WEBVTT 00:00:00.000 --> 00:00:11.520 align:middle line:90% 00:00:11.520 --> 00:00:13.850 align:middle line:84% DAVID KAISER: So today, at long, long last, 00:00:13.850 --> 00:00:16.012 align:middle line:84% we meet this fella named Albert Einstein. 00:00:16.012 --> 00:00:18.470 align:middle line:84% We're going to talk a bit more about how he was approaching 00:00:18.470 --> 00:00:21.110 align:middle line:84% some of these questions in the early years 00:00:21.110 --> 00:00:22.070 align:middle line:90% of the 20th century. 00:00:22.070 --> 00:00:24.980 align:middle line:90% 00:00:24.980 --> 00:00:28.340 align:middle line:84% So as usual, today's class has three main parts. 00:00:28.340 --> 00:00:30.590 align:middle line:84% We're going to look at Einstein leading up 00:00:30.590 --> 00:00:35.900 align:middle line:84% to this year of 1905, what were his early educational 00:00:35.900 --> 00:00:37.970 align:middle line:84% experiences like, how did he come 00:00:37.970 --> 00:00:40.280 align:middle line:84% to this question of the electrodynamics of moving 00:00:40.280 --> 00:00:43.220 align:middle line:84% bodies, and what did he think was the most 00:00:43.220 --> 00:00:46.160 align:middle line:84% kind of compelling way to start addressing 00:00:46.160 --> 00:00:47.510 align:middle line:90% some of these questions? 00:00:47.510 --> 00:00:51.560 align:middle line:84% For the middle part of today, we'll talk about this paper, 00:00:51.560 --> 00:00:52.640 align:middle line:90% in particular. 00:00:52.640 --> 00:00:55.730 align:middle line:84% This excerpt of the paper that you had in the reader 00:00:55.730 --> 00:00:58.190 align:middle line:84% on the electrodynamics of moving bodies. 00:00:58.190 --> 00:01:01.430 align:middle line:84% What were some of the key ways in which Einstein was talking 00:01:01.430 --> 00:01:03.650 align:middle line:84% about, what we would now call the special theory 00:01:03.650 --> 00:01:04.465 align:middle line:90% of relativity. 00:01:04.465 --> 00:01:05.840 align:middle line:84% And I have a little asterisk here 00:01:05.840 --> 00:01:09.470 align:middle line:84% to remind you for this section, for this class session, 00:01:09.470 --> 00:01:11.670 align:middle line:84% I wrote up a little short set of extra notes, 00:01:11.670 --> 00:01:14.610 align:middle line:84% not nearly so detailed as the previous set. 00:01:14.610 --> 00:01:16.770 align:middle line:84% And those are really just as a supplement 00:01:16.770 --> 00:01:19.260 align:middle line:84% for something I'm going to probably not have much time 00:01:19.260 --> 00:01:21.900 align:middle line:84% to linger on in the class session itself today. 00:01:21.900 --> 00:01:24.660 align:middle line:84% And that's a consequence of Einstein's work 00:01:24.660 --> 00:01:27.690 align:middle line:84% that he published in a separate follow-up article in which he 00:01:27.690 --> 00:01:30.930 align:middle line:84% derived this now-rather famous relation that E 00:01:30.930 --> 00:01:32.020 align:middle line:90% equals mc squared. 00:01:32.020 --> 00:01:35.040 align:middle line:84% So I'm going to go through, quickly today, 00:01:35.040 --> 00:01:36.960 align:middle line:84% the nature of Einstein's argument 00:01:36.960 --> 00:01:38.835 align:middle line:84% that led him to that conclusion, and then you 00:01:38.835 --> 00:01:40.002 align:middle line:90% can have a couple of pages-- 00:01:40.002 --> 00:01:41.790 align:middle line:84% I think it's only about five pages or so-- 00:01:41.790 --> 00:01:44.760 align:middle line:84% to read a little bit more detail about some of the ways 00:01:44.760 --> 00:01:47.170 align:middle line:84% that Einstein came about that conclusion. 00:01:47.170 --> 00:01:49.710 align:middle line:84% So a little extra supplemental, strictly optional as always. 00:01:49.710 --> 00:01:51.480 align:middle line:84% But if you are curious about it, there's 00:01:51.480 --> 00:01:52.680 align:middle line:90% some more materials there. 00:01:52.680 --> 00:01:54.480 align:middle line:90% And then, we'll pan out again. 00:01:54.480 --> 00:01:56.340 align:middle line:84% We'll kind of zoom out and try to make sense 00:01:56.340 --> 00:01:59.190 align:middle line:84% of, why did Einstein approach these questions in the ways 00:01:59.190 --> 00:02:00.360 align:middle line:90% that he did? 00:02:00.360 --> 00:02:02.520 align:middle line:84% How can we think about what else Einstein 00:02:02.520 --> 00:02:05.430 align:middle line:84% was thinking about, was immersed in, 00:02:05.430 --> 00:02:07.770 align:middle line:84% what was going on in his life, in his early professional 00:02:07.770 --> 00:02:11.220 align:middle line:84% career, drawing, in this case, very heavily on that article 00:02:11.220 --> 00:02:14.310 align:middle line:84% by Peter Galison on the reader to try to understand why 00:02:14.310 --> 00:02:15.810 align:middle line:84% Einstein approached, as we'll see, 00:02:15.810 --> 00:02:19.110 align:middle line:84% a very conventional question in rather unconventional ways. 00:02:19.110 --> 00:02:20.920 align:middle line:90% That's our plan for today. 00:02:20.920 --> 00:02:22.060 align:middle line:90% So let's jump in. 00:02:22.060 --> 00:02:24.030 align:middle line:84% So remember what we're responding to. 00:02:24.030 --> 00:02:27.850 align:middle line:84% What's Einstein inheriting by the time he comes on the scene? 00:02:27.850 --> 00:02:31.650 align:middle line:84% So we saw, in the previous few lectures from last week, 00:02:31.650 --> 00:02:34.500 align:middle line:84% the questions about the behavior or the propagation 00:02:34.500 --> 00:02:38.310 align:middle line:84% of light waves in the ether in that all-pervasive, elastic 00:02:38.310 --> 00:02:41.490 align:middle line:84% medium called the light bearing or luminiferous ether. 00:02:41.490 --> 00:02:43.710 align:middle line:84% Those questions were really at the forefront. 00:02:43.710 --> 00:02:47.310 align:middle line:84% That was mainstream physics by the end of the 19th century. 00:02:47.310 --> 00:02:48.840 align:middle line:84% And especially when we get to people 00:02:48.840 --> 00:02:51.420 align:middle line:84% like Hendrik Lorentz or Michelson and Morley, 00:02:51.420 --> 00:02:54.180 align:middle line:84% the topic that was often described 00:02:54.180 --> 00:02:56.520 align:middle line:84% was the electrodynamics of moving bodies, 00:02:56.520 --> 00:03:00.180 align:middle line:84% the effort to generalize from James Clerk Maxwell's work 00:03:00.180 --> 00:03:03.870 align:middle line:84% from the middle decades of the 19th century in which Maxwell 00:03:03.870 --> 00:03:08.580 align:middle line:84% had worked out this really quite beautiful combination 00:03:08.580 --> 00:03:11.220 align:middle line:84% of electricity, magnetism, and optics. 00:03:11.220 --> 00:03:14.430 align:middle line:84% But he really was treating light waves 00:03:14.430 --> 00:03:16.740 align:middle line:84% for the special case in which both the emitter 00:03:16.740 --> 00:03:18.600 align:middle line:84% and the receiver of those light waves 00:03:18.600 --> 00:03:22.440 align:middle line:84% were both at rest with respect to this light-bearing ether. 00:03:22.440 --> 00:03:25.920 align:middle line:84% So the question then becomes, what about moving bodies? 00:03:25.920 --> 00:03:29.520 align:middle line:84% What if either the sender or the receiver of light or both 00:03:29.520 --> 00:03:32.190 align:middle line:84% were in motion with respect to each other and with respect 00:03:32.190 --> 00:03:33.000 align:middle line:90% to the ether? 00:03:33.000 --> 00:03:36.450 align:middle line:84% That became known by this catch phrase, "the electrodynamics 00:03:36.450 --> 00:03:38.850 align:middle line:90% of moving bodies." 00:03:38.850 --> 00:03:42.420 align:middle line:84% One of the key moments in that investigation that we 00:03:42.420 --> 00:03:46.380 align:middle line:84% saw from the 1880s was performed by Albert Michelson and Edward 00:03:46.380 --> 00:03:48.480 align:middle line:84% Morley in what's now Case Western Reserve 00:03:48.480 --> 00:03:51.390 align:middle line:84% University in Cleveland in the United States. 00:03:51.390 --> 00:03:55.200 align:middle line:84% So they used this enormous, specially built interferometer 00:03:55.200 --> 00:03:56.910 align:middle line:90% of Michelson's own design. 00:03:56.910 --> 00:03:59.250 align:middle line:84% By the 1880s, late '80s, they were 00:03:59.250 --> 00:04:02.040 align:middle line:84% using an interferometer where each leg 00:04:02.040 --> 00:04:04.920 align:middle line:84% of this l-shaped instrument was 11m long. 00:04:04.920 --> 00:04:07.200 align:middle line:90% That's about 34ft on a side. 00:04:07.200 --> 00:04:11.070 align:middle line:84% Huge, huge, huge instrument that they designed and built 00:04:11.070 --> 00:04:13.650 align:middle line:84% expressly to try to measure changes 00:04:13.650 --> 00:04:15.210 align:middle line:84% in the behavior of light waves, in 00:04:15.210 --> 00:04:18.450 align:middle line:84% particular in the relative speed with which waves would move 00:04:18.450 --> 00:04:22.620 align:middle line:84% through the ether, depending on whether our own laboratory here 00:04:22.620 --> 00:04:25.740 align:middle line:84% on Earth was moving directly into the ether 00:04:25.740 --> 00:04:28.350 align:middle line:84% or some perpendicular-- or the light waves 00:04:28.350 --> 00:04:30.570 align:middle line:84% were moving perpendicular to the Earth's motion. 00:04:30.570 --> 00:04:33.930 align:middle line:84% So whether it be what we could think of as an ether headwind, 00:04:33.930 --> 00:04:36.480 align:middle line:84% like if you're pedaling on your bicycle on an otherwise 00:04:36.480 --> 00:04:38.700 align:middle line:84% still day, you'll feel a breeze on your face 00:04:38.700 --> 00:04:40.950 align:middle line:84% in the direction of your own motion. 00:04:40.950 --> 00:04:42.605 align:middle line:84% And as we saw last time, Michelson 00:04:42.605 --> 00:04:43.980 align:middle line:84% had reasoned that there should be 00:04:43.980 --> 00:04:46.950 align:middle line:84% a similar effect for light waves because our whole laboratory 00:04:46.950 --> 00:04:49.830 align:middle line:84% on Earth was, assuredly, they were 00:04:49.830 --> 00:04:52.200 align:middle line:84% quite confident, was moving through the ether, 00:04:52.200 --> 00:04:55.290 align:middle line:84% so there should be some relative motion between the behavior 00:04:55.290 --> 00:04:56.760 align:middle line:84% of light waves as we measure them 00:04:56.760 --> 00:04:59.520 align:middle line:84% on Earth on an instrument like the interferometer 00:04:59.520 --> 00:05:01.380 align:middle line:90% and the all-pervasive ether. 00:05:01.380 --> 00:05:04.800 align:middle line:84% And as we saw and even read their brief paper, 00:05:04.800 --> 00:05:07.530 align:middle line:84% despite some really exquisite experimental design 00:05:07.530 --> 00:05:11.280 align:middle line:84% and sensitivity, they never detected any clear evidence 00:05:11.280 --> 00:05:14.410 align:middle line:84% that would have been associated with the Earth's motion 00:05:14.410 --> 00:05:15.400 align:middle line:90% through the ether. 00:05:15.400 --> 00:05:17.530 align:middle line:84% That was what became known as a null result. 00:05:17.530 --> 00:05:21.683 align:middle line:84% The results were consistent with no change in relative speed, 00:05:21.683 --> 00:05:24.100 align:middle line:84% no matter what direction those light beams were traveling. 00:05:24.100 --> 00:05:27.070 align:middle line:84% And as we saw, even though Michelson won the Nobel Prize, 00:05:27.070 --> 00:05:29.590 align:middle line:84% he was the first physicist based in the United States 00:05:29.590 --> 00:05:32.810 align:middle line:84% to win the Nobel Prize for physics, he won in 1907, 00:05:32.810 --> 00:05:34.810 align:middle line:84% he died 20 years later still convinced 00:05:34.810 --> 00:05:36.130 align:middle line:90% that he had just messed up. 00:05:36.130 --> 00:05:39.550 align:middle line:84% So that's sad for him, and maybe we all suffer the same fate. 00:05:39.550 --> 00:05:41.050 align:middle line:84% Maybe we all win the Nobel Prize, 00:05:41.050 --> 00:05:43.600 align:middle line:84% even if we're not satisfied with our work. 00:05:43.600 --> 00:05:47.470 align:middle line:84% OK, meanwhile, some very leading, very elite physicists 00:05:47.470 --> 00:05:50.110 align:middle line:84% back in Western Europe Like Hendrik Lorentz 00:05:50.110 --> 00:05:54.130 align:middle line:84% were following Michelson's and Morley's work quite carefully. 00:05:54.130 --> 00:05:56.890 align:middle line:84% Lorentz was a mathematical physicist closer in spirit 00:05:56.890 --> 00:05:58.330 align:middle line:90% to James Clerk Maxwell. 00:05:58.330 --> 00:06:00.250 align:middle line:84% He wasn't building his own experiments. 00:06:00.250 --> 00:06:03.610 align:middle line:84% But he was very attuned to what results Michelson-Morley 00:06:03.610 --> 00:06:05.530 align:middle line:84% and other experiments were finding. 00:06:05.530 --> 00:06:08.410 align:middle line:84% And Lorentz finally introduces a way 00:06:08.410 --> 00:06:13.703 align:middle line:84% to accommodate this null result to explain why experiments 00:06:13.703 --> 00:06:15.370 align:middle line:84% like Michelson and Morley's might indeed 00:06:15.370 --> 00:06:19.030 align:middle line:84% measure no offset, no change in the relative speed. 00:06:19.030 --> 00:06:21.700 align:middle line:84% And Lorentz argued it was because of dynamics. 00:06:21.700 --> 00:06:24.250 align:middle line:84% Because the previous analyzes had dropped, 00:06:24.250 --> 00:06:26.650 align:middle line:84% had missed one of the relevant forces. 00:06:26.650 --> 00:06:30.520 align:middle line:84% In this case, Lorentz argued that if the entire apparatus, 00:06:30.520 --> 00:06:32.710 align:middle line:84% like everything else, is immersed 00:06:32.710 --> 00:06:35.560 align:middle line:84% in this physical, elastic medium of the ether, 00:06:35.560 --> 00:06:38.720 align:middle line:84% the ether should exert a force on the material, 00:06:38.720 --> 00:06:41.830 align:middle line:84% making up the arm of that instrument, one of those Ls, 00:06:41.830 --> 00:06:45.430 align:middle line:84% one edge of the L. The edge is moving directly 00:06:45.430 --> 00:06:46.750 align:middle line:90% into the ether wind. 00:06:46.750 --> 00:06:49.300 align:middle line:84% That should be compressed or contracted 00:06:49.300 --> 00:06:52.510 align:middle line:84% because of a physical force, a kind of resistive 00:06:52.510 --> 00:06:55.270 align:middle line:84% force onto the interferometer itself. 00:06:55.270 --> 00:06:58.290 align:middle line:84% The Irish mathematical physicist George FitzGerald 00:06:58.290 --> 00:07:00.040 align:middle line:84% came up with a very similar argument right 00:07:00.040 --> 00:07:01.240 align:middle line:90% around the same time. 00:07:01.240 --> 00:07:03.040 align:middle line:84% This was, for some years, known as 00:07:03.040 --> 00:07:05.980 align:middle line:84% "the Lorentz-FitzGerald contraction," or sometimes just 00:07:05.980 --> 00:07:07.570 align:middle line:90% as "Lorentz contraction." 00:07:07.570 --> 00:07:10.540 align:middle line:84% And the idea was that if there's a contraction by just such 00:07:10.540 --> 00:07:14.570 align:middle line:84% an amount, depending on the relative speed of the object 00:07:14.570 --> 00:07:17.720 align:middle line:84% through the ether, V, compared to the speed of light, 00:07:17.720 --> 00:07:21.020 align:middle line:84% C, if you cooked up the amount of contraction 00:07:21.020 --> 00:07:24.080 align:middle line:84% just right by that factor gamma that we encountered 00:07:24.080 --> 00:07:28.490 align:middle line:84% a few times, then the expected offset 00:07:28.490 --> 00:07:31.220 align:middle line:84% in that race between the light waves traveling in the two 00:07:31.220 --> 00:07:32.870 align:middle line:84% different sides of the interferometer 00:07:32.870 --> 00:07:35.062 align:middle line:90% should exactly cancel. 00:07:35.062 --> 00:07:37.310 align:middle line:84% The race should be a tie after all. 00:07:37.310 --> 00:07:39.590 align:middle line:84% One should actually expect a null result. 00:07:39.590 --> 00:07:41.930 align:middle line:84% And all this came down from treating 00:07:41.930 --> 00:07:44.720 align:middle line:84% the electrodynamics of moving bodies by starting 00:07:44.720 --> 00:07:46.130 align:middle line:90% with the question dynamics. 00:07:46.130 --> 00:07:47.930 align:middle line:84% Are there all the forces at play, 00:07:47.930 --> 00:07:49.970 align:middle line:84% rather than kinematics, which is the study 00:07:49.970 --> 00:07:52.920 align:middle line:84% of the motion of objects through space and time. 00:07:52.920 --> 00:07:57.080 align:middle line:84% So young Albert Einstein then inherits that set 00:07:57.080 --> 00:08:00.410 align:middle line:84% of questions and moves into that discussion a little bit later. 00:08:00.410 --> 00:08:02.510 align:middle line:90% He was born in 1879. 00:08:02.510 --> 00:08:05.240 align:middle line:84% Here's a rather adorable photo of young Einstein, 00:08:05.240 --> 00:08:06.830 align:middle line:90% kind of elementary-school aged. 00:08:06.830 --> 00:08:11.300 align:middle line:84% So he was born just before Michelson and Morley actually 00:08:11.300 --> 00:08:12.810 align:middle line:84% began that series of experiments. 00:08:12.810 --> 00:08:15.620 align:middle line:84% So he was born after Maxwell's Treatise 00:08:15.620 --> 00:08:18.260 align:middle line:84% before some of Hendrik Lorentz's main work. 00:08:18.260 --> 00:08:21.110 align:middle line:84% He was born in the town of Ulm in what 00:08:21.110 --> 00:08:24.260 align:middle line:84% was then quite rural Germany, not near any of the main city 00:08:24.260 --> 00:08:25.880 align:middle line:90% centers. 00:08:25.880 --> 00:08:28.760 align:middle line:84% Einstein's main ambition when he was a young child 00:08:28.760 --> 00:08:30.920 align:middle line:84% was actually to join the business 00:08:30.920 --> 00:08:32.809 align:middle line:84% that his father and his uncle had created. 00:08:32.809 --> 00:08:35.630 align:middle line:84% They were some of the first professional electrical 00:08:35.630 --> 00:08:38.929 align:middle line:84% engineers in these later decades of the 19th century, 00:08:38.929 --> 00:08:42.020 align:middle line:84% just like the kind of folks about whom Maxwell had written 00:08:42.020 --> 00:08:45.020 align:middle line:84% in England in the preface to his treatise, 00:08:45.020 --> 00:08:47.450 align:middle line:84% these so-called electricians that would soon be called 00:08:47.450 --> 00:08:48.860 align:middle line:90% "electrical engineers." 00:08:48.860 --> 00:08:51.980 align:middle line:84% So that's what Einstein's own father did and his uncle, 00:08:51.980 --> 00:08:54.110 align:middle line:90% they formed a company together. 00:08:54.110 --> 00:08:56.420 align:middle line:84% They were much better at engineering than at business. 00:08:56.420 --> 00:08:58.135 align:middle line:84% The company went bankrupt multiple times. 00:08:58.135 --> 00:08:59.510 align:middle line:84% They had to actually keep moving. 00:08:59.510 --> 00:09:03.680 align:middle line:84% But they were working in this exciting new area 00:09:03.680 --> 00:09:07.963 align:middle line:84% during the waves of things like wide-scale electrification, 00:09:07.963 --> 00:09:10.130 align:middle line:84% the introduction of electric street lighting in more 00:09:10.130 --> 00:09:13.010 align:middle line:84% and more municipalities, more and more ways 00:09:13.010 --> 00:09:16.400 align:middle line:84% in which electrification and therefore electrical gadgets 00:09:16.400 --> 00:09:18.620 align:middle line:84% were entering into quite common experience. 00:09:18.620 --> 00:09:21.350 align:middle line:84% That's the world into which Einstein was literally born. 00:09:21.350 --> 00:09:23.240 align:middle line:84% And that's what he wanted to work on. 00:09:23.240 --> 00:09:25.640 align:middle line:84% It turns out he dropped out of high school, 00:09:25.640 --> 00:09:28.460 align:middle line:84% so he never got a high school diploma. 00:09:28.460 --> 00:09:31.640 align:middle line:90% He developed a real allergy. 00:09:31.640 --> 00:09:33.920 align:middle line:84% He got very frustrated with what he considered 00:09:33.920 --> 00:09:36.890 align:middle line:84% an overly militaristic approach, a very disciplined-based 00:09:36.890 --> 00:09:39.530 align:middle line:84% approach in these Prussian high schools. 00:09:39.530 --> 00:09:42.320 align:middle line:84% So he ignored his teachers, and got into trouble, 00:09:42.320 --> 00:09:43.700 align:middle line:90% and finally just dropped out. 00:09:43.700 --> 00:09:45.647 align:middle line:84% By all accounts, his principal was just 00:09:45.647 --> 00:09:46.730 align:middle line:90% as happy to see him leave. 00:09:46.730 --> 00:09:48.350 align:middle line:90% No one liked each other. 00:09:48.350 --> 00:09:52.490 align:middle line:84% But he set his mind on entering this elite Federal Institute 00:09:52.490 --> 00:09:56.390 align:middle line:84% of Technology known as the [NON-ENGLISH SPEECH],, or ETH. 00:09:56.390 --> 00:09:59.180 align:middle line:84% That stands for the [NON-ENGLISH SPEECH],, 00:09:59.180 --> 00:10:02.420 align:middle line:84% which is a phrase I never ever tire of trying to pronounce. 00:10:02.420 --> 00:10:03.920 align:middle line:90% We can just call it the ETH. 00:10:03.920 --> 00:10:06.875 align:middle line:84% This was basically like the MIT of Zurich. 00:10:06.875 --> 00:10:08.750 align:middle line:84% Although, that's a bit unfair because the ETH 00:10:08.750 --> 00:10:11.660 align:middle line:84% actually predated the founding of our own MIT. 00:10:11.660 --> 00:10:13.280 align:middle line:84% But it was a place a lot like MIT. 00:10:13.280 --> 00:10:17.930 align:middle line:84% It was a polytechnic institute with a real focus on science 00:10:17.930 --> 00:10:20.030 align:middle line:84% and engineering, including these new areas 00:10:20.030 --> 00:10:21.450 align:middle line:90% like electrical engineering. 00:10:21.450 --> 00:10:25.190 align:middle line:84% His main goal, Einstein's goal, was to-- even though he had no 00:10:25.190 --> 00:10:27.000 align:middle line:84% high school diploma and he dropped out, 00:10:27.000 --> 00:10:30.440 align:middle line:84% he would take the special entrance exam for this one 00:10:30.440 --> 00:10:32.270 align:middle line:84% special place he most wanted to attend, 00:10:32.270 --> 00:10:35.600 align:middle line:84% the ETH or [NON-ENGLISH SPEECH] in Zurich, Switzerland. 00:10:35.600 --> 00:10:37.220 align:middle line:90% And then, he could go in. 00:10:37.220 --> 00:10:38.750 align:middle line:90% Well, he did take the exam. 00:10:38.750 --> 00:10:42.110 align:middle line:84% He failed it because he blew off the subjects 00:10:42.110 --> 00:10:43.610 align:middle line:90% that he didn't care about. 00:10:43.610 --> 00:10:47.330 align:middle line:84% But the examiner for the physics and math sections, a professor 00:10:47.330 --> 00:10:51.650 align:middle line:84% named Weber saw enough promise in Einstein's portions 00:10:51.650 --> 00:10:54.470 align:middle line:84% of the entrance exam, not on humanities, 00:10:54.470 --> 00:10:57.200 align:middle line:84% not on languages, not on history, those he was 00:10:57.200 --> 00:10:58.640 align:middle line:90% quite terrible at this time. 00:10:58.640 --> 00:11:00.380 align:middle line:84% But for the physics and math portions, 00:11:00.380 --> 00:11:04.215 align:middle line:84% he showed enough promise that he pulled young Einstein aside 00:11:04.215 --> 00:11:05.090 align:middle line:90% and said, you failed. 00:11:05.090 --> 00:11:07.380 align:middle line:84% You cannot come to the ETH right now. 00:11:07.380 --> 00:11:10.700 align:middle line:84% But if you go to a local school, effectively a local community 00:11:10.700 --> 00:11:13.380 align:middle line:84% college, a cantonal regional kind 00:11:13.380 --> 00:11:15.720 align:middle line:84% of community college nearby in Switzerland, 00:11:15.720 --> 00:11:19.020 align:middle line:84% go there for a year, work with some new teachers, 00:11:19.020 --> 00:11:20.460 align:middle line:90% take our entrance exam again. 00:11:20.460 --> 00:11:21.418 align:middle line:90% And that's what he did. 00:11:21.418 --> 00:11:24.600 align:middle line:84% So he was admitted to his dream school the second time around 00:11:24.600 --> 00:11:30.210 align:middle line:84% and began studying in Zurich in the very late 1800s. 00:11:30.210 --> 00:11:31.813 align:middle line:84% Once he worked so hard to get in, 00:11:31.813 --> 00:11:33.480 align:middle line:84% including this extra year of just trying 00:11:33.480 --> 00:11:35.250 align:middle line:84% to take their entrance exam, he then 00:11:35.250 --> 00:11:37.470 align:middle line:84% proceeded to cut classes and read on his own. 00:11:37.470 --> 00:11:38.400 align:middle line:90% This guy was-- 00:11:38.400 --> 00:11:39.630 align:middle line:90% I mean, he was no Einstein. 00:11:39.630 --> 00:11:42.160 align:middle line:84% He really just kept doing these stupid, stupid things. 00:11:42.160 --> 00:11:45.420 align:middle line:84% So even after working so hard to get into his dream university, 00:11:45.420 --> 00:11:47.850 align:middle line:84% he basically cut his classes, or at least many of them, 00:11:47.850 --> 00:11:50.550 align:middle line:84% any of the ones that he thought were not worth his time 00:11:50.550 --> 00:11:52.740 align:middle line:84% or for which he didn't really like the professors. 00:11:52.740 --> 00:11:55.050 align:middle line:84% So he would read on his own the latest stuff, 00:11:55.050 --> 00:11:58.380 align:middle line:84% was still pretty new stuff, like Maxwell's treatise 00:11:58.380 --> 00:12:00.300 align:middle line:84% on electricity magnetism, like some 00:12:00.300 --> 00:12:02.940 align:middle line:84% of the very exciting work on statistical mechanics 00:12:02.940 --> 00:12:04.710 align:middle line:84% and the behavior of gases by people 00:12:04.710 --> 00:12:06.600 align:middle line:84% like Ludwig Boltzmann and others, 00:12:06.600 --> 00:12:09.210 align:middle line:90% he would read on his own. 00:12:09.210 --> 00:12:12.270 align:middle line:84% Now for some reason, after cutting classes and letting his 00:12:12.270 --> 00:12:14.220 align:middle line:84% professors know how little he respected them-- 00:12:14.220 --> 00:12:16.980 align:middle line:84% he was not shy, much like when he was in high school-- 00:12:16.980 --> 00:12:19.110 align:middle line:84% for some reason, he couldn't get any good letters 00:12:19.110 --> 00:12:20.660 align:middle line:84% of recommendation upon graduating. 00:12:20.660 --> 00:12:23.320 align:middle line:84% This class is really full of good lessons for today. 00:12:23.320 --> 00:12:24.570 align:middle line:90% So don't do the following. 00:12:24.570 --> 00:12:26.430 align:middle line:84% Don't annoy all of your professors 00:12:26.430 --> 00:12:28.800 align:middle line:84% so much that they all refuse to write 00:12:28.800 --> 00:12:30.360 align:middle line:90% you a strong recommendation. 00:12:30.360 --> 00:12:34.183 align:middle line:84% So basically, Einstein had a middling, fairly mediocre grade 00:12:34.183 --> 00:12:36.600 align:middle line:84% point average because he kept cutting classes and ignoring 00:12:36.600 --> 00:12:38.190 align:middle line:84% stuff that wasn't interesting to him. 00:12:38.190 --> 00:12:41.130 align:middle line:84% He was rude to the majority of his professors 00:12:41.130 --> 00:12:43.740 align:middle line:84% and, for some reason, couldn't get a job upon graduating. 00:12:43.740 --> 00:12:45.198 align:middle line:84% He really couldn't figure this out. 00:12:45.198 --> 00:12:48.700 align:middle line:84% The guy was kind of dumb for an Einstein in these young years. 00:12:48.700 --> 00:12:51.930 align:middle line:84% So what happened was, really in desperation, with help 00:12:51.930 --> 00:12:54.330 align:middle line:84% from the father of one of his very close college 00:12:54.330 --> 00:12:57.000 align:middle line:84% friends, the father of Marcel Grossmann, 00:12:57.000 --> 00:13:00.690 align:middle line:84% he was able to land an entry-level civil service 00:13:00.690 --> 00:13:04.030 align:middle line:84% job in Bern, Switzerland, working in the local patent 00:13:04.030 --> 00:13:04.530 align:middle line:90% office. 00:13:04.530 --> 00:13:07.680 align:middle line:84% He was hired as a patent officer, third class. 00:13:07.680 --> 00:13:09.060 align:middle line:90% There was no fourth class. 00:13:09.060 --> 00:13:12.300 align:middle line:84% That was really the entry-level position 00:13:12.300 --> 00:13:14.970 align:middle line:84% since he had a degree from a leading technical institute 00:13:14.970 --> 00:13:17.040 align:middle line:84% but was not otherwise highly recommended. 00:13:17.040 --> 00:13:19.890 align:middle line:84% So even for young Einstein, it wasn't what he knew 00:13:19.890 --> 00:13:20.700 align:middle line:90% but who he knew. 00:13:20.700 --> 00:13:25.450 align:middle line:84% He had to depend on his friends for help on the job market. 00:13:25.450 --> 00:13:28.330 align:middle line:84% We also know quite well what happened next. 00:13:28.330 --> 00:13:31.650 align:middle line:84% He fell in with some friends who were all around the same age, 00:13:31.650 --> 00:13:35.430 align:middle line:84% all recent university graduates, who were all living in Bern. 00:13:35.430 --> 00:13:38.220 align:middle line:84% And they all had an interest in science. 00:13:38.220 --> 00:13:42.450 align:middle line:84% This included a young Maurice Solovine, Conrad Habicht, 00:13:42.450 --> 00:13:45.060 align:middle line:84% and then recent graduate Albert Einstein. 00:13:45.060 --> 00:13:48.150 align:middle line:84% They gave themselves the name the Olympia Academy 00:13:48.150 --> 00:13:49.650 align:middle line:90% because they were having fun. 00:13:49.650 --> 00:13:55.120 align:middle line:84% That sounds like a triumphant, very prestigious academy, 00:13:55.120 --> 00:13:57.510 align:middle line:84% like Mount Olympus like the Greek legends. 00:13:57.510 --> 00:13:59.460 align:middle line:84% It was actually three recent college graduates 00:13:59.460 --> 00:14:02.580 align:middle line:84% meeting literally in the pub to drink a lot of beer 00:14:02.580 --> 00:14:03.810 align:middle line:90% and talk about philosophy. 00:14:03.810 --> 00:14:06.185 align:middle line:84% But they figured if they gave themselves an exalted name, 00:14:06.185 --> 00:14:07.570 align:middle line:84% it would sound much more serious. 00:14:07.570 --> 00:14:09.060 align:middle line:84% So the Olympia Academy was mostly 00:14:09.060 --> 00:14:11.610 align:middle line:84% those three folks reading on their own 00:14:11.610 --> 00:14:13.748 align:middle line:90% after hours after work. 00:14:13.748 --> 00:14:16.040 align:middle line:84% Now we even know quite a bit of what they were reading. 00:14:16.040 --> 00:14:18.440 align:middle line:84% They wrote lots of letters to each other in between. 00:14:18.440 --> 00:14:20.130 align:middle line:84% Many of those letters have survived, 00:14:20.130 --> 00:14:22.580 align:middle line:84% so we can reconstruct the kinds of questions 00:14:22.580 --> 00:14:25.160 align:middle line:84% and the kinds of materials of particular books 00:14:25.160 --> 00:14:27.990 align:middle line:84% that the Olympia Academy found really exciting. 00:14:27.990 --> 00:14:30.080 align:middle line:84% One of the authors that they were especially 00:14:30.080 --> 00:14:33.920 align:middle line:84% excited about in the early years around 1900 00:14:33.920 --> 00:14:37.190 align:middle line:84% was the Austrian polymath, Ernst Mach. 00:14:37.190 --> 00:14:39.950 align:middle line:84% Here's an image of the English translation of one 00:14:39.950 --> 00:14:41.330 align:middle line:90% of his very influential books. 00:14:41.330 --> 00:14:44.810 align:middle line:84% Mach was originally Austrian, wrote his own books in German. 00:14:44.810 --> 00:14:47.810 align:middle line:84% Einstein and his friends really just devoured these. 00:14:47.810 --> 00:14:50.360 align:middle line:84% Mach was trained in mathematical physics, 00:14:50.360 --> 00:14:51.830 align:middle line:90% in experimental physics. 00:14:51.830 --> 00:14:54.923 align:middle line:84% We still talk about Mach numbers, 00:14:54.923 --> 00:14:56.090 align:middle line:90% like for the speed of sound. 00:14:56.090 --> 00:14:58.410 align:middle line:84% Mach 1, Mach 2 for jet planes and so on. 00:14:58.410 --> 00:14:59.780 align:middle line:90% That's the same Ernst Mach. 00:14:59.780 --> 00:15:03.202 align:middle line:84% He later held a professorship in surgery and, then finally, 00:15:03.202 --> 00:15:04.910 align:middle line:84% in the history and philosophy of science. 00:15:04.910 --> 00:15:07.170 align:middle line:84% Mach had quite a remarkable career. 00:15:07.170 --> 00:15:09.630 align:middle line:84% So what he did in this series of books, 00:15:09.630 --> 00:15:12.150 align:middle line:84% including the one which in English translations known 00:15:12.150 --> 00:15:14.340 align:middle line:84% as a science of mechanics, which we know Einstein 00:15:14.340 --> 00:15:16.950 align:middle line:84% and his friends were really reading carefully, 00:15:16.950 --> 00:15:22.560 align:middle line:84% Mach proposed this scientific philosophy called positivism. 00:15:22.560 --> 00:15:25.800 align:middle line:84% His argument was that only quantities that 00:15:25.800 --> 00:15:30.120 align:middle line:84% could be, in his phrase, become objects of positive experience, 00:15:30.120 --> 00:15:34.110 align:middle line:84% things we could literally touch, and measure, and handle 00:15:34.110 --> 00:15:36.570 align:middle line:84% empirically and quantitatively, only 00:15:36.570 --> 00:15:38.670 align:middle line:84% these objects of positive experience 00:15:38.670 --> 00:15:41.520 align:middle line:84% belonged in any proper scientific theory. 00:15:41.520 --> 00:15:43.440 align:middle line:84% Anything else, Mach argued, would 00:15:43.440 --> 00:15:46.650 align:middle line:84% lead to just confusion and empty metaphysics, which was 00:15:46.650 --> 00:15:49.410 align:middle line:90% his word for bad, bad stuff. 00:15:49.410 --> 00:15:51.722 align:middle line:84% You'll just get yourself confused 00:15:51.722 --> 00:15:54.180 align:middle line:84% arguing about the equivalent of how many angels could dance 00:15:54.180 --> 00:15:57.600 align:middle line:84% on the head of a pin if you're not able to actually subject 00:15:57.600 --> 00:16:02.440 align:middle line:84% those questions to measurement or any kind of empirical input. 00:16:02.440 --> 00:16:04.470 align:middle line:90% That became known as positivism. 00:16:04.470 --> 00:16:07.380 align:middle line:84% And a lot of what Mach did in this particular book, 00:16:07.380 --> 00:16:10.470 align:middle line:84% very thick book, The Science Of Mechanics, was basically 00:16:10.470 --> 00:16:12.960 align:middle line:84% take Isaac Newton's work to task. 00:16:12.960 --> 00:16:15.930 align:middle line:84% So Mach laid out this entire program 00:16:15.930 --> 00:16:18.030 align:middle line:84% to basically say that Newtonian physics, 00:16:18.030 --> 00:16:21.090 align:middle line:84% as successful as it was in celestial mechanics 00:16:21.090 --> 00:16:24.090 align:middle line:84% and all kinds of applications, it was riddled, 00:16:24.090 --> 00:16:29.040 align:middle line:84% charged Ernst Mach, with these empty notions that could never 00:16:29.040 --> 00:16:32.640 align:middle line:84% be subject to careful empirical measurement, things 00:16:32.640 --> 00:16:34.800 align:middle line:84% like absolute space and absolute time. 00:16:34.800 --> 00:16:38.040 align:middle line:84% So Mach says no matter the successes of Newton's physics, 00:16:38.040 --> 00:16:39.870 align:middle line:84% it's riddled with these problems. 00:16:39.870 --> 00:16:43.950 align:middle line:84% We should get rid of all these empty metaphysical notions 00:16:43.950 --> 00:16:46.620 align:middle line:84% like absolute space and absolute time. 00:16:46.620 --> 00:16:49.530 align:middle line:84% The Olympia Academy just ate this stuff up. 00:16:49.530 --> 00:16:53.340 align:middle line:84% So Einstein, we know from contemporaneous letters 00:16:53.340 --> 00:16:56.370 align:middle line:84% and notes and so on, was very directly inspired 00:16:56.370 --> 00:17:00.360 align:middle line:84% by Ernst Mach, and he pursued this critical reevaluation, 00:17:00.360 --> 00:17:03.840 align:middle line:84% deciding that we should begin with kinematics before even 00:17:03.840 --> 00:17:05.040 align:middle line:90% worrying about dynamics. 00:17:05.040 --> 00:17:08.260 align:middle line:84% Remember, kinematics is the study of bodies in motion 00:17:08.260 --> 00:17:09.760 align:middle line:84% through space and time, things that, 00:17:09.760 --> 00:17:12.460 align:middle line:84% at least in principle, could be subject to observation 00:17:12.460 --> 00:17:13.300 align:middle line:90% and measurement. 00:17:13.300 --> 00:17:17.190 align:middle line:84% So we better get that straight with this new critical edge 00:17:17.190 --> 00:17:19.440 align:middle line:84% granted by Ernst Mach before we even 00:17:19.440 --> 00:17:21.960 align:middle line:84% worry about things like the interplay of forces 00:17:21.960 --> 00:17:24.609 align:middle line:90% or the study of dynamics. 00:17:24.609 --> 00:17:27.030 align:middle line:84% So while he's working at the patent office, 00:17:27.030 --> 00:17:30.060 align:middle line:84% he's still a patent officer third class meeting 00:17:30.060 --> 00:17:32.070 align:middle line:84% after hours with the Olympia Academy, 00:17:32.070 --> 00:17:35.658 align:middle line:84% increasing neglecting his first wife and his young child, 00:17:35.658 --> 00:17:37.950 align:middle line:84% basically blowing them off to go drink with his friends 00:17:37.950 --> 00:17:39.120 align:middle line:90% and talk about philosophy. 00:17:39.120 --> 00:17:43.350 align:middle line:84% In the space of that time, he submitted several papers 00:17:43.350 --> 00:17:45.270 align:middle line:84% to the leading journal of physics, 00:17:45.270 --> 00:17:47.670 align:middle line:84% really, in certainly in Europe or North 00:17:47.670 --> 00:17:50.400 align:middle line:84% America at the time, the Annalen der Physik, at this point, 00:17:50.400 --> 00:17:53.100 align:middle line:84% it was edited by Max Planck, someone whose work we'll come 00:17:53.100 --> 00:17:55.200 align:middle line:90% to pretty soon in this class. 00:17:55.200 --> 00:17:59.070 align:middle line:84% In 1905, Einstein had what is often called his miracle year, 00:17:59.070 --> 00:18:01.200 align:middle line:90% or his annus mirabilis in Latin. 00:18:01.200 --> 00:18:03.370 align:middle line:84% It turns out it actually wasn't even a whole year. 00:18:03.370 --> 00:18:05.160 align:middle line:84% It was like a miracle two seasons. 00:18:05.160 --> 00:18:07.980 align:middle line:84% He needed less than six months to introduce 00:18:07.980 --> 00:18:09.760 align:middle line:90% this entire body of work. 00:18:09.760 --> 00:18:11.340 align:middle line:84% So here, I'm showing just the dates 00:18:11.340 --> 00:18:13.830 align:middle line:84% at which these separate articles were received 00:18:13.830 --> 00:18:16.770 align:middle line:84% at the journal, separate submissions that were clocked 00:18:16.770 --> 00:18:18.600 align:middle line:90% in at the Annalen der Physik. 00:18:18.600 --> 00:18:20.220 align:middle line:84% And for now, what we're going to do 00:18:20.220 --> 00:18:22.950 align:middle line:84% is focus on this third in his series, 00:18:22.950 --> 00:18:26.260 align:middle line:84% which again, today, we refer to about 00:18:26.260 --> 00:18:28.660 align:middle line:84% by calling it the special theory of relativity. 00:18:28.660 --> 00:18:31.990 align:middle line:84% The actual article, the first page of which is shown here, 00:18:31.990 --> 00:18:34.360 align:middle line:84% is entitled, "On the Electrodynamics 00:18:34.360 --> 00:18:38.170 align:middle line:84% of Moving Bodies," a title, a phrase that, by now, sounded 00:18:38.170 --> 00:18:41.060 align:middle line:84% conventional to us thanks to the last few lectures, 00:18:41.060 --> 00:18:43.690 align:middle line:84% but especially to Einstein's readers back in the day, 00:18:43.690 --> 00:18:46.630 align:middle line:84% that was exactly the topic which leading figures 00:18:46.630 --> 00:18:49.600 align:middle line:84% like Hendrik Lorentz, and George FitzGerald, and Michelson 00:18:49.600 --> 00:18:52.170 align:middle line:84% and Morley, and many, many of their colleagues, that's 00:18:52.170 --> 00:18:53.920 align:middle line:84% what they cared about and what they agreed 00:18:53.920 --> 00:18:56.350 align:middle line:84% was front and center for cutting-edge physics. 00:18:56.350 --> 00:18:59.050 align:middle line:84% So Einstein's paper on the electrodynamics 00:18:59.050 --> 00:19:02.290 align:middle line:84% of moving bodies has a conventional or recognizable 00:19:02.290 --> 00:19:03.260 align:middle line:90% title. 00:19:03.260 --> 00:19:05.770 align:middle line:84% And yet, as we'll talk about through much of today's class, 00:19:05.770 --> 00:19:08.440 align:middle line:84% the rest of his approach to that conventional topic 00:19:08.440 --> 00:19:10.090 align:middle line:90% was anything but conventional. 00:19:10.090 --> 00:19:11.950 align:middle line:90% It's quite unusual. 00:19:11.950 --> 00:19:15.250 align:middle line:84% It didn't help his colleagues that the only real indication 00:19:15.250 --> 00:19:17.200 align:middle line:84% of where these unusual ideas came from 00:19:17.200 --> 00:19:20.350 align:middle line:84% was in the acknowledgments, where he says, in conclusion, 00:19:20.350 --> 00:19:24.580 align:middle line:84% let me note that my friend and colleague Michelangelo Besso 00:19:24.580 --> 00:19:26.230 align:middle line:84% steadfastly stood by me in my work 00:19:26.230 --> 00:19:27.480 align:middle line:90% on the problem discussed here. 00:19:27.480 --> 00:19:29.688 align:middle line:84% I'm indebted to him for several valuable suggestions. 00:19:29.688 --> 00:19:32.240 align:middle line:84% That didn't help clarify because Besso was equally unknown. 00:19:32.240 --> 00:19:33.490 align:middle line:84% He was another, basically, college friend 00:19:33.490 --> 00:19:35.500 align:middle line:84% of Einstein's, another occasional member 00:19:35.500 --> 00:19:36.790 align:middle line:90% of that Olympia Academy. 00:19:36.790 --> 00:19:39.880 align:middle line:84% So one totally unknown person is thanking another basically 00:19:39.880 --> 00:19:41.830 align:middle line:84% unknown person, and otherwise his paper 00:19:41.830 --> 00:19:44.470 align:middle line:90% appears like it's from Mars. 00:19:44.470 --> 00:19:46.690 align:middle line:84% Let me pause there, ask if there are any questions 00:19:46.690 --> 00:19:48.070 align:middle line:90% on that first part. 00:19:48.070 --> 00:19:49.180 align:middle line:90% Any questions so far? 00:19:49.180 --> 00:19:53.850 align:middle line:90% 00:19:53.850 --> 00:19:56.505 align:middle line:84% Yeah, so in the paper itself, what I 00:19:56.505 --> 00:19:58.380 align:middle line:84% showed you just now on screen is the entirety 00:19:58.380 --> 00:19:59.338 align:middle line:90% of the acknowledgments. 00:19:59.338 --> 00:20:01.110 align:middle line:90% He only thanked Besso by name. 00:20:01.110 --> 00:20:03.447 align:middle line:84% And for some of the specific points in that paper, 00:20:03.447 --> 00:20:06.030 align:middle line:84% it does seem, from other letters that have survived and so on, 00:20:06.030 --> 00:20:09.060 align:middle line:84% that he discussed these things especially closely with Besso. 00:20:09.060 --> 00:20:11.790 align:middle line:84% He did not thank his then-wife Mileva Maric. 00:20:11.790 --> 00:20:12.870 align:middle line:90% We can talk about that. 00:20:12.870 --> 00:20:15.630 align:middle line:84% They had talked about some of the ideas some years earlier. 00:20:15.630 --> 00:20:18.300 align:middle line:84% It's a continuing point of historical interest 00:20:18.300 --> 00:20:21.990 align:middle line:84% how much Mileva had talked about these specific ideas closer 00:20:21.990 --> 00:20:22.860 align:middle line:90% to 1905. 00:20:22.860 --> 00:20:29.685 align:middle line:84% It looks like not so much, partly because she was working 00:20:29.685 --> 00:20:32.427 align:middle line:84% in her new motherhood role in a very-- what 00:20:32.427 --> 00:20:34.260 align:middle line:84% was by then a very traditional gendered role 00:20:34.260 --> 00:20:36.760 align:middle line:84% and not able to really keep up with her own physics and math 00:20:36.760 --> 00:20:37.470 align:middle line:90% studies. 00:20:37.470 --> 00:20:40.350 align:middle line:84% So he was not thanking Mileva in the paper. 00:20:40.350 --> 00:20:43.710 align:middle line:84% He did not thank by name, either, Konrad Habicht 00:20:43.710 --> 00:20:46.210 align:middle line:84% or Maurice Solovine, although he was writing with them. 00:20:46.210 --> 00:20:48.385 align:middle line:84% In fact, he was talking with them in the letters 00:20:48.385 --> 00:20:50.760 align:middle line:84% more about some of those other papers that year, at least 00:20:50.760 --> 00:20:52.260 align:middle line:84% from the letters that have survived. 00:20:52.260 --> 00:20:54.520 align:middle line:84% In the actual printed paper the only person 00:20:54.520 --> 00:20:57.400 align:middle line:84% he thanks is this, again, largely unknown figure, 00:20:57.400 --> 00:20:58.360 align:middle line:90% Michele Besso 00:20:58.360 --> 00:21:01.300 align:middle line:84% He also, as you've seen even in the excerpt that 00:21:01.300 --> 00:21:03.280 align:middle line:84% is in the reader for today, he cites 00:21:03.280 --> 00:21:05.900 align:middle line:90% almost no other literature. 00:21:05.900 --> 00:21:07.570 align:middle line:84% So we do know from some of the reading 00:21:07.570 --> 00:21:09.640 align:middle line:84% notes that have survived they were actually 00:21:09.640 --> 00:21:12.250 align:middle line:84% quite interested in work by people like Maxwell 00:21:12.250 --> 00:21:16.270 align:middle line:84% but also more recent work by people like Hendrik Lorentz. 00:21:16.270 --> 00:21:19.450 align:middle line:84% But he doesn't even cite Lorentz's work in the paper, 00:21:19.450 --> 00:21:20.830 align:middle line:90% very, very sparingly anyway. 00:21:20.830 --> 00:21:22.978 align:middle line:84% So he's being very, very, we could 00:21:22.978 --> 00:21:25.270 align:middle line:84% say selective, which is a nice way of saying he's being 00:21:25.270 --> 00:21:26.740 align:middle line:90% kind of a jerk, frankly-- 00:21:26.740 --> 00:21:29.562 align:middle line:84% being incomplete, at least, in not citing his sources. 00:21:29.562 --> 00:21:31.270 align:middle line:84% If he submitted that paper for our class, 00:21:31.270 --> 00:21:32.290 align:middle line:90% he would not get a good grade. 00:21:32.290 --> 00:21:33.498 align:middle line:90% You should cite your sources. 00:21:33.498 --> 00:21:35.500 align:middle line:84% That's a little reminder for everyone. 00:21:35.500 --> 00:21:37.600 align:middle line:84% So in the actual published version, 00:21:37.600 --> 00:21:40.390 align:middle line:84% he was not sharing the love very broadly. 00:21:40.390 --> 00:21:42.280 align:middle line:84% It was very, very limited acknowledgment 00:21:42.280 --> 00:21:44.090 align:middle line:90% of where this was coming from. 00:21:44.090 --> 00:21:45.528 align:middle line:90% Any other questions? 00:21:45.528 --> 00:21:48.880 align:middle line:90% 00:21:48.880 --> 00:21:50.430 align:middle line:90% Let's continue on. 00:21:50.430 --> 00:21:52.640 align:middle line:84% Let's see what else we can do now with Einstein 00:21:52.640 --> 00:21:55.700 align:middle line:84% once he actually does then move into the electrodynamics 00:21:55.700 --> 00:21:57.458 align:middle line:90% of moving bodies. 00:21:57.458 --> 00:21:59.000 align:middle line:84% You can see the screen again, I hope? 00:21:59.000 --> 00:22:01.040 align:middle line:90% It's back on for everyone? 00:22:01.040 --> 00:22:01.940 align:middle line:90% OK. 00:22:01.940 --> 00:22:04.640 align:middle line:84% So as you've seen, the very opening paragraph 00:22:04.640 --> 00:22:07.010 align:middle line:84% begins with this puzzling pronouncement, 00:22:07.010 --> 00:22:09.890 align:middle line:84% puzzling at least to readers of the most prestigious physics 00:22:09.890 --> 00:22:13.010 align:middle line:84% journal in, at least, Western Europe and North America 00:22:13.010 --> 00:22:14.210 align:middle line:90% at the time. 00:22:14.210 --> 00:22:17.600 align:middle line:84% He starts out by saying not that there is an error in Maxwell's 00:22:17.600 --> 00:22:18.110 align:middle line:90% equations. 00:22:18.110 --> 00:22:19.790 align:middle line:84% He doesn't say, I found a missing factor 00:22:19.790 --> 00:22:22.220 align:middle line:90% of 2 pi or missing minus sign. 00:22:22.220 --> 00:22:25.640 align:middle line:84% He doesn't say I've conducted new high-precision experiments 00:22:25.640 --> 00:22:29.360 align:middle line:84% and I found a glitch or some empirical anomaly 00:22:29.360 --> 00:22:31.070 align:middle line:84% compared to previous experiments. 00:22:31.070 --> 00:22:33.620 align:middle line:84% He starts out by saying, there's "an asymmetry 00:22:33.620 --> 00:22:38.540 align:middle line:84% in the explanation" that is not present in the phenomena. 00:22:38.540 --> 00:22:40.220 align:middle line:84% That's a pretty astonishing opening. 00:22:40.220 --> 00:22:41.240 align:middle line:90% What is he referring to? 00:22:41.240 --> 00:22:43.430 align:middle line:84% Not some very complicated hard thing 00:22:43.430 --> 00:22:47.120 align:middle line:84% to calculate, he's referring to something 00:22:47.120 --> 00:22:49.995 align:middle line:84% turns out to have been something like a school exercise 00:22:49.995 --> 00:22:52.370 align:middle line:84% that he'd encountered very similar to what he encountered 00:22:52.370 --> 00:22:54.050 align:middle line:84% when he was a University student. 00:22:54.050 --> 00:22:57.200 align:middle line:84% What if we take a simple bar magnet, just a simple north 00:22:57.200 --> 00:23:00.440 align:middle line:84% and south pole, and a simple conducting coil that's 00:23:00.440 --> 00:23:02.330 align:middle line:84% connected to an ammeter we can measure 00:23:02.330 --> 00:23:05.030 align:middle line:84% if any electric current is flowing through that conducting 00:23:05.030 --> 00:23:06.260 align:middle line:90% coil? 00:23:06.260 --> 00:23:08.600 align:middle line:84% What if the bar magnet and the coil 00:23:08.600 --> 00:23:11.820 align:middle line:84% are in some relative motion with respect to each other? 00:23:11.820 --> 00:23:15.440 align:middle line:84% Then, it's a rather simple demonstration to find. 00:23:15.440 --> 00:23:17.450 align:middle line:84% It's actually quite similar to what 00:23:17.450 --> 00:23:21.170 align:middle line:84% Ernst had done in the 1820s and then Faraday soon after-- 00:23:21.170 --> 00:23:24.350 align:middle line:84% that when the magnet and the coil are in relative motion, 00:23:24.350 --> 00:23:27.360 align:middle line:84% a measurable electric current will be induced. 00:23:27.360 --> 00:23:30.350 align:middle line:84% So the phenomenon is, these two things moving with respect 00:23:30.350 --> 00:23:33.410 align:middle line:84% to each other, current begins to flow, where otherwise none 00:23:33.410 --> 00:23:36.150 align:middle line:90% had flown before. 00:23:36.150 --> 00:23:39.380 align:middle line:84% So physicists, Einstein insists, had given two 00:23:39.380 --> 00:23:41.060 align:middle line:84% completely different explanations 00:23:41.060 --> 00:23:44.270 align:middle line:84% for what he argued was only one single physical effect. 00:23:44.270 --> 00:23:46.460 align:middle line:84% The physicists' explanations, to date, 00:23:46.460 --> 00:23:50.100 align:middle line:84% had depended entirely on which item was really moving. 00:23:50.100 --> 00:23:53.060 align:middle line:84% So if you imagine there's a state of absolute rest, 00:23:53.060 --> 00:23:56.120 align:middle line:84% then perhaps the bar magnet is really moving, 00:23:56.120 --> 00:23:59.000 align:middle line:84% and the ammeter and the coil are really at rest. 00:23:59.000 --> 00:24:02.070 align:middle line:84% And then, you could analyze the system one way or the inverse. 00:24:02.070 --> 00:24:04.280 align:middle line:84% This is the asymmetry in the explanation 00:24:04.280 --> 00:24:07.010 align:middle line:84% that Einstein says is not present in the phenomenon. 00:24:07.010 --> 00:24:08.130 align:middle line:90% Let's take the first case. 00:24:08.130 --> 00:24:10.400 align:middle line:84% Let's imagine that the magnet is what's moving, 00:24:10.400 --> 00:24:12.320 align:middle line:84% the bar magnet is moving back and forth. 00:24:12.320 --> 00:24:15.530 align:middle line:84% This is the Faraday induction case from 1820-21. 00:24:15.530 --> 00:24:18.170 align:middle line:84% We keep the electric coil perfectly at rest. 00:24:18.170 --> 00:24:20.540 align:middle line:84% Then, using Maxwell's equations, which we can read off 00:24:20.540 --> 00:24:23.450 align:middle line:84% from our t-shirt of which Einstein well 00:24:23.450 --> 00:24:24.860 align:middle line:84% knew by this point, there's going 00:24:24.860 --> 00:24:27.560 align:middle line:84% to be a changing magnetic field in this region of space. 00:24:27.560 --> 00:24:29.810 align:middle line:84% We're shaking, we're moving that magnet back 00:24:29.810 --> 00:24:32.600 align:middle line:84% and forth so, at any given location nearby, 00:24:32.600 --> 00:24:35.580 align:middle line:84% the strength of the magnetic field and even the direction 00:24:35.580 --> 00:24:37.600 align:middle line:84% is a change in quantity over time. 00:24:37.600 --> 00:24:39.630 align:middle line:84% So the variation in time is non-0. 00:24:39.630 --> 00:24:41.520 align:middle line:84% Because we're actively moving the magnet. 00:24:41.520 --> 00:24:45.390 align:middle line:84% From Maxwell's equations, that will induce necessarily 00:24:45.390 --> 00:24:48.330 align:middle line:84% some electric field in that same region of space. 00:24:48.330 --> 00:24:51.720 align:middle line:84% Then, we know that there's an electric field present in, say, 00:24:51.720 --> 00:24:53.100 align:middle line:90% around this area. 00:24:53.100 --> 00:24:55.260 align:middle line:84% The electric field will exert a force 00:24:55.260 --> 00:24:58.050 align:middle line:84% on any little, charged object that's within, for example, 00:24:58.050 --> 00:24:59.250 align:middle line:90% this conducting coil. 00:24:59.250 --> 00:25:01.800 align:middle line:84% It will push the charges along the coil. 00:25:01.800 --> 00:25:03.090 align:middle line:90% It will generate a current. 00:25:03.090 --> 00:25:07.030 align:middle line:84% Electric current was nothing but the motion of electric charges. 00:25:07.030 --> 00:25:10.320 align:middle line:84% So the argument here would have been, we're moving the magnet, 00:25:10.320 --> 00:25:13.140 align:middle line:84% and that makes a time-varying magnetic field 00:25:13.140 --> 00:25:14.332 align:middle line:90% from Maxwell's equations. 00:25:14.332 --> 00:25:16.290 align:middle line:84% And this particular one of Maxwell's equations, 00:25:16.290 --> 00:25:19.350 align:middle line:84% a third one, that induces an electric field, that 00:25:19.350 --> 00:25:21.150 align:middle line:84% exerts a force that pushes charges along. 00:25:21.150 --> 00:25:21.942 align:middle line:90% We measure current. 00:25:21.942 --> 00:25:23.670 align:middle line:90% That's case one. 00:25:23.670 --> 00:25:26.320 align:middle line:84% Einstein goes on to say, what about the inverse? 00:25:26.320 --> 00:25:28.350 align:middle line:84% This is the one that actually Ernst 00:25:28.350 --> 00:25:30.790 align:middle line:90% had first found by accident. 00:25:30.790 --> 00:25:34.350 align:middle line:84% What if the coil is moving but the magnet is at rest? 00:25:34.350 --> 00:25:37.290 align:middle line:84% Well, then, we'd say there's a static magnetic field that 00:25:37.290 --> 00:25:38.820 align:middle line:84% nonetheless varies through space. 00:25:38.820 --> 00:25:42.030 align:middle line:84% Remember those curving field lines, the Faraday field 00:25:42.030 --> 00:25:43.620 align:middle line:90% lines around a bar magnet? 00:25:43.620 --> 00:25:47.190 align:middle line:84% So there's some inhomogeneity in space, even though it's static. 00:25:47.190 --> 00:25:48.550 align:middle line:90% It's stuck in time. 00:25:48.550 --> 00:25:52.440 align:middle line:90% So this spatial curl is non-0. 00:25:52.440 --> 00:25:54.990 align:middle line:84% By Maxwell's fourth equation, that 00:25:54.990 --> 00:25:57.060 align:middle line:84% will induce some electric current nearby. 00:25:57.060 --> 00:26:01.500 align:middle line:84% And then, you have this static electric field 00:26:01.500 --> 00:26:03.780 align:middle line:90% with charges moving around it. 00:26:03.780 --> 00:26:05.700 align:middle line:90% So they have some velocity. 00:26:05.700 --> 00:26:07.710 align:middle line:84% And the cross-product of their velocity 00:26:07.710 --> 00:26:10.080 align:middle line:84% times the magnetic field will induce a force. 00:26:10.080 --> 00:26:12.580 align:middle line:84% That will push the charges along, will induce a current. 00:26:12.580 --> 00:26:14.520 align:middle line:84% So Einstein argues that there's actually 00:26:14.520 --> 00:26:17.940 align:middle line:84% only one phenomenon when the magnet and coil are 00:26:17.940 --> 00:26:18.870 align:middle line:90% in relative motion. 00:26:18.870 --> 00:26:20.940 align:middle line:90% You should measure a current. 00:26:20.940 --> 00:26:22.920 align:middle line:84% And it can't matter, he argues, it 00:26:22.920 --> 00:26:27.300 align:middle line:84% shouldn't matter which one you say is really at rest or not. 00:26:27.300 --> 00:26:29.250 align:middle line:84% Although not citing it, he's borrowing that 00:26:29.250 --> 00:26:31.800 align:middle line:84% from Ernst Mach's critique of Newton. 00:26:31.800 --> 00:26:34.260 align:middle line:84% So you have one phenomenon that had been given two 00:26:34.260 --> 00:26:36.690 align:middle line:84% completely separate explanations, 00:26:36.690 --> 00:26:39.000 align:middle line:84% and he says that's the asymmetry in the explanation. 00:26:39.000 --> 00:26:40.260 align:middle line:84% There should only be one explanation. 00:26:40.260 --> 00:26:41.580 align:middle line:90% There's some relative motion. 00:26:41.580 --> 00:26:44.720 align:middle line:90% Current is induced. 00:26:44.720 --> 00:26:47.170 align:middle line:84% So that's the opening paragraph of this somewhat 00:26:47.170 --> 00:26:48.340 align:middle line:90% strange-looking article. 00:26:48.340 --> 00:26:51.820 align:middle line:84% A little while later, just still on that first opening 00:26:51.820 --> 00:26:56.830 align:middle line:84% two pages, he then introduces two postulates, two axioms 00:26:56.830 --> 00:26:58.060 align:middle line:90% or conjectures. 00:26:58.060 --> 00:26:59.680 align:middle line:90% He doesn't defend them. 00:26:59.680 --> 00:27:00.638 align:middle line:90% He doesn't derive them. 00:27:00.638 --> 00:27:02.638 align:middle line:84% He doesn't say I've tested them in a laboratory, 00:27:02.638 --> 00:27:04.600 align:middle line:84% and they hold up to within experimental error. 00:27:04.600 --> 00:27:08.030 align:middle line:84% He says, as you can see the quotation here on the screen, 00:27:08.030 --> 00:27:10.360 align:middle line:84% we're going to raise this conjecture to a postulate 00:27:10.360 --> 00:27:12.560 align:middle line:84% and, basically, see what follows from it. 00:27:12.560 --> 00:27:15.670 align:middle line:84% The first one is that the laws of physics, 00:27:15.670 --> 00:27:18.310 align:middle line:84% all the laws of physics, must remain valid 00:27:18.310 --> 00:27:23.260 align:middle line:84% in any frame, any state of observation that's 00:27:23.260 --> 00:27:24.550 align:middle line:90% moving at a constant speed. 00:27:24.550 --> 00:27:27.400 align:middle line:84% These would later be called inertial frames of reference, 00:27:27.400 --> 00:27:28.900 align:middle line:90% meaning not accelerating. 00:27:28.900 --> 00:27:30.460 align:middle line:90% It doesn't have to be at rest. 00:27:30.460 --> 00:27:32.740 align:middle line:84% It can be moving at some constant speed, 00:27:32.740 --> 00:27:34.600 align:middle line:84% as long as it doesn't speed up or slow down, 00:27:34.600 --> 00:27:36.190 align:middle line:90% so no acceleration. 00:27:36.190 --> 00:27:40.300 align:middle line:84% Now that's just elevating the well-known relativity 00:27:40.300 --> 00:27:43.940 align:middle line:84% from Galileo, going back to the early 1600s. 00:27:43.940 --> 00:27:46.130 align:middle line:84% What had been called Galilean relativity 00:27:46.130 --> 00:27:48.890 align:middle line:84% applied to the laws of mechanics. 00:27:48.890 --> 00:27:50.840 align:middle line:84% Galileo himself had argued, and Newton 00:27:50.840 --> 00:27:53.090 align:middle line:84% agreed, that the laws of mechanics 00:27:53.090 --> 00:27:55.880 align:middle line:84% should remain valid in any inertial frame of reference. 00:27:55.880 --> 00:27:57.770 align:middle line:84% And all Einstein is doing here, as he says, 00:27:57.770 --> 00:28:00.710 align:middle line:84% he's raising it to a postulate and extend it 00:28:00.710 --> 00:28:04.253 align:middle line:90% to all the laws of physics. 00:28:04.253 --> 00:28:06.170 align:middle line:84% Not just mechanics you see in this first part, 00:28:06.170 --> 00:28:09.290 align:middle line:84% but electromagnetism, optics, even thermodynamics. 00:28:09.290 --> 00:28:12.370 align:middle line:84% That's just an extension of the Galilean relativity. 00:28:12.370 --> 00:28:15.070 align:middle line:84% The second posit, he says, is only 00:28:15.070 --> 00:28:17.860 align:middle line:84% apparently irreconcilable with the first, 00:28:17.860 --> 00:28:20.440 align:middle line:84% is that the speed of light will be constant 00:28:20.440 --> 00:28:23.030 align:middle line:84% independent of the motion of the source. 00:28:23.030 --> 00:28:25.750 align:middle line:84% So any observer, no matter what their state of motion, 00:28:25.750 --> 00:28:28.600 align:middle line:84% as long as they're in some inertial frame of reference, 00:28:28.600 --> 00:28:31.870 align:middle line:84% will always measure light to be moving at the same speed C. 00:28:31.870 --> 00:28:34.420 align:middle line:84% Even if they're barreling down the road in the same direction 00:28:34.420 --> 00:28:36.730 align:middle line:84% as that light wave, they'll measure that light wave 00:28:36.730 --> 00:28:38.800 align:middle line:84% moving away from them at the same speed C 00:28:38.800 --> 00:28:41.560 align:middle line:90% as if they were sitting at rest. 00:28:41.560 --> 00:28:43.060 align:middle line:84% And he says, it's only apparently 00:28:43.060 --> 00:28:44.410 align:middle line:90% irreconcilable with the first. 00:28:44.410 --> 00:28:45.760 align:middle line:90% We'll see that in a moment. 00:28:45.760 --> 00:28:48.473 align:middle line:84% He says, if we adopt these two postulates-- again, 00:28:48.473 --> 00:28:49.390 align:middle line:90% he hasn't proven them. 00:28:49.390 --> 00:28:51.100 align:middle line:84% He hasn't really told us necessarily yet 00:28:51.100 --> 00:28:53.060 align:middle line:90% why we should buy any of this. 00:28:53.060 --> 00:28:55.000 align:middle line:84% But if we adopt those two postulates 00:28:55.000 --> 00:28:58.060 align:middle line:84% to start our argument, then he says, as you see later 00:28:58.060 --> 00:29:01.150 align:middle line:84% in that paragraph, "the luminiferous ether 00:29:01.150 --> 00:29:02.950 align:middle line:90% will prove to be superfluous." 00:29:02.950 --> 00:29:03.770 align:middle line:90% It's amazing. 00:29:03.770 --> 00:29:05.470 align:middle line:90% [GERMAN] is the word in German. 00:29:05.470 --> 00:29:07.900 align:middle line:84% He doesn't say he'll disprove the ether. 00:29:07.900 --> 00:29:09.880 align:middle line:90% He'll say it's just irrelevant. 00:29:09.880 --> 00:29:13.760 align:middle line:84% In one sentence on page two on an article by an unknown patent 00:29:13.760 --> 00:29:15.740 align:middle line:84% clerk, he's basically not just said 00:29:15.740 --> 00:29:18.590 align:middle line:84% that people have misunderstood Maxwell's equations. 00:29:18.590 --> 00:29:21.770 align:middle line:84% People for 100 years have been chasing an object that, 00:29:21.770 --> 00:29:23.930 align:middle line:90% he says, is merely irrelevant. 00:29:23.930 --> 00:29:25.310 align:middle line:84% It is literally a red herring, he 00:29:25.310 --> 00:29:27.860 align:middle line:84% argues, that it would be merely superfluous. 00:29:27.860 --> 00:29:30.650 align:middle line:84% That is quite a strong opening to this paper. 00:29:30.650 --> 00:29:33.470 align:middle line:84% Now, why did Einstein introduce that second postulate, 00:29:33.470 --> 00:29:35.960 align:middle line:84% the one about the constancy of the speed of light 00:29:35.960 --> 00:29:37.610 align:middle line:90% for any inertial observer? 00:29:37.610 --> 00:29:41.300 align:middle line:84% Again, he doesn't tell us why in this paper itself. 00:29:41.300 --> 00:29:45.410 align:middle line:84% In the intervening more than 100 years, 00:29:45.410 --> 00:29:48.260 align:middle line:84% other scholars have been able to fill in some of those pieces 00:29:48.260 --> 00:29:51.980 align:middle line:84% based on, at the time, in unpublished notes, 00:29:51.980 --> 00:29:54.600 align:middle line:84% and correspondence, and reminiscences, and so on. 00:29:54.600 --> 00:29:56.450 align:middle line:84% So we now have a pretty good understanding 00:29:56.450 --> 00:29:59.000 align:middle line:84% of what led Einstein to that strange-sounding second 00:29:59.000 --> 00:29:59.780 align:middle line:90% postulate. 00:29:59.780 --> 00:30:02.090 align:middle line:84% And, in fact, it goes back to a thought experiment 00:30:02.090 --> 00:30:06.080 align:middle line:84% he'd had as a high school dropout at age 16. 00:30:06.080 --> 00:30:08.360 align:middle line:84% One of the things that literally kept him up at night 00:30:08.360 --> 00:30:11.690 align:middle line:84% was, what would happen if you could catch up to a light wave? 00:30:11.690 --> 00:30:13.970 align:middle line:84% So imagine being like a surfer here, 00:30:13.970 --> 00:30:16.460 align:middle line:90% riding a long wave on the ocean. 00:30:16.460 --> 00:30:18.800 align:middle line:84% If you're moving with that wave, if you're 00:30:18.800 --> 00:30:22.490 align:middle line:84% surfing at the same speed as that wave and you look up, 00:30:22.490 --> 00:30:25.940 align:middle line:84% you chance to look up and see this wave crest menacingly 00:30:25.940 --> 00:30:28.400 align:middle line:84% over your head, at that moment, the wave 00:30:28.400 --> 00:30:30.470 align:middle line:90% will appear frozen in space. 00:30:30.470 --> 00:30:32.960 align:middle line:84% You're moving at the same speed as the ocean wave, 00:30:32.960 --> 00:30:35.780 align:middle line:84% so you and the wave move together toward the shore. 00:30:35.780 --> 00:30:39.290 align:middle line:84% And it looks like you have a static wave configuration. 00:30:39.290 --> 00:30:41.900 align:middle line:84% The wave has a crest here, a trough there, 00:30:41.900 --> 00:30:42.920 align:middle line:90% and they're moving-- 00:30:42.920 --> 00:30:47.630 align:middle line:84% they're not changing as you move together toward the shore. 00:30:47.630 --> 00:30:50.000 align:middle line:84% Now, Einstein argued that should never 00:30:50.000 --> 00:30:52.160 align:middle line:84% be able to happen for a light wave. 00:30:52.160 --> 00:30:54.140 align:middle line:90% He first just kind of intuited. 00:30:54.140 --> 00:30:55.850 align:middle line:84% Later, he learned more at university 00:30:55.850 --> 00:30:58.250 align:middle line:84% when he studied a little bit of Maxwell's equations. 00:30:58.250 --> 00:31:01.430 align:middle line:84% He could fill this in a bit more quantitative detail 00:31:01.430 --> 00:31:03.830 align:middle line:84% that, with the power of Maxwell's equations, 00:31:03.830 --> 00:31:07.100 align:middle line:84% if you're in a region of space away from charged matter 00:31:07.100 --> 00:31:08.820 align:middle line:84% with no electric currents flowing-- 00:31:08.820 --> 00:31:11.990 align:middle line:84% so if rho and J both vanish, rho and J, then 00:31:11.990 --> 00:31:16.190 align:middle line:84% there's no way to use these equations, Maxwell's equations, 00:31:16.190 --> 00:31:19.070 align:middle line:84% to construct a static field configuration, where 00:31:19.070 --> 00:31:23.360 align:middle line:84% you have a fixed frozen crest here and trough there. 00:31:23.360 --> 00:31:25.010 align:middle line:84% The electric and magnetic fields just 00:31:25.010 --> 00:31:27.290 align:middle line:84% don't behave that way if you're in a region that 00:31:27.290 --> 00:31:29.640 align:middle line:90% has no immediate sources. 00:31:29.640 --> 00:31:33.650 align:middle line:84% So then, if you could never see this frozen, static field 00:31:33.650 --> 00:31:38.720 align:middle line:84% configuration with a crest that just stays fixed like that, 00:31:38.720 --> 00:31:41.120 align:middle line:84% then you'd better make sure no one could ever see that. 00:31:41.120 --> 00:31:42.703 align:middle line:84% You better make sure no one could ever 00:31:42.703 --> 00:31:45.920 align:middle line:84% do like the surfer does and ride at the same speed 00:31:45.920 --> 00:31:47.060 align:middle line:90% as that light wave. 00:31:47.060 --> 00:31:50.300 align:middle line:84% So he's really trying to avoid a reductio ad absurdum. 00:31:50.300 --> 00:31:52.340 align:middle line:84% He's trying to avoid a contradiction. 00:31:52.340 --> 00:31:54.920 align:middle line:84% How do you make sure no one ever would encounter 00:31:54.920 --> 00:31:57.240 align:middle line:84% this frozen field configuration, which he argues, 00:31:57.240 --> 00:31:59.810 align:middle line:84% is not at all consistent with the linear form of Maxwell's 00:31:59.810 --> 00:32:00.740 align:middle line:90% equations? 00:32:00.740 --> 00:32:03.830 align:middle line:84% Make sure no one could ever catch up with a light wave. 00:32:03.830 --> 00:32:06.710 align:middle line:84% If we could never surf at the same speed as a light wave, 00:32:06.710 --> 00:32:09.500 align:middle line:84% we would never see this frozen field configuration 00:32:09.500 --> 00:32:12.650 align:middle line:84% with a height here and a trough there but otherwise static 00:32:12.650 --> 00:32:13.610 align:middle line:90% in time. 00:32:13.610 --> 00:32:15.530 align:middle line:84% If we could never catch up to the light wave, 00:32:15.530 --> 00:32:18.350 align:middle line:84% we'll always see it traveling past us at the speed of light. 00:32:18.350 --> 00:32:19.880 align:middle line:84% That was, at least, the intuition 00:32:19.880 --> 00:32:22.490 align:middle line:84% that he nursed over the course of 10 years 00:32:22.490 --> 00:32:24.845 align:middle line:90% between the age of 16 and 26. 00:32:24.845 --> 00:32:28.830 align:middle line:90% 00:32:28.830 --> 00:32:30.480 align:middle line:84% Thank you, Lucas by way of Julia. 00:32:30.480 --> 00:32:31.480 align:middle line:90% That's a great question. 00:32:31.480 --> 00:32:34.120 align:middle line:84% So I didn't want to spoil this because your first assignment, 00:32:34.120 --> 00:32:36.030 align:middle line:84% as I'm sure you've seen, is to imagine 00:32:36.030 --> 00:32:38.040 align:middle line:84% you're a referee for the journal reporting 00:32:38.040 --> 00:32:40.150 align:middle line:90% to the main editor, Max Planck. 00:32:40.150 --> 00:32:41.400 align:middle line:90% That is still your assignment. 00:32:41.400 --> 00:32:42.483 align:middle line:90% You still have to do that. 00:32:42.483 --> 00:32:46.950 align:middle line:84% However, the real answer as to why this paper was most likely 00:32:46.950 --> 00:32:48.750 align:middle line:84% published, it was almost certainly 00:32:48.750 --> 00:32:50.790 align:middle line:90% never sent out for refereeing. 00:32:50.790 --> 00:32:53.340 align:middle line:84% Our modern idea that every single scientific paper 00:32:53.340 --> 00:32:55.740 align:middle line:84% should be subjected to peer review is quite recent. 00:32:55.740 --> 00:32:59.160 align:middle line:84% In fact, it only gets put in place with real regularity 00:32:59.160 --> 00:33:03.120 align:middle line:84% or standardization in the second half of the 20th century, 00:33:03.120 --> 00:33:05.160 align:middle line:90% well after this time. 00:33:05.160 --> 00:33:06.848 align:middle line:84% What was happening at many journals, 00:33:06.848 --> 00:33:08.640 align:middle line:84% including the Annalen der Physik, including 00:33:08.640 --> 00:33:09.990 align:middle line:84% Physical Review here in the United States 00:33:09.990 --> 00:33:12.000 align:middle line:84% and many other leading journals at the time 00:33:12.000 --> 00:33:14.910 align:middle line:84% was that the first one or two submissions 00:33:14.910 --> 00:33:19.530 align:middle line:84% to a journal from an early author, a new author, those 00:33:19.530 --> 00:33:22.528 align:middle line:84% would often be very carefully scrutinized and reviewed. 00:33:22.528 --> 00:33:24.070 align:middle line:84% They would be subject to peer review. 00:33:24.070 --> 00:33:25.070 align:middle line:90% Peer review had existed. 00:33:25.070 --> 00:33:26.970 align:middle line:84% It just wasn't applied uniformly. 00:33:26.970 --> 00:33:29.980 align:middle line:84% Einstein, it turns out, had published half a dozen or more 00:33:29.980 --> 00:33:32.140 align:middle line:84% articles in this journal before this time 00:33:32.140 --> 00:33:35.260 align:middle line:84% on, frankly, minor topics, minor even 00:33:35.260 --> 00:33:37.090 align:middle line:90% by Einstein's own reckoning. 00:33:37.090 --> 00:33:39.880 align:middle line:84% He had published fairly conventional, perfectly 00:33:39.880 --> 00:33:42.820 align:middle line:84% legitimate scientific articles in this journal 00:33:42.820 --> 00:33:47.170 align:middle line:84% so a few years downstream from that, like most other authors 00:33:47.170 --> 00:33:49.990 align:middle line:84% at the time, his later communications 00:33:49.990 --> 00:33:52.690 align:middle line:84% could be published at the discretion of the editor, 00:33:52.690 --> 00:33:55.330 align:middle line:84% without going through this rigorous refereeing process. 00:33:55.330 --> 00:33:59.860 align:middle line:84% And by all likelihood, Max Planck thought this was 00:33:59.860 --> 00:34:02.500 align:middle line:84% interesting enough-- it was on a timely topic because people 00:34:02.500 --> 00:34:05.080 align:middle line:84% were clearly concerned about the electrodynamics of moving 00:34:05.080 --> 00:34:05.650 align:middle line:90% buddies-- 00:34:05.650 --> 00:34:07.930 align:middle line:84% that it got into the journal without being subjected 00:34:07.930 --> 00:34:10.457 align:middle line:84% to the kind of scrutiny that Einstein's own first articles 00:34:10.457 --> 00:34:12.790 align:middle line:84% would have been or that any new authors would have been. 00:34:12.790 --> 00:34:15.550 align:middle line:84% You should ignore all that when you write your paper one. 00:34:15.550 --> 00:34:17.139 align:middle line:84% Pretend that this paper really is 00:34:17.139 --> 00:34:21.813 align:middle line:84% being subjected to careful and thorough peer review. 00:34:21.813 --> 00:34:23.230 align:middle line:84% The short answer, historically, is 00:34:23.230 --> 00:34:25.750 align:middle line:84% that this wasn't a special favor to Einstein. 00:34:25.750 --> 00:34:29.530 align:middle line:84% The general policy was usually to basically let later articles 00:34:29.530 --> 00:34:32.590 align:middle line:84% by an established contributor get into the journal, 00:34:32.590 --> 00:34:36.608 align:middle line:84% with much more discretion to the editor. 00:34:36.608 --> 00:34:37.400 align:middle line:90% Very good question. 00:34:37.400 --> 00:34:38.567 align:middle line:90% Any other questions on that? 00:34:38.567 --> 00:34:41.400 align:middle line:90% 00:34:41.400 --> 00:34:43.560 align:middle line:84% Yeah, I mean, so he was known enough 00:34:43.560 --> 00:34:45.060 align:middle line:84% by people like Max Planck to say, 00:34:45.060 --> 00:34:48.750 align:middle line:84% let's let this young guy's next article come in. 00:34:48.750 --> 00:34:51.005 align:middle line:90% This wasn't his first work ever. 00:34:51.005 --> 00:34:53.130 align:middle line:84% On the other hand, the other work that he published 00:34:53.130 --> 00:34:56.159 align:middle line:84% was kind of, we might say, workaday. 00:34:56.159 --> 00:34:58.800 align:middle line:84% It was perfectly competent, neither interesting 00:34:58.800 --> 00:35:01.320 align:middle line:84% nor innervated by the standards of the day, even 00:35:01.320 --> 00:35:03.450 align:middle line:84% by Einstein's own-- he was very harsh about even 00:35:03.450 --> 00:35:04.690 align:middle line:90% his own earlier work. 00:35:04.690 --> 00:35:07.660 align:middle line:84% So he had a small early paper trail. 00:35:07.660 --> 00:35:10.020 align:middle line:84% He, in the meantime, had, as I mentioned before, 00:35:10.020 --> 00:35:13.313 align:middle line:84% had annoyed almost all of his superiors, 00:35:13.313 --> 00:35:14.730 align:middle line:84% both at the patent office and when 00:35:14.730 --> 00:35:16.290 align:middle line:90% he was a university student. 00:35:16.290 --> 00:35:18.880 align:middle line:84% And he was, by this point, out of the mainstream. 00:35:18.880 --> 00:35:23.850 align:middle line:84% He was not working in any of the prestigious scientific research 00:35:23.850 --> 00:35:24.570 align:middle line:90% institutes. 00:35:24.570 --> 00:35:26.190 align:middle line:84% He was not being invited to attend 00:35:26.190 --> 00:35:27.600 align:middle line:84% the usual scientific conferences. 00:35:27.600 --> 00:35:29.920 align:middle line:84% He was, by this point, not well known. 00:35:29.920 --> 00:35:32.640 align:middle line:84% He was a person who contributed the occasional article 00:35:32.640 --> 00:35:35.040 align:middle line:84% to an otherwise very busy journal. 00:35:35.040 --> 00:35:39.000 align:middle line:84% And so he had the bare credentials-- 00:35:39.000 --> 00:35:40.890 align:middle line:84% he had not yet, by this point, even finished 00:35:40.890 --> 00:35:42.900 align:middle line:90% his PhD in the early years. 00:35:42.900 --> 00:35:45.990 align:middle line:84% He was a competent recent graduate 00:35:45.990 --> 00:35:48.300 align:middle line:84% from a highly respected technical institute 00:35:48.300 --> 00:35:51.780 align:middle line:84% but was otherwise not considered any great shakes. 00:35:51.780 --> 00:35:53.003 align:middle line:90% It's a good question, Diego. 00:35:53.003 --> 00:35:55.170 align:middle line:84% We'll come back to that actually in the next lecture 00:35:55.170 --> 00:35:58.710 align:middle line:84% on Wednesday, more the reception of Einstein the person, 00:35:58.710 --> 00:36:00.760 align:middle line:90% his career, and also this work. 00:36:00.760 --> 00:36:04.470 align:middle line:84% But the short answer was that it was not standing out. 00:36:04.470 --> 00:36:06.003 align:middle line:84% So I see Jade asked a good question. 00:36:06.003 --> 00:36:08.170 align:middle line:84% How large was the scientific community at this time? 00:36:08.170 --> 00:36:09.450 align:middle line:90% Very good. 00:36:09.450 --> 00:36:12.570 align:middle line:84% So around 1900-- a number of my colleagues 00:36:12.570 --> 00:36:15.540 align:middle line:84% did this famous census some years ago. 00:36:15.540 --> 00:36:18.090 align:middle line:84% In round numbers, there were around 1,000 00:36:18.090 --> 00:36:21.070 align:middle line:84% professional physicists in the world, 00:36:21.070 --> 00:36:22.860 align:middle line:84% not just in Western Europe but including 00:36:22.860 --> 00:36:25.450 align:middle line:84% what could be reconstructed from Japan, from parts of China, 00:36:25.450 --> 00:36:27.450 align:middle line:84% from many, many parts of the world-- from India. 00:36:27.450 --> 00:36:29.430 align:middle line:84% There were basically 1,000 people 00:36:29.430 --> 00:36:31.860 align:middle line:84% whose day job, whose actual profession 00:36:31.860 --> 00:36:35.280 align:middle line:84% was something like working physicist, 1,000. 00:36:35.280 --> 00:36:37.082 align:middle line:84% So Einstein was, whether you count him in 00:36:37.082 --> 00:36:38.790 align:middle line:84% that 1,000 or not, he wasn't really being 00:36:38.790 --> 00:36:41.450 align:middle line:90% paid as a working physicist. 00:36:41.450 --> 00:36:43.390 align:middle line:84% He was one of on the order of 1,000 00:36:43.390 --> 00:36:45.457 align:middle line:84% or a few thousand who might be contributing, 00:36:45.457 --> 00:36:47.290 align:middle line:84% at any given time, to these leading journals 00:36:47.290 --> 00:36:48.100 align:middle line:90% like the Annalen. 00:36:48.100 --> 00:36:50.350 align:middle line:84% So it's not hundreds of thousands, not 00:36:50.350 --> 00:36:51.455 align:middle line:90% a million people. 00:36:51.455 --> 00:36:53.080 align:middle line:84% But it's not like there's only a dozen. 00:36:53.080 --> 00:36:55.810 align:middle line:84% So it really was easy to have a young person get 00:36:55.810 --> 00:36:57.760 align:middle line:84% a few competent articles in a journal 00:36:57.760 --> 00:37:00.040 align:middle line:84% but otherwise not stand out, not really be noticed. 00:37:00.040 --> 00:37:01.957 align:middle line:84% And that really seems to be where Einstein was 00:37:01.957 --> 00:37:03.160 align:middle line:90% in this point in his career. 00:37:03.160 --> 00:37:05.893 align:middle line:90% Excellent question. 00:37:05.893 --> 00:37:06.560 align:middle line:90% Let me press on. 00:37:06.560 --> 00:37:11.330 align:middle line:84% I want to get on to what Einstein does in this paper. 00:37:11.330 --> 00:37:16.040 align:middle line:84% We'll walk through these first few sections of his paper from 00:37:16.040 --> 00:37:16.910 align:middle line:90% 05. 00:37:16.910 --> 00:37:19.400 align:middle line:84% So again, he doesn't tell us he's inspired by Ernst Mach, 00:37:19.400 --> 00:37:20.810 align:middle line:84% though it's quite clear from some 00:37:20.810 --> 00:37:23.720 align:middle line:84% of his other unpublished materials at the time. 00:37:23.720 --> 00:37:26.570 align:middle line:84% He wants to begin by rethinking kinematics, 00:37:26.570 --> 00:37:28.460 align:middle line:84% the motion of objects through space and time, 00:37:28.460 --> 00:37:30.470 align:middle line:90% not start with dynamics. 00:37:30.470 --> 00:37:33.200 align:middle line:84% What can we observe about how these things move? 00:37:33.200 --> 00:37:36.663 align:middle line:84% And so he has these comments like this early, 00:37:36.663 --> 00:37:38.330 align:middle line:84% again, on either page two or page three, 00:37:38.330 --> 00:37:40.080 align:middle line:90% quite early in the article. 00:37:40.080 --> 00:37:43.050 align:middle line:84% "If we wish to describe the motion of a material point, 00:37:43.050 --> 00:37:44.820 align:middle line:84% we give the values of its coordinates 00:37:44.820 --> 00:37:46.080 align:middle line:90% as functions of the time." 00:37:46.080 --> 00:37:49.320 align:middle line:84% This is like-- we expect most high school students would have 00:37:49.320 --> 00:37:55.110 align:middle line:84% encountered how you use coordinates to describe 00:37:55.110 --> 00:37:56.700 align:middle line:90% the motion of objects. 00:37:56.700 --> 00:37:57.600 align:middle line:90% He goes on. 00:37:57.600 --> 00:37:59.310 align:middle line:84% "Now we must bear carefully in mind 00:37:59.310 --> 00:38:01.143 align:middle line:84% that a mathematical description of this kind 00:38:01.143 --> 00:38:03.960 align:middle line:84% has no physical meaning--" that's very mocking-- 00:38:03.960 --> 00:38:05.460 align:middle line:84% "unless we're quite clear as to what 00:38:05.460 --> 00:38:07.140 align:middle line:90% we will understand by time. 00:38:07.140 --> 00:38:10.170 align:middle line:84% We have to take into account that all our judgments in which 00:38:10.170 --> 00:38:12.300 align:middle line:84% time plays a role are always judgments 00:38:12.300 --> 00:38:14.280 align:middle line:90% of simultaneous events. 00:38:14.280 --> 00:38:17.437 align:middle line:84% If, for instance, I say 'That train arrives here at 7 00:38:17.437 --> 00:38:19.020 align:middle line:84% o'clock,' I mean, something like this. 00:38:19.020 --> 00:38:21.930 align:middle line:84% The pointing of a small hand on my watch to 7:00 00:38:21.930 --> 00:38:24.870 align:middle line:84% and the arrival of the train are simultaneous events." 00:38:24.870 --> 00:38:28.028 align:middle line:84% This is in page 2 or 3 of one of the world's leading physics 00:38:28.028 --> 00:38:29.820 align:middle line:84% journals, he's trying to explain how to use 00:38:29.820 --> 00:38:32.430 align:middle line:84% coordinates to describe things like the passage of time. 00:38:32.430 --> 00:38:33.660 align:middle line:90% It's unbelievable. 00:38:33.660 --> 00:38:36.810 align:middle line:84% He was, as you probably noticed, enamored of trains. 00:38:36.810 --> 00:38:38.310 align:middle line:84% Trains come up over and over again 00:38:38.310 --> 00:38:40.470 align:middle line:90% in his examples in this era. 00:38:40.470 --> 00:38:43.790 align:middle line:84% OK, so if there's no absolute time, 00:38:43.790 --> 00:38:45.540 align:middle line:84% if we're going to be forced to think about 00:38:45.540 --> 00:38:48.630 align:middle line:84% what he comes to call the "relativity of simultaneity," 00:38:48.630 --> 00:38:51.503 align:middle line:84% how can we compare the times associated 00:38:51.503 --> 00:38:52.420 align:middle line:90% with different events? 00:38:52.420 --> 00:38:55.680 align:middle line:84% He says, well, we can send light signals because at least 00:38:55.680 --> 00:38:59.160 align:middle line:84% if we by that second postulate that every inertial observer 00:38:59.160 --> 00:39:01.650 align:middle line:84% will agree on the speed at which light travels. 00:39:01.650 --> 00:39:05.580 align:middle line:84% Then, we can use light signals as a universal tool. 00:39:05.580 --> 00:39:08.040 align:middle line:84% So imagine, again, this train scenario. 00:39:08.040 --> 00:39:09.810 align:middle line:90% We have us standing here. 00:39:09.810 --> 00:39:13.260 align:middle line:84% We're at position M on the train platform or the embankment, 00:39:13.260 --> 00:39:18.180 align:middle line:84% watching this train go by at some constant speed. 00:39:18.180 --> 00:39:20.070 align:middle line:84% As far as we're concerned, when we stand here 00:39:20.070 --> 00:39:23.040 align:middle line:84% watching the train go by, there were two assistants of ours, 00:39:23.040 --> 00:39:26.190 align:middle line:84% two partners standing at locations A and B, 00:39:26.190 --> 00:39:28.800 align:middle line:84% and they both had lanterns in their hands. 00:39:28.800 --> 00:39:31.410 align:middle line:84% And the question is, did they turn on their lanterns 00:39:31.410 --> 00:39:32.490 align:middle line:90% simultaneously? 00:39:32.490 --> 00:39:33.900 align:middle line:90% How could we tell? 00:39:33.900 --> 00:39:36.540 align:middle line:84% If we know by prior measurement that we 00:39:36.540 --> 00:39:39.840 align:middle line:84% are equal distance from both A and B, we're standing here, 00:39:39.840 --> 00:39:41.670 align:middle line:84% we've measured out maybe ahead of time 00:39:41.670 --> 00:39:44.860 align:middle line:84% the exact distance between each of our colleagues, 00:39:44.860 --> 00:39:48.180 align:middle line:84% our partners, we're in the middle. 00:39:48.180 --> 00:39:50.550 align:middle line:84% If we receive those light signals at the same time, 00:39:50.550 --> 00:39:53.070 align:middle line:84% if they reach our nose at the same time as the small hand 00:39:53.070 --> 00:39:55.200 align:middle line:84% of our watch clicks to 7:00-- so like that-- 00:39:55.200 --> 00:39:59.100 align:middle line:84% then we must conclude that the emission of that light 00:39:59.100 --> 00:40:00.450 align:middle line:90% happened simultaneously. 00:40:00.450 --> 00:40:04.200 align:middle line:84% The event of A and B turning on their lanterns 00:40:04.200 --> 00:40:06.360 align:middle line:84% must have occurred simultaneously. 00:40:06.360 --> 00:40:09.600 align:middle line:84% Because the light waves traveled the same distance. 00:40:09.600 --> 00:40:12.120 align:middle line:84% The light waves couldn't have sped up or slowed down. 00:40:12.120 --> 00:40:13.518 align:middle line:84% So they arrived at the same time; 00:40:13.518 --> 00:40:15.060 align:middle line:84% they must have left at the same time. 00:40:15.060 --> 00:40:18.170 align:middle line:84% The emissions must have been simultaneous. 00:40:18.170 --> 00:40:21.380 align:middle line:84% What about our colleague who's riding 00:40:21.380 --> 00:40:24.230 align:middle line:84% at the midpoint of the train as the entire train rides 00:40:24.230 --> 00:40:26.810 align:middle line:84% past the train platform or the embankment 00:40:26.810 --> 00:40:28.370 align:middle line:90% at some constant speed? 00:40:28.370 --> 00:40:30.410 align:middle line:84% The person's in the middle of the train, 00:40:30.410 --> 00:40:32.690 align:middle line:84% so she knows she's equidistant from the people who 00:40:32.690 --> 00:40:35.450 align:middle line:84% are at the front of the back of the train at A and B. 00:40:35.450 --> 00:40:37.820 align:middle line:84% She sees them both turn their lanterns on, 00:40:37.820 --> 00:40:42.990 align:middle line:84% but she receives the light signal from person B first. 00:40:42.990 --> 00:40:46.770 align:middle line:84% Now she concludes that A and B did not turn their lanterns 00:40:46.770 --> 00:40:47.760 align:middle line:90% on simultaneously. 00:40:47.760 --> 00:40:49.020 align:middle line:90% How could they have? 00:40:49.020 --> 00:40:51.280 align:middle line:84% She's clearly equidistant between them. 00:40:51.280 --> 00:40:53.640 align:middle line:84% She clearly receives a light from event B 00:40:53.640 --> 00:40:57.420 align:middle line:84% before the light from event A. So clearly, A and B 00:40:57.420 --> 00:41:01.450 align:middle line:84% could not have been emitted simultaneously. 00:41:01.450 --> 00:41:02.888 align:middle line:90% Now, who's correct? 00:41:02.888 --> 00:41:04.680 align:middle line:84% We might stomp our feet and say no, no, no. 00:41:04.680 --> 00:41:05.280 align:middle line:90% You're moving. 00:41:05.280 --> 00:41:06.450 align:middle line:90% It doesn't work for you. 00:41:06.450 --> 00:41:10.590 align:middle line:84% And she will just as stubbornly stomp her own feet 00:41:10.590 --> 00:41:14.410 align:middle line:84% and say, according to Einstein's own postulate number one, 00:41:14.410 --> 00:41:17.400 align:middle line:84% the laws of physics are exactly as legitimate for her 00:41:17.400 --> 00:41:18.840 align:middle line:90% as they are for us. 00:41:18.840 --> 00:41:21.420 align:middle line:84% She's moving in an inertial frame of reference. 00:41:21.420 --> 00:41:23.400 align:middle line:84% She's moving in a constant speed. 00:41:23.400 --> 00:41:25.180 align:middle line:84% All the laws of physics work for her. 00:41:25.180 --> 00:41:27.810 align:middle line:84% She can draw all the same conclusions that we can. 00:41:27.810 --> 00:41:30.180 align:middle line:84% She clearly was at the midpoint of A and B. 00:41:30.180 --> 00:41:33.180 align:middle line:84% She clearly received light flash from B first. 00:41:33.180 --> 00:41:35.220 align:middle line:84% This is what Einstein means by saying, 00:41:35.220 --> 00:41:37.350 align:middle line:84% as he writes in the paper, we can attribute 00:41:37.350 --> 00:41:40.380 align:middle line:84% no absolute meaning to the concept of simultaneity 00:41:40.380 --> 00:41:42.030 align:middle line:84% but rather that two events, which 00:41:42.030 --> 00:41:44.710 align:middle line:84% examined from one coordinate system are simultaneous, 00:41:44.710 --> 00:41:48.100 align:middle line:84% like us on the train platform, can no longer be interpreted 00:41:48.100 --> 00:41:50.170 align:middle line:84% as simultaneous events when examined 00:41:50.170 --> 00:41:52.870 align:middle line:84% from a system which is in motion relative to that system. 00:41:52.870 --> 00:41:54.850 align:middle line:84% Remember, nothing about forces, not about her 00:41:54.850 --> 00:41:56.200 align:middle line:90% being knocked off course. 00:41:56.200 --> 00:41:59.170 align:middle line:84% She's in a perfectly legitimate physical laboratory, 00:41:59.170 --> 00:42:01.180 align:middle line:90% moving at a constant speed. 00:42:01.180 --> 00:42:04.540 align:middle line:84% Her conclusion is exactly as valid, Einstein says, 00:42:04.540 --> 00:42:05.440 align:middle line:90% as ours is. 00:42:05.440 --> 00:42:10.860 align:middle line:84% Therefore, simultaneity is not shared across reference frames. 00:42:10.860 --> 00:42:13.200 align:middle line:84% OK, what do you do with that information? 00:42:13.200 --> 00:42:15.770 align:middle line:90% 00:42:15.770 --> 00:42:19.330 align:middle line:84% This is what begins to lead to some new phenomena, new 00:42:19.330 --> 00:42:21.130 align:middle line:90% at least for Einstein. 00:42:21.130 --> 00:42:23.290 align:middle line:84% How do we measure the length of an object? 00:42:23.290 --> 00:42:27.550 align:middle line:84% Well, as any good Machian philosopher would say, 00:42:27.550 --> 00:42:30.460 align:middle line:84% tell me exactly the empirical procedure to be followed. 00:42:30.460 --> 00:42:31.900 align:middle line:90% Well, here's a good procedure. 00:42:31.900 --> 00:42:35.380 align:middle line:84% At the same time, measure the locations 00:42:35.380 --> 00:42:37.900 align:middle line:84% of the front and back of the object and then subtract. 00:42:37.900 --> 00:42:40.820 align:middle line:84% Take the difference at the same time. 00:42:40.820 --> 00:42:43.900 align:middle line:84% So here's the train at rest in the station platform. 00:42:43.900 --> 00:42:45.880 align:middle line:90% We're on the train-- 00:42:45.880 --> 00:42:46.840 align:middle line:90% on the embankment. 00:42:46.840 --> 00:42:49.000 align:middle line:84% We measure the front of the train, the back of the train, 00:42:49.000 --> 00:42:49.600 align:middle line:90% take the difference. 00:42:49.600 --> 00:42:51.100 align:middle line:84% We measure the length of the train 00:42:51.100 --> 00:42:55.120 align:middle line:84% to be length L. What if we on the platform 00:42:55.120 --> 00:42:57.640 align:middle line:84% measure the length of the moving train as the train 00:42:57.640 --> 00:43:00.760 align:middle line:84% speeds past us at a constant speed V? 00:43:00.760 --> 00:43:04.600 align:middle line:84% Well, at one moment in time, simultaneously, we 00:43:04.600 --> 00:43:07.030 align:middle line:84% measure the positions of the front and back of the train, 00:43:07.030 --> 00:43:08.860 align:middle line:84% and we measure the train to be short. 00:43:08.860 --> 00:43:13.690 align:middle line:84% We measure some length L prime, which is shorter than L. 00:43:13.690 --> 00:43:17.710 align:middle line:84% In fact, we'll see shorter by how much in a moment. 00:43:17.710 --> 00:43:19.780 align:middle line:84% Now, the passenger on the train, our colleague 00:43:19.780 --> 00:43:23.350 align:middle line:84% who's sitting at that midpoint m prime says, no, you messed up. 00:43:23.350 --> 00:43:27.880 align:middle line:84% You got the wrong length because you messed up on simultaneity. 00:43:27.880 --> 00:43:30.460 align:middle line:84% She accuses us, we first measured the location 00:43:30.460 --> 00:43:33.100 align:middle line:84% of the front of the train, waited for the train 00:43:33.100 --> 00:43:35.148 align:middle line:84% to slide by, and later measured the position 00:43:35.148 --> 00:43:36.190 align:middle line:90% of the back of the train. 00:43:36.190 --> 00:43:38.050 align:middle line:84% So, of course, our measurement was shorter 00:43:38.050 --> 00:43:39.280 align:middle line:90% than it should have been. 00:43:39.280 --> 00:43:41.683 align:middle line:84% How does she know that we did them at different times? 00:43:41.683 --> 00:43:44.350 align:middle line:84% Because she asked her friends at the front and back of the train 00:43:44.350 --> 00:43:46.090 align:middle line:90% to release their lanterns. 00:43:46.090 --> 00:43:48.490 align:middle line:84% She clearly got the light signal from B first, 00:43:48.490 --> 00:43:50.680 align:middle line:84% so she knows we measured the front of the train 00:43:50.680 --> 00:43:51.880 align:middle line:90% at one moment. 00:43:51.880 --> 00:43:54.590 align:middle line:84% And at some later time, not simultaneously, we 00:43:54.590 --> 00:43:55.840 align:middle line:90% measure the back of the train. 00:43:55.840 --> 00:43:57.423 align:middle line:84% So, of course, we got the wrong answer 00:43:57.423 --> 00:43:59.620 align:middle line:84% because we messed up the measurement. 00:43:59.620 --> 00:44:02.260 align:middle line:84% With only a little bit more work, 00:44:02.260 --> 00:44:04.870 align:middle line:84% Einstein shows we can find out by how much these two 00:44:04.870 --> 00:44:06.400 align:middle line:90% measurements will disagree. 00:44:06.400 --> 00:44:09.040 align:middle line:84% They disagree by exactly that factor, Gamma, 00:44:09.040 --> 00:44:10.810 align:middle line:84% that we've now seen many, many times, 00:44:10.810 --> 00:44:14.230 align:middle line:84% that 1 over the square root of 1 minus the quantity V over C 00:44:14.230 --> 00:44:15.100 align:middle line:90% squared. 00:44:15.100 --> 00:44:17.780 align:middle line:84% Just by taking into account kinematics, 00:44:17.780 --> 00:44:19.790 align:middle line:84% how do we account for the motion of objects 00:44:19.790 --> 00:44:21.140 align:middle line:90% through space and time? 00:44:21.140 --> 00:44:23.840 align:middle line:84% Nothing about forces, nothing about an ether. 00:44:23.840 --> 00:44:27.140 align:middle line:84% Einstein arrives at exactly the same quantitative form 00:44:27.140 --> 00:44:29.390 align:middle line:84% as the Lorentz contraction because 00:44:29.390 --> 00:44:31.640 align:middle line:84% of our relativity of simultaneity, 00:44:31.640 --> 00:44:35.680 align:middle line:84% not because of forces from the ether. 00:44:35.680 --> 00:44:39.010 align:middle line:84% So just to beat this dead horse, length contraction 00:44:39.010 --> 00:44:41.398 align:middle line:84% have nothing to do with forces or an ether. 00:44:41.398 --> 00:44:42.440 align:middle line:90% It wasn't about dynamics. 00:44:42.440 --> 00:44:45.040 align:middle line:84% It was simply a consequence of kinematics 00:44:45.040 --> 00:44:48.563 align:middle line:84% once we take the time to understand how objects move 00:44:48.563 --> 00:44:50.230 align:middle line:84% through space and time and how we assign 00:44:50.230 --> 00:44:54.840 align:middle line:84% coordinates to that force-free motion. 00:44:54.840 --> 00:44:55.470 align:middle line:90% He goes on. 00:44:55.470 --> 00:44:59.220 align:middle line:84% The next step that he discusses is actually 00:44:59.220 --> 00:45:00.930 align:middle line:84% what comes to be known as time dilation. 00:45:00.930 --> 00:45:04.200 align:middle line:84% How can we measure the duration between two events, the time 00:45:04.200 --> 00:45:05.880 align:middle line:84% duration, how long between how much 00:45:05.880 --> 00:45:07.260 align:middle line:90% time passes between the events? 00:45:07.260 --> 00:45:10.060 align:middle line:84% Well, we can imagine building something called a light clock, 00:45:10.060 --> 00:45:11.040 align:middle line:90% a thought experiment. 00:45:11.040 --> 00:45:13.500 align:middle line:84% Take two mirrors, two reflecting mirrors, 00:45:13.500 --> 00:45:15.113 align:middle line:90% and fix their relative height. 00:45:15.113 --> 00:45:16.530 align:middle line:84% Hold them in position so they have 00:45:16.530 --> 00:45:19.030 align:middle line:90% some height, H, between them. 00:45:19.030 --> 00:45:20.970 align:middle line:84% And we'll tell the tick of a clock 00:45:20.970 --> 00:45:23.850 align:middle line:84% by bouncing a single light wave between them. 00:45:23.850 --> 00:45:27.790 align:middle line:84% That's what sets our reference time between ticks. 00:45:27.790 --> 00:45:29.490 align:middle line:84% And so the time between ticks, when 00:45:29.490 --> 00:45:32.520 align:middle line:84% we're standing at rest with this clock, 00:45:32.520 --> 00:45:35.280 align:middle line:84% is just the height between those mirrors divided by the speed 00:45:35.280 --> 00:45:36.570 align:middle line:90% with which the light-- 00:45:36.570 --> 00:45:38.260 align:middle line:84% speed with which the light will travel. 00:45:38.260 --> 00:45:40.080 align:middle line:84% So we have a fixed-clock rate when 00:45:40.080 --> 00:45:42.510 align:middle line:84% we hold this clock at rest with respect to us. 00:45:42.510 --> 00:45:46.410 align:middle line:84% It's given by the height and the speed of light. 00:45:46.410 --> 00:45:49.860 align:middle line:84% What if our partner has an identical clock as she races 00:45:49.860 --> 00:45:51.810 align:middle line:90% past us on that moving train? 00:45:51.810 --> 00:45:54.750 align:middle line:84% She's now moving on the train at a constant speed, 00:45:54.750 --> 00:45:58.890 align:middle line:84% V. How do we on the train platform 00:45:58.890 --> 00:46:01.680 align:middle line:84% watch the rate of her moving clock? 00:46:01.680 --> 00:46:05.400 align:middle line:84% Well, we see this light wave travel this sawtooth pattern, 00:46:05.400 --> 00:46:06.360 align:middle line:90% right? 00:46:06.360 --> 00:46:08.340 align:middle line:84% It's emitted from the bottom mirror, 00:46:08.340 --> 00:46:10.890 align:middle line:84% the entire assembly drifts to the right 00:46:10.890 --> 00:46:12.660 align:middle line:90% as the whole train moves by. 00:46:12.660 --> 00:46:15.570 align:middle line:84% So by the time that light wave reaches the top mirror, 00:46:15.570 --> 00:46:17.280 align:middle line:90% the entire assembly has moved. 00:46:17.280 --> 00:46:19.890 align:middle line:84% It's moved some distance B. Likewise, 00:46:19.890 --> 00:46:22.290 align:middle line:84% from the top to the bottom, it's moved another distance B 00:46:22.290 --> 00:46:23.200 align:middle line:90% and so on. 00:46:23.200 --> 00:46:26.850 align:middle line:84% So we're watching their light beam in the moving light clock 00:46:26.850 --> 00:46:29.430 align:middle line:84% trace out this sawtooth pattern as opposed 00:46:29.430 --> 00:46:31.050 align:middle line:84% to moving with what, for us, would 00:46:31.050 --> 00:46:32.560 align:middle line:90% look like straight up and down. 00:46:32.560 --> 00:46:34.990 align:middle line:84% So once again, we can use this great invention 00:46:34.990 --> 00:46:36.190 align:middle line:90% of the Pythagorean theorem. 00:46:36.190 --> 00:46:38.110 align:middle line:84% We have a beautiful right triangle. 00:46:38.110 --> 00:46:40.270 align:middle line:84% We can relate the distance traveled 00:46:40.270 --> 00:46:43.870 align:middle line:84% as seen by us of the light beam in the moving clock. 00:46:43.870 --> 00:46:46.720 align:middle line:84% That's this distance capital D. We 00:46:46.720 --> 00:46:48.340 align:middle line:84% can relate the square of that distance 00:46:48.340 --> 00:46:51.370 align:middle line:84% to the sum of squares of the two sides of this right triangle 00:46:51.370 --> 00:46:53.410 align:middle line:90% to the drift distance. 00:46:53.410 --> 00:46:55.030 align:middle line:84% While that light waves in motion, 00:46:55.030 --> 00:46:58.570 align:middle line:84% the entire clock drifts a distance B. Square that length, 00:46:58.570 --> 00:47:02.620 align:middle line:84% plus the square of the height, the height between mirrors, OK? 00:47:02.620 --> 00:47:04.090 align:middle line:84% Well, now, we know, much like when 00:47:04.090 --> 00:47:05.800 align:middle line:84% we talked about the swimmers in the race 00:47:05.800 --> 00:47:08.230 align:middle line:84% last time about the Michelson-Morley experiment, 00:47:08.230 --> 00:47:10.520 align:middle line:84% we can fill in a bit more information. 00:47:10.520 --> 00:47:12.820 align:middle line:84% We know that this distance, capital D, 00:47:12.820 --> 00:47:16.120 align:middle line:84% is the distance at which that light wave traveled-- 00:47:16.120 --> 00:47:18.670 align:middle line:84% that's this one and only constant C-- 00:47:18.670 --> 00:47:20.870 align:middle line:90% times how long it was in motion. 00:47:20.870 --> 00:47:22.840 align:middle line:84% It was in transit from the bottom mirror 00:47:22.840 --> 00:47:25.450 align:middle line:84% to the top mirror, some time, delta T prime. 00:47:25.450 --> 00:47:27.730 align:middle line:84% That's our measurement of the duration 00:47:27.730 --> 00:47:29.620 align:middle line:90% of ticks of the moving clock. 00:47:29.620 --> 00:47:32.120 align:middle line:84% That's our measurement of their clock rate. 00:47:32.120 --> 00:47:37.450 align:middle line:84% So the distance it traveled is its speed times the duration 00:47:37.450 --> 00:47:38.950 align:middle line:90% it's in flight, OK? 00:47:38.950 --> 00:47:41.950 align:middle line:84% Likewise, it's drift distance is the speed 00:47:41.950 --> 00:47:43.780 align:middle line:84% at which the entire assembly is moving, 00:47:43.780 --> 00:47:46.480 align:middle line:84% that's the capital V, times that same duration, 00:47:46.480 --> 00:47:48.760 align:middle line:84% how long between when the light wave is 00:47:48.760 --> 00:47:51.340 align:middle line:84% at the bottom mirror and the top mirror. 00:47:51.340 --> 00:47:53.830 align:middle line:84% And then, we still have h squared on the end. 00:47:53.830 --> 00:47:55.500 align:middle line:90% Sorry, gang. 00:47:55.500 --> 00:47:57.500 align:middle line:84% Well now, we can fill in some other information. 00:47:57.500 --> 00:47:58.880 align:middle line:90% We know what h squared is. 00:47:58.880 --> 00:48:01.730 align:middle line:84% That's just related to our clock rate in our own reference 00:48:01.730 --> 00:48:02.570 align:middle line:90% frame. 00:48:02.570 --> 00:48:06.170 align:middle line:84% H, remember, we can relate to the speed 00:48:06.170 --> 00:48:08.840 align:middle line:84% at which light is traveling times our tick rate 00:48:08.840 --> 00:48:09.980 align:middle line:90% on our clock. 00:48:09.980 --> 00:48:12.530 align:middle line:84% And now, it just takes that same amount of algebra, 00:48:12.530 --> 00:48:14.450 align:middle line:84% just like in the Michelson-Morley experiment, 00:48:14.450 --> 00:48:17.750 align:middle line:84% just like therefore in the lecture notes from last week, 00:48:17.750 --> 00:48:19.760 align:middle line:84% it takes very little work to derive 00:48:19.760 --> 00:48:22.970 align:middle line:84% a relationship between our measurement of the moving 00:48:22.970 --> 00:48:26.900 align:middle line:84% clock's tick rate and our measurement of our own clock's 00:48:26.900 --> 00:48:27.930 align:middle line:90% tick rate. 00:48:27.930 --> 00:48:31.250 align:middle line:84% And in fact, remember that gamma is always larger than 1 00:48:31.250 --> 00:48:33.110 align:middle line:90% if there's any relative speed. 00:48:33.110 --> 00:48:36.860 align:middle line:84% We measure their clock to be running slowly. 00:48:36.860 --> 00:48:39.710 align:middle line:84% The time between ticks on the moving clock 00:48:39.710 --> 00:48:41.597 align:middle line:84% will be slower than the time between ticks 00:48:41.597 --> 00:48:43.430 align:middle line:84% on our own clock that's at rest with respect 00:48:43.430 --> 00:48:46.160 align:middle line:84% to us, not because there's a force, not because 00:48:46.160 --> 00:48:47.720 align:middle line:84% of any resistance from the ether, 00:48:47.720 --> 00:48:51.890 align:middle line:84% but simply because of kinematics. 00:48:51.890 --> 00:48:54.177 align:middle line:84% This last part here will be especially sketchy, 00:48:54.177 --> 00:48:56.385 align:middle line:84% but here's why I invite you to look it up-- optional, 00:48:56.385 --> 00:48:59.550 align:middle line:84% but you're invited to look at the brief lecture 00:48:59.550 --> 00:49:01.620 align:middle line:90% notes on the Canvas site. 00:49:01.620 --> 00:49:04.115 align:middle line:84% A few weeks later, he submits this article, 00:49:04.115 --> 00:49:05.490 align:middle line:84% the one we've been talking about, 00:49:05.490 --> 00:49:07.110 align:middle line:84% the electrodynamics of moving bodies, 00:49:07.110 --> 00:49:11.940 align:middle line:84% he submits to the Annalen der Physik in early June of 1905. 00:49:11.940 --> 00:49:14.520 align:middle line:84% He writes up a three-page follow-up 00:49:14.520 --> 00:49:17.760 align:middle line:84% that's submitted to the journal in September of 1905. 00:49:17.760 --> 00:49:20.130 align:middle line:84% So he basically takes the summer and derives 00:49:20.130 --> 00:49:22.425 align:middle line:84% what is probably his best-known equation ever, which 00:49:22.425 --> 00:49:23.610 align:middle line:90% is E equals mc squared. 00:49:23.610 --> 00:49:26.380 align:middle line:84% The nature of his original derivation goes like this. 00:49:26.380 --> 00:49:29.640 align:middle line:84% And again, the notes fill in some details 00:49:29.640 --> 00:49:32.040 align:middle line:90% of an alternate derivation. 00:49:32.040 --> 00:49:34.830 align:middle line:84% Einstein imagines a box, a sealed box 00:49:34.830 --> 00:49:36.840 align:middle line:84% that's moving at some constant speed, 00:49:36.840 --> 00:49:39.800 align:middle line:84% v, just moving otherwise in isolation 00:49:39.800 --> 00:49:41.860 align:middle line:90% at some constant speed. 00:49:41.860 --> 00:49:44.620 align:middle line:84% In the middle of its journey, two bursts 00:49:44.620 --> 00:49:47.080 align:middle line:84% of radiation of equal amounts but moving 00:49:47.080 --> 00:49:50.500 align:middle line:84% in opposite directions are emitted by that box. 00:49:50.500 --> 00:49:53.110 align:middle line:84% So the box emits a total amount of energy 00:49:53.110 --> 00:49:56.320 align:middle line:84% in the form of light waves and radiation, total energy 00:49:56.320 --> 00:49:59.410 align:middle line:84% E, half the energy carried off in one direction, half 00:49:59.410 --> 00:50:00.320 align:middle line:90% in the other. 00:50:00.320 --> 00:50:03.340 align:middle line:84% Now, because the momentum carried by that radiation 00:50:03.340 --> 00:50:05.410 align:middle line:84% is equal and opposite, he argues it 00:50:05.410 --> 00:50:10.360 align:middle line:84% has no impact on the speed with which the box is moving, right? 00:50:10.360 --> 00:50:12.250 align:middle line:84% The recoil from the emission in one 00:50:12.250 --> 00:50:14.360 align:middle line:84% side is exactly balanced by the recoil 00:50:14.360 --> 00:50:15.860 align:middle line:84% from the emission in the other side. 00:50:15.860 --> 00:50:18.910 align:middle line:84% So the box's motion is unchanged-- 00:50:18.910 --> 00:50:22.360 align:middle line:84% its velocity is unchanged, even as it emits a total energy, E, 00:50:22.360 --> 00:50:24.065 align:middle line:84% in the form of radiation, and then 00:50:24.065 --> 00:50:25.930 align:middle line:84% it just keeps speeding along its way. 00:50:25.930 --> 00:50:28.600 align:middle line:84% Well, Einstein argues-- again, it only takes three pages 00:50:28.600 --> 00:50:29.350 align:middle line:90% of the journal-- 00:50:29.350 --> 00:50:33.070 align:middle line:84% that the kinetic energy of the box must have changed. 00:50:33.070 --> 00:50:35.050 align:middle line:84% We have to conserve total energy. 00:50:35.050 --> 00:50:38.080 align:middle line:84% It has given up on energy E in the form of this radiation, 00:50:38.080 --> 00:50:40.130 align:middle line:90% but its speed hasn't changed. 00:50:40.130 --> 00:50:41.990 align:middle line:90% So what must have changed? 00:50:41.990 --> 00:50:43.250 align:middle line:90% Its mass. 00:50:43.250 --> 00:50:46.130 align:middle line:84% If we imagine starting with the kinetic energy of the box, 00:50:46.130 --> 00:50:49.130 align:middle line:84% one half mv squared, he's convinced himself 00:50:49.130 --> 00:50:51.650 align:middle line:90% that v hasn't changed. 00:50:51.650 --> 00:50:53.810 align:middle line:84% Yet, the kinetic energy of the box 00:50:53.810 --> 00:50:56.367 align:middle line:84% must have been reduced by some amount, E. 00:50:56.367 --> 00:50:57.950 align:middle line:84% The only thing that could have changed 00:50:57.950 --> 00:50:59.990 align:middle line:90% was the mass of the box. 00:50:59.990 --> 00:51:03.800 align:middle line:84% So he argues-- he actually has a brief calculation-- 00:51:03.800 --> 00:51:05.900 align:middle line:84% that some amount of mass of the box 00:51:05.900 --> 00:51:08.660 align:middle line:84% has been converted into the energy carried off 00:51:08.660 --> 00:51:09.500 align:middle line:90% by the radiation. 00:51:09.500 --> 00:51:10.940 align:middle line:90% How much mass? 00:51:10.940 --> 00:51:12.900 align:middle line:90% E divided by C squared. 00:51:12.900 --> 00:51:17.235 align:middle line:84% And in fact, if you do a little more work for arbitrary speeds 00:51:17.235 --> 00:51:19.610 align:middle line:84% v, they're not just small compared to the speed of light. 00:51:19.610 --> 00:51:22.257 align:middle line:84% In fact, the expression is gamma mc squared. 00:51:22.257 --> 00:51:24.590 align:middle line:84% And again, I'll go through that a little bit more detail 00:51:24.590 --> 00:51:25.465 align:middle line:90% in the lecture notes. 00:51:25.465 --> 00:51:27.980 align:middle line:84% The point is this is a kind of three-page afterthought 00:51:27.980 --> 00:51:31.790 align:middle line:84% that he submits to the Annalen der Physik in September of 1905 00:51:31.790 --> 00:51:34.790 align:middle line:84% in the context of his work on the electrodynamics of moving 00:51:34.790 --> 00:51:36.950 align:middle line:84% bodies that he'd submitted in June. 00:51:36.950 --> 00:51:37.790 align:middle line:90% Let me pause there. 00:51:37.790 --> 00:51:40.100 align:middle line:84% Any questions on how Einstein is approaching 00:51:40.100 --> 00:51:43.277 align:middle line:84% this quite familiar question of electrodynamics 00:51:43.277 --> 00:51:43.985 align:middle line:90% of moving bodies? 00:51:43.985 --> 00:51:50.610 align:middle line:90% 00:51:50.610 --> 00:51:54.180 align:middle line:84% I see, DA asks in the chat, did Einstein's earlier papers 00:51:54.180 --> 00:51:55.350 align:middle line:90% have improper citations? 00:51:55.350 --> 00:51:59.428 align:middle line:84% Well, they had-- that's a good question. 00:51:59.428 --> 00:52:01.720 align:middle line:84% I haven't reread his early papers in quite a long time. 00:52:01.720 --> 00:52:04.360 align:middle line:84% He was never overly generous in these years. 00:52:04.360 --> 00:52:05.710 align:middle line:90% He wasn't oversighting. 00:52:05.710 --> 00:52:07.360 align:middle line:84% So that's true, even from his articles 00:52:07.360 --> 00:52:10.300 align:middle line:90% from the very early 1900s. 00:52:10.300 --> 00:52:11.860 align:middle line:84% I don't know that they were quite as 00:52:11.860 --> 00:52:16.927 align:middle line:84% bereft of relevant citations as this 1905 paper was. 00:52:16.927 --> 00:52:18.760 align:middle line:84% And his earlier ones, frankly, were probably 00:52:18.760 --> 00:52:21.460 align:middle line:84% a little more conscientious because it 00:52:21.460 --> 00:52:22.720 align:middle line:90% was his first set of papers. 00:52:22.720 --> 00:52:24.250 align:middle line:84% They were going to be-- he would have assumed 00:52:24.250 --> 00:52:26.542 align:middle line:84% they would have been subjected to more careful scrutiny 00:52:26.542 --> 00:52:27.670 align:middle line:90% and review. 00:52:27.670 --> 00:52:30.100 align:middle line:84% So it wouldn't surprise me if he was a bit more 00:52:30.100 --> 00:52:32.068 align:middle line:90% conscientious in citing work. 00:52:32.068 --> 00:52:33.110 align:middle line:90% But it's a good question. 00:52:33.110 --> 00:52:34.240 align:middle line:90% We can look 'em up. 00:52:34.240 --> 00:52:36.400 align:middle line:84% His papers are now easily available, 00:52:36.400 --> 00:52:39.370 align:middle line:84% thanks to an international team of scholars in something 00:52:39.370 --> 00:52:42.790 align:middle line:84% called the Collected Papers of Albert Einstein. 00:52:42.790 --> 00:52:43.732 align:middle line:90% And so I don't know. 00:52:43.732 --> 00:52:44.690 align:middle line:90% That's a good question. 00:52:44.690 --> 00:52:46.287 align:middle line:90% I have to go back. 00:52:46.287 --> 00:52:48.370 align:middle line:84% How would you describe the advantage of his theory 00:52:48.370 --> 00:52:50.210 align:middle line:84% over the leading theory of the time, Seedler asks. 00:52:50.210 --> 00:52:51.290 align:middle line:84% That's a great question, Seedler. 00:52:51.290 --> 00:52:52.665 align:middle line:84% So I'm going to actually pause on 00:52:52.665 --> 00:52:55.810 align:middle line:84% that because we're going to look a lot at that exact question 00:52:55.810 --> 00:52:57.780 align:middle line:90% in the next lecture. 00:52:57.780 --> 00:52:59.510 align:middle line:84% So it's one thing for us to ask today, do 00:52:59.510 --> 00:53:02.640 align:middle line:84% we think it's better or not as good, and we can vote 00:53:02.640 --> 00:53:05.165 align:middle line:84% and so on, and have our ideas about that. 00:53:05.165 --> 00:53:06.540 align:middle line:84% I think it's a separate question, 00:53:06.540 --> 00:53:08.207 align:middle line:84% but I think it's more like what you're-- 00:53:08.207 --> 00:53:10.790 align:middle line:84% maybe what you're after, how did experts at the time 00:53:10.790 --> 00:53:11.930 align:middle line:90% evaluate this work? 00:53:11.930 --> 00:53:14.010 align:middle line:84% What did they think was novel about it? 00:53:14.010 --> 00:53:14.750 align:middle line:90% Did they care? 00:53:14.750 --> 00:53:17.400 align:middle line:84% Did they consider this an important improvement? 00:53:17.400 --> 00:53:20.000 align:middle line:84% And we'll look at that early reception, 00:53:20.000 --> 00:53:22.640 align:middle line:84% really, for the entire class next round. 00:53:22.640 --> 00:53:25.070 align:middle line:84% Jade asks, why was the mass energy equivalence 00:53:25.070 --> 00:53:26.850 align:middle line:84% included in the paper on electrodynamics 00:53:26.850 --> 00:53:27.558 align:middle line:90% of moving bodies? 00:53:27.558 --> 00:53:28.100 align:middle line:90% Oh, good. 00:53:28.100 --> 00:53:28.940 align:middle line:90% That's a good question, Jade. 00:53:28.940 --> 00:53:31.130 align:middle line:84% So Einstein came at that because he was still 00:53:31.130 --> 00:53:34.400 align:middle line:84% thinking about this motion of radiation, the way 00:53:34.400 --> 00:53:36.890 align:middle line:84% that different observers would handle the question 00:53:36.890 --> 00:53:38.570 align:middle line:90% of the radiation of light. 00:53:38.570 --> 00:53:41.720 align:middle line:84% This was light being emitted from a moving source. 00:53:41.720 --> 00:53:45.680 align:middle line:84% This is us sitting at rest watching a box move past us 00:53:45.680 --> 00:53:48.770 align:middle line:84% at some constant speed, emitting light. 00:53:48.770 --> 00:53:52.100 align:middle line:84% In the rubric of the day, that was 00:53:52.100 --> 00:53:54.320 align:middle line:84% an example of the electrodynamics of moving 00:53:54.320 --> 00:53:56.960 align:middle line:84% bodies, the emission of electromagnetic radiation, 00:53:56.960 --> 00:53:59.880 align:middle line:84% as seen from a reference frame different from our own. 00:53:59.880 --> 00:54:02.330 align:middle line:84% So in that sense, it fit within the rubric. 00:54:02.330 --> 00:54:04.670 align:middle line:84% Einstein then made use of some particular relations 00:54:04.670 --> 00:54:06.470 align:middle line:84% he had derived in his longer paper 00:54:06.470 --> 00:54:08.150 align:middle line:84% on the electrodynamics of moving bodies. 00:54:08.150 --> 00:54:09.800 align:middle line:84% But for Einstein, at first, it really 00:54:09.800 --> 00:54:13.550 align:middle line:84% came from thinking about how different observers, observers 00:54:13.550 --> 00:54:17.630 align:middle line:84% in different states of motion, characterized this radiation 00:54:17.630 --> 00:54:20.270 align:middle line:84% from a source that was either moving with respect to them 00:54:20.270 --> 00:54:21.020 align:middle line:90% or not. 00:54:21.020 --> 00:54:23.630 align:middle line:84% He later comes to argue this is actually quite general. 00:54:23.630 --> 00:54:25.610 align:middle line:84% It's not restricted to light waves or radiation 00:54:25.610 --> 00:54:28.100 align:middle line:84% at all, or really even about electrodynamics. 00:54:28.100 --> 00:54:32.600 align:middle line:84% He comes to see this in a very, very general relation. 00:54:32.600 --> 00:54:35.180 align:middle line:84% But he comes to it, originally, from very directly 00:54:35.180 --> 00:54:37.700 align:middle line:84% from his work on electrodynamics of moving bodies. 00:54:37.700 --> 00:54:39.070 align:middle line:90% Good question. 00:54:39.070 --> 00:54:40.440 align:middle line:90% Any other questions on that? 00:54:40.440 --> 00:54:42.450 align:middle line:84% Now, we can turn to the last part for today. 00:54:42.450 --> 00:54:45.660 align:middle line:90% 00:54:45.660 --> 00:54:48.920 align:middle line:84% So let's talk about Einstein, and experiment, and something 00:54:48.920 --> 00:54:51.420 align:middle line:90% like engineering practice. 00:54:51.420 --> 00:54:55.290 align:middle line:84% For a long, long time, really from early in the 20th century 00:54:55.290 --> 00:54:57.930 align:middle line:84% once Einstein's work did become known, and celebrated, 00:54:57.930 --> 00:54:58.980 align:middle line:90% and then scrutinized-- 00:54:58.980 --> 00:55:02.820 align:middle line:90% 00:55:02.820 --> 00:55:07.740 align:middle line:84% for a long time, there was a tradition by scientists, 00:55:07.740 --> 00:55:11.400 align:middle line:84% by philosophers, by historians, by many kinds of scholars, 00:55:11.400 --> 00:55:15.570 align:middle line:84% a tradition of trying to read Einstein's paper from 1905 00:55:15.570 --> 00:55:19.890 align:middle line:84% as some of direct response to the null result 00:55:19.890 --> 00:55:22.600 align:middle line:84% of the Michelson-Morley experiment. 00:55:22.600 --> 00:55:24.990 align:middle line:84% So let's say the fact that Michelson-Morley could not 00:55:24.990 --> 00:55:30.450 align:middle line:84% find any measurable effects of our motion through the ether, 00:55:30.450 --> 00:55:33.670 align:middle line:84% the argument had gone, must have convinced Einstein to then 00:55:33.670 --> 00:55:35.670 align:middle line:84% get rid of the ether because it had been somehow 00:55:35.670 --> 00:55:37.890 align:middle line:90% empirically disproven. 00:55:37.890 --> 00:55:40.230 align:middle line:84% And that was really the conventional way 00:55:40.230 --> 00:55:42.990 align:middle line:84% of trying to make sense of Einstein's own work 00:55:42.990 --> 00:55:45.690 align:middle line:84% on the electrodynamics of moving bodies. 00:55:45.690 --> 00:55:49.710 align:middle line:84% There's a really quite amazing critical review 00:55:49.710 --> 00:55:53.350 align:middle line:84% of that line of thought in this book by Gerald Holton. 00:55:53.350 --> 00:55:56.713 align:middle line:84% Professor Holton is a retired professor at Harvard. 00:55:56.713 --> 00:55:58.630 align:middle line:84% He was a member of both the Physics department 00:55:58.630 --> 00:56:00.213 align:middle line:84% and the History of Science department. 00:56:00.213 --> 00:56:02.680 align:middle line:84% And he wrote this really iconic, quite lovely collection 00:56:02.680 --> 00:56:04.957 align:middle line:84% of essays that was first published-- 00:56:04.957 --> 00:56:07.540 align:middle line:84% well, the essays were published throughout the 1950s and '60s. 00:56:07.540 --> 00:56:09.670 align:middle line:84% The book pulled together in the early '70s. 00:56:09.670 --> 00:56:12.190 align:middle line:84% Still in print, it's a lovely book. 00:56:12.190 --> 00:56:15.520 align:middle line:84% And Holton argues, I think really quite persuasively, 00:56:15.520 --> 00:56:19.660 align:middle line:84% that this reading of Einstein as somehow responding consciously 00:56:19.660 --> 00:56:22.330 align:middle line:84% and directly to this Michelson-Morley null result 00:56:22.330 --> 00:56:26.540 align:middle line:90% has almost no basis in fact. 00:56:26.540 --> 00:56:28.960 align:middle line:84% In fact, it's not clear whether Einstein even 00:56:28.960 --> 00:56:31.510 align:middle line:84% knew about the Michelson-Morley results at the time. 00:56:31.510 --> 00:56:34.150 align:middle line:84% If he did, he seemed pretty unconcerned about them. 00:56:34.150 --> 00:56:36.760 align:middle line:84% They did not seem to play any major role in his thinking. 00:56:36.760 --> 00:56:38.218 align:middle line:84% And that's an important distinction 00:56:38.218 --> 00:56:40.780 align:middle line:84% from people like Lorentz, like George FitzGerald, 00:56:40.780 --> 00:56:43.390 align:middle line:84% or like others whom we've mentioned. 00:56:43.390 --> 00:56:45.910 align:middle line:84% Plenty of people in Europe at the time 00:56:45.910 --> 00:56:48.670 align:middle line:84% were very concerned about the Michelson-Morley results. 00:56:48.670 --> 00:56:50.503 align:middle line:84% Einstein seems not to have been one of them. 00:56:50.503 --> 00:56:52.670 align:middle line:84% He might literally have not even heard about it yet. 00:56:52.670 --> 00:56:54.650 align:middle line:84% Or if he did, he didn't pay it much attention. 00:56:54.650 --> 00:56:57.940 align:middle line:84% We get some textual evidence just by looking carefully 00:56:57.940 --> 00:56:59.320 align:middle line:90% at Einstein's paper itself. 00:56:59.320 --> 00:57:02.140 align:middle line:84% This is, again, in the excerpt that you had for today. 00:57:02.140 --> 00:57:04.870 align:middle line:84% Right in the early, early part of the paper, 00:57:04.870 --> 00:57:08.230 align:middle line:84% he talks about what he calls unsuccessful attempts 00:57:08.230 --> 00:57:10.510 align:middle line:84% to discover any motion of the Earth relative 00:57:10.510 --> 00:57:11.890 align:middle line:90% to the light medium, the ether. 00:57:11.890 --> 00:57:13.750 align:middle line:90% They've all been unsuccessful. 00:57:13.750 --> 00:57:17.950 align:middle line:84% And he's talking about the quantities of the first order. 00:57:17.950 --> 00:57:21.640 align:middle line:84% Let's say it's a quantity to excuse me to the ratio V over C 00:57:21.640 --> 00:57:23.050 align:middle line:90% to the first power. 00:57:23.050 --> 00:57:25.540 align:middle line:84% One of the things that was so exciting to people 00:57:25.540 --> 00:57:27.400 align:middle line:84% about the Michelson-Morley experiment 00:57:27.400 --> 00:57:30.760 align:middle line:84% was actually sensitive to quantities of the second order. 00:57:30.760 --> 00:57:33.100 align:middle line:84% So Einstein is not only not citing a source 00:57:33.100 --> 00:57:35.540 align:middle line:84% as telling us which particular experiments he had in mind, 00:57:35.540 --> 00:57:38.470 align:middle line:84% which were these unsuccessful attempts to measure any motion 00:57:38.470 --> 00:57:40.630 align:middle line:84% of the Earth relative to the ether, 00:57:40.630 --> 00:57:43.990 align:middle line:84% he's dismissing his entire class of first-order experiments 00:57:43.990 --> 00:57:46.900 align:middle line:84% of which there were many, Fresnel aberration and so on. 00:57:46.900 --> 00:57:49.450 align:middle line:84% He's not even talking about second-order experiments, 00:57:49.450 --> 00:57:51.790 align:middle line:84% let alone mentioning more specifically 00:57:51.790 --> 00:57:53.360 align:middle line:90% the Michelson-Morley experiment. 00:57:53.360 --> 00:57:56.710 align:middle line:84% So Holton, I think, makes a pretty compelling argument 00:57:56.710 --> 00:57:58.150 align:middle line:84% that whatever Einstein was doing, 00:57:58.150 --> 00:58:00.670 align:middle line:84% it was probably not responding in any kind 00:58:00.670 --> 00:58:03.100 align:middle line:84% of self-conscious careful direct way 00:58:03.100 --> 00:58:05.620 align:middle line:84% to the Michelson-Morley null result. 00:58:05.620 --> 00:58:08.560 align:middle line:84% Now, that was sometimes taken by other people downstream, 00:58:08.560 --> 00:58:10.420 align:middle line:84% even from Professor Holton's work, 00:58:10.420 --> 00:58:12.100 align:middle line:84% to suggest that Einstein was somehow 00:58:12.100 --> 00:58:13.930 align:middle line:84% uninterested in experiments altogether. 00:58:13.930 --> 00:58:16.540 align:middle line:84% And that seems like not correct, either. 00:58:16.540 --> 00:58:18.370 align:middle line:84% That's the kind of overinterpretation 00:58:18.370 --> 00:58:21.160 align:middle line:84% of this question that's more specifically about Michelson 00:58:21.160 --> 00:58:23.590 align:middle line:90% and Morley. 00:58:23.590 --> 00:58:25.825 align:middle line:84% So here's where this article by Peter Galison 00:58:25.825 --> 00:58:28.870 align:middle line:84% is really drawn from a really fascinating book. 00:58:28.870 --> 00:58:31.180 align:middle line:84% That's why I think Galison's work can help put us back 00:58:31.180 --> 00:58:34.600 align:middle line:84% into Einstein's very specific world, to his context, 00:58:34.600 --> 00:58:37.060 align:middle line:84% to the things he really was concerned about and sometimes 00:58:37.060 --> 00:58:40.330 align:middle line:84% even quite obsessed about in the years, and months, and days, 00:58:40.330 --> 00:58:42.790 align:middle line:84% and weeks leading up to his work on the electrodynamics 00:58:42.790 --> 00:58:43.498 align:middle line:90% of moving bodies. 00:58:43.498 --> 00:58:45.832 align:middle line:84% And a lot of it has to do with things that we've already 00:58:45.832 --> 00:58:48.200 align:middle line:84% talked about, things like train travel, which he really, 00:58:48.200 --> 00:58:49.930 align:middle line:90% really was enamored with. 00:58:49.930 --> 00:58:53.140 align:middle line:84% So until the late 19th century, during Einstein's 00:58:53.140 --> 00:58:57.965 align:middle line:84% own childhood, in fact, there were no coordinated time zones. 00:58:57.965 --> 00:58:59.590 align:middle line:84% We now know about time zones very well. 00:58:59.590 --> 00:59:01.548 align:middle line:84% We have to navigate them carefully with these-- 00:59:01.548 --> 00:59:04.000 align:middle line:84% our asynchronous Zoom sessions and all the rest. 00:59:04.000 --> 00:59:07.030 align:middle line:84% But even into Einstein's own childhood, 00:59:07.030 --> 00:59:09.670 align:middle line:84% there were no coordinated time zones. 00:59:09.670 --> 00:59:12.970 align:middle line:84% Each town kept its own local time based, usually, 00:59:12.970 --> 00:59:15.640 align:middle line:84% on a clock in its town square, basically make sure 00:59:15.640 --> 00:59:18.730 align:middle line:84% an easily visible clock that everyone 00:59:18.730 --> 00:59:20.230 align:middle line:90% could see and agree on. 00:59:20.230 --> 00:59:22.490 align:middle line:84% That would set time, and you set your watch 00:59:22.490 --> 00:59:26.502 align:middle line:84% based on the highest clock tower in your town. 00:59:26.502 --> 00:59:28.710 align:middle line:84% And there were these clock towers all over the place, 00:59:28.710 --> 00:59:30.460 align:middle line:84% including, of course, at places like train 00:59:30.460 --> 00:59:34.100 align:middle line:84% stations, or churches, or other tall buildings. 00:59:34.100 --> 00:59:35.900 align:middle line:84% And that wasn't true only in Europe, that 00:59:35.900 --> 00:59:37.560 align:middle line:90% was also true in North America. 00:59:37.560 --> 00:59:39.410 align:middle line:84% So, for example, in this time period, 00:59:39.410 --> 00:59:42.020 align:middle line:84% passengers riding the train between Boston and New York 00:59:42.020 --> 00:59:44.720 align:middle line:84% City had to change their watches, on average, 00:59:44.720 --> 00:59:47.330 align:middle line:84% by about 37 minutes after the trip 00:59:47.330 --> 00:59:50.510 align:middle line:84% because there was no long-distance coordination 00:59:50.510 --> 00:59:53.460 align:middle line:90% for clock, for time. 00:59:53.460 --> 00:59:56.030 align:middle line:84% So what we would have called 12 noon in Boston 00:59:56.030 --> 00:59:58.887 align:middle line:84% was off by, on average, more than half an hour 00:59:58.887 --> 01:00:01.220 align:middle line:84% compared to what would have been called noon in New York 01:00:01.220 --> 01:00:04.110 align:middle line:90% City and vice versa. 01:00:04.110 --> 01:00:06.890 align:middle line:84% Now, that was true already, starting from the earliest 01:00:06.890 --> 01:00:08.330 align:middle line:90% days of rail travel. 01:00:08.330 --> 01:00:10.970 align:middle line:84% This became an especially pressing concern, 01:00:10.970 --> 01:00:12.980 align:middle line:84% one that now had both commercial and soon 01:00:12.980 --> 01:00:18.140 align:middle line:84% military concerns for people like General von Moltke 01:00:18.140 --> 01:00:20.630 align:middle line:90% in the newly unified Germany. 01:00:20.630 --> 01:00:22.640 align:middle line:84% You may remember, I mentioned briefly 01:00:22.640 --> 01:00:28.237 align:middle line:84% before, Germany was actually a collection of separate-- 01:00:28.237 --> 01:00:29.570 align:middle line:90% there was no country of Germany. 01:00:29.570 --> 01:00:33.020 align:middle line:84% It was a bunch of separate, German-speaking lands 01:00:33.020 --> 01:00:35.420 align:middle line:84% until unified into a single country of Germany 01:00:35.420 --> 01:00:40.130 align:middle line:84% in 1871 right on the heels of its war with France in 1870. 01:00:40.130 --> 01:00:44.390 align:middle line:84% And one of the leading military leaders from that who was 01:00:44.390 --> 01:00:47.720 align:middle line:84% elevated to a count became a-- he was knighted, essentially-- 01:00:47.720 --> 01:00:50.480 align:middle line:84% Count von Moltke is recounting why 01:00:50.480 --> 01:00:52.250 align:middle line:84% it was so important in this new system 01:00:52.250 --> 01:00:55.940 align:middle line:84% of a single unified Germany to pay closer attention to how 01:00:55.940 --> 01:00:57.320 align:middle line:90% we coordinate time. 01:00:57.320 --> 01:01:00.440 align:middle line:84% And this is now a quotation that I learned from Peter Galison's 01:01:00.440 --> 01:01:01.940 align:middle line:90% articles in your reading. 01:01:01.940 --> 01:01:04.350 align:middle line:84% He says that "unity of time is indispensable 01:01:04.350 --> 01:01:06.570 align:middle line:84% for the satisfactory operating of railways 01:01:06.570 --> 01:01:09.420 align:middle line:84% that's now universally recognized as not disputed. 01:01:09.420 --> 01:01:11.910 align:middle line:84% But, my gentleman, meine Herren, we 01:01:11.910 --> 01:01:14.520 align:middle line:84% have, in Germany, five different units of time. 01:01:14.520 --> 01:01:17.515 align:middle line:84% We have, in Germany, five zones with all the drawbacks 01:01:17.515 --> 01:01:19.140 align:middle line:84% and disadvantages which result" There's 01:01:19.140 --> 01:01:21.270 align:middle line:90% no nationwide coordination. 01:01:21.270 --> 01:01:23.790 align:middle line:90% 01:01:23.790 --> 01:01:25.440 align:middle line:84% "These we have in our own fatherland 01:01:25.440 --> 01:01:28.370 align:middle line:84% besides those we dread to meet at the French and Russian 01:01:28.370 --> 01:01:28.870 align:middle line:90% borders." 01:01:28.870 --> 01:01:30.960 align:middle line:84% We dread because those were sites of recent war. 01:01:30.960 --> 01:01:32.755 align:middle line:84% "This is, I must say, a ruin, which 01:01:32.755 --> 01:01:35.130 align:middle line:84% has remained standing out of the one splintered condition 01:01:35.130 --> 01:01:37.470 align:middle line:84% of" a Germany when it wasn't yet a unified country. 01:01:37.470 --> 01:01:40.257 align:middle line:84% "But which since we have become an empire, it is proper 01:01:40.257 --> 01:01:41.340 align:middle line:90% should be done away with." 01:01:41.340 --> 01:01:43.595 align:middle line:84% We need to coordinate clocks at a distance. 01:01:43.595 --> 01:01:44.970 align:middle line:84% And as I say, this was especially 01:01:44.970 --> 01:01:47.190 align:middle line:84% relevant after the recent war with France 01:01:47.190 --> 01:01:50.470 align:middle line:84% that led to the unification of a single country of Germany. 01:01:50.470 --> 01:01:51.980 align:middle line:84% This is all happening, literally, 01:01:51.980 --> 01:01:52.980 align:middle line:90% in Einstein's childhood. 01:01:52.980 --> 01:01:55.800 align:middle line:84% Remember, Einstein was born in 1879. 01:01:55.800 --> 01:01:57.570 align:middle line:84% The country into which he was born itself 01:01:57.570 --> 01:02:00.150 align:middle line:90% was actually quite new. 01:02:00.150 --> 01:02:03.500 align:middle line:84% So one of the main ideas that a lot of engineers and scientists 01:02:03.500 --> 01:02:05.450 align:middle line:84% were working on throughout Central Europe, 01:02:05.450 --> 01:02:08.390 align:middle line:84% not just in Germany, was to install 01:02:08.390 --> 01:02:11.570 align:middle line:84% what became known as mother clocks, 01:02:11.570 --> 01:02:14.840 align:middle line:84% and to install them in central train stations connected 01:02:14.840 --> 01:02:17.600 align:middle line:84% to other clocks by way of electromagnetic signals, 01:02:17.600 --> 01:02:20.790 align:middle line:84% either telegraph or increasingly radio waves. 01:02:20.790 --> 01:02:23.360 align:middle line:84% This is what Peter Galison wrote about in his really quite 01:02:23.360 --> 01:02:25.942 align:middle line:84% lovely book, "Einstein's Clocks, Poincaré's Maps." 01:02:25.942 --> 01:02:27.650 align:middle line:84% And, of course, the reading we had today, 01:02:27.650 --> 01:02:31.980 align:middle line:84% Peter's article kind of draws on that larger body of work. 01:02:31.980 --> 01:02:34.790 align:middle line:84% And so some of you may know the Eiffel Tower in Paris 01:02:34.790 --> 01:02:37.220 align:middle line:84% was under construction around 1910. 01:02:37.220 --> 01:02:38.930 align:middle line:84% One of the earliest uses for that 01:02:38.930 --> 01:02:40.910 align:middle line:84% was not only to draw American tourists. 01:02:40.910 --> 01:02:44.180 align:middle line:84% That wasn't such a bad outcome, either, for the French. 01:02:44.180 --> 01:02:46.670 align:middle line:84% But it was actually to serve as a transmitting tower 01:02:46.670 --> 01:02:51.000 align:middle line:84% for radio waves, in part, to transmit clock coordination 01:02:51.000 --> 01:02:51.500 align:middle line:90% signals. 01:02:51.500 --> 01:02:53.870 align:middle line:84% It was one of the standardizing beacons 01:02:53.870 --> 01:02:55.580 align:middle line:90% to send out standard time. 01:02:55.580 --> 01:02:57.800 align:middle line:84% "It is now 12:00 noon" and beam that out 01:02:57.800 --> 01:02:59.990 align:middle line:90% by electromagnetic signal. 01:02:59.990 --> 01:03:04.040 align:middle line:84% Other municipalities were laying telegraph lines 01:03:04.040 --> 01:03:07.280 align:middle line:84% or stringing above ground telegraph cable 01:03:07.280 --> 01:03:10.610 align:middle line:84% to do the same thing, to connect especially main hubs 01:03:10.610 --> 01:03:13.820 align:middle line:84% on this now intercity rail system 01:03:13.820 --> 01:03:16.730 align:middle line:84% so they could coordinate clock signals, 01:03:16.730 --> 01:03:20.850 align:middle line:84% even across the entire expanse of the continent. 01:03:20.850 --> 01:03:24.020 align:middle line:84% And so every single part of these new systems 01:03:24.020 --> 01:03:26.060 align:middle line:90% were subject to patent claims. 01:03:26.060 --> 01:03:28.070 align:middle line:84% This is exactly what Einstein was immersed in. 01:03:28.070 --> 01:03:30.620 align:middle line:84% I was talking with some students before the class really 01:03:30.620 --> 01:03:32.330 align:middle line:90% began this afternoon. 01:03:32.330 --> 01:03:33.740 align:middle line:90% It's really quite extraordinary. 01:03:33.740 --> 01:03:36.590 align:middle line:84% Peter writes about this a bit in his book. 01:03:36.590 --> 01:03:39.770 align:middle line:84% There was a rule at the barren patent office, where Einstein 01:03:39.770 --> 01:03:41.840 align:middle line:84% was a patent officer third class, 01:03:41.840 --> 01:03:45.140 align:middle line:84% that any records, any unpublished records regarding 01:03:45.140 --> 01:03:47.150 align:middle line:84% the review of patent applications 01:03:47.150 --> 01:03:49.340 align:middle line:84% had to be destroyed after some passage of time, 01:03:49.340 --> 01:03:50.460 align:middle line:90% a couple of decades. 01:03:50.460 --> 01:03:52.400 align:middle line:84% And so they wound up destroying even the stuff 01:03:52.400 --> 01:03:54.890 align:middle line:84% that Einstein had served as a principal examiner on. 01:03:54.890 --> 01:03:58.760 align:middle line:84% So we have very few clues as to the very specific patents 01:03:58.760 --> 01:04:01.410 align:middle line:84% on which Einstein would have served as the lead examiner. 01:04:01.410 --> 01:04:03.090 align:middle line:84% What we do know, however, and what 01:04:03.090 --> 01:04:05.880 align:middle line:84% Peter makes very good use of in his study, 01:04:05.880 --> 01:04:08.940 align:middle line:84% are the patents that were issued from that patent 01:04:08.940 --> 01:04:10.567 align:middle line:90% office in various years. 01:04:10.567 --> 01:04:12.150 align:middle line:84% We also know that Einstein was working 01:04:12.150 --> 01:04:14.250 align:middle line:84% on the so-called electrotechnical desk 01:04:14.250 --> 01:04:15.400 align:middle line:90% in particular. 01:04:15.400 --> 01:04:19.590 align:middle line:84% So it's all but unavoidable to conclude that Einstein 01:04:19.590 --> 01:04:21.540 align:middle line:84% was examining at least some of these gadgets 01:04:21.540 --> 01:04:23.900 align:middle line:84% along the way, which exact ones we don't know. 01:04:23.900 --> 01:04:27.570 align:middle line:84% We do know from the volume of patents being applied for 01:04:27.570 --> 01:04:30.270 align:middle line:84% and the kinds of work being done that this 01:04:30.270 --> 01:04:34.440 align:middle line:84% was very much a major concern in the Bern patent office 01:04:34.440 --> 01:04:36.330 align:middle line:84% as well as other parts of Europe. 01:04:36.330 --> 01:04:39.900 align:middle line:84% Peter goes on, this is one of my favorite examples, 01:04:39.900 --> 01:04:41.490 align:middle line:84% he actually was able to reconstruct 01:04:41.490 --> 01:04:44.520 align:middle line:84% from Einstein's correspondence the walking path that Einstein 01:04:44.520 --> 01:04:47.670 align:middle line:84% would have taken between his apartment in Baron 01:04:47.670 --> 01:04:49.920 align:middle line:84% and his office at the patent office. 01:04:49.920 --> 01:04:52.110 align:middle line:84% And here, you see this map of all 01:04:52.110 --> 01:04:54.930 align:middle line:84% of the newly coordinated clocks literally dotting 01:04:54.930 --> 01:04:58.107 align:middle line:84% the line of the path along which Einstein would have walked 01:04:58.107 --> 01:04:59.940 align:middle line:84% that would have just recently been connected 01:04:59.940 --> 01:05:02.820 align:middle line:84% by these telegraph and/or radial signal methods, 01:05:02.820 --> 01:05:06.270 align:middle line:84% to say that when you receive this electromagnetic signal, 01:05:06.270 --> 01:05:09.360 align:middle line:84% that means that it's 12 noon at the mother clock. 01:05:09.360 --> 01:05:12.540 align:middle line:84% Implement an appropriate offset to take into account 01:05:12.540 --> 01:05:15.697 align:middle line:84% your distance from that mother clock and the speed of light. 01:05:15.697 --> 01:05:17.280 align:middle line:84% So we know that Einstein was literally 01:05:17.280 --> 01:05:19.980 align:middle line:84% immersed in these kinds of things even on his walk 01:05:19.980 --> 01:05:23.070 align:middle line:84% to work, let alone at his patent desk. 01:05:23.070 --> 01:05:27.030 align:middle line:84% So we come back to this very strange-looking paper submitted 01:05:27.030 --> 01:05:30.090 align:middle line:84% to the Annalen der Physik in June of 1905 01:05:30.090 --> 01:05:32.490 align:middle line:84% on the electrodynamics of moving bodies. 01:05:32.490 --> 01:05:34.170 align:middle line:84% Again, as I've mentioned many times, 01:05:34.170 --> 01:05:36.390 align:middle line:84% the title sounds quite conventional. 01:05:36.390 --> 01:05:39.150 align:middle line:84% The approach seems anything but conventional in terms 01:05:39.150 --> 01:05:42.940 align:middle line:84% of ordinary physics articles of the day, of their own day, 01:05:42.940 --> 01:05:45.060 align:middle line:90% let alone of our day today. 01:05:45.060 --> 01:05:48.090 align:middle line:84% And yet, if we think of this as the work of a patent clerk 01:05:48.090 --> 01:05:51.780 align:middle line:84% who's obsessed, who's enamored with this new technological 01:05:51.780 --> 01:05:55.270 align:middle line:84% stuff, maybe begins to make a little more sense. 01:05:55.270 --> 01:05:57.360 align:middle line:84% The lack of references might not only 01:05:57.360 --> 01:06:00.420 align:middle line:84% have been Einstein being lazy or uncharitable. 01:06:00.420 --> 01:06:03.900 align:middle line:84% It also could be a way to emphasize priority and downplay 01:06:03.900 --> 01:06:07.300 align:middle line:84% precedence, much like one would have to do to get a patent. 01:06:07.300 --> 01:06:09.330 align:middle line:84% I mean, this is actually novel compared 01:06:09.330 --> 01:06:11.980 align:middle line:90% to what was done before. 01:06:11.980 --> 01:06:13.920 align:middle line:84% There's a very close focus on what we might 01:06:13.920 --> 01:06:15.750 align:middle line:90% call the operational details. 01:06:15.750 --> 01:06:19.380 align:middle line:84% How would we really measure distances of space and time? 01:06:19.380 --> 01:06:21.930 align:middle line:84% How would we actually coordinate our clocks 01:06:21.930 --> 01:06:24.180 align:middle line:84% if we're not right next to each other? 01:06:24.180 --> 01:06:26.940 align:middle line:84% Or, if we have some intervening state of motion, 01:06:26.940 --> 01:06:29.220 align:middle line:84% how would you step by step establish 01:06:29.220 --> 01:06:31.080 align:middle line:84% things like clock coordination, taking 01:06:31.080 --> 01:06:33.720 align:middle line:84% advantage of the exchange of electromagnetic signals? 01:06:33.720 --> 01:06:37.380 align:middle line:84% It begins to look a bit more like a patent application 01:06:37.380 --> 01:06:40.020 align:middle line:84% and less like an exercise in mathematical physics 01:06:40.020 --> 01:06:43.650 align:middle line:84% of the sort that Hendrik Lorentz or others had done. 01:06:43.650 --> 01:06:46.980 align:middle line:84% So that's the main takeaway, that I keep in mind at least, 01:06:46.980 --> 01:06:50.040 align:middle line:84% from Peter Galison's article and book. 01:06:50.040 --> 01:06:52.365 align:middle line:90% And we can pause there. 01:06:52.365 --> 01:06:54.240 align:middle line:84% And again, I'll ask, are there any questions? 01:06:54.240 --> 01:06:57.260 align:middle line:90% 01:06:57.260 --> 01:06:59.088 align:middle line:84% So Babu-Abel says, I noticed the paper 01:06:59.088 --> 01:07:01.130 align:middle line:84% began with saying the Michelson-Morley experiment 01:07:01.130 --> 01:07:03.265 align:middle line:90% as a prerequisite. 01:07:03.265 --> 01:07:04.640 align:middle line:84% That's certainly not by Einstein. 01:07:04.640 --> 01:07:06.848 align:middle line:84% So it depends on which translation you're looking at. 01:07:06.848 --> 01:07:09.380 align:middle line:84% It's true that later editors, including Arnold Sommerfeld, 01:07:09.380 --> 01:07:13.010 align:middle line:84% who actually made one of the first translations, 01:07:13.010 --> 01:07:13.970 align:middle line:90% or one of the first-- 01:07:13.970 --> 01:07:15.980 align:middle line:84% actually, one of the first annotations-- 01:07:15.980 --> 01:07:19.370 align:middle line:84% many later editors have put stuff onto Einstein's paper, 01:07:19.370 --> 01:07:22.220 align:middle line:84% and they're usually marked carefully with footnotes. 01:07:22.220 --> 01:07:25.340 align:middle line:84% In some of the translations, it gets a little cluttered 01:07:25.340 --> 01:07:27.630 align:middle line:90% as to who put that footnote in. 01:07:27.630 --> 01:07:29.120 align:middle line:84% So you have to be a little careful. 01:07:29.120 --> 01:07:32.630 align:middle line:84% So Babu-Abel, I'm quite confident that whatever 01:07:32.630 --> 01:07:35.690 align:middle line:84% footnote you have in mind was one of these later additions 01:07:35.690 --> 01:07:37.492 align:middle line:84% from a well-meaning editor, someone 01:07:37.492 --> 01:07:39.200 align:middle line:84% who thought they were helping to clarify, 01:07:39.200 --> 01:07:42.140 align:middle line:84% but in fact was falling into this, what becomes now, 01:07:42.140 --> 01:07:44.430 align:middle line:90% a kind of historical trap. 01:07:44.430 --> 01:07:47.360 align:middle line:84% So if we go back to the Annalen der Physik itself or some 01:07:47.360 --> 01:07:51.327 align:middle line:84% of the more bare translations, for example from the Einstein 01:07:51.327 --> 01:07:53.660 align:middle line:84% papers project, the Collected Papers of Albert Einstein, 01:07:53.660 --> 01:07:55.850 align:middle line:84% now the kind of industry-standard version, 01:07:55.850 --> 01:07:58.980 align:middle line:84% we can go very clearly, what was exactly in Einstein's first 01:07:58.980 --> 01:08:01.260 align:middle line:84% published version and what was added by later-- 01:08:01.260 --> 01:08:03.912 align:middle line:90% well-meaning, but later editors. 01:08:03.912 --> 01:08:04.870 align:middle line:90% So that's a good point. 01:08:04.870 --> 01:08:05.912 align:middle line:90% Thank you for raising it. 01:08:05.912 --> 01:08:07.975 align:middle line:84% Stanley asks, can we explain again 01:08:07.975 --> 01:08:10.350 align:middle line:84% why a stationary observer measures the length of a moving 01:08:10.350 --> 01:08:11.220 align:middle line:90% train to be smaller? 01:08:11.220 --> 01:08:12.015 align:middle line:90% Yeah, very good. 01:08:12.015 --> 01:08:13.890 align:middle line:84% Because of different notions of simultaneity. 01:08:13.890 --> 01:08:15.570 align:middle line:90% It's a great question Stanley. 01:08:15.570 --> 01:08:17.745 align:middle line:84% It's worth sitting with this a little bit longer. 01:08:17.745 --> 01:08:21.788 align:middle line:90% 01:08:21.788 --> 01:08:23.330 align:middle line:84% Let me preview by saying, we're going 01:08:23.330 --> 01:08:26.660 align:middle line:84% to come back to that in the next class session 01:08:26.660 --> 01:08:30.140 align:middle line:84% as well to consider not how Einstein himself made sense 01:08:30.140 --> 01:08:32.689 align:middle line:84% of that, by how some later people wrestling 01:08:32.689 --> 01:08:34.640 align:middle line:84% with Einstein's work made sense of things 01:08:34.640 --> 01:08:35.670 align:middle line:90% like length contraction. 01:08:35.670 --> 01:08:37.420 align:middle line:84% So this is not the last time we'll see it, 01:08:37.420 --> 01:08:40.393 align:middle line:90% even in this class. 01:08:40.393 --> 01:08:42.560 align:middle line:84% But what did Einstein argue was the origin of length 01:08:42.560 --> 01:08:43.939 align:middle line:90% contraction? 01:08:43.939 --> 01:08:45.950 align:middle line:84% Remember, he very clearly says the ether 01:08:45.950 --> 01:08:47.582 align:middle line:90% will be merely superfluous. 01:08:47.582 --> 01:08:49.790 align:middle line:84% He's going to not talk about a physical medium that's 01:08:49.790 --> 01:08:51.890 align:middle line:84% going to exert forces the way Lorentz did 01:08:51.890 --> 01:08:53.810 align:middle line:90% about that squeezed beach ball. 01:08:53.810 --> 01:08:56.510 align:middle line:84% For Einstein, it's all about how we perform the measurement, 01:08:56.510 --> 01:08:59.120 align:middle line:84% that kind of mock-like operation for how do you 01:08:59.120 --> 01:09:00.149 align:middle line:90% perform a measurement. 01:09:00.149 --> 01:09:02.600 align:middle line:84% So he says, here's how you perform a measurement of length 01:09:02.600 --> 01:09:03.590 align:middle line:90% or of distance. 01:09:03.590 --> 01:09:06.020 align:middle line:84% Measure the front of the train and the back of the train 01:09:06.020 --> 01:09:07.880 align:middle line:90% at the same time and subtract. 01:09:07.880 --> 01:09:09.270 align:middle line:90% Take the difference. 01:09:09.270 --> 01:09:11.660 align:middle line:84% So if we're at rest with respect to the object, 01:09:11.660 --> 01:09:13.109 align:middle line:90% that's not very challenging. 01:09:13.109 --> 01:09:14.660 align:middle line:84% The train is at rest in the station, 01:09:14.660 --> 01:09:16.859 align:middle line:84% we can leisurely measure the front, the position 01:09:16.859 --> 01:09:19.340 align:middle line:84% of the front, mark it off on the train platform, 01:09:19.340 --> 01:09:22.380 align:middle line:84% leisurely mark the back, we can then take the difference 01:09:22.380 --> 01:09:24.899 align:middle line:84% and say, OK, the train is 25m long 01:09:24.899 --> 01:09:27.060 align:middle line:90% or whatever the answer might be. 01:09:27.060 --> 01:09:28.710 align:middle line:84% What happens when we try to measure 01:09:28.710 --> 01:09:31.319 align:middle line:90% the length of the moving train? 01:09:31.319 --> 01:09:33.107 align:middle line:84% When we watch the moving train, we 01:09:33.107 --> 01:09:34.649 align:middle line:84% should measure the front of the train 01:09:34.649 --> 01:09:37.319 align:middle line:84% and the rear of the train, mark those positions 01:09:37.319 --> 01:09:39.330 align:middle line:90% at the same time, and subtract. 01:09:39.330 --> 01:09:41.790 align:middle line:84% The problem is, based on this argument 01:09:41.790 --> 01:09:43.590 align:middle line:84% about the exchanged light signals, 01:09:43.590 --> 01:09:47.100 align:middle line:84% we no longer agree on what counts as, "at the same time," 01:09:47.100 --> 01:09:49.319 align:middle line:84% as the observer on the moving train does. 01:09:49.319 --> 01:09:51.149 align:middle line:84% So the observer on the moving train 01:09:51.149 --> 01:09:53.550 align:middle line:84% watches us do this and watches us do things 01:09:53.550 --> 01:09:57.070 align:middle line:84% at different times because of our relative states of motion. 01:09:57.070 --> 01:09:59.370 align:middle line:84% So we think we've been very careful measuring 01:09:59.370 --> 01:10:01.230 align:middle line:84% at the same time, the locations front 01:10:01.230 --> 01:10:02.970 align:middle line:90% to back and take the difference. 01:10:02.970 --> 01:10:04.710 align:middle line:84% Our partner on the train says, you 01:10:04.710 --> 01:10:07.380 align:middle line:84% measured the front of the train first. 01:10:07.380 --> 01:10:08.910 align:middle line:90% And then, you waited. 01:10:08.910 --> 01:10:11.970 align:middle line:84% Some time went by during which the train is sliding past. 01:10:11.970 --> 01:10:14.610 align:middle line:84% And then, you mark the position of the rear. 01:10:14.610 --> 01:10:16.770 align:middle line:90% So it's an unfair measurement. 01:10:16.770 --> 01:10:20.292 align:middle line:84% They watch us mark the front of the train, wait a while, 01:10:20.292 --> 01:10:21.750 align:middle line:84% and then mark the rear of the train 01:10:21.750 --> 01:10:22.920 align:middle line:90% after the train has moved. 01:10:22.920 --> 01:10:25.150 align:middle line:84% So along the direction of motion, of course, 01:10:25.150 --> 01:10:27.420 align:middle line:84% we measure a shorter distance because they argue 01:10:27.420 --> 01:10:29.220 align:middle line:90% we messed up on the timing. 01:10:29.220 --> 01:10:31.170 align:middle line:84% Now we could say, no, no, you're wrong. 01:10:31.170 --> 01:10:32.937 align:middle line:84% We did it right because of this and that. 01:10:32.937 --> 01:10:34.770 align:middle line:84% And they'll say, no, no, I'm right because I 01:10:34.770 --> 01:10:38.475 align:middle line:84% have these light signals that were exchanged from my partners 01:10:38.475 --> 01:10:41.070 align:middle line:84% A and B, who were stationed at the front 01:10:41.070 --> 01:10:43.172 align:middle line:84% and rear of the train, and I got the light signal 01:10:43.172 --> 01:10:44.880 align:middle line:84% from the person at the front of the train 01:10:44.880 --> 01:10:46.778 align:middle line:84% before I got the light signal from the person 01:10:46.778 --> 01:10:47.820 align:middle line:90% at the back of the train. 01:10:47.820 --> 01:10:49.620 align:middle line:84% So you can't tell me you were simultaneous. 01:10:49.620 --> 01:10:50.220 align:middle line:90% You messed up. 01:10:50.220 --> 01:10:50.803 align:middle line:90% You were lazy. 01:10:50.803 --> 01:10:51.870 align:middle line:90% You were too slow. 01:10:51.870 --> 01:10:52.980 align:middle line:90% You messed up. 01:10:52.980 --> 01:10:55.020 align:middle line:84% And we can't say, I'm right; you're wrong. 01:10:55.020 --> 01:10:58.320 align:middle line:84% We can, but she can say it with equal confidence 01:10:58.320 --> 01:10:59.400 align:middle line:90% and equal fervor. 01:10:59.400 --> 01:11:03.840 align:middle line:84% That's what Einstein wanted to get at by pairing those two 01:11:03.840 --> 01:11:07.140 align:middle line:84% starting postulates, that all the laws of physics, including 01:11:07.140 --> 01:11:09.900 align:middle line:84% all the laws of mechanics, electricity, magnetism, optics, 01:11:09.900 --> 01:11:11.880 align:middle line:84% thermodynamics, all the laws of physics 01:11:11.880 --> 01:11:14.340 align:middle line:84% hold just as valid for our partner 01:11:14.340 --> 01:11:16.920 align:middle line:84% on the moving train, if she's not speeding up or slowing 01:11:16.920 --> 01:11:19.290 align:middle line:84% down, if it's an inertial motion, 01:11:19.290 --> 01:11:22.300 align:middle line:84% they hold just as valid for her as they do for us. 01:11:22.300 --> 01:11:24.420 align:middle line:84% So she can appeal to things like the behavior 01:11:24.420 --> 01:11:26.580 align:middle line:84% of light signals, the behavior of her clocks 01:11:26.580 --> 01:11:27.940 align:middle line:90% on board and so on. 01:11:27.940 --> 01:11:30.260 align:middle line:84% And she very clearly unambiguously receives 01:11:30.260 --> 01:11:32.010 align:middle line:84% a light signal from the front of the train 01:11:32.010 --> 01:11:34.830 align:middle line:84% first and later from the rear of the train. 01:11:34.830 --> 01:11:36.805 align:middle line:84% So therefore, if these light signals 01:11:36.805 --> 01:11:38.430 align:middle line:84% were emitted at the moment people tried 01:11:38.430 --> 01:11:40.050 align:middle line:84% to measure the front and back of the train, 01:11:40.050 --> 01:11:41.460 align:middle line:90% she said, well, you messed up. 01:11:41.460 --> 01:11:43.890 align:middle line:84% You didn't get the timing right because you measured 01:11:43.890 --> 01:11:46.558 align:middle line:84% the front of the train, and then some time later you 01:11:46.558 --> 01:11:47.850 align:middle line:90% measured the rear of the train. 01:11:47.850 --> 01:11:49.965 align:middle line:84% And in the intervening moments, the train 01:11:49.965 --> 01:11:51.340 align:middle line:84% slid in that direction of motion. 01:11:51.340 --> 01:11:54.360 align:middle line:84% So you measured the wrong location of the rear 01:11:54.360 --> 01:11:57.638 align:middle line:84% because you measured the rear of the train at the wrong time. 01:11:57.638 --> 01:11:59.430 align:middle line:84% So, again, if that's still not super clear, 01:11:59.430 --> 01:12:00.870 align:middle line:90% go over the slides. 01:12:00.870 --> 01:12:02.370 align:middle line:84% The picture might help a little bit. 01:12:02.370 --> 01:12:04.662 align:middle line:84% I'd be glad to chat more during office hours and so on. 01:12:04.662 --> 01:12:06.953 align:middle line:84% But we'll also come to that again on Wednesday's class, 01:12:06.953 --> 01:12:08.860 align:middle line:84% seeing it from still a different perspective. 01:12:08.860 --> 01:12:11.620 align:middle line:84% So if it still doesn't quite sit right, it's OK. 01:12:11.620 --> 01:12:14.113 align:middle line:84% We'll get another crack at it on Wednesday. 01:12:14.113 --> 01:12:18.280 align:middle line:90% 01:12:18.280 --> 01:12:19.840 align:middle line:90% Great, [INAUDIBLE], thank you. 01:12:19.840 --> 01:12:20.920 align:middle line:90% Very good observation. 01:12:20.920 --> 01:12:23.550 align:middle line:84% So I think the way Einstein would have reconciled 01:12:23.550 --> 01:12:25.410 align:middle line:84% those two, he's saying, we can always 01:12:25.410 --> 01:12:27.400 align:middle line:90% establish a coordinate system. 01:12:27.400 --> 01:12:30.030 align:middle line:84% We can always say, this is my reference frame with respect 01:12:30.030 --> 01:12:31.800 align:middle line:84% to which I measure the passage of time. 01:12:31.800 --> 01:12:33.420 align:middle line:90% I assign some coordinate t. 01:12:33.420 --> 01:12:36.180 align:middle line:84% He even tells us how to measure the time of an event 01:12:36.180 --> 01:12:39.600 align:middle line:84% when the train pulls in, and my watch says 7:00, right? 01:12:39.600 --> 01:12:42.120 align:middle line:84% So we can always-- in fact, we have to always establish 01:12:42.120 --> 01:12:45.720 align:middle line:84% our own coordinate system that's especially convenient for us, 01:12:45.720 --> 01:12:48.660 align:middle line:84% let's say at rest with respect to our own motion. 01:12:48.660 --> 01:12:52.362 align:middle line:84% We can't appeal to any "real," any true coordinate system 01:12:52.362 --> 01:12:54.570 align:middle line:84% or any absolute coordinate system because, he argues, 01:12:54.570 --> 01:12:56.130 align:middle line:90% there is no such thing. 01:12:56.130 --> 01:12:59.158 align:middle line:84% But that doesn't stop us from laying out our own coordinates. 01:12:59.158 --> 01:12:59.950 align:middle line:90% We have to do that. 01:12:59.950 --> 01:13:02.450 align:middle line:84% In fact, we have no choice but to set up our own coordinates 01:13:02.450 --> 01:13:05.590 align:middle line:84% because there's no absolute system to which we can appeal. 01:13:05.590 --> 01:13:09.240 align:middle line:84% So he's arguing, in the case of the clock coordination, 01:13:09.240 --> 01:13:14.100 align:middle line:84% that all these locations down the line, the Bern train 01:13:14.100 --> 01:13:16.380 align:middle line:84% station wasn't picking up and moving with respect 01:13:16.380 --> 01:13:18.130 align:middle line:90% to the Zurich train station. 01:13:18.130 --> 01:13:20.650 align:middle line:84% We should be able to apply one set of coordinates 01:13:20.650 --> 01:13:23.120 align:middle line:84% to all those things across space. 01:13:23.120 --> 01:13:25.570 align:middle line:84% But how do we get our time coordinates to line up? 01:13:25.570 --> 01:13:26.950 align:middle line:84% We have to do a little more work. 01:13:26.950 --> 01:13:29.020 align:middle line:84% Because they can't appeal to absolute time 01:13:29.020 --> 01:13:30.790 align:middle line:90% any more than we can, right? 01:13:30.790 --> 01:13:34.660 align:middle line:84% So we have to therefore find a mechanism, find an operation 01:13:34.660 --> 01:13:37.330 align:middle line:84% according to which we can line up our own coordinate system, 01:13:37.330 --> 01:13:39.010 align:middle line:84% we can get our coordinate systems to be 01:13:39.010 --> 01:13:41.110 align:middle line:90% in agreement or in alignment. 01:13:41.110 --> 01:13:43.480 align:middle line:84% Because there is no absolute standard to which 01:13:43.480 --> 01:13:44.920 align:middle line:90% we can separately appeal. 01:13:44.920 --> 01:13:46.040 align:middle line:90% How can we do that? 01:13:46.040 --> 01:13:48.993 align:middle line:84% Well, we're all going to agree on the speed of light. 01:13:48.993 --> 01:13:50.410 align:middle line:84% Whether we're at rest with respect 01:13:50.410 --> 01:13:52.060 align:middle line:84% to each other or moving, according 01:13:52.060 --> 01:13:55.780 align:middle line:84% to his second postulate, light becomes this absolute meter 01:13:55.780 --> 01:13:59.050 align:middle line:84% stick or measuring tool because we'll all agree on it. 01:13:59.050 --> 01:14:01.992 align:middle line:84% That means that if we're using, say, radio 01:14:01.992 --> 01:14:03.700 align:middle line:84% waves from the Eiffel Tower to coordinate 01:14:03.700 --> 01:14:08.020 align:middle line:84% our clocks at a distance, we know exactly how much time must 01:14:08.020 --> 01:14:11.830 align:middle line:84% have elapsed in our own coordinate system between when 01:14:11.830 --> 01:14:15.640 align:middle line:84% the clock struck 12 noon in Paris at the Eiffel Tower 01:14:15.640 --> 01:14:18.640 align:middle line:84% and that electromagnetic wave carried that signal, 01:14:18.640 --> 01:14:20.650 align:middle line:84% it's 12 noon in Paris, it's 12 noon in Paris, 01:14:20.650 --> 01:14:21.567 align:middle line:90% it's 12 noon in Paris. 01:14:21.567 --> 01:14:23.800 align:middle line:84% And then, we receive that signal some time later, 01:14:23.800 --> 01:14:27.160 align:middle line:84% we know exactly how long in our time units, 01:14:27.160 --> 01:14:29.620 align:middle line:84% how long it's taken that signal to arrive 01:14:29.620 --> 01:14:31.510 align:middle line:84% because the light wave could only have 01:14:31.510 --> 01:14:33.440 align:middle line:90% traveled at the speed of light. 01:14:33.440 --> 01:14:35.890 align:middle line:84% So we can use this as a universalizing tool 01:14:35.890 --> 01:14:38.920 align:middle line:84% to coordinate our coordinate systems at a distance, 01:14:38.920 --> 01:14:41.410 align:middle line:84% and then we can make sure that our clock is 01:14:41.410 --> 01:14:45.553 align:middle line:84% in the same reference frame as the Paris clock, not by saying, 01:14:45.553 --> 01:14:46.720 align:middle line:90% I got the signal from Paris. 01:14:46.720 --> 01:14:48.580 align:middle line:84% Now, I'll make my clock say 12 noon. 01:14:48.580 --> 01:14:50.230 align:middle line:90% That wouldn't work. 01:14:50.230 --> 01:14:52.150 align:middle line:84% By saying, I got the signal from Paris, 01:14:52.150 --> 01:14:56.290 align:middle line:84% I now know it's 12 noon plus the propagation time. 01:14:56.290 --> 01:14:58.690 align:middle line:84% And I can calculate that without worry 01:14:58.690 --> 01:15:00.340 align:middle line:84% because the propagation of that signal 01:15:00.340 --> 01:15:03.620 align:middle line:84% is some universal constant, the propagation rate. 01:15:03.620 --> 01:15:07.300 align:middle line:84% So if I have separately measured the distance between my house 01:15:07.300 --> 01:15:10.180 align:middle line:84% and my train station in Paris or whatever the mother clock is 01:15:10.180 --> 01:15:12.013 align:middle line:84% we're referring to-- the Germans would never 01:15:12.013 --> 01:15:13.180 align:middle line:90% have used Paris, by the way. 01:15:13.180 --> 01:15:14.320 align:middle line:90% They would have hated that. 01:15:14.320 --> 01:15:15.695 align:middle line:84% But whatever the mother clock is, 01:15:15.695 --> 01:15:18.700 align:middle line:84% whatever standard we're using, you 01:15:18.700 --> 01:15:20.440 align:middle line:84% can separately at your leisure measure 01:15:20.440 --> 01:15:21.830 align:middle line:90% your distance between them. 01:15:21.830 --> 01:15:23.380 align:middle line:84% And then, you'll know how long it 01:15:23.380 --> 01:15:25.720 align:middle line:84% will take for an electromagnetic wave 01:15:25.720 --> 01:15:27.750 align:middle line:84% to get from that mother clock signal to you. 01:15:27.750 --> 01:15:29.750 align:middle line:84% It can't speed up or slow down because it's just 01:15:29.750 --> 01:15:31.270 align:middle line:90% the speed of light. 01:15:31.270 --> 01:15:33.430 align:middle line:84% And so now, you say, I got the 12 o'clock 01:15:33.430 --> 01:15:36.190 align:middle line:84% signal from my relevant so-called mother clock. 01:15:36.190 --> 01:15:38.290 align:middle line:84% I now set my clock automatically to be 01:15:38.290 --> 01:15:40.720 align:middle line:90% 12 plus appropriate offset. 01:15:40.720 --> 01:15:42.980 align:middle line:84% And now, I know my clocks are synchronized. 01:15:42.980 --> 01:15:45.250 align:middle line:84% So if I had a partner standing between us, 01:15:45.250 --> 01:15:47.980 align:middle line:84% midway between say Zurich and Paris or Zurich and Bern 01:15:47.980 --> 01:15:50.200 align:middle line:84% or whatever and we did the lantern trick, 01:15:50.200 --> 01:15:53.080 align:middle line:84% we could confirm that our coordinates are now aligned. 01:15:53.080 --> 01:15:58.190 align:middle line:84% How could we agree on the time coordinates at distant events? 01:15:58.190 --> 01:15:59.410 align:middle line:90% Trade light signals. 01:15:59.410 --> 01:16:02.200 align:middle line:84% If I have a partner who's midway between me 01:16:02.200 --> 01:16:04.202 align:middle line:84% and the distant mother clock, we can make 01:16:04.202 --> 01:16:05.410 align:middle line:90% sure we're still coordinated. 01:16:05.410 --> 01:16:07.630 align:middle line:84% We can do something like a calibration 01:16:07.630 --> 01:16:09.380 align:middle line:84% by doing another trick with light signals. 01:16:09.380 --> 01:16:11.797 align:middle line:84% Did the person in the middle receive the two light signals 01:16:11.797 --> 01:16:13.660 align:middle line:84% at the same time if she was equidistant? 01:16:13.660 --> 01:16:14.230 align:middle line:90% Yes? 01:16:14.230 --> 01:16:16.400 align:middle line:84% OK, then our clocks, indeed, are synchronized. 01:16:16.400 --> 01:16:20.080 align:middle line:84% So the idea is to take advantage of this universality 01:16:20.080 --> 01:16:24.440 align:middle line:84% of electromagnetic waves, even if Bern is not literally flying 01:16:24.440 --> 01:16:26.073 align:middle line:90% past Berlin. 01:16:26.073 --> 01:16:27.740 align:middle line:84% They're not in relative motion that way, 01:16:27.740 --> 01:16:29.532 align:middle line:84% but they're still using a universal feature 01:16:29.532 --> 01:16:32.930 align:middle line:84% of electromagnetic waves and doing local coordination 01:16:32.930 --> 01:16:36.147 align:middle line:84% because that's all we can ever do because Einstein says 01:16:36.147 --> 01:16:38.480 align:middle line:84% there's no absolute standard to which we could otherwise 01:16:38.480 --> 01:16:39.380 align:middle line:90% appeal. 01:16:39.380 --> 01:16:41.812 align:middle line:90% Does that make a little sense? 01:16:41.812 --> 01:16:42.520 align:middle line:90% Great, thank you. 01:16:42.520 --> 01:16:45.340 align:middle line:84% OK, Babu-Abel says, does anyone know why [INAUDIBLE]?? 01:16:45.340 --> 01:16:47.425 align:middle line:90% Is it just a postulate? 01:16:47.425 --> 01:16:49.390 align:middle line:84% That's a really deep and hard question, Babu. 01:16:49.390 --> 01:16:54.415 align:middle line:84% So Einstein made no effort to prove this or even justify it. 01:16:54.415 --> 01:16:56.290 align:middle line:84% He didn't even tell us about his surfer idea, 01:16:56.290 --> 01:16:57.610 align:middle line:90% which was a pretty cool idea. 01:16:57.610 --> 01:17:00.110 align:middle line:84% I mean, that thought experiment is pretty awesome. 01:17:00.110 --> 01:17:01.510 align:middle line:90% It's awesome for a 16-year-old. 01:17:01.510 --> 01:17:02.890 align:middle line:90% It's awesome for a 49-year-old. 01:17:02.890 --> 01:17:04.330 align:middle line:84% It's just an awesome thought experiment. 01:17:04.330 --> 01:17:06.310 align:middle line:84% He didn't even tell his readers that, the dummy. 01:17:06.310 --> 01:17:08.185 align:middle line:84% He could have at least put that in his paper. 01:17:08.185 --> 01:17:12.490 align:middle line:84% He gives us no reason, no compelling argument 01:17:12.490 --> 01:17:15.790 align:middle line:84% in this article to take on board this very strange-sounding 01:17:15.790 --> 01:17:18.220 align:middle line:84% postulate about the constancy of the speed of light. 01:17:18.220 --> 01:17:21.220 align:middle line:84% He has that very strange, abbreviated paragraph 01:17:21.220 --> 01:17:23.320 align:middle line:84% I read out to you near the end of the class 01:17:23.320 --> 01:17:27.040 align:middle line:84% today about the failure of efforts 01:17:27.040 --> 01:17:29.530 align:middle line:84% to measure relative speed with respect 01:17:29.530 --> 01:17:30.880 align:middle line:90% to our motion in the ether. 01:17:30.880 --> 01:17:32.080 align:middle line:84% He doesn't tell us which experiments. 01:17:32.080 --> 01:17:33.490 align:middle line:84% He almost certainly doesn't mean Michaelson-Morley. 01:17:33.490 --> 01:17:36.070 align:middle line:84% So there's some modest, weak empirical evidence that 01:17:36.070 --> 01:17:38.470 align:middle line:90% seems to argue against that. 01:17:38.470 --> 01:17:40.060 align:middle line:90% He's not giving us a hard proof. 01:17:40.060 --> 01:17:42.280 align:middle line:84% In the years since then, there have 01:17:42.280 --> 01:17:45.100 align:middle line:84% been more and more ideas built up 01:17:45.100 --> 01:17:47.410 align:middle line:84% going well beyond the original framework of Einstein's 01:17:47.410 --> 01:17:50.400 align:middle line:84% own work towards, which we can appeal 01:17:50.400 --> 01:17:52.150 align:middle line:84% and we'll get a glimmer of, actually, some 01:17:52.150 --> 01:17:53.740 align:middle line:84% of those first kinds of arguments, 01:17:53.740 --> 01:17:56.557 align:middle line:84% actually in Wednesday's class, other kinds of symmetry 01:17:56.557 --> 01:17:59.140 align:middle line:84% arguments which were absolutely not the kind to which Einstein 01:17:59.140 --> 01:18:01.338 align:middle line:84% appealed at the time, that guarantees 01:18:01.338 --> 01:18:03.130 align:middle line:84% certain kinds of invariances, certain kinds 01:18:03.130 --> 01:18:05.770 align:middle line:84% of geometrical properties that we'll look at quite squarely 01:18:05.770 --> 01:18:07.210 align:middle line:90% on Wednesday's class. 01:18:07.210 --> 01:18:09.610 align:middle line:84% But in Einstein's own day, it was, frankly, 01:18:09.610 --> 01:18:10.570 align:middle line:90% an article of faith. 01:18:10.570 --> 01:18:13.090 align:middle line:84% That's why he calls it a postulate. 01:18:13.090 --> 01:18:15.220 align:middle line:84% And Stanley asks a follow-up about measuring 01:18:15.220 --> 01:18:16.428 align:middle line:90% the length of a moving train. 01:18:16.428 --> 01:18:18.512 align:middle line:84% Slicing and measuring the locations front and back 01:18:18.512 --> 01:18:20.800 align:middle line:84% at the same time, take the difference, but they did-- 01:18:20.800 --> 01:18:22.640 align:middle line:84% at the same time is not well defined. 01:18:22.640 --> 01:18:23.350 align:middle line:90% That's right. 01:18:23.350 --> 01:18:24.725 align:middle line:84% So Stanley, that's exactly right. 01:18:24.725 --> 01:18:27.040 align:middle line:84% So the idea is if our operation to measure that length 01:18:27.040 --> 01:18:29.290 align:middle line:84% is measured front and back at the same time, 01:18:29.290 --> 01:18:31.570 align:middle line:84% and we disagree about what counts as at the same time, 01:18:31.570 --> 01:18:33.070 align:middle line:84% and everything else flows from that, 01:18:33.070 --> 01:18:37.750 align:middle line:84% argues Einstein, which is why it's all about kinematics, 01:18:37.750 --> 01:18:39.100 align:middle line:90% not dynamics for him. 01:18:39.100 --> 01:18:40.540 align:middle line:84% It's all about, how do we lay down 01:18:40.540 --> 01:18:43.850 align:middle line:84% coordinates with which to reckon the motion of objects 01:18:43.850 --> 01:18:44.912 align:middle line:90% through space and time. 01:18:44.912 --> 01:18:46.370 align:middle line:84% So Stanley asks, do we need to make 01:18:46.370 --> 01:18:48.380 align:middle line:84% sure the measurements taken are simultaneous? 01:18:48.380 --> 01:18:49.220 align:middle line:90% Yes, that's right. 01:18:49.220 --> 01:18:52.070 align:middle line:84% Or rather, it's to say, our measurement of length 01:18:52.070 --> 01:18:54.860 align:middle line:84% will be relative to our reference frame. 01:18:54.860 --> 01:18:57.560 align:middle line:84% It'll be totally correct in our own reference frame, 01:18:57.560 --> 01:18:58.850 align:middle line:90% according to our coordinates. 01:18:58.850 --> 01:19:02.300 align:middle line:84% It just will no longer agree with someone's equally correct 01:19:02.300 --> 01:19:05.053 align:middle line:84% set of measurements in their own equally valid but moving 01:19:05.053 --> 01:19:05.720 align:middle line:90% reference frame. 01:19:05.720 --> 01:19:09.088 align:middle line:84% That's what is pretty hard to get our heads around. 01:19:09.088 --> 01:19:11.630 align:middle line:84% Julian says, do you even need the second postulate if you use 01:19:11.630 --> 01:19:13.255 align:middle line:84% the argument of the thought experiment. 01:19:13.255 --> 01:19:14.480 align:middle line:90% Good question, Julian. 01:19:14.480 --> 01:19:17.090 align:middle line:84% Einstein himself returned to this in later writings. 01:19:17.090 --> 01:19:18.765 align:middle line:90% If we really, really-- 01:19:18.765 --> 01:19:20.390 align:middle line:84% we'll actually come to this a bit later 01:19:20.390 --> 01:19:21.650 align:middle line:90% in Wednesday's class, too. 01:19:21.650 --> 01:19:24.950 align:middle line:84% If we really take on board that Maxwell's equation should apply 01:19:24.950 --> 01:19:26.810 align:middle line:84% equally in every frame of reference, then 01:19:26.810 --> 01:19:29.990 align:middle line:84% once you know the answer, once you're a post-Einsteinian, 01:19:29.990 --> 01:19:32.360 align:middle line:84% you can go back and say, oh Maxwell's equations 01:19:32.360 --> 01:19:35.382 align:middle line:84% are invariant with respect to the speed of light. 01:19:35.382 --> 01:19:37.590 align:middle line:84% They predict it should be the same for all observers, 01:19:37.590 --> 01:19:40.030 align:middle line:84% so maybe you just need postulate one. 01:19:40.030 --> 01:19:42.110 align:middle line:84% That's convincing if you already know the answer. 01:19:42.110 --> 01:19:45.020 align:middle line:84% Einstein, in 1905, didn't get there that way. 01:19:45.020 --> 01:19:47.697 align:middle line:84% He wrestled with whether it was an auxiliary hypothesis later 01:19:47.697 --> 01:19:48.280 align:middle line:90% in his career. 01:19:48.280 --> 01:19:49.410 align:middle line:90% That's a great question. 01:19:49.410 --> 01:19:50.070 align:middle line:90% I'm going to pause there. 01:19:50.070 --> 01:19:50.900 align:middle line:84% I know some folks will probably have 01:19:50.900 --> 01:19:52.250 align:middle line:90% to jump off for other classes. 01:19:52.250 --> 01:19:53.208 align:middle line:90% Great, great questions. 01:19:53.208 --> 01:19:55.292 align:middle line:84% Feel free to email me if you have other questions. 01:19:55.292 --> 01:19:58.220 align:middle line:84% I'll have office hours on Wednesday this week at 11:00 01:19:58.220 --> 01:19:59.060 align:middle line:90% AM Eastern. 01:19:59.060 --> 01:20:00.800 align:middle line:90% Feel free to pop in for that. 01:20:00.800 --> 01:20:03.067 align:middle line:84% And we'll pick up the story then on Wednesday. 01:20:03.067 --> 01:20:03.900 align:middle line:90% Stay well, everyone. 01:20:03.900 --> 01:20:05.560 align:middle line:90% See you soon. 01:20:05.560 --> 01:20:19.000 align:middle line:90%