. 00:11:54.920 --> 00:11:57.943 align:middle line:84% But remember, that's an easy choice, a trade-off. 00:11:57.943 --> 00:12:00.110 align:middle line:84% We can always relate the frequency of the light that 00:12:00.110 --> 00:12:02.510 align:middle line:84% comes out, nu-- we'll use the Greek letter nu-- 00:12:02.510 --> 00:12:05.300 align:middle line:84% that's inversely proportional to the wavelength, 00:12:05.300 --> 00:12:06.470 align:middle line:90% like in these data here. 00:12:06.470 --> 00:12:08.330 align:middle line:84% And the constant of proportionality 00:12:08.330 --> 00:12:10.850 align:middle line:84% is just given by the speed at which those light waves are 00:12:10.850 --> 00:12:12.420 align:middle line:90% traveling, the speed of light. 00:12:12.420 --> 00:12:15.440 align:middle line:84% So let's look at this curve, U. U 00:12:15.440 --> 00:12:19.250 align:middle line:84% is a certain kind of quantity called a spectral energy 00:12:19.250 --> 00:12:20.177 align:middle line:90% density. 00:12:20.177 --> 00:12:21.260 align:middle line:90% That's kind of a mouthful. 00:12:21.260 --> 00:12:23.302 align:middle line:84% And again, I go through this in some more details 00:12:23.302 --> 00:12:25.978 align:middle line:90% in the optional lecture notes. 00:12:25.978 --> 00:12:27.770 align:middle line:84% What these curves are showing is the amount 00:12:27.770 --> 00:12:31.580 align:middle line:84% of energy per unit volume in some region of space 00:12:31.580 --> 00:12:33.240 align:middle line:90% per frequency-- 00:12:33.240 --> 00:12:36.530 align:middle line:84% so how much light gets shown out in the form of-- 00:12:36.530 --> 00:12:39.290 align:middle line:84% how much energy gets shown out in the form of radiation 00:12:39.290 --> 00:12:43.190 align:middle line:84% in some box of fixed size within unit volume 00:12:43.190 --> 00:12:45.278 align:middle line:84% as you vary the color of the light. 00:12:45.278 --> 00:12:47.570 align:middle line:84% And so this suggests you get a certain amount of energy 00:12:47.570 --> 00:12:48.980 align:middle line:90% radiated from one color. 00:12:48.980 --> 00:12:51.170 align:middle line:84% As you vary the frequency of the light, 00:12:51.170 --> 00:12:52.820 align:middle line:84% a different amount of energy comes out, 00:12:52.820 --> 00:12:54.320 align:middle line:84% in this case more energy, as you go 00:12:54.320 --> 00:12:59.240 align:middle line:84% to a higher frequency, different color, and so on. 00:12:59.240 --> 00:13:01.400 align:middle line:84% What the researchers kept finding 00:13:01.400 --> 00:13:03.620 align:middle line:84% was that the nature of this curve 00:13:03.620 --> 00:13:07.130 align:middle line:84% depended only on the temperature to which the objects had 00:13:07.130 --> 00:13:08.840 align:middle line:84% been heated, but not the material 00:13:08.840 --> 00:13:10.520 align:middle line:90% composition of those objects. 00:13:10.520 --> 00:13:13.430 align:middle line:84% This universal feature became more and more evident 00:13:13.430 --> 00:13:15.890 align:middle line:84% as they conducted more and more tests. 00:13:15.890 --> 00:13:18.410 align:middle line:84% And so this is a plot now showing 00:13:18.410 --> 00:13:22.400 align:middle line:84% the form of this spectral energy density for three 00:13:22.400 --> 00:13:23.720 align:middle line:90% different temperatures. 00:13:23.720 --> 00:13:25.250 align:middle line:90% It varies only with temperature. 00:13:25.250 --> 00:13:27.290 align:middle line:84% Let's consider a relatively low temperature 00:13:27.290 --> 00:13:30.980 align:middle line:84% here, some medium temperature, and some high temperature. 00:13:30.980 --> 00:13:34.010 align:middle line:84% Already, we see the trend becomes pretty clear. 00:13:34.010 --> 00:13:36.290 align:middle line:84% As you raise the temperature to which you've 00:13:36.290 --> 00:13:38.240 align:middle line:84% heated that blackbody, that object, 00:13:38.240 --> 00:13:40.408 align:middle line:84% the amount of energy that's radiated grows. 00:13:40.408 --> 00:13:42.200 align:middle line:84% So you get more and more energy coming out. 00:13:42.200 --> 00:13:44.810 align:middle line:84% The area under this curve, of the blue one, 00:13:44.810 --> 00:13:48.080 align:middle line:84% is much larger than the area under the other curves. 00:13:48.080 --> 00:13:50.810 align:middle line:84% Total energy output, or the intensity, 00:13:50.810 --> 00:13:52.220 align:middle line:90% increases with temperature. 00:13:52.220 --> 00:13:54.170 align:middle line:84% And the peak frequency, the frequency 00:13:54.170 --> 00:13:57.170 align:middle line:84% at which most energy gets emitted 00:13:57.170 --> 00:13:59.210 align:middle line:84% in the form of light, that also shifts 00:13:59.210 --> 00:14:01.080 align:middle line:90% to higher and higher frequency. 00:14:01.080 --> 00:14:03.860 align:middle line:84% So at a relatively low temperature, 00:14:03.860 --> 00:14:06.740 align:middle line:84% the peak frequency is a kind of reddish color. 00:14:06.740 --> 00:14:08.770 align:middle line:84% As you increase the temperature, it 00:14:08.770 --> 00:14:12.080 align:middle line:84% shifts through the spectrum to orange and ultimately 00:14:12.080 --> 00:14:13.010 align:middle line:90% to the blue end. 00:14:13.010 --> 00:14:15.730 align:middle line:84% So you have this pattern emerging. 00:14:15.730 --> 00:14:19.300 align:middle line:84% So as the empirical pattern, as these empirical measurements 00:14:19.300 --> 00:14:21.790 align:middle line:84% in the laboratories became more and more clear, 00:14:21.790 --> 00:14:23.530 align:middle line:84% how do you make sense of that pattern? 00:14:23.530 --> 00:14:25.690 align:middle line:84% That actually was very, very non-trivial. 00:14:25.690 --> 00:14:28.960 align:middle line:84% That was not at all clear to these early researchers. 00:14:28.960 --> 00:14:30.910 align:middle line:84% So one of the first to really delve into this 00:14:30.910 --> 00:14:33.700 align:middle line:84% to try to give a theoretical explanation for that pattern 00:14:33.700 --> 00:14:34.870 align:middle line:90% was Max Planck. 00:14:34.870 --> 00:14:38.030 align:middle line:84% So Planck had only recently moved to Berlin. 00:14:38.030 --> 00:14:40.330 align:middle line:84% He was one of the first people in all of Germany 00:14:40.330 --> 00:14:43.120 align:middle line:84% to have this full professor, this special Ordinarius 00:14:43.120 --> 00:14:45.310 align:middle line:84% professor chair in theoretical physics. 00:14:45.310 --> 00:14:48.280 align:middle line:84% Remember, we talked several weeks ago, several classes ago, 00:14:48.280 --> 00:14:52.840 align:middle line:84% that until the later years of the 19th century, especially 00:14:52.840 --> 00:14:55.030 align:middle line:84% in the German language universities, 00:14:55.030 --> 00:14:58.330 align:middle line:84% there would be one full professor, one Ordinarius, 00:14:58.330 --> 00:14:59.470 align:middle line:90% for all of physics. 00:14:59.470 --> 00:15:02.440 align:middle line:84% And that person was, by default, an experimental physicist. 00:15:02.440 --> 00:15:05.500 align:middle line:84% Only by the later decades of the 19th century 00:15:05.500 --> 00:15:08.440 align:middle line:84% were there sometimes two full professors of physics-- one 00:15:08.440 --> 00:15:11.110 align:middle line:84% to handle experiments and one for theory. 00:15:11.110 --> 00:15:13.360 align:middle line:84% Planck was one of these early Ordinarius professors 00:15:13.360 --> 00:15:14.890 align:middle line:84% of theoretical physics in Berlin, 00:15:14.890 --> 00:15:17.630 align:middle line:90% starting in the early 1890s. 00:15:17.630 --> 00:15:19.940 align:middle line:84% He was not at the PTR, but he was nearby. 00:15:19.940 --> 00:15:21.890 align:middle line:84% And he was in touch with his colleagues there. 00:15:21.890 --> 00:15:24.560 align:middle line:84% Planck was an expert, in particular, 00:15:24.560 --> 00:15:26.420 align:middle line:84% on the new work on statistical mechanics 00:15:26.420 --> 00:15:29.420 align:middle line:84% by people like James Clark Maxwell and Ludwig 00:15:29.420 --> 00:15:30.450 align:middle line:90% Boltzmann and others. 00:15:30.450 --> 00:15:32.900 align:middle line:84% How do you make sense of large collections of objects 00:15:32.900 --> 00:15:35.270 align:middle line:90% like molecules in a gas? 00:15:35.270 --> 00:15:37.370 align:middle line:84% How do you assess their collective properties? 00:15:37.370 --> 00:15:38.810 align:middle line:90% That's what he focused on. 00:15:38.810 --> 00:15:40.455 align:middle line:84% Because he was now close to the PTR, 00:15:40.455 --> 00:15:42.080 align:middle line:84% he began paying more and more attention 00:15:42.080 --> 00:15:44.120 align:middle line:84% to this blackbody research as well. 00:15:44.120 --> 00:15:46.040 align:middle line:84% And he realized, as many others did, 00:15:46.040 --> 00:15:47.870 align:middle line:84% that it was really, really hard to make 00:15:47.870 --> 00:15:49.520 align:middle line:84% sense of this characteristic pattern, 00:15:49.520 --> 00:15:53.480 align:middle line:84% this seemingly universal shape of this blackbody spectrum, 00:15:53.480 --> 00:15:56.880 align:middle line:84% the amount of energy per unit volume per frequency. 00:15:56.880 --> 00:15:59.660 align:middle line:84% And in fact, if you used quite standard-- 00:15:59.660 --> 00:16:01.610 align:middle line:84% by that point, very familiar arguments-- 00:16:01.610 --> 00:16:03.680 align:middle line:84% from people like Boltzmann and Maxwell, 00:16:03.680 --> 00:16:05.780 align:middle line:84% the kind of people whose work Planck 00:16:05.780 --> 00:16:09.530 align:middle line:84% was an expert in studying, you should predict a very different 00:16:09.530 --> 00:16:11.480 align:middle line:90% behavior from first principles. 00:16:11.480 --> 00:16:15.080 align:middle line:84% In fact, it should look like this dashed purple curve, which 00:16:15.080 --> 00:16:17.268 align:middle line:84% doesn't look anything like the ultimate curve that 00:16:17.268 --> 00:16:17.810 align:middle line:90% was measured. 00:16:17.810 --> 00:16:20.750 align:middle line:84% They agree very well at very low frequencies. 00:16:20.750 --> 00:16:22.460 align:middle line:90% They both overlap here. 00:16:22.460 --> 00:16:24.920 align:middle line:84% But then you see a very significant difference 00:16:24.920 --> 00:16:26.212 align:middle line:90% between their patterns. 00:16:26.212 --> 00:16:27.920 align:middle line:84% And in fact, this purple one became known 00:16:27.920 --> 00:16:29.930 align:middle line:90% as the ultraviolet catastrophe. 00:16:29.930 --> 00:16:30.740 align:middle line:90% I love that term. 00:16:30.740 --> 00:16:32.390 align:middle line:90% It's a catastrophe. 00:16:32.390 --> 00:16:35.092 align:middle line:84% If you follow the then standard arguments-- 00:16:35.092 --> 00:16:37.550 align:middle line:84% and I go through these, again, in some more detail in those 00:16:37.550 --> 00:16:38.990 align:middle line:90% optional lecture notes-- 00:16:38.990 --> 00:16:41.150 align:middle line:84% then the theoretical model seemed 00:16:41.150 --> 00:16:44.870 align:middle line:84% to predict that you should get more and more energy per volume 00:16:44.870 --> 00:16:46.970 align:middle line:90% as you raise the frequency. 00:16:46.970 --> 00:16:48.710 align:middle line:84% And it should grow without bound. 00:16:48.710 --> 00:16:49.905 align:middle line:90% It should never stop. 00:16:49.905 --> 00:16:52.280 align:middle line:84% So it seemed like everything should be glowing infinitely 00:16:52.280 --> 00:16:53.090 align:middle line:90% all the time. 00:16:53.090 --> 00:16:55.010 align:middle line:90% We clearly don't see that. 00:16:55.010 --> 00:16:57.440 align:middle line:84% That argument came from two different pieces. 00:16:57.440 --> 00:17:00.030 align:middle line:84% Again, I go through that in a bit more detail in the notes. 00:17:00.030 --> 00:17:02.810 align:middle line:84% But the high level summary is that, according 00:17:02.810 --> 00:17:05.720 align:middle line:84% to work by people like Maxwell and Boltzmann, 00:17:05.720 --> 00:17:08.329 align:middle line:84% very well established by the time Planck began 00:17:08.329 --> 00:17:11.300 align:middle line:84% to worry about this stuff, in thermal equilibrium, 00:17:11.300 --> 00:17:13.280 align:middle line:84% very generally it had been argued, 00:17:13.280 --> 00:17:16.400 align:middle line:84% each degree of freedom, each way that these 00:17:16.400 --> 00:17:19.280 align:middle line:84% either the light waves or little bits of matter 00:17:19.280 --> 00:17:21.770 align:middle line:84% in that blackbody-- each of these things 00:17:21.770 --> 00:17:26.638 align:middle line:84% should share a kind of average energy proportional 00:17:26.638 --> 00:17:28.930 align:middle line:84% to the temperature to which the object had been heated. 00:17:28.930 --> 00:17:32.170 align:middle line:84% And with a constant known as k, we now 00:17:32.170 --> 00:17:33.730 align:middle line:90% call that Boltzmann's constant. 00:17:33.730 --> 00:17:35.860 align:middle line:84% This was known as the equipartition theorem, 00:17:35.860 --> 00:17:39.400 align:middle line:84% that each way in which a system could wiggle or move, 00:17:39.400 --> 00:17:40.900 align:middle line:84% each so-called degree of freedom, 00:17:40.900 --> 00:17:44.020 align:middle line:84% should have an equal average energy. 00:17:44.020 --> 00:17:44.710 align:middle line:90% That's step 1. 00:17:44.710 --> 00:17:47.590 align:middle line:84% Step 2, using Maxwell's treatment of light, 00:17:47.590 --> 00:17:50.890 align:middle line:84% of electromagnetic radiation, the argument 00:17:50.890 --> 00:17:54.730 align:middle line:84% was that the number of radiation modes, degrees 00:17:54.730 --> 00:17:57.457 align:middle line:84% of freedom per unit volume per frequency 00:17:57.457 --> 00:17:58.540 align:middle line:90% should go like nu squared. 00:17:58.540 --> 00:18:01.660 align:middle line:84% Combine those together, you get this expectation 00:18:01.660 --> 00:18:04.870 align:middle line:84% that the spectral energy density, u, should 00:18:04.870 --> 00:18:08.890 align:middle line:84% grow quadratically, grow as a square of the frequency 00:18:08.890 --> 00:18:09.662 align:middle line:90% without bound. 00:18:09.662 --> 00:18:10.870 align:middle line:90% It should rise without limit. 00:18:10.870 --> 00:18:12.430 align:middle line:84% So everything should be glowing all the time, 00:18:12.430 --> 00:18:13.720 align:middle line:90% giving off an infinite energy. 00:18:13.720 --> 00:18:16.300 align:middle line:90% That clearly is not what we see. 00:18:16.300 --> 00:18:18.580 align:middle line:84% So Planck, as I say, had special access 00:18:18.580 --> 00:18:21.940 align:middle line:84% to his colleagues doing these experiments in real time. 00:18:21.940 --> 00:18:25.180 align:middle line:84% He knew better than anyone that the real curves looked nothing 00:18:25.180 --> 00:18:29.020 align:middle line:84% like this constantly growing curve 00:18:29.020 --> 00:18:31.630 align:middle line:90% of the ultraviolet catastrophe. 00:18:31.630 --> 00:18:33.400 align:middle line:84% Everyone knew that these curves must 00:18:33.400 --> 00:18:35.530 align:middle line:84% begin to fall with increasing frequency. 00:18:35.530 --> 00:18:39.520 align:middle line:84% Planck had an extra insight, or extra information, 00:18:39.520 --> 00:18:41.410 align:middle line:84% not just that the curve should fall, 00:18:41.410 --> 00:18:44.710 align:middle line:84% but how it should fall the, actual shape of that curve, 00:18:44.710 --> 00:18:45.880 align:middle line:90% like this part here-- 00:18:45.880 --> 00:18:47.950 align:middle line:84% actually, this part here in wavelength. 00:18:47.950 --> 00:18:49.720 align:middle line:84% How that curve begin to fall as you 00:18:49.720 --> 00:18:52.390 align:middle line:84% go to shorter and shorter wavelengths or higher 00:18:52.390 --> 00:18:53.570 align:middle line:90% and higher frequencies? 00:18:53.570 --> 00:18:55.150 align:middle line:90% So he began to tinker. 00:18:55.150 --> 00:18:59.620 align:middle line:84% And in fact, very famously, on a particular date December 14, 00:18:59.620 --> 00:19:02.500 align:middle line:84% 1900, he presented a paper to his colleagues 00:19:02.500 --> 00:19:06.070 align:middle line:84% at a Physics Society meeting, in which he presented this form 00:19:06.070 --> 00:19:09.610 align:middle line:84% for this spectral energy density, 00:19:09.610 --> 00:19:12.130 align:middle line:84% that it should rise not as nu squared, 00:19:12.130 --> 00:19:14.158 align:middle line:84% like the ultraviolet catastrophe. 00:19:14.158 --> 00:19:16.450 align:middle line:84% But in fact, it should have this a bit more complicated 00:19:16.450 --> 00:19:18.100 align:middle line:90% structure. 00:19:18.100 --> 00:19:20.260 align:middle line:84% And this was really interesting because it 00:19:20.260 --> 00:19:24.130 align:middle line:84% would match very well both the arguments from people 00:19:24.130 --> 00:19:29.180 align:middle line:84% like Boltzmann and Maxwell in one region of the graph-- 00:19:29.180 --> 00:19:32.700 align:middle line:84% sorry, for very low frequencies, very long wavelengths, 00:19:32.700 --> 00:19:35.810 align:middle line:84% so over here on this real data, or over here on this plot. 00:19:35.810 --> 00:19:39.140 align:middle line:84% It converges to the original expectation. 00:19:39.140 --> 00:19:42.590 align:middle line:84% But then it has this natural turnaround 00:19:42.590 --> 00:19:45.710 align:middle line:84% so that at higher frequencies, at shorter wavelengths, 00:19:45.710 --> 00:19:47.990 align:middle line:84% in fact, you should have this gently decaying 00:19:47.990 --> 00:19:49.730 align:middle line:90% tail, this exponential tail. 00:19:49.730 --> 00:19:51.950 align:middle line:84% Both of those features are contained 00:19:51.950 --> 00:19:55.100 align:middle line:84% in this one expression, as you take the appropriate limits. 00:19:55.100 --> 00:19:58.280 align:middle line:84% He also had to introduce this new constant, h, which 00:19:58.280 --> 00:20:00.170 align:middle line:90% had not been introduced before. 00:20:00.170 --> 00:20:02.660 align:middle line:84% We now call it Planck's constant. 00:20:02.660 --> 00:20:05.090 align:middle line:84% That was at least in part to make his units match. 00:20:05.090 --> 00:20:08.210 align:middle line:84% The quantity kT has units of energy. 00:20:08.210 --> 00:20:10.760 align:middle line:84% T is the temperature, k Boltzmann constant, 00:20:10.760 --> 00:20:13.250 align:middle line:90% together form units of energy. 00:20:13.250 --> 00:20:17.900 align:middle line:84% Nu here is the frequency, 1 over time, 1 over seconds, Hertz. 00:20:17.900 --> 00:20:20.220 align:middle line:84% So that doesn't have the same units as energy. 00:20:20.220 --> 00:20:23.090 align:middle line:84% So he added this extra kind of fudge 00:20:23.090 --> 00:20:25.550 align:middle line:84% called h to make sure the units would match 00:20:25.550 --> 00:20:27.320 align:middle line:84% and also to try to begin to match 00:20:27.320 --> 00:20:32.400 align:middle line:84% the actual quantitative shape of the data from his colleagues. 00:20:32.400 --> 00:20:36.440 align:middle line:84% So in this treatment, the very closing days of the year 1900, 00:20:36.440 --> 00:20:39.530 align:middle line:84% Planck introduced not only a new form for the spectral energy 00:20:39.530 --> 00:20:43.310 align:middle line:84% density-- and there's more on that in those lecture notes-- 00:20:43.310 --> 00:20:45.770 align:middle line:84% he also introduces this new universal constant 00:20:45.770 --> 00:20:47.220 align:middle line:90% we now call Planck's constant. 00:20:47.220 --> 00:20:49.490 align:middle line:84% It's this number, h, just a constant 00:20:49.490 --> 00:20:53.930 align:middle line:84% that really sets the scale for these departures based 00:20:53.930 --> 00:20:55.610 align:middle line:84% on the calculations we would make 00:20:55.610 --> 00:20:58.310 align:middle line:84% from Newton's physics or even Maxwell's equations. 00:20:58.310 --> 00:21:00.710 align:middle line:84% How much do these newer ideas of what becomes 00:21:00.710 --> 00:21:01.970 align:middle line:90% known as quantum theory-- 00:21:01.970 --> 00:21:03.230 align:middle line:90% how much should they depart? 00:21:03.230 --> 00:21:05.690 align:middle line:84% Or when should we expect a deviation? 00:21:05.690 --> 00:21:09.140 align:middle line:84% And Planck's value that he inferred from his colleagues' 00:21:09.140 --> 00:21:12.200 align:middle line:84% measurements at the PTR was actually remarkably close 00:21:12.200 --> 00:21:14.340 align:middle line:84% to the modern value we use to this day. 00:21:14.340 --> 00:21:15.440 align:middle line:90% Here's a modern value. 00:21:15.440 --> 00:21:17.780 align:middle line:84% Planck's inferred value was pretty close. 00:21:17.780 --> 00:21:21.860 align:middle line:84% In units that are familiar for macroscopic everyday human 00:21:21.860 --> 00:21:24.980 align:middle line:84% activities, the so-called CGS system, 00:21:24.980 --> 00:21:28.250 align:middle line:84% where we measure distances in centimeters, masses in grams, 00:21:28.250 --> 00:21:31.250 align:middle line:84% and times and seconds-- that's where the CGS comes from-- 00:21:31.250 --> 00:21:34.080 align:middle line:84% energy, as you may recall, is given this unit 00:21:34.080 --> 00:21:37.320 align:middle line:84% of erg, which really is just 1 gram centimeter 00:21:37.320 --> 00:21:38.730 align:middle line:90% squared per second squared. 00:21:38.730 --> 00:21:42.310 align:middle line:84% In those CGS units, h is incredibly small. 00:21:42.310 --> 00:21:45.450 align:middle line:84% It's exponentially tiny in those natural units 00:21:45.450 --> 00:21:47.670 align:middle line:90% for human-scaled affairs. 00:21:47.670 --> 00:21:48.840 align:middle line:90% So h is small. 00:21:48.840 --> 00:21:51.750 align:middle line:84% If we consider, for example, drop a single grape 00:21:51.750 --> 00:21:54.780 align:middle line:84% from a height of 5 centimeters, roughly 2 inches, 00:21:54.780 --> 00:21:58.410 align:middle line:84% and then ask what's the kinetic energy that grape will acquire 00:21:58.410 --> 00:22:02.040 align:middle line:84% over that very short journey, let the grape fall from rest 00:22:02.040 --> 00:22:03.750 align:middle line:90% a total of 5 centimeters. 00:22:03.750 --> 00:22:06.750 align:middle line:84% Multiply its acquired kinetic energy 00:22:06.750 --> 00:22:09.210 align:middle line:84% times the duration during which it was falling, 00:22:09.210 --> 00:22:11.220 align:middle line:90% roughly a second or so. 00:22:11.220 --> 00:22:14.950 align:middle line:84% And you get an enormous amount of energy times time, 00:22:14.950 --> 00:22:17.070 align:middle line:90% if we measure in this Planck-- 00:22:17.070 --> 00:22:18.780 align:middle line:90% in these Planck units. 00:22:18.780 --> 00:22:21.570 align:middle line:84% So just that tiny little grape falling for about 1 00:22:21.570 --> 00:22:23.670 align:middle line:84% second from roughly 2 inches high 00:22:23.670 --> 00:22:27.960 align:middle line:84% has 10 to the 28 of Planck units of energy time. 00:22:27.960 --> 00:22:31.260 align:middle line:84% Some of you might know that this particular combination 00:22:31.260 --> 00:22:34.740 align:middle line:84% of units, or energy times a times unit, erg seconds, 00:22:34.740 --> 00:22:36.930 align:middle line:84% is also the unit in which we measure things 00:22:36.930 --> 00:22:38.200 align:middle line:90% like angular momentum. 00:22:38.200 --> 00:22:41.050 align:middle line:84% What's the momentum of circular motion? 00:22:41.050 --> 00:22:44.065 align:middle line:84% So again, let's take a household example. 00:22:44.065 --> 00:22:46.440 align:middle line:84% Instead of dropping a grape, imagine some really annoying 00:22:46.440 --> 00:22:48.900 align:middle line:84% housefly buzzing around your head 00:22:48.900 --> 00:22:51.690 align:middle line:84% at some radius of a couple centimeters from your head, 00:22:51.690 --> 00:22:52.950 align:middle line:90% super annoying. 00:22:52.950 --> 00:22:56.190 align:middle line:84% What's the angular momentum of that tiny little fly as it just 00:22:56.190 --> 00:22:58.620 align:middle line:90% buzzes lazily around your head? 00:22:58.620 --> 00:23:02.640 align:middle line:84% Again, it will have angular momentum exponentially large 00:23:02.640 --> 00:23:05.070 align:middle line:84% if we were to measure it in units of Planck's constant-- 00:23:05.070 --> 00:23:06.850 align:middle line:90% again, around 10 to the 28. 00:23:06.850 --> 00:23:08.700 align:middle line:84% So this is not a scale in which we 00:23:08.700 --> 00:23:11.520 align:middle line:84% expect to find strange quantum features in our everyday life-- 00:23:11.520 --> 00:23:14.320 align:middle line:84% grapes, houseflies, automobiles, and so on. 00:23:14.320 --> 00:23:17.280 align:middle line:84% And yet, Planck could only make sense of that PTR data 00:23:17.280 --> 00:23:20.220 align:middle line:84% if he introduced this new scale, this new constant, 00:23:20.220 --> 00:23:23.100 align:middle line:84% very different from human experience, and yet not 0, 00:23:23.100 --> 00:23:27.330 align:middle line:84% some finite value, even if it's small, in our human terms. 00:23:27.330 --> 00:23:29.220 align:middle line:84% Now, one of the readings you had for today 00:23:29.220 --> 00:23:32.610 align:middle line:84% was by the historian Thomas Kuhn. 00:23:32.610 --> 00:23:34.890 align:middle line:84% Kuhn wrote a really fascinating book. 00:23:34.890 --> 00:23:35.860 align:middle line:90% Here's the book cover. 00:23:35.860 --> 00:23:38.730 align:middle line:84% And the article version that you had 00:23:38.730 --> 00:23:41.130 align:middle line:90% draws on the same body of work. 00:23:41.130 --> 00:23:43.060 align:middle line:84% And I find this super fascinating. 00:23:43.060 --> 00:23:46.170 align:middle line:84% So we know that Planck published that formula, the one that I 00:23:46.170 --> 00:23:48.450 align:middle line:84% showed before, where the frequencies go 00:23:48.450 --> 00:23:52.050 align:middle line:84% like nu cubed over e to the h nu over kT minus 1. 00:23:52.050 --> 00:23:53.640 align:middle line:84% We now call that the Planck spectrum. 00:23:53.640 --> 00:23:54.888 align:middle line:90% We use it all the time. 00:23:54.888 --> 00:23:57.180 align:middle line:84% We know exactly when he wrote it down and published it. 00:23:57.180 --> 00:24:00.750 align:middle line:84% What we still don't really know, or still is controversial, 00:24:00.750 --> 00:24:02.940 align:middle line:84% is what did Planck think he was doing when 00:24:02.940 --> 00:24:04.290 align:middle line:90% he wrote down that expression. 00:24:04.290 --> 00:24:06.790 align:middle line:84% How did Planck interpret his own equation? 00:24:06.790 --> 00:24:08.790 align:middle line:84% Here we are, yet again, thrown into this really, 00:24:08.790 --> 00:24:12.300 align:middle line:84% I think, delicious question of how a single equation could 00:24:12.300 --> 00:24:15.600 align:middle line:84% be subject to many often competing interpretations. 00:24:15.600 --> 00:24:18.840 align:middle line:84% And Kuhn was among the first to try to argue, 00:24:18.840 --> 00:24:22.920 align:middle line:84% in particular, that Planck's own roots to that now very famous 00:24:22.920 --> 00:24:27.580 align:middle line:84% equation looked nothing like how we interpret the result. 00:24:27.580 --> 00:24:30.600 align:middle line:84% So when we derive Planck's expression-- like, for example, 00:24:30.600 --> 00:24:33.120 align:middle line:84% in my own notes or any textbook-- you might look it up 00:24:33.120 --> 00:24:35.780 align:middle line:84% in a modern textbook-- we say we get 00:24:35.780 --> 00:24:38.180 align:middle line:84% Planck's result for that form for this spectral energy 00:24:38.180 --> 00:24:42.800 align:middle line:84% density by making a new conceptual leap by requiring 00:24:42.800 --> 00:24:46.190 align:middle line:84% that the energy exchanged between matter and radiation 00:24:46.190 --> 00:24:47.960 align:middle line:90% can't take any old value. 00:24:47.960 --> 00:24:52.010 align:middle line:84% It can't be 6, or 6.01, or 6.02 in appropriate units, 00:24:52.010 --> 00:24:53.330 align:middle line:90% but has to come chunked. 00:24:53.330 --> 00:24:56.540 align:middle line:84% It has to come quantized in these units 00:24:56.540 --> 00:25:00.380 align:middle line:84% of a particular size, Planck's constant h times the frequency 00:25:00.380 --> 00:25:04.280 align:middle line:84% of the light involved, rather than treating the energy 00:25:04.280 --> 00:25:06.770 align:middle line:84% exchange between matter and radiation 00:25:06.770 --> 00:25:09.320 align:middle line:84% as continuous the way we would if we were describing 00:25:09.320 --> 00:25:11.438 align:middle line:84% light, for example, as Maxwellian waves. 00:25:11.438 --> 00:25:13.730 align:middle line:84% It shouldn't matter what the frequency is of that wave. 00:25:13.730 --> 00:25:15.710 align:middle line:84% We know how to calculate the energy associated 00:25:15.710 --> 00:25:17.060 align:middle line:90% with any process. 00:25:17.060 --> 00:25:20.580 align:middle line:84% And there should be no limit, no chunking or quantization. 00:25:20.580 --> 00:25:23.570 align:middle line:84% So Kuhn was asking very directly, 00:25:23.570 --> 00:25:26.960 align:middle line:84% did Max Planck think that's what he was doing in 00:25:26.960 --> 00:25:29.030 align:middle line:84% around 1900 when he introduced what we now 00:25:29.030 --> 00:25:31.470 align:middle line:90% call Planck's formula? 00:25:31.470 --> 00:25:34.340 align:middle line:84% And so just to give the highlight of Kuhn's article-- 00:25:34.340 --> 00:25:35.660 align:middle line:90% it's a complicated article. 00:25:35.660 --> 00:25:37.407 align:middle line:90% If it was confusing, that's OK. 00:25:37.407 --> 00:25:38.990 align:middle line:84% I want to talk through what I consider 00:25:38.990 --> 00:25:42.440 align:middle line:84% the headline news, the main takeaways from Kuhn's argument. 00:25:42.440 --> 00:25:44.190 align:middle line:84% It's a very complicated argument. 00:25:44.190 --> 00:25:47.630 align:middle line:84% Here's what I consider the biggest revelations. 00:25:47.630 --> 00:25:51.080 align:middle line:84% So Kuhn argues that, in Planck's original derivation, 00:25:51.080 --> 00:25:54.380 align:middle line:84% this now very famous canonical formula, Planck fixed 00:25:54.380 --> 00:25:56.780 align:middle line:84% the total energy of the system, all the 00:25:56.780 --> 00:26:00.470 align:middle line:84% imagined little resonators or make believe molecules 00:26:00.470 --> 00:26:02.150 align:middle line:90% in that blackbody-- 00:26:02.150 --> 00:26:04.940 align:middle line:84% he fixed the total energy of that system 00:26:04.940 --> 00:26:08.060 align:middle line:84% to be an integer number of these units h nu. 00:26:08.060 --> 00:26:10.340 align:middle line:84% But according to Kuhn, Planck did not 00:26:10.340 --> 00:26:13.550 align:middle line:84% fix each actual resonator, each degree 00:26:13.550 --> 00:26:17.750 align:middle line:84% of freedom of that system, to separately have this value h 00:26:17.750 --> 00:26:22.010 align:middle line:84% nu so that Planck was fixing the total energy for convenience 00:26:22.010 --> 00:26:24.500 align:middle line:84% as a kind of accounting trick, not fixing 00:26:24.500 --> 00:26:26.630 align:middle line:90% the unit of each moving part. 00:26:26.630 --> 00:26:29.060 align:middle line:84% Whereas today-- again, as I go through in some details 00:26:29.060 --> 00:26:29.840 align:middle line:90% in those notes-- 00:26:29.840 --> 00:26:32.480 align:middle line:84% we derive Planck's result by fixing 00:26:32.480 --> 00:26:36.710 align:middle line:84% the allowable energy of each individual part, each E sub i, 00:26:36.710 --> 00:26:37.480 align:middle line:90% so to speak. 00:26:37.480 --> 00:26:38.220 align:middle line:90% OK. 00:26:38.220 --> 00:26:41.750 align:middle line:84% In Planck's description, as Kuhn reconstructs it, 00:26:41.750 --> 00:26:44.450 align:middle line:84% the energies for each of these subsystems, each kind of moving 00:26:44.450 --> 00:26:46.760 align:middle line:84% part according to Planck's original derivation, 00:26:46.760 --> 00:26:49.880 align:middle line:84% was actually assumed to fall within some continuous range 00:26:49.880 --> 00:26:54.440 align:middle line:84% between E and E plus delta E, not fixed, snapping in place 00:26:54.440 --> 00:26:56.270 align:middle line:90% in these quantized units. 00:26:56.270 --> 00:26:57.500 align:middle line:90% So Kuhn goes on. 00:26:57.500 --> 00:26:59.150 align:middle line:84% It's a very complicated argument. 00:26:59.150 --> 00:27:01.250 align:middle line:84% The book is even more complicated. 00:27:01.250 --> 00:27:03.350 align:middle line:84% But according to Kuhn's analysis, 00:27:03.350 --> 00:27:07.250 align:middle line:84% Planck uses bins of size-- we might use the Greek letter 00:27:07.250 --> 00:27:08.180 align:middle line:90% epsilon-- 00:27:08.180 --> 00:27:11.120 align:middle line:84% bins of size h nu for his accounting-- 00:27:11.120 --> 00:27:14.810 align:middle line:84% but again, only to say how many of these resonators 00:27:14.810 --> 00:27:16.520 align:middle line:84% or oscillators-- again, roughly speaking, 00:27:16.520 --> 00:27:21.320 align:middle line:84% moving parts how many of them had energies within 0 00:27:21.320 --> 00:27:24.590 align:middle line:84% and epsilon, within 1 unit, between 1 and 2 units, 00:27:24.590 --> 00:27:27.410 align:middle line:84% not that they had to have exactly 1 or 2 units, the way 00:27:27.410 --> 00:27:29.220 align:middle line:90% we'd say today. 00:27:29.220 --> 00:27:31.200 align:middle line:90% Moreover, Kuhn goes on again-- 00:27:31.200 --> 00:27:33.570 align:middle line:84% he does this in more detail in this longer book. 00:27:33.570 --> 00:27:36.150 align:middle line:84% Years later, six years later, Plank 00:27:36.150 --> 00:27:39.910 align:middle line:84% was giving lectures at the university about this topic. 00:27:39.910 --> 00:27:42.300 align:middle line:84% And he still spoke in his lecture notes 00:27:42.300 --> 00:27:46.410 align:middle line:84% of a kind of continuous rather than quantized energy exchange. 00:27:46.410 --> 00:27:49.890 align:middle line:84% It wasn't just a momentary lapse in December of 1900, 00:27:49.890 --> 00:27:51.090 align:middle line:90% argues Thomas Kuhn. 00:27:51.090 --> 00:27:54.000 align:middle line:84% It was years and years during which 00:27:54.000 --> 00:27:56.480 align:middle line:84% Plank thought about his own equation quite differently 00:27:56.480 --> 00:27:58.980 align:middle line:84% than the way we would today, even though the equation itself 00:27:58.980 --> 00:28:00.010 align:middle line:90% hasn't changed. 00:28:00.010 --> 00:28:01.500 align:middle line:90% Now, that's Kuhn's argument. 00:28:01.500 --> 00:28:04.082 align:middle line:84% He has lots of evidence that I found very interesting. 00:28:04.082 --> 00:28:05.290 align:middle line:90% It's also really complicated. 00:28:05.290 --> 00:28:07.800 align:middle line:84% There's a fascinating much more recent article 00:28:07.800 --> 00:28:10.410 align:middle line:84% by the physicist and historian Michael Nauenberg 00:28:10.410 --> 00:28:14.160 align:middle line:84% you can look up that actually draws the opposite conclusion, 00:28:14.160 --> 00:28:17.100 align:middle line:84% that Plank had a much more similar notion to what we have 00:28:17.100 --> 00:28:19.230 align:middle line:90% today, even as early as 1900. 00:28:19.230 --> 00:28:20.800 align:middle line:90% It's really complicated. 00:28:20.800 --> 00:28:23.220 align:middle line:84% So I don't know who of these analysts is right. 00:28:23.220 --> 00:28:26.130 align:middle line:84% What I do know is it was really, really not clear, even 00:28:26.130 --> 00:28:28.810 align:middle line:84% to Planck's own contemporaries, what exactly 00:28:28.810 --> 00:28:31.180 align:middle line:90% to make of this new formula. 00:28:31.180 --> 00:28:33.490 align:middle line:84% And Planck himself was not shy about that. 00:28:33.490 --> 00:28:35.770 align:middle line:84% He wrote to a colleague decades later, 00:28:35.770 --> 00:28:39.920 align:middle line:84% 31 years after deriving his now famous equation-- 00:28:39.920 --> 00:28:42.490 align:middle line:84% he wrote, what I did back in 1900 00:28:42.490 --> 00:28:45.370 align:middle line:84% can be described as simply an act of desperation. 00:28:45.370 --> 00:28:49.120 align:middle line:84% He was trying to match the updated data from the PTR. 00:28:49.120 --> 00:28:51.430 align:middle line:84% He knew that curve couldn't just keep rising forever. 00:28:51.430 --> 00:28:52.810 align:middle line:90% He was desperate. 00:28:52.810 --> 00:28:56.560 align:middle line:84% Introducing these bins of fixed quantized size, 00:28:56.560 --> 00:28:59.980 align:middle line:84% Planck continued, was purely a formal assumption. 00:28:59.980 --> 00:29:03.333 align:middle line:84% And I really do not give it much thought, which is interesting. 00:29:03.333 --> 00:29:04.250 align:middle line:90% So let me pause there. 00:29:04.250 --> 00:29:05.680 align:middle line:84% That's what I wanted to share about Planck 00:29:05.680 --> 00:29:06.940 align:middle line:90% and the blackbody spectrum. 00:29:06.940 --> 00:29:08.020 align:middle line:90% Any questions about that? 00:29:08.020 --> 00:29:11.788 align:middle line:90% 00:29:11.788 --> 00:29:13.608 align:middle line:84% Ah, Jade asked a good question in the chat. 00:29:13.608 --> 00:29:15.650 align:middle line:84% How did they measure the spectral energy density? 00:29:15.650 --> 00:29:16.260 align:middle line:90% Very good. 00:29:16.260 --> 00:29:18.260 align:middle line:84% So the short answer is this is the kind of thing 00:29:18.260 --> 00:29:22.070 align:middle line:84% that the experimentalists at the PTR were very, very good at. 00:29:22.070 --> 00:29:27.050 align:middle line:84% So they could use basically things like diffraction 00:29:27.050 --> 00:29:29.720 align:middle line:84% gratings-- and they might have even had access to fine 00:29:29.720 --> 00:29:30.410 align:middle line:90% prisms-- 00:29:30.410 --> 00:29:34.190 align:middle line:84% to measure very specific energy outputs in very specific 00:29:34.190 --> 00:29:35.342 align:middle line:90% wavelength bins. 00:29:35.342 --> 00:29:37.800 align:middle line:84% So that's the kind of thing they were getting very good at. 00:29:37.800 --> 00:29:39.380 align:middle line:84% I think they did mostly use diffraction gratings. 00:29:39.380 --> 00:29:40.370 align:middle line:90% I'm not positive. 00:29:40.370 --> 00:29:44.310 align:middle line:84% So they had a cavity, a vacuated chamber, 00:29:44.310 --> 00:29:46.820 align:middle line:84% that they could heat up in an oven 00:29:46.820 --> 00:29:49.340 align:middle line:90% with a little hole in the side. 00:29:49.340 --> 00:29:52.580 align:middle line:84% So mostly, they had this empty space that would heat up. 00:29:52.580 --> 00:29:55.340 align:middle line:84% And they would let a-- it was a cavity-- 00:29:55.340 --> 00:29:58.920 align:middle line:84% let a little bit of this light sneak out a little window. 00:29:58.920 --> 00:30:01.620 align:middle line:84% And that's what was taking the place of this blackbody. 00:30:01.620 --> 00:30:04.160 align:middle line:84% So no light was coming in onto that box. 00:30:04.160 --> 00:30:08.000 align:middle line:84% It was sealed up like a metal trap, cavity. 00:30:08.000 --> 00:30:10.310 align:middle line:84% A little light escapes through a little porthole. 00:30:10.310 --> 00:30:12.660 align:middle line:84% And so what you should be measuring is only the light 00:30:12.660 --> 00:30:14.790 align:middle line:84% due to this thermal radiation because nothing's 00:30:14.790 --> 00:30:16.170 align:middle line:90% reflecting on that stuff. 00:30:16.170 --> 00:30:18.387 align:middle line:84% That's how they made the blackbody in real life, 00:30:18.387 --> 00:30:19.470 align:middle line:90% in the actual experiments. 00:30:19.470 --> 00:30:21.300 align:middle line:84% Then they could subject that light that 00:30:21.300 --> 00:30:23.340 align:middle line:84% came out to very fine measurements 00:30:23.340 --> 00:30:26.640 align:middle line:84% by splitting it up into its colors with things 00:30:26.640 --> 00:30:29.850 align:middle line:84% like diffraction gratings or prisms, 00:30:29.850 --> 00:30:31.080 align:middle line:90% and then measure-- let's see. 00:30:31.080 --> 00:30:33.840 align:middle line:84% They must have measured the intensity, the brightness. 00:30:33.840 --> 00:30:35.712 align:middle line:84% They must have had some kind of photometers. 00:30:35.712 --> 00:30:37.170 align:middle line:84% And I'm not sure how they did that. 00:30:37.170 --> 00:30:38.140 align:middle line:90% We can look it up. 00:30:38.140 --> 00:30:40.170 align:middle line:84% But they were good at measuring very finely 00:30:40.170 --> 00:30:41.880 align:middle line:90% detailed wavelengths. 00:30:41.880 --> 00:30:43.650 align:middle line:84% And in fact, they were getting better 00:30:43.650 --> 00:30:47.310 align:middle line:84% over the 1890s in various parts of the spectrum. 00:30:47.310 --> 00:30:49.590 align:middle line:84% They knew some of the early data points early on, 00:30:49.590 --> 00:30:52.020 align:middle line:84% the ones that matched this rising curve that 00:30:52.020 --> 00:30:54.805 align:middle line:84% looks like it would lead to this runaway energy, 00:30:54.805 --> 00:30:56.430 align:middle line:84% this so-called ultraviolet catastrophe. 00:30:56.430 --> 00:31:00.270 align:middle line:84% The earliest data were at low wavelengths, small frequencies, 00:31:00.270 --> 00:31:02.613 align:middle line:84% where it really did go like nu squared. 00:31:02.613 --> 00:31:04.530 align:middle line:84% And what was most important, as everyone knew, 00:31:04.530 --> 00:31:06.405 align:middle line:84% was to measure the other end of the spectrum. 00:31:06.405 --> 00:31:08.040 align:middle line:84% That couldn't keep rising forever. 00:31:08.040 --> 00:31:11.100 align:middle line:84% And the researchers, like Lummer and Pringsheim, 00:31:11.100 --> 00:31:13.470 align:middle line:84% were getting more and more data at the other part 00:31:13.470 --> 00:31:16.320 align:middle line:84% of the spectrum, at shorter wavelengths, higher 00:31:16.320 --> 00:31:19.740 align:middle line:84% frequencies, and watching just how that curve began to fall, 00:31:19.740 --> 00:31:22.740 align:middle line:84% what we now would recognize as this exponential tail. 00:31:22.740 --> 00:31:26.898 align:middle line:84% So they were doing that, again, with more and more precision. 00:31:26.898 --> 00:31:27.690 align:middle line:90% Excellent question. 00:31:27.690 --> 00:31:29.170 align:middle line:90% Johan asks a very good question. 00:31:29.170 --> 00:31:30.990 align:middle line:84% How did they do that without a graphing calculator? 00:31:30.990 --> 00:31:32.250 align:middle line:90% He was no Cambridge Wrangler. 00:31:32.250 --> 00:31:34.920 align:middle line:84% But Planck was a pretty well trained mathematical physicist. 00:31:34.920 --> 00:31:38.107 align:middle line:84% It was-- and the the other fact, it was painstaking. 00:31:38.107 --> 00:31:40.440 align:middle line:84% And also, how did he come up with these particular forms 00:31:40.440 --> 00:31:41.550 align:middle line:90% of his equations? 00:31:41.550 --> 00:31:45.240 align:middle line:84% You can read Thomas Kuhn's 400-page monograph, 00:31:45.240 --> 00:31:46.410 align:middle line:90% which I have forced-- 00:31:46.410 --> 00:31:49.650 align:middle line:84% rather, encouraged-- some of the TAs to do directly. 00:31:49.650 --> 00:31:51.300 align:middle line:90% I will say encouraged. 00:31:51.300 --> 00:31:53.160 align:middle line:90% I reread it every few years. 00:31:53.160 --> 00:31:54.910 align:middle line:90% It's really complicated. 00:31:54.910 --> 00:31:57.330 align:middle line:84% I mean, what was Planck doing what was he doing when? 00:31:57.330 --> 00:31:58.900 align:middle line:90% What did he think he was doing? 00:31:58.900 --> 00:32:00.900 align:middle line:90% That is really complicated. 00:32:00.900 --> 00:32:03.420 align:middle line:84% And other really smart, dedicated researchers 00:32:03.420 --> 00:32:05.190 align:middle line:84% like Michael Nauenberg come back to some 00:32:05.190 --> 00:32:08.190 align:middle line:84% of the same materials, the same obscure lecture 00:32:08.190 --> 00:32:09.890 align:middle line:90% notes, the same publications. 00:32:09.890 --> 00:32:12.082 align:middle line:84% He says, no, look very carefully at equation 25b. 00:32:12.082 --> 00:32:13.290 align:middle line:90% He does something else there. 00:32:13.290 --> 00:32:16.260 align:middle line:90% It gets really, really hard. 00:32:16.260 --> 00:32:18.660 align:middle line:84% What is clear, as I'll say actually in the next section, 00:32:18.660 --> 00:32:21.030 align:middle line:84% is that some other of Planck's own contemporaries, 00:32:21.030 --> 00:32:23.250 align:middle line:84% like a still very young Albert Einstein-- 00:32:23.250 --> 00:32:25.110 align:middle line:84% Einstein was convinced that Planck actually 00:32:25.110 --> 00:32:26.460 align:middle line:90% hadn't gone far enough. 00:32:26.460 --> 00:32:28.470 align:middle line:84% So it's not just historians who debate 00:32:28.470 --> 00:32:31.680 align:middle line:84% this the better part of a century later after Planck. 00:32:31.680 --> 00:32:33.210 align:middle line:84% Even some contemporaries who were 00:32:33.210 --> 00:32:35.310 align:middle line:84% trying to make sense of Planck's own argument 00:32:35.310 --> 00:32:38.040 align:middle line:84% thought that Planck's reasoning was, at best, muddled 00:32:38.040 --> 00:32:40.295 align:middle line:84% and maybe different from what they themselves thought. 00:32:40.295 --> 00:32:42.420 align:middle line:84% And that's why I like that letter that Planck wrote 00:32:42.420 --> 00:32:45.468 align:middle line:84% in the early '30s saying, yeah, I didn't know what I was doing, 00:32:45.468 --> 00:32:47.010 align:middle line:84% is essentially how I read that quote. 00:32:47.010 --> 00:32:48.688 align:middle line:90% I was desperate. 00:32:48.688 --> 00:32:50.230 align:middle line:84% So I think that's really interesting. 00:32:50.230 --> 00:32:52.480 align:middle line:84% Any other questions on the blackbody spectrum 00:32:52.480 --> 00:32:54.770 align:middle line:90% or Planck's formula? 00:32:54.770 --> 00:32:56.680 align:middle line:84% If not, let's go on and see what Einstein 00:32:56.680 --> 00:33:00.600 align:middle line:84% begins to do with that in that same famous year of 1905. 00:33:00.600 --> 00:33:02.680 align:middle line:90% So let's go to that next part. 00:33:02.680 --> 00:33:04.980 align:middle line:84% So now, we're talking about Einstein 00:33:04.980 --> 00:33:07.155 align:middle line:84% and what becomes known as the photoelectric effect. 00:33:07.155 --> 00:33:11.120 align:middle line:90% 00:33:11.120 --> 00:33:15.838 align:middle line:84% It turns out Planck was concerned about the interaction 00:33:15.838 --> 00:33:16.880 align:middle line:90% between light and matter. 00:33:16.880 --> 00:33:18.800 align:middle line:84% He wasn't even, in his own writings, 00:33:18.800 --> 00:33:21.560 align:middle line:84% talking about the propagation of light on its own 00:33:21.560 --> 00:33:24.920 align:middle line:84% for which he just took right off the shelf Maxwell's by then 00:33:24.920 --> 00:33:26.960 align:middle line:84% quite standard treatment that light is clearly 00:33:26.960 --> 00:33:30.210 align:middle line:84% a continuous wave spread out through space. 00:33:30.210 --> 00:33:33.380 align:middle line:84% And so in 1905, just a few years later, 00:33:33.380 --> 00:33:34.910 align:middle line:84% young Albert Einstein, as we still 00:33:34.910 --> 00:33:37.640 align:middle line:84% know patent clerk third class, began 00:33:37.640 --> 00:33:40.310 align:middle line:84% to think about the nature of light on its own, 00:33:40.310 --> 00:33:43.250 align:middle line:84% even when it's not necessarily interacting with matter. 00:33:43.250 --> 00:33:45.530 align:middle line:84% This was actually the first of these four kind 00:33:45.530 --> 00:33:48.830 align:middle line:84% of amazing or surprising papers that Einstein wound up 00:33:48.830 --> 00:33:52.070 align:middle line:84% submitting to the Annalen der Physik in that year, 1905. 00:33:52.070 --> 00:33:54.740 align:middle line:84% The first of them that he sent in to the journal, 00:33:54.740 --> 00:33:58.850 align:middle line:84% back in March of that year, was the one on what he calls light. 00:33:58.850 --> 00:34:01.280 align:middle line:84% Now, Einstein was thinking not only about Planck's work, 00:34:01.280 --> 00:34:03.110 align:middle line:84% though he was thinking about that. 00:34:03.110 --> 00:34:06.140 align:middle line:84% He had other recent experiments or descriptions of light 00:34:06.140 --> 00:34:09.469 align:middle line:84% in mind as well, one of which-- the one that he was even more 00:34:09.469 --> 00:34:11.270 align:middle line:90% focused on-- 00:34:11.270 --> 00:34:14.810 align:middle line:84% was a series of, again, puzzling experimental results that 00:34:14.810 --> 00:34:16.940 align:middle line:84% had just been coming out through the years 00:34:16.940 --> 00:34:20.540 align:middle line:84% up through 1902 by the German researcher Philipp Lenard. 00:34:20.540 --> 00:34:22.100 align:middle line:84% If that name sounds familiar, it's 00:34:22.100 --> 00:34:24.020 align:middle line:84% because we just talked briefly about Lenard 00:34:24.020 --> 00:34:25.460 align:middle line:90% in the previous lecture. 00:34:25.460 --> 00:34:28.400 align:middle line:84% Lenard went on, years later, to become 00:34:28.400 --> 00:34:31.014 align:middle line:84% one of the front men, so to speak, 00:34:31.014 --> 00:34:33.139 align:middle line:84% of that Deutsche Physik movement, one of the people 00:34:33.139 --> 00:34:35.989 align:middle line:84% who began denouncing Einstein and relativity 00:34:35.989 --> 00:34:38.449 align:middle line:90% starting as early as 1920. 00:34:38.449 --> 00:34:40.190 align:middle line:84% Lenard was conducting these experiments 00:34:40.190 --> 00:34:42.190 align:middle line:84% on what became known as the photoelectric effect 00:34:42.190 --> 00:34:45.770 align:middle line:84% in the early years of the 20th century. 00:34:45.770 --> 00:34:48.980 align:middle line:84% The sharpest, clearest experimental results 00:34:48.980 --> 00:34:50.870 align:middle line:90% were published in 1902. 00:34:50.870 --> 00:34:53.300 align:middle line:84% He was recognized very early on for that work. 00:34:53.300 --> 00:34:55.699 align:middle line:84% He won the Nobel Prize in 1905, the very year 00:34:55.699 --> 00:34:57.890 align:middle line:84% that Einstein begins trying to come up 00:34:57.890 --> 00:35:02.360 align:middle line:84% with a theoretical explanation for these experimental results. 00:35:02.360 --> 00:35:03.890 align:middle line:90% So what were Lenard's results? 00:35:03.890 --> 00:35:08.180 align:middle line:84% Here again, in of cartoon form, are the fundamentals 00:35:08.180 --> 00:35:11.152 align:middle line:84% of the experiments that Lenard was pursuing. 00:35:11.152 --> 00:35:13.610 align:middle line:84% In fact, others around the world were doing similar things. 00:35:13.610 --> 00:35:16.340 align:middle line:84% Lenard had, in some sense, the cleanest data 00:35:16.340 --> 00:35:19.610 align:middle line:84% that forced the most sharp showdown with how 00:35:19.610 --> 00:35:21.140 align:middle line:90% to make sense of these results. 00:35:21.140 --> 00:35:22.580 align:middle line:84% Others were doing similar things. 00:35:22.580 --> 00:35:25.070 align:middle line:84% He had a very simple kind of apparatus. 00:35:25.070 --> 00:35:28.370 align:middle line:84% So these two blue pieces here represent 00:35:28.370 --> 00:35:31.190 align:middle line:90% metallic conducting plates. 00:35:31.190 --> 00:35:34.340 align:middle line:84% And across, Lenard could apply a voltage 00:35:34.340 --> 00:35:36.260 align:middle line:90% of an amount he could vary. 00:35:36.260 --> 00:35:39.390 align:middle line:84% He had a tunable voltage between his conducting plates. 00:35:39.390 --> 00:35:42.330 align:middle line:84% He would then direct an ultraviolet light source-- 00:35:42.330 --> 00:35:44.850 align:middle line:84% sorry, an ultraviolet light source onto one of those 00:35:44.850 --> 00:35:45.510 align:middle line:90% plates. 00:35:45.510 --> 00:35:47.820 align:middle line:84% So he has some source of ultraviolet light shining it 00:35:47.820 --> 00:35:49.410 align:middle line:90% on one of those plates. 00:35:49.410 --> 00:35:52.350 align:middle line:84% And under certain conditions, the light source, 00:35:52.350 --> 00:35:55.320 align:middle line:84% when it irradiates that plate, would eject, would kick out, 00:35:55.320 --> 00:35:56.890 align:middle line:90% some electrons. 00:35:56.890 --> 00:35:59.610 align:middle line:84% The electrons would then travel toward the other conducting 00:35:59.610 --> 00:36:01.540 align:middle line:90% plate, completing a circuit. 00:36:01.540 --> 00:36:04.560 align:middle line:84% So when the light kicked out electrons, ejected electrons 00:36:04.560 --> 00:36:09.060 align:middle line:84% from this so-called cathode, from that metal conducting 00:36:09.060 --> 00:36:10.927 align:middle line:84% plate, you could complete a circuit 00:36:10.927 --> 00:36:12.510 align:middle line:84% because the electrons would now travel 00:36:12.510 --> 00:36:14.722 align:middle line:84% through the intervening space and hit this plate. 00:36:14.722 --> 00:36:16.680 align:middle line:84% And you'd know you had electric current flowing 00:36:16.680 --> 00:36:20.290 align:middle line:84% because he hooked up an ammeter, a measure of electric current. 00:36:20.290 --> 00:36:21.780 align:middle line:84% So he knew he had current flowing. 00:36:21.780 --> 00:36:23.322 align:middle line:84% He knew electrons had been kicked out 00:36:23.322 --> 00:36:26.370 align:middle line:84% of the metal when the ammeter measured an electric current. 00:36:26.370 --> 00:36:28.950 align:middle line:84% And then he could use this tunable voltage-- 00:36:28.950 --> 00:36:30.960 align:middle line:84% he could change the amount of voltage applied-- 00:36:30.960 --> 00:36:33.240 align:middle line:84% to basically ask, how much energy 00:36:33.240 --> 00:36:35.820 align:middle line:84% were those electrons kicked out with, 00:36:35.820 --> 00:36:38.880 align:middle line:84% by asking how strong a voltage he had to tune up 00:36:38.880 --> 00:36:41.550 align:middle line:90% to block their passage. 00:36:41.550 --> 00:36:44.550 align:middle line:84% So when he applied basically no voltage, 00:36:44.550 --> 00:36:46.680 align:middle line:84% the electrons would come across the plate 00:36:46.680 --> 00:36:47.730 align:middle line:90% and complete the circuit. 00:36:47.730 --> 00:36:50.790 align:middle line:84% So how much countervailing voltage 00:36:50.790 --> 00:36:53.520 align:middle line:84% would Lenard have to apply to block 00:36:53.520 --> 00:36:57.120 align:middle line:84% their passage, a kind of repulsive electric force 00:36:57.120 --> 00:36:59.100 align:middle line:84% to basically repel the electrons away 00:36:59.100 --> 00:37:00.600 align:middle line:90% from reaching this far plate? 00:37:00.600 --> 00:37:03.000 align:middle line:90% So when will the current stop? 00:37:03.000 --> 00:37:05.430 align:middle line:84% Then he knows what's called the stopping voltage. 00:37:05.430 --> 00:37:07.830 align:middle line:84% And that tells him exactly how much energy the electrons 00:37:07.830 --> 00:37:11.760 align:middle line:84% had because he had to counteract that much energy, that much 00:37:11.760 --> 00:37:15.880 align:middle line:84% electrostatic force, to turn off that current. 00:37:15.880 --> 00:37:18.960 align:middle line:84% So now, he could start comparing the stopping voltage, which 00:37:18.960 --> 00:37:21.240 align:middle line:84% for him is a measure of the energy with which 00:37:21.240 --> 00:37:22.590 align:middle line:90% these electrons are ejected. 00:37:22.590 --> 00:37:24.930 align:middle line:84% So he can compare the energy of the electrons 00:37:24.930 --> 00:37:27.540 align:middle line:84% with the frequency of this light source. 00:37:27.540 --> 00:37:29.460 align:middle line:84% He shines light of certain frequencies 00:37:29.460 --> 00:37:32.580 align:middle line:84% within the ultraviolet range onto this metallic plate. 00:37:32.580 --> 00:37:34.380 align:middle line:84% And he measures the amount of energy 00:37:34.380 --> 00:37:35.910 align:middle line:90% of the ejected electrons. 00:37:35.910 --> 00:37:38.277 align:middle line:84% And again, in cleaned up form, the data 00:37:38.277 --> 00:37:39.360 align:middle line:90% started looking like this. 00:37:39.360 --> 00:37:42.940 align:middle line:84% It had a very specific, very striking shape. 00:37:42.940 --> 00:37:46.950 align:middle line:84% So on a plot of the energy of the ejected electrons 00:37:46.950 --> 00:37:49.390 align:middle line:84% versus the frequency of the incident light, 00:37:49.390 --> 00:37:53.530 align:middle line:84% the energy electrons seemed to rise linearly, but only 00:37:53.530 --> 00:37:55.730 align:middle line:90% above some threshold frequency. 00:37:55.730 --> 00:37:59.020 align:middle line:84% So as the light was tuned to lower and lower frequencies-- 00:37:59.020 --> 00:38:01.450 align:middle line:84% the light that's being shown from this source-- 00:38:01.450 --> 00:38:04.450 align:middle line:84% there would be no electrons ejected at all. 00:38:04.450 --> 00:38:06.490 align:middle line:84% There would be zero electrons ejected, 00:38:06.490 --> 00:38:08.440 align:middle line:90% no energy crossing that gap. 00:38:08.440 --> 00:38:11.350 align:middle line:84% After you reach some very specific threshold 00:38:11.350 --> 00:38:15.310 align:middle line:84% frequency of the light, you start kicking electrons out. 00:38:15.310 --> 00:38:17.540 align:middle line:84% As you increase the frequency of that light, 00:38:17.540 --> 00:38:20.710 align:middle line:84% the energy that the electrons carry rises. 00:38:20.710 --> 00:38:22.630 align:middle line:84% The energy of the electrons seems 00:38:22.630 --> 00:38:25.090 align:middle line:84% to rise only with-- seem to depend only 00:38:25.090 --> 00:38:28.000 align:middle line:84% with the frequency of that light, not with the intensity. 00:38:28.000 --> 00:38:30.400 align:middle line:84% You can make this a brighter or less bright 00:38:30.400 --> 00:38:33.550 align:middle line:84% light source, holding the frequency fixed. 00:38:33.550 --> 00:38:36.250 align:middle line:84% And that had no impact on the stopping voltage, 00:38:36.250 --> 00:38:38.620 align:middle line:84% on the amount of energy required to stop those electrons 00:38:38.620 --> 00:38:40.585 align:middle line:90% from traversing that gap. 00:38:40.585 --> 00:38:41.710 align:middle line:90% That seemed pretty strange. 00:38:41.710 --> 00:38:44.110 align:middle line:90% Why was that so strange? 00:38:44.110 --> 00:38:46.602 align:middle line:84% Why was it strange to have a threshold frequency? 00:38:46.602 --> 00:38:48.310 align:middle line:84% And why was it strange to have the energy 00:38:48.310 --> 00:38:51.580 align:middle line:84% of the electrons independent of the intensity of that light, 00:38:51.580 --> 00:38:53.840 align:middle line:84% depending only on the frequency of the light? 00:38:53.840 --> 00:38:57.290 align:middle line:84% Well, again, if one took on Maxwell's by then quite 00:38:57.290 --> 00:38:59.760 align:middle line:84% standard description of electromagnetic waves, 00:38:59.760 --> 00:39:02.540 align:middle line:84% including in the ultraviolet part of the spectrum, 00:39:02.540 --> 00:39:04.790 align:middle line:84% the energy carried by those light waves 00:39:04.790 --> 00:39:07.850 align:middle line:84% from Lenard's device should have been proportional 00:39:07.850 --> 00:39:09.360 align:middle line:90% to the wave's intensity. 00:39:09.360 --> 00:39:12.410 align:middle line:84% The energy, script E here, was proportional 00:39:12.410 --> 00:39:14.540 align:middle line:90% to the intensity of the waves. 00:39:14.540 --> 00:39:17.750 align:middle line:84% The intensity, in turn, went by the square 00:39:17.750 --> 00:39:20.270 align:middle line:84% of those field strengths, the electric and magnetic field 00:39:20.270 --> 00:39:21.290 align:middle line:90% strengths. 00:39:21.290 --> 00:39:23.210 align:middle line:84% So why shouldn't Lenard have been 00:39:23.210 --> 00:39:27.860 align:middle line:84% able to get very large amplitude fields, high intensity 00:39:27.860 --> 00:39:30.830 align:middle line:84% fields that happen to have a long wavelength, that 00:39:30.830 --> 00:39:32.870 align:middle line:90% were a low frequency? 00:39:32.870 --> 00:39:37.240 align:middle line:84% That should carry as much energy as a short frequency wave, 00:39:37.240 --> 00:39:38.750 align:middle line:90% but of a smaller amplitude. 00:39:38.750 --> 00:39:41.030 align:middle line:84% Meaning, why couldn't he tune the intensity up 00:39:41.030 --> 00:39:45.410 align:middle line:84% and still get electrons ejected all the way down here? 00:39:45.410 --> 00:39:48.140 align:middle line:84% If light really acted like Maxwellian waves, 00:39:48.140 --> 00:39:50.900 align:middle line:84% why should there be any threshold frequency at all? 00:39:50.900 --> 00:39:54.590 align:middle line:84% You could always tune up the intensity of lower frequency 00:39:54.590 --> 00:39:57.080 align:middle line:84% light, was at least the expectation. 00:39:57.080 --> 00:39:59.780 align:middle line:84% Likewise, according to Maxwell's work, turning the argument 00:39:59.780 --> 00:40:02.300 align:middle line:84% around, once you do kick electrons out 00:40:02.300 --> 00:40:05.750 align:middle line:84% above that threshold, why should the energy that they carry 00:40:05.750 --> 00:40:07.490 align:middle line:84% be independent of what people thought 00:40:07.490 --> 00:40:10.345 align:middle line:84% would be the energy imparted by the light? 00:40:10.345 --> 00:40:11.720 align:middle line:84% The energy imparted by the light, 00:40:11.720 --> 00:40:14.120 align:middle line:84% again, should vary like the intensity. 00:40:14.120 --> 00:40:17.150 align:middle line:84% And yet, the energy that these electrons get kicked out with 00:40:17.150 --> 00:40:18.920 align:middle line:84% seemed not to depend on the brightness, 00:40:18.920 --> 00:40:21.510 align:middle line:84% the intensity of the source, only on the frequency. 00:40:21.510 --> 00:40:22.010 align:middle line:90% OK. 00:40:22.010 --> 00:40:24.770 align:middle line:84% So that was becoming increasingly clear 00:40:24.770 --> 00:40:26.810 align:middle line:84% experimental data, so clear that Lenard 00:40:26.810 --> 00:40:29.720 align:middle line:84% received the Prize just a few years later, the Nobel Prize. 00:40:29.720 --> 00:40:31.700 align:middle line:84% But it was by no means clear how to make sense 00:40:31.700 --> 00:40:33.470 align:middle line:90% of that combination of results. 00:40:33.470 --> 00:40:38.360 align:middle line:84% So Einstein's first paper of this remarkable year of 1905 00:40:38.360 --> 00:40:40.282 align:middle line:84% was trying to tackle this directly. 00:40:40.282 --> 00:40:42.740 align:middle line:84% In fact, in a letter to one of his friends from the Olympia 00:40:42.740 --> 00:40:45.050 align:middle line:84% Academy-- his friend, Conrad Habicht-- 00:40:45.050 --> 00:40:46.940 align:middle line:84% here, Einstein actually called this 00:40:46.940 --> 00:40:49.040 align:middle line:84% his most radical of all the papers 00:40:49.040 --> 00:40:50.300 align:middle line:90% he was working on that year. 00:40:50.300 --> 00:40:53.780 align:middle line:84% He thought this one was the most strange or most unexpected-- 00:40:53.780 --> 00:40:56.540 align:middle line:84% more so than relativity, more so than all the rest. 00:40:56.540 --> 00:40:59.480 align:middle line:84% So what he offers he calls a heuristic explanation. 00:40:59.480 --> 00:41:02.780 align:middle line:84% You see in the title, [GERMAN],, a heuristic 00:41:02.780 --> 00:41:06.050 align:middle line:84% kind of hypothetical or suggestive explanation. 00:41:06.050 --> 00:41:09.760 align:middle line:84% He's not saying, eureka, I found it. 00:41:09.760 --> 00:41:11.810 align:middle line:84% He's being maybe uncharacteristically 00:41:11.810 --> 00:41:13.580 align:middle line:90% a bit more modest here. 00:41:13.580 --> 00:41:16.850 align:middle line:84% He says, here's one way to think about these results. 00:41:16.850 --> 00:41:18.960 align:middle line:84% A heuristic idea would be to say, 00:41:18.960 --> 00:41:21.470 align:middle line:84% what if light itself were quantized? 00:41:21.470 --> 00:41:23.480 align:middle line:84% What if light traveled through space 00:41:23.480 --> 00:41:26.480 align:middle line:84% not like a continuous spread out wave, 00:41:26.480 --> 00:41:28.520 align:middle line:84% like Maxwell's theory would suggest, 00:41:28.520 --> 00:41:32.570 align:middle line:84% but instead like a collection of localized quanta? 00:41:32.570 --> 00:41:34.250 align:middle line:84% Here's a quotation from this paper 00:41:34.250 --> 00:41:36.770 align:middle line:90% in 1905 translated to English. 00:41:36.770 --> 00:41:39.650 align:middle line:84% He writes that, it seems to me these observations 00:41:39.650 --> 00:41:41.600 align:middle line:84% about the production of cathode rays-- 00:41:41.600 --> 00:41:45.320 align:middle line:84% those ejected electrons off that cathode by ultraviolet light-- 00:41:45.320 --> 00:41:47.215 align:middle line:84% he's now talking about Lenard's experiments. 00:41:47.215 --> 00:41:48.590 align:middle line:84% It seems to me these observations 00:41:48.590 --> 00:41:52.550 align:middle line:84% are more readily understood if one assumes the energy of light 00:41:52.550 --> 00:41:56.090 align:middle line:84% is discontinuously distributed in space. 00:41:56.090 --> 00:41:57.950 align:middle line:84% The energy of a light ray spreading out 00:41:57.950 --> 00:42:00.500 align:middle line:84% from a point source is not continuously 00:42:00.500 --> 00:42:04.070 align:middle line:84% distributed over an increasing space like a wave would be, 00:42:04.070 --> 00:42:06.950 align:middle line:84% like a Maximilian wave, or an ocean wave at that, 00:42:06.950 --> 00:42:12.020 align:middle line:84% but rather consists of a finite number of energy quanta, which 00:42:12.020 --> 00:42:14.690 align:middle line:84% are localized at points in space, which 00:42:14.690 --> 00:42:16.700 align:middle line:84% move without dividing-- they literally 00:42:16.700 --> 00:42:17.960 align:middle line:90% can't be further divided. 00:42:17.960 --> 00:42:21.230 align:middle line:84% They are quantized-- and which can only be produced 00:42:21.230 --> 00:42:23.600 align:middle line:90% and absorbed as complete units. 00:42:23.600 --> 00:42:25.820 align:middle line:84% These become known as light quanta, 00:42:25.820 --> 00:42:29.400 align:middle line:84% as little particles or corpuscles of light, 00:42:29.400 --> 00:42:32.960 align:middle line:84% rather than what was by then, going back to 1800 00:42:32.960 --> 00:42:36.110 align:middle line:84% let alone the 1860s, the taken for granted assumption 00:42:36.110 --> 00:42:39.200 align:middle line:84% that light was a wave, going all the way back to, say, 00:42:39.200 --> 00:42:42.020 align:middle line:84% Thomas Young's work or the work of several French scholars. 00:42:42.020 --> 00:42:44.232 align:middle line:84% So Einstein is suggesting heuristically-- he's not 00:42:44.232 --> 00:42:45.440 align:middle line:90% saying this must be the case. 00:42:45.440 --> 00:42:48.410 align:middle line:84% He's saying it's suggestive and worth considering 00:42:48.410 --> 00:42:51.140 align:middle line:84% that experiments like Lenard's might make sense 00:42:51.140 --> 00:42:55.560 align:middle line:84% if we change an everything we know about light. 00:42:55.560 --> 00:42:56.630 align:middle line:90% So why would that help? 00:42:56.630 --> 00:43:00.530 align:middle line:84% Let's go back to this cartoon version of Lenard's data. 00:43:00.530 --> 00:43:03.680 align:middle line:84% Einstein was, in fact, following Lenard's experiments, 00:43:03.680 --> 00:43:05.473 align:middle line:84% the publications quite closely-- much, much 00:43:05.473 --> 00:43:07.640 align:middle line:84% more closely than anything like the Michelson-Morley 00:43:07.640 --> 00:43:08.180 align:middle line:90% experiment. 00:43:08.180 --> 00:43:10.250 align:middle line:84% He really was looking up Lenard's papers 00:43:10.250 --> 00:43:13.370 align:middle line:84% and looking at the graphs and tables very carefully. 00:43:13.370 --> 00:43:15.320 align:middle line:84% Einstein recognized that it wasn't only 00:43:15.320 --> 00:43:17.750 align:middle line:84% a linear relationship between the energy 00:43:17.750 --> 00:43:21.210 align:middle line:84% of those ejected electrons and the frequency of the incident 00:43:21.210 --> 00:43:21.710 align:middle line:90% light. 00:43:21.710 --> 00:43:23.690 align:middle line:84% But the slope, in particular, looked 00:43:23.690 --> 00:43:26.618 align:middle line:84% awfully close to this new value that 00:43:26.618 --> 00:43:28.910 align:middle line:84% had just been introduced in a totally different context 00:43:28.910 --> 00:43:30.000 align:middle line:90% by Max Planck. 00:43:30.000 --> 00:43:32.060 align:middle line:84% The slope of this plot looked very much 00:43:32.060 --> 00:43:33.878 align:middle line:90% like Planck's constant, h. 00:43:33.878 --> 00:43:35.420 align:middle line:84% That's something that Einstein begins 00:43:35.420 --> 00:43:37.880 align:middle line:84% to recognize by going carefully over these experimental 00:43:37.880 --> 00:43:39.360 align:middle line:90% results. 00:43:39.360 --> 00:43:42.650 align:middle line:84% So that leads Einstein to think in the following way. 00:43:42.650 --> 00:43:45.410 align:middle line:84% What if each of these discrete little bundles 00:43:45.410 --> 00:43:46.500 align:middle line:90% of light energy-- 00:43:46.500 --> 00:43:50.780 align:middle line:84% what if each individual light quantum carried a fixed amount 00:43:50.780 --> 00:43:54.050 align:middle line:84% of energy proportional to the frequency of light 00:43:54.050 --> 00:43:56.460 align:middle line:84% with the constant of proportionality 00:43:56.460 --> 00:43:59.430 align:middle line:84% being this new constant introduced by Max Planck? 00:43:59.430 --> 00:44:03.240 align:middle line:84% What if light quanta, these indivisible pellets of light, 00:44:03.240 --> 00:44:06.360 align:middle line:84% had to carry a fixed, quantized amount of energy, 00:44:06.360 --> 00:44:10.320 align:middle line:84% not some continuous range that could have been any old value? 00:44:10.320 --> 00:44:13.530 align:middle line:84% If that's the case, then you have on this photocathode-- 00:44:13.530 --> 00:44:16.260 align:middle line:84% on this conducting plate in Lenard's experiment, 00:44:16.260 --> 00:44:19.530 align:middle line:84% you have raining down on it pellets and pellets each 00:44:19.530 --> 00:44:22.740 align:middle line:84% carrying a fixed amount of energy, h nu. 00:44:22.740 --> 00:44:25.890 align:middle line:84% So then you can imagine an individual light quantum, not 00:44:25.890 --> 00:44:27.540 align:middle line:90% some spread out wave-- 00:44:27.540 --> 00:44:30.420 align:middle line:84% an individual particle basically smacking 00:44:30.420 --> 00:44:32.610 align:middle line:90% into an individual electron. 00:44:32.610 --> 00:44:34.980 align:middle line:84% Now, it looks like colliding billiard balls. 00:44:34.980 --> 00:44:37.770 align:middle line:84% So how will the energy of the electron 00:44:37.770 --> 00:44:42.420 align:middle line:84% change after it gets smacked by a discrete pellet of energy, 00:44:42.420 --> 00:44:45.060 align:middle line:84% a light quantum with energy h nu? 00:44:45.060 --> 00:44:48.360 align:middle line:84% The electron should acquire a predictable amount of energy. 00:44:48.360 --> 00:44:52.380 align:middle line:84% It should absorb that energy carried by the light quantum. 00:44:52.380 --> 00:44:55.230 align:middle line:84% And yet, there will be some extra energy 00:44:55.230 --> 00:44:59.370 align:middle line:84% holding that electron bound to its atoms and molecules 00:44:59.370 --> 00:45:00.270 align:middle line:90% in the metal. 00:45:00.270 --> 00:45:02.070 align:middle line:84% That became known as the work function. 00:45:02.070 --> 00:45:03.840 align:middle line:84% That's kind of like the binding energy. 00:45:03.840 --> 00:45:06.180 align:middle line:84% These aren't free electrons in space. 00:45:06.180 --> 00:45:08.250 align:middle line:84% These are electrons bound to a piece of metal. 00:45:08.250 --> 00:45:11.190 align:middle line:84% There's some intermolecular or atomic forces. 00:45:11.190 --> 00:45:13.840 align:middle line:84% Whatever they are-- and they might vary by material-- 00:45:13.840 --> 00:45:16.920 align:middle line:84% there's some function that is often called by the Greek 00:45:16.920 --> 00:45:18.450 align:middle line:90% letter capital Phi-- 00:45:18.450 --> 00:45:20.770 align:middle line:90% again, a kind of binding energy. 00:45:20.770 --> 00:45:22.650 align:middle line:84% And so the electron won't be kicked out 00:45:22.650 --> 00:45:25.500 align:middle line:84% of that piece of metal unless the energy it absorbs 00:45:25.500 --> 00:45:29.820 align:middle line:84% from that discrete light quantum exceeds that binding energy. 00:45:29.820 --> 00:45:33.030 align:middle line:84% The energy holding it in place has to be overcome or exceeded 00:45:33.030 --> 00:45:35.100 align:middle line:84% by the light-- by the energy transferred 00:45:35.100 --> 00:45:37.020 align:middle line:90% by that light quantum. 00:45:37.020 --> 00:45:39.250 align:middle line:84% If that's the case, then, of course, 00:45:39.250 --> 00:45:41.700 align:middle line:84% there should be a threshold frequency. 00:45:41.700 --> 00:45:44.550 align:middle line:84% Only when each individual quantum 00:45:44.550 --> 00:45:47.850 align:middle line:84% of light, each little pellet, discrete carrier of energy 00:45:47.850 --> 00:45:52.860 align:middle line:84% in that incoming light carries enough energy individually 00:45:52.860 --> 00:45:54.840 align:middle line:84% to overcome that binding energy or the work 00:45:54.840 --> 00:45:57.450 align:middle line:84% function-- only then would any electrons 00:45:57.450 --> 00:45:59.890 align:middle line:84% be ejected from that piece of metal. 00:45:59.890 --> 00:46:01.770 align:middle line:84% So the threshold frequency should 00:46:01.770 --> 00:46:04.920 align:middle line:84% depend on that binding energy, that work function, divided 00:46:04.920 --> 00:46:05.910 align:middle line:90% by Planck's constant. 00:46:05.910 --> 00:46:07.470 align:middle line:84% Basically, what's the threshold that 00:46:07.470 --> 00:46:09.600 align:middle line:84% would set this energy exactly to 0, 00:46:09.600 --> 00:46:11.640 align:middle line:84% as opposed to it having a negative energy, which 00:46:11.640 --> 00:46:13.410 align:middle line:90% would say it's bound in place? 00:46:13.410 --> 00:46:15.600 align:middle line:84% So you just solve for when does the electron just 00:46:15.600 --> 00:46:17.820 align:middle line:90% cross that threshold as energy. 00:46:17.820 --> 00:46:21.930 align:middle line:84% Ah, it's when nu equals phi over h. 00:46:21.930 --> 00:46:23.580 align:middle line:84% That would give you the threshold. 00:46:23.580 --> 00:46:25.950 align:middle line:84% Any additional energy, any higher energy 00:46:25.950 --> 00:46:27.900 align:middle line:84% carried by light quanta, as you tune 00:46:27.900 --> 00:46:30.300 align:middle line:84% the frequency of the incident light higher and higher, 00:46:30.300 --> 00:46:34.080 align:middle line:84% each electron will absorb more energy than that threshold. 00:46:34.080 --> 00:46:37.800 align:middle line:84% And it will continue to grow linearly with slope h. 00:46:37.800 --> 00:46:40.440 align:middle line:84% So the idea that Einstein puts together-- this heuristic idea, 00:46:40.440 --> 00:46:43.350 align:middle line:84% this suggestive idea in this 1905 paper-- 00:46:43.350 --> 00:46:45.510 align:middle line:84% is that the light shining on this metal plate 00:46:45.510 --> 00:46:48.990 align:middle line:84% is not some extended continuous wave lapping up 00:46:48.990 --> 00:46:51.780 align:middle line:84% on shore like a Maxwellian wave, but actually 00:46:51.780 --> 00:46:54.810 align:middle line:84% a shower of discrete marbles, each of which 00:46:54.810 --> 00:46:56.910 align:middle line:84% could collide like two-body collisions, 00:46:56.910 --> 00:46:59.220 align:middle line:84% like billiard balls on a billiard table, 00:46:59.220 --> 00:47:00.480 align:middle line:90% or on a pool table. 00:47:00.480 --> 00:47:03.360 align:middle line:84% They would have two-body collisions, each of which 00:47:03.360 --> 00:47:07.533 align:middle line:84% could then impart certain energy to their colliding electrons. 00:47:07.533 --> 00:47:08.950 align:middle line:84% So I like to think of it this way. 00:47:08.950 --> 00:47:12.610 align:middle line:84% Imagine electrons are like bucket full of ping pong balls. 00:47:12.610 --> 00:47:14.608 align:middle line:84% So ordinarily, they're bound in place. 00:47:14.608 --> 00:47:15.900 align:middle line:90% That's like that work function. 00:47:15.900 --> 00:47:18.150 align:middle line:84% The ping pong balls aren't free to move any old place. 00:47:18.150 --> 00:47:18.870 align:middle line:90% They're stuck. 00:47:18.870 --> 00:47:20.770 align:middle line:84% They have a certain kind of binding energy. 00:47:20.770 --> 00:47:24.180 align:middle line:84% Think of that as like that work function phi. 00:47:24.180 --> 00:47:26.220 align:middle line:84% Then you start chucking marbles at it. 00:47:26.220 --> 00:47:28.890 align:middle line:84% You imagine flinging marbles into that bucket. 00:47:28.890 --> 00:47:32.370 align:middle line:84% If the marbles individually carry enough energy, 00:47:32.370 --> 00:47:35.220 align:middle line:84% they're going to collide with individual ping pong balls. 00:47:35.220 --> 00:47:38.250 align:middle line:84% And if the marble's incoming energy 00:47:38.250 --> 00:47:40.980 align:middle line:84% is more than this binding energy holding the ping pong 00:47:40.980 --> 00:47:43.230 align:middle line:84% balls in the bucket, you'll kick a few out. 00:47:43.230 --> 00:47:45.270 align:middle line:84% That's the picture that Einstein has in mind. 00:47:45.270 --> 00:47:48.540 align:middle line:84% In that same actually quite long article, this very same article 00:47:48.540 --> 00:47:52.470 align:middle line:84% in 1905, Einstein also revisits Planck's derivation 00:47:52.470 --> 00:47:54.480 align:middle line:84% of the blackbody formula, that function 00:47:54.480 --> 00:47:57.810 align:middle line:84% that we called the spectral energy density, little u. 00:47:57.810 --> 00:48:00.270 align:middle line:84% And he rederives Planck's formula 00:48:00.270 --> 00:48:02.430 align:middle line:84% assuming that the radiation being emitted 00:48:02.430 --> 00:48:05.280 align:middle line:84% from that cavity radiation could be treated 00:48:05.280 --> 00:48:08.400 align:middle line:84% like a gas of these individual particles, each of which 00:48:08.400 --> 00:48:11.520 align:middle line:84% has a quantized energy E equals h nu. 00:48:11.520 --> 00:48:14.520 align:middle line:84% This is the modern derivation that we inherit and use 00:48:14.520 --> 00:48:16.830 align:middle line:84% today that's much more like the derivation I give 00:48:16.830 --> 00:48:18.820 align:middle line:90% in those brief optional notes. 00:48:18.820 --> 00:48:21.330 align:middle line:84% So in the same article, Einstein both 00:48:21.330 --> 00:48:25.320 align:middle line:84% offers a heuristic explanation for Lenard's otherwise quite 00:48:25.320 --> 00:48:29.310 align:middle line:84% puzzling experiment results, he revisits and reinterprets 00:48:29.310 --> 00:48:32.640 align:middle line:84% Planck's own by now rather well-known expression 00:48:32.640 --> 00:48:35.880 align:middle line:84% for blackbody radiation, all from the starting point of view 00:48:35.880 --> 00:48:39.420 align:middle line:84% that light is quantized and each individual light quantum 00:48:39.420 --> 00:48:42.600 align:middle line:84% carries a unit amount of energy set by h nu. 00:48:42.600 --> 00:48:45.220 align:middle line:84% So we might figure, OK, he solved everything. 00:48:45.220 --> 00:48:47.460 align:middle line:84% Everyone must have been convinced, right? 00:48:47.460 --> 00:48:48.660 align:middle line:90% No, no, no. 00:48:48.660 --> 00:48:50.460 align:middle line:84% We've learned from this course already, 00:48:50.460 --> 00:48:52.740 align:middle line:84% things hardly ever work that way. 00:48:52.740 --> 00:48:54.940 align:middle line:84% And in Einstein's case in particular-- remember, 00:48:54.940 --> 00:48:57.610 align:middle line:84% he was still a little known patent clerk 00:48:57.610 --> 00:49:00.430 align:middle line:84% out of the main elite centers of research-- 00:49:00.430 --> 00:49:03.580 align:middle line:84% this was facing enormous skepticism, even 00:49:03.580 --> 00:49:06.760 align:middle line:84% years after Einstein himself became much more prominent. 00:49:06.760 --> 00:49:12.490 align:middle line:84% It was really more than 15 years until the majority of members 00:49:12.490 --> 00:49:15.190 align:middle line:84% of the physics community really took this idea at all 00:49:15.190 --> 00:49:15.700 align:middle line:90% seriously. 00:49:15.700 --> 00:49:18.290 align:middle line:84% And here's, again, one of my favorite examples of that. 00:49:18.290 --> 00:49:20.860 align:middle line:84% Here's, again, our old friend, Max Planck, 00:49:20.860 --> 00:49:22.690 align:middle line:84% writing this, a letter of recommendation. 00:49:22.690 --> 00:49:25.670 align:middle line:84% He's trying to say how great Einstein's work is by 1913. 00:49:25.670 --> 00:49:29.290 align:middle line:84% Now, Einstein is no longer the unknown patent clerk. 00:49:29.290 --> 00:49:31.210 align:middle line:84% Planck was trying to convince his colleagues 00:49:31.210 --> 00:49:33.993 align:middle line:84% to offer a very prestigious new job to Einstein 00:49:33.993 --> 00:49:36.160 align:middle line:84% at the Prussian Academy of Sciences, which, in fact, 00:49:36.160 --> 00:49:38.140 align:middle line:90% Einstein would soon be offered. 00:49:38.140 --> 00:49:39.250 align:middle line:90% He would move to Berlin. 00:49:39.250 --> 00:49:42.670 align:middle line:84% And in his letter saying how great Einstein's work is, 00:49:42.670 --> 00:49:45.070 align:middle line:84% Planck says the following, "In sum, 00:49:45.070 --> 00:49:48.190 align:middle line:84% one can say there is hardly one among the great problems 00:49:48.190 --> 00:49:51.280 align:middle line:84% in which modern physics is so rich to which Einstein has not 00:49:51.280 --> 00:49:52.960 align:middle line:90% made a remarkable contribution." 00:49:52.960 --> 00:49:53.920 align:middle line:90% That sounds nice. 00:49:53.920 --> 00:49:56.410 align:middle line:84% "But he may sometimes have missed the target in his 00:49:56.410 --> 00:49:59.740 align:middle line:84% speculations, as, for example, in his hypothesis of light 00:49:59.740 --> 00:50:02.360 align:middle line:84% quanta cannot really be held too much against him," 00:50:02.360 --> 00:50:04.960 align:middle line:84% which is to say, a lot of the work this person has done is 00:50:04.960 --> 00:50:05.950 align:middle line:90% very interesting. 00:50:05.950 --> 00:50:07.968 align:middle line:84% He's clearly mistaken about light quanta. 00:50:07.968 --> 00:50:09.760 align:middle line:84% But let's let him into our new club anyway. 00:50:09.760 --> 00:50:11.470 align:middle line:90% I find that terrific. 00:50:11.470 --> 00:50:12.010 align:middle line:90% OK. 00:50:12.010 --> 00:50:13.630 align:middle line:84% Let me pause there again to ask any questions 00:50:13.630 --> 00:50:14.950 align:middle line:90% on the light quantum learning. 00:50:14.950 --> 00:50:20.660 align:middle line:90% 00:50:20.660 --> 00:50:23.568 align:middle line:84% Fisher asks, in Einstein's paper, 00:50:23.568 --> 00:50:25.610 align:middle line:84% did it make any nods to Newton's original thought 00:50:25.610 --> 00:50:26.930 align:middle line:90% that light was corpuscles? 00:50:26.930 --> 00:50:27.815 align:middle line:90% Very good. 00:50:27.815 --> 00:50:28.940 align:middle line:90% Honestly, I don't remember. 00:50:28.940 --> 00:50:30.148 align:middle line:90% That's an excellent question. 00:50:30.148 --> 00:50:30.800 align:middle line:90% Let me back up. 00:50:30.800 --> 00:50:32.630 align:middle line:90% Others might know as well. 00:50:32.630 --> 00:50:34.100 align:middle line:90% But it's worth emphasizing. 00:50:34.100 --> 00:50:37.430 align:middle line:84% The big picture question-- does light consist 00:50:37.430 --> 00:50:39.020 align:middle line:84% of waves or particles-- that actually 00:50:39.020 --> 00:50:40.880 align:middle line:90% has a really long history. 00:50:40.880 --> 00:50:42.770 align:middle line:84% I guess I gave a little preview of that, 00:50:42.770 --> 00:50:45.470 align:middle line:84% although I didn't linger on it, even in one of our first class 00:50:45.470 --> 00:50:45.800 align:middle line:90% sessions. 00:50:45.800 --> 00:50:47.175 align:middle line:84% For this class, you might know it 00:50:47.175 --> 00:50:49.280 align:middle line:84% from other readings or other classes. 00:50:49.280 --> 00:50:52.280 align:middle line:84% The reason it was actually a big deal around 1800, 00:50:52.280 --> 00:50:56.450 align:middle line:84% going back to early in Michael Faraday's own career-- 00:50:56.450 --> 00:51:00.170 align:middle line:84% it was a big deal to think of light as waves because, since 00:51:00.170 --> 00:51:03.560 align:middle line:84% at least Newton's day-- another century and a quarter before 00:51:03.560 --> 00:51:07.700 align:middle line:84% that, going back to the later years of the 17th century, 00:51:07.700 --> 00:51:09.890 align:middle line:90% the 1660s and so on-- 00:51:09.890 --> 00:51:11.660 align:middle line:84% Newton and other leading scholars 00:51:11.660 --> 00:51:14.120 align:middle line:84% had convinced themselves that light actually consisted 00:51:14.120 --> 00:51:15.320 align:middle line:90% of a stream of particles. 00:51:15.320 --> 00:51:18.290 align:middle line:84% Newton called them corpuscles, exactly as Fisher says. 00:51:18.290 --> 00:51:20.767 align:middle line:84% So Newton was convinced that light was corpuscular. 00:51:20.767 --> 00:51:22.350 align:middle line:84% We might now say the light was made up 00:51:22.350 --> 00:51:23.850 align:middle line:90% of a stream of particles. 00:51:23.850 --> 00:51:26.315 align:middle line:90% That's in 1660s, '70s, '80s. 00:51:26.315 --> 00:51:28.110 align:middle line:84% It would become super influential. 00:51:28.110 --> 00:51:30.360 align:middle line:84% He writes a whole book called Opticks, Newton does, 00:51:30.360 --> 00:51:32.890 align:middle line:84% first published in around 1703 or something like that. 00:51:32.890 --> 00:51:34.740 align:middle line:84% It was like, OK, Newton has spoken. 00:51:34.740 --> 00:51:35.640 align:middle line:90% Light's particles. 00:51:35.640 --> 00:51:36.880 align:middle line:90% Got it. 00:51:36.880 --> 00:51:38.670 align:middle line:84% And so it was a pretty big deal when, 00:51:38.670 --> 00:51:41.760 align:middle line:84% about 100 years after that, the consensus shifts, 00:51:41.760 --> 00:51:43.860 align:middle line:84% both in Britain, and in France, and ultimately 00:51:43.860 --> 00:51:46.170 align:middle line:84% many, many other places that, hang on, 00:51:46.170 --> 00:51:48.450 align:middle line:84% light seems to have all these wavelike properties 00:51:48.450 --> 00:51:50.920 align:middle line:84% like interference, and diffraction, and refraction, 00:51:50.920 --> 00:51:53.460 align:middle line:84% and all these things that helped set in motion 00:51:53.460 --> 00:51:55.290 align:middle line:84% the ideas of a light-bearing ether. 00:51:55.290 --> 00:51:57.390 align:middle line:84% If light is a wave, what is it a wave in? 00:51:57.390 --> 00:52:00.720 align:middle line:84% So you have these huge century-long shifts 00:52:00.720 --> 00:52:03.030 align:middle line:84% between assumptions about just what's 00:52:03.030 --> 00:52:06.150 align:middle line:84% light made of in general, let alone these specific questions 00:52:06.150 --> 00:52:08.010 align:middle line:84% about how it interacts with matter. 00:52:08.010 --> 00:52:11.160 align:middle line:84% So it was certainly well-known well before Einstein's day 00:52:11.160 --> 00:52:13.890 align:middle line:84% that Newton had been, let's say, a corpuscularist. 00:52:13.890 --> 00:52:15.420 align:middle line:84% But it's a great question, Fisher. 00:52:15.420 --> 00:52:18.810 align:middle line:84% And I'd have to go back to my own copy in English translation 00:52:18.810 --> 00:52:20.910 align:middle line:84% by [INAUDIBLE] to see whether Einstein 00:52:20.910 --> 00:52:22.512 align:middle line:90% paused to reflect on that. 00:52:22.512 --> 00:52:23.220 align:middle line:90% I don't remember. 00:52:23.220 --> 00:52:24.917 align:middle line:90% Interesting question. 00:52:24.917 --> 00:52:26.625 align:middle line:84% Gary asks, having written as a heuristic, 00:52:26.625 --> 00:52:29.610 align:middle line:84% did Einstein believe it'd be quanta in 1905 or only later? 00:52:29.610 --> 00:52:30.330 align:middle line:90% Very good, Gary. 00:52:30.330 --> 00:52:32.508 align:middle line:84% So my best understanding-- and again, 00:52:32.508 --> 00:52:34.050 align:middle line:84% I haven't looked as directly in this. 00:52:34.050 --> 00:52:35.633 align:middle line:84% But from my colleagues who have really 00:52:35.633 --> 00:52:38.730 align:middle line:84% pored over Einstein's, at the time, 00:52:38.730 --> 00:52:41.160 align:middle line:84% unpublished correspondence, his notes, and so on-- again, 00:52:41.160 --> 00:52:44.610 align:middle line:84% we have a huge documentary base of how his thinking was 00:52:44.610 --> 00:52:45.900 align:middle line:90% evolving in those years. 00:52:45.900 --> 00:52:49.080 align:middle line:84% It seems that Einstein thought this really, really was true. 00:52:49.080 --> 00:52:52.360 align:middle line:84% But for once, he kind of hedged rhetorically. 00:52:52.360 --> 00:52:55.530 align:middle line:84% So it seems that he was offering a heuristic explanation 00:52:55.530 --> 00:52:59.970 align:middle line:84% and going through actually a whole number of episodes 00:52:59.970 --> 00:53:03.150 align:middle line:84% or scenarios where this suggestive hypothesis might 00:53:03.150 --> 00:53:04.660 align:middle line:90% be helpful. 00:53:04.660 --> 00:53:09.210 align:middle line:84% But it seems that he thought that this was not only 00:53:09.210 --> 00:53:10.620 align:middle line:90% a fiction. 00:53:10.620 --> 00:53:12.960 align:middle line:84% He was, however, not sure how to square this. 00:53:12.960 --> 00:53:14.910 align:middle line:84% In 1905, he wasn't sure how to square that 00:53:14.910 --> 00:53:16.950 align:middle line:84% with a centuries worth of evidence 00:53:16.950 --> 00:53:20.190 align:middle line:84% that light had wavelike behavior like reflection, refraction, 00:53:20.190 --> 00:53:22.770 align:middle line:84% diffraction, interference in general. 00:53:22.770 --> 00:53:25.370 align:middle line:84% So it's not that Einstein said there's nothing ever 00:53:25.370 --> 00:53:28.850 align:middle line:84% wavy about light, it's always only particles. 00:53:28.850 --> 00:53:32.180 align:middle line:84% But he was certainly-- and in his own more private musings, 00:53:32.180 --> 00:53:35.870 align:middle line:84% he seemed to think that one had to adopt this it's really 00:53:35.870 --> 00:53:39.650 align:middle line:84% like particles a position in some scenarios 00:53:39.650 --> 00:53:40.730 align:middle line:90% more than others. 00:53:40.730 --> 00:53:43.255 align:middle line:84% He was groping toward what we see actually 00:53:43.255 --> 00:53:44.630 align:middle line:84% in the next part of today's class 00:53:44.630 --> 00:53:47.048 align:middle line:84% and what will chase us through upcoming class sessions. 00:53:47.048 --> 00:53:48.590 align:middle line:84% He was beginning to grapple with what 00:53:48.590 --> 00:53:51.080 align:middle line:84% would come to be called wave particle duality. 00:53:51.080 --> 00:53:54.020 align:middle line:84% He certainly wasn't calling it that yet in 1905. 00:53:54.020 --> 00:53:57.650 align:middle line:84% But as his additional documents from the time 00:53:57.650 --> 00:54:01.040 align:middle line:84% seemed to suggest, he was already grappling with we 00:54:01.040 --> 00:54:02.690 align:middle line:84% really, really need to treat light 00:54:02.690 --> 00:54:04.400 align:middle line:84% like waves for certain scenarios-- 00:54:04.400 --> 00:54:06.650 align:middle line:84% interference fringes being an obvious one. 00:54:06.650 --> 00:54:09.740 align:middle line:84% And yet, in his own heart of hearts, 00:54:09.740 --> 00:54:12.380 align:middle line:84% he seemed pretty convinced that this corpuscular or quantum 00:54:12.380 --> 00:54:14.330 align:middle line:84% nature seemed more than just a coincidence 00:54:14.330 --> 00:54:15.980 align:middle line:90% in other kinds of scenarios. 00:54:15.980 --> 00:54:21.380 align:middle line:84% And that would become more and more of a paradox 00:54:21.380 --> 00:54:24.820 align:middle line:84% to some or a challenge, even beyond Einstein himself. 00:54:24.820 --> 00:54:26.370 align:middle line:84% And so the real question actually 00:54:26.370 --> 00:54:28.830 align:middle line:84% becomes, why was Einstein hedging his bets rhetorically 00:54:28.830 --> 00:54:30.330 align:middle line:84% rather than what he really believed? 00:54:30.330 --> 00:54:33.640 align:middle line:84% Because we saw it in his paper just a few weeks later 00:54:33.640 --> 00:54:35.640 align:middle line:84% that he submits on the electrodynamics of moving 00:54:35.640 --> 00:54:38.460 align:middle line:84% bodies, he's certainly not shy about dismissing the ether. 00:54:38.460 --> 00:54:41.880 align:middle line:84% He's making other rather bold and almost irresponsible 00:54:41.880 --> 00:54:45.280 align:middle line:84% statements, given the standard assumptions of his day. 00:54:45.280 --> 00:54:48.090 align:middle line:90% He wasn't shy, in 1905. 00:54:48.090 --> 00:54:49.890 align:middle line:84% With this particular one, I imagine 00:54:49.890 --> 00:54:51.390 align:middle line:84% it was more like he didn't yet know 00:54:51.390 --> 00:54:53.880 align:middle line:84% how to square the circle here of what comes to be 00:54:53.880 --> 00:54:55.230 align:middle line:90% known as wave particle duality. 00:54:55.230 --> 00:54:56.070 align:middle line:90% So that's a great question. 00:54:56.070 --> 00:54:58.200 align:middle line:84% And again, we'll see an example of that even in the next part 00:54:58.200 --> 00:54:58.830 align:middle line:90% today. 00:54:58.830 --> 00:55:00.510 align:middle line:84% And we'll see echoes of that throughout 00:55:00.510 --> 00:55:01.385 align:middle line:90% the next few classes. 00:55:01.385 --> 00:55:02.190 align:middle line:90% Good. 00:55:02.190 --> 00:55:04.710 align:middle line:84% Any other questions on the photoelectric effect, 00:55:04.710 --> 00:55:07.995 align:middle line:84% on what was Lenard measuring, on Einstein's explanation? 00:55:07.995 --> 00:55:11.250 align:middle line:90% It's all pretty clear? 00:55:11.250 --> 00:55:11.750 align:middle line:90% OK. 00:55:11.750 --> 00:55:14.320 align:middle line:90% 00:55:14.320 --> 00:55:14.820 align:middle line:90% Right. 00:55:14.820 --> 00:55:15.960 align:middle line:90% Good questions. 00:55:15.960 --> 00:55:17.850 align:middle line:84% Let's look at this last part for today. 00:55:17.850 --> 00:55:21.420 align:middle line:84% Why did anyone begin to take light quanta a bit 00:55:21.420 --> 00:55:22.620 align:middle line:90% more seriously? 00:55:22.620 --> 00:55:26.790 align:middle line:84% One of the most compelling sets of new information, new inputs 00:55:26.790 --> 00:55:29.790 align:middle line:84% for this came yet again from a laboratory 00:55:29.790 --> 00:55:32.340 align:middle line:84% in the United States, which, again, is itself still pretty 00:55:32.340 --> 00:55:33.280 align:middle line:90% unusual. 00:55:33.280 --> 00:55:36.090 align:middle line:84% This was among the next set of really significant 00:55:36.090 --> 00:55:38.100 align:middle line:84% experimental work in physics that 00:55:38.100 --> 00:55:41.970 align:middle line:84% got even the experts, sometimes very snobby experts in Western 00:55:41.970 --> 00:55:43.230 align:middle line:90% Europe, to pay attention. 00:55:43.230 --> 00:55:45.622 align:middle line:84% This was now decades after Albert Michelson. 00:55:45.622 --> 00:55:47.080 align:middle line:84% And the Michelson-Morley experiment 00:55:47.080 --> 00:55:50.790 align:middle line:84% is now the early 1920s, not the 1880s. 00:55:50.790 --> 00:55:53.790 align:middle line:84% But this was, again, an example held up almost immediately 00:55:53.790 --> 00:55:56.040 align:middle line:90% for real acclaim. 00:55:56.040 --> 00:55:58.350 align:middle line:84% A series of experiments performed by the physicist 00:55:58.350 --> 00:56:02.765 align:middle line:84% Arthur Compton at the University of Chicago in 1922-- 00:56:02.765 --> 00:56:03.390 align:middle line:90% here's Compton. 00:56:03.390 --> 00:56:05.070 align:middle line:84% He looks like a kind of movie star. 00:56:05.070 --> 00:56:07.110 align:middle line:84% You might recognize the name Compton. 00:56:07.110 --> 00:56:09.750 align:middle line:84% Arthur's brother was Karl Compton, 00:56:09.750 --> 00:56:12.240 align:middle line:90% also a trained physicist. 00:56:12.240 --> 00:56:14.810 align:middle line:84% Karl Compton then went on to a different kind of career. 00:56:14.810 --> 00:56:17.530 align:middle line:84% He became the president of MIT starting in 1930. 00:56:17.530 --> 00:56:19.300 align:middle line:84% And he served for nearly 20 years. 00:56:19.300 --> 00:56:24.460 align:middle line:84% So a number of enormously consequential reforms at MIT 00:56:24.460 --> 00:56:27.910 align:middle line:84% were put in place by Karl Compton just at the moment 00:56:27.910 --> 00:56:30.100 align:middle line:84% or around the same time that his brother Arthur 00:56:30.100 --> 00:56:32.830 align:middle line:84% Compton was experimenting on the nature of light. 00:56:32.830 --> 00:56:34.720 align:middle line:84% And again, as I say, this is one of the sets 00:56:34.720 --> 00:56:38.560 align:middle line:84% of new kind of inputs coming out of US-based laboratories that 00:56:38.560 --> 00:56:41.290 align:middle line:84% really began to make even experts in Europe 00:56:41.290 --> 00:56:42.820 align:middle line:90% pay close attention. 00:56:42.820 --> 00:56:45.490 align:middle line:84% So Compton, Arthur Compton, had not set out 00:56:45.490 --> 00:56:47.200 align:middle line:90% to test Einstein's hypothesis. 00:56:47.200 --> 00:56:50.020 align:middle line:84% He, like everyone, practically everyone in the field, 00:56:50.020 --> 00:56:52.540 align:middle line:84% remained pretty skeptical, much like in that letter 00:56:52.540 --> 00:56:55.390 align:middle line:90% from Max Planck from 1913. 00:56:55.390 --> 00:56:57.400 align:middle line:84% They figured Einstein, by this point, 00:56:57.400 --> 00:57:00.220 align:middle line:84% was pretty smart, had some amazing successes 00:57:00.220 --> 00:57:01.150 align:middle line:90% to his career. 00:57:01.150 --> 00:57:04.540 align:middle line:84% But this light quantum thing was probably not one of them. 00:57:04.540 --> 00:57:06.970 align:middle line:84% Compton instead was really interested in the behavior 00:57:06.970 --> 00:57:11.320 align:middle line:84% of high energy x-rays and how these x-rays would interact 00:57:11.320 --> 00:57:12.580 align:middle line:90% with little bits of matter. 00:57:12.580 --> 00:57:16.630 align:middle line:84% So he was conducting experiments by basically beaming x-rays, 00:57:16.630 --> 00:57:18.730 align:middle line:84% very high energy electromagnetic light-- 00:57:18.730 --> 00:57:21.790 align:middle line:84% as far as he was concerned, Maxwellian waves of very short 00:57:21.790 --> 00:57:23.740 align:middle line:84% wavelength, very high frequency-- 00:57:23.740 --> 00:57:25.930 align:middle line:84% and bouncing them off of graphite, 00:57:25.930 --> 00:57:28.070 align:middle line:90% basically carbon molecules. 00:57:28.070 --> 00:57:31.480 align:middle line:84% So he wanted to bounce them off the electrons in carbon. 00:57:31.480 --> 00:57:33.730 align:middle line:84% What Compton was measuring in particular 00:57:33.730 --> 00:57:36.910 align:middle line:84% was change in the wavelength, in the wavelength 00:57:36.910 --> 00:57:40.420 align:middle line:84% of those electromagnetic waves, the x-rays, after scattering. 00:57:40.420 --> 00:57:42.850 align:middle line:84% So you might be familiar, of course-- 00:57:42.850 --> 00:57:44.890 align:middle line:84% for any of these Maxwellian waves, 00:57:44.890 --> 00:57:47.650 align:middle line:84% we can measure the wavelength, the distance, 00:57:47.650 --> 00:57:50.890 align:middle line:84% the physical distance between neighboring crests, neighboring 00:57:50.890 --> 00:57:53.748 align:middle line:84% peaks, of, say, the associated electric field. 00:57:53.748 --> 00:57:55.540 align:middle line:84% So what Compton was doing in his laboratory 00:57:55.540 --> 00:57:58.060 align:middle line:84% was measuring the wavelength prior 00:57:58.060 --> 00:58:01.280 align:middle line:84% to scattering and the shifted wavelength following 00:58:01.280 --> 00:58:01.780 align:middle line:90% scattering. 00:58:01.780 --> 00:58:04.480 align:middle line:84% So the prime here means after the scattering. 00:58:04.480 --> 00:58:06.130 align:middle line:84% He knew the wavelength ahead of time. 00:58:06.130 --> 00:58:08.590 align:middle line:84% He could control that with his apparatus. 00:58:08.590 --> 00:58:11.710 align:middle line:84% Very much like the PTR, he could use very finely spaced 00:58:11.710 --> 00:58:13.930 align:middle line:84% diffraction gratings and similar techniques 00:58:13.930 --> 00:58:15.910 align:middle line:84% to measure the shift in wavelength 00:58:15.910 --> 00:58:20.410 align:middle line:84% after the x-rays have basically scattered off these electrons. 00:58:20.410 --> 00:58:22.840 align:middle line:90% He found that there was a shift. 00:58:22.840 --> 00:58:24.670 align:middle line:84% The wavelength following collision 00:58:24.670 --> 00:58:27.100 align:middle line:84% was not equal to the wavelength prior to collision. 00:58:27.100 --> 00:58:30.820 align:middle line:84% And there was a very specific angular dependence 00:58:30.820 --> 00:58:34.360 align:middle line:84% that the angle at which these x-rays bounced off, 00:58:34.360 --> 00:58:37.660 align:middle line:84% this angle theta, was somehow related 00:58:37.660 --> 00:58:40.420 align:middle line:84% to the degree in which their wavelength changed. 00:58:40.420 --> 00:58:42.670 align:middle line:84% That is to say, the shift in wavelength 00:58:42.670 --> 00:58:46.245 align:middle line:84% went like 1 minus cosine of the light wave's scattering angle. 00:58:46.245 --> 00:58:47.620 align:middle line:84% And that's what he could measure. 00:58:47.620 --> 00:58:49.450 align:middle line:84% You can see here it's mounted on a wheel. 00:58:49.450 --> 00:58:53.530 align:middle line:84% He could actually pivot his diffraction gratings 00:58:53.530 --> 00:58:55.630 align:middle line:84% essentially and measure the scattered light 00:58:55.630 --> 00:58:57.280 align:middle line:84% at different angles as it bounced off 00:58:57.280 --> 00:58:59.230 align:middle line:90% that graphite target. 00:58:59.230 --> 00:59:00.970 align:middle line:84% So Compton was convinced that this 00:59:00.970 --> 00:59:03.940 align:middle line:84% could be made sense of using totally standard, 00:59:03.940 --> 00:59:06.880 align:middle line:84% by that point, Maxwellian electromagnetic waves. 00:59:06.880 --> 00:59:09.940 align:middle line:84% These were high frequency Maxwell waves scattering off 00:59:09.940 --> 00:59:11.110 align:middle line:90% of a certain target. 00:59:11.110 --> 00:59:13.660 align:middle line:84% And yet try, and try, and try as he might, 00:59:13.660 --> 00:59:16.630 align:middle line:84% he could not come up with any sensible explanation 00:59:16.630 --> 00:59:19.150 align:middle line:84% or accounting for this empirical relationship. 00:59:19.150 --> 00:59:22.000 align:middle line:84% When he kept finding conducting the experiment measuring more 00:59:22.000 --> 00:59:24.100 align:middle line:84% and more carefully the shift in frequency 00:59:24.100 --> 00:59:27.130 align:middle line:84% with the scattered angle, he couldn't come up 00:59:27.130 --> 00:59:29.140 align:middle line:84% with any kind of theoretical explanation 00:59:29.140 --> 00:59:30.550 align:middle line:84% that would account for that shift 00:59:30.550 --> 00:59:34.060 align:middle line:84% until, in yet another act of desperation much 00:59:34.060 --> 00:59:37.720 align:middle line:84% like Max Planck, he then grudgingly tries on-- 00:59:37.720 --> 00:59:40.630 align:middle line:84% takes on this Einstein hypothesis or heuristic 00:59:40.630 --> 00:59:41.470 align:middle line:90% suggestion. 00:59:41.470 --> 00:59:45.490 align:middle line:84% Only when Arthur Compton, again kind of grudgingly, 00:59:45.490 --> 00:59:48.910 align:middle line:84% adopts this suggestion from Albert Einstein to treat 00:59:48.910 --> 00:59:51.550 align:middle line:84% light-- in this case, the very high energy x-rays-- 00:59:51.550 --> 00:59:54.190 align:middle line:84% as little collections of discrete particles each 00:59:54.190 --> 00:59:56.620 align:middle line:84% with their own discrete packets of energy 00:59:56.620 --> 00:59:59.500 align:middle line:84% rather than as Maximilian waves-- only then can 00:59:59.500 --> 01:00:02.930 align:middle line:84% he make sense of this empirical pattern in his laboratory. 01:00:02.930 --> 01:00:05.440 align:middle line:84% So here's the diagram from his actual published 01:00:05.440 --> 01:00:06.910 align:middle line:90% article in the Physical Review. 01:00:06.910 --> 01:00:09.395 align:middle line:84% It was submitted in the very closing days of calendar year 01:00:09.395 --> 01:00:09.895 align:middle line:90% 1922. 01:00:09.895 --> 01:00:13.060 align:middle line:90% It was published spring of '23. 01:00:13.060 --> 01:00:15.320 align:middle line:84% So here's the actual illustration from his article. 01:00:15.320 --> 01:00:19.370 align:middle line:84% And again, in the accompanying optional lecture notes, 01:00:19.370 --> 01:00:22.980 align:middle line:84% I go through the algebra a bit more slowly. 01:00:22.980 --> 01:00:25.010 align:middle line:84% So I'm going to show you where it gets. 01:00:25.010 --> 01:00:26.427 align:middle line:84% Don't worry if some of these steps 01:00:26.427 --> 01:00:27.593 align:middle line:90% are hard to do in your head. 01:00:27.593 --> 01:00:29.160 align:middle line:84% They're hard for me to do in my head. 01:00:29.160 --> 01:00:32.600 align:middle line:84% Take your time, if you'd like, and go through the algebra 01:00:32.600 --> 01:00:33.630 align:middle line:90% in the notes. 01:00:33.630 --> 01:00:35.750 align:middle line:84% So what Compton winds up doing is 01:00:35.750 --> 01:00:39.160 align:middle line:84% treating the interaction between the incoming x-ray-- that's 01:00:39.160 --> 01:00:39.750 align:middle line:90% what's here. 01:00:39.750 --> 01:00:41.570 align:middle line:84% He now, by the published version, 01:00:41.570 --> 01:00:44.900 align:middle line:84% has decided to call this incident light quantum. 01:00:44.900 --> 01:00:47.430 align:middle line:84% He's already now borrowing Einstein's ideas. 01:00:47.430 --> 01:00:50.240 align:middle line:90% It's not restarted. 01:00:50.240 --> 01:00:51.110 align:middle line:90% Pardon me. 01:00:51.110 --> 01:00:54.770 align:middle line:90% So here's the incoming x-ray. 01:00:54.770 --> 01:00:57.680 align:middle line:84% And how would you characterize the energy 01:00:57.680 --> 01:01:01.400 align:middle line:84% or the momentum of that incoming source of light? 01:01:01.400 --> 01:01:06.130 align:middle line:84% That's what Compton starts with, before collision. 01:01:06.130 --> 01:01:10.510 align:middle line:84% So even by using Maxwell's theory, 01:01:10.510 --> 01:01:14.860 align:middle line:84% people knew they could calculate an associated momentum carried 01:01:14.860 --> 01:01:18.065 align:middle line:84% by a light wave as related to things like the Poynting 01:01:18.065 --> 01:01:19.690 align:middle line:84% vector, if you want to get super fancy. 01:01:19.690 --> 01:01:21.107 align:middle line:84% But basically, Maxwell's equations 01:01:21.107 --> 01:01:25.510 align:middle line:84% suggested the momentum carried by radiation, by light, 01:01:25.510 --> 01:01:28.060 align:middle line:84% is equal to the energy carried by that light wave divided 01:01:28.060 --> 01:01:28.750 align:middle line:90% by its speed. 01:01:28.750 --> 01:01:30.970 align:middle line:84% That was, again, a classical result, even 01:01:30.970 --> 01:01:32.530 align:middle line:90% from wave theory of light. 01:01:32.530 --> 01:01:35.410 align:middle line:84% And now, Compton starts adding in this new heuristic 01:01:35.410 --> 01:01:36.310 align:middle line:90% stuff from Einstein. 01:01:36.310 --> 01:01:39.190 align:middle line:84% What if each individual light quantum-- 01:01:39.190 --> 01:01:41.320 align:middle line:84% and now, I'll be a little anachronistic 01:01:41.320 --> 01:01:42.940 align:middle line:90% and just use the term photon. 01:01:42.940 --> 01:01:44.890 align:middle line:84% That's not the term that Compton used. 01:01:44.890 --> 01:01:48.700 align:middle line:84% It gets introduced soon after Compton's results. 01:01:48.700 --> 01:01:51.160 align:middle line:84% Within the 1920s, it had already become 01:01:51.160 --> 01:01:53.950 align:middle line:84% common to use the term photon, as we still do today, 01:01:53.950 --> 01:01:55.510 align:middle line:90% to describe these light quanta. 01:01:55.510 --> 01:01:58.180 align:middle line:84% So now, let's take on Einstein's suggestion 01:01:58.180 --> 01:02:00.400 align:middle line:84% that each individual photon of light 01:02:00.400 --> 01:02:03.100 align:middle line:84% carries a quantized amount of energy proportional 01:02:03.100 --> 01:02:04.840 align:middle line:90% to its frequency. 01:02:04.840 --> 01:02:07.010 align:middle line:84% Then let's use the usual relation 01:02:07.010 --> 01:02:09.650 align:middle line:84% for any wave between frequency and wavelength 01:02:09.650 --> 01:02:12.680 align:middle line:84% with the constant of proportionality, the speed. 01:02:12.680 --> 01:02:15.680 align:middle line:84% So now, you can come back to this Maxwellian expression 01:02:15.680 --> 01:02:19.370 align:middle line:84% for the momentum carried by a classical light wave, 01:02:19.370 --> 01:02:22.370 align:middle line:84% add in this new Einstein-like quantum thing, 01:02:22.370 --> 01:02:24.770 align:middle line:84% and come up with an expression for the momentum carried 01:02:24.770 --> 01:02:28.430 align:middle line:84% by each individual photon, or light quantum. 01:02:28.430 --> 01:02:30.890 align:middle line:84% And that would be the energy divided 01:02:30.890 --> 01:02:32.770 align:middle line:90% by its speed, h over lambda. 01:02:32.770 --> 01:02:34.520 align:middle line:84% Remember, that's not where Compton starts. 01:02:34.520 --> 01:02:36.290 align:middle line:84% That's where it gets out of desperation. 01:02:36.290 --> 01:02:37.970 align:middle line:84% So now, Compton has an expression 01:02:37.970 --> 01:02:41.240 align:middle line:84% for both the momentum and the energy of this light quantum 01:02:41.240 --> 01:02:43.150 align:middle line:90% prior to scattering. 01:02:43.150 --> 01:02:45.650 align:middle line:84% He's going to treat this, as I say, like a two-body problem, 01:02:45.650 --> 01:02:47.330 align:middle line:84% as if these were two billiard balls 01:02:47.330 --> 01:02:49.280 align:middle line:84% rather than like a wave scattering off 01:02:49.280 --> 01:02:50.780 align:middle line:90% of a little chunk of matter. 01:02:50.780 --> 01:02:53.630 align:middle line:84% So prior to the collision, he's going to say this electron-- 01:02:53.630 --> 01:02:55.850 align:middle line:84% over here, this target, this little dot here-- 01:02:55.850 --> 01:02:57.170 align:middle line:90% is just sitting there at rest. 01:02:57.170 --> 01:02:58.160 align:middle line:90% Its momentum is zero. 01:02:58.160 --> 01:02:59.600 align:middle line:90% It has no velocity. 01:02:59.600 --> 01:03:02.360 align:middle line:84% And it has some rest energy, mc squared. 01:03:02.360 --> 01:03:05.900 align:middle line:84% Remember, by 1922, Einstein's work on relativity 01:03:05.900 --> 01:03:07.550 align:middle line:84% was indeed much more better known 01:03:07.550 --> 01:03:10.500 align:middle line:84% and seemed to have passed a number of tests. 01:03:10.500 --> 01:03:14.390 align:middle line:84% So Compton had no qualms about borrowing Einstein's work 01:03:14.390 --> 01:03:17.360 align:middle line:84% on relativity, including things like this rest energy, 01:03:17.360 --> 01:03:20.240 align:middle line:84% mc squared, even though he was not 01:03:20.240 --> 01:03:22.550 align:middle line:84% going into this convinced of the light quantum stuff. 01:03:22.550 --> 01:03:24.130 align:middle line:84% So now, we have the ingredients we 01:03:24.130 --> 01:03:27.170 align:middle line:84% need to describe the two scattering billiard balls, 01:03:27.170 --> 01:03:29.540 align:middle line:84% the two objects, prior to collision. 01:03:29.540 --> 01:03:31.610 align:middle line:84% We can characterize the energy and momentum 01:03:31.610 --> 01:03:33.980 align:middle line:84% of the incoming x-ray as a collection 01:03:33.980 --> 01:03:36.620 align:middle line:84% of discrete pellet-like light quanta. 01:03:36.620 --> 01:03:38.840 align:middle line:84% We have the energy and momentum before collision 01:03:38.840 --> 01:03:41.270 align:middle line:84% of the target, this electron just sitting still about 01:03:41.270 --> 01:03:43.130 align:middle line:90% to get smacked. 01:03:43.130 --> 01:03:46.160 align:middle line:84% After the collision, the light quantum 01:03:46.160 --> 01:03:49.562 align:middle line:84% gets scattered off at some angle, theta, 01:03:49.562 --> 01:03:51.020 align:middle line:84% compared to its incoming direction. 01:03:51.020 --> 01:03:52.370 align:middle line:90% That's the angle theta here. 01:03:52.370 --> 01:03:55.740 align:middle line:84% It now has, in general, some different wavelength. 01:03:55.740 --> 01:03:57.950 align:middle line:90% So the momentum of that photon-- 01:03:57.950 --> 01:04:00.780 align:middle line:84% Compton now taking on Einstein's work-- 01:04:00.780 --> 01:04:02.780 align:middle line:84% is going to be given by some universal constant. 01:04:02.780 --> 01:04:03.750 align:middle line:90% That hasn't changed. 01:04:03.750 --> 01:04:05.000 align:middle line:90% That's just Planck's constant. 01:04:05.000 --> 01:04:06.990 align:middle line:84% But the wavelength indeed might have changed. 01:04:06.990 --> 01:04:08.865 align:middle line:84% In fact, he was measuring exactly that change 01:04:08.865 --> 01:04:09.680 align:middle line:90% in wavelength. 01:04:09.680 --> 01:04:11.300 align:middle line:84% Likewise, the energy of the photon 01:04:11.300 --> 01:04:12.920 align:middle line:84% therefore will change because its wavelength 01:04:12.920 --> 01:04:13.670 align:middle line:90% will have changed. 01:04:13.670 --> 01:04:15.770 align:middle line:84% So he has now an expression for energy momentum 01:04:15.770 --> 01:04:18.223 align:middle line:84% of a light quantum following collision. 01:04:18.223 --> 01:04:19.640 align:middle line:84% And likewise, the electron has now 01:04:19.640 --> 01:04:23.690 align:middle line:84% been smacked by some very high energy pellet, this high energy 01:04:23.690 --> 01:04:26.150 align:middle line:90% light quantum of the x-rays. 01:04:26.150 --> 01:04:30.590 align:middle line:84% So now, it will recoil in some other direction, some angle-- 01:04:30.590 --> 01:04:32.120 align:middle line:90% let's call it phi-- 01:04:32.120 --> 01:04:34.310 align:middle line:84% after getting smacked by the incoming light quantum. 01:04:34.310 --> 01:04:36.450 align:middle line:84% So now, it has some non-zero momentum. 01:04:36.450 --> 01:04:39.320 align:middle line:84% In fact, if it's a high enough energy incoming x-ray-- 01:04:39.320 --> 01:04:42.513 align:middle line:84% x-rays are very energetic light waves in general-- 01:04:42.513 --> 01:04:44.180 align:middle line:84% then the electron might actually acquire 01:04:44.180 --> 01:04:45.620 align:middle line:90% a relativistic momentum. 01:04:45.620 --> 01:04:48.110 align:middle line:84% Its recoil speed could, in general, 01:04:48.110 --> 01:04:49.940 align:middle line:84% be comparable to the speed of light. 01:04:49.940 --> 01:04:52.350 align:middle line:84% It could get quite a jolt from that collision. 01:04:52.350 --> 01:04:55.790 align:middle line:84% So again, Compton uses by then the standard relativistic 01:04:55.790 --> 01:04:58.460 align:middle line:84% expressions for momentum and likewise for energy. 01:04:58.460 --> 01:05:00.260 align:middle line:84% And again, I have a set of lecture notes 01:05:00.260 --> 01:05:02.870 align:middle line:84% that were optional on the Canvas site 01:05:02.870 --> 01:05:05.240 align:middle line:84% from when we talked about Einstein and relativity to go 01:05:05.240 --> 01:05:08.038 align:middle line:84% over things like E equals mc squared, relativistic momentum, 01:05:08.038 --> 01:05:08.580 align:middle line:90% and all that. 01:05:08.580 --> 01:05:10.760 align:middle line:84% So you have a chance to go back to those notes, 01:05:10.760 --> 01:05:13.520 align:middle line:90% if that's not familiar. 01:05:13.520 --> 01:05:16.760 align:middle line:84% For what we need to know today, this stuff was, by that point, 01:05:16.760 --> 01:05:17.630 align:middle line:90% standard issue. 01:05:17.630 --> 01:05:19.820 align:middle line:84% Compton was doing nothing controversial here 01:05:19.820 --> 01:05:22.550 align:middle line:84% in adopting the relativistic energy and momentum 01:05:22.550 --> 01:05:24.230 align:middle line:90% for the scattered electron. 01:05:24.230 --> 01:05:24.740 align:middle line:90% OK. 01:05:24.740 --> 01:05:26.240 align:middle line:84% Now, he does what anyone would do 01:05:26.240 --> 01:05:29.150 align:middle line:84% when you have two particles colliding-- not a wave 01:05:29.150 --> 01:05:32.540 align:middle line:84% smacking into the shore, but two discrete little bundles 01:05:32.540 --> 01:05:36.840 align:middle line:84% of energy that collide like billiard balls on a pool table. 01:05:36.840 --> 01:05:39.320 align:middle line:84% One thing we have to do in any two-body collision 01:05:39.320 --> 01:05:42.680 align:middle line:84% is conserve energy, just as we would do in ordinary Newtonian 01:05:42.680 --> 01:05:43.460 align:middle line:90% mechanics. 01:05:43.460 --> 01:05:45.230 align:middle line:84% So what's the total energy coming 01:05:45.230 --> 01:05:49.070 align:middle line:84% in before collision, the incoming energy of the photon, 01:05:49.070 --> 01:05:49.820 align:middle line:90% this one here. 01:05:49.820 --> 01:05:51.380 align:middle line:84% The incoming energy of the electron 01:05:51.380 --> 01:05:52.640 align:middle line:90% is just this rest mass. 01:05:52.640 --> 01:05:54.620 align:middle line:84% And that total energy has to balance 01:05:54.620 --> 01:05:57.230 align:middle line:84% the total energy of the system following collision. 01:05:57.230 --> 01:05:59.210 align:middle line:84% So he has his corresponding expressions 01:05:59.210 --> 01:06:01.920 align:middle line:84% for the energy of the photon and the electron following 01:06:01.920 --> 01:06:02.420 align:middle line:90% scattering. 01:06:02.420 --> 01:06:03.962 align:middle line:84% And we can now fill in from his table 01:06:03.962 --> 01:06:06.290 align:middle line:90% what those values should be. 01:06:06.290 --> 01:06:08.060 align:middle line:84% Likewise, we have to conserve momentum. 01:06:08.060 --> 01:06:11.220 align:middle line:84% As we all know, momentum is a vector quantity. 01:06:11.220 --> 01:06:14.390 align:middle line:84% So we have to conserve momentum both in the x-direction 01:06:14.390 --> 01:06:17.660 align:middle line:84% along the original direction of travel for the incoming light 01:06:17.660 --> 01:06:20.000 align:middle line:84% quantum, as well as in the perpendicular direction, 01:06:20.000 --> 01:06:21.660 align:middle line:90% in this case the y-direction. 01:06:21.660 --> 01:06:24.410 align:middle line:84% And so again, this is done in a bit more detail in the notes, 01:06:24.410 --> 01:06:27.632 align:middle line:84% if this is hard to parse in real time. 01:06:27.632 --> 01:06:29.090 align:middle line:84% But the upshot to this it Compton's 01:06:29.090 --> 01:06:32.630 align:middle line:84% doing completely standard stuff for two-body scattering, 01:06:32.630 --> 01:06:34.580 align:middle line:84% once he's done the non-standard thing 01:06:34.580 --> 01:06:38.420 align:middle line:84% of treating this light as an incoming pellet or particle. 01:06:38.420 --> 01:06:40.250 align:middle line:84% So now, what's so great is Compton 01:06:40.250 --> 01:06:42.260 align:middle line:84% has three equations and three unknowns. 01:06:42.260 --> 01:06:45.410 align:middle line:84% I've just now rewritten those expressions we just had. 01:06:45.410 --> 01:06:48.410 align:middle line:84% By treating the problem like ordinary two-body scattering 01:06:48.410 --> 01:06:51.770 align:middle line:84% between discrete localized particles, 01:06:51.770 --> 01:06:53.750 align:middle line:84% Compton has three expressions-- conservation 01:06:53.750 --> 01:06:55.520 align:middle line:84% of energy, conservation of momentum 01:06:55.520 --> 01:06:57.620 align:middle line:84% in each of the two perpendicular directions-- 01:06:57.620 --> 01:06:58.820 align:middle line:90% and he has three unknowns. 01:06:58.820 --> 01:07:00.983 align:middle line:84% He doesn't know what the scattered wavelength is. 01:07:00.983 --> 01:07:02.900 align:middle line:84% And he doesn't know what the angles of scatter 01:07:02.900 --> 01:07:06.030 align:middle line:84% are-- either the angle theta for the light quantum or the angle 01:07:06.030 --> 01:07:08.260 align:middle line:90% phi for the recoiling electron. 01:07:08.260 --> 01:07:09.690 align:middle line:90% So now, it's just algebra. 01:07:09.690 --> 01:07:11.500 align:middle line:84% He has three equations for three unknowns. 01:07:11.500 --> 01:07:13.680 align:middle line:84% And as you'll see in the notes, now it's 01:07:13.680 --> 01:07:15.830 align:middle line:84% really just a short number of steps 01:07:15.830 --> 01:07:19.170 align:middle line:84% to relate the change in wavelength, 01:07:19.170 --> 01:07:22.200 align:middle line:84% the lambda-prime following scattering, 01:07:22.200 --> 01:07:24.270 align:middle line:84% compare that to the incoming wavelength, which 01:07:24.270 --> 01:07:25.150 align:middle line:90% you can control. 01:07:25.150 --> 01:07:27.800 align:middle line:90% He controls the x-ray source. 01:07:27.800 --> 01:07:30.510 align:middle line:84% And it gets related in an automatic way 01:07:30.510 --> 01:07:32.880 align:middle line:84% to that scattering angle in exactly the form 01:07:32.880 --> 01:07:35.070 align:middle line:84% that Compton had been finding empirically. 01:07:35.070 --> 01:07:37.350 align:middle line:84% Not only does he get the angular dependence 01:07:37.350 --> 01:07:41.130 align:middle line:84% correct, or at least matches his empirical results, 01:07:41.130 --> 01:07:43.210 align:middle line:84% he actually even finds a quantitative shift, 01:07:43.210 --> 01:07:44.370 align:middle line:90% this coefficient. 01:07:44.370 --> 01:07:47.040 align:middle line:84% The amount by which the wavelength should shift 01:07:47.040 --> 01:07:49.710 align:middle line:84% is now fixed by these universal constants-- 01:07:49.710 --> 01:07:52.830 align:middle line:84% Planck's constant, the mass of the electron, that target, 01:07:52.830 --> 01:07:55.030 align:middle line:90% and the speed of light. 01:07:55.030 --> 01:07:57.180 align:middle line:84% And so Compton is treating light like particles. 01:07:57.180 --> 01:07:59.250 align:middle line:84% And he's measuring changes in wavelength. 01:07:59.250 --> 01:08:02.490 align:middle line:84% Just going back to Gary's point from a few moments ago, 01:08:02.490 --> 01:08:06.990 align:middle line:84% Compton is now finding further examples where half the time he 01:08:06.990 --> 01:08:09.630 align:middle line:84% has to pretend that light is just a wave, because he's 01:08:09.630 --> 01:08:12.360 align:middle line:84% measuring wavelike properties-- like wavelength instead 01:08:12.360 --> 01:08:14.820 align:middle line:84% of necessarily a wavelike property. 01:08:14.820 --> 01:08:17.948 align:middle line:84% It's the distance between crests of a wave, after all. 01:08:17.948 --> 01:08:19.740 align:middle line:84% That's what he's controlling and measuring. 01:08:19.740 --> 01:08:22.620 align:middle line:84% That's his empirical input, is a wavelike quantity, 01:08:22.620 --> 01:08:23.729 align:middle line:90% a shift in wavelength. 01:08:23.729 --> 01:08:25.859 align:middle line:84% And yet, he's accounting for that 01:08:25.859 --> 01:08:28.800 align:middle line:84% by talking about a discrete particle scattering off 01:08:28.800 --> 01:08:30.479 align:middle line:90% another discrete particle. 01:08:30.479 --> 01:08:33.840 align:middle line:84% And so this becomes known as the Compton wavelength, 01:08:33.840 --> 01:08:36.750 align:middle line:84% this combination of fundamental constants, that tells us 01:08:36.750 --> 01:08:39.090 align:middle line:84% how much the wavelength of the scattered light 01:08:39.090 --> 01:08:41.279 align:middle line:84% should shift as one changes the angle, what's 01:08:41.279 --> 01:08:45.479 align:middle line:84% the overall scale by which this wavedness should shift. 01:08:45.479 --> 01:08:49.770 align:middle line:84% And so this becomes a kind of yet another hybrid or blend 01:08:49.770 --> 01:08:54.220 align:middle line:84% of particle-like and wavelike ways of reasoning about light. 01:08:54.220 --> 01:08:56.859 align:middle line:84% As I mentioned I think in the lecture notes for today, 01:08:56.859 --> 01:09:00.220 align:middle line:84% this work, much like Philip Lenard's, was immediately 01:09:00.220 --> 01:09:02.680 align:middle line:90% greeted as very important. 01:09:02.680 --> 01:09:05.800 align:middle line:84% Compton received a Nobel Prize, I think, by 1927. 01:09:05.800 --> 01:09:08.470 align:middle line:84% The paper was published in spring of 1923. 01:09:08.470 --> 01:09:12.069 align:middle line:84% So much like with Lenard's work, just a handful of years 01:09:12.069 --> 01:09:14.560 align:middle line:84% passed between the very first publication 01:09:14.560 --> 01:09:16.840 align:middle line:84% of these experimental results and the work 01:09:16.840 --> 01:09:18.370 align:middle line:84% being honored with the Nobel Prize. 01:09:18.370 --> 01:09:20.470 align:middle line:84% So people were paying attention to Compton's work 01:09:20.470 --> 01:09:23.020 align:middle line:84% very closely, very carefully in real time. 01:09:23.020 --> 01:09:24.670 align:middle line:84% And it was this kind of work that 01:09:24.670 --> 01:09:26.890 align:middle line:84% began to convince even the remaining 01:09:26.890 --> 01:09:31.000 align:middle line:84% skeptics that Einstein's heuristic suggestion that light 01:09:31.000 --> 01:09:33.850 align:middle line:84% should be treated at least in some aspects like a collection 01:09:33.850 --> 01:09:37.149 align:middle line:84% of particles-- that finally begins to gel and achieve 01:09:37.149 --> 01:09:39.670 align:middle line:84% something like community agreement whereas in Einstein's 01:09:39.670 --> 01:09:42.050 align:middle line:84% his earlier expressions that had been lacking. 01:09:42.050 --> 01:09:42.550 align:middle line:90% OK. 01:09:42.550 --> 01:09:43.585 align:middle line:90% Let me sum up. 01:09:43.585 --> 01:09:45.470 align:middle line:84% Then we'll have time for some more questions. 01:09:45.470 --> 01:09:47.740 align:middle line:84% So these three moments in what became 01:09:47.740 --> 01:09:49.750 align:middle line:90% known as old quantum theory-- 01:09:49.750 --> 01:09:51.760 align:middle line:84% each moment is physicists grappling 01:09:51.760 --> 01:09:54.640 align:middle line:90% with the nature of light. 01:09:54.640 --> 01:09:56.890 align:middle line:84% And remember, this is not happening in a vacuum. 01:09:56.890 --> 01:09:59.830 align:middle line:84% To begin to understand why anyone cared at all, let alone 01:09:59.830 --> 01:10:03.400 align:middle line:84% invested with such priority in these particular experiments, 01:10:03.400 --> 01:10:06.400 align:middle line:84% that really does go back to larger framing 01:10:06.400 --> 01:10:09.670 align:middle line:84% of a newly independent country of Germany, 01:10:09.670 --> 01:10:12.460 align:middle line:84% decisions by its leadership to invest in industrialization 01:10:12.460 --> 01:10:16.120 align:middle line:84% to make new kinds of places like the PTR and so on. 01:10:16.120 --> 01:10:20.440 align:middle line:84% It's within those spaces for specific industrial 01:10:20.440 --> 01:10:22.870 align:middle line:84% applications, like electric street lighting, 01:10:22.870 --> 01:10:25.540 align:middle line:84% that they were really committed to studying things 01:10:25.540 --> 01:10:28.030 align:middle line:84% like blackbody radiation and what 01:10:28.030 --> 01:10:32.650 align:middle line:84% it might reveal about universal properties of light and matter. 01:10:32.650 --> 01:10:35.110 align:middle line:84% Max Planck had just moved to Berlin 01:10:35.110 --> 01:10:37.540 align:middle line:84% as this full professor of theoretical physics, still 01:10:37.540 --> 01:10:40.660 align:middle line:84% a pretty rare job to hold within any German University. 01:10:40.660 --> 01:10:42.670 align:middle line:90% He was close by to PTR. 01:10:42.670 --> 01:10:44.980 align:middle line:84% And he was getting updates from his colleagues, 01:10:44.980 --> 01:10:48.490 align:middle line:84% sometimes day by day, with their increasingly precise 01:10:48.490 --> 01:10:51.280 align:middle line:84% measurements of that spectrum, the pattern of radiation 01:10:51.280 --> 01:10:55.030 align:middle line:84% emitted when you heat up any material to a sufficiently 01:10:55.030 --> 01:10:56.160 align:middle line:90% high temperature. 01:10:56.160 --> 01:10:59.100 align:middle line:84% No matter how he got there, by the end of December, 01:10:59.100 --> 01:11:03.510 align:middle line:84% Planck had introduced this now-famous expression 01:11:03.510 --> 01:11:06.090 align:middle line:90% for the spectral energy density. 01:11:06.090 --> 01:11:09.180 align:middle line:84% To get there, he had introduced this new constant of nature. 01:11:09.180 --> 01:11:11.580 align:middle line:84% We now call it Planck's constant-- very, very 01:11:11.580 --> 01:11:14.100 align:middle line:84% tiny on human scales, and yet not zero. 01:11:14.100 --> 01:11:16.710 align:middle line:84% And then we saw that whatever Planck thought 01:11:16.710 --> 01:11:19.470 align:middle line:84% that meant, within a few years, Einstein takes that 01:11:19.470 --> 01:11:22.680 align:middle line:84% up and, in a sense, treats it more seriously than Planck 01:11:22.680 --> 01:11:23.880 align:middle line:90% himself had even done. 01:11:23.880 --> 01:11:26.550 align:middle line:84% So Einstein not only rederives Planck's result 01:11:26.550 --> 01:11:29.520 align:middle line:84% from a very specific conceptual starting point-- 01:11:29.520 --> 01:11:33.030 align:middle line:84% what if light consists of collections of discrete quanta, 01:11:33.030 --> 01:11:34.660 align:middle line:90% soon to be called photons? 01:11:34.660 --> 01:11:39.420 align:middle line:84% And that same new concept, new set of ideas 01:11:39.420 --> 01:11:42.870 align:middle line:84% helps Einstein make sense of experiments like Lenard's 01:11:42.870 --> 01:11:44.380 align:middle line:90% on the photoelectric effect. 01:11:44.380 --> 01:11:46.290 align:middle line:84% However, as I've emphasized many times, 01:11:46.290 --> 01:11:48.150 align:middle line:84% that seemed to be compelling to Einstein 01:11:48.150 --> 01:11:51.270 align:middle line:84% in 1905, but to very few others for years and years later. 01:11:51.270 --> 01:11:54.660 align:middle line:84% And it really took the better part of two decades 01:11:54.660 --> 01:11:57.130 align:middle line:84% until consensus began to converge around 01:11:57.130 --> 01:11:59.710 align:middle line:84% this idea of light quanta, or photons. 01:11:59.710 --> 01:12:03.070 align:middle line:84% A very important piece of that was these new set 01:12:03.070 --> 01:12:05.830 align:middle line:84% of experiments by Arthur Compton at Chicago, 01:12:05.830 --> 01:12:08.980 align:middle line:84% where he could only make sense of his own new results 01:12:08.980 --> 01:12:12.790 align:middle line:84% by doing this kind of dance, by talking about x-rays 01:12:12.790 --> 01:12:15.790 align:middle line:84% as waves with wavelengths, and then accounting 01:12:15.790 --> 01:12:18.880 align:middle line:84% for the shift of those wavelength properties in terms 01:12:18.880 --> 01:12:22.000 align:middle line:84% of the particulate, or quantum-like scattering 01:12:22.000 --> 01:12:23.230 align:middle line:90% of discrete bodies. 01:12:23.230 --> 01:12:24.110 align:middle line:90% So I'll stop there. 01:12:24.110 --> 01:12:26.820 align:middle line:84% We've got time for some more questions and discussion. 01:12:26.820 --> 01:12:28.730 align:middle line:90% So let's see. 01:12:28.730 --> 01:12:30.620 align:middle line:84% Stanley writes, is there a reason 01:12:30.620 --> 01:12:32.030 align:middle line:90% Compton was able to measure-- 01:12:32.030 --> 01:12:34.190 align:middle line:84% was able to assume energy was conserved? 01:12:34.190 --> 01:12:35.600 align:middle line:90% Oh, very good. 01:12:35.600 --> 01:12:37.160 align:middle line:84% How did he know energy was not lost? 01:12:37.160 --> 01:12:39.470 align:middle line:84% In a sense, that was actually an assumption, Stanley. 01:12:39.470 --> 01:12:41.250 align:middle line:90% It's an excellent question. 01:12:41.250 --> 01:12:43.670 align:middle line:84% And in fact, it's a very powerful question 01:12:43.670 --> 01:12:46.940 align:middle line:84% because, at around the same time, other leading figures, 01:12:46.940 --> 01:12:50.570 align:middle line:84% like Niels Bohr himself-- almost exactly the same time, by 1923 01:12:50.570 --> 01:12:52.400 align:middle line:90% and '24, in fact. 01:12:52.400 --> 01:12:56.030 align:middle line:84% Niels Bohr, in responding to other curious features 01:12:56.030 --> 01:13:00.320 align:middle line:84% of recent results, suggested that maybe energy is not 01:13:00.320 --> 01:13:03.020 align:middle line:84% conserved at the scale of atoms and parts of atoms. 01:13:03.020 --> 01:13:04.162 align:middle line:90% Compton didn't go that far. 01:13:04.162 --> 01:13:06.120 align:middle line:84% And most of his colleagues never went that far. 01:13:06.120 --> 01:13:07.650 align:middle line:84% Even Bohr switched back and said, 01:13:07.650 --> 01:13:09.240 align:middle line:84% nope, energy should be conserved. 01:13:09.240 --> 01:13:12.860 align:middle line:84% So Compton was basically taking on board the assumption-- just 01:13:12.860 --> 01:13:16.340 align:middle line:84% an assumption-- that energy is conserved always even 01:13:16.340 --> 01:13:17.540 align:middle line:90% at the atomic scale. 01:13:17.540 --> 01:13:18.560 align:middle line:90% That was not proven. 01:13:18.560 --> 01:13:19.588 align:middle line:90% That was an assumption. 01:13:19.588 --> 01:13:21.380 align:middle line:84% What Compton was trying to do was basically 01:13:21.380 --> 01:13:25.640 align:middle line:84% make as few changes as needed to a straightforward 01:13:25.640 --> 01:13:27.720 align:middle line:84% way of analyzing the scattering data. 01:13:27.720 --> 01:13:30.120 align:middle line:84% How would any of us analyze, say, 01:13:30.120 --> 01:13:34.560 align:middle line:84% the collision of two balls on human scales, 01:13:34.560 --> 01:13:36.812 align:middle line:84% two billiard balls, a baseball and a baseball bat, 01:13:36.812 --> 01:13:37.770 align:middle line:90% or any of these things? 01:13:37.770 --> 01:13:39.900 align:middle line:84% We would assume energy is conserved. 01:13:39.900 --> 01:13:41.790 align:middle line:84% We would assume momentum is conserved in each 01:13:41.790 --> 01:13:44.075 align:middle line:90% of its relevant components. 01:13:44.075 --> 01:13:45.450 align:middle line:84% And that's what Compton is doing. 01:13:45.450 --> 01:13:47.850 align:middle line:84% And that was actually what most physicists continued to do. 01:13:47.850 --> 01:13:50.475 align:middle line:84% Although, you're quite right to point out, Stanley, that really 01:13:50.475 --> 01:13:51.240 align:middle line:90% was an assumption. 01:13:51.240 --> 01:13:53.280 align:middle line:90% It wasn't written in stone. 01:13:53.280 --> 01:13:54.660 align:middle line:90% It wasn't guaranteed. 01:13:54.660 --> 01:13:57.570 align:middle line:84% Nowadays, when we look back, we have tons and tons 01:13:57.570 --> 01:13:59.760 align:middle line:84% of reasons to think that energy really is conserved, 01:13:59.760 --> 01:14:01.590 align:middle line:84% even at the atomic scale, even when 01:14:01.590 --> 01:14:02.910 align:middle line:90% we think about light quanta. 01:14:02.910 --> 01:14:08.340 align:middle line:84% That was by no means hard and fast evidence at the time. 01:14:08.340 --> 01:14:09.282 align:middle line:90% Compton assumed it. 01:14:09.282 --> 01:14:11.490 align:middle line:84% And that helped him get the results that he otherwise 01:14:11.490 --> 01:14:13.110 align:middle line:90% was aiming to explain. 01:14:13.110 --> 01:14:14.220 align:middle line:90% Excellent question. 01:14:14.220 --> 01:14:16.890 align:middle line:84% Obi asks, it's interesting that Einstein accepted this duality 01:14:16.890 --> 01:14:19.388 align:middle line:84% because he rejected the ether before because it required 01:14:19.388 --> 01:14:20.430 align:middle line:90% conflicting explanations. 01:14:20.430 --> 01:14:21.250 align:middle line:90% Obi, I agree. 01:14:21.250 --> 01:14:23.455 align:middle line:84% That's an excellent point actually. 01:14:23.455 --> 01:14:24.330 align:middle line:90% You're totally right. 01:14:24.330 --> 01:14:26.670 align:middle line:84% So one might have expected him to say, 01:14:26.670 --> 01:14:28.320 align:middle line:84% the assumption of Maxwellian waves 01:14:28.320 --> 01:14:30.065 align:middle line:90% is merely superfluous, right? 01:14:30.065 --> 01:14:32.190 align:middle line:84% That was the same language he used about the ether. 01:14:32.190 --> 01:14:35.080 align:middle line:90% 01:14:35.080 --> 01:14:37.080 align:middle line:84% You've got me back to Gary's point from earlier. 01:14:37.080 --> 01:14:41.450 align:middle line:84% I wonder if Einstein didn't make that move here because he 01:14:41.450 --> 01:14:43.990 align:middle line:84% himself knew that there were things 01:14:43.990 --> 01:14:45.740 align:middle line:84% that he thought wavelike properties really 01:14:45.740 --> 01:14:46.940 align:middle line:90% could explain. 01:14:46.940 --> 01:14:49.640 align:middle line:84% I think Einstein had convinced himself, by 1905, 01:14:49.640 --> 01:14:52.040 align:middle line:84% that invoking the luminiferous ether 01:14:52.040 --> 01:14:53.730 align:middle line:84% didn't help people understand anything 01:14:53.730 --> 01:14:55.730 align:middle line:84% that it was meant to explain, that the ether was 01:14:55.730 --> 01:14:58.090 align:middle line:90% meant to explain. 01:14:58.090 --> 01:14:59.740 align:middle line:84% Thinking about light as waves still 01:14:59.740 --> 01:15:02.200 align:middle line:84% had explanatory power for things like interference, 01:15:02.200 --> 01:15:03.580 align:middle line:90% diffraction, refraction. 01:15:03.580 --> 01:15:05.200 align:middle line:90% So I think he was-- 01:15:05.200 --> 01:15:05.890 align:middle line:90% I'm assuming. 01:15:05.890 --> 01:15:07.098 align:middle line:90% We can go back and look more. 01:15:07.098 --> 01:15:09.268 align:middle line:84% And other scholars look more carefully at this. 01:15:09.268 --> 01:15:10.810 align:middle line:84% My assumption is that Einstein didn't 01:15:10.810 --> 01:15:14.080 align:middle line:84% want to give up on waves as never being helpful to think 01:15:14.080 --> 01:15:16.240 align:middle line:84% about light because of this body of evidence 01:15:16.240 --> 01:15:19.000 align:middle line:84% that he thought really could be for which a wave explanation 01:15:19.000 --> 01:15:20.380 align:middle line:90% was actually helpful. 01:15:20.380 --> 01:15:21.940 align:middle line:84% Whereas he had convinced himself, 01:15:21.940 --> 01:15:24.010 align:middle line:84% partly from his reading of Ernst Mach and so on, 01:15:24.010 --> 01:15:27.680 align:middle line:84% that invoking an ether seemed never to be helpful. 01:15:27.680 --> 01:15:30.760 align:middle line:84% Wavelike behaviors, there were all kinds of phenomena, 01:15:30.760 --> 01:15:33.040 align:middle line:84% even in casual daily experience, let alone 01:15:33.040 --> 01:15:35.500 align:middle line:84% in precision experiments, where things 01:15:35.500 --> 01:15:39.010 align:middle line:84% like interference, fringes, and so on were essential. 01:15:39.010 --> 01:15:43.597 align:middle line:84% That's my guess for why Einstein called this heuristic, 01:15:43.597 --> 01:15:45.930 align:middle line:84% didn't announce the notion of thinking about light waves 01:15:45.930 --> 01:15:46.530 align:middle line:90% again. 01:15:46.530 --> 01:15:51.585 align:middle line:84% And again, Einstein becomes one of the most, frankly fearless-- 01:15:51.585 --> 01:15:53.085 align:middle line:84% one of the most conceptually daring, 01:15:53.085 --> 01:15:55.650 align:middle line:84% I think is the word to say, in really 01:15:55.650 --> 01:15:57.570 align:middle line:84% trying to pursue this wave particle duality 01:15:57.570 --> 01:15:59.320 align:middle line:90% over the next two decades. 01:15:59.320 --> 01:16:00.720 align:middle line:90% He really sits with it. 01:16:00.720 --> 01:16:02.500 align:middle line:84% He doesn't say, oh, this hurts my head. 01:16:02.500 --> 01:16:03.667 align:middle line:90% It must be one or the other. 01:16:03.667 --> 01:16:06.720 align:middle line:84% He actually digs in actually, in a series 01:16:06.720 --> 01:16:08.370 align:middle line:84% of developments throughout what becomes 01:16:08.370 --> 01:16:10.540 align:middle line:90% known as quantum mechanics. 01:16:10.540 --> 01:16:14.155 align:middle line:84% So he really found this delicious and enticing. 01:16:14.155 --> 01:16:15.780 align:middle line:84% Maybe those are the wrong words to use. 01:16:15.780 --> 01:16:18.390 align:middle line:84% But he certainly found it worth sitting with, as opposed to it 01:16:18.390 --> 01:16:22.320 align:middle line:84% must be A or B. And we'll see some examples of that 01:16:22.320 --> 01:16:23.940 align:middle line:84% again in the coming class sessions. 01:16:23.940 --> 01:16:25.420 align:middle line:90% Excellent observation, though. 01:16:25.420 --> 01:16:26.310 align:middle line:90% Any other questions? 01:16:26.310 --> 01:16:31.580 align:middle line:90% 01:16:31.580 --> 01:16:34.140 align:middle line:84% Since I have three minutes, I'll share the following. 01:16:34.140 --> 01:16:36.500 align:middle line:84% One of the things that was done by not Arthur Compton 01:16:36.500 --> 01:16:38.930 align:middle line:84% but by Karl Compton soon after he became president 01:16:38.930 --> 01:16:41.130 align:middle line:90% in 1930, president of MIT-- 01:16:41.130 --> 01:16:42.890 align:middle line:84% and this is for all you physics majors. 01:16:42.890 --> 01:16:45.050 align:middle line:84% And my apologies to every other engineering major. 01:16:45.050 --> 01:16:45.980 align:middle line:90% You know who you are. 01:16:45.980 --> 01:16:47.810 align:middle line:84% Compton decided that MIT had become 01:16:47.810 --> 01:16:50.960 align:middle line:84% too closely aligned to both engineering and industry. 01:16:50.960 --> 01:16:52.640 align:middle line:84% He thought, in Compton's own words, 01:16:52.640 --> 01:16:56.030 align:middle line:84% that MIT had sold its soul to industrialists. 01:16:56.030 --> 01:17:00.140 align:middle line:84% And so it was time for MIT to redouble on the basic sciences. 01:17:00.140 --> 01:17:03.020 align:middle line:84% It was at this time, starting in 1930, 01:17:03.020 --> 01:17:05.720 align:middle line:84% when Compton, Karl Compton, put into a reform 01:17:05.720 --> 01:17:08.000 align:middle line:84% that every single undergraduate at MIT 01:17:08.000 --> 01:17:10.370 align:middle line:84% had to take two whole years of physics. 01:17:10.370 --> 01:17:12.590 align:middle line:84% You little wimps-- kidding, just kidding. 01:17:12.590 --> 01:17:15.950 align:middle line:84% You wonderful students only have to take one year of physics 01:17:15.950 --> 01:17:19.310 align:middle line:90% because MIT relented in 1965. 01:17:19.310 --> 01:17:22.250 align:middle line:84% For 35 years, Karl Compton's vision held. 01:17:22.250 --> 01:17:25.880 align:middle line:84% And literally every MIT student, whether they were management 01:17:25.880 --> 01:17:27.440 align:middle line:90% majors at the Sloan School-- 01:17:27.440 --> 01:17:28.400 align:middle line:90% I'm looking at Gary-- 01:17:28.400 --> 01:17:33.095 align:middle line:84% or economics majors, or history, or mathematics 01:17:33.095 --> 01:17:34.470 align:middle line:84% had to take two years of physics. 01:17:34.470 --> 01:17:36.137 align:middle line:84% It wasn't quite the Cambridge Wranglers. 01:17:36.137 --> 01:17:39.450 align:middle line:84% But we had two years because Karl Compton, the physicist, 01:17:39.450 --> 01:17:40.980 align:middle line:84% was convinced that we had to have 01:17:40.980 --> 01:17:43.537 align:middle line:84% a whole new emphasis on the so-called basic sciences. 01:17:43.537 --> 01:17:45.870 align:middle line:84% It's at this time when the laboratory requirements start 01:17:45.870 --> 01:17:49.950 align:middle line:84% coming in for biology, and chemistry, and mathematics. 01:17:49.950 --> 01:17:53.940 align:middle line:84% And it was only 35 years later, in the mid-1960s, 01:17:53.940 --> 01:17:58.860 align:middle line:84% when some colleagues long after Karl Compton stepped down said, 01:17:58.860 --> 01:18:02.040 align:middle line:84% maybe that's too much physics for every single student. 01:18:02.040 --> 01:18:05.340 align:middle line:84% And honestly, when I started teaching at MIT in 2000, 01:18:05.340 --> 01:18:07.680 align:middle line:84% some of my by then rather senior colleagues 01:18:07.680 --> 01:18:10.410 align:middle line:84% still remembered 1965 and thought everything 01:18:10.410 --> 01:18:12.197 align:middle line:90% had gone downhill since then. 01:18:12.197 --> 01:18:13.530 align:middle line:90% Those people have since retired. 01:18:13.530 --> 01:18:16.260 align:middle line:84% But MIT has never been the same, in their point of view, 01:18:16.260 --> 01:18:19.170 align:middle line:84% since we gave up forcing/inviting 01:18:19.170 --> 01:18:20.755 align:middle line:84% every single undergraduate to take 01:18:20.755 --> 01:18:21.880 align:middle line:90% two whole years of physics. 01:18:21.880 --> 01:18:24.780 align:middle line:84% So that's one of the legacies of Karl Compton, not 01:18:24.780 --> 01:18:27.300 align:middle line:90% Arthur Compton. 01:18:27.300 --> 01:18:27.870 align:middle line:90% It's true. 01:18:27.870 --> 01:18:30.360 align:middle line:84% Alex puts in the chat-- weren't the problem sets originally 01:18:30.360 --> 01:18:31.050 align:middle line:90% questions from industry? 01:18:31.050 --> 01:18:32.910 align:middle line:84% Many of them were, in fact, if not problem sets, then 01:18:32.910 --> 01:18:34.330 align:middle line:90% certainly research projects. 01:18:34.330 --> 01:18:37.980 align:middle line:84% There was a kind of research for hire program, which never 01:18:37.980 --> 01:18:41.580 align:middle line:84% really ended, but was a very high focus at MIT 01:18:41.580 --> 01:18:43.860 align:middle line:84% starting soon after the First World War, 01:18:43.860 --> 01:18:46.140 align:middle line:90% in the years right after 1918. 01:18:46.140 --> 01:18:49.470 align:middle line:84% It was called the MIT Plan or the Tech Plan. 01:18:49.470 --> 01:18:52.680 align:middle line:84% And roughly 12 to 15 years into that, 01:18:52.680 --> 01:18:55.050 align:middle line:84% there was a kind of course correction. 01:18:55.050 --> 01:18:57.600 align:middle line:84% And people like Karl Compton said, we have to rejigger that. 01:18:57.600 --> 01:18:59.370 align:middle line:84% Fisher says, I assume this requirement naturally 01:18:59.370 --> 01:19:00.912 align:middle line:84% only applied to physics and-- oh, no. 01:19:00.912 --> 01:19:01.830 align:middle line:90% That's right. 01:19:01.830 --> 01:19:02.970 align:middle line:90% Fisher's exactly right. 01:19:02.970 --> 01:19:05.730 align:middle line:84% So the requirement of two years of physics coursework 01:19:05.730 --> 01:19:08.520 align:middle line:84% applied only to physics for every single undergraduate. 01:19:08.520 --> 01:19:11.400 align:middle line:84% And grudgingly, if you had to take chemistry or biology, 01:19:11.400 --> 01:19:12.410 align:middle line:90% fine, that was required. 01:19:12.410 --> 01:19:13.660 align:middle line:90% You have to take laboratories. 01:19:13.660 --> 01:19:15.850 align:middle line:84% You had to take at least one year of mathematics. 01:19:15.850 --> 01:19:18.990 align:middle line:84% So we can recognize parts of our so-called GIRs 01:19:18.990 --> 01:19:21.480 align:middle line:84% to this day survive from Karl Compton's era, 01:19:21.480 --> 01:19:25.152 align:middle line:84% even though critically the one horrible moral lapse, 01:19:25.152 --> 01:19:26.610 align:middle line:84% according to some of my colleagues, 01:19:26.610 --> 01:19:30.480 align:middle line:84% was dropping the two years of physics in place of only one. 01:19:30.480 --> 01:19:31.818 align:middle line:90% I leave you with that thought. 01:19:31.818 --> 01:19:34.110 align:middle line:84% I invite you all to take more than one year of physics. 01:19:34.110 --> 01:19:35.100 align:middle line:84% I think many of you have been anyway 01:19:35.100 --> 01:19:36.350 align:middle line:90% because you're physics majors. 01:19:36.350 --> 01:19:38.108 align:middle line:90% That's Karl Compton. 01:19:38.108 --> 01:19:39.900 align:middle line:84% We'll actually talk more about Karl Compton 01:19:39.900 --> 01:19:42.510 align:middle line:84% at MIT in the coming weeks when we talk about MIT, 01:19:42.510 --> 01:19:44.010 align:middle line:84% and the Second World War, and radar. 01:19:44.010 --> 01:19:46.050 align:middle line:84% We'll hear Karl Compton's name again soon. 01:19:46.050 --> 01:19:47.550 align:middle line:84% In the meantime, we'll pause and sit 01:19:47.550 --> 01:19:50.220 align:middle line:84% with Arthur Compton's results for which, again, there's 01:19:50.220 --> 01:19:51.930 align:middle line:84% more of the algebra in those notes, 01:19:51.930 --> 01:19:53.400 align:middle line:90% if that went by too quickly. 01:19:53.400 --> 01:19:55.802 align:middle line:84% Any other questions about this material? 01:19:55.802 --> 01:19:58.260 align:middle line:84% Anyone wish that everyone had to take two years of physics? 01:19:58.260 --> 01:20:00.810 align:middle line:84% Or any other comments on today's class? 01:20:00.810 --> 01:20:02.770 align:middle line:90% If not, I'll leave it there. 01:20:02.770 --> 01:20:05.580 align:middle line:84% I'll wish you good luck wrapping up your paper 1 draft. 01:20:05.580 --> 01:20:07.990 align:middle line:84% Please don't forget, it's due this Friday. 01:20:07.990 --> 01:20:10.410 align:middle line:84% And we'll pick up the story of old quantum theory 01:20:10.410 --> 01:20:12.145 align:middle line:90% again with our next class. 01:20:12.145 --> 01:20:13.020 align:middle line:90% Thanks so much, gang. 01:20:13.020 --> 01:20:14.750 align:middle line:90% Stay well. 01:20:14.750 --> 01:20:22.000 align:middle line:90%