WEBVTT 00:00:00.000 --> 00:00:01.988 [SQUEAKING] 00:00:01.988 --> 00:00:03.976 [RUSTLING] 00:00:03.976 --> 00:00:04.970 [CLICKING] 00:00:18.389 --> 00:00:20.390 PROFESSOR: So I'm going to come to 8.20-- 00:00:20.390 --> 00:00:21.350 Special Relativity. 00:00:21.350 --> 00:00:24.260 It's a great pleasure to introduce David Kaiser. 00:00:24.260 --> 00:00:28.520 David is a faculty in the physics department. 00:00:28.520 --> 00:00:30.780 He's also a historian of science. 00:00:30.780 --> 00:00:33.080 So he's in a super great position 00:00:33.080 --> 00:00:36.830 to talk about Einstein and special relativity 00:00:36.830 --> 00:00:39.210 and give kind of the frame for this class. 00:00:39.210 --> 00:00:42.290 So please welcome David. 00:00:42.290 --> 00:00:44.247 And take it along. 00:00:44.247 --> 00:00:45.080 DAVID KAISER: Great. 00:00:45.080 --> 00:00:46.200 Well, hello, everyone. 00:00:46.200 --> 00:00:47.000 Happy New Year. 00:00:47.000 --> 00:00:49.640 Welcome back at least virtually to MIT. 00:00:49.640 --> 00:00:52.070 It's really a great pleasure to talk with you today 00:00:52.070 --> 00:00:52.920 about this material. 00:00:52.920 --> 00:00:54.260 I love this material. 00:00:54.260 --> 00:00:57.500 So hopefully you can all see that first slide-- 00:00:57.500 --> 00:00:59.030 smiling Einstein on the bicycle. 00:00:59.030 --> 00:01:01.470 OK. 00:01:01.470 --> 00:01:04.290 So I want to talk about three main parts today 00:01:04.290 --> 00:01:06.580 for the material. 00:01:06.580 --> 00:01:09.900 And we'll talk about how all of the most 00:01:09.900 --> 00:01:15.600 accomplished physicists were thinking about motion of bodies 00:01:15.600 --> 00:01:19.020 through space and time during the middle, late years 00:01:19.020 --> 00:01:23.200 of the 19th century, roughly, say, 100 to 150 years ago, 00:01:23.200 --> 00:01:25.110 give or take, because that really sets up 00:01:25.110 --> 00:01:27.930 a pretty sharp contrast with how at the time 00:01:27.930 --> 00:01:30.270 a rather young and very little known 00:01:30.270 --> 00:01:33.660 person named Albert Einstein began asking similar questions 00:01:33.660 --> 00:01:35.620 but often in very different ways. 00:01:35.620 --> 00:01:37.620 So we'll start with some of this context of what 00:01:37.620 --> 00:01:40.350 was happening before Einstein even came on the scene 00:01:40.350 --> 00:01:43.380 to help us better make sense of why his approach seemed 00:01:43.380 --> 00:01:47.500 really so unfamiliar and so surprising at the time. 00:01:47.500 --> 00:01:49.350 And then for the last part-- 00:01:49.350 --> 00:01:51.780 I find it really fascinating, drawing on work 00:01:51.780 --> 00:01:54.450 from some of my friends and colleagues, other historians-- 00:01:54.450 --> 00:01:57.150 we'll try to ask, what was going on with Einstein? 00:01:57.150 --> 00:01:59.740 Why was Einstein's approach so different? 00:01:59.740 --> 00:02:01.740 And can we make sense of it since it wasn't just 00:02:01.740 --> 00:02:04.260 the ordinary routine that we might have otherwise expected? 00:02:04.260 --> 00:02:06.650 That's that last part about coordinating clocks. 00:02:06.650 --> 00:02:08.470 Well, let's jump right in. 00:02:08.470 --> 00:02:09.970 Let's start not with Albert Einstein 00:02:09.970 --> 00:02:13.500 but with another very familiar name, James Clerk Maxwell. 00:02:13.500 --> 00:02:16.012 I thought about growing a beard like that during COVID. 00:02:16.012 --> 00:02:17.220 I haven't made much progress. 00:02:17.220 --> 00:02:22.020 But that's a typical 19th century, fine Cambridge beard-- 00:02:22.020 --> 00:02:23.640 Cambridge, England. 00:02:23.640 --> 00:02:25.950 So we all know Maxwell's name. 00:02:25.950 --> 00:02:28.830 Many of you probably own a t-shirt 00:02:28.830 --> 00:02:31.800 with Maxwell's equations on it. 00:02:31.800 --> 00:02:33.000 If you do, I'm very jealous. 00:02:33.000 --> 00:02:34.042 I don't have one anymore. 00:02:34.042 --> 00:02:37.440 Anyway, so we still use his approach 00:02:37.440 --> 00:02:40.590 to electromagnetism, as of course you all know very well. 00:02:40.590 --> 00:02:42.360 And we've been able to boil it down 00:02:42.360 --> 00:02:45.300 to basically a tweet or a single t-shirt. 00:02:45.300 --> 00:02:46.980 It turns out, as you may know, what 00:02:46.980 --> 00:02:51.450 we now call Maxwell's equations were hammered out by Maxwell 00:02:51.450 --> 00:02:53.160 and actually some other colleagues 00:02:53.160 --> 00:02:56.130 during the 1860s and early 1870s, 00:02:56.130 --> 00:02:58.620 so approximately 150 years ago. 00:02:58.620 --> 00:03:00.640 And in fact when he first wrote them down, 00:03:00.640 --> 00:03:02.910 they weren't in such a nice, compact form. 00:03:02.910 --> 00:03:07.620 It was in a 900-page, two-volume treatise that was first 00:03:07.620 --> 00:03:09.480 published in 1873-- 00:03:09.480 --> 00:03:11.640 two volumes, a total of 900 pages. 00:03:11.640 --> 00:03:12.463 It was a weapon. 00:03:12.463 --> 00:03:14.130 You could hurt someone with these books, 00:03:14.130 --> 00:03:16.740 it was so fat, even though now we can boil it down 00:03:16.740 --> 00:03:18.570 to a simple t-shirt. 00:03:18.570 --> 00:03:20.640 And so what's even more interesting to me 00:03:20.640 --> 00:03:24.090 is that even though we still use Maxwell's equations, what 00:03:24.090 --> 00:03:26.220 we think they say about the world 00:03:26.220 --> 00:03:28.080 is really, really different than what 00:03:28.080 --> 00:03:30.600 Maxwell and his immediate circle thought. 00:03:30.600 --> 00:03:32.490 And the biggest difference of all 00:03:32.490 --> 00:03:35.580 is that for Maxwell and really for all of his contemporaries 00:03:35.580 --> 00:03:39.420 and his students, the equations of electricity and magnetism, 00:03:39.420 --> 00:03:41.820 as far as they were concerned, had everything 00:03:41.820 --> 00:03:44.940 to do with some physical substance, 00:03:44.940 --> 00:03:48.300 a medium that they called the ether that they assumed 00:03:48.300 --> 00:03:51.600 must be spread evenly throughout the entire universe, 00:03:51.600 --> 00:03:54.190 filling every nook and cranny of space. 00:03:54.190 --> 00:03:56.310 So all of the phenomena that we would associate 00:03:56.310 --> 00:04:00.030 with electricity or magnetism, the flow of currents, 00:04:00.030 --> 00:04:03.970 the splaying of iron filings around a bar magnet, 00:04:03.970 --> 00:04:06.240 and even much more complicated things, 00:04:06.240 --> 00:04:10.650 to Maxwell and his group, these were all just 00:04:10.650 --> 00:04:15.420 evidence of the state of stress of this underlying 00:04:15.420 --> 00:04:16.140 physical medium. 00:04:16.140 --> 00:04:19.709 It was like a springy, substantial, resistive medium 00:04:19.709 --> 00:04:21.185 that they called the ether. 00:04:21.185 --> 00:04:23.310 And he says that in the opening pages, for example, 00:04:23.310 --> 00:04:26.130 of his now very famous treatise and throughout, 00:04:26.130 --> 00:04:28.830 that the whole point of studying this field, as far as he 00:04:28.830 --> 00:04:32.610 was concerned, was to study the behavior of the distribution 00:04:32.610 --> 00:04:35.850 of stress in this medium extending continuously 00:04:35.850 --> 00:04:38.400 throughout the universe, the ether. 00:04:38.400 --> 00:04:40.050 It wasn't just Maxwell. 00:04:40.050 --> 00:04:44.100 His a little bit more senior colleague, William Thomson, 00:04:44.100 --> 00:04:47.160 who went on to be known as Lord Kelvin, like the Kelvin 00:04:47.160 --> 00:04:48.870 temperature scale and many things 00:04:48.870 --> 00:04:53.460 we still use from Thomson's work, 00:04:53.460 --> 00:04:57.330 he wanted to give a sense to non-scientists 00:04:57.330 --> 00:05:00.360 a few years later in a popular lecture what 00:05:00.360 --> 00:05:01.860 all the excitement was about. 00:05:01.860 --> 00:05:03.420 He said, here's what we're doing. 00:05:03.420 --> 00:05:05.420 We want you to get a sense for what we're doing. 00:05:05.420 --> 00:05:07.980 We're studying the physics of this elastic, physical medium 00:05:07.980 --> 00:05:09.240 called the ether. 00:05:09.240 --> 00:05:12.390 And he instructed his very elite, very fancy audience 00:05:12.390 --> 00:05:14.940 who went to one of these popular lectures, 00:05:14.940 --> 00:05:17.700 stick your hand in a bowl of jelly, he tells them. 00:05:17.700 --> 00:05:19.642 And see how it wiggles and vibrates 00:05:19.642 --> 00:05:20.850 as you move your hand around. 00:05:20.850 --> 00:05:25.080 That's the highest of high-end physics in the 1860s and '70s. 00:05:25.080 --> 00:05:26.970 It was all about understanding the behavior 00:05:26.970 --> 00:05:30.840 of this elastic medium called the ether. 00:05:30.840 --> 00:05:34.740 And that had very specific follow-on implications 00:05:34.740 --> 00:05:35.710 for this group. 00:05:35.710 --> 00:05:38.400 So one of the first things that you all know already, 00:05:38.400 --> 00:05:41.640 one of the most exciting features of Maxwell's work 00:05:41.640 --> 00:05:46.710 that really got himself excited and solidified his reputation 00:05:46.710 --> 00:05:49.740 was this unexpected unification that he put together 00:05:49.740 --> 00:05:51.420 in the 1860s. 00:05:51.420 --> 00:05:53.160 Not only was there a deep relationship 00:05:53.160 --> 00:05:55.140 between electricity and magnetism. 00:05:55.140 --> 00:05:58.050 That had been wondered about but never really formalized. 00:05:58.050 --> 00:06:01.890 But even more surprising, that these two areas, 00:06:01.890 --> 00:06:04.260 electricity and magnetism, were also 00:06:04.260 --> 00:06:08.130 deeply associated with optics, with the propagation of light. 00:06:08.130 --> 00:06:10.500 So it was Maxwell, as I'm sure you know and probably 00:06:10.500 --> 00:06:12.240 have already done this on problem sets 00:06:12.240 --> 00:06:13.770 by now yourselves-- 00:06:13.770 --> 00:06:15.510 using Maxwell's equations, you can 00:06:15.510 --> 00:06:20.220 derive the quantitative behavior of light 00:06:20.220 --> 00:06:22.110 as it travels through space. 00:06:22.110 --> 00:06:25.530 Light, as Maxwell intuited, was nothing 00:06:25.530 --> 00:06:28.800 but a certain pattern of propagating 00:06:28.800 --> 00:06:31.380 electric and magnetic fields. 00:06:31.380 --> 00:06:35.160 Again, to Maxwell, these were propagating in this material, 00:06:35.160 --> 00:06:36.570 physical ether. 00:06:36.570 --> 00:06:39.510 They were disturbances propagating, 00:06:39.510 --> 00:06:42.960 skittering through this physical stuff that filled all of space. 00:06:42.960 --> 00:06:45.900 And in fact, by trying to calculate the speed 00:06:45.900 --> 00:06:49.830 with which disturbances would travel through space based 00:06:49.830 --> 00:06:51.510 on other properties of the ether that he 00:06:51.510 --> 00:06:53.177 and his colleagues had already measured, 00:06:53.177 --> 00:06:55.410 basically sets up like spring constants, 00:06:55.410 --> 00:06:57.900 he found that the speed of propagation 00:06:57.900 --> 00:07:00.930 would be equal to the value that had already 00:07:00.930 --> 00:07:04.470 been calculated many years before for the speed with which 00:07:04.470 --> 00:07:06.130 light travels. 00:07:06.130 --> 00:07:09.000 And he says in his own words, in this lovely old-fashioned 00:07:09.000 --> 00:07:13.110 phrasing, "The velocity of transverse undulations"-- 00:07:13.110 --> 00:07:15.240 a certain kind of wave-- 00:07:15.240 --> 00:07:18.480 "in our hypothetical medium agrees so exactly 00:07:18.480 --> 00:07:20.760 with the velocity of light calculated 00:07:20.760 --> 00:07:24.000 from optical experiments"-- mostly astronomy at the time-- 00:07:24.000 --> 00:07:26.370 "that we can scarcely avoid the inference 00:07:26.370 --> 00:07:29.910 that light consists of the transverse undulations 00:07:29.910 --> 00:07:32.490 of the same medium which is the cause 00:07:32.490 --> 00:07:34.200 of electric and magnetic phenomena." 00:07:34.200 --> 00:07:36.060 That's why his book was 900 pages, right? 00:07:36.060 --> 00:07:37.110 Today we can put in on a t-shirt. 00:07:37.110 --> 00:07:39.527 He was really just walking through this very old fashioned 00:07:39.527 --> 00:07:41.340 language to come to the point saying 00:07:41.340 --> 00:07:46.140 light was nothing but a certain kind of pattern in the ether. 00:07:46.140 --> 00:07:49.320 And so in fact they often called this not just the ether 00:07:49.320 --> 00:07:50.970 but an even fancier name. 00:07:50.970 --> 00:07:53.070 They called it the luminiferous ether. 00:07:53.070 --> 00:07:56.730 And from the Latin, it means "light bearing" 00:07:56.730 --> 00:07:58.080 or "light carrying." 00:07:58.080 --> 00:08:02.190 So "lumin", like "lumos" for you Harry Potter fans, that part 00:08:02.190 --> 00:08:03.240 you probably recognize. 00:08:03.240 --> 00:08:05.730 And the "ferous" is like a Ferris wheel. 00:08:05.730 --> 00:08:10.690 That means, like, to carry or to move through space. 00:08:10.690 --> 00:08:14.130 So this was the light-bearing or light-carrying ether. 00:08:14.130 --> 00:08:15.840 And that's what Maxwell and really all 00:08:15.840 --> 00:08:17.580 of his contemporaries were convinced 00:08:17.580 --> 00:08:20.160 was most exciting about Maxwell's work, 00:08:20.160 --> 00:08:21.720 that this was a way of characterizing 00:08:21.720 --> 00:08:25.470 the state of the ether including these optical phenomena. 00:08:25.470 --> 00:08:30.180 OK, so that's where things stood in the 1860s and 1870s. 00:08:30.180 --> 00:08:32.830 But that led to a whole new set of questions. 00:08:32.830 --> 00:08:36.480 And the next generation quite understandably 00:08:36.480 --> 00:08:38.039 wanted to kind of follow up on that 00:08:38.039 --> 00:08:41.880 and ask ways to generalize that framework. 00:08:41.880 --> 00:08:44.010 Maxwell's work had really assumed 00:08:44.010 --> 00:08:46.800 that there was no relative motion between either 00:08:46.800 --> 00:08:49.348 the source of light or the receiver of light, 00:08:49.348 --> 00:08:51.390 that everything was analyzed in what we would now 00:08:51.390 --> 00:08:55.530 call the same rest frame, or frame of reference, 00:08:55.530 --> 00:08:57.060 as the ether itself. 00:08:57.060 --> 00:08:59.640 But of course that wasn't the most general situation, 00:08:59.640 --> 00:09:04.200 as Maxwell's own contemporaries or the next younger generation 00:09:04.200 --> 00:09:05.790 began to wonder about. 00:09:05.790 --> 00:09:08.250 One of the most influential of that next wave 00:09:08.250 --> 00:09:10.800 is this gentleman shown here, Hendrik Lorentz 00:09:10.800 --> 00:09:13.320 from the Netherlands, from Leiden. 00:09:13.320 --> 00:09:16.830 So Lorentz wanted to ask about the electrodynamics of moving 00:09:16.830 --> 00:09:17.340 bodies. 00:09:17.340 --> 00:09:21.000 What if either the emitter of light or the receiver or both 00:09:21.000 --> 00:09:24.630 were moving with respect to this all-pervasive medium? 00:09:24.630 --> 00:09:26.760 And so Lorentz, as we'll see, had 00:09:26.760 --> 00:09:29.970 really two distinct motivations in mind 00:09:29.970 --> 00:09:33.420 when he tried to think about the electrodynamics of moving 00:09:33.420 --> 00:09:37.380 bodies, or let's say optics for moving sources or receivers. 00:09:37.380 --> 00:09:40.095 He had a kind of mathematical set of quandaries. 00:09:40.095 --> 00:09:42.870 And we'll talk about those first. 00:09:42.870 --> 00:09:46.600 But he also had a series of very puzzling experimental results. 00:09:46.600 --> 00:09:48.900 So he had an empirical set of ideas 00:09:48.900 --> 00:09:51.000 that we'll come to in a moment and also these more 00:09:51.000 --> 00:09:52.380 formal or mathematical. 00:09:52.380 --> 00:09:54.750 We'll start with the math. 00:09:54.750 --> 00:09:58.050 Lorentz was really one of the best-trained, leading 00:09:58.050 --> 00:10:00.390 mathematical physicists of his age. 00:10:00.390 --> 00:10:03.150 So he knew very well how to handle relative motion. 00:10:03.150 --> 00:10:06.330 Galileo had derived that in the 1610s. 00:10:06.330 --> 00:10:09.510 That was hardly news in the 1890s. 00:10:09.510 --> 00:10:12.570 We would do what we still call the Galileo-Newton 00:10:12.570 --> 00:10:14.670 transformation. 00:10:14.670 --> 00:10:16.770 For example, Galileo wrote very famously 00:10:16.770 --> 00:10:20.580 in his charming dialogues in the 17th century, 00:10:20.580 --> 00:10:23.850 if you watch your friend float down a river on a boat that 00:10:23.850 --> 00:10:26.850 moves at a constant speed, neither speeding up nor slowing 00:10:26.850 --> 00:10:28.890 down, then you know very well how 00:10:28.890 --> 00:10:31.760 to compare the coordinates between you, sitting 00:10:31.760 --> 00:10:34.280 at rest on the bank of that river, 00:10:34.280 --> 00:10:37.670 and your friend as she floats down on her boat, 00:10:37.670 --> 00:10:40.280 that what you call the origin, the spatial origin, 00:10:40.280 --> 00:10:43.730 of your coordinate system, you can fix at, say, x equals 0. 00:10:43.730 --> 00:10:46.460 But your friend could call the center of her boat 00:10:46.460 --> 00:10:48.530 the origin for her coordinate system. 00:10:48.530 --> 00:10:53.450 And then you can see how her system coordinates will 00:10:53.450 --> 00:10:55.320 move with respect to yours. 00:10:55.320 --> 00:10:57.530 If the boat moves at a constant speed, 00:10:57.530 --> 00:11:00.650 little v, then you just have to calculate 00:11:00.650 --> 00:11:04.430 the offset between where the origin, the center of her boat, 00:11:04.430 --> 00:11:08.000 is as it floats further and further down the river. 00:11:08.000 --> 00:11:12.260 So what she calls the origin of her spatial coordinates 00:11:12.260 --> 00:11:15.050 will be offset from yours because this relative motion, 00:11:15.050 --> 00:11:16.550 this relative drift. 00:11:16.550 --> 00:11:19.100 Meanwhile, as Newton himself famously said 00:11:19.100 --> 00:11:22.520 in the beginning of his Principia 00:11:22.520 --> 00:11:25.370 where we learn about Newton's laws of mechanics, 00:11:25.370 --> 00:11:26.900 that time is time is time. 00:11:26.900 --> 00:11:28.460 There's some absolute time. 00:11:28.460 --> 00:11:30.950 He actually referred it to the sensorium of God. 00:11:30.950 --> 00:11:34.080 He thought there was only one possible time to consider. 00:11:34.080 --> 00:11:35.690 And so formally there'd be no change 00:11:35.690 --> 00:11:37.940 to the rate at which your clock ticked 00:11:37.940 --> 00:11:40.730 versus the rate at which your friend's clock ticked 00:11:40.730 --> 00:11:41.810 on her boat. 00:11:41.810 --> 00:11:44.180 This is called the Galileo-Newton transformation. 00:11:44.180 --> 00:11:45.380 I made a big deal out of it. 00:11:45.380 --> 00:11:47.380 You probably would have done this in your sleep. 00:11:47.380 --> 00:11:49.260 Lorentz did this in his sleep. 00:11:49.260 --> 00:11:51.085 However, it drove him to nightmares 00:11:51.085 --> 00:11:52.460 because when he then applied this 00:11:52.460 --> 00:11:54.770 to Maxwell's really beautiful and much newer 00:11:54.770 --> 00:11:56.780 set of equations for things like optics 00:11:56.780 --> 00:12:00.020 or the propagation of electric and magnetic disturbances 00:12:00.020 --> 00:12:02.180 in the ether, he found that in that 00:12:02.180 --> 00:12:04.220 transformed reference frame if you 00:12:04.220 --> 00:12:07.550 take into account that relative motion between either emitter 00:12:07.550 --> 00:12:11.300 or receiver of light, then Maxwell's beautiful description 00:12:11.300 --> 00:12:15.470 of light, his quantitative description, looked very ugly. 00:12:15.470 --> 00:12:17.330 And in particular, it would no longer 00:12:17.330 --> 00:12:20.300 suggest that light should behave as oscillating 00:12:20.300 --> 00:12:21.770 sines and cosines. 00:12:21.770 --> 00:12:23.760 It worked beautifully with Maxwell's equations 00:12:23.760 --> 00:12:29.090 if you look only at both sources and receivers of light that 00:12:29.090 --> 00:12:31.880 are fixed in place and not moving with respect 00:12:31.880 --> 00:12:32.870 to the ether. 00:12:32.870 --> 00:12:36.560 Once you apply the very, very well-known transformation 00:12:36.560 --> 00:12:38.330 to take into account relative motion, 00:12:38.330 --> 00:12:41.120 then your description of light gets all literally out 00:12:41.120 --> 00:12:42.020 of whack. 00:12:42.020 --> 00:12:44.750 And this was a mathematical conundrum for Lorentz. 00:12:44.750 --> 00:12:47.060 It didn't seem to make any sense because on the Earth, 00:12:47.060 --> 00:12:50.762 on the moving Earth presumably moving through the ether, 00:12:50.762 --> 00:12:52.220 he and his colleagues could measure 00:12:52.220 --> 00:12:55.590 light to behave like beautiful sines and cosines all the time. 00:12:55.590 --> 00:13:00.170 So we have an empirical reminder that Maxwell's description 00:13:00.170 --> 00:13:03.260 seems really, really accurate for describing optics 00:13:03.260 --> 00:13:06.020 even on our own moving ship of the Earth. 00:13:06.020 --> 00:13:08.340 So this is a real conundrum for him. 00:13:08.340 --> 00:13:10.760 He was a very, very clever, mathematically 00:13:10.760 --> 00:13:12.860 gifted physicist. 00:13:12.860 --> 00:13:15.080 So he introduced a mathematical clue. 00:13:15.080 --> 00:13:20.210 He introduced a mathematical stopgap to address this. 00:13:20.210 --> 00:13:22.160 He called it local time. 00:13:22.160 --> 00:13:24.140 And he was actually very clear in his writings. 00:13:24.140 --> 00:13:26.160 He said it was a mathematical fiction-- 00:13:26.160 --> 00:13:26.660 his word. 00:13:26.660 --> 00:13:29.780 It was literally just a mathematical trick. 00:13:29.780 --> 00:13:31.970 If he introduced a new transformation 00:13:31.970 --> 00:13:35.840 for the time variable, so when you compare your coordinates 00:13:35.840 --> 00:13:37.770 with those of your friend on the boat, 00:13:37.770 --> 00:13:41.600 what if you actually did make a transformation of t prime, 00:13:41.600 --> 00:13:43.580 not just of x prime? 00:13:43.580 --> 00:13:45.650 And the transformation he kind of worked out, 00:13:45.650 --> 00:13:47.690 he reverse engineered the form it 00:13:47.690 --> 00:13:50.690 would need to have so that Maxwell's description 00:13:50.690 --> 00:13:54.470 of light waves would be restored to the very simple form 00:13:54.470 --> 00:13:57.600 that Maxwell himself had written down a few years earlier. 00:13:57.600 --> 00:13:59.810 So this is where we still call this the Lorentz 00:13:59.810 --> 00:14:00.590 transformation. 00:14:00.590 --> 00:14:01.550 Many of you might have seen it. 00:14:01.550 --> 00:14:03.717 If not, you'll have plenty of time to learn about it 00:14:03.717 --> 00:14:05.480 and practice it during IAP. 00:14:05.480 --> 00:14:07.490 We call it Lorentz, not Einstein, 00:14:07.490 --> 00:14:10.820 because Lorentz derived these equations first in a series 00:14:10.820 --> 00:14:13.250 of papers in the 1890s. 00:14:13.250 --> 00:14:16.340 And he was responding to this question of the electrodynamics 00:14:16.340 --> 00:14:17.300 of moving bodies. 00:14:17.300 --> 00:14:20.630 How do you preserve this beautiful description of light 00:14:20.630 --> 00:14:24.080 from Maxwell even if there's relative motion with respect 00:14:24.080 --> 00:14:25.100 to the ether? 00:14:25.100 --> 00:14:26.190 He said it was a trick. 00:14:26.190 --> 00:14:27.380 It was merely mathematics. 00:14:27.380 --> 00:14:31.180 But it would at least get the right form back. 00:14:31.180 --> 00:14:33.540 So that was the mathematical motivation. 00:14:33.540 --> 00:14:35.730 Lorentz, as we know, was also concerned 00:14:35.730 --> 00:14:39.180 about an empirical or experimental curiosity. 00:14:39.180 --> 00:14:41.850 He was following very closely the work 00:14:41.850 --> 00:14:44.460 of a US-based physicist named Albert Michelson. 00:14:44.460 --> 00:14:46.270 Michelson's story is really fascinating. 00:14:46.270 --> 00:14:49.290 I won't take too much time now, but super interesting. 00:14:49.290 --> 00:14:53.010 He was actually an immigrant from what's now Germany, 00:14:53.010 --> 00:14:55.650 was often part of Poland, central Europe. 00:14:55.650 --> 00:14:58.050 He moved to the US when he was about two years old, very 00:14:58.050 --> 00:14:59.910 young, and was raised right around the time 00:14:59.910 --> 00:15:01.932 of the gold rush in California. 00:15:01.932 --> 00:15:03.390 And before I get carried away, I'll 00:15:03.390 --> 00:15:04.800 stop talking about Michelson, although he's 00:15:04.800 --> 00:15:05.670 super interesting. 00:15:05.670 --> 00:15:08.400 So what Michelson wound up doing was 00:15:08.400 --> 00:15:11.250 he was fascinated by this question of Maxwell waves, 00:15:11.250 --> 00:15:14.730 of waves of electricity and magnetism in the ether. 00:15:14.730 --> 00:15:16.920 And he was convinced that if we are on this moving 00:15:16.920 --> 00:15:19.560 ship of the Earth moving through the ether, 00:15:19.560 --> 00:15:23.370 that should have a measurable impact on the light waves 00:15:23.370 --> 00:15:27.600 that we can produce and measure here on Earth. 00:15:27.600 --> 00:15:30.250 So he set really his life's goal starting from very, 00:15:30.250 --> 00:15:32.850 very early trying to build devices, 00:15:32.850 --> 00:15:35.550 extremely sensitive instruments with which 00:15:35.550 --> 00:15:37.530 he could measure the fact that the Earth was 00:15:37.530 --> 00:15:40.080 moving through this ether. 00:15:40.080 --> 00:15:42.090 Like all his contemporaries, Michelson 00:15:42.090 --> 00:15:44.820 believed without any hesitation that there must 00:15:44.820 --> 00:15:48.030 exist the material, the ether. 00:15:48.030 --> 00:15:51.630 What else could light waves be but disturbances in the ether? 00:15:51.630 --> 00:15:53.820 And then he figured that much like 00:15:53.820 --> 00:15:57.540 if a bicyclist going for a bike ride, 00:15:57.540 --> 00:15:59.040 we should be able to tell that we're 00:15:59.040 --> 00:16:00.550 moving through that medium. 00:16:00.550 --> 00:16:03.390 So before I describe his device called the interferometer, 00:16:03.390 --> 00:16:06.300 let me just give a little more of an analogy for why Michelson 00:16:06.300 --> 00:16:09.690 was so convinced there should be a measurable effect. 00:16:09.690 --> 00:16:12.900 If we walk outside our houses, which is now a luxury-- 00:16:12.900 --> 00:16:15.000 we can still do it with masks on-- 00:16:15.000 --> 00:16:18.930 walk outside on a still day when there's no wind or no breeze, 00:16:18.930 --> 00:16:21.090 we won't feel any particular wind on our face 00:16:21.090 --> 00:16:22.660 if we're standing still. 00:16:22.660 --> 00:16:24.460 So we're outside in a physical medium. 00:16:24.460 --> 00:16:26.230 There's a physical atmosphere. 00:16:26.230 --> 00:16:28.740 But if we're at rest with respect to that atmosphere, 00:16:28.740 --> 00:16:31.620 if there's no wind, we don't feel it on our face. 00:16:31.620 --> 00:16:34.170 On the other hand, if it's still a still day, 00:16:34.170 --> 00:16:36.780 there's no breeze, when we get on our bicycle 00:16:36.780 --> 00:16:40.290 and pedal really quickly, we'll now feel a breeze on our face 00:16:40.290 --> 00:16:43.290 because we're moving through that physical medium. 00:16:43.290 --> 00:16:45.510 We're moving through the Earth's atmosphere. 00:16:45.510 --> 00:16:47.670 Even if the atmosphere seems to be perfectly 00:16:47.670 --> 00:16:49.920 at rest, no strong breeze, no hurricane, 00:16:49.920 --> 00:16:52.560 whatever, if we're going quickly enough through it, 00:16:52.560 --> 00:16:54.450 we'll feel a breeze on our face. 00:16:54.450 --> 00:16:55.950 And Michelson thought the same thing 00:16:55.950 --> 00:16:57.930 should be happening for light waves 00:16:57.930 --> 00:17:01.980 as they are carried by the Earth through this medium, not 00:17:01.980 --> 00:17:05.400 the Earth's atmosphere but this all-pervasive, light-bearing 00:17:05.400 --> 00:17:06.240 ether. 00:17:06.240 --> 00:17:08.430 So he really thought it would be like the bicyclist. 00:17:08.430 --> 00:17:12.000 Now, his real genius was devising this device, 00:17:12.000 --> 00:17:13.800 we now call it the interferometer, 00:17:13.800 --> 00:17:15.390 with which he could try to measure 00:17:15.390 --> 00:17:19.140 the impact of that motion of the Earth, the entire Earth, 00:17:19.140 --> 00:17:20.640 through the medium. 00:17:20.640 --> 00:17:22.260 So he took a source of light. 00:17:22.260 --> 00:17:24.960 Today we use lasers because they're awesome 00:17:24.960 --> 00:17:26.640 and they're also monochromatic. 00:17:26.640 --> 00:17:30.540 Their light shines basically at one frequency, or very 00:17:30.540 --> 00:17:32.040 dominantly one frequency. 00:17:32.040 --> 00:17:34.530 Lasers of course weren't available to Michelson. 00:17:34.530 --> 00:17:38.040 So he used very bright sodium arc lamps. 00:17:38.040 --> 00:17:41.580 Sodium lamps will shine mostly at one dominant color, 00:17:41.580 --> 00:17:43.770 not nearly so monochromatic as modern lasers. 00:17:43.770 --> 00:17:46.600 But they were the industry standard at the time. 00:17:46.600 --> 00:17:48.060 So he basically took sodium lamps 00:17:48.060 --> 00:17:51.270 that mostly shine a particular yellow color, shined them 00:17:51.270 --> 00:17:53.490 at what we now call a beam splitter. 00:17:53.490 --> 00:17:56.340 It was a half-silvered mirror, as its name implies, 00:17:56.340 --> 00:17:58.290 that would let half the light through. 00:17:58.290 --> 00:18:01.240 It would act like a window roughly half the time. 00:18:01.240 --> 00:18:03.850 But it would act like a mirror the other half of the time. 00:18:03.850 --> 00:18:07.050 So half of this incident beam will go right through this 00:18:07.050 --> 00:18:09.420 as if it were just a plate of glass. 00:18:09.420 --> 00:18:11.010 It would be transmitted. 00:18:11.010 --> 00:18:13.470 It will then make its way to a fully reflecting mirror-- 00:18:13.470 --> 00:18:16.385 sorry-- a fully reflecting mirror at the end of the path. 00:18:16.385 --> 00:18:17.760 It'll be reflected and come back. 00:18:17.760 --> 00:18:20.400 And then, again, half of that return light 00:18:20.400 --> 00:18:23.910 will be reflected by the mirror and come out to a screen. 00:18:23.910 --> 00:18:26.190 Meanwhile, you can run the same kind of story 00:18:26.190 --> 00:18:29.190 for light that gets deflected towards path 2. 00:18:29.190 --> 00:18:32.400 From that same, single incident source, 00:18:32.400 --> 00:18:33.900 half of the incident beam will be 00:18:33.900 --> 00:18:36.990 reflected by that beam splitter, that half-silvered mirror. 00:18:36.990 --> 00:18:40.300 It'll travel a path down to a fully reflecting mirror, come 00:18:40.300 --> 00:18:40.800 back. 00:18:40.800 --> 00:18:43.900 And then half of that returning light will be transmitted. 00:18:43.900 --> 00:18:46.350 So you have light coming together on some detector 00:18:46.350 --> 00:18:49.500 screen, that it started out as a single light wave 00:18:49.500 --> 00:18:52.350 from a single, nearly monochromatic source. 00:18:52.350 --> 00:18:54.570 But you split it into two beams so the beams 00:18:54.570 --> 00:18:56.490 travel different paths. 00:18:56.490 --> 00:18:59.640 And now the light starts out fully in phase with itself. 00:18:59.640 --> 00:19:00.660 It's one light beam. 00:19:00.660 --> 00:19:03.720 So crests are with crests and troughs with troughs. 00:19:03.720 --> 00:19:05.580 And the idea was that you then split 00:19:05.580 --> 00:19:09.270 it to set up a race to see if there 00:19:09.270 --> 00:19:11.820 was any difference in the travel for light 00:19:11.820 --> 00:19:13.740 that traveled through path 1 and out 00:19:13.740 --> 00:19:15.750 to the screen versus light that traveled 00:19:15.750 --> 00:19:18.090 path 2 and back to the screen. 00:19:18.090 --> 00:19:21.420 All the light starts as a single light wave in sync or in phase 00:19:21.420 --> 00:19:22.380 with itself. 00:19:22.380 --> 00:19:25.110 If there was any difference in the travels 00:19:25.110 --> 00:19:26.970 of that light between path 1 and path 2, 00:19:26.970 --> 00:19:30.210 you should see a shift in the interference pattern. 00:19:30.210 --> 00:19:33.120 Crests should no longer arrive lining up with crests 00:19:33.120 --> 00:19:34.210 or troughs with troughs. 00:19:34.210 --> 00:19:35.877 You should see a very characteristic set 00:19:35.877 --> 00:19:37.140 of interference fringes. 00:19:37.140 --> 00:19:38.880 What is called an interferometer, 00:19:38.880 --> 00:19:41.070 extremely sensitive. 00:19:41.070 --> 00:19:43.980 Now, his idea was if, like the bicyclist, 00:19:43.980 --> 00:19:47.700 we're on the moving Earth, then the path is heading directly 00:19:47.700 --> 00:19:48.720 into the ether. 00:19:48.720 --> 00:19:51.780 That is, say, the path that's along the Earth's motion 00:19:51.780 --> 00:19:54.840 through the ether should be just like the bicyclists feeling 00:19:54.840 --> 00:19:58.260 the direct headwind of that breeze directly 00:19:58.260 --> 00:20:00.900 on her or his face. 00:20:00.900 --> 00:20:02.650 That means the effective speed-- 00:20:02.650 --> 00:20:05.160 let's say this is the direction of the Earth's motion. 00:20:05.160 --> 00:20:07.080 The effective speed with which this light beam 00:20:07.080 --> 00:20:09.180 could travel toward its mirror should 00:20:09.180 --> 00:20:13.530 be experiencing a direct headwind for its upward path 00:20:13.530 --> 00:20:16.350 and a direct tailwind for its downward path. 00:20:16.350 --> 00:20:19.290 It should have a different speed than the light that 00:20:19.290 --> 00:20:22.530 follows the more orthogonal path so that even the light starts 00:20:22.530 --> 00:20:24.750 out perfectly in phase, you should find 00:20:24.750 --> 00:20:26.430 a shift in the interference fringes 00:20:26.430 --> 00:20:30.270 because the light's effective speed through the medium 00:20:30.270 --> 00:20:32.880 is different for path 1 than path 2-- 00:20:32.880 --> 00:20:35.100 again, an analogy to the ether wind of a bicyclist 00:20:35.100 --> 00:20:37.060 through the atmosphere. 00:20:37.060 --> 00:20:39.820 Not only that-- a little foreshadowing 00:20:39.820 --> 00:20:41.050 for what's to come later-- 00:20:41.050 --> 00:20:43.240 this device is so sensitive, it's 00:20:43.240 --> 00:20:47.240 sensitive to second order in a very small quantity. 00:20:47.240 --> 00:20:51.790 So it could measure differences to the second order 00:20:51.790 --> 00:20:55.120 in the relative speed of, say, the Earth through the ether 00:20:55.120 --> 00:20:58.040 compared to the speed of light. 00:20:58.040 --> 00:21:00.220 So that's called a second order because it goes 00:21:00.220 --> 00:21:02.200 this small quantity squared. 00:21:02.200 --> 00:21:04.450 That's how sensitive this really ingenious device was. 00:21:04.450 --> 00:21:06.280 And as many of you might know, we 00:21:06.280 --> 00:21:08.800 use interferometers all the time now in all kinds 00:21:08.800 --> 00:21:10.060 of industrial applications. 00:21:10.060 --> 00:21:12.010 Even more, my favorite example is 00:21:12.010 --> 00:21:16.510 from our friends who detect gravitational waves with LIGO. 00:21:16.510 --> 00:21:19.060 That's essentially a super-sized interferometer 00:21:19.060 --> 00:21:21.610 with very, very similar principles of design. 00:21:21.610 --> 00:21:24.670 So Michelson was doing this really cool work. 00:21:24.670 --> 00:21:26.350 It was among the earliest work that any 00:21:26.350 --> 00:21:29.050 of the super fancy, elite European scientists 00:21:29.050 --> 00:21:31.660 paid any attention to coming out of the US. 00:21:31.660 --> 00:21:33.190 Michelson was among the first who 00:21:33.190 --> 00:21:36.250 made even the people like Hendrik Lorentz sit up and pay 00:21:36.250 --> 00:21:39.850 attention at a time when the US was still otherwise pretty much 00:21:39.850 --> 00:21:41.680 a scientific backwater. 00:21:41.680 --> 00:21:43.060 So it's a really cool idea. 00:21:43.060 --> 00:21:46.690 It's a remarkably clever design for a device. 00:21:46.690 --> 00:21:48.670 Michelson built a small prototype. 00:21:48.670 --> 00:21:51.760 Then he super sized it with his colleague Edward Morley. 00:21:51.760 --> 00:21:54.130 They built a device 11 meters long 00:21:54.130 --> 00:21:57.610 for each arm, so roughly 33 or 34 feet long-- 00:21:57.610 --> 00:22:00.940 huge, huge for its day, very long arms. 00:22:00.940 --> 00:22:03.290 They floated the whole thing in a vat of mercury, 00:22:03.290 --> 00:22:04.450 which I don't recommend. 00:22:04.450 --> 00:22:06.760 But they were trying to tamp down any vibrations 00:22:06.760 --> 00:22:09.040 from nearby cable cars. 00:22:09.040 --> 00:22:11.320 They wanted to have a clean laboratory environment. 00:22:11.320 --> 00:22:13.000 Then they did this for years and years 00:22:13.000 --> 00:22:15.340 and years, months and months and years and years 00:22:15.340 --> 00:22:16.780 because, of course, you never know 00:22:16.780 --> 00:22:21.040 what the ether's actual rest frame is. 00:22:21.040 --> 00:22:22.690 Who's to say that at this moment, 00:22:22.690 --> 00:22:24.348 this is the direction of the Earth's 00:22:24.348 --> 00:22:25.390 motion through the ether? 00:22:25.390 --> 00:22:28.300 Maybe it's this direction or some other angle in between. 00:22:28.300 --> 00:22:30.790 They would look for day to night variations. 00:22:30.790 --> 00:22:32.590 They would look for annual variations 00:22:32.590 --> 00:22:34.840 as the Earth went around its orbit around the sun. 00:22:34.840 --> 00:22:38.890 They would try to find any time, day or night, winter 00:22:38.890 --> 00:22:41.710 versus spring, year after year when 00:22:41.710 --> 00:22:44.950 they could measure some measurable offset or change 00:22:44.950 --> 00:22:48.220 in those interference fringes because at some point, 00:22:48.220 --> 00:22:49.690 this direction should have lined up 00:22:49.690 --> 00:22:51.232 with the Earth's direction of motion, 00:22:51.232 --> 00:22:52.750 even it wouldn't be every time. 00:22:52.750 --> 00:22:56.270 That's why they kept doing this over and over and over again. 00:22:56.270 --> 00:23:00.370 And as you might know, they found nothing. 00:23:00.370 --> 00:23:06.010 So after years of painstaking data collection, 00:23:06.010 --> 00:23:10.330 they found no compelling empirical evidence 00:23:10.330 --> 00:23:12.640 of the Earth's motion through the ether. 00:23:12.640 --> 00:23:15.640 Michelson won the Nobel Prize for this and related work. 00:23:15.640 --> 00:23:19.150 He was an astoundingly accomplished experimentalist. 00:23:19.150 --> 00:23:21.010 He was the first US-based physicist 00:23:21.010 --> 00:23:22.660 to win the Nobel Prize. 00:23:22.660 --> 00:23:24.610 He lived 20 more years after that 00:23:24.610 --> 00:23:27.440 and died considering himself a failure. 00:23:27.440 --> 00:23:29.023 So I hope you all win the Nobel Prize. 00:23:29.023 --> 00:23:30.732 And I hope you think better of yourselves 00:23:30.732 --> 00:23:32.620 and give yourselves more credit. 00:23:32.620 --> 00:23:35.950 Michelson knew for certain the ether must exist. 00:23:35.950 --> 00:23:38.140 And yet he had failed to find it. 00:23:38.140 --> 00:23:40.970 So Lorentz was following this back in Europe. 00:23:40.970 --> 00:23:43.300 And this was really his second main motivation 00:23:43.300 --> 00:23:45.820 to think about these funny ways of handling 00:23:45.820 --> 00:23:49.010 coordinates in what we now call the Lorentz transformation. 00:23:49.010 --> 00:23:51.010 So I mentioned his mathematical concerns 00:23:51.010 --> 00:23:52.660 about the transformation properties 00:23:52.660 --> 00:23:54.550 of Maxwell's equations. 00:23:54.550 --> 00:23:57.783 He was also following the Michelson-Morley work 00:23:57.783 --> 00:23:59.200 with great interest and citing it. 00:23:59.200 --> 00:24:01.570 And we know he was really following each update. 00:24:01.570 --> 00:24:03.730 So he was concerned about this failure 00:24:03.730 --> 00:24:08.043 to measure a shift in the interference fringes. 00:24:08.043 --> 00:24:09.460 But Lorentz said, oh, but actually 00:24:09.460 --> 00:24:12.080 maybe there's a physical reason to account for that. 00:24:12.080 --> 00:24:15.040 If there really is, as he knew there must be, 00:24:15.040 --> 00:24:18.400 this physical, resistive medium, kind of elastic medium 00:24:18.400 --> 00:24:22.150 through which the Earth and everything else is moving, 00:24:22.150 --> 00:24:27.220 then there must be a force exerted by that viscous medium 00:24:27.220 --> 00:24:29.530 on every single atom and molecule 00:24:29.530 --> 00:24:32.350 making up all the stuff in Michelson's device 00:24:32.350 --> 00:24:34.010 as well as in everything else. 00:24:34.010 --> 00:24:36.910 And so it would be like picturing a beach ball. 00:24:36.910 --> 00:24:39.370 If you try to drag a beach ball underwater, 00:24:39.370 --> 00:24:42.400 in a resistive medium, the shape will be deformed 00:24:42.400 --> 00:24:43.730 along the direction of motion. 00:24:43.730 --> 00:24:46.600 If you drag that beach ball fast enough underwater, 00:24:46.600 --> 00:24:48.400 it will shrink in the direction of motion. 00:24:48.400 --> 00:24:51.830 It will be deformed like this picture here. 00:24:51.830 --> 00:24:53.710 And so Lorentz said that must be happening 00:24:53.710 --> 00:24:57.220 for every bit of matter in the arm of Michelson's 00:24:57.220 --> 00:25:00.880 interferometer that's most subject to that resistive force 00:25:00.880 --> 00:25:01.720 of the ether. 00:25:01.720 --> 00:25:05.013 There should be a contraction along the direction of motion. 00:25:05.013 --> 00:25:06.430 So then, again because he's a very 00:25:06.430 --> 00:25:08.470 gifted mathematical physicist, he 00:25:08.470 --> 00:25:11.110 calculated exactly how much shift must there 00:25:11.110 --> 00:25:17.440 be for the resultant path to be shortened just enough to make 00:25:17.440 --> 00:25:19.610 it a tie race after all. 00:25:19.610 --> 00:25:22.540 So the arm of the interferometer that's 00:25:22.540 --> 00:25:25.600 experiencing this shrinking, this extra force 00:25:25.600 --> 00:25:27.880 due to the resistive medium, would 00:25:27.880 --> 00:25:30.520 have to shrink by a specific calculable amount. 00:25:30.520 --> 00:25:33.285 We now use the Greek letter gamma. 00:25:33.285 --> 00:25:34.660 If you haven't seen that already, 00:25:34.660 --> 00:25:37.620 you'll see it throughout IAP and the rest of your life. 00:25:37.620 --> 00:25:40.050 It takes this somewhat simple-looking form-- 00:25:40.050 --> 00:25:44.790 1 over the square root of 1 minus v over c squared. 00:25:44.790 --> 00:25:46.800 If you plot it, you can see it diverges. 00:25:46.800 --> 00:25:50.200 When the relative speed gets close to the speed of light, 00:25:50.200 --> 00:25:51.990 you have 1 minus 1 in the denominator. 00:25:51.990 --> 00:25:53.400 You divide by 0. 00:25:53.400 --> 00:25:54.210 Your eyes bug out. 00:25:54.210 --> 00:25:55.230 And cats and dogs live together. 00:25:55.230 --> 00:25:56.290 Everything goes crazy. 00:25:56.290 --> 00:25:58.650 So it diverges at v equals c. 00:25:58.650 --> 00:26:00.240 On the other hand, for small speeds, 00:26:00.240 --> 00:26:02.250 small compared to the speed of light, 00:26:02.250 --> 00:26:05.130 this factor is indistinguishable from 1. 00:26:05.130 --> 00:26:06.720 So here's a quick plot. 00:26:06.720 --> 00:26:09.450 For ordinary speeds that we encounter on the highway, 00:26:09.450 --> 00:26:11.760 let alone on a bicycle, our speed 00:26:11.760 --> 00:26:14.500 compared to the speed of light is vanishingly small. 00:26:14.500 --> 00:26:18.150 So this factor gamma is very, very close to 1. 00:26:18.150 --> 00:26:20.640 Only when you get to speeds approaching the speed of light 00:26:20.640 --> 00:26:23.820 would you expect to measure any shift from that. 00:26:23.820 --> 00:26:26.010 Nonetheless, Lorentz said in principle this 00:26:26.010 --> 00:26:27.930 happens at any speed. 00:26:27.930 --> 00:26:30.630 And the shrink, the amount of contraction, 00:26:30.630 --> 00:26:32.310 is governed by that relative speed 00:26:32.310 --> 00:26:34.440 given by this Greek letter gamma. 00:26:34.440 --> 00:26:37.170 So gamma is always greater than or equal to 1. 00:26:37.170 --> 00:26:41.670 That means 1 over gamma must be smaller than 1. 00:26:41.670 --> 00:26:43.950 And that's saying that the contracted length of one 00:26:43.950 --> 00:26:45.450 of those arms of the interferometer 00:26:45.450 --> 00:26:49.620 got shorter by a certain amount depending 00:26:49.620 --> 00:26:51.930 on the relative speed. 00:26:51.930 --> 00:26:55.080 That would be enough to account for this null result, 00:26:55.080 --> 00:26:56.010 Lorentz argued. 00:26:56.010 --> 00:26:58.080 It turned out that exact form of gamma 00:26:58.080 --> 00:27:03.030 was the same form he'd found for his mathematical local time 00:27:03.030 --> 00:27:04.050 manipulations. 00:27:04.050 --> 00:27:06.932 So here's how we can live in a physical ether 00:27:06.932 --> 00:27:08.640 even though we don't measure its effects. 00:27:08.640 --> 00:27:09.960 OK. 00:27:09.960 --> 00:27:12.870 Let me now shift to how a different person began 00:27:12.870 --> 00:27:15.510 thinking about very familiar questions by that point 00:27:15.510 --> 00:27:17.460 but coming at them quite differently. 00:27:17.460 --> 00:27:19.650 That's young Albert Einstein. 00:27:19.650 --> 00:27:22.170 So Einstein was born in the midst of all this. 00:27:22.170 --> 00:27:25.740 He was born in 1879 in kind of rural, 00:27:25.740 --> 00:27:27.510 roughly speaking, nowheresville Germany, 00:27:27.510 --> 00:27:29.370 not near any of the big cities. 00:27:29.370 --> 00:27:32.670 So Lorentz was already a practicing physicist 00:27:32.670 --> 00:27:34.230 when Einstein was born. 00:27:34.230 --> 00:27:36.030 He was much younger. 00:27:36.030 --> 00:27:37.710 Einstein's main ambition was actually 00:27:37.710 --> 00:27:40.680 to become an electrical engineer at a time 00:27:40.680 --> 00:27:43.860 when that term itself was actually brand new. 00:27:43.860 --> 00:27:46.830 Einstein's father and uncle had gone into business 00:27:46.830 --> 00:27:49.380 together in this really brand new field 00:27:49.380 --> 00:27:50.530 of electrical engineering. 00:27:50.530 --> 00:27:52.560 This was the age of electrification. 00:27:52.560 --> 00:27:55.260 Think about extended street lighting, 00:27:55.260 --> 00:27:59.730 trolley cars with the shared electric lines above. 00:27:59.730 --> 00:28:02.730 This was transforming the face of everyday life 00:28:02.730 --> 00:28:05.520 in cities and eventually even in more rural areas. 00:28:05.520 --> 00:28:08.520 And Einstein's father and uncle were in on that. 00:28:08.520 --> 00:28:10.497 They were early professionals in this new field 00:28:10.497 --> 00:28:11.580 of electrical engineering. 00:28:11.580 --> 00:28:12.497 And Einstein loved it. 00:28:12.497 --> 00:28:17.100 He loved to tinker with electrotechnical gadgets. 00:28:17.100 --> 00:28:20.280 He had many strong feelings about many things. 00:28:20.280 --> 00:28:22.020 Among them, he hated what he considered 00:28:22.020 --> 00:28:25.650 the overly militaristic German high school that he attended. 00:28:25.650 --> 00:28:28.157 He would argue and insult his teachers. 00:28:28.157 --> 00:28:29.490 They didn't like him any better. 00:28:29.490 --> 00:28:31.110 They were delighted when he dropped out, 00:28:31.110 --> 00:28:32.190 so they didn't have to kick him out. 00:28:32.190 --> 00:28:34.290 He was really very obnoxious, it turns out. 00:28:34.290 --> 00:28:36.600 So he was a high-school dropout. 00:28:36.600 --> 00:28:42.368 He dreamed of entering the Swiss Federal Technical Institute. 00:28:42.368 --> 00:28:44.160 It was kind of like the MIT of Switzerland. 00:28:44.160 --> 00:28:48.123 Except to be more proper, MIT is the Massachusetts version 00:28:48.123 --> 00:28:48.790 of their school. 00:28:48.790 --> 00:28:50.640 Zurich's was founded first. 00:28:50.640 --> 00:28:54.020 It's often called the ETH, or the Eidgenossische Technische 00:28:54.020 --> 00:28:55.080 Hochschule. 00:28:55.080 --> 00:28:57.330 It was really a very elite technical university 00:28:57.330 --> 00:28:59.250 in Zurich, Switzerland. 00:28:59.250 --> 00:29:01.260 Einstein, by this point, had renounced 00:29:01.260 --> 00:29:02.560 his German citizenship. 00:29:02.560 --> 00:29:03.810 He dropped out of high school. 00:29:03.810 --> 00:29:06.323 And one of the best things about this technical university 00:29:06.323 --> 00:29:07.740 in Zurich was that you didn't have 00:29:07.740 --> 00:29:09.000 to have a high school diploma. 00:29:09.000 --> 00:29:09.750 He said, perfect. 00:29:09.750 --> 00:29:11.490 That's the place for me. 00:29:11.490 --> 00:29:14.820 So they had an entrance exam, which he very dutifully studied 00:29:14.820 --> 00:29:17.160 for and then failed because, after all, he 00:29:17.160 --> 00:29:19.750 ignored the topics that weren't of interest to him. 00:29:19.750 --> 00:29:22.560 He did well enough on the physics and math 00:29:22.560 --> 00:29:27.413 portions of the overall exam that a kindly physics professor 00:29:27.413 --> 00:29:28.830 took him aside and said, you know, 00:29:28.830 --> 00:29:31.740 if you go to basically a kind of regional, something 00:29:31.740 --> 00:29:33.360 almost like a community college, go 00:29:33.360 --> 00:29:35.610 to a local, regional school for a year, 00:29:35.610 --> 00:29:37.792 study up, retake the exam, you might do better. 00:29:37.792 --> 00:29:39.000 And that's what Einstein did. 00:29:39.000 --> 00:29:40.680 So he went to a little regional school 00:29:40.680 --> 00:29:44.610 in, again, in rural Switzerland for a year, 00:29:44.610 --> 00:29:46.690 took the exam again, and passed. 00:29:46.690 --> 00:29:48.330 So now he's able to enter his dream 00:29:48.330 --> 00:29:51.030 school, the ETH in Zurich. 00:29:51.030 --> 00:29:52.680 Once he then worked so hard to get in, 00:29:52.680 --> 00:29:54.150 he proceeded to cut classes. 00:29:54.150 --> 00:29:56.040 This guy was a horrible student. 00:29:56.040 --> 00:29:58.110 Whatever you do, don't be like Albert Einstein, 00:29:58.110 --> 00:30:00.213 at least while you're in university. 00:30:00.213 --> 00:30:01.380 He worked so hard to get in. 00:30:01.380 --> 00:30:03.338 And then he, again, would insult his professors 00:30:03.338 --> 00:30:05.430 as much as he'd insulted his high school teachers. 00:30:05.430 --> 00:30:07.195 He thought everything they did was boring. 00:30:07.195 --> 00:30:09.070 They didn't know what was really interesting. 00:30:09.070 --> 00:30:10.862 So he would cut classes and read on his own 00:30:10.862 --> 00:30:12.630 and then borrow notes from his girlfriend, 00:30:12.630 --> 00:30:15.240 his long, suffering, very patient girlfriend, Mileva 00:30:15.240 --> 00:30:17.970 Maric, who was doing very well in her own physics and math 00:30:17.970 --> 00:30:18.470 courses. 00:30:18.470 --> 00:30:20.595 And likewise, he borrowed notes from another friend 00:30:20.595 --> 00:30:21.690 of his, Marcel Grossmann. 00:30:21.690 --> 00:30:24.450 So he'd just cram and scrape through for the exams. 00:30:24.450 --> 00:30:26.550 Not an ideal student. 00:30:26.550 --> 00:30:29.190 For some reason that Einstein couldn't possibly fathom, 00:30:29.190 --> 00:30:31.650 because he actually was a dolt frankly, 00:30:31.650 --> 00:30:34.320 he impressed none of his professors. 00:30:34.320 --> 00:30:36.487 So when it came time to graduate, none of them 00:30:36.487 --> 00:30:38.570 would write him a strong letter of recommendation. 00:30:38.570 --> 00:30:42.860 Again, his life bears many important lessons for us today. 00:30:42.860 --> 00:30:43.760 Attend class. 00:30:43.760 --> 00:30:46.760 And be slightly less obnoxious to your instructors. 00:30:46.760 --> 00:30:48.390 And maybe things will turn out better. 00:30:48.390 --> 00:30:49.730 So none of his teachers would basically 00:30:49.730 --> 00:30:51.650 support him because he had middling grades 00:30:51.650 --> 00:30:53.610 and he was rude to them. 00:30:53.610 --> 00:30:56.040 So he couldn't get a job after graduation. 00:30:56.040 --> 00:30:58.250 So finally one of his close friends, 00:30:58.250 --> 00:30:59.960 Marcel Grossmann, one of the folks 00:30:59.960 --> 00:31:03.470 from whom he'd borrowed notes, his father had connections. 00:31:03.470 --> 00:31:05.240 And so basically through connections, 00:31:05.240 --> 00:31:08.720 he was able to get Einstein an entry-level civil service 00:31:08.720 --> 00:31:11.810 job at the patent office in Bern, Switzerland. 00:31:11.810 --> 00:31:13.320 So still in Switzerland. 00:31:13.320 --> 00:31:15.867 He was a patent officer, third class. 00:31:15.867 --> 00:31:18.200 As I'm always fond of saying, there was no fourth class. 00:31:18.200 --> 00:31:20.900 You were the lowest entry-level gig. 00:31:20.900 --> 00:31:23.570 So even for young Einstein, it wasn't what you know. 00:31:23.570 --> 00:31:24.980 It was who you know. 00:31:24.980 --> 00:31:27.320 What he then proceeded to do was he 00:31:27.320 --> 00:31:29.060 had a day job at what they called 00:31:29.060 --> 00:31:32.570 the electrotechnical desk, much like what his father and uncle 00:31:32.570 --> 00:31:33.290 were doing. 00:31:33.290 --> 00:31:34.970 He was a patent examiner for a lot 00:31:34.970 --> 00:31:37.490 of these cool, new electrical gadgets. 00:31:37.490 --> 00:31:39.470 And then he would go hang out with a bunch 00:31:39.470 --> 00:31:43.610 of friends and drink beer a lot at the pubs. 00:31:43.610 --> 00:31:46.190 So they formed what they called the Olympia Academy. 00:31:46.190 --> 00:31:47.780 And this was very ironic. 00:31:47.780 --> 00:31:49.275 They gave themselves the most elite 00:31:49.275 --> 00:31:50.900 sounding name because they're basically 00:31:50.900 --> 00:31:52.760 three semi-bums hanging out, reading, 00:31:52.760 --> 00:31:54.680 and blowing off their families. 00:31:54.680 --> 00:31:57.318 So they gave themselves a very, very prestigious name, 00:31:57.318 --> 00:31:59.360 even though it was literally three recent college 00:31:59.360 --> 00:32:01.310 graduates hanging out. 00:32:01.310 --> 00:32:04.310 It was Maurice Solovine, Conrad Habicht, 00:32:04.310 --> 00:32:06.200 and young Albert Einstein. 00:32:06.200 --> 00:32:09.620 And they would go and sometimes drink coffee, often drink beer, 00:32:09.620 --> 00:32:11.750 and talk about stuff they'd read. 00:32:11.750 --> 00:32:13.370 And they would read a lot of physics 00:32:13.370 --> 00:32:16.290 and read a lot of philosophy and talk about it. 00:32:16.290 --> 00:32:19.220 And one of the books that we know from their correspondence 00:32:19.220 --> 00:32:21.410 at the time that they were really interested in 00:32:21.410 --> 00:32:25.160 was this fascinating book by an Austrian polymath 00:32:25.160 --> 00:32:26.120 named Ernst Mach. 00:32:26.120 --> 00:32:29.120 Here's the book translated into English, known 00:32:29.120 --> 00:32:30.490 as The Science of Mechanics. 00:32:30.490 --> 00:32:33.710 It had come out in the 1880s. 00:32:33.710 --> 00:32:35.610 Mach was really remarkable. 00:32:35.610 --> 00:32:38.390 He was both a mathematical physicist 00:32:38.390 --> 00:32:39.680 and experimental physicist. 00:32:39.680 --> 00:32:42.110 You might know the terminology for Mach number, 00:32:42.110 --> 00:32:45.710 like speed of sound, Mach 1, Mach 2, Mach 3-- same Mach. 00:32:45.710 --> 00:32:47.930 He did a lot of studies of acoustics and optics 00:32:47.930 --> 00:32:50.960 but also of what we would now call psychology, 00:32:50.960 --> 00:32:55.190 like sensory experiments and so on, and eventually 00:32:55.190 --> 00:32:56.543 medical surgery. 00:32:56.543 --> 00:32:57.960 And then at the end of his career, 00:32:57.960 --> 00:32:59.600 he was a professor of the history and philosophy 00:32:59.600 --> 00:33:00.100 of science. 00:33:00.100 --> 00:33:01.650 This guy did it all. 00:33:01.650 --> 00:33:05.930 He wrote these very, very dense, conceptual critiques 00:33:05.930 --> 00:33:08.790 of Newtonian physics, among other things. 00:33:08.790 --> 00:33:12.200 And Mach was convinced that Newton was really 00:33:12.200 --> 00:33:14.330 getting himself into a horrible muddle 00:33:14.330 --> 00:33:16.370 because he had not paid sufficient attention 00:33:16.370 --> 00:33:17.450 philosophically. 00:33:17.450 --> 00:33:20.120 And this is what the young members of the Olympia Academy 00:33:20.120 --> 00:33:21.260 got really excited about. 00:33:21.260 --> 00:33:24.020 We know from their letters and their notes at the time. 00:33:24.020 --> 00:33:27.050 Mach was advocating a position that 00:33:27.050 --> 00:33:29.450 came to be known as positivism. 00:33:29.450 --> 00:33:32.360 According to Ernst Mach, unlike Isaac Newton, 00:33:32.360 --> 00:33:36.320 or for that matter even some folks like Maxwell, Mach 00:33:36.320 --> 00:33:39.360 argued that only quantities that could become objects 00:33:39.360 --> 00:33:41.360 of positive experience, that is to say things we 00:33:41.360 --> 00:33:45.530 could actively measure or sense or feel or touch, 00:33:45.530 --> 00:33:48.860 only those things belonged in our scientific theories. 00:33:48.860 --> 00:33:51.620 Anything else was just like mere speculation, 00:33:51.620 --> 00:33:53.660 like counting the number of angels that could 00:33:53.660 --> 00:33:54.785 dance on the head of a pin. 00:33:54.785 --> 00:33:57.290 He was scathingly critical of Newton. 00:33:57.290 --> 00:33:59.960 And in particular, Mach wrote in detail 00:33:59.960 --> 00:34:02.600 that Newton's notions of absolute space 00:34:02.600 --> 00:34:05.000 and absolute time had no meaning because how could you 00:34:05.000 --> 00:34:06.290 ever measure absolute time? 00:34:06.290 --> 00:34:08.960 Show me the clock that could measure absolute time. 00:34:08.960 --> 00:34:11.449 That was the kind of classic Machian response. 00:34:11.449 --> 00:34:14.540 I can measure the passage of time by using a clock. 00:34:14.540 --> 00:34:17.239 But who says that's what Newton wrote absolute time was? 00:34:17.239 --> 00:34:22.699 This had an amazing impact, as we know, on the young Einstein. 00:34:22.699 --> 00:34:23.989 So he's in this milieu. 00:34:23.989 --> 00:34:26.239 He's now not in a university setting. 00:34:26.239 --> 00:34:29.000 He scraped through his undergraduate studies. 00:34:29.000 --> 00:34:30.949 He has a nice day job. 00:34:30.949 --> 00:34:34.025 But he's not doing particularly well professionally. 00:34:34.025 --> 00:34:35.400 He's hanging out with his buddies 00:34:35.400 --> 00:34:38.449 and reading some interesting and hard, obscure philosophy 00:34:38.449 --> 00:34:40.580 science in the evenings. 00:34:40.580 --> 00:34:43.909 Well, he has what's now commonly called his miraculous year, 00:34:43.909 --> 00:34:46.614 his annus mirabilis, in 1905. 00:34:46.614 --> 00:34:48.239 In fact, he only took about six months. 00:34:48.239 --> 00:34:50.870 It was, like, half a year, during which he submitted 00:34:50.870 --> 00:34:54.662 four really astonishing, original papers to the leading 00:34:54.662 --> 00:34:56.120 journal of physics, the Annalen der 00:34:56.120 --> 00:34:58.820 Physik in Germany at the time. 00:34:58.820 --> 00:35:01.130 They've since been published and translated. 00:35:01.130 --> 00:35:02.690 There's a particularly nice edition 00:35:02.690 --> 00:35:07.370 you can find edited by John Stachel with very nice essays 00:35:07.370 --> 00:35:08.190 to accompany them. 00:35:08.190 --> 00:35:10.550 You can find them online. 00:35:10.550 --> 00:35:12.470 So for IAP and for the rest of today 00:35:12.470 --> 00:35:14.570 and even throughout the month, we're 00:35:14.570 --> 00:35:17.030 really interested in what was the third of these articles 00:35:17.030 --> 00:35:17.960 that he submitted. 00:35:17.960 --> 00:35:20.600 He submitted it to the journal in June of 1905. 00:35:20.600 --> 00:35:23.330 It's on what we would now call special relativity. 00:35:23.330 --> 00:35:25.340 Its title, as you can see up top, 00:35:25.340 --> 00:35:28.760 was actually, in translation, "On the Electrodynamics 00:35:28.760 --> 00:35:32.480 of Moving Bodies," a thoroughly familiar title, exactly what 00:35:32.480 --> 00:35:34.670 Lorentz and all of Lorentz's colleagues 00:35:34.670 --> 00:35:37.380 have been talking about for decades by that point. 00:35:37.380 --> 00:35:40.160 So the title of Einstein's paper in 1905 00:35:40.160 --> 00:35:42.410 was not surprising, even though, as we'll see, 00:35:42.410 --> 00:35:43.760 his approach was quite distinct. 00:35:48.580 --> 00:35:53.020 He begins this now very well done paper not by saying, 00:35:53.020 --> 00:35:55.420 I found an error in Lorentz's calculation. 00:35:55.420 --> 00:35:58.570 There was a missing factor of 2 pi or whatever. 00:35:58.570 --> 00:36:00.910 He doesn't say, I conducted my own measurements. 00:36:00.910 --> 00:36:04.180 And I found these results with an experimental error. 00:36:04.180 --> 00:36:06.640 He starts out by saying there's an asymmetry 00:36:06.640 --> 00:36:09.940 in the explanation which is not present in the phenomena. 00:36:09.940 --> 00:36:12.820 It sounds very philosophical. 00:36:12.820 --> 00:36:15.220 He goes on in his very opening paragraph 00:36:15.220 --> 00:36:19.180 to say that when we use Maxwell's equations, 00:36:19.180 --> 00:36:22.240 we come up with very different kinds of accounts for what 00:36:22.240 --> 00:36:24.010 should be the same phenomenon. 00:36:24.010 --> 00:36:24.760 Very simple. 00:36:24.760 --> 00:36:26.650 Nothing super fancy like an interferometer. 00:36:26.650 --> 00:36:30.280 Just take a bar magnet and a coil through which current 00:36:30.280 --> 00:36:31.510 could flow. 00:36:31.510 --> 00:36:34.330 And make sure you have a current meter, an ammeter attached 00:36:34.330 --> 00:36:35.390 to the coil. 00:36:35.390 --> 00:36:38.627 So if electric current flows through the coil, 00:36:38.627 --> 00:36:39.460 it will be measured. 00:36:39.460 --> 00:36:41.410 The ammeter needle will be deflected. 00:36:41.410 --> 00:36:45.160 And we are free to move either the magnet or the coil. 00:36:45.160 --> 00:36:47.980 In his opening paragraph, Einstein says, physicists 00:36:47.980 --> 00:36:51.970 had treated this situation completely orthogonally even 00:36:51.970 --> 00:36:54.770 though, as far as Einstein was concerned, 00:36:54.770 --> 00:36:57.320 there's only one explanation needed. 00:36:57.320 --> 00:36:59.210 And so with case 1, if you assume 00:36:59.210 --> 00:37:01.640 the bar magnet is moving, you're shaking the magnet 00:37:01.640 --> 00:37:05.300 back and forth and keeping the coil fixed in location, 00:37:05.300 --> 00:37:08.810 then you would appeal to one set of Maxwell's equations. 00:37:08.810 --> 00:37:11.720 And again, on the t-shirt it would be this one. 00:37:11.720 --> 00:37:14.910 You have a time-varying magnetic field 00:37:14.910 --> 00:37:17.810 which will induce a spatially varying electric field. 00:37:17.810 --> 00:37:21.890 And that will exert a push, a force on the little ions, 00:37:21.890 --> 00:37:24.170 the little electric charges within that coil. 00:37:24.170 --> 00:37:25.100 They'll feel a push. 00:37:25.100 --> 00:37:26.630 They'll move along the coil. 00:37:26.630 --> 00:37:29.030 Electric current, as Maxwell himself had argued, 00:37:29.030 --> 00:37:33.650 was nothing but the motion of these electric-charge bearers. 00:37:33.650 --> 00:37:36.200 So because you have a time-varying magnetic field, 00:37:36.200 --> 00:37:39.650 the little bits of matter in the coil will be pushed along. 00:37:39.650 --> 00:37:41.480 You'll induce a current. 00:37:41.480 --> 00:37:44.600 That's case 1-- moving magnets, stationary coil. 00:37:44.600 --> 00:37:47.790 But if you want to analyze the other situation, 00:37:47.790 --> 00:37:50.420 to hold the magnet rigidly fixed in place 00:37:50.420 --> 00:37:52.460 and shift the coil back and forth, 00:37:52.460 --> 00:37:55.580 then physicists would give an entirely separate explanation. 00:37:55.580 --> 00:37:58.610 They would appeal to a different one of Maxwell's equations. 00:37:58.610 --> 00:38:02.150 Now they'd say that there's a static magnetic field that 00:38:02.150 --> 00:38:03.590 varied in space. 00:38:03.590 --> 00:38:06.800 It's spatial gradients were non-vanishing. 00:38:06.800 --> 00:38:10.250 And that would exert a force, like a kind of Lorentz force 00:38:10.250 --> 00:38:11.900 law, on those charges. 00:38:11.900 --> 00:38:15.170 So they have some velocity in a magnetic field. 00:38:15.170 --> 00:38:16.700 They'll be pushed along the wire. 00:38:16.700 --> 00:38:18.600 And you'll measure a current. 00:38:18.600 --> 00:38:21.710 Einstein said that's one explanation too many. 00:38:21.710 --> 00:38:23.330 All that we could ever measure-- 00:38:23.330 --> 00:38:26.660 again, you can almost hear the kind of Mach coming through-- 00:38:26.660 --> 00:38:29.810 all we can ever see as an element of positive experience 00:38:29.810 --> 00:38:33.590 is some relative motion between the magnet and the coil 00:38:33.590 --> 00:38:35.540 which induces an electric current. 00:38:35.540 --> 00:38:37.580 Who's to say one was actually still 00:38:37.580 --> 00:38:38.780 while the other was moving? 00:38:38.780 --> 00:38:40.940 So Einstein begins this paper by saying 00:38:40.940 --> 00:38:42.980 that there's something wrong with the stories 00:38:42.980 --> 00:38:44.660 we tell about the equations. 00:38:44.660 --> 00:38:46.310 He doesn't argue about the equations. 00:38:46.310 --> 00:38:47.960 He argues about our interpretation 00:38:47.960 --> 00:38:48.740 of the equations. 00:38:48.740 --> 00:38:50.530 Very striking. 00:38:50.530 --> 00:38:53.170 He then goes on, just in, like, paragraph 3-- still 00:38:53.170 --> 00:38:57.640 very early in the introduction-- to posit two postulates. 00:38:57.640 --> 00:38:58.600 He doesn't prove them. 00:38:58.600 --> 00:39:00.340 He doesn't derive them. 00:39:00.340 --> 00:39:03.340 He doesn't say, I have demonstrated these 00:39:03.340 --> 00:39:04.960 by doing experiments. 00:39:04.960 --> 00:39:08.170 He says, let me hypothesize these and see what follows. 00:39:08.170 --> 00:39:11.800 And these are the two in rough paraphrase. 00:39:11.800 --> 00:39:14.500 The first one was actually already called 00:39:14.500 --> 00:39:16.840 the principle of relativity, or sometimes simply called 00:39:16.840 --> 00:39:21.070 Galilean relativity, going back again to the 17th century. 00:39:21.070 --> 00:39:24.040 Galileo had argued by thinking about that boat 00:39:24.040 --> 00:39:27.550 floating down the river, that to a person on the boat, as long 00:39:27.550 --> 00:39:30.070 as the boat is moving at a constant speed, 00:39:30.070 --> 00:39:32.200 neither speeding up nor slowing down, 00:39:32.200 --> 00:39:34.990 that all the laws of mechanics should work perfectly well 00:39:34.990 --> 00:39:37.090 for that observer the same as they would 00:39:37.090 --> 00:39:40.030 for us at rest on the shore. 00:39:40.030 --> 00:39:42.417 If you toss a ball, it'll land back in your hand 00:39:42.417 --> 00:39:43.000 as you expect. 00:39:43.000 --> 00:39:45.850 Even though to us, we see the ball trace 00:39:45.850 --> 00:39:49.060 a complicated parabola, to the person on the boat, 00:39:49.060 --> 00:39:51.370 she's perfectly entitled to say, I'm sitting at rest. 00:39:51.370 --> 00:39:53.050 The ball went straight up and landed straight 00:39:53.050 --> 00:39:53.717 back in my hand. 00:39:53.717 --> 00:39:56.170 All the laws of mechanics should work equally well 00:39:56.170 --> 00:39:59.320 in any reference frame that's moving at a constant speed. 00:39:59.320 --> 00:40:01.600 Einstein just takes that existing principle 00:40:01.600 --> 00:40:04.760 of relativity from mechanics and just assumes, 00:40:04.760 --> 00:40:07.120 just hypothesizes that that should 00:40:07.120 --> 00:40:10.390 apply not only to mechanics but to every physical phenomenon-- 00:40:10.390 --> 00:40:13.002 electricity, magnetism, optics, thermodynamics. 00:40:13.002 --> 00:40:13.960 And that's just a leap. 00:40:13.960 --> 00:40:15.100 He just says, what if? 00:40:15.100 --> 00:40:18.100 What if this applies to any kind of physical phenomenon, not 00:40:18.100 --> 00:40:19.660 just mechanics? 00:40:19.660 --> 00:40:22.270 And then he introduces the second postulate 00:40:22.270 --> 00:40:25.970 which seems actually to be in tension a bit with the first. 00:40:25.970 --> 00:40:27.940 His second postulate is, the speed of light 00:40:27.940 --> 00:40:32.740 is a constant independent of the motion of the source. 00:40:32.740 --> 00:40:33.280 What? 00:40:33.280 --> 00:40:34.540 That doesn't sound right. 00:40:34.540 --> 00:40:36.820 If you go back to Galileo and watching his friend 00:40:36.820 --> 00:40:39.940 on the boat, if she fires a cannon, 00:40:39.940 --> 00:40:42.370 the speed with which we measure the cannonball 00:40:42.370 --> 00:40:45.760 is different than the speed she measures it, right? 00:40:45.760 --> 00:40:49.030 If you watch her lobbing a tennis ball, 00:40:49.030 --> 00:40:51.550 our measurement of the speed of an object in her reference 00:40:51.550 --> 00:40:52.820 frame is not the same as ours. 00:40:52.820 --> 00:40:54.430 And Einstein here is saying light 00:40:54.430 --> 00:40:58.000 is special, that unlike tennis balls, ping pong balls, 00:40:58.000 --> 00:41:00.580 cannonballs, or trains, or anything else, 00:41:00.580 --> 00:41:03.040 the speed of light, as a postulate, 00:41:03.040 --> 00:41:05.500 will be constant for any observer 00:41:05.500 --> 00:41:08.950 as long as they're in an inertial frame of reference. 00:41:08.950 --> 00:41:11.437 And here's an excerpt from the English translation. 00:41:11.437 --> 00:41:12.520 I won't read all this out. 00:41:12.520 --> 00:41:15.220 But he says, what follows from these postulates 00:41:15.220 --> 00:41:18.860 is that the luminiferous ether will prove to be superfluous-- 00:41:18.860 --> 00:41:19.660 [GERMAN] 00:41:19.660 --> 00:41:21.380 He doesn't say, I've disproven it, ether. 00:41:21.380 --> 00:41:23.290 He says it's just irrelevant. 00:41:23.290 --> 00:41:26.560 50 years' worth, by that point 100 years' worth of study 00:41:26.560 --> 00:41:29.950 by all of Europe's most prestigious physicists was 00:41:29.950 --> 00:41:31.163 irrelevant. 00:41:31.163 --> 00:41:33.580 That's probably why he didn't have many friends in physics 00:41:33.580 --> 00:41:34.280 at the time. 00:41:34.280 --> 00:41:35.860 So he doesn't disprove the ether. 00:41:35.860 --> 00:41:38.170 He says we just won't even need to refer to it anymore. 00:41:38.170 --> 00:41:40.210 It makes the entire set of questions 00:41:40.210 --> 00:41:42.100 that had driven people like Lorentz 00:41:42.100 --> 00:41:44.440 really kind of fall away, at least as far as Einstein 00:41:44.440 --> 00:41:46.640 himself is concerned. 00:41:46.640 --> 00:41:49.180 So why does Einstein introduce that second postulate? 00:41:49.180 --> 00:41:52.690 And again, historians and physicists and philosophers 00:41:52.690 --> 00:41:54.700 have studied this question a lot. 00:41:54.700 --> 00:41:56.560 And we have some good documentary evidence 00:41:56.560 --> 00:41:58.570 because Einstein was writing letters and diaries 00:41:58.570 --> 00:41:59.530 and stuff all the time. 00:41:59.530 --> 00:42:01.610 And a lot of those have survived. 00:42:01.610 --> 00:42:03.970 So we have some contemporaneous documentation as well as 00:42:03.970 --> 00:42:06.340 his own later recollections and so on. 00:42:06.340 --> 00:42:09.520 We know that actually 10 years before this paper, back 00:42:09.520 --> 00:42:12.370 when Einstein was a mere teenager, 00:42:12.370 --> 00:42:14.590 he'd like to pose these kind of thought experiments 00:42:14.590 --> 00:42:16.133 or questions to himself. 00:42:16.133 --> 00:42:17.800 And one of the questions he would return 00:42:17.800 --> 00:42:20.560 to really over the course of a full decade 00:42:20.560 --> 00:42:23.410 was, what would it look like, what would you experience, 00:42:23.410 --> 00:42:25.390 if you could catch up to a light wave? 00:42:25.390 --> 00:42:29.680 And he reasoned it would be like a surfer riding along an ocean 00:42:29.680 --> 00:42:32.200 wave, that to us on the shore, we'd 00:42:32.200 --> 00:42:33.700 see both these things moving. 00:42:33.700 --> 00:42:38.380 We would see a dynamical wave moving over time, 00:42:38.380 --> 00:42:41.110 not just a frozen waveform in space. 00:42:41.110 --> 00:42:42.940 But to the surfer, if she's really 00:42:42.940 --> 00:42:45.880 moving at the same speed as the wave, 00:42:45.880 --> 00:42:50.090 then she would see the wave frozen in time. 00:42:50.090 --> 00:42:55.000 It would be a crest here, a trough there. 00:42:55.000 --> 00:42:56.980 At least for some extended period of time, 00:42:56.980 --> 00:42:59.140 the surfer would see the wave frozen, 00:42:59.140 --> 00:43:04.090 not dynamical-- a frozen waveform varying in space 00:43:04.090 --> 00:43:06.077 but frozen in time. 00:43:06.077 --> 00:43:08.410 So Einstein said that doesn't make any sense if we think 00:43:08.410 --> 00:43:09.493 about Maxwell's equations. 00:43:09.493 --> 00:43:11.320 When he got a little more sophisticated 00:43:11.320 --> 00:43:13.210 and learned more about Maxwell, he 00:43:13.210 --> 00:43:16.120 said there's no solution to Maxwell's equations. 00:43:16.120 --> 00:43:17.980 If you're in a source-free region, 00:43:17.980 --> 00:43:20.500 if there's no clump of electric charge around, 00:43:20.500 --> 00:43:24.520 no electric currents around, if both rho and J vanish, 00:43:24.520 --> 00:43:27.730 then there's no way to have spatially varying 00:43:27.730 --> 00:43:30.430 electric and magnetic fields that 00:43:30.430 --> 00:43:33.130 are nonetheless static, right? 00:43:33.130 --> 00:43:34.820 That seems to be a contradiction. 00:43:34.820 --> 00:43:36.730 So how do you get out of this contradiction 00:43:36.730 --> 00:43:40.460 of thinking you would have a static waveform of light 00:43:40.460 --> 00:43:42.460 if you could catch up and move at the same speed 00:43:42.460 --> 00:43:44.063 as that light wave? 00:43:44.063 --> 00:43:44.980 How do you avoid that? 00:43:44.980 --> 00:43:47.650 You just make sure you can never catch up to the wave. 00:43:47.650 --> 00:43:50.170 How can you never ever catch up to the wave 00:43:50.170 --> 00:43:52.960 if the wave is always traveling at the speed c 00:43:52.960 --> 00:43:56.240 even if you're traveling on a very fast train or now 00:43:56.240 --> 00:44:00.040 a hypersonic jet or a spaceship of your imagination? 00:44:00.040 --> 00:44:03.130 That second postulate for Einstein we now know 00:44:03.130 --> 00:44:06.280 was really the endpoint of a 10-year series of thought 00:44:06.280 --> 00:44:08.200 experiments about, what would it look 00:44:08.200 --> 00:44:09.940 like to catch up with a light wave? 00:44:09.940 --> 00:44:13.030 And he said that would make so many other things mutually 00:44:13.030 --> 00:44:13.630 inconsistent. 00:44:13.630 --> 00:44:16.210 Let's make sure no one could ever catch a light wave. 00:44:16.210 --> 00:44:18.130 And that's what starts driving much 00:44:18.130 --> 00:44:21.190 of the rest of his thinking, not worrying about interferometers 00:44:21.190 --> 00:44:22.400 and all the rest. 00:44:22.400 --> 00:44:26.080 So what he does, unlike Lorentz and really all the masters 00:44:26.080 --> 00:44:28.990 in the field at the time, Einstein 00:44:28.990 --> 00:44:32.950 begins with kinematics, with the force-free motion 00:44:32.950 --> 00:44:35.330 of bodies through space and time, 00:44:35.330 --> 00:44:36.940 which is a very Machian thing to do. 00:44:36.940 --> 00:44:37.780 What can we see? 00:44:37.780 --> 00:44:40.750 We measure objects moving through space and time. 00:44:40.750 --> 00:44:43.243 Whereas people like Lorentz, and Maxwell for that matter, 00:44:43.243 --> 00:44:45.160 have been starting with forces, with dynamics. 00:44:45.160 --> 00:44:47.290 Remember, Lorentz has this great idea 00:44:47.290 --> 00:44:49.570 that there's a force from the ether on the matter. 00:44:49.570 --> 00:44:51.430 And in Michelson's instrument, it's 00:44:51.430 --> 00:44:53.500 all about dynamics, forces. 00:44:53.500 --> 00:44:55.125 Einstein inverts that order. 00:44:55.125 --> 00:44:56.500 He says forces will be important. 00:44:56.500 --> 00:44:59.140 But first let's make sure we understand force-free motion 00:44:59.140 --> 00:45:00.620 kinematics first. 00:45:00.620 --> 00:45:03.190 After all, that's what could become 00:45:03.190 --> 00:45:05.962 objects of positive experience. 00:45:05.962 --> 00:45:07.670 And so he has these wonderful quotations. 00:45:07.670 --> 00:45:09.970 It's now from the introduction of the paper. 00:45:09.970 --> 00:45:12.280 It's on the bottom of page 2. 00:45:12.280 --> 00:45:16.360 He's really redescribing how to lay out coordinates. 00:45:16.360 --> 00:45:17.500 It sounds childish. 00:45:17.500 --> 00:45:21.170 It sounds thoroughly unprofessional to the folks 00:45:21.170 --> 00:45:22.660 of the time. 00:45:22.660 --> 00:45:26.110 Hendrik Lorentz says don't bother with 'what do we mean 00:45:26.110 --> 00:45:26.920 by coordinates?' 00:45:26.920 --> 00:45:28.337 But Einstein was convinced we have 00:45:28.337 --> 00:45:30.600 to think through how do we describe motion 00:45:30.600 --> 00:45:32.333 through space and time first. 00:45:32.333 --> 00:45:33.750 And I won't bother reading it out. 00:45:33.750 --> 00:45:34.700 I'll share this slide. 00:45:34.700 --> 00:45:35.000 And you can see it. 00:45:35.000 --> 00:45:37.208 But that's really what he's doing in the very opening 00:45:37.208 --> 00:45:39.230 paragraphs of this paper. 00:45:39.230 --> 00:45:42.090 And that leads him to other follow-up conclusions, 00:45:42.090 --> 00:45:44.270 one of which very famously becomes 00:45:44.270 --> 00:45:45.993 known as the relativity of simultaneity. 00:45:45.993 --> 00:45:47.660 And you might have heard of that before. 00:45:47.660 --> 00:45:51.140 You'll spend more time with this in IAP, I'm sure. 00:45:51.140 --> 00:45:53.450 If there's no such thing as absolute time, 00:45:53.450 --> 00:45:56.660 if time is what we measure with time-measuring devices 00:45:56.660 --> 00:45:58.910 like clocks, if that's all time is, 00:45:58.910 --> 00:46:02.120 is what can be measured by an actual instrument like a clock, 00:46:02.120 --> 00:46:05.840 then how can we compare the times in different places? 00:46:05.840 --> 00:46:08.150 After all, I'm sitting here with my clock. 00:46:08.150 --> 00:46:09.740 Well, he says one thing we could do 00:46:09.740 --> 00:46:12.470 is trade light signals because, at least according 00:46:12.470 --> 00:46:15.650 to his postulate number 2, light is special. 00:46:15.650 --> 00:46:18.620 If I throw ping pong balls, that's not so special 00:46:18.620 --> 00:46:21.880 because we will disagree on the speed with which 00:46:21.880 --> 00:46:23.500 those ping pong balls travel. 00:46:23.500 --> 00:46:25.870 If I send a light wave, then we had better 00:46:25.870 --> 00:46:29.080 agree on the speed with which that light moved from point A 00:46:29.080 --> 00:46:31.210 to point B because of postulate 2. 00:46:31.210 --> 00:46:33.460 So he starts thinking about one of his favorite things 00:46:33.460 --> 00:46:34.870 in the universe, trains. 00:46:34.870 --> 00:46:36.190 He loved trains. 00:46:36.190 --> 00:46:37.610 It came up all the time. 00:46:37.610 --> 00:46:40.000 So he imagines a train moving along a platform 00:46:40.000 --> 00:46:43.600 at a constant speed, a nice, inertial frame of reference. 00:46:43.600 --> 00:46:47.320 Einstein is standing here on the embankment, the train platform. 00:46:47.320 --> 00:46:48.430 He has two friends. 00:46:48.430 --> 00:46:53.260 We can call them Alice and Bob, A and B. Einstein 00:46:53.260 --> 00:46:56.470 has marked himself out to be in the perfect midpoint of where 00:46:56.470 --> 00:46:58.570 Alice and Bob are standing. 00:46:58.570 --> 00:47:00.560 So they mark this all out ahead of time. 00:47:00.560 --> 00:47:02.590 He marks himself perfectly in the middle. 00:47:02.590 --> 00:47:07.030 Alice and Bob are each equipped with a lantern and a watch. 00:47:07.030 --> 00:47:09.010 And by prior arrangement, they say 00:47:09.010 --> 00:47:12.640 at 12:00 noon on the dot, turn on your lanterns. 00:47:12.640 --> 00:47:15.790 So the light will travel from both A and B 00:47:15.790 --> 00:47:17.560 toward the midpoint. 00:47:17.560 --> 00:47:19.780 Point your lanterns toward Einstein 00:47:19.780 --> 00:47:23.590 at point M. Turn them on at the same time. 00:47:23.590 --> 00:47:27.100 Meanwhile on this zooming train, there's 00:47:27.100 --> 00:47:29.320 another friend of Einstein's sitting 00:47:29.320 --> 00:47:31.150 at the midpoint of the train. 00:47:31.150 --> 00:47:33.920 At the point, this is Marge, M prime here. 00:47:33.920 --> 00:47:36.670 She knows that she's in the exact midpoint of the train. 00:47:36.670 --> 00:47:38.890 She knows by prior arrangement that Alice and Bob 00:47:38.890 --> 00:47:42.140 are standing one train length apart from each other. 00:47:42.140 --> 00:47:45.160 And again, she's expecting that they will turn their lanterns 00:47:45.160 --> 00:47:47.030 on at the same time. 00:47:47.030 --> 00:47:49.870 So how do these different folks describe this series 00:47:49.870 --> 00:47:51.490 of events that follow? 00:47:51.490 --> 00:47:53.710 Let's focus first on what Einstein 00:47:53.710 --> 00:47:55.630 sees when he's standing still on the train 00:47:55.630 --> 00:47:59.560 platform, the embankment, watching the train go by. 00:47:59.560 --> 00:48:01.360 The observer who's standing still 00:48:01.360 --> 00:48:05.680 on the platform at point M was, by prior arrangement, 00:48:05.680 --> 00:48:08.405 at equal distance from Alice and Bob. 00:48:08.405 --> 00:48:09.280 I guess I changed it. 00:48:09.280 --> 00:48:09.940 Now it's a she. 00:48:09.940 --> 00:48:13.060 So Mileva, his wife, is standing there. 00:48:13.060 --> 00:48:14.320 Maybe M stands for Mileva. 00:48:14.320 --> 00:48:17.170 So she receives the light waves from points A and B 00:48:17.170 --> 00:48:18.560 at the same time. 00:48:18.560 --> 00:48:22.090 So she can conclude that the light flashes were emitted 00:48:22.090 --> 00:48:26.350 at the same time, that the event of person A and person 00:48:26.350 --> 00:48:29.350 B shining the lights, those events were simultaneous. 00:48:29.350 --> 00:48:30.730 How do you know? 00:48:30.730 --> 00:48:34.560 Because the light had equal distances to travel. 00:48:34.560 --> 00:48:37.920 And the light could only travel at but one speed. 00:48:37.920 --> 00:48:39.520 And they arrived at the same time. 00:48:39.520 --> 00:48:41.760 They must have started the journeys at the same time. 00:48:41.760 --> 00:48:43.530 The act of shining those lanterns 00:48:43.530 --> 00:48:46.480 must have been simultaneous. 00:48:46.480 --> 00:48:50.080 But what about the person who's on the moving train? 00:48:50.080 --> 00:48:56.500 She sees the following as she is zooming along at point M prime. 00:48:56.500 --> 00:49:01.120 She sees the light from point B arrive at her location first. 00:49:01.120 --> 00:49:02.945 Now, Mileva or Einstein would say, oh, 00:49:02.945 --> 00:49:04.570 that's because you're racing toward it. 00:49:04.570 --> 00:49:06.430 She says, not so fast. 00:49:06.430 --> 00:49:08.200 I'm in a perfectly self-consistent 00:49:08.200 --> 00:49:09.790 mechanical system. 00:49:09.790 --> 00:49:12.610 All the laws of physics work as well for me as for you. 00:49:12.610 --> 00:49:14.140 And the light couldn't have sped up 00:49:14.140 --> 00:49:15.940 or slowed down by your own postulate, 00:49:15.940 --> 00:49:18.340 she would say-- she would be entitled to say. 00:49:18.340 --> 00:49:21.460 So if she's equal distant between points A and B 00:49:21.460 --> 00:49:24.160 and she receives the light from B first, 00:49:24.160 --> 00:49:28.210 the only possible explanation is that the lights were not 00:49:28.210 --> 00:49:31.810 shown simultaneously, that A and B did not turn the lanterns 00:49:31.810 --> 00:49:33.500 on at the same time. 00:49:33.500 --> 00:49:36.940 So the person on the train platform and the person 00:49:36.940 --> 00:49:39.460 on the moving train disagree about what 00:49:39.460 --> 00:49:41.110 happens simultaneously. 00:49:41.110 --> 00:49:43.840 This becomes known as the relativity of simultaneity. 00:49:43.840 --> 00:49:45.280 So who's correct? 00:49:45.280 --> 00:49:48.460 I've already said, according to Einstein, no one or both 00:49:48.460 --> 00:49:51.430 of them because of postulate 1. 00:49:51.430 --> 00:49:53.050 They're both entitled to work out 00:49:53.050 --> 00:49:57.610 a perfectly self-consistent set of laws 00:49:57.610 --> 00:50:00.700 involving electromagnetism, optics, and mechanics. 00:50:00.700 --> 00:50:02.260 They agree they were at the midpoint. 00:50:02.260 --> 00:50:04.385 They agree that light didn't speed up or slow down. 00:50:04.385 --> 00:50:06.430 So they are both right, which is to say 00:50:06.430 --> 00:50:08.470 there is no right answer to the question, what 00:50:08.470 --> 00:50:10.150 was really simultaneous? 00:50:10.150 --> 00:50:13.600 Simultaneity becomes relative to one's frame of reference. 00:50:13.600 --> 00:50:16.900 That's a pretty deep change from the Newtonian system. 00:50:16.900 --> 00:50:19.330 And as Einstein says-- again, it's bottom of page 2, 00:50:19.330 --> 00:50:20.950 very early in the paper-- 00:50:20.950 --> 00:50:23.830 "we see that we can attribute no absolute meaning 00:50:23.830 --> 00:50:27.100 to the concept of simultaneity, but that two events which 00:50:27.100 --> 00:50:28.660 examined from a coordinate system 00:50:28.660 --> 00:50:32.140 are simultaneous"-- like him on the embankment-- 00:50:32.140 --> 00:50:35.142 "can no longer be interpreted as simultaneous events when 00:50:35.142 --> 00:50:36.850 examined from a system which is in motion 00:50:36.850 --> 00:50:38.020 relative to that system." 00:50:38.020 --> 00:50:39.520 OK, that's about kinematics. 00:50:39.520 --> 00:50:43.090 It's not about forces or resistive medium or dynamics. 00:50:45.690 --> 00:50:48.620 So now he goes on-- again, very early on in the paper-- 00:50:48.620 --> 00:50:51.360 once you get to the relativity of simultaneity-- again, 00:50:51.360 --> 00:50:53.810 as you'll have a chance to unpack with more patience 00:50:53.810 --> 00:50:55.820 in the coming days and weeks-- 00:50:55.820 --> 00:50:58.370 other strange phenomena seem to follow from that, 00:50:58.370 --> 00:50:59.780 argues Einstein. 00:50:59.780 --> 00:51:03.360 One of the first he talks about is length contraction. 00:51:03.360 --> 00:51:05.480 So this had been found and published by Lorentz. 00:51:05.480 --> 00:51:08.750 Einstein is about to give an entirely different derivation, 00:51:08.750 --> 00:51:12.147 even though quantitatively it's the same form of the equation. 00:51:12.147 --> 00:51:14.105 For Einstein, it has nothing to do with forces. 00:51:14.105 --> 00:51:17.150 It's all about kinematics. 00:51:17.150 --> 00:51:19.600 In general, like a good Machian, he asks, 00:51:19.600 --> 00:51:21.350 how do we measure the length of an object? 00:51:21.350 --> 00:51:25.460 How do we make length an object of positive experience? 00:51:25.460 --> 00:51:28.322 Well, at the same time measure the location 00:51:28.322 --> 00:51:30.530 of the front of the object and the back of the object 00:51:30.530 --> 00:51:31.890 and take the difference. 00:51:31.890 --> 00:51:33.350 So if you want to measure the length of the train, 00:51:33.350 --> 00:51:34.010 that's fine. 00:51:34.010 --> 00:51:35.990 Just measure where the front is and the back 00:51:35.990 --> 00:51:38.390 is at the same time, and then mark off 00:51:38.390 --> 00:51:41.900 the difference between those two locations in space. 00:51:41.900 --> 00:51:44.510 Our friends Alice and Bob can do that with the train. 00:51:44.510 --> 00:51:52.010 And they find the answer capital L. The train is length L long. 00:51:52.010 --> 00:51:54.410 Meanwhile, Alice and Bob-- 00:51:54.410 --> 00:51:56.870 and I should say that's when the train is at rest. 00:51:56.870 --> 00:51:59.120 When they do this with a moving train, 00:51:59.120 --> 00:52:01.700 Alice and Bob measure the length of a moving train, 00:52:01.700 --> 00:52:03.950 they measure some length shorter than what 00:52:03.950 --> 00:52:06.470 the person on the train was expecting. 00:52:06.470 --> 00:52:10.190 The person on the train expected the full length L. The person 00:52:10.190 --> 00:52:12.920 who's moving with the object, either at rest with it 00:52:12.920 --> 00:52:17.090 or moving together with it, says the train is L units long. 00:52:17.090 --> 00:52:19.280 But when Alice and Bob measure the train 00:52:19.280 --> 00:52:21.590 by measuring the front and back at the same time, 00:52:21.590 --> 00:52:23.120 they find a shorter answer. 00:52:23.120 --> 00:52:25.430 They found it shrunk along the direction of motion 00:52:25.430 --> 00:52:28.130 by some specific amount. 00:52:28.130 --> 00:52:29.180 Now, how could that be? 00:52:29.180 --> 00:52:32.070 Remember, we disagree about "at the same time." 00:52:32.070 --> 00:52:33.740 So if we disagree about simultaneity, 00:52:33.740 --> 00:52:35.900 we will-- perforce, we must start 00:52:35.900 --> 00:52:38.250 to disagree about lengths. 00:52:38.250 --> 00:52:41.870 So the person on the train says, you did your measurement wrong. 00:52:41.870 --> 00:52:44.660 You measured the front of the train first. 00:52:44.660 --> 00:52:47.990 We know that event B happened first, she says, 00:52:47.990 --> 00:52:50.997 because we got the light from event B first. 00:52:50.997 --> 00:52:52.580 So you measured the front of the train 00:52:52.580 --> 00:52:55.880 and then waited while the train slid and then later measured 00:52:55.880 --> 00:52:57.620 the position of the rear of the train. 00:52:57.620 --> 00:52:59.810 So of course you have a shorter distance 00:52:59.810 --> 00:53:01.640 because you performed a bad measurement, 00:53:01.640 --> 00:53:03.140 because you didn't measure the front 00:53:03.140 --> 00:53:04.940 and back at the same time. 00:53:04.940 --> 00:53:06.065 We say, don't be silly. 00:53:06.065 --> 00:53:07.190 They were at the same time. 00:53:07.190 --> 00:53:09.440 We checked by trading light beams. 00:53:09.440 --> 00:53:10.820 We know they were simultaneous. 00:53:10.820 --> 00:53:12.560 And we got the answer L prime. 00:53:12.560 --> 00:53:13.820 Your train is short. 00:53:13.820 --> 00:53:14.630 Who's right? 00:53:14.630 --> 00:53:18.170 Sort of both and neither, that because we disagree 00:53:18.170 --> 00:53:21.230 on simultaneity, we disagree on the outcomes 00:53:21.230 --> 00:53:25.310 of simultaneous events like measurements of length. 00:53:25.310 --> 00:53:27.950 And so he goes on with just a few lines of algebra 00:53:27.950 --> 00:53:30.170 to find the exact form of what was already 00:53:30.170 --> 00:53:32.960 known as the Lorentz contraction, that same factor 00:53:32.960 --> 00:53:36.800 gamma that you'll be using all IAP, 00:53:36.800 --> 00:53:40.010 that the measurement of an object in motion 00:53:40.010 --> 00:53:42.380 shrinks along the direction of motion. 00:53:42.380 --> 00:53:44.330 Whereas if we were at rest with that object, 00:53:44.330 --> 00:53:45.770 we'd find a longer length. 00:53:45.770 --> 00:53:48.950 And the amount it shrinks depends on that relative speed 00:53:48.950 --> 00:53:50.045 v over c. 00:53:50.045 --> 00:53:53.270 It depends, in particular, on this form gamma. 00:53:53.270 --> 00:53:56.180 This has nothing, for Einstein, to do with forces or dynamics. 00:53:56.180 --> 00:53:59.390 It's a totally different derivation than Lorentz's. 00:53:59.390 --> 00:54:02.570 It's simply a consequence of kinematics and, in particular, 00:54:02.570 --> 00:54:04.830 about simultaneity. 00:54:04.830 --> 00:54:06.210 It's a very simple exercise. 00:54:06.210 --> 00:54:09.030 You'll probably wind up doing it very soon 00:54:09.030 --> 00:54:12.000 to find a similar consequence for the rate at which clocks 00:54:12.000 --> 00:54:12.720 will tick. 00:54:12.720 --> 00:54:15.300 This has now became known as time dilation. 00:54:15.300 --> 00:54:18.570 Imagine a very simple kind of clock, the simplest one-- 00:54:18.570 --> 00:54:21.570 two highly polished mirrors with a light beam 00:54:21.570 --> 00:54:24.580 that just bounces straight back and forth between them. 00:54:24.580 --> 00:54:27.030 If the clock is at rest with respect to us, 00:54:27.030 --> 00:54:30.510 we hold the clock perfectly still at a fixed height, 00:54:30.510 --> 00:54:32.280 then the time it takes for that light 00:54:32.280 --> 00:54:35.430 to travel from the bottom mirror to the top mirror 00:54:35.430 --> 00:54:37.830 will count as one tick of our clock. 00:54:37.830 --> 00:54:39.030 [SNAPPING] 00:54:39.030 --> 00:54:41.560 And we know that light can only travel at a fixed speed. 00:54:41.560 --> 00:54:44.190 So it's a really great, uniform clock. 00:54:44.190 --> 00:54:46.780 As long as we can hold that height really fixed, 00:54:46.780 --> 00:54:50.070 this is a great way of defining a unit of time and therefore 00:54:50.070 --> 00:54:51.870 our clock rate. 00:54:51.870 --> 00:54:54.390 What happens if our friend has an identical clock, 00:54:54.390 --> 00:54:57.150 same mirrors, held equally rigidly at the same height 00:54:57.150 --> 00:55:01.350 apart but zooming past us on that moving train? 00:55:01.350 --> 00:55:04.230 Then we watch the light have to travel this longer 00:55:04.230 --> 00:55:08.585 path because after the light beam leaves the bottom mirror, 00:55:08.585 --> 00:55:09.960 in order to reach the top mirror, 00:55:09.960 --> 00:55:13.080 the whole assembly has moved with the train to the right, 00:55:13.080 --> 00:55:16.860 some distance v times t in the time during which 00:55:16.860 --> 00:55:19.410 that light beam was in transit. 00:55:19.410 --> 00:55:21.690 So it has to travel the hypotenuse 00:55:21.690 --> 00:55:22.800 of this right triangle. 00:55:22.800 --> 00:55:24.780 Instead of just this simple up and down, 00:55:24.780 --> 00:55:27.750 it travels perforce a longer distance 00:55:27.750 --> 00:55:29.550 and likewise back down. 00:55:29.550 --> 00:55:32.970 So our observation of the moving clock 00:55:32.970 --> 00:55:36.870 is that it takes longer between ticks. 00:55:36.870 --> 00:55:38.910 That becomes known as time dilation. 00:55:38.910 --> 00:55:41.830 The time between ticks has stretched, 00:55:41.830 --> 00:55:46.170 which is to say the clock is running slowly as we measure. 00:55:46.170 --> 00:55:48.780 We measure the moving clock to run slowly 00:55:48.780 --> 00:55:51.270 by that same factor gamma. 00:55:51.270 --> 00:55:53.160 The time between ticks gets stretched. 00:55:53.160 --> 00:55:56.010 Remember, gamma is greater than 1. 00:55:56.010 --> 00:55:58.950 So the time between ticks gets stretched. 00:55:58.950 --> 00:56:02.100 And that's the same with the clock is running slowly. 00:56:02.100 --> 00:56:04.558 Meanwhile, the person on the train says, you're ridiculous. 00:56:04.558 --> 00:56:06.183 I had the clock with me the whole time. 00:56:06.183 --> 00:56:07.110 It kept perfect time. 00:56:07.110 --> 00:56:08.790 But your clock ran slowly. 00:56:08.790 --> 00:56:10.920 I watched as I ran by the station. 00:56:10.920 --> 00:56:14.590 Perfectly symmetrical conclusions. 00:56:14.590 --> 00:56:17.610 So Einstein was working all this out, very much inspired 00:56:17.610 --> 00:56:21.810 by Ernst Mach, by this notion of positivism, of what can we 00:56:21.810 --> 00:56:24.840 hope to measure, not starting with forces 00:56:24.840 --> 00:56:27.570 but with the force-free motion of objects 00:56:27.570 --> 00:56:30.420 through space and time, and really trying to bring it back 00:56:30.420 --> 00:56:31.740 to, what would be measurable? 00:56:31.740 --> 00:56:35.100 What would I see if I were in this situation? 00:56:35.100 --> 00:56:38.610 One of his teachers at the ETH, a mathematician 00:56:38.610 --> 00:56:42.450 named Hermann Minkowski, had formed a deservedly low opinion 00:56:42.450 --> 00:56:43.710 of student Einstein. 00:56:43.710 --> 00:56:46.060 Einstein used to cut class, was very rude. 00:56:46.060 --> 00:56:49.290 But one of their mutual friends, after Einstein's paper 00:56:49.290 --> 00:56:52.710 came out, sent the paper to Minkowski saying, you know, 00:56:52.710 --> 00:56:54.370 it's actually kind of interesting. 00:56:54.370 --> 00:56:56.610 Take a look, to paraphrase. 00:56:56.610 --> 00:56:59.700 And Minkowski said, well, despite the fact 00:56:59.700 --> 00:57:02.430 that I knew Einstein was never going to amount to anything, 00:57:02.430 --> 00:57:03.300 I read the paper. 00:57:03.300 --> 00:57:05.310 And I was right, Minkowski says. 00:57:05.310 --> 00:57:08.110 He really made a mess of this, as well. 00:57:08.110 --> 00:57:11.010 So Minkowski's just interested enough 00:57:11.010 --> 00:57:13.380 to redo Einstein's work in a form that 00:57:13.380 --> 00:57:15.090 made much more sense to Minkowski, 00:57:15.090 --> 00:57:18.060 who was, after all, a professional geometer. 00:57:18.060 --> 00:57:19.450 He wasn't just a mathematician. 00:57:19.450 --> 00:57:21.660 He loved geometry most of all. 00:57:21.660 --> 00:57:24.600 So Minkowski, not Einstein, is the one 00:57:24.600 --> 00:57:26.310 who actually brings these pieces together 00:57:26.310 --> 00:57:28.470 a few years later in-- it was published 00:57:28.470 --> 00:57:31.410 in 1908 instead of 1905. 00:57:31.410 --> 00:57:34.080 And he says, all this talk about moving trains 00:57:34.080 --> 00:57:37.830 and polished mirrors, all of that's just a distraction. 00:57:37.830 --> 00:57:40.860 To a properly trained mathematician, 00:57:40.860 --> 00:57:43.350 which Einstein was not, all we're doing 00:57:43.350 --> 00:57:46.290 is performing rotations or projections 00:57:46.290 --> 00:57:49.200 in a certain kind of space, in this case 00:57:49.200 --> 00:57:53.940 a spacetime in which there's, say, one direction of space 00:57:53.940 --> 00:57:56.100 running along the horizontal axis 00:57:56.100 --> 00:57:58.990 and one dimension of time running up the page. 00:57:58.990 --> 00:58:01.140 We now call these Minkowski diagrams 00:58:01.140 --> 00:58:04.380 in his honor, or simply spacetime diagrams. 00:58:04.380 --> 00:58:06.720 None of this appears in Einstein's early work. 00:58:06.720 --> 00:58:10.020 This was done by his former teacher in response 00:58:10.020 --> 00:58:13.680 to what Minkowski considered to be Einstein's continuing 00:58:13.680 --> 00:58:15.810 confusion and sloppiness. 00:58:15.810 --> 00:58:19.740 And there's a benefit from doing that, Minkowski finds. 00:58:19.740 --> 00:58:23.100 He agrees with Einstein that we will disagree 00:58:23.100 --> 00:58:24.760 on certain kinds of measurements, 00:58:24.760 --> 00:58:27.360 for example lengths and durations of time, 00:58:27.360 --> 00:58:29.730 because we disagree on simultaneity. 00:58:29.730 --> 00:58:31.800 But Minkowski finds something that had not been 00:58:31.800 --> 00:58:33.640 so clear to Einstein himself. 00:58:33.640 --> 00:58:37.380 There are combinations of those kinds of intervals 00:58:37.380 --> 00:58:39.450 on which we will all agree. 00:58:39.450 --> 00:58:43.080 This is what we would now call a spacetime invariant. 00:58:43.080 --> 00:58:46.590 Put together, a combination of the time interval 00:58:46.590 --> 00:58:51.630 minus the space interval, a relative minus sign and each 00:58:51.630 --> 00:58:53.880 of those quantities squared, that combination 00:58:53.880 --> 00:58:55.650 we will all agree on as long as we're 00:58:55.650 --> 00:58:59.790 each in states of non-accelerating motion 00:58:59.790 --> 00:59:01.500 even though we disagree separately 00:59:01.500 --> 00:59:04.530 on the duration between two events, delta t, or the lengths 00:59:04.530 --> 00:59:06.030 between them, delta x. 00:59:06.030 --> 00:59:09.240 And that, from Minkowski, is what any geometer should do. 00:59:09.240 --> 00:59:11.130 Some relationships remain invariant 00:59:11.130 --> 00:59:12.600 even under changes of coordinates. 00:59:12.600 --> 00:59:16.440 And for Minkowski, that was what any undergraduate geometry 00:59:16.440 --> 00:59:18.430 student should know to do first. 00:59:18.430 --> 00:59:21.060 So we actually have this notion of one kind 00:59:21.060 --> 00:59:25.095 of thing called spacetime coming from Minkowski kind of redoing 00:59:25.095 --> 00:59:26.340 Einstein's work. 00:59:26.340 --> 00:59:29.160 And as Minkowski famously writes in his own article-- 00:59:29.160 --> 00:59:31.360 it was published posthumously; he died quite young. 00:59:31.360 --> 00:59:32.340 And he gave a lecture. 00:59:32.340 --> 00:59:34.560 And it was published soon after he died. 00:59:34.560 --> 00:59:37.420 And he wrote upon introducing this new work, 00:59:37.420 --> 00:59:40.500 "Henceforth space by itself and time 00:59:40.500 --> 00:59:44.070 by itself are doomed to fade away into mere shadows 00:59:44.070 --> 00:59:46.323 and only a kind of union of the two 00:59:46.323 --> 00:59:47.490 will preserve independence." 00:59:47.490 --> 00:59:49.740 And by shadows, he really meant projections, just 00:59:49.740 --> 00:59:53.280 drop perpendicular to the appropriate axis 00:59:53.280 --> 00:59:55.380 and then think about coordinate transformations 00:59:55.380 --> 00:59:58.883 in that spacetime of x and t. 00:59:58.883 --> 01:00:00.300 So that's, again, something you'll 01:00:00.300 --> 01:00:03.030 get much more practice with if you haven't seen it already. 01:00:03.030 --> 01:00:03.960 But that's a preview. 01:00:03.960 --> 01:00:06.138 That comes in response to Einstein's work. 01:00:06.138 --> 01:00:07.680 It wasn't an Einstein's own original. 01:00:07.680 --> 01:00:10.440 Although, just to jump ahead very briefly, 01:00:10.440 --> 01:00:12.185 Einstein first thought that was horrible 01:00:12.185 --> 01:00:13.560 because he didn't like Minkowski. 01:00:13.560 --> 01:00:15.820 But then over the next several years, 01:00:15.820 --> 01:00:17.910 the better part of a decade, Einstein 01:00:17.910 --> 01:00:20.310 himself became more impressed by that way of thinking 01:00:20.310 --> 01:00:22.465 and really adopted it for his own later work 01:00:22.465 --> 01:00:24.840 on what became known as the general theory of relativity. 01:00:24.840 --> 01:00:26.010 That's for later. 01:00:29.470 --> 01:00:31.998 OK, very briefly here's the third part 01:00:31.998 --> 01:00:33.790 of the material I wanted to share with you. 01:00:33.790 --> 01:00:36.123 And then hopefully there'll be some time for discussion, 01:00:36.123 --> 01:00:37.190 as well. 01:00:37.190 --> 01:00:39.670 So this last part is much more brief. 01:00:39.670 --> 01:00:41.680 But it's, how do we make sense of this? 01:00:41.680 --> 01:00:44.500 Why was Einstein doing all this seemingly unusual, 01:00:44.500 --> 01:00:46.210 maybe even crazy stuff, certainly 01:00:46.210 --> 01:00:48.520 out of step with Lorentz, with his own teachers 01:00:48.520 --> 01:00:50.530 like Minkowski? 01:00:50.530 --> 01:00:53.020 How can we account for Einstein's quite idiosyncratic 01:00:53.020 --> 01:00:56.350 approach to what was otherwise a common set of questions 01:00:56.350 --> 01:00:58.745 about the electrodynamics of moving bodies? 01:00:58.745 --> 01:01:01.120 Now, here's some of my favorite work by other colleagues, 01:01:01.120 --> 01:01:03.010 by other historians and physicists who really 01:01:03.010 --> 01:01:06.170 looked at this in great detail. 01:01:06.170 --> 01:01:08.350 So for a long, long time, I mean literally 01:01:08.350 --> 01:01:10.180 for the better part of 100 years, 01:01:10.180 --> 01:01:13.010 since people began taking relativity seriously, 01:01:13.010 --> 01:01:17.555 which is a long time by now, it had become very common to say, 01:01:17.555 --> 01:01:19.180 well, Einstein must have been motivated 01:01:19.180 --> 01:01:21.370 much like Hendrik Lorentz was, really like that 01:01:21.370 --> 01:01:23.530 much of that generation was. 01:01:23.530 --> 01:01:25.690 Einstein must have been responding 01:01:25.690 --> 01:01:28.780 to the null result from Michelson and Morley 01:01:28.780 --> 01:01:31.060 and their interferometer, that Einstein 01:01:31.060 --> 01:01:34.030 must have been trying to explain why they couldn't measure 01:01:34.030 --> 01:01:37.240 our motion through the ether much as Lorentz, we know, 01:01:37.240 --> 01:01:39.190 very explicitly was trying to do. 01:01:39.190 --> 01:01:42.130 And there's a fascinating-- one of the first really careful 01:01:42.130 --> 01:01:45.040 examinations of that claim was by Gerald Holton, who's 01:01:45.040 --> 01:01:47.380 a real kind of hero of mine. 01:01:47.380 --> 01:01:51.700 Holton did his first PhD in physics, 01:01:51.700 --> 01:01:54.460 low-temperature physics, and then retooled many years later 01:01:54.460 --> 01:01:55.750 in the history of science. 01:01:55.750 --> 01:01:58.450 And he wrote a series of really remarkable essays 01:01:58.450 --> 01:02:02.320 about Einstein once a lot of Einstein's papers and letters 01:02:02.320 --> 01:02:04.330 and notes became available. 01:02:04.330 --> 01:02:06.010 Holton was among the first to really dig 01:02:06.010 --> 01:02:09.040 through these with great care and almost 01:02:09.040 --> 01:02:11.650 like a detective going through the evidence. 01:02:11.650 --> 01:02:13.450 And what Holton concluded was it's 01:02:13.450 --> 01:02:15.580 not clear that Einstein even knew 01:02:15.580 --> 01:02:17.890 about the Michelson-Morley interferometer. 01:02:17.890 --> 01:02:20.268 Lorentz knew about it and followed it carefully. 01:02:20.268 --> 01:02:22.810 There's very little trace that Einstein paid it any attention 01:02:22.810 --> 01:02:23.310 at all. 01:02:23.310 --> 01:02:25.780 If he did know about it, it was kind of in passing. 01:02:25.780 --> 01:02:29.560 It was certainly not front of mind in the months and years 01:02:29.560 --> 01:02:32.110 leading up to the 1905 paper. 01:02:32.110 --> 01:02:34.000 He might have known about it secondhand 01:02:34.000 --> 01:02:36.340 from reading through all the footnotes of Lorentz. 01:02:36.340 --> 01:02:38.800 But it's not something he seems to have been paying 01:02:38.800 --> 01:02:42.110 much attention to at all. 01:02:42.110 --> 01:02:43.780 And so there's nice textual evidence 01:02:43.780 --> 01:02:45.940 even in Einstein's paper, that 1905 paper 01:02:45.940 --> 01:02:48.910 that I keep showing some brief excerpts from. 01:02:48.910 --> 01:02:51.790 Again, this is on the first or second page. 01:02:51.790 --> 01:02:56.650 When he's trying to reason why we should think about maybe 01:02:56.650 --> 01:02:58.990 giving up on the ether, he mentions-- 01:02:58.990 --> 01:03:00.730 without citing any of them-- he mentions 01:03:00.730 --> 01:03:03.700 several unsuccessful attempts to discover 01:03:03.700 --> 01:03:06.850 any motion of the Earth relative to the light medium, the ether. 01:03:06.850 --> 01:03:08.693 He doesn't say which ones he means. 01:03:08.693 --> 01:03:11.110 But he actually then goes on to say in the same paragraph, 01:03:11.110 --> 01:03:14.875 none of these have found any deviation to first order in v 01:03:14.875 --> 01:03:16.030 over c. 01:03:16.030 --> 01:03:18.040 And what's so striking, as Holton reminds us, 01:03:18.040 --> 01:03:20.950 is Michelson-Morley was actually second order. 01:03:20.950 --> 01:03:23.650 Einstein seems to be talking about a whole different class 01:03:23.650 --> 01:03:26.133 of earlier experiments even before Michelson 01:03:26.133 --> 01:03:26.800 got in the game. 01:03:29.500 --> 01:03:31.030 He's certainly not obsessing over 01:03:31.030 --> 01:03:32.822 the Michelson-Morley interferometer the way 01:03:32.822 --> 01:03:34.180 other people were. 01:03:34.180 --> 01:03:37.060 And so some people then read Holton's analysis 01:03:37.060 --> 01:03:39.322 to say a kind of overcorrection. 01:03:39.322 --> 01:03:40.780 Does that mean Einstein didn't care 01:03:40.780 --> 01:03:43.060 about any kinds of experiments at all? 01:03:43.060 --> 01:03:45.220 If he wasn't trying to respond directly 01:03:45.220 --> 01:03:46.750 to the Michelson-Morley experiment, 01:03:46.750 --> 01:03:49.635 was he just off in a kind of philosophical dream world? 01:03:49.635 --> 01:03:51.010 And that's where I think we again 01:03:51.010 --> 01:03:53.770 can now say quite firmly no. 01:03:53.770 --> 01:03:55.330 In fact, it makes sense to go back 01:03:55.330 --> 01:03:59.770 to Einstein's own early years, his early fascination 01:03:59.770 --> 01:04:02.490 with electrotechnical gadgets, and remind ourselves 01:04:02.490 --> 01:04:07.660 what his day job was in the early 1900s, including 1905. 01:04:07.660 --> 01:04:11.200 Put him back in the patent office in Central Europe 01:04:11.200 --> 01:04:13.610 at this very specific moment. 01:04:13.610 --> 01:04:16.870 So let's think about Einstein's favorite technology, trains. 01:04:16.870 --> 01:04:18.820 Trains and railroads themselves were actually 01:04:18.820 --> 01:04:21.170 fairly new in the 19th century. 01:04:21.170 --> 01:04:24.640 They were introduced to widespread commercial usage 01:04:24.640 --> 01:04:28.090 for commercial transportation really only 01:04:28.090 --> 01:04:29.950 in the 1830s and '40s. 01:04:29.950 --> 01:04:31.870 Remember, Einstein was born in 1879. 01:04:31.870 --> 01:04:35.650 They were relatively new even in his childhood. 01:04:35.650 --> 01:04:39.770 During this whole time until very late in the 19th century, 01:04:39.770 --> 01:04:42.610 there were no coordinated time zones. 01:04:42.610 --> 01:04:45.340 There was nothing like Eastern Standard Time or Pacific 01:04:45.340 --> 01:04:48.580 Time or Central European Time. 01:04:48.580 --> 01:04:51.160 Each town set its own local time. 01:04:51.160 --> 01:04:52.930 And all the residents could coordinate 01:04:52.930 --> 01:04:56.200 by agreeing that we'll use that clock tower, either 01:04:56.200 --> 01:04:59.710 some municipal building or often a tall church in the town 01:04:59.710 --> 01:05:02.890 square, say that's our local time. 01:05:02.890 --> 01:05:04.630 We'll set our local watches to when 01:05:04.630 --> 01:05:07.810 that clock chimes 12:00 noon. 01:05:07.810 --> 01:05:09.730 So each town kept its own local time. 01:05:09.730 --> 01:05:12.790 And before railway, who would ever need anything else? 01:05:12.790 --> 01:05:15.910 Because one was rarely encountering more than one 01:05:15.910 --> 01:05:18.250 town in a given day. 01:05:18.250 --> 01:05:21.730 After the advent of railroads, you still have this local time. 01:05:21.730 --> 01:05:24.070 But that became more and more of a problem. 01:05:24.070 --> 01:05:26.020 It was true in North America as in Europe 01:05:26.020 --> 01:05:28.650 and other parts of the world, as well. 01:05:28.650 --> 01:05:32.480 So here, closer to Boston, passengers 01:05:32.480 --> 01:05:35.060 riding on the train between Boston and New York 01:05:35.060 --> 01:05:37.580 during this time would have to change their watches 01:05:37.580 --> 01:05:39.590 by an average of 37 minutes. 01:05:39.590 --> 01:05:41.360 Today we're all in the same time zone. 01:05:41.360 --> 01:05:44.360 But that's how different the local variations 01:05:44.360 --> 01:05:47.180 tended to be just up and down the US 01:05:47.180 --> 01:05:49.280 portion of the mid-Atlantic seacoast 01:05:49.280 --> 01:05:51.290 and likewise throughout Europe. 01:05:51.290 --> 01:05:53.960 That was becoming more and more of a problem 01:05:53.960 --> 01:05:56.480 when you have to coordinate lots of trains traveling 01:05:56.480 --> 01:05:59.330 across large distances. 01:05:59.330 --> 01:06:01.820 It wasn't only a problem for commercial railway 01:06:01.820 --> 01:06:03.200 or for shipping. 01:06:03.200 --> 01:06:06.350 It became a very potent, added challenge in Germany 01:06:06.350 --> 01:06:08.330 during Einstein's youth. 01:06:08.330 --> 01:06:10.850 So again, as many of you may know, 01:06:10.850 --> 01:06:13.010 there only became one single country 01:06:13.010 --> 01:06:17.240 of Germany, a unified Germany, in 1871 following 01:06:17.240 --> 01:06:18.590 yet another war with France. 01:06:18.590 --> 01:06:21.435 That was basically the story of the previous 500 years, 01:06:21.435 --> 01:06:23.810 German-speaking lands fighting with French-speaking ones. 01:06:23.810 --> 01:06:25.768 There was another one, the Franco-Prussian war, 01:06:25.768 --> 01:06:27.380 throughout 1870. 01:06:27.380 --> 01:06:28.880 The German-speaking folks prevailed. 01:06:28.880 --> 01:06:31.220 And it was at that moment, in the wake of that war, 01:06:31.220 --> 01:06:34.160 that there was then a first unification 01:06:34.160 --> 01:06:38.660 of a country of Germany, now a much larger expanse of what 01:06:38.660 --> 01:06:42.470 had otherwise been independent German-speaking territories. 01:06:42.470 --> 01:06:44.420 So now there's an added reason to worry 01:06:44.420 --> 01:06:47.600 about trains that have to be coordinated across distances. 01:06:47.600 --> 01:06:49.700 There's now a new country's worth 01:06:49.700 --> 01:06:52.730 that has to defend its borders all the way from basically 01:06:52.730 --> 01:06:58.580 Poland or Russia on the East and France on the West. 01:06:58.580 --> 01:07:02.810 And there's a famous quotation from a leading German general, 01:07:02.810 --> 01:07:06.770 Count von Moltke, who in the 1890s, 20 01:07:06.770 --> 01:07:09.530 years into German unification, is basically saying, 01:07:09.530 --> 01:07:10.950 we have a problem on our hands. 01:07:10.950 --> 01:07:13.760 We have to coordinate trains for military purposes 01:07:13.760 --> 01:07:19.710 as well as commercial, passenger rail, and merchant shipping. 01:07:19.710 --> 01:07:21.350 We have a problem with the fact that we 01:07:21.350 --> 01:07:23.390 don't have unified time zones. 01:07:23.390 --> 01:07:25.470 This is all happening in Einstein's childhood. 01:07:25.470 --> 01:07:27.980 Remember, Einstein was born in 1879, 01:07:27.980 --> 01:07:30.620 very early in this period of unified Germany 01:07:30.620 --> 01:07:35.070 and a new focus on coordinating clocks at a distance. 01:07:35.070 --> 01:07:37.960 So one of the main ideas that many clever people, inventors, 01:07:37.960 --> 01:07:40.460 came up with throughout Europe and other parts of the world, 01:07:40.460 --> 01:07:43.460 as well, was to try to coordinate clocks 01:07:43.460 --> 01:07:46.160 and therefore help coordinate train stations 01:07:46.160 --> 01:07:47.960 in these different cities. 01:07:47.960 --> 01:07:49.850 Now, much of continental Europe was now 01:07:49.850 --> 01:07:52.250 being connected by rail. 01:07:52.250 --> 01:07:55.790 If the major hubs, if the major train stations 01:07:55.790 --> 01:07:58.820 could agree on the time, then you could set your watch then. 01:07:58.820 --> 01:08:02.720 And the trains could be better coordinated throughout even 01:08:02.720 --> 01:08:04.190 into the hinterlands. 01:08:04.190 --> 01:08:06.830 And the main idea that many inventors and entrepreneurs 01:08:06.830 --> 01:08:11.180 kind of zeroed in on was to install these so-called 01:08:11.180 --> 01:08:13.970 [GERMAN] clocks, mother clocks, central clocks 01:08:13.970 --> 01:08:16.340 that you would say were the standard ones. 01:08:16.340 --> 01:08:19.729 And then connect those by electromagnetic signal, 01:08:19.729 --> 01:08:22.370 either telegraph or, increasingly, radio waves, 01:08:22.370 --> 01:08:24.410 literally traveling electromagnetic waves 01:08:24.410 --> 01:08:25.675 in the ether. 01:08:25.675 --> 01:08:27.800 Some of you might know that the Eiffel Tower, which 01:08:27.800 --> 01:08:29.870 is under construction in just this period, 01:08:29.870 --> 01:08:32.510 was originally built to aid radio communication. 01:08:32.510 --> 01:08:34.939 It was a radio beacon before it was a reason for all of us 01:08:34.939 --> 01:08:35.899 to go visit Paris. 01:08:35.899 --> 01:08:37.729 There were other reasons before that. 01:08:37.729 --> 01:08:39.290 The Eiffel Tower was built really 01:08:39.290 --> 01:08:42.950 in this period in large part to become a radio 01:08:42.950 --> 01:08:46.310 beacon to broadcast standardized time signals. 01:08:46.310 --> 01:08:48.319 And then the idea was you would know 01:08:48.319 --> 01:08:49.789 how far you were from Paris. 01:08:49.789 --> 01:08:52.729 You know there'd be some delay of when you'd expect 01:08:52.729 --> 01:08:54.529 to receive the radio beacon. 01:08:54.529 --> 01:08:57.229 If it's 12:00 noon in Paris when that beam was sent, 01:08:57.229 --> 01:09:00.180 you have an offset based on how far away you are 01:09:00.180 --> 01:09:02.580 and the speed of light that it would take to get there. 01:09:02.580 --> 01:09:04.279 So then these very clever folks who 01:09:04.279 --> 01:09:06.830 make all these gadgets to both receive 01:09:06.830 --> 01:09:10.340 the time, either telegraph or radio wave, 01:09:10.340 --> 01:09:13.939 and then implement the offset and then reset 01:09:13.939 --> 01:09:16.250 the clock in your next train station clock 01:09:16.250 --> 01:09:17.340 and down the line. 01:09:17.340 --> 01:09:20.390 So imagine these coordinated sets of coordinates 01:09:20.390 --> 01:09:24.800 where you have local clocks at every important location that 01:09:24.800 --> 01:09:27.510 are sending and receiving electromagnetic signals 01:09:27.510 --> 01:09:29.729 to coordinate the local time. 01:09:29.729 --> 01:09:31.725 That's exactly the scenario that Einstein 01:09:31.725 --> 01:09:33.350 mentions in the abstract in the opening 01:09:33.350 --> 01:09:36.240 pages of his 1905 paper. 01:09:36.240 --> 01:09:39.649 He doesn't talk about these patent applications 01:09:39.649 --> 01:09:45.300 or about trains in this more practical way. 01:09:45.300 --> 01:09:49.550 But it turns out, as my friend Peter Galison shows 01:09:49.550 --> 01:09:51.609 in this beautiful book Einstein's Clocks, 01:09:51.609 --> 01:09:53.569 Poincare's Maps, this is the subject 01:09:53.569 --> 01:09:56.360 of an enormous tech spree. 01:09:56.360 --> 01:09:59.210 This was the tech challenge of the day for all these 01:09:59.210 --> 01:10:01.400 very smart, young electrical engineers 01:10:01.400 --> 01:10:04.940 to build up and patent every bit, every switch and gear, 01:10:04.940 --> 01:10:07.550 for this way of coordinating clocks at a distance often 01:10:07.550 --> 01:10:11.740 using electromagnetic signals. 01:10:11.740 --> 01:10:15.100 Not only that, Einstein was at the electrotechnical part 01:10:15.100 --> 01:10:17.920 of the Bern patent office, where a lot of these 01:10:17.920 --> 01:10:18.940 were flowing through. 01:10:18.940 --> 01:10:22.000 So he was an examiner on many of the little widgets 01:10:22.000 --> 01:10:25.090 and gadgets as part of this clock-coordination sequence. 01:10:25.090 --> 01:10:27.700 Even better, my favorite part of Peter's otherwise quite 01:10:27.700 --> 01:10:31.090 fascinating book, was that Peter and his research assistants 01:10:31.090 --> 01:10:33.340 pieced together the walk that Einstein 01:10:33.340 --> 01:10:35.620 used to take from his apartment to the office-- 01:10:35.620 --> 01:10:37.750 he had a lovely stroll through Bern 01:10:37.750 --> 01:10:39.370 during this time of his life-- 01:10:39.370 --> 01:10:42.970 and then finding out when each of the clocks along his route 01:10:42.970 --> 01:10:46.498 were wired up to this now coordinated system. 01:10:46.498 --> 01:10:48.040 So literally the clocks that Einstein 01:10:48.040 --> 01:10:50.500 would walk past between his apartment 01:10:50.500 --> 01:10:53.830 and his office were in this exact moment being wired up 01:10:53.830 --> 01:10:56.830 in this new, explicit, electrotechnical clock 01:10:56.830 --> 01:10:59.920 coordination system, not just across distant train stations 01:10:59.920 --> 01:11:03.220 but soon even across the semi-urban regions 01:11:03.220 --> 01:11:04.630 where he lived. 01:11:04.630 --> 01:11:07.810 It was literally his day job and the path 01:11:07.810 --> 01:11:10.030 that he walked to get to work. 01:11:10.030 --> 01:11:13.030 So this notion of using electromagnetic signals 01:11:13.030 --> 01:11:16.840 to coordinate clocks in a measurable, repeatable way 01:11:16.840 --> 01:11:19.450 was of philosophical interest. 01:11:19.450 --> 01:11:21.130 It was certainly inspired in part 01:11:21.130 --> 01:11:22.810 by the writing of Ernst Mach. 01:11:22.810 --> 01:11:26.080 But Einstein was also immersed in a different set of realities 01:11:26.080 --> 01:11:28.330 than someone like Hendrik Lorentz 01:11:28.330 --> 01:11:30.190 or the other Maxwellians. 01:11:30.190 --> 01:11:33.640 And so when he comes to the question of electrodynamics 01:11:33.640 --> 01:11:35.680 of moving bodies, Einstein's immersed 01:11:35.680 --> 01:11:39.310 in different conversations and day-to-day questions 01:11:39.310 --> 01:11:43.780 compared to those of the physics elite of his day. 01:11:43.780 --> 01:11:48.370 So we come back to this very iconic but kind of unusual 01:11:48.370 --> 01:11:50.800 paper from 1905, "On the Electrodynamics 01:11:50.800 --> 01:11:52.510 of Moving Bodies." 01:11:52.510 --> 01:11:55.720 I think we can make a bit more sense of it, informed by work 01:11:55.720 --> 01:11:59.590 by people like Peter Galison. 01:11:59.590 --> 01:12:03.740 Einstein's paper has almost no references. 01:12:03.740 --> 01:12:06.410 Much like many patent applications, 01:12:06.410 --> 01:12:10.640 you want to emphasize priority and downplay precedence. 01:12:10.640 --> 01:12:13.098 Einstein focuses on the operational details. 01:12:13.098 --> 01:12:15.140 How would you actually perform these measurements 01:12:15.140 --> 01:12:17.540 and compare the answers at some distance? 01:12:17.540 --> 01:12:20.240 It starts to look sort of like a patent application, 01:12:20.240 --> 01:12:24.423 not like a fancy exercise in mathematical physics. 01:12:24.423 --> 01:12:26.090 So we can come back to this question of, 01:12:26.090 --> 01:12:27.840 why was Einstein doing things differently? 01:12:27.840 --> 01:12:28.910 And what was he up to? 01:12:28.910 --> 01:12:31.970 And we see him really enmeshed in just a different set 01:12:31.970 --> 01:12:35.240 of ideas, of philosophical conversations, 01:12:35.240 --> 01:12:38.870 of mathematical techniques, and also of actual gadgets 01:12:38.870 --> 01:12:42.430 compared to some of the other experts of his day.