WEBVTT 00:00:01.665 --> 00:00:03.960 The following content is provided under a Creative 00:00:03.960 --> 00:00:05.380 Commons license. 00:00:05.380 --> 00:00:07.590 Your support will help MIT OpenCourseWare 00:00:07.590 --> 00:00:11.680 continue to offer high quality educational resources for free. 00:00:11.680 --> 00:00:14.220 To make a donation or to view additional materials 00:00:14.220 --> 00:00:18.180 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:18.180 --> 00:00:19.050 at ocw.mit.edu. 00:00:23.210 --> 00:00:26.040 YEN-JIE LEE: So what are we going to do today? 00:00:26.040 --> 00:00:29.990 So today, we're going to continue the discussion, 00:00:29.990 --> 00:00:35.080 based on what we have learned from the diffraction and also 00:00:35.080 --> 00:00:36.530 other interesting phenomena. 00:00:36.530 --> 00:00:38.660 And we are going to make connections 00:00:38.660 --> 00:00:44.030 to quantum mechanics and discuss in greater 00:00:44.030 --> 00:00:46.730 detail about this connection. 00:00:46.730 --> 00:00:49.550 And also, if time allows, we are going 00:00:49.550 --> 00:00:58.650 to cover information about gravitational waves as well. 00:00:58.650 --> 00:01:02.750 So last time, we have discussed diffraction pattern 00:01:02.750 --> 00:01:04.790 coming from a laser beam. 00:01:04.790 --> 00:01:08.540 And we discussed about resolution. 00:01:08.540 --> 00:01:11.940 And you can see that this is the graph we see, last time already 00:01:11.940 --> 00:01:13.190 in the lecture. 00:01:13.190 --> 00:01:15.860 Basically, all the point light source 00:01:15.860 --> 00:01:23.300 coming through a single slit is going to be doing interference 00:01:23.300 --> 00:01:24.540 to each other. 00:01:24.540 --> 00:01:27.530 So basically, you see interesting pattern, 00:01:27.530 --> 00:01:32.060 which you have a central peak. 00:01:32.060 --> 00:01:35.780 And the total constructing for interference 00:01:35.780 --> 00:01:39.680 happens at the center of the screen. 00:01:39.680 --> 00:01:43.550 And at some point, you have a deep-- 00:01:43.550 --> 00:01:48.330 which is actually where total destructive interference 00:01:48.330 --> 00:01:49.450 actually happened. 00:01:49.450 --> 00:01:53.570 And we were able to understand this with mathematics, 00:01:53.570 --> 00:01:56.490 which we learned in 18.03. 00:01:56.490 --> 00:01:58.550 Another interesting result we find 00:01:58.550 --> 00:02:02.780 is that, if we shoot a laser beam to the moon-- 00:02:02.780 --> 00:02:06.290 by now, you should be able to conclude that it's not going 00:02:06.290 --> 00:02:09.650 to be a point on the moon. 00:02:09.650 --> 00:02:15.140 Instead, it's going to be a spot as large as the whole Missouri 00:02:15.140 --> 00:02:16.460 state. 00:02:16.460 --> 00:02:19.620 So that's actually another interesting result 00:02:19.620 --> 00:02:23.880 we found from that discussion last time. 00:02:23.880 --> 00:02:27.080 And finally, we are able to put together 00:02:27.080 --> 00:02:30.320 all the things we have learned from the last few lectures. 00:02:30.320 --> 00:02:34.200 Basically, you can have, at the same time, 00:02:34.200 --> 00:02:38.910 the effect of multi-slit interference and also 00:02:38.910 --> 00:02:41.900 the effect of a single slit diffraction-- 00:02:41.900 --> 00:02:43.760 all then put together. 00:02:43.760 --> 00:02:47.960 Then you have this complicated but also beautiful pattern, 00:02:47.960 --> 00:02:50.510 which you will be able to observe on the screen. 00:02:50.510 --> 00:02:55.040 And basically, the point is that you are going to have, 00:02:55.040 --> 00:02:59.670 for example, in this case, five-slit interference pattern. 00:02:59.670 --> 00:03:02.110 But that is actually modulated. 00:03:02.110 --> 00:03:05.660 The intensity is modulated by the pattern 00:03:05.660 --> 00:03:09.280 from a single-slit diffraction. 00:03:09.280 --> 00:03:12.650 OK, so that is actually what we have 00:03:12.650 --> 00:03:16.070 learned from the last lecture. 00:03:16.070 --> 00:03:25.370 Coming back to the original question, why do we study 8.03? 00:03:25.370 --> 00:03:30.890 The reason is that we would like to understand-- 00:03:30.890 --> 00:03:35.250 we would like to hear from that universe. 00:03:35.250 --> 00:03:38.800 So we cannot even recognize the universe, 00:03:38.800 --> 00:03:42.090 without using waves and vibrations. 00:03:42.090 --> 00:03:46.460 So that's the course in which we have been doing here. 00:03:46.460 --> 00:03:50.010 And we have seen waves of matter. 00:03:50.010 --> 00:03:54.920 So for example, here, we have this water wave generator. 00:03:54.920 --> 00:03:56.450 You can see water waves. 00:03:56.450 --> 00:03:59.120 We have this Bell Lab machine. 00:03:59.120 --> 00:04:03.320 Because you can see the coupled oscillator-- 00:04:03.320 --> 00:04:05.540 a multiple coupled oscillator. 00:04:05.540 --> 00:04:08.090 And they are doing their job together 00:04:08.090 --> 00:04:10.190 to form beautiful waves. 00:04:10.190 --> 00:04:15.050 And you can see those beautiful results from there. 00:04:15.050 --> 00:04:19.980 Last time and also including the last few lectures, 00:04:19.980 --> 00:04:23.120 we have been using this laser to produce 00:04:23.120 --> 00:04:27.110 interesting interference patterns and the diffraction 00:04:27.110 --> 00:04:28.910 pattern. 00:04:28.910 --> 00:04:32.720 So that's the second kind of wave, which we encounter. 00:04:32.720 --> 00:04:36.600 The first kind is the waves of matters. 00:04:36.600 --> 00:04:39.660 The second kind is waves of what? 00:04:39.660 --> 00:04:42.930 Waves of vector fields. 00:04:42.930 --> 00:04:44.570 It's not matter anymore. 00:04:44.570 --> 00:04:48.830 Because this field, this oscillation field, 00:04:48.830 --> 00:04:51.630 can also travel through vacuum. 00:04:51.630 --> 00:04:53.600 So that is actually the second kind 00:04:53.600 --> 00:04:59.660 of wave, which we should learn for 8.03. 00:04:59.660 --> 00:05:05.090 They provide a pretty adequate description 00:05:05.090 --> 00:05:08.270 of the nature, description of the phenomenon, which 00:05:08.270 --> 00:05:12.890 we can actually measure, and see from the experiment we 00:05:12.890 --> 00:05:15.120 went over. 00:05:15.120 --> 00:05:19.640 So what I would like to say in the lecture today 00:05:19.640 --> 00:05:25.310 is that there are two kinds of completely different waves, 00:05:25.310 --> 00:05:27.750 which we haven't talked about. 00:05:27.750 --> 00:05:32.450 The first one is the probability density wave, 00:05:32.450 --> 00:05:36.230 which I will cover that in a few moments. 00:05:36.230 --> 00:05:40.010 The second one is gravitational waves. 00:05:40.010 --> 00:05:43.940 This is actually a space-time distortion 00:05:43.940 --> 00:05:48.830 coming from the motion of massive objects. 00:05:48.830 --> 00:05:51.490 And we would like to see what we can also 00:05:51.490 --> 00:05:55.100 learn from there, using the existing knowledge of which we 00:05:55.100 --> 00:05:59.530 have learned from matter waves and the vector-field waves. 00:05:59.530 --> 00:06:02.970 And that they are, actually, pretty similar to each other 00:06:02.970 --> 00:06:06.210 if you look at their behavior. 00:06:06.210 --> 00:06:12.220 So the first thing which I would like to discuss is light. 00:06:12.220 --> 00:06:16.260 So far, what is light? 00:06:16.260 --> 00:06:20.630 Light is like electromagnetic waves. 00:06:20.630 --> 00:06:22.530 So that is actually what we have learned 00:06:22.530 --> 00:06:25.530 so far from 8.02 and 8.03. 00:06:25.530 --> 00:06:27.210 So they are like waves. 00:06:27.210 --> 00:06:29.670 They are waves, all right. 00:06:29.670 --> 00:06:34.290 On the other hand, in the 20th century, 00:06:34.290 --> 00:06:38.050 there are many, many crises going on. 00:06:38.050 --> 00:06:40.260 So the first thing which is happening 00:06:40.260 --> 00:06:43.900 is photoelectric effect. 00:06:43.900 --> 00:06:48.270 So this experimental result was actually 00:06:48.270 --> 00:06:52.290 first discovered by Hertz. 00:06:52.290 --> 00:06:57.390 So he found that, if you want to kick one electron out 00:06:57.390 --> 00:07:01.960 of some material or some charged material, 00:07:01.960 --> 00:07:08.160 it is easier if you use a high-frequency light compared 00:07:08.160 --> 00:07:10.470 to low-frequency light. 00:07:10.470 --> 00:07:11.430 So that's the issue-- 00:07:11.430 --> 00:07:12.840 really strange. 00:07:12.840 --> 00:07:17.880 Because based on waves and also the intensity formula-- 00:07:17.880 --> 00:07:21.270 while we really care, intensity is 00:07:21.270 --> 00:07:25.580 proportional to the square of the electric field amplitude. 00:07:25.580 --> 00:07:28.110 So that's actually what we learned 00:07:28.110 --> 00:07:30.070 from the previous lectures. 00:07:30.070 --> 00:07:35.100 But what Hertz was saying is that the frequency also 00:07:35.100 --> 00:07:36.300 matters. 00:07:36.300 --> 00:07:40.710 OK, so that's really a bit strange. 00:07:40.710 --> 00:07:44.780 And Einstein actually came in and explained 00:07:44.780 --> 00:07:48.120 this photoelectric effect. 00:07:48.120 --> 00:07:51.510 So what we found is that this effect 00:07:51.510 --> 00:08:01.950 can be explained by viewing the light of small quantas. 00:08:01.950 --> 00:08:07.780 And light is actually not like waves any more, 00:08:07.780 --> 00:08:09.950 but like quantas-- 00:08:09.950 --> 00:08:12.540 the small quantas-- discrete ones-- 00:08:12.540 --> 00:08:18.470 with energy proportional to the frequency. 00:08:18.470 --> 00:08:20.020 All right? 00:08:20.020 --> 00:08:25.380 And basically, the energy of those little quanta-- 00:08:25.380 --> 00:08:28.440 or we now call them photons-- 00:08:28.440 --> 00:08:35.370 is actually equal to h, which is some constant-- 00:08:35.370 --> 00:08:41.100 relate the frequency and the energy of the quanta. 00:08:41.100 --> 00:08:45.570 And with this explanation, the view 00:08:45.570 --> 00:08:50.250 is that the photons are like particles. 00:08:50.250 --> 00:08:53.940 And therefore, he can actually explain that, OK, 00:08:53.940 --> 00:09:02.530 if I measure the kinetic energy, the maxima kinetic energy 00:09:02.530 --> 00:09:09.900 of the electrons, which are kicked out 00:09:09.900 --> 00:09:14.820 from this photoelectric effect experiment. 00:09:14.820 --> 00:09:16.255 I call it K-max. 00:09:19.420 --> 00:09:23.230 What you are going to get is a formula like this. 00:09:23.230 --> 00:09:26.850 The maxima kinetic energy of electrons 00:09:26.850 --> 00:09:34.120 will be equal to h bar mu minus phi. 00:09:34.120 --> 00:09:37.110 Phi is actually some kind of threshold, 00:09:37.110 --> 00:09:39.450 which you need or, say, some kind 00:09:39.450 --> 00:09:42.420 of energy, which you need to overcome to kick one 00:09:42.420 --> 00:09:47.070 electron out of the material. 00:09:47.070 --> 00:09:52.860 So you can see from here that, if the frequency of the light 00:09:52.860 --> 00:09:56.660 is too low, then this will never work. 00:09:56.660 --> 00:10:01.460 Because the maximum kinetic energy will be below 0. 00:10:01.460 --> 00:10:06.170 Therefore, you cannot kick out a electron. 00:10:06.170 --> 00:10:12.950 But if the frequency is high, as shown by Hertz experiment, 00:10:12.950 --> 00:10:13.982 it is possible. 00:10:13.982 --> 00:10:20.300 And also, you can create energetic electron, 00:10:20.300 --> 00:10:23.240 have them kicked out of the material. 00:10:23.240 --> 00:10:26.730 And this is actually verified by experiment. 00:10:26.730 --> 00:10:29.990 And that's essentially why Einstein should 00:10:29.990 --> 00:10:33.860 get the Nobel Prize in 1921. 00:10:33.860 --> 00:10:38.260 So let me tell you what the feeling here-- 00:10:38.260 --> 00:10:42.340 the feeling here is that, now, things are really becoming 00:10:42.340 --> 00:10:43.570 more and more interesting. 00:10:43.570 --> 00:10:46.330 Because first of all, we see really 00:10:46.330 --> 00:10:51.310 well that the electromagnetic wave describes 00:10:51.310 --> 00:10:53.240 the behavior of the light. 00:10:53.240 --> 00:10:54.270 We see diffraction. 00:10:54.270 --> 00:10:56.190 We see interference. 00:10:56.190 --> 00:10:57.910 All those things can be explained 00:10:57.910 --> 00:11:02.380 by the beautiful mathematics, which we have been employing 00:11:02.380 --> 00:11:04.270 to explain all those results. 00:11:04.270 --> 00:11:07.870 But here, you can see that, at the same time, 00:11:07.870 --> 00:11:15.730 the photons are very good tool or very good viewpoint 00:11:15.730 --> 00:11:18.280 to explain the photoelectric effect. 00:11:18.280 --> 00:11:24.130 So that's actually really surprising. 00:11:24.130 --> 00:11:27.430 Because that means you have, suddenly, 00:11:27.430 --> 00:11:30.860 both kinds of explanation of light, which should 00:11:30.860 --> 00:11:34.240 be describing the same thing. 00:11:34.240 --> 00:11:39.050 So now, one idea is to describe them by waves. 00:11:39.050 --> 00:11:43.390 The other idea is to describe them by particles. 00:11:43.390 --> 00:11:45.740 And also, at the same time, as we actually 00:11:45.740 --> 00:11:48.820 discussed in the previous lecture, 00:11:48.820 --> 00:11:55.930 we can do a two-slit experiment with billiard balls 00:11:55.930 --> 00:11:58.720 or with bullets. 00:11:58.720 --> 00:12:01.530 Suppose we do this experiment. 00:12:01.530 --> 00:12:08.900 We fire the balls or bullets through some source. 00:12:08.900 --> 00:12:16.100 And we have some kind of two-slit set up here, 00:12:16.100 --> 00:12:20.060 so that the bullets or balls can actually pass through. 00:12:20.060 --> 00:12:21.880 And then we were wondering, what will 00:12:21.880 --> 00:12:25.270 be the pattern which we see from the detector 00:12:25.270 --> 00:12:27.230 in the right-hand side. 00:12:27.230 --> 00:12:29.610 And basically, what we see is the following. 00:12:29.610 --> 00:12:31.910 So basically, we have a distribution 00:12:31.910 --> 00:12:39.800 of the balls coming from slit number one. 00:12:39.800 --> 00:12:44.750 And we have another distribution of balls, which is actually 00:12:44.750 --> 00:12:48.230 coming from slit number two. 00:12:48.230 --> 00:12:52.220 And I can call it P-1 and P-2, which is actually 00:12:52.220 --> 00:12:55.940 the probability density distribution 00:12:55.940 --> 00:12:58.350 of the experimental result. 00:12:58.350 --> 00:13:03.350 And the final result, or say, if you just 00:13:03.350 --> 00:13:05.920 look at the distribution of balls 00:13:05.920 --> 00:13:11.990 without separating the balls from slit number 00:13:11.990 --> 00:13:14.810 one and slit number two, basically you 00:13:14.810 --> 00:13:18.320 get some distribution like this, which 00:13:18.320 --> 00:13:23.750 is a superpositional P-1 and the P-2 distributions. 00:13:23.750 --> 00:13:28.530 All of these things doesn't surprise anybody. 00:13:28.530 --> 00:13:34.540 The experiment one, which we perform-- 00:13:34.540 --> 00:13:41.130 now, instead of billiard balls, we perform the same experiment 00:13:41.130 --> 00:13:44.380 with electrons. 00:13:44.380 --> 00:13:47.230 And again, we have all those electrons 00:13:47.230 --> 00:13:53.790 pass through this two-slit two-slit experiment. 00:13:53.790 --> 00:13:58.390 As we see before, basically, again, we 00:13:58.390 --> 00:14:04.060 can actually separate electrons from the first slit, which 00:14:04.060 --> 00:14:12.220 I called I-1, and the intensity of electrons 00:14:12.220 --> 00:14:16.840 coming from the second slit, which I called I-2. 00:14:16.840 --> 00:14:20.510 Then, basically, if you can identify and make sure 00:14:20.510 --> 00:14:22.990 that the electron is coming from one of the slits, 00:14:22.990 --> 00:14:26.910 you are going to get distribution like this. 00:14:26.910 --> 00:14:28.000 OK? 00:14:28.000 --> 00:14:33.790 And of course, I can always write these I-1 as a sine wave 00:14:33.790 --> 00:14:37.480 function, psi-1 squared. 00:14:37.480 --> 00:14:41.280 And I can always write this I-2, which is the intensity 00:14:41.280 --> 00:14:45.610 as a function of position of the electron coming from the second 00:14:45.610 --> 00:14:46.870 slit-- 00:14:46.870 --> 00:14:50.580 I can always write it as psi-2 squared. 00:14:53.660 --> 00:14:56.980 In the case of light, it's actually 00:14:56.980 --> 00:15:02.380 just proportional to the electric field. 00:15:02.380 --> 00:15:06.520 So if you accept this, and now you actually 00:15:06.520 --> 00:15:10.620 don't measure where the electron actually 00:15:10.620 --> 00:15:14.050 pass through when the electron from the source 00:15:14.050 --> 00:15:15.910 passed through this experiment-- 00:15:15.910 --> 00:15:20.650 we now don't measure if it passed through one or two. 00:15:20.650 --> 00:15:23.850 Then, the pattern becomes like this. 00:15:23.850 --> 00:15:29.690 You have something like this which, essentially, 00:15:29.690 --> 00:15:35.860 is very, very similar to the two-slit interference 00:15:35.860 --> 00:15:42.190 experimental result of the laser experiment. 00:15:42.190 --> 00:15:46.570 As you see from this experimental result, 00:15:46.570 --> 00:15:50.480 you see some kind of pattern. 00:15:50.480 --> 00:15:52.300 You have the peak. 00:15:52.300 --> 00:15:54.570 You have the valley, as a function 00:15:54.570 --> 00:15:57.470 of position in the detector. 00:15:57.470 --> 00:16:02.590 And we can actually call this I-1-2, which is actually 00:16:02.590 --> 00:16:08.320 when you don't measure or you don't identify 00:16:08.320 --> 00:16:11.600 which slit the electron goes through, 00:16:11.600 --> 00:16:14.740 then you have the intensity, which is actually called I-1-2. 00:16:17.330 --> 00:16:22.400 And what we actually found is that I-1-2 is actually 00:16:22.400 --> 00:16:26.890 not I-1 plus I-2. 00:16:26.890 --> 00:16:32.020 What we found is that I-1-2 is actually psi-1 00:16:32.020 --> 00:16:34.045 plus psi-2 squared. 00:16:36.730 --> 00:16:43.000 So basically, we see interference pattern. 00:16:43.000 --> 00:16:49.952 And this will be equal to I-1 plus I-2 plus 2 squared root 00:16:49.952 --> 00:16:55.840 of I-1 plus I-2 and the cosine delta, 00:16:55.840 --> 00:17:03.170 where the delta is coming from the path length difference. 00:17:03.170 --> 00:17:07.490 So based on this experimental result, 00:17:07.490 --> 00:17:10.609 this is actually really surprising. 00:17:10.609 --> 00:17:16.829 First of all, electrons are arriving like a particle, 00:17:16.829 --> 00:17:17.329 right? 00:17:17.329 --> 00:17:20.869 Because we can see from this slide, 00:17:20.869 --> 00:17:26.662 if you look at the upper left figure, you see doo-doo-doo. 00:17:26.662 --> 00:17:31.010 Every time, you have something hitting the screen. 00:17:31.010 --> 00:17:33.160 And what is actually left over? 00:17:33.160 --> 00:17:37.260 It's a single hit on the screen. 00:17:37.260 --> 00:17:43.190 Therefore, the electrons are arriving like a particle, 00:17:43.190 --> 00:17:46.250 producing a hit in the detector. 00:17:46.250 --> 00:17:49.760 On the other hand, what we are saying here 00:17:49.760 --> 00:17:56.420 is that, before they hit the screen, 00:17:56.420 --> 00:17:59.800 they are behaving like a wave. 00:17:59.800 --> 00:18:03.940 It has interference with itself, like a wave. 00:18:03.940 --> 00:18:07.310 All right, so is electron a particle? 00:18:07.310 --> 00:18:09.845 Or is the electron a wave? 00:18:15.120 --> 00:18:17.130 Strange. 00:18:17.130 --> 00:18:20.490 The answer is electron is actually 00:18:20.490 --> 00:18:22.225 neither of them in reality. 00:18:27.790 --> 00:18:31.240 So how about we actually do some more experiments 00:18:31.240 --> 00:18:36.110 to convince ourselves what is actually really going on. 00:18:36.110 --> 00:18:37.550 So what we could do-- 00:18:37.550 --> 00:18:39.730 as I actually mentioned. 00:18:39.730 --> 00:18:41.620 I can still have the electronic gun. 00:18:44.368 --> 00:18:49.740 I have electron source in the left-hand side. 00:18:49.740 --> 00:18:52.980 Again, I have this two-slit experiment here. 00:18:59.620 --> 00:19:07.170 Then what I'm going to do is to produce a light source here. 00:19:07.170 --> 00:19:13.590 OK, I put a light source there to shine the whole experiment. 00:19:13.590 --> 00:19:16.040 Then, I was wondering what is going 00:19:16.040 --> 00:19:21.350 to happen to the distribution. 00:19:21.350 --> 00:19:28.930 So if I first close the lower slit, slit number two, 00:19:28.930 --> 00:19:32.880 and only measure the intensity coming front slit number 1, 00:19:32.880 --> 00:19:36.116 then this is the distribution I get, which is I-1. 00:19:36.116 --> 00:19:41.030 If I close the upper one and open only the lower one, 00:19:41.030 --> 00:19:45.410 I get a distribution which is I-2. 00:19:45.410 --> 00:19:49.480 And this light source, essentially 00:19:49.480 --> 00:19:53.780 interacting with the electron-- when electrons 00:19:53.780 --> 00:19:58.270 pass through this slit, what is going to happen 00:19:58.270 --> 00:20:02.000 is that you'll see some scattered light coming 00:20:02.000 --> 00:20:03.410 from the slit. 00:20:03.410 --> 00:20:07.690 Therefore, you can know which slit the electron actually 00:20:07.690 --> 00:20:09.770 passed through. 00:20:09.770 --> 00:20:13.370 And if I do this experiment result-- 00:20:13.370 --> 00:20:17.730 if I block one of the slits, this is the distribution, I-1 00:20:17.730 --> 00:20:22.400 and I-2 and now I'm going to open both slits, 00:20:22.400 --> 00:20:26.090 and you will see light coming out of the slit 00:20:26.090 --> 00:20:31.160 when the electron pass slit number one or slit number two. 00:20:31.160 --> 00:20:35.190 You can identify which slit fora all the electrons passing 00:20:35.190 --> 00:20:37.160 through this experiment. 00:20:37.160 --> 00:20:44.900 And the resulting distribution of electrons on the screen 00:20:44.900 --> 00:20:46.500 is actually like this. 00:20:46.500 --> 00:20:49.370 It's actually like I-1 plus I-2. 00:20:49.370 --> 00:20:53.870 There will be no interference. 00:20:53.870 --> 00:20:55.850 Why is that? 00:20:55.850 --> 00:21:00.360 Now, this because you know very precisely which 00:21:00.360 --> 00:21:03.190 slit the electron actually passed through, 00:21:03.190 --> 00:21:06.070 this experiment. 00:21:06.070 --> 00:21:11.520 And also, we can say that, huh, the electrons are actually 00:21:11.520 --> 00:21:13.420 disturbed. 00:21:13.420 --> 00:21:18.580 Therefore, they now behave like bullets or like billiard balls. 00:21:21.100 --> 00:21:24.160 So this is actually a bit strange. 00:21:27.100 --> 00:21:32.020 Maybe it is because the intensity of the light 00:21:32.020 --> 00:21:33.860 is too large. 00:21:33.860 --> 00:21:38.380 Therefore, it's changing the behavior of the electron. 00:21:38.380 --> 00:21:41.890 So what are we going to do now? 00:21:41.890 --> 00:21:45.040 Experimental result number three is 00:21:45.040 --> 00:21:53.000 to lower the intensity of the light. 00:21:56.210 --> 00:22:00.580 So what will happen if I lower the intensity 00:22:00.580 --> 00:22:06.040 of the light source so that we would like to see the behavior, 00:22:06.040 --> 00:22:08.020 as a function of intensity? 00:22:10.970 --> 00:22:18.060 So at some point, we will find that some of the electrons 00:22:18.060 --> 00:22:21.420 are not heated by a photon. 00:22:21.420 --> 00:22:26.520 Or say, there will be no scattered light of the electron 00:22:26.520 --> 00:22:29.730 when it passes through the experiment. 00:22:29.730 --> 00:22:34.710 Because the intensity of the light is too small. 00:22:34.710 --> 00:22:40.410 And we already know, from photoelectric experiments, 00:22:40.410 --> 00:22:43.800 light is, essentially, also like quanta. 00:22:43.800 --> 00:22:47.580 So when the intensity is low enough, 00:22:47.580 --> 00:22:54.210 the effectiveness of the light source decreases. 00:22:54.210 --> 00:22:57.890 Then the experimental result would be like what? 00:22:57.890 --> 00:23:01.570 Can somebody actually give a guess? 00:23:01.570 --> 00:23:06.840 Is that going to be like experimental result number one? 00:23:06.840 --> 00:23:11.570 Or is that going to be like experimental result number two? 00:23:14.460 --> 00:23:16.165 Anybody want to get-- 00:23:16.165 --> 00:23:18.812 AUDIENCE: [INAUDIBLE] 00:23:18.812 --> 00:23:19.770 YEN-JIE LEE: Very good. 00:23:19.770 --> 00:23:26.130 So the result-- as I mentioned before, sometimes the electrons 00:23:26.130 --> 00:23:30.490 are detected by the light source. 00:23:30.490 --> 00:23:34.860 Sometimes the electrons are lucky. 00:23:34.860 --> 00:23:38.610 They pass through without getting heated by a photon. 00:23:38.610 --> 00:23:41.430 Therefore, you cannot know which slit, actually, 00:23:41.430 --> 00:23:44.110 this electron went through. 00:23:44.110 --> 00:23:46.170 Therefore, the experimental result 00:23:46.170 --> 00:23:51.180 is that, if I just lower the intensity of the light source, 00:23:51.180 --> 00:23:55.760 then what I'm going to get is a mixture of experimental result 00:23:55.760 --> 00:24:02.310 number one and the experimental result number two. 00:24:02.310 --> 00:24:05.910 When I have the intensity low enough-- 00:24:05.910 --> 00:24:09.200 going to really, really low intensity limit-- 00:24:09.200 --> 00:24:14.280 the result will become experimental result number one. 00:24:14.280 --> 00:24:17.520 Because then you are not really impacting 00:24:17.520 --> 00:24:20.120 the position of the electrons. 00:24:23.000 --> 00:24:26.990 Finally, you can actually suggest something else. 00:24:26.990 --> 00:24:33.110 So OK, now I have low intensity of light. 00:24:33.110 --> 00:24:37.190 One way to lower the intensity is like what I was saying. 00:24:37.190 --> 00:24:39.410 The rate of the photon emission-- 00:24:39.410 --> 00:24:42.470 I can make it lower and lower. 00:24:42.470 --> 00:24:43.590 All right? 00:24:43.590 --> 00:24:47.690 There's another way to do this. 00:24:51.430 --> 00:24:53.870 Experimental result number four-- 00:24:53.870 --> 00:24:57.980 so what will happen if I use this formula 00:24:57.980 --> 00:25:04.100 E equal to h bar mu equal to hc divided by lambda? 00:25:04.100 --> 00:25:08.470 Because mu is actually just c over lambda. 00:25:08.470 --> 00:25:14.690 What will happen if I, instead of lowering 00:25:14.690 --> 00:25:20.830 the rate of photon emission, I lower the energy 00:25:20.830 --> 00:25:23.410 of individual photons? 00:25:23.410 --> 00:25:25.610 How do I do that? 00:25:25.610 --> 00:25:31.440 What I could do is to lower the frequency 00:25:31.440 --> 00:25:35.700 of the electromagnetic wave of the light source 00:25:35.700 --> 00:25:40.380 or, say, increase the wavelengths 00:25:40.380 --> 00:25:41.850 of the light source. 00:25:41.850 --> 00:25:45.090 OK, this is very nice. 00:25:45.090 --> 00:25:47.640 Because now, I can keep this in, right? 00:25:47.640 --> 00:25:50.340 So that I make sure all the electrons 00:25:50.340 --> 00:25:54.660 are bothered by the photon. 00:25:54.660 --> 00:25:57.310 Because I can emit very high rate. 00:25:57.310 --> 00:26:00.850 But at the same time, I can also lower the intensity, 00:26:00.850 --> 00:26:04.920 so that the intensity is very, very low. 00:26:04.920 --> 00:26:07.620 Can anybody guess what is going to happen? 00:26:10.940 --> 00:26:14.670 With a result like experimental result number one, 00:26:14.670 --> 00:26:18.870 when I go to extremely low intensity? 00:26:18.870 --> 00:26:24.330 Or my result will be like experimental result number two? 00:26:24.330 --> 00:26:29.620 Because each electrons are bothered, 00:26:29.620 --> 00:26:37.170 are heated, by the emission from the light source. 00:26:37.170 --> 00:26:40.330 Anybody want to try? 00:26:40.330 --> 00:26:42.180 Just guess, no? 00:26:42.180 --> 00:26:43.796 One or two? 00:26:43.796 --> 00:26:47.325 Or a mixture of them? 00:26:47.325 --> 00:26:49.200 AUDIENCE: Be like two. 00:26:49.200 --> 00:26:50.940 YEN-JIE LEE: The guess is that it's 00:26:50.940 --> 00:26:54.450 going to be like two, which was actually well-motivated. 00:26:54.450 --> 00:26:57.120 Very good try. 00:26:57.120 --> 00:26:59.400 What essentially, happens is that-- 00:26:59.400 --> 00:27:00.580 OK, I can say, oh! 00:27:00.580 --> 00:27:05.280 Each electron are bothered by many, many photons. 00:27:05.280 --> 00:27:08.160 So those are disturbed. 00:27:08.160 --> 00:27:15.480 Therefore, it has to look like experimental result number two. 00:27:15.480 --> 00:27:18.360 The answer may surprise you. 00:27:18.360 --> 00:27:22.290 The answer is that, if I have the limit 00:27:22.290 --> 00:27:28.370 lambda goes to infinity, mu goes to 0, 00:27:28.370 --> 00:27:32.170 what is going to happen is that, no matter how 00:27:32.170 --> 00:27:37.330 high frequency of photon emission I have, 00:27:37.330 --> 00:27:44.700 I am going to get the result of experimental number one. 00:27:44.700 --> 00:27:46.651 Why is that? 00:27:46.651 --> 00:27:51.190 Now, this is because when the wavelengths 00:27:51.190 --> 00:27:55.840 of the electromagnetic wave or the photon is going 00:27:55.840 --> 00:28:07.370 to infinity, that means you cannot resolve which slit, 00:28:07.370 --> 00:28:10.780 actually, the electron goes through. 00:28:10.780 --> 00:28:15.790 Because if I draw the wavelengths here, 00:28:15.790 --> 00:28:17.770 it's going to be like this. 00:28:17.770 --> 00:28:22.450 If you observe some kind of scattered light 00:28:22.450 --> 00:28:31.190 from the electron, it could come from both slits, 00:28:31.190 --> 00:28:33.620 because the wavelength is too long. 00:28:33.620 --> 00:28:35.780 So if you go to infinity, then it's 00:28:35.780 --> 00:28:39.640 like you have a constant electric field there. 00:28:39.640 --> 00:28:41.690 It doesn't really actually help you 00:28:41.690 --> 00:28:45.480 to identify which slit the electron actually 00:28:45.480 --> 00:28:47.150 passed through. 00:28:47.150 --> 00:28:52.490 So therefore, the interference pattern reappears. 00:28:52.490 --> 00:28:58.430 So this is really crazy thing, if you look at all these four 00:28:58.430 --> 00:29:01.870 experimental results. 00:29:01.870 --> 00:29:07.090 The conclusion from these four imaginary experiments 00:29:07.090 --> 00:29:11.830 is that it is not yet possible to tell 00:29:11.830 --> 00:29:17.320 the position of the electron and also, at the same time, 00:29:17.320 --> 00:29:20.830 do not disturb it. 00:29:20.830 --> 00:29:26.470 If you were able to tell the position of the electron, 00:29:26.470 --> 00:29:29.950 then there would be no interference pattern. 00:29:29.950 --> 00:29:33.700 On the other hand, if your experimental set-up 00:29:33.700 --> 00:29:38.810 have no ability at all to tell if the electron's coming 00:29:38.810 --> 00:29:42.550 from slit number one compared to slit number two, 00:29:42.550 --> 00:29:49.310 then you are going to get interference pattern. 00:29:49.310 --> 00:29:53.470 There's another thing which I would like to make connection 00:29:53.470 --> 00:29:57.490 to the Uncertainty Principle, which we actually learn 00:29:57.490 --> 00:30:01.210 from waves and vibrations. 00:30:01.210 --> 00:30:12.170 So we have learned that Heisenberg's Uncertainty 00:30:12.170 --> 00:30:12.860 Principle-- 00:30:21.100 --> 00:30:23.420 this is essentially purity coming 00:30:23.420 --> 00:30:28.760 from the property of the wave, if you actually 00:30:28.760 --> 00:30:31.700 remember the deviation which we have 00:30:31.700 --> 00:30:33.830 done in the previous lecture. 00:30:33.830 --> 00:30:38.690 So what is this uncertainty principle telling us? 00:30:38.690 --> 00:30:44.595 Is that the standard deviation of the position 00:30:44.595 --> 00:30:50.840 times the standard deviation of the momentum 00:30:50.840 --> 00:30:57.560 is going to be greater or equal to h bar over 2 some constant. 00:30:57.560 --> 00:31:00.710 And how do we actually understand this 00:31:00.710 --> 00:31:05.430 from the electron experiment. 00:31:05.430 --> 00:31:10.220 That is actually highly related to the single-slit experiment 00:31:10.220 --> 00:31:11.810 with electrons. 00:31:11.810 --> 00:31:17.810 So what we could do now is to have a fifth experiment. 00:31:17.810 --> 00:31:21.470 I have electron source here. 00:31:21.470 --> 00:31:25.820 And I have a single slit. 00:31:25.820 --> 00:31:32.000 And the width of the slit is capital D. 00:31:32.000 --> 00:31:35.780 And we were wondering, what is going to happen? 00:31:35.780 --> 00:31:39.250 What will be recorded by the smoke detector 00:31:39.250 --> 00:31:40.880 in the right-hand side? 00:31:40.880 --> 00:31:43.610 And by now, it should not surprise you 00:31:43.610 --> 00:31:49.250 that this would give you some kind of diffraction pattern, 00:31:49.250 --> 00:31:51.990 which you say should be very similar to what we actually 00:31:51.990 --> 00:31:56.740 observe with laser experiments. 00:31:56.740 --> 00:31:58.390 So you can see that. 00:31:58.390 --> 00:32:02.590 The electron-- the momentum-- 00:32:02.590 --> 00:32:06.950 now, I would like to actually define my coordinate system. 00:32:06.950 --> 00:32:14.050 The vertical direction, pointing upward, is my x direction. 00:32:14.050 --> 00:32:19.060 So now, take a look at this experimental result. 00:32:19.060 --> 00:32:23.530 So what this is actually telling us is the following. 00:32:23.530 --> 00:32:28.030 We know the position of the electron 00:32:28.030 --> 00:32:35.870 to a accuracy of the width of this slit, which 00:32:35.870 --> 00:32:39.700 is D. So that is actually telling you 00:32:39.700 --> 00:32:49.300 about the uncertainty over the position in the x direction. 00:32:49.300 --> 00:32:53.710 Now, this electron goes through. 00:32:53.710 --> 00:32:58.910 And they actually hit the screen. 00:32:58.910 --> 00:33:06.070 And each electron is having a single path. 00:33:06.070 --> 00:33:11.770 If I look at one of the paths, the upper one, what I'm getting 00:33:11.770 --> 00:33:17.496 is that there must be a momentum quintessentially 00:33:17.496 --> 00:33:22.820 in the x direction, when this electronic goes 00:33:22.820 --> 00:33:28.440 through the slit and hits the screen. 00:33:32.060 --> 00:33:35.180 One interesting thing we learned from the deviation 00:33:35.180 --> 00:33:40.790 from last time is that, if I just look at the slide here-- 00:33:40.790 --> 00:33:43.910 if I look at the left-hand side slide-- 00:33:43.910 --> 00:33:49.150 if I have a very small slit-- 00:33:49.150 --> 00:33:53.180 D is small-- what does that correspond to? 00:33:53.180 --> 00:34:01.820 That corresponds to delta x goes to very small value case. 00:34:01.820 --> 00:34:04.250 We have a small delta x value. 00:34:04.250 --> 00:34:08.360 You are really sure where is the electron 00:34:08.360 --> 00:34:15.940 at some instant of time, when it passed through the experiment. 00:34:15.940 --> 00:34:17.179 Then what is going to happen? 00:34:17.179 --> 00:34:19.429 If you look at the right-hand side, 00:34:19.429 --> 00:34:25.810 the distribution on the screen, you have a wide distribution. 00:34:25.810 --> 00:34:29.570 The central maximum peak will be very wide. 00:34:29.570 --> 00:34:30.830 So what does that mean? 00:34:30.830 --> 00:34:34.250 That means you have a wide distribution 00:34:34.250 --> 00:34:37.957 of momentum in the x direction. 00:34:40.889 --> 00:34:45.759 Therefore, that will give you that 00:34:45.759 --> 00:34:48.860 is actually consistent with what we've actually written here, 00:34:48.860 --> 00:34:50.460 Heisenberg's Principle. 00:34:50.460 --> 00:34:55.239 Delta x times delta p will be greater or equal to some value. 00:34:55.239 --> 00:35:01.410 On the other hand, if I increase the width of the slit, 00:35:01.410 --> 00:35:03.735 the D is now large. 00:35:03.735 --> 00:35:08.460 As you are making a D larger and larger, what is happening 00:35:08.460 --> 00:35:13.550 is that the central peak, the width, 00:35:13.550 --> 00:35:18.120 is actually going to be narrower and narrower. 00:35:18.120 --> 00:35:20.130 Now, this is actually also consistent with what 00:35:20.130 --> 00:35:23.250 we have learned from Heisenberg's Uncertainty 00:35:23.250 --> 00:35:24.030 Principle. 00:35:24.030 --> 00:35:29.990 When delta x become even larger, then the uncertainty or, say, 00:35:29.990 --> 00:35:35.320 the distribution of the momentum in the x direction, 00:35:35.320 --> 00:35:38.310 becomes smaller. 00:35:38.310 --> 00:35:41.940 So now, we actually also understand a little bit more 00:35:41.940 --> 00:35:46.200 about what the single diffraction actually means. 00:35:46.200 --> 00:35:51.720 And this issue is really closely connected to the Uncertainty 00:35:51.720 --> 00:35:55.500 Principle Heisenberg actually proposed. 00:35:55.500 --> 00:35:58.530 And if we use the mathematics which 00:35:58.530 --> 00:36:01.780 we learned from last time, the C function 00:36:01.780 --> 00:36:06.060 is going to be proportional to integration from minus D 00:36:06.060 --> 00:36:09.150 over 2 to D over 2. 00:36:09.150 --> 00:36:15.990 dx exponential as ikx times x. 00:36:15.990 --> 00:36:19.870 And if I have D goes to infinity, 00:36:19.870 --> 00:36:24.240 which means that you have an infinitely wide slit-- 00:36:24.240 --> 00:36:28.530 based on the formula which we have derived last time-- 00:36:28.530 --> 00:36:34.680 basically, we will see that C function is a function of kx. 00:36:34.680 --> 00:36:37.380 It's going to become a delta function. 00:36:41.250 --> 00:36:47.270 And this delta function is delta kx. 00:36:47.270 --> 00:36:51.720 So that means, if you have absolutely no idea 00:36:51.720 --> 00:36:56.670 about the position of the electron, 00:36:56.670 --> 00:37:03.950 you are going to get very, very precise information about-- 00:37:03.950 --> 00:37:07.200 the momentum in the x direction is actually 00:37:07.200 --> 00:37:10.620 going to be equal to 0. 00:37:10.620 --> 00:37:12.160 Because it's a delta function. 00:37:12.160 --> 00:37:19.820 It's only nonzero at kx, which is the directional propagation 00:37:19.820 --> 00:37:23.050 equal to 0. 00:37:23.050 --> 00:37:24.090 Any questions so far? 00:37:27.760 --> 00:37:31.930 OK, so from those experimental results, 00:37:31.930 --> 00:37:40.900 we've found that the probability of getting heat on the screen 00:37:40.900 --> 00:37:45.850 is proportional to psi-1 square, if I only 00:37:45.850 --> 00:37:49.550 have the first lead there. 00:37:49.550 --> 00:37:56.430 That means the probability, p, is proportional to psi squared. 00:37:59.330 --> 00:38:03.650 And this is actually probably one 00:38:03.650 --> 00:38:11.420 of the most crazy results in the physics we learned so far. 00:38:11.420 --> 00:38:15.550 In some sense, it's kind of sad as well. 00:38:15.550 --> 00:38:18.020 Why sad? 00:38:18.020 --> 00:38:24.680 This means that, OK, I can calculate those wave functions. 00:38:24.680 --> 00:38:28.220 And the probability of getting an outcome 00:38:28.220 --> 00:38:32.910 at a specific position is proportional to this wave 00:38:32.910 --> 00:38:33.685 function squared. 00:38:37.400 --> 00:38:40.990 But I feel, maybe, demotivated, right? 00:38:40.990 --> 00:38:44.150 Because originally, we are like god. 00:38:44.150 --> 00:38:45.520 You can predict-- 00:38:45.520 --> 00:38:48.440 OK, I have this thing, this object. 00:38:48.440 --> 00:38:50.150 And I have force. 00:38:50.150 --> 00:38:52.790 And then it goes like-- oh-- like this way. 00:38:52.790 --> 00:38:58.510 I can calculate the trajectory of this chalk thing 00:38:58.510 --> 00:39:00.530 all over the place, as a function of time. 00:39:00.530 --> 00:39:02.930 And I know what is going to happen. 00:39:02.930 --> 00:39:07.490 I have the full control of all the objects 00:39:07.490 --> 00:39:12.160 which I have in my hand in my experiment. 00:39:12.160 --> 00:39:18.560 But now, quantum mechanics or this experimental result 00:39:18.560 --> 00:39:23.360 tells me that we can only predict 00:39:23.360 --> 00:39:29.350 the probability, the odd, instead of the outcome. 00:39:29.350 --> 00:39:31.460 You see my point? 00:39:31.460 --> 00:39:35.110 I can only pretend the wave function, the distribution 00:39:35.110 --> 00:39:36.730 of the wave function. 00:39:36.730 --> 00:39:40.660 And the probability of getting a result here 00:39:40.660 --> 00:39:43.810 is proportional to the wave function squared. 00:39:43.810 --> 00:39:48.600 But I cannot predict the outcome before I do the experiment. 00:39:51.600 --> 00:39:58.180 That's really a big change in your view 00:39:58.180 --> 00:40:03.105 or, they say, in our current understanding of the physics. 00:40:06.130 --> 00:40:11.080 You can say that, well, maybe Yen-Jie's not 00:40:11.080 --> 00:40:14.800 working hard enough. 00:40:14.800 --> 00:40:22.840 Maybe all those electrons which are emitted from the electron 00:40:22.840 --> 00:40:26.830 source already made up their mind 00:40:26.830 --> 00:40:30.520 where this electron is going to. 00:40:30.520 --> 00:40:35.444 For example, electron number one is doing this-- rrrrr-- 00:40:35.444 --> 00:40:36.760 and going to here. 00:40:36.760 --> 00:40:39.820 And electron number two already made up his mind. 00:40:39.820 --> 00:40:41.560 He's just going to do this. 00:40:41.560 --> 00:40:43.940 And the electron number three is-- uh-- 00:40:43.940 --> 00:40:47.630 maybe do this-- vwooo-do-do-do-do. 00:40:47.630 --> 00:40:53.410 And then all those trajectories are already determined. 00:40:53.410 --> 00:40:59.960 And they are heating variables which Yen-Jie doesn't know. 00:40:59.960 --> 00:41:03.280 Therefore, he screwed this up and said, oh, come on. 00:41:03.280 --> 00:41:07.898 We can only predict the probability. 00:41:07.898 --> 00:41:15.400 But the thing is that, from the experimental result number two, 00:41:15.400 --> 00:41:19.660 experimental result number three and number four, 00:41:19.660 --> 00:41:26.560 you can see that the electrons cannot make up their mind when 00:41:26.560 --> 00:41:28.210 they are emitted. 00:41:28.210 --> 00:41:32.620 Because when they got heated by that light-- 00:41:32.620 --> 00:41:36.370 electrons cannot know in advance that it is going to be heated 00:41:36.370 --> 00:41:38.830 by a light. 00:41:38.830 --> 00:41:43.690 And the light can be a very, very mild, very, very small 00:41:43.690 --> 00:41:44.300 energy. 00:41:44.300 --> 00:41:50.410 So that it should not affect the predetermined 00:41:50.410 --> 00:41:53.760 path of the electron. 00:41:53.760 --> 00:41:56.420 Do you get this? 00:41:56.420 --> 00:41:57.790 So that doesn't makes sense. 00:41:57.790 --> 00:42:03.050 So it is not because Yen-Jie is not trying hard. 00:42:03.050 --> 00:42:07.580 It is really because nobody can really 00:42:07.580 --> 00:42:14.720 tell before the experimental result is actually shown 00:42:14.720 --> 00:42:18.200 or the measurement is already done. 00:42:18.200 --> 00:42:23.970 If you can find any case, maybe you 00:42:23.970 --> 00:42:27.430 will win another 100 Nobel Prize. 00:42:27.430 --> 00:42:32.170 Because you are showing that the whole understanding of quantum 00:42:32.170 --> 00:42:37.820 mechanics is not correct, really. 00:42:37.820 --> 00:42:40.900 Please tell me when you actually have done this experiment. 00:42:40.900 --> 00:42:46.290 I will be very proud of you, for sure. 00:42:46.290 --> 00:42:49.170 So now, we are entering a position 00:42:49.170 --> 00:42:53.370 to discuss this result. So now, actually, we 00:42:53.370 --> 00:42:57.540 can also make use of this understanding 00:42:57.540 --> 00:43:01.560 and predict what would be the particle probability 00:43:01.560 --> 00:43:05.370 distribution in a potential well. 00:43:05.370 --> 00:43:12.240 Suppose I have an experiment, which I have a well, 00:43:12.240 --> 00:43:16.140 where I have potential goes to infinity 00:43:16.140 --> 00:43:18.060 in the left-hand side or right-hand side 00:43:18.060 --> 00:43:21.010 edge of this well. 00:43:21.010 --> 00:43:23.740 And I will define my coordinate system 00:43:23.740 --> 00:43:27.750 so that the well is actually equal to 0, 00:43:27.750 --> 00:43:35.140 or x equal to L. So by now, when you see this, 00:43:35.140 --> 00:43:37.980 this looks really familiar to you. 00:43:37.980 --> 00:43:40.320 In the center part, you have some kind 00:43:40.320 --> 00:43:42.630 of translation symmetry. 00:43:42.630 --> 00:43:45.780 And the boundary-- those are forbidden regions. 00:43:45.780 --> 00:43:48.540 You cannot actually have particles there, 00:43:48.540 --> 00:43:52.290 because the potential is infinity. 00:43:52.290 --> 00:43:55.530 Therefore, this is actually giving you 00:43:55.530 --> 00:44:04.250 boundary conditions of the wave function, 00:44:04.250 --> 00:44:11.920 describing the state of the particle inside this box. 00:44:11.920 --> 00:44:15.000 So the boundary condition would be psi 0. 00:44:15.000 --> 00:44:18.340 It will be equal to 0, because it's actually 00:44:18.340 --> 00:44:22.080 at the left-hand side edge of the well, 00:44:22.080 --> 00:44:26.070 where you have infinite potential. 00:44:26.070 --> 00:44:31.880 And also, you can have psi L. This will be equal to 0, 00:44:31.880 --> 00:44:34.380 because the right-hand side edge, 00:44:34.380 --> 00:44:43.890 you also have infinitely high potential. 00:44:43.890 --> 00:44:49.620 Therefore, when you see this, your immediate reaction 00:44:49.620 --> 00:44:52.485 will be, how do I know what is this? 00:44:52.485 --> 00:44:54.560 This is actually psi m. 00:44:54.560 --> 00:44:56.430 The solution to this problem must 00:44:56.430 --> 00:44:59.810 be something like psi m of x should be 00:44:59.810 --> 00:45:02.580 the normal mode of this system. 00:45:02.580 --> 00:45:09.330 And it's going to be A-m sin km-x, 00:45:09.330 --> 00:45:16.095 where km will be equal to m-pi divided by L, 00:45:16.095 --> 00:45:17.880 where m is a number. 00:45:17.880 --> 00:45:21.660 It can be 1, 2, 3-- it goes to infinity, right? 00:45:21.660 --> 00:45:23.730 By far, you have actually learned 00:45:23.730 --> 00:45:28.900 all these practical calculations from the previous examples 00:45:28.900 --> 00:45:31.100 we had. 00:45:31.100 --> 00:45:38.510 Therefore, what would be the psi m, x as a function of time? 00:45:38.510 --> 00:45:44.410 Then what I am going to get is A-m sin km 00:45:44.410 --> 00:45:48.570 x exponential minus i omega-m t. 00:45:52.900 --> 00:45:59.350 Of course, we can also really plot all those results. 00:45:59.350 --> 00:46:02.990 So for example, n is equal to 1. 00:46:02.990 --> 00:46:07.360 Basically, what you are getting is like this. 00:46:07.360 --> 00:46:09.730 Doesn't surprise you. 00:46:09.730 --> 00:46:14.250 This is actually psi as a function of x. 00:46:14.250 --> 00:46:17.050 And n equal to 2-- 00:46:17.050 --> 00:46:19.480 this will correspond to the situation 00:46:19.480 --> 00:46:29.680 where you have one node in the middle, et cetera, et cetera. 00:46:29.680 --> 00:46:36.780 You can't have many, many higher m value solutions. 00:46:36.780 --> 00:46:40.180 And what would be the probability 00:46:40.180 --> 00:46:45.160 to find the particle in a specific location? 00:46:45.160 --> 00:46:48.460 That's why we mentioned before, the probability is 00:46:48.460 --> 00:46:52.390 proportional to a wave function squared. 00:46:52.390 --> 00:47:01.540 Therefore, the probability will be proportional to sin squared 00:47:01.540 --> 00:47:04.470 k-m x. 00:47:04.470 --> 00:47:06.630 And what we are going to get is like this. 00:47:06.630 --> 00:47:12.150 If I plot m equal to 1, using P as a function of x, 00:47:12.150 --> 00:47:19.720 the probability of getting a particle at a specific place, 00:47:19.720 --> 00:47:24.670 if we are looking at the situation in normal mode number 00:47:24.670 --> 00:47:27.400 one, that is like this. 00:47:27.400 --> 00:47:31.210 You are much more likely to find a particle 00:47:31.210 --> 00:47:34.620 in the middle of the box. 00:47:34.620 --> 00:47:39.600 On the other hand, we can also plot the probability 00:47:39.600 --> 00:47:43.870 as function of x, where m equals to 2 k's. 00:47:43.870 --> 00:47:48.850 If we are actually operating in a second normal mode, 00:47:48.850 --> 00:47:53.080 then basically you have some distribution-- looks like this. 00:47:53.080 --> 00:47:56.410 In this situation, it is forbidden-- or say, 00:47:56.410 --> 00:47:58.780 there's zero probability you will 00:47:58.780 --> 00:48:02.820 find the particle in the middle of the box, 00:48:02.820 --> 00:48:04.010 et cetera, et cetera. 00:48:04.010 --> 00:48:09.850 You can actually calculate all those corresponding probability 00:48:09.850 --> 00:48:14.170 distributions as a function of m value 00:48:14.170 --> 00:48:17.630 and as a function of position. 00:48:17.630 --> 00:48:18.680 OK? 00:48:18.680 --> 00:48:21.560 Sounds like a very good story. 00:48:21.560 --> 00:48:24.660 But there's something missing, right? 00:48:24.660 --> 00:48:27.630 What is actually missing? 00:48:27.630 --> 00:48:29.710 You have the normal modes. 00:48:29.710 --> 00:48:31.680 You have the k-m. 00:48:31.680 --> 00:48:37.320 What is missing is the wave equation. 00:48:37.320 --> 00:48:40.920 The wave equation is missing, right? 00:48:40.920 --> 00:48:44.070 You don't have the dispersion relation. 00:48:44.070 --> 00:48:47.250 This solution is incomplete. 00:48:47.250 --> 00:48:50.370 You don't know what is actually the omega value. 00:48:54.120 --> 00:48:56.650 Because you don't have dispersion relation. 00:48:56.650 --> 00:49:03.750 So what is actually the wave equation 00:49:03.750 --> 00:49:06.820 for the quantum mechanics? 00:49:06.820 --> 00:49:11.170 So it is actually Schrodinger's equation. 00:49:11.170 --> 00:49:14.890 So Feynman once commented on the origin 00:49:14.890 --> 00:49:17.590 of the Schrodinger's Equation. 00:49:17.590 --> 00:49:18.910 It's from where? 00:49:18.910 --> 00:49:25.360 It's not possible to derive it from anything you know. 00:49:25.360 --> 00:49:30.050 It's just coming out of the might Schrodinger, actually. 00:49:30.050 --> 00:49:31.540 So there's no reason. 00:49:31.540 --> 00:49:33.970 And it works. 00:49:33.970 --> 00:49:36.280 That's the beautiful part. 00:49:36.280 --> 00:49:38.840 So what is, actually, this equation? 00:49:38.840 --> 00:49:41.700 So this is the equation Schrodinger actually 00:49:41.700 --> 00:49:43.450 writes down. 00:49:43.450 --> 00:49:47.410 It's like i h-bar-- 00:49:47.410 --> 00:49:53.170 Plank's constant, partial/partial t, psi xt. 00:49:53.170 --> 00:49:57.840 And this will be equal to minus h bar squared 00:49:57.840 --> 00:50:08.672 over 2m partial square, partial x square, plus v xt, psi xt. 00:50:11.470 --> 00:50:14.140 So this is really nice. 00:50:14.140 --> 00:50:19.060 And it works and matches with experimental results. 00:50:19.060 --> 00:50:22.010 And now, I have already the normal mode. 00:50:22.010 --> 00:50:24.460 I can plug that into this equation 00:50:24.460 --> 00:50:27.070 to see what I can actually learn from there. 00:50:27.070 --> 00:50:31.780 So what I am going to do is to plug in psi-m xt 00:50:31.780 --> 00:50:36.220 into this equation, to get the dispersion relation. 00:50:36.220 --> 00:50:38.290 So what this issue, the dispersion relation. 00:50:38.290 --> 00:50:40.450 So here, I have partial/partial t. 00:50:40.450 --> 00:50:46.000 So I extract one omega minus i omega out of this. 00:50:46.000 --> 00:50:52.935 Then, basically, I get h bar omega-m psi-m xt 00:50:52.935 --> 00:50:54.310 in the lambda psi. 00:50:54.310 --> 00:51:00.470 OK, plugging in psi-m into this equation and see what happens. 00:51:00.470 --> 00:51:03.070 Then this will be equal to-- 00:51:03.070 --> 00:51:09.550 I also know that, in the middle of the box, v, essentially, 00:51:09.550 --> 00:51:11.700 the potential-- 00:51:11.700 --> 00:51:14.500 the potential is 0 inside the box. 00:51:14.500 --> 00:51:19.180 The potential is infinity at the edge of the box. 00:51:19.180 --> 00:51:23.800 Therefore, I can safely ignore this term, to be equal to 0. 00:51:23.800 --> 00:51:27.760 So you have a free path to go inside the box. 00:51:27.760 --> 00:51:31.330 And what, essentially, this term-- 00:51:31.330 --> 00:51:36.560 this term will give you minus h-bar square over 2m. 00:51:36.560 --> 00:51:38.950 OK, I have a double differential of x. 00:51:38.950 --> 00:51:45.680 And therefore, I get, basically, minus km squared, right? 00:51:45.680 --> 00:51:47.320 Because it's psi zeta, right? 00:51:47.320 --> 00:51:50.240 So basically, I get minus k squared. 00:51:50.240 --> 00:51:53.890 So therefore, I cancel this minus sign. 00:51:53.890 --> 00:51:59.530 I have km squared out of this calculation. 00:51:59.530 --> 00:52:02.650 And I still have psi-m xt. 00:52:06.310 --> 00:52:08.050 I can cancel this too. 00:52:08.050 --> 00:52:16.850 Then, what I'm getting is that omega-m is equal to km squared, 00:52:16.850 --> 00:52:17.820 h-bar-- 00:52:17.820 --> 00:52:22.360 I cancel one of the h-bar here-- 00:52:22.360 --> 00:52:23.620 divided by 2m. 00:52:26.320 --> 00:52:33.132 This-- essentially, dispersion relation of the wave function. 00:52:37.950 --> 00:52:54.850 De Broglie proposed that wavelengths of the matter wave, 00:52:54.850 --> 00:53:01.690 essentially, highly related to the momentum of the matter. 00:53:01.690 --> 00:53:07.000 So basically, he propose that p, the momentum of the particle 00:53:07.000 --> 00:53:11.140 is actually equal to h-bar k, where k is the wave 00:53:11.140 --> 00:53:14.680 number of the matter wave. 00:53:14.680 --> 00:53:20.950 If you accept de Broglie's interpretation, basically what 00:53:20.950 --> 00:53:24.340 we are getting is something really, really interesting. 00:53:24.340 --> 00:53:29.510 If we put together this dispersion relation 00:53:29.510 --> 00:53:35.730 and the de Broglie's interpretation of matter wave-- 00:53:35.730 --> 00:53:44.100 what I am going to do is to calculate the group velocity 00:53:44.100 --> 00:53:46.350 of this dispersion relation. 00:53:46.350 --> 00:53:48.600 So I can now calculate-- 00:53:48.600 --> 00:53:55.500 group velocity, V-g, will be equal to d omega, dk. 00:53:55.500 --> 00:54:00.090 And I know that omega is equal to h-bar k squared divided 00:54:00.090 --> 00:54:01.730 by 2m. 00:54:01.730 --> 00:54:09.420 This is essentially equal to h-bar k divided by m. 00:54:09.420 --> 00:54:12.350 Everybody is following? 00:54:12.350 --> 00:54:13.800 OK. 00:54:13.800 --> 00:54:16.050 And this is equal to what? 00:54:16.050 --> 00:54:21.710 This is equal to p divided by m, if I use de Broglie's matter 00:54:21.710 --> 00:54:23.670 wave. 00:54:23.670 --> 00:54:29.910 Therefore, you have p equal to m times ng. 00:54:29.910 --> 00:54:31.020 Wow! 00:54:31.020 --> 00:54:31.615 Look at this. 00:54:34.440 --> 00:54:36.400 What are we getting here? 00:54:36.400 --> 00:54:43.590 What we are getting here is that the group velocity of the wave 00:54:43.590 --> 00:54:48.340 equation of the waves is actually 00:54:48.340 --> 00:54:56.860 the classical velocity, p equal to m times v. Now, 00:54:56.860 --> 00:55:01.330 everything actually is becoming more and more clear. 00:55:01.330 --> 00:55:08.050 We know and we learned already, from 8.03, what is 00:55:08.050 --> 00:55:10.670 the meaning of group velocity. 00:55:10.670 --> 00:55:14.590 The meaning of the group velocity 00:55:14.590 --> 00:55:22.540 is the speed of the propagation of a wave package, right? 00:55:22.540 --> 00:55:30.010 Remember our discussion before about a AM radio? 00:55:30.010 --> 00:55:35.350 So what is actually the speed of propagation of a wave packet 00:55:35.350 --> 00:55:38.830 is the group velocity. 00:55:38.830 --> 00:55:42.640 So now we have solved the problem-- 00:55:42.640 --> 00:55:48.120 why electron can be a particle, at the same time, 00:55:48.120 --> 00:55:51.288 also like waves. 00:55:51.288 --> 00:55:58.190 It's essentially described by wave functions. 00:55:58.190 --> 00:56:03.820 The classical behavior we see on the electron 00:56:03.820 --> 00:56:06.730 is because it is, as you described, 00:56:06.730 --> 00:56:09.740 by these wave packages. 00:56:09.740 --> 00:56:12.280 It's pretty localized. 00:56:12.280 --> 00:56:18.710 And the motion of this wave package in a free space 00:56:18.710 --> 00:56:23.050 is actually the speed of the propagation-- 00:56:23.050 --> 00:56:25.550 is the group velocity. 00:56:25.550 --> 00:56:29.570 Therefore, there is no contradiction 00:56:29.570 --> 00:56:32.270 between the classical calculation 00:56:32.270 --> 00:56:36.030 and the wave interpretation of the electron. 00:56:36.030 --> 00:56:40.830 So that really surprised me very much. 00:56:40.830 --> 00:56:47.000 And you can see that, given the dispersion relation, also, 00:56:47.000 --> 00:56:53.640 this is a rather dynamical result. 00:56:53.640 --> 00:56:56.990 The real part of the wave function is actually blue. 00:56:56.990 --> 00:57:00.200 And the imaginary part is actually red. 00:57:00.200 --> 00:57:02.960 It's actually oscillating up and down. 00:57:02.960 --> 00:57:06.440 And the oscillation frequency, by now, 00:57:06.440 --> 00:57:11.410 you know is governed by that dispersion relation. 00:57:11.410 --> 00:57:16.900 OK, now actually, everything seems to make sense now-- 00:57:16.900 --> 00:57:20.570 really, really, very cool. 00:57:20.570 --> 00:57:22.940 So on the other hand, we also have 00:57:22.940 --> 00:57:25.850 to live with probability density. 00:57:25.850 --> 00:57:31.070 So you cannot tell the exact position of a particle any 00:57:31.070 --> 00:57:31.670 more. 00:57:31.670 --> 00:57:36.470 You cannot tell the exact outcome of an experiment 00:57:36.470 --> 00:57:37.510 anymore. 00:57:37.510 --> 00:57:42.560 And that is actually to do with this interpretation. 00:57:42.560 --> 00:57:47.690 And all of those phenomena, at a very, very small scale, 00:57:47.690 --> 00:57:50.900 is actually described by quantum mechanics, which we 00:57:50.900 --> 00:57:53.150 will learn some more in 8.04. 00:57:53.150 --> 00:57:55.430 And also, in the future, you will 00:57:55.430 --> 00:58:00.980 be governed by the quantum field theory, which 00:58:00.980 --> 00:58:04.360 is actually a father future. 00:58:04.360 --> 00:58:10.270 And what is actually the life living with quantum mechanics 00:58:10.270 --> 00:58:12.440 and quantum field theory? 00:58:12.440 --> 00:58:14.567 So this is a very simple-- 00:58:14.567 --> 00:58:15.361 [LAUGHTER] 00:58:15.361 --> 00:58:19.810 --Lagrangian of the standard model. 00:58:19.810 --> 00:58:26.080 And it describes everything except the gravity. 00:58:26.080 --> 00:58:26.860 OK? 00:58:26.860 --> 00:58:28.160 And it's really simple. 00:58:28.160 --> 00:58:30.850 It's called Standard Model. 00:58:30.850 --> 00:58:34.630 And look at this part. 00:58:34.630 --> 00:58:42.010 This is governing the Higgs decay to Z boson. 00:58:42.010 --> 00:58:47.060 And the experimental result-- we don't really know what 00:58:47.060 --> 00:58:49.120 is the mass of the Higgs. 00:58:49.120 --> 00:58:53.320 It's a missing observable before. 00:58:53.320 --> 00:58:57.730 And on the other hand, as a particle physicist 00:58:57.730 --> 00:59:02.020 or as a high energy nuclear physicists, 00:59:02.020 --> 00:59:07.630 I have no idea about what will happen in the next collision. 00:59:07.630 --> 00:59:08.210 Why is that? 00:59:08.210 --> 00:59:10.270 You know the reason now, right? 00:59:10.270 --> 00:59:14.290 Because we cannot predict the exact outcome 00:59:14.290 --> 00:59:15.580 of our experiment. 00:59:15.580 --> 00:59:19.120 It's all governed by wave functions. 00:59:19.120 --> 00:59:23.600 Therefore, what we are doing is the following. 00:59:23.600 --> 00:59:27.020 We are doing the brute force. 00:59:27.020 --> 00:59:30.130 So we collide like crazy-- 00:59:30.130 --> 00:59:33.340 collide, collide, collide, collide like crazy, 00:59:33.340 --> 00:59:36.975 until something interesting pops out. 00:59:36.975 --> 00:59:38.350 That's actually what we're really 00:59:38.350 --> 00:59:42.160 doing as a particle physicist. 00:59:42.160 --> 00:59:47.500 And this is your beautiful event from proton-proton collisions 00:59:47.500 --> 00:59:51.940 at the Large Hadron Collider-- is a Higgs to the boson event. 00:59:51.940 --> 00:59:58.680 And one of the Z bosons becomes the two red lines. 00:59:58.680 --> 01:00:01.000 It's actually the two muons. 01:00:01.000 --> 01:00:03.980 And the other decays to electrons, 01:00:03.980 --> 01:00:07.070 which are detected by the kilometer as the two 01:00:07.070 --> 01:00:10.230 blue things there. 01:00:10.230 --> 01:00:14.590 As a high-energy nuclear physicist, 01:00:14.590 --> 01:00:18.730 I am interested in the production 01:00:18.730 --> 01:00:23.590 of quark-gluon plasma from lead ion collisions. 01:00:23.590 --> 01:00:29.560 So I am now putting together two ions, have them collide. 01:00:29.560 --> 01:00:32.680 And I hope that, by chance, I can 01:00:32.680 --> 01:00:37.780 deposit a huge amount of energy in a very small volume. 01:00:37.780 --> 01:00:41.930 And then I would like to see this crazy matter, 01:00:41.930 --> 01:00:47.060 actually, gradually expand and become a lot of particles. 01:00:47.060 --> 01:00:50.020 And I study those particles to understand, 01:00:50.020 --> 01:00:53.470 what would be the nature of this material, which 01:00:53.470 --> 01:00:56.410 starts to exist in the very early part 01:00:56.410 --> 01:00:59.200 of the whole universe history? 01:00:59.200 --> 01:01:01.630 Just one microsecond after the Big Bang, 01:01:01.630 --> 01:01:05.710 we have the whole universe filled by this crazy material. 01:01:05.710 --> 01:01:08.850 And we are creating this in the experiment. 01:01:08.850 --> 01:01:13.810 And we will only be able to hope that, OK, by chance, I 01:01:13.810 --> 01:01:15.550 have the collision happen. 01:01:15.550 --> 01:01:19.840 By chance, I have a very high-density environment. 01:01:19.840 --> 01:01:24.190 Somehow, multiple quanta decide to scatter on each other. 01:01:24.190 --> 01:01:27.140 And they deposit the energy in a very small volume. 01:01:27.140 --> 01:01:30.910 And then we collect all those spectacular events 01:01:30.910 --> 01:01:34.780 to study the properties of all those little Big Bangs. 01:01:34.780 --> 01:01:40.720 So that is actually the consequence of this wave 01:01:40.720 --> 01:01:43.880 function interpretation. 01:01:43.880 --> 01:01:48.890 So now, coming back to the Standard Model, this really 01:01:48.890 --> 01:01:54.290 simple one, you can't see, that is a theory of almost 01:01:54.290 --> 01:01:58.630 everything, except the gravity. 01:01:58.630 --> 01:01:59.570 Really sad. 01:01:59.570 --> 01:02:02.820 So if you can actually put them all together, 01:02:02.820 --> 01:02:04.540 then you will also win the Nobel Prize. 01:02:04.540 --> 01:02:08.840 And giving you all those ideas, so that I 01:02:08.840 --> 01:02:12.260 can have a very good student winning the Nobel Prize. 01:02:12.260 --> 01:02:14.090 Of course you will. 01:02:14.090 --> 01:02:19.250 And now, I would like to discuss and use the remaining, maybe, 01:02:19.250 --> 01:02:24.800 10 minutes to discuss with you the gravity. 01:02:24.800 --> 01:02:31.560 So here is actually something related to gravity. 01:02:31.560 --> 01:02:38.180 So Einstein actually predicted that the distortion 01:02:38.180 --> 01:02:42.650 of the space-time generated by objects 01:02:42.650 --> 01:02:45.860 can travel through the space. 01:02:45.860 --> 01:02:48.020 I don't have the derivation here, 01:02:48.020 --> 01:02:52.350 because it would take another, maybe, two hours to do this. 01:02:52.350 --> 01:02:55.910 But I would like to ask you to trust me. 01:02:55.910 --> 01:03:01.850 This is actually a result coming from general relativity. 01:03:01.850 --> 01:03:07.040 And you can see that we can actually 01:03:07.040 --> 01:03:09.850 generate gravitational waves. 01:03:09.850 --> 01:03:13.550 And I can actually do the generation here, 01:03:13.550 --> 01:03:16.760 like this and rotating. 01:03:16.760 --> 01:03:19.320 I'm generating gravitational waves. 01:03:19.320 --> 01:03:21.320 And that student in the back is also generating. 01:03:21.320 --> 01:03:21.970 Yes, you are. 01:03:21.970 --> 01:03:23.330 Yeah, you are generating. 01:03:23.330 --> 01:03:24.290 Everybody's generating. 01:03:24.290 --> 01:03:25.880 Ah, you are also generating. 01:03:25.880 --> 01:03:27.460 Yeah, very good. 01:03:27.460 --> 01:03:31.820 But the problem is that the space-time distortion 01:03:31.820 --> 01:03:38.120 is really small for people who are not very massive, like me. 01:03:38.120 --> 01:03:40.020 So that's a problem. 01:03:40.020 --> 01:03:41.710 So I can generate. 01:03:41.710 --> 01:03:43.290 I'm doing the demo here. 01:03:43.290 --> 01:03:45.740 But it doesn't help. 01:03:45.740 --> 01:03:48.800 You cannot really detect them. 01:03:48.800 --> 01:03:53.420 And even Einstein himself thinks it's impossible to detect them, 01:03:53.420 --> 01:03:56.720 maybe, in our lifetime. 01:03:56.720 --> 01:04:00.260 And what would be the outcome of the calculation? 01:04:00.260 --> 01:04:02.330 The outcome of the calculation-- 01:04:02.330 --> 01:04:10.130 if you have gravitational wave passing toward you-- 01:04:10.130 --> 01:04:12.540 so what it does is the following. 01:04:12.540 --> 01:04:17.480 So basically, the space is distorted in a way such 01:04:17.480 --> 01:04:20.390 that it first expands in this direction 01:04:20.390 --> 01:04:23.510 and then expanding the other direction, perpendicular 01:04:23.510 --> 01:04:25.470 to the original distortion. 01:04:25.470 --> 01:04:29.000 And if you put a ray of particles, 01:04:29.000 --> 01:04:34.160 the circular array of particles, and look at what is going on, 01:04:34.160 --> 01:04:37.030 when the gravitational wave pass through it, 01:04:37.030 --> 01:04:40.580 it pass through the array in this direction, what 01:04:40.580 --> 01:04:45.040 you are going to get is effect like that. 01:04:45.040 --> 01:04:47.620 Of course, this is actually highly 01:04:47.620 --> 01:04:50.920 exaggerated in this set-up. 01:04:50.920 --> 01:04:55.990 You don't really see this kind of sizable distortion 01:04:55.990 --> 01:04:58.600 when Yen-Jie is dancing around. 01:05:01.170 --> 01:05:06.780 OK, so how about we actually visualize this thing. 01:05:06.780 --> 01:05:10.200 The problem is that we cannot really see the space 01:05:10.200 --> 01:05:11.690 distortion. 01:05:11.690 --> 01:05:15.740 But what we can, as you see, is the light 01:05:15.740 --> 01:05:19.500 which actually pass through those little distortions. 01:05:19.500 --> 01:05:23.810 So this is a stimulation from LIGO Collaboration. 01:05:23.810 --> 01:05:30.740 They are simulating the merging of the two massive black holes. 01:05:30.740 --> 01:05:32.480 And you can see that they are rotating 01:05:32.480 --> 01:05:34.490 with respect to each other. 01:05:34.490 --> 01:05:41.010 They are radiating energy out of this two-body system. 01:05:41.010 --> 01:05:42.710 Let's take a look at this again. 01:05:42.710 --> 01:05:49.400 So this is actually a simulation of the event observed by LIGO. 01:05:49.400 --> 01:05:58.640 So both black holes have a mass roughly 30 times of our sun. 01:05:58.640 --> 01:05:59.840 It's very massive. 01:05:59.840 --> 01:06:02.750 And they are rotating with respect to each other. 01:06:02.750 --> 01:06:05.430 And that generates space-time distortion. 01:06:05.430 --> 01:06:10.050 And you can see that the space-time distortion stops 01:06:10.050 --> 01:06:12.400 after they merge each other. 01:06:12.400 --> 01:06:16.430 And we were hoping that we can detect those. 01:06:16.430 --> 01:06:17.750 How crazy is that? 01:06:21.050 --> 01:06:23.140 So how do we detect them? 01:06:23.140 --> 01:06:26.870 Actually, you already have the knowledge 01:06:26.870 --> 01:06:30.750 to design the experiment to detect this kind of effect. 01:06:30.750 --> 01:06:35.960 So remember, the effect of the gravitational wave 01:06:35.960 --> 01:06:36.710 is like this. 01:06:36.710 --> 01:06:40.640 So you have distortion like this. 01:06:40.640 --> 01:06:43.180 What we actually-- 01:06:43.180 --> 01:06:47.300 MIT and Cal Tech and the many other collaborators 01:06:47.300 --> 01:06:50.634 designed the LIGO experiment. 01:06:50.634 --> 01:06:51.800 Are what is, actually, LIGO? 01:06:51.800 --> 01:06:57.350 It's a Laser Interferometer Gravitational wave Observatory. 01:06:57.350 --> 01:07:00.320 It is actually always good to have a very good name 01:07:00.320 --> 01:07:02.880 of your experiment. 01:07:02.880 --> 01:07:04.880 So this is actually LIGO. 01:07:04.880 --> 01:07:07.410 So what, actually, it does is the following. 01:07:07.410 --> 01:07:10.370 So basically, it emits a laser. 01:07:10.370 --> 01:07:13.260 And you split the laser into two pieces. 01:07:13.260 --> 01:07:18.170 And there were mirrors in the very far end, reflect 01:07:18.170 --> 01:07:19.490 those lasers. 01:07:19.490 --> 01:07:21.080 And they come together. 01:07:21.080 --> 01:07:24.560 And there is a photo-detector, which 01:07:24.560 --> 01:07:29.100 detects the interference pattern of these two optical path 01:07:29.100 --> 01:07:29.600 lengths. 01:07:29.600 --> 01:07:30.100 Wow! 01:07:30.100 --> 01:07:31.780 Sounds familiar to you, right? 01:07:31.780 --> 01:07:34.610 Hey, you already know how to explain this to your friends 01:07:34.610 --> 01:07:35.480 already. 01:07:35.480 --> 01:07:36.470 Really cool. 01:07:36.470 --> 01:07:42.320 And in order to have redundant management-- 01:07:42.320 --> 01:07:46.310 for example, if you only have a single experiment, 01:07:46.310 --> 01:07:48.350 maybe one graduate student is like, oh, 01:07:48.350 --> 01:07:50.810 doing dancing next to a detector. 01:07:50.810 --> 01:07:53.030 Then you see some fake signal. 01:07:53.030 --> 01:07:55.610 And that's not going to be helpful. 01:07:55.610 --> 01:07:58.400 So what it does is that-- basically, we 01:07:58.400 --> 01:07:59.760 have two experiments. 01:07:59.760 --> 01:08:02.180 One is actually in Hanford. 01:08:02.180 --> 01:08:04.520 The other one is actually in Livingston. 01:08:04.520 --> 01:08:08.990 And they are actually 3,000 kilometers away 01:08:08.990 --> 01:08:10.190 from each other. 01:08:10.190 --> 01:08:15.950 So that there should not be any correlation between the signal 01:08:15.950 --> 01:08:19.430 coming from a earthquake or dancing 01:08:19.430 --> 01:08:22.939 of the graduate students or whatever. 01:08:22.939 --> 01:08:29.330 So they can you use that to suppress any coincidence which 01:08:29.330 --> 01:08:34.080 is actually not related to gravitational waves. 01:08:34.080 --> 01:08:37.020 So what does this do? 01:08:37.020 --> 01:08:39.500 So now, we have, oh, the knowledge 01:08:39.500 --> 01:08:41.270 to actually explain this phenomena. 01:08:41.270 --> 01:08:43.210 So what this does is the following. 01:08:43.210 --> 01:08:45.050 So you meet the laser. 01:08:45.050 --> 01:08:49.460 And when the gravitational waves come in, 01:08:49.460 --> 01:08:53.060 then it does this space-time distortion. 01:08:53.060 --> 01:08:57.680 And then the interference pattern 01:08:57.680 --> 01:09:03.859 of the waves going through different optical path lengths 01:09:03.859 --> 01:09:07.470 is going to change. 01:09:07.470 --> 01:09:09.760 So you can see that, originally, the experiment 01:09:09.760 --> 01:09:13.130 is designed so that you have complete cancellation. 01:09:13.130 --> 01:09:19.220 But when the gravitational waves is hitting the side, 01:09:19.220 --> 01:09:21.319 you will be able to see that. 01:09:21.319 --> 01:09:27.130 Really, you have constructive interference at some point, 01:09:27.130 --> 01:09:31.220 because of the movement of the mirrors. 01:09:31.220 --> 01:09:35.090 And those mirrors are really, really far away 01:09:35.090 --> 01:09:36.270 from the sources. 01:09:36.270 --> 01:09:40.010 Each of them is, like, four kilometers away 01:09:40.010 --> 01:09:42.050 from the mirror. 01:09:42.050 --> 01:09:46.220 And due to the incredible precision 01:09:46.220 --> 01:09:48.979 which were achieved by this experiment, 01:09:48.979 --> 01:09:55.680 we will be able to detect this signal of gravitational waves. 01:09:55.680 --> 01:09:57.650 So you can see, again, from here-- 01:09:57.650 --> 01:10:03.530 so basically, when the gravitational wave comes in, 01:10:03.530 --> 01:10:07.810 first you split the light source into two pieces, 01:10:07.810 --> 01:10:12.200 have them hit the mirror, which is actually four kilometers far 01:10:12.200 --> 01:10:13.280 away from each other. 01:10:13.280 --> 01:10:15.000 And they come back. 01:10:15.000 --> 01:10:20.540 And initially, the experiment is designed so that, very 01:10:20.540 --> 01:10:24.490 precisely, there will be no amplitude 01:10:24.490 --> 01:10:27.350 detected by the photo-detector. 01:10:27.350 --> 01:10:30.810 And when the gravitational waves come in, 01:10:30.810 --> 01:10:35.390 you actually really change the length 01:10:35.390 --> 01:10:39.020 between a splitter and the mirror. 01:10:39.020 --> 01:10:46.290 Therefore, you see light, constructive interference even, 01:10:46.290 --> 01:10:49.440 from the photo-detector. 01:10:49.440 --> 01:10:51.170 So that is really cool. 01:10:51.170 --> 01:10:55.820 And this is actually the experimental result. 01:10:55.820 --> 01:10:58.600 Look at this. 01:10:58.600 --> 01:11:02.360 You actually can see that light actually 01:11:02.360 --> 01:11:06.020 achieve the sensitivity. 01:11:06.020 --> 01:11:14.690 The gravitational wave was first observed on September 14, 2015. 01:11:14.690 --> 01:11:20.530 And the LIGO is actually announcing that February 11-- 01:11:20.530 --> 01:11:23.590 earlier this year. 01:11:23.590 --> 01:11:27.070 And what we actually see from here is that this is actually-- 01:11:27.070 --> 01:11:28.720 as I mentioned to you-- 01:11:28.720 --> 01:11:31.900 there are two measurements, two sides. 01:11:31.900 --> 01:11:36.760 The left hand side is actually the measurement from Hanford. 01:11:36.760 --> 01:11:40.240 And the other one is actually the measurement 01:11:40.240 --> 01:11:42.370 from Livingston. 01:11:42.370 --> 01:11:44.620 So they are two different curves. 01:11:44.620 --> 01:11:51.820 And they all have almost exactly the same pattern. 01:11:51.820 --> 01:11:53.710 Of course, there's time has actually shifted, 01:11:53.710 --> 01:11:57.460 because they are in different places on the earth. 01:11:57.460 --> 01:11:59.920 They are 3,000 kilometers apart. 01:11:59.920 --> 01:12:02.920 So therefore, there will be a shift in time. 01:12:02.920 --> 01:12:05.960 And this is actually a time-shifted result. 01:12:05.960 --> 01:12:09.280 And you can see, also, the calculation below, 01:12:09.280 --> 01:12:11.390 which is actually what you should 01:12:11.390 --> 01:12:20.000 expect if you have the merger of the two massive black holes. 01:12:20.000 --> 01:12:23.680 So you can see that they are actually rotating with respect 01:12:23.680 --> 01:12:26.230 to each other. 01:12:26.230 --> 01:12:31.300 One of them is actually 29 times larger 01:12:31.300 --> 01:12:33.450 than the mass of the sun. 01:12:33.450 --> 01:12:37.210 And the other one is 36 times larger 01:12:37.210 --> 01:12:38.350 than the mass of our sun. 01:12:38.350 --> 01:12:41.110 It's not precision. 01:12:41.110 --> 01:12:44.740 And they generate, theoretically, 01:12:44.740 --> 01:12:47.270 this kind of pattern. 01:12:47.270 --> 01:12:50.440 And this is actually really detected 01:12:50.440 --> 01:12:56.680 by both LIGO experiments, which lay at 3,000 kilometers apart 01:12:56.680 --> 01:12:58.790 from each other. 01:12:58.790 --> 01:13:02.850 So I think this is really a historical moment-- 01:13:02.850 --> 01:13:06.960 that we actually were very lucky to live in this moment. 01:13:06.960 --> 01:13:08.800 What does that mean? 01:13:08.800 --> 01:13:16.300 That means we have a new way to really hear 01:13:16.300 --> 01:13:20.660 about what the universe is actually trying to tell us. 01:13:20.660 --> 01:13:24.470 We have a new way to detect phenomena, 01:13:24.470 --> 01:13:28.310 which is actually really happening very, very far away 01:13:28.310 --> 01:13:29.360 from the Earth. 01:13:29.360 --> 01:13:31.700 How far is, actually, this event? 01:13:31.700 --> 01:13:34.655 This event, according to calculation, 01:13:34.655 --> 01:13:42.860 is actually something like 1.3 billion light years 01:13:42.860 --> 01:13:44.890 away from the Earth. 01:13:44.890 --> 01:13:46.670 And we can detect that. 01:13:46.670 --> 01:13:51.061 And we even know the mass of the two black holes. 01:13:51.061 --> 01:13:51.560 Wow! 01:13:51.560 --> 01:13:52.730 What does that mean? 01:13:52.730 --> 01:13:56.870 This is really crazy to me and really exciting, 01:13:56.870 --> 01:13:58.760 because we are opening up-- 01:13:58.760 --> 01:13:59.930 OK, I have two ears. 01:13:59.930 --> 01:14:04.470 And it's opening up another ear in my brain. 01:14:04.470 --> 01:14:09.980 And that is actually the way to hear the gravitational wave 01:14:09.980 --> 01:14:14.930 with the experiment we've performed on Earth. 01:14:14.930 --> 01:14:19.900 So I hope, until now, I have convinced you 01:14:19.900 --> 01:14:25.970 that this is really not the end of vibration of waves, which 01:14:25.970 --> 01:14:29.000 is actually the end of 8.03. 01:14:29.000 --> 01:14:32.550 Instead, this is actually just the beginning. 01:14:32.550 --> 01:14:36.170 You have a lot more to explore when 01:14:36.170 --> 01:14:39.920 you take general or special relativity course. 01:14:39.920 --> 01:14:43.910 You have a lot, really, more to explore when 01:14:43.910 --> 01:14:46.700 you take quantum mechanics. 01:14:46.700 --> 01:14:51.800 And I hope you really enjoy the content of this course. 01:14:51.800 --> 01:14:55.010 Personally, I really enjoy that very much. 01:14:55.010 --> 01:14:56.360 I love this course. 01:14:56.360 --> 01:14:59.090 And I hope you also love it and understand something 01:14:59.090 --> 01:15:00.460 from my lecture. 01:15:00.460 --> 01:15:02.750 And thank you very much. 01:15:02.750 --> 01:15:04.760 And the next time, we are going to have 01:15:04.760 --> 01:15:09.190 a review of all concepts we have learned from 8.03 next Tuesday. 01:15:09.190 --> 01:15:09.790 Thank you. 01:15:09.790 --> 01:15:11.290 [APPLAUSE] 01:15:13.090 --> 01:15:15.240 Thank you very much.