WEBVTT 00:00:00.000 --> 00:00:01.944 align:middle line:90% [SQUEAKING] 00:00:01.944 --> 00:00:03.888 align:middle line:90% [RUSTLING] 00:00:03.888 --> 00:00:05.832 align:middle line:90% [CLICKING] 00:00:05.832 --> 00:00:11.680 align:middle line:90% 00:00:11.680 --> 00:00:14.620 align:middle line:84% DAVID KAISER: OK, so today we're going 00:00:14.620 --> 00:00:17.950 align:middle line:84% to be talking about waves in the ether-- 00:00:17.950 --> 00:00:20.260 align:middle line:90% a great topic, I think. 00:00:20.260 --> 00:00:26.860 align:middle line:84% Welcome back to 8225 STS 042, Physics in the 20th Century. 00:00:26.860 --> 00:00:30.760 align:middle line:84% To Maxwell and his really quite extraordinary work 00:00:30.760 --> 00:00:35.530 align:middle line:84% from the 1860s where he unites, as we've seen a few times, 00:00:35.530 --> 00:00:38.170 align:middle line:84% really, the study of optics of light 00:00:38.170 --> 00:00:42.160 align:middle line:84% waves and brings that to be very intimately 00:00:42.160 --> 00:00:45.460 align:middle line:84% connected to the study of electric and magnetic fields 00:00:45.460 --> 00:00:46.420 align:middle line:90% in the ether. 00:00:46.420 --> 00:00:49.990 align:middle line:84% And then we'll be looking for much of that first section 00:00:49.990 --> 00:00:52.870 align:middle line:84% on how some very smart people tried 00:00:52.870 --> 00:00:55.690 align:middle line:84% to generalize Maxwell's work in the years 00:00:55.690 --> 00:00:59.530 align:middle line:84% after Maxwell's publications or, indeed, 00:00:59.530 --> 00:01:01.810 align:middle line:84% after his treatise on electricity magnetism 00:01:01.810 --> 00:01:02.920 align:middle line:90% from the 1870s. 00:01:02.920 --> 00:01:04.420 align:middle line:84% So we'll look, in that case, at some 00:01:04.420 --> 00:01:07.900 align:middle line:84% of the work by Hendrik Lorentz, a remarkably 00:01:07.900 --> 00:01:13.240 align:middle line:84% influential mathematical physicist from the Netherlands. 00:01:13.240 --> 00:01:14.890 align:middle line:84% Then we'll look in the second part 00:01:14.890 --> 00:01:17.800 align:middle line:84% at one of the kinds of experiments 00:01:17.800 --> 00:01:19.810 align:middle line:84% that was making a lot of researchers 00:01:19.810 --> 00:01:22.150 align:middle line:84% around many parts of the world really scratched 00:01:22.150 --> 00:01:25.180 align:middle line:84% their heads about how to make sense of this question of waves 00:01:25.180 --> 00:01:26.800 align:middle line:90% in the ether. 00:01:26.800 --> 00:01:29.475 align:middle line:84% And we'll see what was going on with that experiment. 00:01:29.475 --> 00:01:30.850 align:middle line:84% That was, of course, the reading. 00:01:30.850 --> 00:01:32.267 align:middle line:84% The main reading you had for today 00:01:32.267 --> 00:01:34.900 align:middle line:84% was one of the publications by Michelson-Morley 00:01:34.900 --> 00:01:36.170 align:middle line:90% about their work. 00:01:36.170 --> 00:01:38.590 align:middle line:84% And then we'll come back in the last part for today 00:01:38.590 --> 00:01:40.900 align:middle line:84% and see how Hendrik Lorentz responded 00:01:40.900 --> 00:01:43.120 align:middle line:84% to the Michelson-Morley experiment 00:01:43.120 --> 00:01:45.610 align:middle line:84% as well as to the more mathematical aspects 00:01:45.610 --> 00:01:46.550 align:middle line:90% of Maxwell's work. 00:01:46.550 --> 00:01:47.300 align:middle line:84% So that's what we're going today. 00:01:47.300 --> 00:01:48.880 align:middle line:84% And as I say, some of this stuff I'm 00:01:48.880 --> 00:01:52.060 align:middle line:84% going to skip some steps in their derivations. 00:01:52.060 --> 00:01:56.600 align:middle line:84% And the lecture notes will hopefully help fill those in. 00:01:56.600 --> 00:02:00.760 align:middle line:84% So we've seen a few times by now that starting in 1865, 00:02:00.760 --> 00:02:04.420 align:middle line:84% James Clerk Maxwell came to the conclusion 00:02:04.420 --> 00:02:06.490 align:middle line:84% that light waves were nothing other 00:02:06.490 --> 00:02:09.190 align:middle line:84% than transverse undulations-- that is to say, 00:02:09.190 --> 00:02:13.570 align:middle line:84% a certain kind of wave of electric and magnetic fields 00:02:13.570 --> 00:02:15.640 align:middle line:90% propagating in the ether. 00:02:15.640 --> 00:02:18.763 align:middle line:84% And we all now have the possibility 00:02:18.763 --> 00:02:20.680 align:middle line:84% to purchase our own set of Maxwell's equations 00:02:20.680 --> 00:02:21.500 align:middle line:90% on a T-shirt. 00:02:21.500 --> 00:02:22.690 align:middle line:84% Some of you might actually already own 00:02:22.690 --> 00:02:24.273 align:middle line:84% one, in which case, I'm quite jealous. 00:02:24.273 --> 00:02:27.100 align:middle line:84% So what I want to do first is walk through at least briefly, 00:02:27.100 --> 00:02:28.780 align:middle line:90% why did Maxwell think that? 00:02:28.780 --> 00:02:31.690 align:middle line:84% What was the basis for Maxwell's conclusion 00:02:31.690 --> 00:02:35.050 align:middle line:84% that light was nothing but these electric and magnetic waves 00:02:35.050 --> 00:02:36.580 align:middle line:90% in the ether? 00:02:36.580 --> 00:02:39.610 align:middle line:84% So first, you may recall from previous studies 00:02:39.610 --> 00:02:44.290 align:middle line:84% of electromagnetism that there are four different kinds 00:02:44.290 --> 00:02:46.610 align:middle line:84% of fields that appear here on this side, 00:02:46.610 --> 00:02:49.270 align:middle line:84% on the left-hand side of these otherwise quite 00:02:49.270 --> 00:02:51.440 align:middle line:90% succinct Maxwell's equations. 00:02:51.440 --> 00:02:56.840 align:middle line:84% We see a D, a B, an E, and an H. Actually, as you may remember, 00:02:56.840 --> 00:02:59.640 align:middle line:84% those aren't all independent of each other. 00:02:59.640 --> 00:03:02.900 align:middle line:84% And in fact, D is often called the displacement field 00:03:02.900 --> 00:03:05.630 align:middle line:84% is, in most instances, just proportional 00:03:05.630 --> 00:03:07.730 align:middle line:90% to E, the electric field. 00:03:07.730 --> 00:03:09.950 align:middle line:84% And likewise, H, which is sometimes 00:03:09.950 --> 00:03:14.510 align:middle line:84% called the magnetizing field, is also, under many circumstances, 00:03:14.510 --> 00:03:18.320 align:middle line:84% just proportional to the magnetic field B. 00:03:18.320 --> 00:03:21.740 align:middle line:84% So really, what we're looking at for most applications 00:03:21.740 --> 00:03:25.370 align:middle line:84% of interest are four equations governing actually 00:03:25.370 --> 00:03:29.090 align:middle line:84% two physically distinct quantities-- 00:03:29.090 --> 00:03:31.200 align:middle line:84% the electric and magnetic fields. 00:03:31.200 --> 00:03:34.160 align:middle line:84% Now, these terms of proportionality 00:03:34.160 --> 00:03:38.960 align:middle line:84% in modern parlance, epsilon, this Greek letter epsilon, that 00:03:38.960 --> 00:03:41.270 align:middle line:84% relates the displacement field to the electric field, 00:03:41.270 --> 00:03:43.430 align:middle line:84% that's what we would call the dielectric constant. 00:03:43.430 --> 00:03:45.500 align:middle line:84% Sometimes it's called the permittivity. 00:03:45.500 --> 00:03:47.270 align:middle line:84% We saw we had a little indication 00:03:47.270 --> 00:03:49.370 align:middle line:84% in the previous lecture, to Maxwell 00:03:49.370 --> 00:03:52.410 align:middle line:84% and his circle, that was really like a spring constant. 00:03:52.410 --> 00:03:55.640 align:middle line:84% It was a way of characterizing the responsiveness of either 00:03:55.640 --> 00:03:58.280 align:middle line:84% the ether itself or some other material that 00:03:58.280 --> 00:04:00.260 align:middle line:84% might be placed within the ether, 00:04:00.260 --> 00:04:03.200 align:middle line:84% like some insulating or dielectric material. 00:04:03.200 --> 00:04:06.110 align:middle line:84% Likewise, we will call mu-- we today call 00:04:06.110 --> 00:04:08.360 align:middle line:90% mu the magnetic permeability. 00:04:08.360 --> 00:04:10.893 align:middle line:84% For the Maxwellians, it was also, again, 00:04:10.893 --> 00:04:12.560 align:middle line:84% a different kind of-- basically a spring 00:04:12.560 --> 00:04:15.350 align:middle line:84% constant, a kind of elastic feature of the medium. 00:04:15.350 --> 00:04:19.130 align:middle line:84% Now, what's important is that for Maxwell and his generation, 00:04:19.130 --> 00:04:24.200 align:middle line:84% within the ether, these took on simple numerical values. 00:04:24.200 --> 00:04:27.560 align:middle line:84% They just became constants with reference values. 00:04:27.560 --> 00:04:29.810 align:middle line:84% This was a number with a particular value, 00:04:29.810 --> 00:04:34.190 align:middle line:84% and that was the value of, say, the permittivity of the ether 00:04:34.190 --> 00:04:36.020 align:middle line:84% or the magnetic permeability of ether. 00:04:36.020 --> 00:04:38.690 align:middle line:84% So epsilon just became some constant epsilon 0. 00:04:38.690 --> 00:04:42.030 align:middle line:84% Mu likewise became some constant mu 0. 00:04:42.030 --> 00:04:47.190 align:middle line:84% Moreover, Maxwell realized, if you look at the source terms, 00:04:47.190 --> 00:04:50.430 align:middle line:84% the right-hand side of some of these equations-- sorry-- 00:04:50.430 --> 00:04:53.610 align:middle line:84% then you see that there are some terms referring 00:04:53.610 --> 00:04:56.130 align:middle line:84% to either the electric charge density 00:04:56.130 --> 00:04:59.880 align:middle line:84% rho or an electric current capital J. Well, 00:04:59.880 --> 00:05:02.760 align:middle line:84% Maxwell began to apply his own new equations 00:05:02.760 --> 00:05:06.420 align:middle line:84% before they were written in this very nice convenient form 00:05:06.420 --> 00:05:09.000 align:middle line:84% that we inherit from Oliver Heaviside. 00:05:09.000 --> 00:05:10.740 align:middle line:84% Maxwell began applying his equations 00:05:10.740 --> 00:05:13.650 align:middle line:84% to a region of space that was filled only 00:05:13.650 --> 00:05:17.280 align:middle line:84% with ether, a region of what we would call empty space. 00:05:17.280 --> 00:05:19.720 align:middle line:84% To Maxwell, it was never truly empty because, of course, 00:05:19.720 --> 00:05:23.580 align:middle line:84% it was filled at least with this all pervasive luminiferous 00:05:23.580 --> 00:05:24.090 align:middle line:90% ether. 00:05:24.090 --> 00:05:26.190 align:middle line:84% But he wanted to, in particular, consider a region 00:05:26.190 --> 00:05:29.280 align:middle line:84% where there was no bunch of no clump of electrically 00:05:29.280 --> 00:05:33.190 align:middle line:84% charged matter-- so rho would vanish in that region of space. 00:05:33.190 --> 00:05:34.830 align:middle line:84% There was no electric current flowing, 00:05:34.830 --> 00:05:37.800 align:middle line:84% and so J would vanish-- capital J. 00:05:37.800 --> 00:05:40.920 align:middle line:84% Then, it takes only a couple of steps, the kinds of steps 00:05:40.920 --> 00:05:44.560 align:middle line:84% that he was very good at as second wrangler at Cambridge. 00:05:44.560 --> 00:05:48.370 align:middle line:84% It was only a few steps to then rearrange these four equations 00:05:48.370 --> 00:05:52.420 align:middle line:84% on the T-shirt into actually two identical equations, 00:05:52.420 --> 00:05:56.380 align:middle line:84% to a pair of equations-- one for the electric field and one 00:05:56.380 --> 00:05:58.220 align:middle line:90% for the magnetic field. 00:05:58.220 --> 00:06:00.760 align:middle line:84% And so you could manipulate those four equations 00:06:00.760 --> 00:06:03.243 align:middle line:84% by taking the divergence of one and so on 00:06:03.243 --> 00:06:05.410 align:middle line:84% and the curl of the other, the kind of manipulations 00:06:05.410 --> 00:06:07.150 align:middle line:90% that wranglers are very good at. 00:06:07.150 --> 00:06:09.160 align:middle line:84% And he boiled down his four equations 00:06:09.160 --> 00:06:11.200 align:middle line:84% in this simple case of considering 00:06:11.200 --> 00:06:13.750 align:middle line:84% the electric and magnetic fields in regions that were 00:06:13.750 --> 00:06:15.640 align:middle line:90% filled only with the ether. 00:06:15.640 --> 00:06:18.298 align:middle line:84% He could form two versions of the same equation. 00:06:18.298 --> 00:06:19.840 align:middle line:84% Both the electric and magnetic fields 00:06:19.840 --> 00:06:21.682 align:middle line:84% would obey the same form of the equation. 00:06:21.682 --> 00:06:23.890 align:middle line:84% Again, just as a reminder in case you haven't seen it 00:06:23.890 --> 00:06:28.030 align:middle line:84% before, this upside down triangle-- 00:06:28.030 --> 00:06:29.440 align:middle line:90% sometimes called nabla-- 00:06:29.440 --> 00:06:32.560 align:middle line:84% that's a shorthand for the second derivatives 00:06:32.560 --> 00:06:34.150 align:middle line:90% in the spatial directions. 00:06:34.150 --> 00:06:38.770 align:middle line:84% That's like d by dx squared plus d by dy squared 00:06:38.770 --> 00:06:40.300 align:middle line:90% plus d by dz squared. 00:06:40.300 --> 00:06:43.390 align:middle line:84% How is this quantity varying in space 00:06:43.390 --> 00:06:47.330 align:middle line:84% by taking the second derivatives of spatial variation? 00:06:47.330 --> 00:06:51.200 align:middle line:84% And what Maxwell found is he could relate those spatially 00:06:51.200 --> 00:06:54.500 align:middle line:84% varying quantities to the way that same quantity-- 00:06:54.500 --> 00:06:55.700 align:middle line:90% either E or B-- 00:06:55.700 --> 00:06:57.270 align:middle line:90% would vary over time. 00:06:57.270 --> 00:07:00.710 align:middle line:84% So you see, related to the second derivatives of time 00:07:00.710 --> 00:07:03.650 align:middle line:84% with some proportionality that turned out 00:07:03.650 --> 00:07:06.350 align:middle line:84% to be the product of those two spring 00:07:06.350 --> 00:07:08.600 align:middle line:84% constants-- the dielectric constant 00:07:08.600 --> 00:07:10.280 align:middle line:84% and the magnetic permeability when 00:07:10.280 --> 00:07:13.940 align:middle line:84% they take their simple constant values in the vacuum. 00:07:13.940 --> 00:07:18.530 align:middle line:84% So this is why Maxwell started getting quite excited in 1865. 00:07:18.530 --> 00:07:23.540 align:middle line:84% He realized largely because of his Cambridge Wrangler or math 00:07:23.540 --> 00:07:26.450 align:middle line:84% tripos training that this form of the equation 00:07:26.450 --> 00:07:28.490 align:middle line:90% is very, very familiar. 00:07:28.490 --> 00:07:30.140 align:middle line:84% This was, as he already well knew, 00:07:30.140 --> 00:07:33.510 align:middle line:84% the form of a wave equation for a traveling wave. 00:07:33.510 --> 00:07:35.510 align:middle line:84% Again, I go through this in a little more detail 00:07:35.510 --> 00:07:38.113 align:middle line:84% in the lecture notes if this is new for you. 00:07:38.113 --> 00:07:39.030 align:middle line:90% We'll just go through. 00:07:39.030 --> 00:07:42.870 align:middle line:84% We'll take a quick look here, unpack that a bit further. 00:07:42.870 --> 00:07:45.510 align:middle line:84% So every good Cambridge Wrangler knew, in fact, 00:07:45.510 --> 00:07:47.930 align:middle line:84% even some of the not such good Cambridge students 00:07:47.930 --> 00:07:50.990 align:middle line:84% knew by this point that there was a general form 00:07:50.990 --> 00:07:54.385 align:middle line:84% to represent a wave equation for, say, a traveling wave. 00:07:54.385 --> 00:07:55.760 align:middle line:84% And it would take this form where 00:07:55.760 --> 00:07:58.790 align:middle line:84% you have the second derivative over space-- 00:07:58.790 --> 00:08:00.620 align:middle line:90% nabla squared or del squared. 00:08:00.620 --> 00:08:02.450 align:middle line:84% You have second derivatives in time, 00:08:02.450 --> 00:08:04.310 align:middle line:84% and you have this proportionality 00:08:04.310 --> 00:08:07.910 align:middle line:84% given by the speed with which the wave was traveling. 00:08:07.910 --> 00:08:09.920 align:middle line:90% Say v was the speed of the wave. 00:08:09.920 --> 00:08:12.110 align:middle line:84% So if you have some wave-like quantity, like, say, 00:08:12.110 --> 00:08:15.710 align:middle line:84% the amplitude of the wave, it would vary over time and space. 00:08:15.710 --> 00:08:17.930 align:middle line:84% And it would vary according to this differential 00:08:17.930 --> 00:08:21.380 align:middle line:84% equation where the key part was v is the speed of the wave. 00:08:21.380 --> 00:08:24.710 align:middle line:84% Now we go back-- oh, let's just simplify. 00:08:24.710 --> 00:08:27.540 align:middle line:84% Consider motion in a single direction of space. 00:08:27.540 --> 00:08:30.320 align:middle line:84% So instead of considering x, y, and z, let's just 00:08:30.320 --> 00:08:34.409 align:middle line:84% consider, to make it simpler, motion only along the x-axis. 00:08:34.409 --> 00:08:37.039 align:middle line:84% Then we can very quickly solve this equation 00:08:37.039 --> 00:08:39.260 align:middle line:84% where you've all probably done many times. 00:08:39.260 --> 00:08:41.210 align:middle line:84% And the solutions in general will be 00:08:41.210 --> 00:08:43.159 align:middle line:90% a series of sines and cosines. 00:08:43.159 --> 00:08:44.960 align:middle line:84% It's just a periodic oscillation. 00:08:44.960 --> 00:08:48.130 align:middle line:84% It is, indeed, wave-like behavior, as we'd expect. 00:08:48.130 --> 00:08:51.430 align:middle line:84% So I've introduced some notation here again, 00:08:51.430 --> 00:08:53.550 align:middle line:84% which might be very familiar for you. 00:08:53.550 --> 00:08:55.560 align:middle line:84% K is really just an abbreviation. 00:08:55.560 --> 00:08:57.240 align:middle line:90% It's called the wave number. 00:08:57.240 --> 00:08:59.790 align:middle line:84% It just goes inversely with the wavelength, 00:08:59.790 --> 00:09:02.130 align:middle line:90% as you might have seen before. 00:09:02.130 --> 00:09:04.380 align:middle line:84% The lowercase Greek letter omega-- 00:09:04.380 --> 00:09:05.760 align:middle line:90% this one looks kind of like a w. 00:09:05.760 --> 00:09:07.080 align:middle line:90% That's the omega letter. 00:09:07.080 --> 00:09:08.610 align:middle line:90% That is the frequency. 00:09:08.610 --> 00:09:10.680 align:middle line:84% In fact, it's the angular frequency. 00:09:10.680 --> 00:09:13.750 align:middle line:84% And that just goes inversely with the period of the wave. 00:09:13.750 --> 00:09:16.530 align:middle line:84% And so, again, in a way that's probably familiar for you, 00:09:16.530 --> 00:09:21.240 align:middle line:84% when you have a function that satisfies this kind of wave 00:09:21.240 --> 00:09:25.350 align:middle line:84% equation, then the solutions can be thought of as waves 00:09:25.350 --> 00:09:27.280 align:middle line:90% in both space and time. 00:09:27.280 --> 00:09:29.190 align:middle line:84% So here, what I'm doing is presenting 00:09:29.190 --> 00:09:33.600 align:middle line:84% a snapshot at one moment in time-- let's say t equals 0. 00:09:33.600 --> 00:09:36.360 align:middle line:84% How is that wave spread out over space? 00:09:36.360 --> 00:09:39.480 align:middle line:84% If you can imagine just to freeze time and look 00:09:39.480 --> 00:09:41.130 align:middle line:84% to your left and your right, you'd 00:09:41.130 --> 00:09:44.400 align:middle line:84% see some regions where that wave reached a peak, 00:09:44.400 --> 00:09:47.160 align:middle line:84% at a crest, other positions in space, 00:09:47.160 --> 00:09:50.340 align:middle line:84% other values along the x-axis where the wave reached 00:09:50.340 --> 00:09:53.280 align:middle line:84% a trough or a minimum, and it would periodically 00:09:53.280 --> 00:09:55.800 align:middle line:90% rise between crest and trough. 00:09:55.800 --> 00:09:58.680 align:middle line:84% The distance between neighboring crests or peaks 00:09:58.680 --> 00:10:00.998 align:middle line:84% was simply the wavelength lambda inversely 00:10:00.998 --> 00:10:02.040 align:middle line:90% proportional wave number. 00:10:02.040 --> 00:10:06.810 align:middle line:84% Likewise, we could stand at a particular location in space-- 00:10:06.810 --> 00:10:09.630 align:middle line:84% let's say, the origin x equals 0-- 00:10:09.630 --> 00:10:12.390 align:middle line:84% and just clock in how high is the wave 00:10:12.390 --> 00:10:14.230 align:middle line:90% as it passes us over time. 00:10:14.230 --> 00:10:17.460 align:middle line:84% So now we're saying staying in one position in space 00:10:17.460 --> 00:10:21.210 align:middle line:84% and clocking how the amplitude changes as a function of time. 00:10:21.210 --> 00:10:26.010 align:middle line:84% We once again see this very simple oscillating pattern 00:10:26.010 --> 00:10:30.720 align:middle line:84% where, at one moment, we see a peak of the wave passes by. 00:10:30.720 --> 00:10:33.030 align:middle line:84% Some time later, at that same position in space, 00:10:33.030 --> 00:10:34.920 align:middle line:90% we see a trough and vice versa. 00:10:34.920 --> 00:10:37.470 align:middle line:84% And the time duration between peaks 00:10:37.470 --> 00:10:40.680 align:middle line:84% is the period, capital T, inversely proportional 00:10:40.680 --> 00:10:41.820 align:middle line:90% to that frequency omega. 00:10:41.820 --> 00:10:43.530 align:middle line:90% That's very likely familiar. 00:10:43.530 --> 00:10:46.628 align:middle line:84% If that's not so familiar, there's 00:10:46.628 --> 00:10:48.670 align:middle line:84% a little bit more write-up in this lecture notes. 00:10:48.670 --> 00:10:52.800 align:middle line:84% But that's how wranglers had learned to handle things 00:10:52.800 --> 00:10:55.560 align:middle line:84% like the traveling wave mathematically 00:10:55.560 --> 00:10:58.810 align:middle line:84% for a long time in preparation for the Tripos exam. 00:10:58.810 --> 00:11:01.020 align:middle line:84% Now, let's go back to what Maxwell had found, 00:11:01.020 --> 00:11:03.300 align:middle line:84% as I showed you in the previous set of slides. 00:11:03.300 --> 00:11:06.300 align:middle line:84% He found an equation for the electric field 00:11:06.300 --> 00:11:08.250 align:middle line:84% and an equation of identical form 00:11:08.250 --> 00:11:12.480 align:middle line:84% for the magnetic field when he applied his four equations. 00:11:12.480 --> 00:11:15.000 align:middle line:84% In fact, it was more complicated with all the components-- 00:11:15.000 --> 00:11:17.520 align:middle line:84% what we would now consider the four simple equations 00:11:17.520 --> 00:11:20.100 align:middle line:90% for electromagnetism. 00:11:20.100 --> 00:11:23.190 align:middle line:84% When he applied them to a region of only ether, 00:11:23.190 --> 00:11:26.070 align:middle line:90% no nearby charges or currents. 00:11:26.070 --> 00:11:29.490 align:middle line:84% And he found an equation of exactly the same form 00:11:29.490 --> 00:11:32.250 align:middle line:84% that would be obeyed by both the electric and magnetic field. 00:11:32.250 --> 00:11:35.850 align:middle line:84% And not only that, when he plugged in the best-known 00:11:35.850 --> 00:11:38.580 align:middle line:84% values for these kinds of parameters of the ether, 00:11:38.580 --> 00:11:41.587 align:middle line:84% these spring constants, what we would now call the dielectric 00:11:41.587 --> 00:11:43.920 align:middle line:84% constant and the magnetic permittivity or permeability-- 00:11:43.920 --> 00:11:44.700 align:middle line:90% excuse me-- 00:11:44.700 --> 00:11:47.420 align:middle line:84% he found the numerical coincidence 00:11:47.420 --> 00:11:49.820 align:middle line:84% that the product of those two constants 00:11:49.820 --> 00:11:52.640 align:middle line:84% actually was very, very close to what was already 00:11:52.640 --> 00:11:54.860 align:middle line:90% known to be the speed of light. 00:11:54.860 --> 00:11:57.710 align:middle line:84% In fact, he found it went 1 over the square 00:11:57.710 --> 00:11:59.490 align:middle line:90% of that speed of light. 00:11:59.490 --> 00:12:01.910 align:middle line:84% So this quantity looked a lot like 1 00:12:01.910 --> 00:12:04.790 align:middle line:84% over the square of the speed of that traveling wave 00:12:04.790 --> 00:12:08.060 align:middle line:84% as it would look for a generic mathematical treatment 00:12:08.060 --> 00:12:09.080 align:middle line:90% of waves. 00:12:09.080 --> 00:12:14.180 align:middle line:84% Now, the speed of light had been measured for 200 years 00:12:14.180 --> 00:12:16.670 align:middle line:84% by this point, both in optical experiments, 00:12:16.670 --> 00:12:18.690 align:middle line:90% but often in astronomical ones. 00:12:18.690 --> 00:12:21.950 align:middle line:84% So the speed of light was actually a constant, a number 00:12:21.950 --> 00:12:24.440 align:middle line:84% that Maxwell knew about, he'd heard about. 00:12:24.440 --> 00:12:28.790 align:middle line:84% So he was prepared when he began substituting in these seemingly 00:12:28.790 --> 00:12:32.960 align:middle line:84% totally separate parameters or constants-- epsilon and mu. 00:12:32.960 --> 00:12:36.770 align:middle line:84% And he found really, to his surprise, this numerical value 00:12:36.770 --> 00:12:39.810 align:middle line:84% that their product went 1 over the speed of light squared. 00:12:39.810 --> 00:12:44.270 align:middle line:84% That's what drives him to conclude, starting in 1865, 00:12:44.270 --> 00:12:45.620 align:middle line:90% that light waves-- 00:12:45.620 --> 00:12:48.930 align:middle line:84% waves that travel at the characteristic speed c-- 00:12:48.930 --> 00:12:52.200 align:middle line:84% were literally nothing but traveling waves 00:12:52.200 --> 00:12:54.630 align:middle line:84% of electric and magnetic fields in the ether. 00:12:54.630 --> 00:12:56.790 align:middle line:84% These were these transverse undulations 00:12:56.790 --> 00:12:58.620 align:middle line:90% that he began writing about. 00:12:58.620 --> 00:13:00.510 align:middle line:84% That's what gets Maxwell to that conclusion. 00:13:00.510 --> 00:13:03.390 align:middle line:84% I want to give this a little more example of his thought 00:13:03.390 --> 00:13:06.540 align:middle line:84% process for why he concludes that light was nothing 00:13:06.540 --> 00:13:10.210 align:middle line:84% but these waves of electric and magnetic fields in the ether. 00:13:10.210 --> 00:13:13.980 align:middle line:84% OK, so now Maxwell's whole analysis there, 00:13:13.980 --> 00:13:17.010 align:middle line:84% as really quite succinct and elegant as it was, 00:13:17.010 --> 00:13:19.980 align:middle line:84% had made a number of simplifying assumptions. 00:13:19.980 --> 00:13:23.310 align:middle line:84% You might have noticed he was assuming that both the emitter 00:13:23.310 --> 00:13:25.710 align:middle line:84% of those waves, the source of those waves, 00:13:25.710 --> 00:13:28.830 align:middle line:84% and also the receiver of them were both at rest, 00:13:28.830 --> 00:13:30.613 align:middle line:84% not only with respect to each other-- 00:13:30.613 --> 00:13:32.530 align:middle line:84% neither was moving with respect to the other-- 00:13:32.530 --> 00:13:34.980 align:middle line:84% they were both at rest with respect to the ether. 00:13:34.980 --> 00:13:37.860 align:middle line:84% Let's imagine that we have some source-emitting light that's 00:13:37.860 --> 00:13:40.680 align:middle line:84% just sitting absolutely still in the ether, 00:13:40.680 --> 00:13:44.250 align:middle line:84% and it's going to generate those sine and cosine-like waves 00:13:44.250 --> 00:13:46.140 align:middle line:90% of electric and magnetic fields. 00:13:46.140 --> 00:13:48.780 align:middle line:84% And let's say, at some other location, 00:13:48.780 --> 00:13:51.420 align:middle line:84% fixed at rest in the ether is something 00:13:51.420 --> 00:13:54.300 align:middle line:84% that's going to measure or receive them. 00:13:54.300 --> 00:13:56.430 align:middle line:84% So an obvious next question to ask 00:13:56.430 --> 00:14:00.210 align:middle line:84% is, can you generalize Maxwell's treatment of optics 00:14:00.210 --> 00:14:03.060 align:middle line:84% to the case where either the sender or the receiver, 00:14:03.060 --> 00:14:05.340 align:middle line:84% or maybe both, are moving not only 00:14:05.340 --> 00:14:07.440 align:middle line:84% with respect to each other, but even more 00:14:07.440 --> 00:14:09.330 align:middle line:84% important for these folks, moving 00:14:09.330 --> 00:14:11.760 align:middle line:84% with respect to the ether, with respect 00:14:11.760 --> 00:14:15.240 align:middle line:84% to that light-bearing luminiferous ether? 00:14:15.240 --> 00:14:18.570 align:middle line:84% And that was a challenge that many, many leading mathematical 00:14:18.570 --> 00:14:21.720 align:middle line:84% physicists recognized one of the next obvious things 00:14:21.720 --> 00:14:24.690 align:middle line:84% to try downstream from Maxwell's result, 00:14:24.690 --> 00:14:26.460 align:middle line:84% and this became basically the challenge 00:14:26.460 --> 00:14:28.890 align:middle line:84% of the electrodynamics of moving bodies, 00:14:28.890 --> 00:14:32.100 align:middle line:84% a title that we're going to come to many, many times. 00:14:32.100 --> 00:14:34.020 align:middle line:84% For much of today's class, we're going 00:14:34.020 --> 00:14:37.530 align:middle line:84% to look at how a particular mathematical physicist, Hendrik 00:14:37.530 --> 00:14:39.460 align:middle line:84% Lorentz, tried to make sense of this. 00:14:39.460 --> 00:14:41.460 align:middle line:84% So he took on this task, as did many 00:14:41.460 --> 00:14:45.060 align:middle line:84% of his peers, this task of trying to generalize Maxwell's 00:14:45.060 --> 00:14:50.775 align:middle line:84% treatment to the case of moving senders or receivers of light. 00:14:50.775 --> 00:14:52.150 align:middle line:84% Now, on the one hand, this looked 00:14:52.150 --> 00:14:54.310 align:middle line:84% like a pretty straightforward challenge. 00:14:54.310 --> 00:14:58.090 align:middle line:84% Lorentz, like every trained mathematical physicist 00:14:58.090 --> 00:15:00.670 align:middle line:84% of his day, knew how to perform things 00:15:00.670 --> 00:15:02.290 align:middle line:90% like coordinate transformations. 00:15:02.290 --> 00:15:04.930 align:middle line:84% In fact, it was the Galilean coordinate transformation. 00:15:04.930 --> 00:15:07.900 align:middle line:84% Galileo had worked it out in the early 1600s. 00:15:07.900 --> 00:15:10.630 align:middle line:84% It was hardly cutting-edge research. 00:15:10.630 --> 00:15:12.715 align:middle line:84% The idea was, as you may remember 00:15:12.715 --> 00:15:15.310 align:middle line:84% or you may know, Galileo imagined 00:15:15.310 --> 00:15:19.240 align:middle line:84% how to relate the coordinates of, say, someone riding 00:15:19.240 --> 00:15:22.210 align:middle line:84% on a boat moving at a constant speed down a river, 00:15:22.210 --> 00:15:25.810 align:middle line:84% let's say, and how that person might relate her coordinates 00:15:25.810 --> 00:15:29.140 align:middle line:84% to those of an observer standing on the shore 00:15:29.140 --> 00:15:32.830 align:middle line:84% or the side of the lake, standing still, 00:15:32.830 --> 00:15:36.460 align:middle line:84% they would have said, so that you could relate the one 00:15:36.460 --> 00:15:38.950 align:middle line:84% set of coordinates to the other by taking into account 00:15:38.950 --> 00:15:40.700 align:middle line:90% the relative motion. 00:15:40.700 --> 00:15:44.560 align:middle line:84% If we imagine that we're the observer on the shore watching 00:15:44.560 --> 00:15:50.987 align:middle line:84% this boat drift by, then we can relate how the coordinates 00:15:50.987 --> 00:15:52.570 align:middle line:84% of the person on the boat-- let's say, 00:15:52.570 --> 00:15:55.180 align:middle line:84% the origin with that person calls x equals 0-- 00:15:55.180 --> 00:15:59.170 align:middle line:84% how that will shift with respect to our coordinate system. 00:15:59.170 --> 00:16:01.690 align:middle line:84% We realize the boat is drifting at some speed 00:16:01.690 --> 00:16:06.100 align:middle line:84% v. So at later moments in time, the position x 00:16:06.100 --> 00:16:08.530 align:middle line:84% equals 0 on the boat will have drifted away 00:16:08.530 --> 00:16:11.020 align:middle line:84% from what we call x equals 0 on the shore. 00:16:11.020 --> 00:16:13.450 align:middle line:84% And we just take into account of the relative motion 00:16:13.450 --> 00:16:15.670 align:middle line:84% with this speed v. This is what's 00:16:15.670 --> 00:16:18.170 align:middle line:84% called the Galilean Coordinate Transformation, 00:16:18.170 --> 00:16:20.290 align:middle line:84% and this was indeed quite familiar. 00:16:20.290 --> 00:16:24.070 align:middle line:84% It got codified by Newton in the later part of the 1600s. 00:16:24.070 --> 00:16:27.700 align:middle line:84% This was really pretty old, literally textbook stuff 00:16:27.700 --> 00:16:31.930 align:middle line:84% by the time people like Maxwell and Lorentz came along. 00:16:31.930 --> 00:16:35.260 align:middle line:84% But then Lorentz found something that he did not expect. 00:16:35.260 --> 00:16:38.770 align:middle line:84% When he used the totally standard way of relating 00:16:38.770 --> 00:16:40.720 align:middle line:84% coordinates when there's relative motion 00:16:40.720 --> 00:16:43.270 align:middle line:84% between, in this case, say the emitter and the receiver 00:16:43.270 --> 00:16:46.480 align:middle line:84% of light, he put those into Maxwell's equations 00:16:46.480 --> 00:16:50.770 align:middle line:84% that related, remember, derivatives or variations 00:16:50.770 --> 00:16:53.560 align:middle line:84% in space to rates of change over time, 00:16:53.560 --> 00:16:56.050 align:middle line:84% he got something that looked a bit more like a mess. 00:16:56.050 --> 00:16:59.530 align:middle line:84% So when he tried to apply the coordinate transformation 00:16:59.530 --> 00:17:02.320 align:middle line:84% to Maxwell's equations for the propagation 00:17:02.320 --> 00:17:04.720 align:middle line:84% of an electric field in the ether, 00:17:04.720 --> 00:17:07.750 align:middle line:84% he got a form that no longer looked quite so simple 00:17:07.750 --> 00:17:09.609 align:middle line:90% as Maxwell's original form. 00:17:09.609 --> 00:17:12.550 align:middle line:84% Why that have bothered someone like Lorentz? 00:17:12.550 --> 00:17:15.670 align:middle line:84% Because that meant the solutions to this transformed equation 00:17:15.670 --> 00:17:19.000 align:middle line:84% would no longer behave as simple sines and cosines. 00:17:19.000 --> 00:17:20.859 align:middle line:84% And now, you're all on mute, but I 00:17:20.859 --> 00:17:23.740 align:middle line:84% can imagine you're screaming, much like this great Edvard 00:17:23.740 --> 00:17:24.460 align:middle line:90% Munch picture. 00:17:24.460 --> 00:17:25.540 align:middle line:90% That's how I feel. 00:17:25.540 --> 00:17:26.680 align:middle line:90% How could it be? 00:17:26.680 --> 00:17:29.860 align:middle line:84% Why was it such a headache for Lorentz? 00:17:29.860 --> 00:17:31.460 align:middle line:90% Why was it so alarming? 00:17:31.460 --> 00:17:33.590 align:middle line:84% Because people had been measuring light 00:17:33.590 --> 00:17:37.280 align:middle line:84% on Earth for a long, long time and had already figured 00:17:37.280 --> 00:17:41.000 align:middle line:84% out that light behaved more or less like sines and cosines. 00:17:41.000 --> 00:17:45.140 align:middle line:84% In many, many, many applications here on Earth in laboratories 00:17:45.140 --> 00:17:49.190 align:middle line:84% in increasingly precise optical laboratories on Earth, really 00:17:49.190 --> 00:17:52.200 align:middle line:84% getting throughout the 19th century, 00:17:52.200 --> 00:17:56.060 align:middle line:84% people had measured properties of propagating light waves, 00:17:56.060 --> 00:17:57.770 align:middle line:84% or more generally electromagnetic waves 00:17:57.770 --> 00:18:00.080 align:middle line:90% of various wavelengths. 00:18:00.080 --> 00:18:02.390 align:middle line:84% And they routinely found that these waves 00:18:02.390 --> 00:18:06.380 align:middle line:84% were behaving like very, very much like sines and cosines, 00:18:06.380 --> 00:18:08.750 align:middle line:90% exactly as Maxwell had found. 00:18:08.750 --> 00:18:10.170 align:middle line:90% Why that matter? 00:18:10.170 --> 00:18:13.070 align:middle line:84% Well, Lorentz knew that he was doing these measurements, 00:18:13.070 --> 00:18:15.770 align:middle line:84% or his colleagues were on the planet Earth. 00:18:15.770 --> 00:18:18.260 align:middle line:84% He knew the Earth was moving through the ether. 00:18:18.260 --> 00:18:20.488 align:middle line:84% It was moving in its rotation around the sun. 00:18:20.488 --> 00:18:22.280 align:middle line:84% There's no reason to think even the sun was 00:18:22.280 --> 00:18:23.300 align:middle line:90% at rest in the ether. 00:18:23.300 --> 00:18:25.340 align:middle line:84% The Earth was certainly very likely to be 00:18:25.340 --> 00:18:28.070 align:middle line:84% not the center of the universe anymore in the years 00:18:28.070 --> 00:18:29.600 align:middle line:90% well past Copernicus. 00:18:29.600 --> 00:18:33.040 align:middle line:84% So it seemed all but certain that the planet Earth 00:18:33.040 --> 00:18:35.440 align:middle line:84% was in some state of motion through the ether 00:18:35.440 --> 00:18:37.310 align:middle line:90% with this light-bearing ether. 00:18:37.310 --> 00:18:39.190 align:middle line:84% So we should have to take into account 00:18:39.190 --> 00:18:42.940 align:middle line:84% this coordinate transformation because the light waves being 00:18:42.940 --> 00:18:47.260 align:middle line:84% either emitted or received on Earth were not being treated-- 00:18:47.260 --> 00:18:49.720 align:middle line:84% were not at rest with respect to the ether. 00:18:49.720 --> 00:18:50.560 align:middle line:90% They were on Earth. 00:18:50.560 --> 00:18:53.560 align:middle line:84% The Earth is moving, so we're in some relative motion 00:18:53.560 --> 00:18:55.240 align:middle line:90% with respect to the ether. 00:18:55.240 --> 00:18:58.090 align:middle line:84% And yet, in optics labs around the world, 00:18:58.090 --> 00:19:00.520 align:middle line:84% people really did measure properties of light 00:19:00.520 --> 00:19:02.920 align:middle line:84% as if they were just simple sines and cosines. 00:19:02.920 --> 00:19:06.200 align:middle line:84% How could you square these two things? 00:19:06.200 --> 00:19:08.320 align:middle line:84% So Lorentz came up with one part of what 00:19:08.320 --> 00:19:10.112 align:middle line:84% turns out to have been a two-part response. 00:19:10.112 --> 00:19:12.362 align:middle line:84% So we're going to look at both of his responses today. 00:19:12.362 --> 00:19:14.680 align:middle line:84% This is going to take up much of our class today. 00:19:14.680 --> 00:19:18.400 align:middle line:84% His first response was really mathematical. 00:19:18.400 --> 00:19:21.520 align:middle line:84% He was, after all, a remarkably accomplished mathematical 00:19:21.520 --> 00:19:22.210 align:middle line:90% physicist. 00:19:22.210 --> 00:19:25.750 align:middle line:84% So he published this first in the 1890s, this first part. 00:19:25.750 --> 00:19:28.360 align:middle line:84% He just introduces a new time variable. 00:19:28.360 --> 00:19:30.560 align:middle line:90% He calls it local time. 00:19:30.560 --> 00:19:32.980 align:middle line:84% So if you recall in the Galilean transformation-- 00:19:32.980 --> 00:19:35.140 align:middle line:84% let me bring it back up for a moment-- 00:19:35.140 --> 00:19:37.150 align:middle line:84% the standard way to relate coordinates, 00:19:37.150 --> 00:19:38.710 align:middle line:84% I should have emphasized earlier, 00:19:38.710 --> 00:19:42.370 align:middle line:84% you take into account a change between x and x prime. 00:19:42.370 --> 00:19:44.710 align:middle line:84% You watch the boat drift, so you see 00:19:44.710 --> 00:19:49.150 align:middle line:84% that the boat observer's x equals 0 has 00:19:49.150 --> 00:19:50.740 align:middle line:90% moved with respect to your x. 00:19:50.740 --> 00:19:52.870 align:middle line:84% But you assume, as Galileo assumed, 00:19:52.870 --> 00:19:55.030 align:middle line:84% as Newton assumed, that there's no reason 00:19:55.030 --> 00:19:56.860 align:middle line:90% to change your time coordinate. 00:19:56.860 --> 00:19:58.330 align:middle line:84% Your clocks shouldn't be affected 00:19:58.330 --> 00:20:00.490 align:middle line:84% by the fact the boat's drifting down the river. 00:20:00.490 --> 00:20:01.640 align:middle line:90% That was the assumption. 00:20:01.640 --> 00:20:05.140 align:middle line:84% So typically there was no change in the time coordinate, 00:20:05.140 --> 00:20:07.830 align:middle line:84% even when you were considering relative motion. 00:20:07.830 --> 00:20:10.700 align:middle line:84% Well, Lorentz, in a move of really desperation-- 00:20:10.700 --> 00:20:12.770 align:middle line:84% cleverness, but also desperation-- 00:20:12.770 --> 00:20:14.660 align:middle line:84% said, well, what if we revisit that? 00:20:14.660 --> 00:20:18.560 align:middle line:84% What if we introduce a new time that he calls local time 00:20:18.560 --> 00:20:23.570 align:middle line:84% t prime where that also becomes a function of both 00:20:23.570 --> 00:20:25.980 align:middle line:84% the time of the original coordinate system, 00:20:25.980 --> 00:20:30.500 align:middle line:84% the location, say x, and also the relative speed of motion 00:20:30.500 --> 00:20:32.090 align:middle line:90% between them. 00:20:32.090 --> 00:20:36.260 align:middle line:84% If he then reverse engineers what form of transformation 00:20:36.260 --> 00:20:39.440 align:middle line:84% would he need for this new time coordinate t prime, 00:20:39.440 --> 00:20:43.070 align:middle line:84% then he could actually save the form of Maxwell's equations 00:20:43.070 --> 00:20:45.590 align:middle line:84% when he transformed both x and t-- 00:20:45.590 --> 00:20:48.230 align:middle line:84% not only x-- in a particular way, 00:20:48.230 --> 00:20:51.290 align:middle line:84% he could make sure that the Maxwell's wave equation 00:20:51.290 --> 00:20:56.000 align:middle line:84% was invariant under this new set of coordinate transformations. 00:20:56.000 --> 00:20:58.580 align:middle line:84% He could save the form of Maxwell's equations. 00:20:58.580 --> 00:21:02.390 align:middle line:84% Now, Lorentz always, always thought this was just a trick. 00:21:02.390 --> 00:21:06.080 align:middle line:84% He absolutely did not think this was a physical change to how 00:21:06.080 --> 00:21:07.820 align:middle line:90% clocks would measure time. 00:21:07.820 --> 00:21:12.690 align:middle line:84% He did not think that this was a real effect in the world. 00:21:12.690 --> 00:21:15.560 align:middle line:84% It was a clever way to try to relate coordinate systems 00:21:15.560 --> 00:21:18.170 align:middle line:84% that he left really as mathematical. 00:21:18.170 --> 00:21:21.890 align:middle line:84% In fact, he himself calls it fictitious in his own papers. 00:21:21.890 --> 00:21:23.690 align:middle line:84% This was just a way to try to say, 00:21:23.690 --> 00:21:26.600 align:middle line:84% let's refer everything back to the ether rest frame, 00:21:26.600 --> 00:21:28.670 align:middle line:84% and we'll have to do a little more complicated 00:21:28.670 --> 00:21:31.520 align:middle line:84% mathematical jujitsu to understand 00:21:31.520 --> 00:21:35.530 align:middle line:84% why light should continue to behave like sines and cosines. 00:21:35.530 --> 00:21:37.130 align:middle line:84% So I'm going to pause there and ask 00:21:37.130 --> 00:21:41.572 align:middle line:84% if there are any questions on that part so far. 00:21:41.572 --> 00:21:42.780 align:middle line:90% Any questions on any of that? 00:21:42.780 --> 00:21:44.120 align:middle line:90% I see the chat has a few items. 00:21:44.120 --> 00:21:49.260 align:middle line:90% 00:21:49.260 --> 00:21:51.692 align:middle line:84% So indeed, ether has been spelled many ways. 00:21:51.692 --> 00:21:52.650 align:middle line:90% I see that in the chat. 00:21:52.650 --> 00:21:53.610 align:middle line:90% That's definitely true. 00:21:53.610 --> 00:21:57.260 align:middle line:84% And thank you, Tiffany and Julia, for weighing in on that. 00:21:57.260 --> 00:22:00.500 align:middle line:90% 00:22:00.500 --> 00:22:01.870 align:middle line:90% Good question. 00:22:01.870 --> 00:22:06.310 align:middle line:84% He was definitely fixated on this mathematical coordinate 00:22:06.310 --> 00:22:10.390 align:middle line:84% called t, and that had been the time 00:22:10.390 --> 00:22:14.620 align:middle line:84% coordinate since Galileo's time, if not before. 00:22:14.620 --> 00:22:18.010 align:middle line:84% He was intentionally adjusting how 00:22:18.010 --> 00:22:21.730 align:middle line:84% he would compare the time coordinate for, let's say, 00:22:21.730 --> 00:22:24.730 align:middle line:84% one state of motion versus another. 00:22:24.730 --> 00:22:26.920 align:middle line:84% So that part wasn't so surprising, either 00:22:26.920 --> 00:22:28.240 align:middle line:90% for himself or his colleagues. 00:22:28.240 --> 00:22:29.560 align:middle line:90% It was the t coordinate. 00:22:29.560 --> 00:22:32.170 align:middle line:84% T stood for the time read by a clock. 00:22:32.170 --> 00:22:33.258 align:middle line:90% That's what Galileo meant. 00:22:33.258 --> 00:22:34.300 align:middle line:90% That's what Newton meant. 00:22:34.300 --> 00:22:35.500 align:middle line:90% That's what Maxwell meant. 00:22:35.500 --> 00:22:38.860 align:middle line:84% What he wanted to be very careful about was to make sure 00:22:38.860 --> 00:22:41.650 align:middle line:84% his readers knew he didn't take this literally. 00:22:41.650 --> 00:22:44.380 align:middle line:84% It was really a mathematical move to say, 00:22:44.380 --> 00:22:47.800 align:middle line:84% if we somehow have to relate our own local coordinates 00:22:47.800 --> 00:22:51.010 align:middle line:84% to the ether rest frame, which is the physically relevant 00:22:51.010 --> 00:22:53.680 align:middle line:84% comparison, as far as they were concerned-- 00:22:53.680 --> 00:22:55.900 align:middle line:84% these were disturbances in the ether-- 00:22:55.900 --> 00:22:58.930 align:middle line:84% then he wasn't sure what to make of the fact 00:22:58.930 --> 00:23:02.750 align:middle line:84% that the t coordinate for this person might not be the same t 00:23:02.750 --> 00:23:05.300 align:middle line:84% coordinate for someone at rest with respect to the ether. 00:23:05.300 --> 00:23:08.700 align:middle line:84% He would agree it was all about how we measure time on a clock. 00:23:08.700 --> 00:23:12.350 align:middle line:84% He just was convinced it was a kind of illusion. 00:23:12.350 --> 00:23:13.920 align:middle line:90% It was a fictitious thing. 00:23:13.920 --> 00:23:16.730 align:middle line:84% But if you do that, then you can make Maxwell's equations 00:23:16.730 --> 00:23:18.700 align:middle line:90% look like the way one wants to. 00:23:18.700 --> 00:23:21.220 align:middle line:90% 00:23:21.220 --> 00:23:21.720 align:middle line:90% Ah, good. 00:23:21.720 --> 00:23:23.970 align:middle line:84% Gary asked the question, why did Einstein later 00:23:23.970 --> 00:23:27.540 align:middle line:84% say he built his theories on Maxwell rather than on Lorentz? 00:23:27.540 --> 00:23:28.540 align:middle line:90% That's a great question. 00:23:28.540 --> 00:23:31.080 align:middle line:84% I can invite you to ask again in about one or two class 00:23:31.080 --> 00:23:31.830 align:middle line:90% sessions. 00:23:31.830 --> 00:23:34.200 align:middle line:84% We'll talk quite a bit about that, actually. 00:23:34.200 --> 00:23:37.210 align:middle line:84% Yeah, that's an excellent question, Gary. 00:23:37.210 --> 00:23:39.250 align:middle line:84% But I'm going to pause on that one. 00:23:39.250 --> 00:23:42.222 align:middle line:84% Any other questions on what Lorentz was doing in the 1890s? 00:23:42.222 --> 00:23:44.430 align:middle line:84% What was the nature of the challenge or this question 00:23:44.430 --> 00:23:48.840 align:middle line:84% about the behavior of that wave-like equation 00:23:48.840 --> 00:23:50.070 align:middle line:90% that Maxwell found? 00:23:50.070 --> 00:23:52.860 align:middle line:84% It looked so pristine and powerful until you 00:23:52.860 --> 00:23:57.090 align:middle line:84% asked the next obvious question, what if either the sender 00:23:57.090 --> 00:23:59.100 align:middle line:84% or receiver of light is in motion with respect 00:23:59.100 --> 00:23:59.655 align:middle line:90% to the ether? 00:23:59.655 --> 00:24:03.240 align:middle line:84% Uh-oh, the usual tricks for relating coordinates 00:24:03.240 --> 00:24:05.370 align:middle line:84% seem to lead to some real difficulties. 00:24:05.370 --> 00:24:08.203 align:middle line:84% That was the main point of that first part. 00:24:08.203 --> 00:24:09.370 align:middle line:90% Any other questions on that? 00:24:09.370 --> 00:24:10.912 align:middle line:84% If not, I'll jump into the next part. 00:24:10.912 --> 00:24:13.830 align:middle line:90% 00:24:13.830 --> 00:24:15.490 align:middle line:90% OK, good. 00:24:15.490 --> 00:24:19.120 align:middle line:84% Let's go on now to the next part, 00:24:19.120 --> 00:24:21.720 align:middle line:84% which is all about the reading you 00:24:21.720 --> 00:24:24.910 align:middle line:84% had for today, the Michelson-Morley experiment. 00:24:24.910 --> 00:24:29.720 align:middle line:90% 00:24:29.720 --> 00:24:33.160 align:middle line:84% So we've seen many, many times by now Hendrik Lorentz, 00:24:33.160 --> 00:24:36.460 align:middle line:84% like pretty much all active mathematical physicists 00:24:36.460 --> 00:24:38.590 align:middle line:84% and experimental physicists of his day-- 00:24:38.590 --> 00:24:42.700 align:middle line:84% Lorentz knew, just knew, that light propagated in the ether. 00:24:42.700 --> 00:24:45.670 align:middle line:84% These were these transverse undulations in the ether. 00:24:45.670 --> 00:24:47.950 align:middle line:84% So another natural question to ask 00:24:47.950 --> 00:24:50.410 align:middle line:84% is, could you ever detect the fact 00:24:50.410 --> 00:24:53.080 align:middle line:84% that our Earth, our own home laboratory, 00:24:53.080 --> 00:24:54.820 align:middle line:90% was moving through the ether? 00:24:54.820 --> 00:24:57.470 align:middle line:84% As I mentioned on that slide a few slides ago, 00:24:57.470 --> 00:24:59.140 align:middle line:84% the Earth was moving around the Sun. 00:24:59.140 --> 00:25:01.690 align:middle line:84% That was very clearly established for this generation 00:25:01.690 --> 00:25:04.720 align:middle line:84% long ago well past the age of Copernicus. 00:25:04.720 --> 00:25:07.720 align:middle line:84% So there's no reason to think that the Earth is 00:25:07.720 --> 00:25:08.920 align:middle line:90% at rest in the ether. 00:25:08.920 --> 00:25:10.420 align:middle line:84% Maybe even the sun isn't at rest. 00:25:10.420 --> 00:25:12.850 align:middle line:84% There could be all kinds of complicated motions 00:25:12.850 --> 00:25:15.670 align:middle line:84% that we on Earth are going through with respect 00:25:15.670 --> 00:25:18.580 align:middle line:90% to the universal ether. 00:25:18.580 --> 00:25:22.810 align:middle line:84% So could we ever detect our own motions through the ether 00:25:22.810 --> 00:25:24.610 align:middle line:90% based on the behavior of light? 00:25:24.610 --> 00:25:27.190 align:middle line:84% Light are these waves in that all-pervasive ether. 00:25:27.190 --> 00:25:28.720 align:middle line:90% We're moving through the ether. 00:25:28.720 --> 00:25:31.400 align:middle line:84% We measure properties of light all the time. 00:25:31.400 --> 00:25:35.750 align:middle line:84% Could we recognize that we're actually in motion? 00:25:35.750 --> 00:25:37.820 align:middle line:84% And the idea was an analogy much like you 00:25:37.820 --> 00:25:40.760 align:middle line:84% might think of these days if you're 00:25:40.760 --> 00:25:43.670 align:middle line:84% lucky enough to get some fresh air and go for a bicycle ride. 00:25:43.670 --> 00:25:46.550 align:middle line:84% So first, imagine you step outside on a day like today, 00:25:46.550 --> 00:25:48.380 align:middle line:84% where, at least where I'm sitting, 00:25:48.380 --> 00:25:52.040 align:middle line:84% I can see out my windows there's very little breeze or wind. 00:25:52.040 --> 00:25:53.930 align:middle line:84% If I were to walk outside right now, 00:25:53.930 --> 00:25:56.870 align:middle line:84% I would feel no particular wind in my face. 00:25:56.870 --> 00:25:58.460 align:middle line:90% The air is still. 00:25:58.460 --> 00:26:01.700 align:middle line:84% If I just stand still outside, I don't feel anything on my face 00:26:01.700 --> 00:26:07.070 align:middle line:84% because the atmosphere is not in any kind of state of motion. 00:26:07.070 --> 00:26:09.290 align:middle line:84% If, however, I were to either run really 00:26:09.290 --> 00:26:13.160 align:middle line:84% fast or get on a bicycle and pedal really fast, 00:26:13.160 --> 00:26:15.440 align:middle line:90% I would feel a wind on my face. 00:26:15.440 --> 00:26:16.850 align:middle line:90% I would feel the breeze. 00:26:16.850 --> 00:26:19.340 align:middle line:84% Even if I had stopped pedaling and stood still again, 00:26:19.340 --> 00:26:20.630 align:middle line:90% that breeze would go away. 00:26:20.630 --> 00:26:23.390 align:middle line:84% I would feel the effect of my motion 00:26:23.390 --> 00:26:26.510 align:middle line:84% through the medium a headwind, not 00:26:26.510 --> 00:26:28.500 align:middle line:84% because the medium was in motion, 00:26:28.500 --> 00:26:30.980 align:middle line:84% but because I was moving with respect to the medium. 00:26:30.980 --> 00:26:34.370 align:middle line:84% Even on a still day with no breeze, the leaves on the trees 00:26:34.370 --> 00:26:37.790 align:middle line:84% are still, the blades of grass are not being blown around. 00:26:37.790 --> 00:26:40.520 align:middle line:84% If I move rapidly through that medium, 00:26:40.520 --> 00:26:41.880 align:middle line:90% I will literally feel it. 00:26:41.880 --> 00:26:44.750 align:middle line:90% I'll feel a breeze on my face. 00:26:44.750 --> 00:26:47.420 align:middle line:84% I'm belaboring the point probably quite familiar to you, 00:26:47.420 --> 00:26:50.210 align:middle line:84% also like you might see on this cartoon. 00:26:50.210 --> 00:26:52.400 align:middle line:84% So the question was, could we measure 00:26:52.400 --> 00:26:54.980 align:middle line:90% the effect of our own headwind? 00:26:54.980 --> 00:26:57.950 align:middle line:84% Could we feel that effect of our own motion 00:26:57.950 --> 00:26:59.990 align:middle line:90% through this physical medium-- 00:26:59.990 --> 00:27:04.190 align:middle line:84% the medium, in this case, being the all-pervasive elastic 00:27:04.190 --> 00:27:07.400 align:middle line:84% luminiferous ether if we, like the bicyclist, 00:27:07.400 --> 00:27:10.350 align:middle line:84% are in a state of motion through it? 00:27:10.350 --> 00:27:12.410 align:middle line:84% So that was a challenge that many people thought 00:27:12.410 --> 00:27:14.060 align:middle line:90% was a neat question to ask. 00:27:14.060 --> 00:27:16.340 align:middle line:84% One of the first to really tackle it 00:27:16.340 --> 00:27:19.010 align:middle line:84% in a very systematic experimental way 00:27:19.010 --> 00:27:22.280 align:middle line:84% was this remarkable figure named Albert Michelson, 00:27:22.280 --> 00:27:26.720 align:middle line:84% who began in earnest to try to tackle this in the 1880s. 00:27:26.720 --> 00:27:29.660 align:middle line:84% I should just say, I think Michelson is really, really 00:27:29.660 --> 00:27:32.680 align:middle line:84% amazing and fascinating as an individual. 00:27:32.680 --> 00:27:38.200 align:middle line:84% He was born to a very poor Jewish family in Central Europe 00:27:38.200 --> 00:27:40.450 align:middle line:84% on the border of what would soon become the borderland 00:27:40.450 --> 00:27:42.220 align:middle line:90% between Germany and Poland. 00:27:42.220 --> 00:27:44.170 align:middle line:84% When Michelson was two years old, 00:27:44.170 --> 00:27:46.540 align:middle line:84% his family emigrated to the United States. 00:27:46.540 --> 00:27:48.490 align:middle line:84% They actually made their way to California 00:27:48.490 --> 00:27:50.860 align:middle line:84% in the midst of what became known as the Gold Rush 00:27:50.860 --> 00:27:54.280 align:middle line:90% in the late 1840s, early '50s. 00:27:54.280 --> 00:27:56.740 align:middle line:84% And so his father became a merchant 00:27:56.740 --> 00:28:00.790 align:middle line:84% to try to supply the people chasing their fortune 00:28:00.790 --> 00:28:02.530 align:middle line:90% in the Gold Rush in California. 00:28:02.530 --> 00:28:05.080 align:middle line:84% They moved around from one little tiny mining 00:28:05.080 --> 00:28:06.190 align:middle line:90% town to another. 00:28:06.190 --> 00:28:09.130 align:middle line:84% Michelson actually wound up getting a fellowship 00:28:09.130 --> 00:28:12.910 align:middle line:84% to the Naval Academy, so he got a free university education 00:28:12.910 --> 00:28:15.700 align:middle line:84% because he qualified for Annapolis. 00:28:15.700 --> 00:28:18.100 align:middle line:84% And that's where he really fell in love with physics 00:28:18.100 --> 00:28:21.730 align:middle line:84% and mathematics and began thinking about optics, 00:28:21.730 --> 00:28:23.530 align:middle line:84% in particular-- more to be said, totally 00:28:23.530 --> 00:28:25.120 align:middle line:90% crazy, fascinating story. 00:28:25.120 --> 00:28:27.610 align:middle line:84% Michelson then got a fellowship to study 00:28:27.610 --> 00:28:31.100 align:middle line:84% after his undergraduate days in Germany. 00:28:31.100 --> 00:28:33.380 align:middle line:84% So he was able to learn some of the latest 00:28:33.380 --> 00:28:36.680 align:middle line:84% innovations in electromagnetic physics 00:28:36.680 --> 00:28:38.930 align:middle line:84% from some of these experts who had studied with people 00:28:38.930 --> 00:28:41.810 align:middle line:84% like Hendrik Hertz and others who were deeply, deeply 00:28:41.810 --> 00:28:44.990 align:middle line:84% enmeshed in Maxwell's equations and the propagation of light 00:28:44.990 --> 00:28:45.980 align:middle line:90% in the ether. 00:28:45.980 --> 00:28:48.200 align:middle line:84% So Michelson sets himself this task-- 00:28:48.200 --> 00:28:52.160 align:middle line:84% could he design an experiment or a device with which one 00:28:52.160 --> 00:28:55.460 align:middle line:84% might measure this headwind of the Earth's own motion 00:28:55.460 --> 00:28:56.670 align:middle line:90% through the ether? 00:28:56.670 --> 00:28:59.990 align:middle line:84% And what he did was design a really quite novel, very 00:28:59.990 --> 00:29:03.350 align:middle line:84% ingenious device called an interferometer. 00:29:03.350 --> 00:29:07.100 align:middle line:84% And there's a lot on this in those separate lecture notes. 00:29:07.100 --> 00:29:09.380 align:middle line:84% You get a little taste of it from 00:29:09.380 --> 00:29:11.760 align:middle line:84% the Michelson-Morley reading for today as well. 00:29:11.760 --> 00:29:15.470 align:middle line:84% So we'll talk a bit about what this instrument was like. 00:29:15.470 --> 00:29:17.270 align:middle line:84% So Michelson's work is also interesting 00:29:17.270 --> 00:29:20.960 align:middle line:84% not only because of his own quite dramatic life story. 00:29:20.960 --> 00:29:24.290 align:middle line:84% He was a championship boxer when he was at the Naval Academy. 00:29:24.290 --> 00:29:26.450 align:middle line:84% I often joke, perhaps unfairly, he 00:29:26.450 --> 00:29:29.030 align:middle line:84% was probably the only championship boxer who also 00:29:29.030 --> 00:29:30.530 align:middle line:90% won a Nobel Prize in physics. 00:29:30.530 --> 00:29:33.228 align:middle line:84% If you know a counterexample to that, please let me know. 00:29:33.228 --> 00:29:34.520 align:middle line:90% He's the only one I know about. 00:29:34.520 --> 00:29:35.520 align:middle line:90% anyway, interesting guy. 00:29:35.520 --> 00:29:37.560 align:middle line:84% Not only was he interesting because of that, 00:29:37.560 --> 00:29:39.590 align:middle line:84% he was also interesting historically 00:29:39.590 --> 00:29:42.410 align:middle line:84% because the work that we'll look at in this part of today's 00:29:42.410 --> 00:29:46.400 align:middle line:84% class was really among the first examples of research 00:29:46.400 --> 00:29:50.240 align:middle line:84% in any of the natural sciences, including physics, that really 00:29:50.240 --> 00:29:53.540 align:middle line:84% started getting the attention and earning the respect of some 00:29:53.540 --> 00:29:57.020 align:middle line:84% of the very elite scientists in Western Europe. 00:29:57.020 --> 00:29:59.210 align:middle line:84% There were a few others in Michelson's day, 00:29:59.210 --> 00:30:00.380 align:middle line:90% but this was pretty new. 00:30:00.380 --> 00:30:03.980 align:middle line:84% The United States was still seen, often rightly, 00:30:03.980 --> 00:30:06.680 align:middle line:84% as a intellectual scientific backwater, 00:30:06.680 --> 00:30:11.300 align:middle line:84% at least as reckoned by the experts in Western Europe. 00:30:11.300 --> 00:30:13.410 align:middle line:84% Michelson's work begins to change that. 00:30:13.410 --> 00:30:16.020 align:middle line:84% And in fact, as I mentioned, or as you see here, 00:30:16.020 --> 00:30:19.800 align:middle line:84% he becomes the first physicist based within the United States 00:30:19.800 --> 00:30:21.000 align:middle line:90% to win the Nobel Prize. 00:30:21.000 --> 00:30:22.980 align:middle line:90% He wins this Prize in 1907. 00:30:22.980 --> 00:30:26.850 align:middle line:84% And he wins it for the kind of work that we'll talk about now. 00:30:26.850 --> 00:30:30.390 align:middle line:84% So to get our heads into what was going on 00:30:30.390 --> 00:30:33.900 align:middle line:84% with this interferometer, I like to think of this analogy 00:30:33.900 --> 00:30:34.890 align:middle line:90% in terms of swimmers. 00:30:34.890 --> 00:30:36.600 align:middle line:84% And again, we'll go through it here. 00:30:36.600 --> 00:30:38.820 align:middle line:84% Some of the extra steps of these derivations, 00:30:38.820 --> 00:30:41.440 align:middle line:84% you can find in the separate lecture notes. 00:30:41.440 --> 00:30:43.500 align:middle line:84% So what Michelson was really doing-- 00:30:43.500 --> 00:30:46.290 align:middle line:84% as you know from the reading, Michelson, especially 00:30:46.290 --> 00:30:50.640 align:middle line:84% with his partner, Morley, was using the interference 00:30:50.640 --> 00:30:54.270 align:middle line:84% of light waves to conduct tests and experimental tests 00:30:54.270 --> 00:30:58.390 align:middle line:84% of really unprecedented precision and accuracy. 00:30:58.390 --> 00:31:00.810 align:middle line:84% So before we talk about interference of light waves, 00:31:00.810 --> 00:31:05.820 align:middle line:84% let's talk about a race that we can imagine being conducted 00:31:05.820 --> 00:31:07.680 align:middle line:90% by two swimmers in a river. 00:31:07.680 --> 00:31:11.290 align:middle line:84% So we'll sit with this analogy for a few moments here. 00:31:11.290 --> 00:31:14.310 align:middle line:84% So imagine we have a race where one swimmer is going 00:31:14.310 --> 00:31:17.040 align:middle line:84% to leave from point A, swim directly 00:31:17.040 --> 00:31:20.460 align:middle line:84% to point B a distance L, and then swim directly back from B 00:31:20.460 --> 00:31:23.010 align:middle line:90% to A. That's swimmer 1. 00:31:23.010 --> 00:31:26.520 align:middle line:84% Swimmer 2 is going to cover the exact same round-trip distance, 00:31:26.520 --> 00:31:28.350 align:middle line:84% but she's going to swim across the river 00:31:28.350 --> 00:31:31.260 align:middle line:84% instead of directly up the coast here. 00:31:31.260 --> 00:31:33.720 align:middle line:84% So swimmer 2 has to set out from point A, 00:31:33.720 --> 00:31:37.410 align:middle line:84% swim across the river a distance L to point c, 00:31:37.410 --> 00:31:39.090 align:middle line:84% and then swim back to point A again. 00:31:39.090 --> 00:31:40.350 align:middle line:90% The question is, who will win? 00:31:40.350 --> 00:31:44.160 align:middle line:84% Which of those two swimmers will get back to point A first? 00:31:44.160 --> 00:31:45.930 align:middle line:84% And the other thing to bear in mind 00:31:45.930 --> 00:31:47.430 align:middle line:90% is that the river is flowing. 00:31:47.430 --> 00:31:51.360 align:middle line:84% There's a current in the river of a constant speed, v. So 00:31:51.360 --> 00:31:55.760 align:middle line:84% there's a downward current here of a constant speed. 00:31:55.760 --> 00:31:57.550 align:middle line:90% So let's consider swimmer 1. 00:31:57.550 --> 00:31:59.140 align:middle line:84% Swimmer 1 is leaving from point A, 00:31:59.140 --> 00:32:01.480 align:middle line:84% swimming directly against the current 00:32:01.480 --> 00:32:05.720 align:middle line:84% to get to point B. So for that half of her lap, 00:32:05.720 --> 00:32:08.320 align:middle line:84% she's swimming at a net speed of c 00:32:08.320 --> 00:32:11.380 align:middle line:84% minus v. As you can see in the text here, 00:32:11.380 --> 00:32:14.980 align:middle line:84% each swimmer is required to swim at a constant speed 00:32:14.980 --> 00:32:17.120 align:middle line:90% with respect to the water. 00:32:17.120 --> 00:32:21.143 align:middle line:84% And swimmer 1 is swimming at speed c 00:32:21.143 --> 00:32:22.810 align:middle line:84% with respect to the water, but the water 00:32:22.810 --> 00:32:26.800 align:middle line:84% itself is flowing back against her with a current of speed 00:32:26.800 --> 00:32:29.620 align:middle line:84% v. So her net speed is measured, say, 00:32:29.620 --> 00:32:31.990 align:middle line:84% from the shoreline, from, say, the judges sitting here 00:32:31.990 --> 00:32:34.450 align:middle line:84% on the shore or the banks of the river. 00:32:34.450 --> 00:32:37.210 align:middle line:84% Her net speed for that part of the journey is c minus v. 00:32:37.210 --> 00:32:40.270 align:middle line:84% So she takes a time to get from A to B. 00:32:40.270 --> 00:32:42.940 align:middle line:84% That's the distance traveled divided by her speed. 00:32:42.940 --> 00:32:45.220 align:middle line:84% So her time to go from A to B is just the distance 00:32:45.220 --> 00:32:48.340 align:middle line:84% L divided by her net speed, c minus v. 00:32:48.340 --> 00:32:49.840 align:middle line:84% That's probably pretty clear for you 00:32:49.840 --> 00:32:52.080 align:middle line:90% to go through the reasoning. 00:32:52.080 --> 00:32:54.480 align:middle line:84% On the way back, now she gets the boost. 00:32:54.480 --> 00:32:58.680 align:middle line:84% Now she's swimming with speed c with respect to the water. 00:32:58.680 --> 00:33:01.620 align:middle line:84% But the water itself is flowing and helping her out 00:33:01.620 --> 00:33:03.790 align:middle line:84% because she's now going with the current. 00:33:03.790 --> 00:33:05.700 align:middle line:84% So her net speed as measured, say, 00:33:05.700 --> 00:33:08.880 align:middle line:84% from the shore or the riverbank for the return journey 00:33:08.880 --> 00:33:09.930 align:middle line:90% is actually quicker. 00:33:09.930 --> 00:33:13.800 align:middle line:84% It's now c plus v, same distance L. So just a few lines 00:33:13.800 --> 00:33:14.460 align:middle line:90% of algebra-- 00:33:14.460 --> 00:33:16.835 align:middle line:84% and again, you can go through that a bit more on your own 00:33:16.835 --> 00:33:17.820 align:middle line:90% or with the notes. 00:33:17.820 --> 00:33:20.460 align:middle line:84% Her round-trip time, her lap time 00:33:20.460 --> 00:33:22.830 align:middle line:84% to go from A to B and back to A again 00:33:22.830 --> 00:33:25.680 align:middle line:84% turns out to have this relatively simple expression. 00:33:25.680 --> 00:33:28.530 align:middle line:84% It depends, of course, on the distance traveled. 00:33:28.530 --> 00:33:30.780 align:middle line:84% There's a 2 here because she has to go there and back. 00:33:30.780 --> 00:33:35.130 align:middle line:84% She covers total distance 2L, her speed with respect to water 00:33:35.130 --> 00:33:38.520 align:middle line:84% and then, it turns out, going directly against the current 00:33:38.520 --> 00:33:41.070 align:middle line:84% and directly with the current with a little algebra 00:33:41.070 --> 00:33:44.070 align:middle line:84% leads to this correction factor here, 1 over 1 00:33:44.070 --> 00:33:45.990 align:middle line:90% minus the square of v over c. 00:33:45.990 --> 00:33:50.230 align:middle line:84% That's how long it takes swimmer 1 to complete one lap. 00:33:50.230 --> 00:33:51.790 align:middle line:90% Now, what about swimmer 2? 00:33:51.790 --> 00:33:54.940 align:middle line:84% Swimmer 2 knows that she has to accommodate the fact that she's 00:33:54.940 --> 00:33:57.910 align:middle line:84% going to be encountering this current of the river. 00:33:57.910 --> 00:34:00.460 align:middle line:84% So she has to leave point, and she 00:34:00.460 --> 00:34:04.690 align:middle line:84% has to actually land at point C to qualify for her race. 00:34:04.690 --> 00:34:07.150 align:middle line:84% That is a distance L across the river. 00:34:07.150 --> 00:34:09.699 align:middle line:84% To get there, she has to swim at this diagonal. 00:34:09.699 --> 00:34:11.889 align:middle line:84% So while she's swimming across the river, 00:34:11.889 --> 00:34:15.639 align:middle line:84% the current will nudge her downward. 00:34:15.639 --> 00:34:17.650 align:middle line:84% So by the time she crosses the river, 00:34:17.650 --> 00:34:20.409 align:middle line:84% she winds up at point C. If she just set out and tried 00:34:20.409 --> 00:34:21.909 align:middle line:84% to swim straight across river, she'd 00:34:21.909 --> 00:34:25.130 align:middle line:84% get knocked off course by the current. 00:34:25.130 --> 00:34:30.440 align:middle line:84% So she has to travel along the hypotenuse of a right triangle. 00:34:30.440 --> 00:34:34.150 align:middle line:84% So she's traveling along this path, capital R, 00:34:34.150 --> 00:34:40.780 align:middle line:84% during the time that she's heading from A to C, that tAC, 00:34:40.780 --> 00:34:43.780 align:middle line:84% she's drifting down in this direction 00:34:43.780 --> 00:34:48.370 align:middle line:84% a total distance of v times that time. 00:34:48.370 --> 00:34:50.540 align:middle line:84% That's the distance that she'll that she'll 00:34:50.540 --> 00:34:54.320 align:middle line:84% be nudged in this direction by being in the water 00:34:54.320 --> 00:34:56.510 align:middle line:84% for this duration of time and being nudged 00:34:56.510 --> 00:34:58.280 align:middle line:90% by the current at that speed. 00:34:58.280 --> 00:35:02.720 align:middle line:84% So thanks to the greatest invention of ancient Greece-- 00:35:02.720 --> 00:35:05.540 align:middle line:84% which I often say was neither democracy nor the epic poem, 00:35:05.540 --> 00:35:07.460 align:middle line:84% it was, in fact, the Pythagorean theorem-- 00:35:07.460 --> 00:35:10.820 align:middle line:84% we now know how to relate the squares of the lengths 00:35:10.820 --> 00:35:12.650 align:middle line:90% of these sides of the triangle. 00:35:12.650 --> 00:35:16.760 align:middle line:84% The direction the length of this side R squared 00:35:16.760 --> 00:35:20.240 align:middle line:84% is, of course, equal to the sum of the squares of the other two 00:35:20.240 --> 00:35:22.790 align:middle line:84% sides of the right triangle, this side squared, 00:35:22.790 --> 00:35:24.770 align:middle line:90% and this side squared. 00:35:24.770 --> 00:35:26.630 align:middle line:84% We have a little extra information 00:35:26.630 --> 00:35:31.370 align:middle line:84% we can use because we know the length of this line segment R 00:35:31.370 --> 00:35:33.380 align:middle line:84% is the speed with which she swims 00:35:33.380 --> 00:35:35.570 align:middle line:84% with respect to the water times the duration 00:35:35.570 --> 00:35:37.230 align:middle line:84% that it takes her to cross the side. 00:35:37.230 --> 00:35:40.400 align:middle line:84% So now we can plug in a new value for capital R 00:35:40.400 --> 00:35:44.270 align:middle line:84% as well as for this drift displacement, vtAC. 00:35:44.270 --> 00:35:47.390 align:middle line:84% And now, again, just a few lines of algebra, which I know you 00:35:47.390 --> 00:35:50.280 align:middle line:84% can do, and there's a little bit more steps in the notes, 00:35:50.280 --> 00:35:51.770 align:middle line:90% but just a few steps. 00:35:51.770 --> 00:35:54.410 align:middle line:84% We see that her lap time, her total time 00:35:54.410 --> 00:35:57.470 align:middle line:84% to go from A to C and back to A again, 00:35:57.470 --> 00:36:00.440 align:middle line:84% looks pretty similar to swimmer 1, but not identical. 00:36:00.440 --> 00:36:02.750 align:middle line:84% It also is proportional to the total length. 00:36:02.750 --> 00:36:03.920 align:middle line:90% That's a 2L. 00:36:03.920 --> 00:36:07.520 align:middle line:84% It, of course, involves her speed with respect to the water 00:36:07.520 --> 00:36:11.150 align:middle line:84% and has some correction due to the flow of the current. 00:36:11.150 --> 00:36:14.570 align:middle line:84% OK, so I'm going to put these both back up side by side, 00:36:14.570 --> 00:36:18.530 align:middle line:84% the lap time for swimmer 1, the lap time for swimmer 2. 00:36:18.530 --> 00:36:20.060 align:middle line:84% The question is, who wins the race? 00:36:20.060 --> 00:36:23.650 align:middle line:90% Who gets back to point A first? 00:36:23.650 --> 00:36:26.300 align:middle line:84% Now, it might not be so clear if you just eyeball it. 00:36:26.300 --> 00:36:29.110 align:middle line:84% So let me define a very helpful quantity, a quantity 00:36:29.110 --> 00:36:31.360 align:middle line:84% you might have seen before, a quantity we'll 00:36:31.360 --> 00:36:33.560 align:middle line:84% see many, many times in the coming lectures, 00:36:33.560 --> 00:36:36.520 align:middle line:90% including throughout today. 00:36:36.520 --> 00:36:39.590 align:middle line:84% Typically it's abbreviated by the Greek letter gamma. 00:36:39.590 --> 00:36:41.290 align:middle line:84% So I'm just going to define gamma 00:36:41.290 --> 00:36:44.830 align:middle line:84% as a convenient combination of v and c. 00:36:44.830 --> 00:36:47.500 align:middle line:84% I'll define it as 1 over the square root 00:36:47.500 --> 00:36:50.480 align:middle line:84% of 1 minus quantity v over c squared. 00:36:50.480 --> 00:36:52.930 align:middle line:84% And here's a plot of what a gamma looks 00:36:52.930 --> 00:36:55.960 align:middle line:84% like as the ratio v over c gets closer and closer to 1. 00:36:55.960 --> 00:36:57.040 align:middle line:90% In fact, it diverges. 00:36:57.040 --> 00:37:00.220 align:middle line:84% It actually becomes infinite if v is exactly equal to C. 00:37:00.220 --> 00:37:02.240 align:middle line:90% I just truncated my plot here. 00:37:02.240 --> 00:37:07.240 align:middle line:84% But you can see it stays it stays pretty close to 1, 00:37:07.240 --> 00:37:10.660 align:middle line:84% but greater than 1 for any nonzero speed. 00:37:10.660 --> 00:37:14.310 align:middle line:84% And it rapidly becomes very large at larger speeds compared 00:37:14.310 --> 00:37:16.940 align:middle line:90% to the speed C. 00:37:16.940 --> 00:37:19.580 align:middle line:84% So let me ask again, who wins the race? 00:37:19.580 --> 00:37:23.900 align:middle line:84% If I do a little extra algebra, making use of this new quantity 00:37:23.900 --> 00:37:26.690 align:middle line:84% gamma, we can rewrite the total lap time 00:37:26.690 --> 00:37:29.660 align:middle line:84% for swimmer 1, who goes from A to B and back. 00:37:29.660 --> 00:37:32.360 align:middle line:84% Her time is proportional to gamma squared. 00:37:32.360 --> 00:37:34.580 align:middle line:84% Meanwhile, the total lap time for swimmer 2 00:37:34.580 --> 00:37:37.490 align:middle line:84% goes across the lake and back, across the river and back. 00:37:37.490 --> 00:37:40.550 align:middle line:84% Her lap time is proportional only to gamma. 00:37:40.550 --> 00:37:43.040 align:middle line:84% Now I just emphasized for you, gamma is always 00:37:43.040 --> 00:37:44.630 align:middle line:90% greater than or equal to 1. 00:37:44.630 --> 00:37:47.360 align:middle line:84% If there's any current flowing, if v is nonzero, 00:37:47.360 --> 00:37:50.132 align:middle line:84% the gamma is a quantity bigger than 1. 00:37:50.132 --> 00:37:51.590 align:middle line:84% So now hopefully it's a little more 00:37:51.590 --> 00:37:56.120 align:middle line:84% clear to see swimmer 1 will actually lose the race. 00:37:56.120 --> 00:37:59.630 align:middle line:84% Swimmer 1, time tABA, is actually 00:37:59.630 --> 00:38:03.560 align:middle line:84% a larger quantity in general than the time for the return 00:38:03.560 --> 00:38:05.240 align:middle line:90% journey for swimmer 2. 00:38:05.240 --> 00:38:09.860 align:middle line:84% tABA is actually bigger than time tACA. 00:38:09.860 --> 00:38:11.015 align:middle line:90% There's a time difference. 00:38:11.015 --> 00:38:12.680 align:middle line:84% That means there's a clear winner. 00:38:12.680 --> 00:38:15.020 align:middle line:84% They have different times to complete the laps. 00:38:15.020 --> 00:38:17.340 align:middle line:84% And it turns out, the person who goes directly 00:38:17.340 --> 00:38:20.460 align:middle line:84% against the current and then directly with the current 00:38:20.460 --> 00:38:23.790 align:middle line:84% will take overall more time to complete 00:38:23.790 --> 00:38:27.120 align:middle line:84% her lap than the swimmer who goes diagonally 00:38:27.120 --> 00:38:32.430 align:middle line:84% across the river and is with that drift 00:38:32.430 --> 00:38:34.380 align:middle line:90% displacement from the current. 00:38:34.380 --> 00:38:36.900 align:middle line:84% Not only is there a difference in time 00:38:36.900 --> 00:38:39.390 align:middle line:84% that depends on this quantity gamma, 00:38:39.390 --> 00:38:43.080 align:middle line:84% if we expand gamma for speeds that are small compared to c, 00:38:43.080 --> 00:38:45.900 align:middle line:84% if v over c is a small quantity, then 00:38:45.900 --> 00:38:47.970 align:middle line:84% we can just do a Taylor expansion 00:38:47.970 --> 00:38:49.530 align:middle line:90% in that small quantity. 00:38:49.530 --> 00:38:51.720 align:middle line:84% We see the difference in time is what's 00:38:51.720 --> 00:38:53.580 align:middle line:90% called a second-order effect. 00:38:53.580 --> 00:38:55.410 align:middle line:84% That's just a fancy way of saying 00:38:55.410 --> 00:38:58.770 align:middle line:84% that the difference in time goes like the square 00:38:58.770 --> 00:39:02.100 align:middle line:84% of that small quantity, the ratio of v over c. 00:39:02.100 --> 00:39:05.220 align:middle line:84% So there should be a winner if there's any current flowing 00:39:05.220 --> 00:39:06.300 align:middle line:90% in the river. 00:39:06.300 --> 00:39:08.760 align:middle line:84% If v is nonzero, then there should 00:39:08.760 --> 00:39:12.420 align:middle line:84% be an absolute clear winner in this race. 00:39:12.420 --> 00:39:18.000 align:middle line:84% It should go like the second order in the ratio v over c. 00:39:18.000 --> 00:39:22.170 align:middle line:84% So now, why did I talk about this crazy swimming race? 00:39:22.170 --> 00:39:24.030 align:middle line:84% Because that's pretty close to what 00:39:24.030 --> 00:39:26.412 align:middle line:84% Albert Michelson designed for light waves. 00:39:26.412 --> 00:39:28.620 align:middle line:84% And this is his instrument called the interferometer. 00:39:28.620 --> 00:39:30.027 align:middle line:90% It's really quite brilliant. 00:39:30.027 --> 00:39:33.160 align:middle line:90% 00:39:33.160 --> 00:39:36.870 align:middle line:84% So the way the interferometer worked was instead of swimmers, 00:39:36.870 --> 00:39:41.580 align:middle line:84% he had a bright source of light of nearly-- 00:39:41.580 --> 00:39:43.140 align:middle line:90% it was nearly monochromatic. 00:39:43.140 --> 00:39:45.930 align:middle line:84% He was using sodium arc lamps in the beginning. 00:39:45.930 --> 00:39:48.690 align:middle line:84% So it was shining very brightly with basically one 00:39:48.690 --> 00:39:51.900 align:middle line:84% characteristic color or wavelength of light. 00:39:51.900 --> 00:39:52.980 align:middle line:90% That was important. 00:39:52.980 --> 00:39:55.200 align:middle line:84% He shines that light from a single source 00:39:55.200 --> 00:39:57.180 align:middle line:90% onto a half-silvered mirror. 00:39:57.180 --> 00:39:59.700 align:middle line:84% As the name suggests, that's an object 00:39:59.700 --> 00:40:02.130 align:middle line:84% that lets about half the light pass straight 00:40:02.130 --> 00:40:05.160 align:middle line:84% through like a window and reflects about half the light. 00:40:05.160 --> 00:40:07.200 align:middle line:90% So it's not totally reflecting. 00:40:07.200 --> 00:40:10.990 align:middle line:84% It reflects, on average, half the light that falls upon it. 00:40:10.990 --> 00:40:15.000 align:middle line:84% So from this single source of light S, this sodium arc lamp, 00:40:15.000 --> 00:40:17.100 align:middle line:84% half the light will pass through like it just 00:40:17.100 --> 00:40:21.240 align:middle line:84% sees a clear window and travel a path, a distance L, 00:40:21.240 --> 00:40:23.640 align:middle line:84% until it encounters a fully reflecting mirror, 00:40:23.640 --> 00:40:25.320 align:middle line:90% this top mirror up here. 00:40:25.320 --> 00:40:28.680 align:middle line:84% That mirror then will reflect all of the light that hits it. 00:40:28.680 --> 00:40:32.430 align:middle line:84% That light will then bounce back to that half-silvered mirror, 00:40:32.430 --> 00:40:36.730 align:middle line:84% a portion of which will, again, be now reflected and hit 00:40:36.730 --> 00:40:37.390 align:middle line:90% some screen. 00:40:37.390 --> 00:40:39.550 align:middle line:84% That's like swimmer 1 starting at point A, 00:40:39.550 --> 00:40:41.740 align:middle line:84% traveling to point B, and coming back to point A. 00:40:41.740 --> 00:40:44.230 align:middle line:84% Meanwhile, half the light that encounters 00:40:44.230 --> 00:40:46.810 align:middle line:84% this half-silvered mirror will not pass through. 00:40:46.810 --> 00:40:48.400 align:middle line:90% It'll actually be reflected. 00:40:48.400 --> 00:40:50.110 align:middle line:84% And so this becomes like swimmer 2. 00:40:50.110 --> 00:40:51.850 align:middle line:84% So half of the incoming light that 00:40:51.850 --> 00:40:54.280 align:middle line:84% is incident upon this half-silvered mirror 00:40:54.280 --> 00:40:56.920 align:middle line:90% will be deflected along path 2. 00:40:56.920 --> 00:40:59.410 align:middle line:84% It will travel a fixed distance L 00:40:59.410 --> 00:41:01.990 align:middle line:84% until it encounters a fully reflecting mirror 00:41:01.990 --> 00:41:03.580 align:middle line:90% at the end of that path. 00:41:03.580 --> 00:41:05.230 align:middle line:84% That will reflect the light back. 00:41:05.230 --> 00:41:06.675 align:middle line:84% Half of that light will then pass 00:41:06.675 --> 00:41:08.050 align:middle line:84% through the half-silvered mirror. 00:41:08.050 --> 00:41:09.760 align:middle line:90% So now we've set up a race. 00:41:09.760 --> 00:41:13.180 align:middle line:84% We have a single light wave that starts off at the same time. 00:41:13.180 --> 00:41:16.900 align:middle line:84% Swimmers 1 and 2 both start at point A at the same time 00:41:16.900 --> 00:41:20.020 align:middle line:84% and set off on their distinct journeys. 00:41:20.020 --> 00:41:23.800 align:middle line:84% If there's any difference in the distance they need to travel-- 00:41:23.800 --> 00:41:26.470 align:middle line:84% or excuse me-- if there's any difference in the time it takes 00:41:26.470 --> 00:41:29.860 align:middle line:84% them to travel along either path 1 or path 2, 00:41:29.860 --> 00:41:33.160 align:middle line:84% those light waves will come back no longer in phase. 00:41:33.160 --> 00:41:35.530 align:middle line:84% The crest of one will no longer line up 00:41:35.530 --> 00:41:37.195 align:middle line:90% with the crest of the other. 00:41:37.195 --> 00:41:39.320 align:middle line:90% You could get interference. 00:41:39.320 --> 00:41:41.980 align:middle line:84% So if the light waves that travel these distinct paths 00:41:41.980 --> 00:41:44.350 align:middle line:84% take different times, just like the swimmers 00:41:44.350 --> 00:41:46.480 align:middle line:84% took different times to complete their laps, 00:41:46.480 --> 00:41:48.820 align:middle line:84% the waves will come back out of phase with each other. 00:41:48.820 --> 00:41:50.320 align:middle line:84% And you should see interference when 00:41:50.320 --> 00:41:53.860 align:middle line:84% the two waves can be joined back together on some screen. 00:41:53.860 --> 00:41:56.650 align:middle line:84% You should see a characteristic interference pattern. 00:41:56.650 --> 00:42:00.910 align:middle line:84% The amount of offset will depend on the amount of time delay 00:42:00.910 --> 00:42:04.990 align:middle line:84% between traversing these two paths. 00:42:04.990 --> 00:42:06.700 align:middle line:90% So that was the idea. 00:42:06.700 --> 00:42:09.370 align:middle line:84% Michelson first built a 1-meter version, 00:42:09.370 --> 00:42:11.470 align:middle line:84% where each of these paths' capital L 00:42:11.470 --> 00:42:14.380 align:middle line:84% were about 1 meter in distance between the half-silvered 00:42:14.380 --> 00:42:16.600 align:middle line:84% mirror and the fully reflecting mirror. 00:42:16.600 --> 00:42:20.950 align:middle line:84% And then he actually got external funding-- 00:42:20.950 --> 00:42:23.060 align:middle line:84% partly from his father-in-law, or an uncle, 00:42:23.060 --> 00:42:25.060 align:middle line:84% or something like that, and from other sources-- 00:42:25.060 --> 00:42:26.800 align:middle line:90% to build a super-sized version. 00:42:26.800 --> 00:42:29.680 align:middle line:84% And this is the second version he did with his colleague 00:42:29.680 --> 00:42:31.900 align:middle line:84% Morley once he was now on the faculty 00:42:31.900 --> 00:42:35.260 align:middle line:84% at Case University, which is now Case Western Reserve 00:42:35.260 --> 00:42:38.230 align:middle line:90% University in Cleveland, Ohio. 00:42:38.230 --> 00:42:41.380 align:middle line:84% They built a ginormous version of this interferometer. 00:42:41.380 --> 00:42:44.290 align:middle line:84% The lengths between the half-silvered mirror 00:42:44.290 --> 00:42:47.410 align:middle line:84% and the fully reflecting mirrors were 11 meters, 00:42:47.410 --> 00:42:52.330 align:middle line:84% like 33 or 34 feet-- enormous paths. 00:42:52.330 --> 00:42:56.590 align:middle line:84% And to try to damn down on vibrations from things 00:42:56.590 --> 00:43:00.790 align:middle line:84% like not only horse-drawn carriages, but early trolley 00:43:00.790 --> 00:43:03.250 align:middle line:84% cars outside the laboratory to try 00:43:03.250 --> 00:43:06.850 align:middle line:84% to dampen any kind of source of systematic error, 00:43:06.850 --> 00:43:12.010 align:middle line:84% they put this entire 34-foot long optics table 00:43:12.010 --> 00:43:15.350 align:middle line:84% floating on a VAT of mercury, which I do not recommend, 00:43:15.350 --> 00:43:15.850 align:middle line:90% by the way. 00:43:15.850 --> 00:43:18.805 align:middle line:84% They were breathing in horribly, horribly poisonous fumes 00:43:18.805 --> 00:43:19.930 align:middle line:90% throughout this experiment. 00:43:19.930 --> 00:43:22.740 align:middle line:90% Don't try that part at home. 00:43:22.740 --> 00:43:25.218 align:middle line:84% So this is a figure taken from that paper-- 00:43:25.218 --> 00:43:27.010 align:middle line:84% we have the paper in our reader for today-- 00:43:27.010 --> 00:43:30.800 align:middle line:84% where they then finally tried to put together, 00:43:30.800 --> 00:43:31.870 align:middle line:90% was there any offset? 00:43:31.870 --> 00:43:34.060 align:middle line:90% Did the interference fringes-- 00:43:34.060 --> 00:43:36.640 align:middle line:84% when those two light beams came back together 00:43:36.640 --> 00:43:38.980 align:middle line:84% on that collecting screen, was there 00:43:38.980 --> 00:43:42.670 align:middle line:84% any evidence that one path required a different amount 00:43:42.670 --> 00:43:44.500 align:middle line:90% of time than the other? 00:43:44.500 --> 00:43:46.780 align:middle line:90% And the short answer was no. 00:43:46.780 --> 00:43:49.210 align:middle line:84% They found no compelling evidence 00:43:49.210 --> 00:43:52.210 align:middle line:84% that there was any time delay, any time difference, 00:43:52.210 --> 00:43:54.400 align:middle line:84% between the path taken by light that 00:43:54.400 --> 00:43:58.090 align:middle line:84% traveled path 1 versus the light that traveled path 2. 00:43:58.090 --> 00:44:00.085 align:middle line:84% There's a little wiggle to these curves. 00:44:00.085 --> 00:44:01.960 align:middle line:84% They were convinced that was almost certainly 00:44:01.960 --> 00:44:05.160 align:middle line:84% just experimental noise, systematic noise. 00:44:05.160 --> 00:44:08.060 align:middle line:84% In fact, as they wrote, the dotted curves 00:44:08.060 --> 00:44:10.040 align:middle line:84% that you were comparing to are actually 00:44:10.040 --> 00:44:14.090 align:middle line:84% 1/8 of the size of the effect they would expect. 00:44:14.090 --> 00:44:17.630 align:middle line:84% And even that dwarfs the measured variation 00:44:17.630 --> 00:44:19.460 align:middle line:84% they actually managed to measure. 00:44:19.460 --> 00:44:24.350 align:middle line:84% Their instrument was sensitive to the square of v over c. 00:44:24.350 --> 00:44:26.060 align:middle line:84% Remember, there's a second-order effect 00:44:26.060 --> 00:44:27.260 align:middle line:90% according to those swimmers. 00:44:27.260 --> 00:44:30.770 align:middle line:84% So they should have been sensitive to a ratio of speeds 00:44:30.770 --> 00:44:33.110 align:middle line:90% one part in 100 million. 00:44:33.110 --> 00:44:36.290 align:middle line:84% If you think about the likely speed, say, of the Earth 00:44:36.290 --> 00:44:40.220 align:middle line:84% through the ether just taken as an order of magnitude estimate, 00:44:40.220 --> 00:44:44.390 align:middle line:84% the speed with which the planet Earth moves around the sun 00:44:44.390 --> 00:44:47.060 align:middle line:84% during the course of its annual orbit-- 00:44:47.060 --> 00:44:50.150 align:middle line:84% take that as a characteristic speed for our motion 00:44:50.150 --> 00:44:52.400 align:middle line:84% through the ether, compare that to the speed 00:44:52.400 --> 00:44:53.870 align:middle line:90% of light in the ether. 00:44:53.870 --> 00:44:57.980 align:middle line:84% These are incredibly small velocities. 00:44:57.980 --> 00:45:00.710 align:middle line:84% And yet, he should have been sensitive to even 00:45:00.710 --> 00:45:02.630 align:middle line:90% very, very tiny displacements. 00:45:02.630 --> 00:45:04.670 align:middle line:84% There should have been a measurable shift 00:45:04.670 --> 00:45:06.500 align:middle line:84% in the interference fringes, even 00:45:06.500 --> 00:45:08.750 align:middle line:84% from such a small relative motion. 00:45:08.750 --> 00:45:12.410 align:middle line:84% And yet, trying this for days, and days, and nights, 00:45:12.410 --> 00:45:15.110 align:middle line:84% ultimately for months, and months, and even years, 00:45:15.110 --> 00:45:18.230 align:middle line:84% they find what becomes known as a null result. 00:45:18.230 --> 00:45:20.990 align:middle line:84% And here's a quotation from their paper. 00:45:20.990 --> 00:45:23.240 align:middle line:84% "It seems fair to conclude from the figure--" 00:45:23.240 --> 00:45:26.180 align:middle line:84% meaning from this plot here, "--that if there is any 00:45:26.180 --> 00:45:29.030 align:middle line:84% displacement due to the relative motion of the Earth 00:45:29.030 --> 00:45:32.300 align:middle line:84% and the luminiferous ether, this cannot be much greater than 00:45:32.300 --> 00:45:35.480 align:middle line:84% about 1% of the distance between the fringes. 00:45:35.480 --> 00:45:37.640 align:middle line:84% The actual displacement was certainly 00:45:37.640 --> 00:45:40.400 align:middle line:84% less than the twentieth part of this expected value, 00:45:40.400 --> 00:45:42.500 align:middle line:84% probably less than the fortieth part. 00:45:42.500 --> 00:45:45.860 align:middle line:84% It was consistent with no offset at all." 00:45:45.860 --> 00:45:49.700 align:middle line:84% They found no shift in the interference fringes 00:45:49.700 --> 00:45:52.490 align:middle line:84% that they could have attributed to the motion of the Earth 00:45:52.490 --> 00:45:53.720 align:middle line:90% through the ether. 00:45:53.720 --> 00:45:56.810 align:middle line:84% So they found little wiggles that were basically consistent 00:45:56.810 --> 00:45:58.850 align:middle line:90% with no wiggles at all. 00:45:58.850 --> 00:46:02.030 align:middle line:84% So they didn't just try this once. 00:46:02.030 --> 00:46:05.980 align:middle line:84% They wondered about maybe try a day/night effect, 00:46:05.980 --> 00:46:10.300 align:middle line:84% depending on which arm of this big L-shaped interferometer 00:46:10.300 --> 00:46:13.240 align:middle line:84% happens to be moving directly into the ether wind 00:46:13.240 --> 00:46:14.350 align:middle line:90% at a given time. 00:46:14.350 --> 00:46:16.420 align:middle line:84% That might shift day versus night. 00:46:16.420 --> 00:46:18.850 align:middle line:84% It might depend on the time of the Earth's orbit 00:46:18.850 --> 00:46:19.720 align:middle line:90% around the sun. 00:46:19.720 --> 00:46:23.350 align:middle line:84% So they would check fall versus winter versus spring. 00:46:23.350 --> 00:46:25.930 align:middle line:84% And it was this incredibly precise instrument 00:46:25.930 --> 00:46:28.810 align:middle line:84% with data collected very, very, very carefully 00:46:28.810 --> 00:46:32.380 align:middle line:84% and with great order and regularity. 00:46:32.380 --> 00:46:35.960 align:middle line:84% That's what began grabbing the attention of even some very, 00:46:35.960 --> 00:46:37.930 align:middle line:90% very elite scientists in Europe. 00:46:37.930 --> 00:46:40.000 align:middle line:84% And despite all their efforts and all 00:46:40.000 --> 00:46:41.860 align:middle line:84% their attempts to replicate it, they 00:46:41.860 --> 00:46:44.740 align:middle line:84% kept finding results consistent with a tie, 00:46:44.740 --> 00:46:47.240 align:middle line:90% with no time offset at all. 00:46:47.240 --> 00:46:50.590 align:middle line:84% And here is, I think, the saddest part. 00:46:50.590 --> 00:46:53.590 align:middle line:84% Michelson lived for decades after the 1880s. 00:46:53.590 --> 00:46:55.750 align:middle line:90% He died in 1927. 00:46:55.750 --> 00:46:57.970 align:middle line:84% He was the first US-based physicist 00:46:57.970 --> 00:47:00.310 align:middle line:90% to win the Nobel Prize in 1907. 00:47:00.310 --> 00:47:02.890 align:middle line:84% And yet, 20 years later on his own deathbed, 00:47:02.890 --> 00:47:07.310 align:middle line:84% he still considered this work to have been a failure. 00:47:07.310 --> 00:47:09.410 align:middle line:84% I say, may all of us win Nobel prizes 00:47:09.410 --> 00:47:10.670 align:middle line:90% and still not be satisfied. 00:47:10.670 --> 00:47:13.080 align:middle line:90% This is a sad, sad thing. 00:47:13.080 --> 00:47:15.220 align:middle line:84% So let me pause there and stop sharing screen. 00:47:15.220 --> 00:47:16.470 align:middle line:90% Any questions about that part? 00:47:16.470 --> 00:47:19.910 align:middle line:84% I see some things coming up on the chat. 00:47:19.910 --> 00:47:23.810 align:middle line:84% So Jade clearly has read ahead or has taken other courses. 00:47:23.810 --> 00:47:25.430 align:middle line:84% Jade asks, is there any connection 00:47:25.430 --> 00:47:27.320 align:middle line:84% between this correction factor that 00:47:27.320 --> 00:47:30.170 align:middle line:84% involves a square of v of a c and the Lorentz factor? 00:47:30.170 --> 00:47:31.830 align:middle line:90% They look very similar. 00:47:31.830 --> 00:47:32.630 align:middle line:90% They do, Jade. 00:47:32.630 --> 00:47:33.230 align:middle line:90% You're exactly right. 00:47:33.230 --> 00:47:35.230 align:middle line:84% In fact, we're going to come to that even today, 00:47:35.230 --> 00:47:40.100 align:middle line:84% and we'll continue seeing this factor gamma 00:47:40.100 --> 00:47:42.890 align:middle line:84% both today, in the next class, and the class after that. 00:47:42.890 --> 00:47:45.230 align:middle line:84% And to give away the story, you're right. 00:47:45.230 --> 00:47:47.660 align:middle line:84% It should look familiar if any of you 00:47:47.660 --> 00:47:49.970 align:middle line:84% have had any coursework on relativity. 00:47:49.970 --> 00:47:52.070 align:middle line:84% We'll see that factor does come up, 00:47:52.070 --> 00:47:54.607 align:middle line:84% and we'll see exactly what Lorentz thought it would mean. 00:47:54.607 --> 00:47:56.690 align:middle line:84% And then we'll later see what people like Einstein 00:47:56.690 --> 00:47:57.860 align:middle line:90% thought it would mean. 00:47:57.860 --> 00:47:59.360 align:middle line:84% So when we do this experiment today, 00:47:59.360 --> 00:48:01.547 align:middle line:84% Alex asks, and we use lasers, does using sodium 00:48:01.547 --> 00:48:02.630 align:middle line:90% lamps make any difference? 00:48:02.630 --> 00:48:03.860 align:middle line:90% Good, excellent question. 00:48:03.860 --> 00:48:06.080 align:middle line:84% Today we do use lasers, both because, first of all, 00:48:06.080 --> 00:48:07.062 align:middle line:90% lasers are awesome. 00:48:07.062 --> 00:48:09.020 align:middle line:84% Let's just agree on that, because they're cool. 00:48:09.020 --> 00:48:11.690 align:middle line:84% But also more important, slightly more relevant, 00:48:11.690 --> 00:48:14.030 align:middle line:84% lasers are what we call monochromatic. 00:48:14.030 --> 00:48:18.680 align:middle line:84% They emit nearly all their light at one frequency, one color. 00:48:18.680 --> 00:48:22.440 align:middle line:84% So Michelson did not have access to lasers. 00:48:22.440 --> 00:48:24.820 align:middle line:84% No one on the planet did in the 1880s. 00:48:24.820 --> 00:48:27.060 align:middle line:84% So what was really state of the art 00:48:27.060 --> 00:48:30.270 align:middle line:84% was to use sources that emitted most of their light 00:48:30.270 --> 00:48:31.950 align:middle line:90% at one dominant frequency. 00:48:31.950 --> 00:48:34.922 align:middle line:84% And often, they would use these sodium arc lamps. 00:48:34.922 --> 00:48:37.380 align:middle line:84% They could measure the output-- we'll come to this actually 00:48:37.380 --> 00:48:40.470 align:middle line:84% in a few lectures when we think about early quantum theory. 00:48:40.470 --> 00:48:42.300 align:middle line:84% The researchers at the time were getting 00:48:42.300 --> 00:48:45.510 align:middle line:84% quite good at measuring how much energy came out 00:48:45.510 --> 00:48:48.900 align:middle line:84% of a certain emitter in different colors, 00:48:48.900 --> 00:48:50.640 align:middle line:84% in different frequency bins, so they 00:48:50.640 --> 00:48:54.300 align:middle line:84% could characterize what we call the spectrum actually quite 00:48:54.300 --> 00:48:55.290 align:middle line:90% precisely. 00:48:55.290 --> 00:48:57.210 align:middle line:84% So they knew that certain kinds of emitters 00:48:57.210 --> 00:49:00.210 align:middle line:84% were pretty close to being monochromatic, 00:49:00.210 --> 00:49:01.950 align:middle line:84% and sodium was one source that had 00:49:01.950 --> 00:49:03.730 align:middle line:90% become pretty common to use. 00:49:03.730 --> 00:49:08.610 align:middle line:84% So it certainly could have mattered if you were doing-- 00:49:08.610 --> 00:49:10.620 align:middle line:84% it would have mattered in an interferometer 00:49:10.620 --> 00:49:13.080 align:middle line:84% if the light waves were of very different wavelengths 00:49:13.080 --> 00:49:14.970 align:middle line:90% to start with. 00:49:14.970 --> 00:49:16.443 align:middle line:84% But in that case, you would still 00:49:16.443 --> 00:49:18.360 align:middle line:84% be able to use the interferometer because what 00:49:18.360 --> 00:49:21.000 align:middle line:84% you would worry about would be whether the interference 00:49:21.000 --> 00:49:22.440 align:middle line:90% pattern would shift. 00:49:22.440 --> 00:49:24.900 align:middle line:84% If the light that travels the different paths 00:49:24.900 --> 00:49:27.640 align:middle line:84% is of inherently different wavelength, 00:49:27.640 --> 00:49:32.387 align:middle line:84% then you would not expect to find zero interference fringes. 00:49:32.387 --> 00:49:34.470 align:middle line:84% There should be interference fringes even at rest. 00:49:34.470 --> 00:49:36.330 align:middle line:84% Then what you look for is a shift 00:49:36.330 --> 00:49:38.430 align:middle line:84% in that pattern due to the Earth's motion 00:49:38.430 --> 00:49:39.180 align:middle line:90% through the ether. 00:49:39.180 --> 00:49:43.140 align:middle line:84% So you could still use interferometry successfully, 00:49:43.140 --> 00:49:45.780 align:middle line:84% even if you don't have a perfectly monochromatic source. 00:49:45.780 --> 00:49:46.710 align:middle line:90% It's a great question. 00:49:46.710 --> 00:49:48.660 align:middle line:84% But they were aware of that, and they 00:49:48.660 --> 00:49:52.230 align:middle line:84% were able to make pretty strong arguments even without lasers. 00:49:52.230 --> 00:49:54.510 align:middle line:90% Good, another question. 00:49:54.510 --> 00:49:57.960 align:middle line:84% Abdulaziz asks, do you need nanoscale precision 00:49:57.960 --> 00:50:00.425 align:middle line:84% to make sure the tracks are of exactly the same length? 00:50:00.425 --> 00:50:01.050 align:middle line:90% Great question. 00:50:01.050 --> 00:50:03.780 align:middle line:84% Again, it comes back to the same kind of answer I just gave. 00:50:03.780 --> 00:50:05.467 align:middle line:84% In the cartoon version I described, 00:50:05.467 --> 00:50:07.050 align:middle line:84% you would think you would need to have 00:50:07.050 --> 00:50:11.010 align:middle line:84% absolute hyper-precise control over those path lengths. 00:50:11.010 --> 00:50:13.290 align:middle line:84% It turns out, even if the path lengths are 00:50:13.290 --> 00:50:16.320 align:middle line:84% grossly different-- let alone nano scales-- if they're inches 00:50:16.320 --> 00:50:18.840 align:middle line:84% or even meters different, then you 00:50:18.840 --> 00:50:22.710 align:middle line:84% would have some basic reference interference pattern, 00:50:22.710 --> 00:50:24.420 align:middle line:84% and then you could still check to see 00:50:24.420 --> 00:50:28.030 align:middle line:84% if the interference pattern changed due to relative motion. 00:50:28.030 --> 00:50:29.670 align:middle line:84% So what you really are sensitive to 00:50:29.670 --> 00:50:32.700 align:middle line:84% are shifts in the pattern of the interference fringes. 00:50:32.700 --> 00:50:36.690 align:middle line:84% And that is what's sensitive to the square of v over c. 00:50:36.690 --> 00:50:38.880 align:middle line:84% So in fact, you don't have to machine these parts 00:50:38.880 --> 00:50:41.550 align:middle line:84% to one part in a nanometer, thank goodness, right? 00:50:41.550 --> 00:50:44.610 align:middle line:84% You actually are sensitive to a shift in the existing 00:50:44.610 --> 00:50:45.750 align:middle line:90% interference pattern. 00:50:45.750 --> 00:50:47.580 align:middle line:84% And that, again, they could measure 00:50:47.580 --> 00:50:49.800 align:middle line:84% with really quite extraordinary accuracy 00:50:49.800 --> 00:50:52.290 align:middle line:90% with optical frequency light. 00:50:52.290 --> 00:50:55.147 align:middle line:90% 00:50:55.147 --> 00:50:57.730 align:middle line:84% Thickness of the half-silvered mirrors could introduce errors. 00:50:57.730 --> 00:50:58.500 align:middle line:90% These are excellent questions. 00:50:58.500 --> 00:51:00.870 align:middle line:84% Again, what it came down to is none of these effects, 00:51:00.870 --> 00:51:04.620 align:middle line:84% they were convinced, would affect the behavior 00:51:04.620 --> 00:51:07.380 align:middle line:84% of the interference patterns as the whole apparatus 00:51:07.380 --> 00:51:08.880 align:middle line:90% moved through the ether. 00:51:08.880 --> 00:51:12.780 align:middle line:84% They could accommodate an existing zeroth-order baseline 00:51:12.780 --> 00:51:14.220 align:middle line:84% interference pattern, which could 00:51:14.220 --> 00:51:17.820 align:middle line:84% arise from all these very excellent, excellent 00:51:17.820 --> 00:51:19.140 align:middle line:90% observations you're making. 00:51:19.140 --> 00:51:23.790 align:middle line:84% And the question was, did that baseline interference pattern 00:51:23.790 --> 00:51:26.913 align:middle line:84% or a starting pattern of fringes,l did that shift due 00:51:26.913 --> 00:51:28.080 align:middle line:90% to, say, the Earth's motion? 00:51:28.080 --> 00:51:30.720 align:middle line:84% And that's what they kept finding no evidence of. 00:51:30.720 --> 00:51:33.090 align:middle line:84% So we're going to talk-- and I I see other questions 00:51:33.090 --> 00:51:36.150 align:middle line:90% about relativity in 1927. 00:51:36.150 --> 00:51:38.565 align:middle line:84% Oris asks-- Oris, I see you have your hand up. 00:51:38.565 --> 00:51:39.690 align:middle line:90% I also see you in the chat. 00:51:39.690 --> 00:51:40.440 align:middle line:90% Is it the same question? 00:51:40.440 --> 00:51:42.315 align:middle line:84% Or do you want to ask your question directly? 00:51:42.315 --> 00:51:43.410 align:middle line:90% Same question, OK. 00:51:43.410 --> 00:51:46.530 align:middle line:84% Were people just not taking relativity seriously? 00:51:46.530 --> 00:51:49.020 align:middle line:84% And we're going to spend a whole lecture on that coming up 00:51:49.020 --> 00:51:50.340 align:middle line:90% in not too long. 00:51:50.340 --> 00:51:53.370 align:middle line:84% The short answer is relativity of the form 00:51:53.370 --> 00:51:55.080 align:middle line:84% that we would recognize, of the form 00:51:55.080 --> 00:51:57.450 align:middle line:90% that you'll analyze for 1-- 00:51:57.450 --> 00:52:00.420 align:middle line:90% due October 2, don't forget-- 00:52:00.420 --> 00:52:02.430 align:middle line:90% that was published in 1905. 00:52:02.430 --> 00:52:04.770 align:middle line:84% It was certainly not considered a standard 00:52:04.770 --> 00:52:08.880 align:middle line:84% or universally recognized result in 1905. 00:52:08.880 --> 00:52:11.670 align:middle line:84% It was pretty well accepted by many, though not 00:52:11.670 --> 00:52:14.790 align:middle line:90% all physicists, before 1927. 00:52:14.790 --> 00:52:17.130 align:middle line:84% But there is still lingering question, 00:52:17.130 --> 00:52:19.550 align:middle line:84% including by people like Albert Michelson. 00:52:19.550 --> 00:52:22.370 align:middle line:84% So it was not universally accepted, 00:52:22.370 --> 00:52:24.830 align:middle line:84% even in Michelson's own lifetime. 00:52:24.830 --> 00:52:27.650 align:middle line:84% The balance had certainly shifted by 1927. 00:52:27.650 --> 00:52:30.440 align:middle line:84% By 1927, Michelson was a member of a minority, 00:52:30.440 --> 00:52:33.170 align:middle line:84% a Nobel Prize-winning minority, but a minority nonetheless. 00:52:33.170 --> 00:52:36.890 align:middle line:84% In 1910, that would have been quite standard 00:52:36.890 --> 00:52:39.440 align:middle line:84% to either have never heard of Einstein's relativity 00:52:39.440 --> 00:52:42.767 align:middle line:84% or think it's probably wrong, or irrelevant, or trivial, or not 00:52:42.767 --> 00:52:43.850 align:middle line:90% worth paying attention to. 00:52:43.850 --> 00:52:46.310 align:middle line:84% We'll come to that kind of stuff pretty soon, 00:52:46.310 --> 00:52:49.542 align:middle line:84% and same with general relativity. 00:52:49.542 --> 00:52:51.000 align:middle line:84% Julius asked an excellent question. 00:52:51.000 --> 00:52:54.330 align:middle line:84% How did they know the ether is moving at velocity v? 00:52:54.330 --> 00:52:55.920 align:middle line:84% So I probably explained it poorly. 00:52:55.920 --> 00:52:59.670 align:middle line:84% They assumed the ether was totally at rest. 00:52:59.670 --> 00:53:02.700 align:middle line:84% The ether, they assumed, had no inherent motion at all. 00:53:02.700 --> 00:53:05.640 align:middle line:84% It was, on average, just sitting perfectly still. 00:53:05.640 --> 00:53:07.950 align:middle line:84% But things could move through the ether, including 00:53:07.950 --> 00:53:09.810 align:middle line:90% things like us on Earth. 00:53:09.810 --> 00:53:14.730 align:middle line:84% So the idea was the ether set an absolute reference frame. 00:53:14.730 --> 00:53:16.590 align:middle line:84% Things could be at rest with respect 00:53:16.590 --> 00:53:19.740 align:middle line:84% to this comparison substance, the ether, 00:53:19.740 --> 00:53:22.740 align:middle line:84% which they assumed was sitting, on average, perfectly at rest. 00:53:22.740 --> 00:53:24.600 align:middle line:84% But then things could move through it. 00:53:24.600 --> 00:53:27.640 align:middle line:84% Planets and stars could move through it. 00:53:27.640 --> 00:53:30.060 align:middle line:84% And if the Earth was moving around the sun 00:53:30.060 --> 00:53:32.130 align:middle line:84% in our own solar system, then maybe 00:53:32.130 --> 00:53:34.770 align:middle line:84% either the Earth alone or the entire solar system 00:53:34.770 --> 00:53:38.010 align:middle line:84% was actually moving through this elastic medium. 00:53:38.010 --> 00:53:41.460 align:middle line:84% So they were convinced the ether was the reference 00:53:41.460 --> 00:53:44.640 align:middle line:84% point with respect to which our own motion might show up, 00:53:44.640 --> 00:53:48.300 align:middle line:84% much like if we step outside on a still day. 00:53:48.300 --> 00:53:50.710 align:middle line:84% When we're standing at rest with respect to the medium, 00:53:50.710 --> 00:53:52.390 align:middle line:84% we don't feel a breeze on our face. 00:53:52.390 --> 00:53:54.670 align:middle line:84% When we start moving on our bicycle, 00:53:54.670 --> 00:53:56.650 align:middle line:84% then we feel a breeze in our face. 00:53:56.650 --> 00:53:59.920 align:middle line:84% The air hasn't had to move for that to happen. 00:53:59.920 --> 00:54:02.110 align:middle line:84% Our motion through the air, the atmosphere, 00:54:02.110 --> 00:54:04.705 align:middle line:84% will create that kind of headwind. 00:54:04.705 --> 00:54:07.770 align:middle line:90% 00:54:07.770 --> 00:54:10.060 align:middle line:84% So how do they zero the interference? 00:54:10.060 --> 00:54:10.560 align:middle line:90% Good. 00:54:10.560 --> 00:54:15.780 align:middle line:84% So Julian asks, if they were convinced the Earth was moving, 00:54:15.780 --> 00:54:19.128 align:middle line:84% then how could they ever get rid of it? 00:54:19.128 --> 00:54:21.420 align:middle line:84% Again, the answer is they didn't have to get rid of it. 00:54:21.420 --> 00:54:24.540 align:middle line:84% They had to carefully note what the baseline interference 00:54:24.540 --> 00:54:28.410 align:middle line:84% pattern was and then measure any tiny deviations away from that. 00:54:28.410 --> 00:54:34.050 align:middle line:84% And deviations would happen because they 00:54:34.050 --> 00:54:36.010 align:middle line:90% assumed the Earth was moving. 00:54:36.010 --> 00:54:40.200 align:middle line:84% So you set a initial interference pattern. 00:54:40.200 --> 00:54:42.453 align:middle line:84% The spacing between interference fringes, actually 00:54:42.453 --> 00:54:43.620 align:middle line:90% a circular pattern, usually. 00:54:43.620 --> 00:54:45.270 align:middle line:84% There's little circles within circles-- 00:54:45.270 --> 00:54:46.400 align:middle line:90% concentric circles. 00:54:46.400 --> 00:54:48.900 align:middle line:84% And you can measure the space in between those bright spots, 00:54:48.900 --> 00:54:52.170 align:middle line:84% the fringes, actually quite accurately even in the 1880s. 00:54:52.170 --> 00:54:54.360 align:middle line:84% And the question then became, did the spacing 00:54:54.360 --> 00:54:57.738 align:middle line:84% between those tiny fringes expand or contract, a shift 00:54:57.738 --> 00:54:58.905 align:middle line:90% in the interference pattern? 00:54:58.905 --> 00:55:02.770 align:middle line:90% 00:55:02.770 --> 00:55:03.940 align:middle line:90% So a great question. 00:55:03.940 --> 00:55:05.580 align:middle line:84% So again, partly, the big problem 00:55:05.580 --> 00:55:07.288 align:middle line:84% with everyone in this class is you've all 00:55:07.288 --> 00:55:10.080 align:middle line:84% heard of Albert Einstein, which is not such a problem. 00:55:10.080 --> 00:55:15.093 align:middle line:84% Remember that he was born in 1879. 00:55:15.093 --> 00:55:17.010 align:middle line:84% He was barely on the planet during this stuff. 00:55:17.010 --> 00:55:18.450 align:middle line:90% He certainly wasn't active yet. 00:55:18.450 --> 00:55:20.250 align:middle line:84% So part of what we have to remember 00:55:20.250 --> 00:55:22.740 align:middle line:84% is that that wasn't even in play yet. 00:55:22.740 --> 00:55:24.660 align:middle line:84% And part of what I find actually so 00:55:24.660 --> 00:55:26.220 align:middle line:84% fun-- it's challenging because of all 00:55:26.220 --> 00:55:28.512 align:middle line:84% that we've learned in between, but it's actually pretty 00:55:28.512 --> 00:55:30.300 align:middle line:84% fun to try to put our heads back into 00:55:30.300 --> 00:55:35.490 align:middle line:84% say a pre-1905 or pre-1927 mindset. 00:55:35.490 --> 00:55:37.620 align:middle line:84% What was an obvious question to ask? 00:55:37.620 --> 00:55:40.110 align:middle line:84% What would really smart people like Hendrik Lorentz 00:55:40.110 --> 00:55:43.480 align:middle line:84% really want to spend their time on? 00:55:43.480 --> 00:55:46.390 align:middle line:84% The behavior of light waves when either the emitter or receiver 00:55:46.390 --> 00:55:48.220 align:middle line:84% is in motion with respect to ether. 00:55:48.220 --> 00:55:50.830 align:middle line:84% What did Michelson set his life's work to be? 00:55:50.830 --> 00:55:52.600 align:middle line:84% Really, really precise measurements 00:55:52.600 --> 00:55:55.360 align:middle line:84% of optics to go after this big question about things 00:55:55.360 --> 00:55:57.690 align:middle line:84% like the electrodynamics of moving bodies. 00:55:57.690 --> 00:56:01.630 align:middle line:84% So more specifically, DA, you're absolutely right. 00:56:01.630 --> 00:56:05.140 align:middle line:84% There were many ways to try to account for these null results. 00:56:05.140 --> 00:56:06.760 align:middle line:84% Michelson himself thought of several. 00:56:06.760 --> 00:56:08.830 align:middle line:84% Michelson himself redid this experiment 00:56:08.830 --> 00:56:10.240 align:middle line:90% throughout his lifetime. 00:56:10.240 --> 00:56:13.600 align:middle line:84% He helped encourage other really quite world-class 00:56:13.600 --> 00:56:17.200 align:middle line:84% experimentalists to redo the interferometry tests well 00:56:17.200 --> 00:56:20.020 align:middle line:84% into the 20th century, well after the publication 00:56:20.020 --> 00:56:22.540 align:middle line:84% of relativity because it did seem, for at least some 00:56:22.540 --> 00:56:25.570 align:middle line:84% of that time, to be quite reasonable, maybe 00:56:25.570 --> 00:56:28.780 align:middle line:84% even compelling, alternate explanations. 00:56:28.780 --> 00:56:30.940 align:middle line:90% These experiments were tricky. 00:56:30.940 --> 00:56:34.090 align:middle line:84% The interferometer is an exquisite instrument, 00:56:34.090 --> 00:56:36.840 align:middle line:84% but theoretically it works one way. 00:56:36.840 --> 00:56:39.610 align:middle line:84% Anyone who's taken Junior Lab, or will soon take Junior Lab, 00:56:39.610 --> 00:56:42.250 align:middle line:84% or done any experimental work will know the instruments 00:56:42.250 --> 00:56:44.840 align:middle line:84% don't always work the way the manual says they're going to. 00:56:44.840 --> 00:56:47.970 align:middle line:84% That's what happens with me all the time, by the way. 00:56:47.970 --> 00:56:50.180 align:middle line:84% And so there are all kinds of alternate explanations 00:56:50.180 --> 00:56:51.980 align:middle line:84% that actually seem quite compelling to many 00:56:51.980 --> 00:56:54.890 align:middle line:84% of these folks that might account for the null result. 00:56:54.890 --> 00:56:58.520 align:middle line:84% That's why I find it so tragic, not that Michelson considered 00:56:58.520 --> 00:57:00.770 align:middle line:90% himself a failure in 1887. 00:57:00.770 --> 00:57:04.820 align:middle line:84% It's that 40 years later, after many, many more efforts 00:57:04.820 --> 00:57:08.360 align:middle line:84% to test this and really pursue these alternate possible 00:57:08.360 --> 00:57:11.210 align:middle line:84% explanations, that he still considered himself a failure, 00:57:11.210 --> 00:57:14.090 align:middle line:84% even after a variety of new developments 00:57:14.090 --> 00:57:16.110 align:middle line:90% had come up in between. 00:57:16.110 --> 00:57:18.308 align:middle line:84% So there's a question here about Ligo. 00:57:18.308 --> 00:57:19.850 align:middle line:84% Was the interferometer an inspiration 00:57:19.850 --> 00:57:23.240 align:middle line:84% for Ligo, Muriel asks and the short answer is yep. 00:57:23.240 --> 00:57:26.540 align:middle line:84% And so part of what the ironies here, again-- 00:57:26.540 --> 00:57:29.720 align:middle line:84% and we will come to some of this a bit later in the term-- 00:57:29.720 --> 00:57:31.550 align:middle line:84% is that the Michelson-Morley experiment 00:57:31.550 --> 00:57:37.080 align:middle line:84% was done really to try to test for the existence of the ether. 00:57:37.080 --> 00:57:38.810 align:middle line:84% As we're finding, Michelson and Morley 00:57:38.810 --> 00:57:41.660 align:middle line:84% themselves find no compelling evidence for the ether. 00:57:41.660 --> 00:57:44.450 align:middle line:84% And yet, roughly 100 years later, 00:57:44.450 --> 00:57:46.280 align:middle line:84% a very similar kind of experiment 00:57:46.280 --> 00:57:49.955 align:middle line:84% could be used to now try to test relativity, which denies 00:57:49.955 --> 00:57:51.080 align:middle line:90% the existence of the ether. 00:57:51.080 --> 00:57:54.200 align:middle line:84% So the instrument has a remarkable intellectual 00:57:54.200 --> 00:57:56.660 align:middle line:84% continuity, even as the theories it's somehow 00:57:56.660 --> 00:57:59.120 align:middle line:84% designed to be testing or in conversation with 00:57:59.120 --> 00:58:00.190 align:middle line:90% have changed quite a lot. 00:58:00.190 --> 00:58:02.990 align:middle line:84% So we'll come to that pretty soon. 00:58:02.990 --> 00:58:04.340 align:middle line:90% So let's see. 00:58:04.340 --> 00:58:08.520 align:middle line:84% Johan asks about these constants like c, mu 0, and epsilon 0, 00:58:08.520 --> 00:58:10.520 align:middle line:84% they were measured separately and independently. 00:58:10.520 --> 00:58:11.062 align:middle line:90% That's right. 00:58:11.062 --> 00:58:11.690 align:middle line:90% Ah, good. 00:58:11.690 --> 00:58:18.170 align:middle line:84% So basically, Maxwell, in 1865, was really 00:58:18.170 --> 00:58:22.760 align:middle line:84% impressed by just how close the product of these values 00:58:22.760 --> 00:58:25.130 align:middle line:90% mu 0 and epsilon 0 happen to be. 00:58:25.130 --> 00:58:27.553 align:middle line:84% They didn't equal exactly what the textbook 00:58:27.553 --> 00:58:28.970 align:middle line:84% answer for the speed of light was, 00:58:28.970 --> 00:58:30.650 align:middle line:84% but they were really pretty close 00:58:30.650 --> 00:58:34.430 align:middle line:84% within what seemed to be too close to be merely coincidence. 00:58:34.430 --> 00:58:37.040 align:middle line:84% Maxwell, by this point, actually did have a lot of experience 00:58:37.040 --> 00:58:38.000 align:middle line:90% with laboratories. 00:58:38.000 --> 00:58:41.090 align:middle line:84% He actually became the director of the Cavendish Laboratory 00:58:41.090 --> 00:58:44.067 align:middle line:84% for Experiment at Cambridge around that time. 00:58:44.067 --> 00:58:45.650 align:middle line:84% So he was quite aware that there would 00:58:45.650 --> 00:58:49.640 align:middle line:84% be a unavoidable jostle around any of these experimentally 00:58:49.640 --> 00:58:51.398 align:middle line:90% determined numbers. 00:58:51.398 --> 00:58:52.940 align:middle line:84% But in principle, there was no reason 00:58:52.940 --> 00:58:54.357 align:middle line:84% why the product should be anywhere 00:58:54.357 --> 00:58:56.600 align:middle line:84% near 1 over the square of the speed of light, 00:58:56.600 --> 00:58:58.640 align:middle line:84% let alone within actually a pretty 00:58:58.640 --> 00:59:00.830 align:middle line:90% compelling small interval. 00:59:00.830 --> 00:59:03.140 align:middle line:84% So he really takes that as indicative 00:59:03.140 --> 00:59:05.300 align:middle line:84% that this probably isn't coincidence. 00:59:05.300 --> 00:59:06.920 align:middle line:84% And then that sets up new efforts 00:59:06.920 --> 00:59:09.260 align:middle line:84% to both measure the speed of light with more accuracy. 00:59:09.260 --> 00:59:11.468 align:middle line:84% That's actually the first thing that Albert Michelson 00:59:11.468 --> 00:59:13.490 align:middle line:84% did that really got attention on the continent. 00:59:13.490 --> 00:59:16.040 align:middle line:84% He built new efforts to measure the speed of light 00:59:16.040 --> 00:59:19.280 align:middle line:84% to new accuracy, and he came within amazing closeness 00:59:19.280 --> 00:59:21.360 align:middle line:90% to the modern value. 00:59:21.360 --> 00:59:23.910 align:middle line:84% So that's one thing that the Maxwellian work inspired is, 00:59:23.910 --> 00:59:26.300 align:middle line:84% can we measure any of these constants to more precision 00:59:26.300 --> 00:59:28.550 align:middle line:84% and then pursue theoretical implications 00:59:28.550 --> 00:59:30.558 align:middle line:84% if it really is not a coincidence 00:59:30.558 --> 00:59:31.850 align:middle line:90% that these things fit together? 00:59:31.850 --> 00:59:32.910 align:middle line:90% It's a great question. 00:59:32.910 --> 00:59:33.950 align:middle line:84% I'm going to go back to share screen. 00:59:33.950 --> 00:59:34.910 align:middle line:90% These are great questions. 00:59:34.910 --> 00:59:36.285 align:middle line:84% Let me go back for that last part 00:59:36.285 --> 00:59:39.222 align:middle line:90% of today's prepared material. 00:59:39.222 --> 00:59:40.680 align:middle line:84% And as usual, if questions come up, 00:59:40.680 --> 00:59:43.590 align:middle line:90% please do put them in the chat. 00:59:43.590 --> 00:59:46.110 align:middle line:90% OK, last part for today. 00:59:46.110 --> 00:59:50.060 align:middle line:84% So we saw that Lorentz had this mathematical response 00:59:50.060 --> 00:59:53.450 align:middle line:84% for the behavior of Maxwell's equations 00:59:53.450 --> 00:59:56.040 align:middle line:84% when he applies them to bodies moving 00:59:56.040 --> 00:59:57.260 align:middle line:90% with respect to the ether. 00:59:57.260 --> 00:59:59.660 align:middle line:84% Lorentz absolutely was also following 00:59:59.660 --> 01:00:01.110 align:middle line:90% the Michelson-Morley work. 01:00:01.110 --> 01:00:03.740 align:middle line:84% You see it in his citations, in his own articles. 01:00:03.740 --> 01:00:05.630 align:middle line:84% When the Michelson-Morley stuff starts 01:00:05.630 --> 01:00:07.550 align:middle line:84% getting published in the 1880s, Lorentz 01:00:07.550 --> 01:00:10.980 align:middle line:84% is very eager to keep up with the latest experimental work. 01:00:10.980 --> 01:00:14.750 align:middle line:84% And this really convinces him of a second reason 01:00:14.750 --> 01:00:17.420 align:middle line:84% to keep pursuing it, dig in even more 01:00:17.420 --> 01:00:19.910 align:middle line:84% on this topic of the electrodynamics of moving 01:00:19.910 --> 01:00:21.240 align:middle line:90% bodies. 01:00:21.240 --> 01:00:22.950 align:middle line:84% Partly, he wants to actually respond 01:00:22.950 --> 01:00:25.470 align:middle line:84% even more directly to this null result 01:00:25.470 --> 01:00:27.740 align:middle line:90% from Michelson and Morley. 01:00:27.740 --> 01:00:30.090 align:middle line:84% And he comes up with this idea that, to this day, 01:00:30.090 --> 01:00:32.060 align:middle line:84% we still call Lorentz Contraction. 01:00:32.060 --> 01:00:33.350 align:middle line:84% If you remember-- I'm sorry, I don't remember 01:00:33.350 --> 01:00:34.308 align:middle line:90% who put it in the chat. 01:00:34.308 --> 01:00:36.560 align:middle line:84% Someone had asked, hey, that factor gamma 01:00:36.560 --> 01:00:38.540 align:middle line:90% looks familiar from Lorentz. 01:00:38.540 --> 01:00:39.290 align:middle line:90% It sure does. 01:00:39.290 --> 01:00:41.330 align:middle line:84% And here's how Lorentz came to it. 01:00:41.330 --> 01:00:43.400 align:middle line:84% Lorentz argued that we'd actually 01:00:43.400 --> 01:00:46.610 align:middle line:84% left out part of the balance of forces 01:00:46.610 --> 01:00:49.400 align:middle line:84% when trying to analyze things like the Michelson-Morley 01:00:49.400 --> 01:00:50.690 align:middle line:90% interferometer. 01:00:50.690 --> 01:00:54.020 align:middle line:84% He argued that the molecules within one arm 01:00:54.020 --> 01:00:56.480 align:middle line:84% of the interferometer, the arm that's heading directly 01:00:56.480 --> 01:01:00.050 align:middle line:84% into the ether wind, would actually feel a force on it. 01:01:00.050 --> 01:01:03.320 align:middle line:84% There would be a net force squeezing 01:01:03.320 --> 01:01:04.430 align:middle line:90% literally the matter-- 01:01:04.430 --> 01:01:07.910 align:middle line:84% the molecules in that one arm of the device-- 01:01:07.910 --> 01:01:09.830 align:middle line:84% squeezing them closer together because they're 01:01:09.830 --> 01:01:13.820 align:middle line:84% moving through this physical resistive medium. 01:01:13.820 --> 01:01:15.710 align:middle line:84% I like to think of this in my mind 01:01:15.710 --> 01:01:18.530 align:middle line:84% as trying to take an inflated beach ball 01:01:18.530 --> 01:01:23.310 align:middle line:84% and dragging it underwater in a viscous resistive medium. 01:01:23.310 --> 01:01:25.610 align:middle line:84% The shape of that ball will change. 01:01:25.610 --> 01:01:28.410 align:middle line:84% It will get flattened in the direction of motion. 01:01:28.410 --> 01:01:31.177 align:middle line:90% It'll become oblate or prolate. 01:01:31.177 --> 01:01:32.010 align:middle line:90% I think it's oblate. 01:01:32.010 --> 01:01:34.780 align:middle line:84% Anyway, it'll get squeezed in the direction of motion 01:01:34.780 --> 01:01:38.100 align:middle line:84% so that the beach ball might be perfectly spherical, 01:01:38.100 --> 01:01:40.020 align:middle line:84% at least to our naked when it's outside 01:01:40.020 --> 01:01:41.910 align:middle line:90% of that medium of the water. 01:01:41.910 --> 01:01:44.700 align:middle line:84% Put it underwater and drag it at some high speed. 01:01:44.700 --> 01:01:48.900 align:middle line:84% The water will exert a force literally 01:01:48.900 --> 01:01:52.385 align:middle line:84% on the matter of that beach ball. 01:01:52.385 --> 01:01:54.510 align:middle line:84% And it'll squeeze it along the direction of motion. 01:01:54.510 --> 01:01:56.970 align:middle line:84% Lorentz says the same thing must be happening 01:01:56.970 --> 01:02:01.230 align:middle line:84% to every single molecule that makes up that interferometer 01:02:01.230 --> 01:02:04.170 align:middle line:84% arm of length L of, say, 11 meters. 01:02:04.170 --> 01:02:07.050 align:middle line:84% The arm that's heading directly into the ether, 01:02:07.050 --> 01:02:10.830 align:middle line:84% is getting the full brunt of that resistive force, 01:02:10.830 --> 01:02:12.870 align:middle line:90% and it should shrink. 01:02:12.870 --> 01:02:16.050 align:middle line:84% What if it shrinks by exactly this factor gamma? 01:02:16.050 --> 01:02:18.270 align:middle line:84% What if it doesn't just shrink by any old amount? 01:02:18.270 --> 01:02:20.400 align:middle line:84% What if the amount of contraction 01:02:20.400 --> 01:02:24.660 align:middle line:84% is controlled by that ratio of the object speed v 01:02:24.660 --> 01:02:27.150 align:middle line:84% with respect to the speed of light c? 01:02:27.150 --> 01:02:30.030 align:middle line:84% Then the arm of the interferometer 01:02:30.030 --> 01:02:32.490 align:middle line:84% that's heading directly into that ether wind 01:02:32.490 --> 01:02:36.360 align:middle line:84% would have every molecule shrunk by just such a small amount, 01:02:36.360 --> 01:02:41.100 align:middle line:84% by a nonzero but tiny amount given by gamma. 01:02:41.100 --> 01:02:44.800 align:middle line:84% And there would be a contraction in that direction. 01:02:44.800 --> 01:02:47.560 align:middle line:84% In that case, if you think back to the swimmers, let alone 01:02:47.560 --> 01:02:49.450 align:middle line:84% the light waves, that's like saying 01:02:49.450 --> 01:02:51.490 align:middle line:84% that swimmer 1, who heads directly 01:02:51.490 --> 01:02:55.060 align:middle line:84% into the current for the first part of her journey 01:02:55.060 --> 01:02:57.670 align:middle line:84% and the directly with the current for the second part, 01:02:57.670 --> 01:03:01.480 align:middle line:84% the literal distance she has to travel between points A and B 01:03:01.480 --> 01:03:04.060 align:middle line:90% has been shrunk by a little bit. 01:03:04.060 --> 01:03:07.755 align:middle line:84% It's been contracted by 1 power of gamma. 01:03:07.755 --> 01:03:08.890 align:middle line:90% And he hypothesized. 01:03:08.890 --> 01:03:10.420 align:middle line:90% He wonders, is that the case? 01:03:10.420 --> 01:03:12.550 align:middle line:84% Is there just enough force exerted 01:03:12.550 --> 01:03:15.880 align:middle line:84% by this resistive elastic medium to actually make it 01:03:15.880 --> 01:03:17.500 align:middle line:90% an unfair race? 01:03:17.500 --> 01:03:20.320 align:middle line:84% Can swimmer 1 actually had a shorter total distance 01:03:20.320 --> 01:03:21.340 align:middle line:90% to travel? 01:03:21.340 --> 01:03:23.860 align:middle line:84% If you go back to what we calculated earlier, 01:03:23.860 --> 01:03:27.190 align:middle line:84% how long her total lap time would be to go from point A 01:03:27.190 --> 01:03:31.570 align:middle line:84% to B and back, and you adjust the length she had to travel-- 01:03:31.570 --> 01:03:34.240 align:middle line:84% that length of shoreline had been shrunk 01:03:34.240 --> 01:03:37.040 align:middle line:84% because of the effect of the current-- 01:03:37.040 --> 01:03:39.880 align:middle line:84% then actually you cancel out one of those factors of gamma 01:03:39.880 --> 01:03:41.650 align:middle line:90% because her length is shorter. 01:03:41.650 --> 01:03:44.570 align:middle line:84% And then it should actually be a complete tie. 01:03:44.570 --> 01:03:47.750 align:middle line:84% So if you take into account this physical contraction, 01:03:47.750 --> 01:03:50.610 align:middle line:84% a physical shrinking in the direction of motion, 01:03:50.610 --> 01:03:53.240 align:middle line:84% then the total duration for swimmer 1 01:03:53.240 --> 01:03:56.810 align:middle line:84% should now be predicted to be identical to the total duration 01:03:56.810 --> 01:03:57.590 align:middle line:90% for swimmer 2. 01:03:57.590 --> 01:03:59.940 align:middle line:90% It should be a tie after all. 01:03:59.940 --> 01:04:03.260 align:middle line:84% And so if there's a physical effect from our motion through 01:04:03.260 --> 01:04:05.840 align:middle line:84% the ether, if there's a force exerted by that physical 01:04:05.840 --> 01:04:09.320 align:middle line:84% elastic resistive stuff, like that bowl of jelly that Lord 01:04:09.320 --> 01:04:11.750 align:middle line:84% Kelvin asked us to put our hands into-- it acts back 01:04:11.750 --> 01:04:13.370 align:middle line:90% on our device-- 01:04:13.370 --> 01:04:16.250 align:middle line:84% then you would predict 0 total time 01:04:16.250 --> 01:04:18.140 align:middle line:90% offset between the two paths. 01:04:18.140 --> 01:04:20.870 align:middle line:84% The race should be a tie, just as much 01:04:20.870 --> 01:04:23.870 align:middle line:84% for those two light waves as for the two swimmers. 01:04:23.870 --> 01:04:26.900 align:middle line:84% So Lorentz is now trying to respond literally directly 01:04:26.900 --> 01:04:28.548 align:middle line:90% to the Michelson-Morley results. 01:04:28.548 --> 01:04:30.590 align:middle line:84% He says, this could account for why they actually 01:04:30.590 --> 01:04:34.300 align:middle line:84% find no shift in the interference fringes. 01:04:34.300 --> 01:04:37.530 align:middle line:84% So now Lorentz has two different motivations 01:04:37.530 --> 01:04:40.560 align:middle line:84% for reconsidering how to handle coordinates. 01:04:40.560 --> 01:04:43.500 align:middle line:84% We had that first one we looked at the first part for today's 01:04:43.500 --> 01:04:47.078 align:middle line:84% presentation, this local fictitious time 01:04:47.078 --> 01:04:49.620 align:middle line:84% where he's really just trying to figure out how does the wave 01:04:49.620 --> 01:04:51.090 align:middle line:90% equation transform? 01:04:51.090 --> 01:04:53.580 align:middle line:84% Do I have to do something funny with time or not? 01:04:53.580 --> 01:04:57.870 align:middle line:84% And now he has a second, more experimentally inspired 01:04:57.870 --> 01:05:00.600 align:middle line:84% or empirical reason to keep drilling down 01:05:00.600 --> 01:05:03.750 align:middle line:84% on that same question about how do we transform 01:05:03.750 --> 01:05:06.750 align:middle line:84% our coordinates, now with this notion of a physical length 01:05:06.750 --> 01:05:08.250 align:middle line:90% contraction. 01:05:08.250 --> 01:05:10.230 align:middle line:84% So keeping that same factor gamma 01:05:10.230 --> 01:05:12.660 align:middle line:84% in mind, which already looked familiar to some of you, 01:05:12.660 --> 01:05:15.600 align:middle line:84% Lorentz introduces what we would now call the Lorentz 01:05:15.600 --> 01:05:16.980 align:middle line:90% Transformation. 01:05:16.980 --> 01:05:19.950 align:middle line:84% It is to replace the Galilean Transformation. 01:05:19.950 --> 01:05:22.105 align:middle line:90% 01:05:22.105 --> 01:05:23.980 align:middle line:84% As you can see, and as you might have learned 01:05:23.980 --> 01:05:27.760 align:middle line:84% in other classes, this ubiquitous factor gamma, 01:05:27.760 --> 01:05:31.240 align:middle line:84% 1 over the square root of 1 minus quantity v over c 01:05:31.240 --> 01:05:32.110 align:middle line:90% squared-- 01:05:32.110 --> 01:05:34.240 align:middle line:84% that now shows up both when we take 01:05:34.240 --> 01:05:36.970 align:middle line:84% care of our spatial coordinate and theirs 01:05:36.970 --> 01:05:39.650 align:middle line:84% and our temporal coordinate and theirs. 01:05:39.650 --> 01:05:44.620 align:middle line:84% We have a gamma factor, both for x prime and for t prime. 01:05:44.620 --> 01:05:47.410 align:middle line:84% And also, both the x prime and the t prime 01:05:47.410 --> 01:05:50.860 align:middle line:84% both are directional of motion, our comparison 01:05:50.860 --> 01:05:52.780 align:middle line:84% for the spatial direction along which 01:05:52.780 --> 01:05:56.170 align:middle line:84% the relative motion occurs, and our comparison of the clock 01:05:56.170 --> 01:05:57.760 align:middle line:90% rates, t and t prime. 01:05:57.760 --> 01:06:00.670 align:middle line:84% Both of those depend on the relative speed 01:06:00.670 --> 01:06:02.300 align:middle line:90% as well as on the positions. 01:06:02.300 --> 01:06:04.750 align:middle line:84% So you have a drift or an offset, 01:06:04.750 --> 01:06:08.140 align:middle line:84% both in time and in space, the amount of which 01:06:08.140 --> 01:06:11.330 align:middle line:84% is governed by that new quantity gamma. 01:06:11.330 --> 01:06:13.580 align:middle line:84% And so here's that factor gamma again. 01:06:13.580 --> 01:06:15.410 align:middle line:84% And just as we had done before, we 01:06:15.410 --> 01:06:18.170 align:middle line:84% can expand this quantity in general 01:06:18.170 --> 01:06:21.710 align:middle line:84% for a small ratio of the relative speed v 01:06:21.710 --> 01:06:23.210 align:middle line:90% compared to the speed of light. 01:06:23.210 --> 01:06:26.480 align:middle line:84% It's a second-order quantity to lowest order, 01:06:26.480 --> 01:06:29.840 align:middle line:84% which would explain why Galileo, or Newton, or anyone 01:06:29.840 --> 01:06:32.930 align:middle line:84% in between their time and Lorentz's time 01:06:32.930 --> 01:06:37.790 align:middle line:84% had never measured or noticed these new kinds of ways 01:06:37.790 --> 01:06:39.500 align:middle line:90% to relate our coordinates. 01:06:39.500 --> 01:06:42.590 align:middle line:84% Galileo's transformations had worked perfectly well 01:06:42.590 --> 01:06:45.350 align:middle line:84% quantitatively for every example they'd 01:06:45.350 --> 01:06:47.630 align:middle line:84% been able to test up until that time 01:06:47.630 --> 01:06:51.020 align:middle line:84% precisely because the relative speeds involved had always 01:06:51.020 --> 01:06:54.630 align:middle line:84% been, it turned out, much, much slower than the speed of light. 01:06:54.630 --> 01:06:57.770 align:middle line:84% And so you were worried about a square 01:06:57.770 --> 01:06:59.480 align:middle line:90% of an already small quantity. 01:06:59.480 --> 01:07:01.730 align:middle line:84% The correction to the Galilean transformation 01:07:01.730 --> 01:07:05.270 align:middle line:84% would have been minuscule in nearly every application 01:07:05.270 --> 01:07:08.240 align:middle line:90% until you get to light. 01:07:08.240 --> 01:07:11.550 align:middle line:84% Until you think about light and either a moving 01:07:11.550 --> 01:07:14.910 align:middle line:84% emitter or moving receiver, then, Lorentz says, there's 01:07:14.910 --> 01:07:18.840 align:middle line:84% a physical force that will contract any object made 01:07:18.840 --> 01:07:20.970 align:middle line:84% of any real atoms and molecules in one direction 01:07:20.970 --> 01:07:22.170 align:middle line:90% in the direction of motion. 01:07:22.170 --> 01:07:25.080 align:middle line:84% It's a small effect, but a nontrivial one. 01:07:25.080 --> 01:07:27.210 align:middle line:84% When we incorporate that, we both get back 01:07:27.210 --> 01:07:30.570 align:middle line:84% to the expected form for Maxwell's wave equation 01:07:30.570 --> 01:07:32.770 align:middle line:84% for electric and magnetic fields, 01:07:32.770 --> 01:07:35.100 align:middle line:84% and we can account for these latest experiments 01:07:35.100 --> 01:07:37.230 align:middle line:90% like the Michelson-Morley. 01:07:37.230 --> 01:07:41.070 align:middle line:84% So as I had hinted at a moment ago, 01:07:41.070 --> 01:07:44.070 align:middle line:84% when Lorentz used his own new system for relating coordinates 01:07:44.070 --> 01:07:46.140 align:middle line:84% that incorporates that gamma factor 01:07:46.140 --> 01:07:49.120 align:middle line:84% as well as the t prime, his so-called local time, 01:07:49.120 --> 01:07:51.870 align:middle line:84% now even in this new set of coordinates, 01:07:51.870 --> 01:07:55.950 align:middle line:84% even if either the emitter or receiver or both are moving 01:07:55.950 --> 01:07:58.800 align:middle line:84% with respect to this still ether, 01:07:58.800 --> 01:08:02.280 align:middle line:84% the way that electric and magnetic fields should behave 01:08:02.280 --> 01:08:04.230 align:middle line:84% goes back to looking the way we'd expect. 01:08:04.230 --> 01:08:08.080 align:middle line:84% It goes back to being the simple traveling wave expression 01:08:08.080 --> 01:08:11.070 align:middle line:84% so that the solutions, even in a moving laboratory-- 01:08:11.070 --> 01:08:12.690 align:middle line:90% like for us on Earth-- 01:08:12.690 --> 01:08:15.000 align:middle line:84% really should travel at the speed of light, 01:08:15.000 --> 01:08:19.378 align:middle line:84% really should behave like oscillating sines and cosines. 01:08:19.378 --> 01:08:21.420 align:middle line:84% And so now just to wrap up this part for Lorentz, 01:08:21.420 --> 01:08:23.003 align:middle line:84% and we'll have some time for some more 01:08:23.003 --> 01:08:23.970 align:middle line:90% discussion in a moment. 01:08:23.970 --> 01:08:26.609 align:middle line:84% Lorentz addresses these two puzzles 01:08:26.609 --> 01:08:28.260 align:middle line:84% about the electrodynamics of moving 01:08:28.260 --> 01:08:30.569 align:middle line:84% bodies-- a mathematical one just about 01:08:30.569 --> 01:08:34.109 align:middle line:84% the behavior of a certain kind of equation as he handles 01:08:34.109 --> 01:08:36.689 align:middle line:84% coordinates in various ways, and also 01:08:36.689 --> 01:08:38.399 align:middle line:84% an experimental or empirical one. 01:08:38.399 --> 01:08:41.310 align:middle line:84% He really was following Michelson and Morley's work 01:08:41.310 --> 01:08:42.600 align:middle line:90% quite carefully. 01:08:42.600 --> 01:08:44.399 align:middle line:84% As I was just emphasizing, Lorentz 01:08:44.399 --> 01:08:47.100 align:middle line:84% says there's a physical force, dynamics-- 01:08:47.100 --> 01:08:50.760 align:middle line:84% there's a force being exerted by the ether on this object, 01:08:50.760 --> 01:08:52.740 align:middle line:84% like the arm of the interferometer, that's 01:08:52.740 --> 01:08:55.649 align:middle line:84% going to cause a physical effect, a contraction. 01:08:55.649 --> 01:08:58.590 align:middle line:84% The quantitative effect is governed by that new factor 01:08:58.590 --> 01:09:02.240 align:middle line:84% gamma, which is there for small speeds 01:09:02.240 --> 01:09:03.990 align:middle line:90% compared to the speed of light. 01:09:03.990 --> 01:09:06.303 align:middle line:84% So as I say, the strategy for Lorentz and indeed 01:09:06.303 --> 01:09:08.720 align:middle line:84% for his whole generation, as we'll see for several classes 01:09:08.720 --> 01:09:11.240 align:middle line:84% to come, is you begin with dynamics. 01:09:11.240 --> 01:09:13.340 align:middle line:84% You begin with a study of all the forces 01:09:13.340 --> 01:09:15.410 align:middle line:84% that are relevant for the physical system you 01:09:15.410 --> 01:09:16.640 align:middle line:90% hope to analyze. 01:09:16.640 --> 01:09:19.220 align:middle line:84% And you use that to figure out how are things going to move. 01:09:19.220 --> 01:09:21.800 align:middle line:84% What are the impacts on what we call kinematics? 01:09:21.800 --> 01:09:23.510 align:middle line:90% Start with dynamics. 01:09:23.510 --> 01:09:26.090 align:middle line:84% Ask about the full range of forces at play, 01:09:26.090 --> 01:09:28.940 align:middle line:84% and use that to solve what we call the equations of motion 01:09:28.940 --> 01:09:31.310 align:middle line:84% to say how will objects move through space and time, 01:09:31.310 --> 01:09:32.779 align:middle line:90% or kinematics. 01:09:32.779 --> 01:09:35.479 align:middle line:84% As we'll see-- and some of you probably have seen already-- 01:09:35.479 --> 01:09:37.460 align:middle line:84% there was a different person who was just 01:09:37.460 --> 01:09:40.010 align:middle line:84% coming onto the scene at this point 01:09:40.010 --> 01:09:42.200 align:middle line:84% at the time, a rather unknown patent clerk 01:09:42.200 --> 01:09:45.380 align:middle line:84% by the name of Albert Einstein, who had a bunch of other ideas 01:09:45.380 --> 01:09:46.590 align:middle line:90% about that. 01:09:46.590 --> 01:09:48.439 align:middle line:84% So I'll stop sharing screen there. 01:09:48.439 --> 01:09:52.260 align:middle line:84% We have time for a couple of more questions. 01:09:52.260 --> 01:09:55.740 align:middle line:84% So Oris writes quite, quite accurately, this 01:09:55.740 --> 01:09:58.620 align:middle line:84% sounds a lot like length contraction special relativity 01:09:58.620 --> 01:10:00.750 align:middle line:84% with a strikingly different interpretation. 01:10:00.750 --> 01:10:01.590 align:middle line:90% Totally right. 01:10:01.590 --> 01:10:02.170 align:middle line:90% I agree. 01:10:02.170 --> 01:10:04.350 align:middle line:84% So we're going to see, starting in the next class, 01:10:04.350 --> 01:10:07.170 align:middle line:84% Einstein starts coming up with the exact same equations, 01:10:07.170 --> 01:10:09.990 align:middle line:84% in many cases, as Lorentz had done. 01:10:09.990 --> 01:10:13.110 align:middle line:84% And not only Lorentz, others have found these things too. 01:10:13.110 --> 01:10:15.630 align:middle line:84% Sometimes it's called Lorentz-Fitzgerald contraction. 01:10:15.630 --> 01:10:19.380 align:middle line:84% There was a researcher in Britain, Fitzgerald, who 01:10:19.380 --> 01:10:21.720 align:middle line:84% found the exact same form of gamma right 01:10:21.720 --> 01:10:23.760 align:middle line:90% around the same time as Lorentz. 01:10:23.760 --> 01:10:26.410 align:middle line:84% Poincaré in France was doing very similar things. 01:10:26.410 --> 01:10:28.290 align:middle line:84% So we'll see that Einstein comes to 01:10:28.290 --> 01:10:30.720 align:middle line:90% many, many identical equations. 01:10:30.720 --> 01:10:33.780 align:middle line:84% And yet, he reads them as telling us 01:10:33.780 --> 01:10:35.918 align:middle line:84% quite different things about how the world works, 01:10:35.918 --> 01:10:38.460 align:middle line:84% much as we saw with Maxwell's equations then, and now, and so 01:10:38.460 --> 01:10:40.110 align:middle line:90% on. 01:10:40.110 --> 01:10:42.750 align:middle line:84% Julian had a question about Lorentz's 01:10:42.750 --> 01:10:43.740 align:middle line:90% educational background. 01:10:43.740 --> 01:10:44.370 align:middle line:90% Very good. 01:10:44.370 --> 01:10:46.050 align:middle line:90% I don't remember the details. 01:10:46.050 --> 01:10:48.750 align:middle line:90% We could each look it up. 01:10:48.750 --> 01:10:51.660 align:middle line:84% Lorentz had certainly become a world 01:10:51.660 --> 01:10:54.310 align:middle line:84% premier mathematical physicist by this time. 01:10:54.310 --> 01:10:57.370 align:middle line:84% So his training would have been similar to the Cambridge 01:10:57.370 --> 01:10:57.870 align:middle line:90% Wranglers. 01:10:57.870 --> 01:10:59.970 align:middle line:84% He didn't literally go to Cambridge University, 01:10:59.970 --> 01:11:02.220 align:middle line:84% but he was very well steeped in the latest 01:11:02.220 --> 01:11:04.110 align:middle line:90% tools of mathematical analysis. 01:11:04.110 --> 01:11:05.880 align:middle line:84% He was very, very good at solving 01:11:05.880 --> 01:11:08.460 align:middle line:84% complicated differential equations very quickly-- 01:11:08.460 --> 01:11:11.220 align:middle line:84% a lot of stuff the Wranglers were drilled in. 01:11:11.220 --> 01:11:15.120 align:middle line:84% And so his background would have been pretty similar to, say, 01:11:15.120 --> 01:11:16.380 align:middle line:90% James Clerk Maxwell's. 01:11:16.380 --> 01:11:18.810 align:middle line:84% He was a little younger, but he would 01:11:18.810 --> 01:11:23.130 align:middle line:84% have been drilled in pretty hard math, including differential 01:11:23.130 --> 01:11:25.620 align:middle line:90% equations quite a lot. 01:11:25.620 --> 01:11:28.553 align:middle line:84% Did Einstein refer to Lorentz when he found the equations? 01:11:28.553 --> 01:11:29.970 align:middle line:84% Or was he aware of Lorentz's work? 01:11:29.970 --> 01:11:31.712 align:middle line:90% Ha-ha, good question. 01:11:31.712 --> 01:11:33.420 align:middle line:84% One of the things that you might consider 01:11:33.420 --> 01:11:35.580 align:middle line:84% if you were to review Einstein's paper 01:11:35.580 --> 01:11:40.320 align:middle line:84% is whether he makes adequate reference to the work that 01:11:40.320 --> 01:11:41.280 align:middle line:90% had come before. 01:11:41.280 --> 01:11:43.560 align:middle line:84% Did he cite his sources appropriately? 01:11:43.560 --> 01:11:48.450 align:middle line:84% When you tackle paper 1, which is due October 2, 01:11:48.450 --> 01:11:51.480 align:middle line:84% your job will be to pretend/imagine 01:11:51.480 --> 01:11:54.790 align:middle line:84% you're an editorial assistant at the journal, The Annalen der 01:11:54.790 --> 01:11:57.580 align:middle line:84% Physik, to which Einstein had submitted his paper. 01:11:57.580 --> 01:12:00.880 align:middle line:84% One of the questions a referee should ask, then as now, 01:12:00.880 --> 01:12:03.700 align:middle line:84% is whether the summation accurately reflects 01:12:03.700 --> 01:12:04.900 align:middle line:90% the existing literature. 01:12:04.900 --> 01:12:07.038 align:middle line:84% Was Einstein appropriately citing the work 01:12:07.038 --> 01:12:08.080 align:middle line:90% that had come before him? 01:12:08.080 --> 01:12:11.020 align:middle line:84% I'll pose that as a question, and then I'll answer no. 01:12:11.020 --> 01:12:11.980 align:middle line:90% The answer is no. 01:12:11.980 --> 01:12:15.160 align:middle line:84% He was not citing the stuff at all appropriately, as we'll 01:12:15.160 --> 01:12:17.920 align:middle line:84% see actually starting even in this coming next class session. 01:12:17.920 --> 01:12:21.098 align:middle line:90% 01:12:21.098 --> 01:12:23.140 align:middle line:84% Gary asks, other than the poor citation practice, 01:12:23.140 --> 01:12:24.850 align:middle line:84% did Einstein know of Lorentz's work? 01:12:24.850 --> 01:12:27.940 align:middle line:84% The short answer is he probably did. 01:12:27.940 --> 01:12:30.130 align:middle line:84% As we'll see in the coming class sessions, 01:12:30.130 --> 01:12:33.070 align:middle line:84% Einstein was very avidly reading a lot of this work-- 01:12:33.070 --> 01:12:36.460 align:middle line:84% probably not Michelson's work, actually, but certainly 01:12:36.460 --> 01:12:39.610 align:middle line:84% the work by people like Lorentz and Poincaré in Paris. 01:12:39.610 --> 01:12:43.060 align:middle line:84% He was not citing it very carefully. 01:12:43.060 --> 01:12:45.730 align:middle line:84% But he and his buddies were encountering 01:12:45.730 --> 01:12:49.340 align:middle line:84% this as their off-hours reading group. 01:12:49.340 --> 01:12:53.980 align:middle line:84% This is what they did for fun, which I recommend. 01:12:53.980 --> 01:13:03.000 align:middle line:90%