WEBVTT 00:00:00.090 --> 00:00:01.670 The following content is provided 00:00:01.670 --> 00:00:03.820 under a Creative Commons license. 00:00:03.820 --> 00:00:06.550 Your support will help MIT OpenCourseWare continue 00:00:06.550 --> 00:00:10.160 to offer high quality educational resources for free. 00:00:10.160 --> 00:00:12.700 To make a donation or to view additional materials 00:00:12.700 --> 00:00:16.620 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:16.620 --> 00:00:17.280 at ocw.mit.edu. 00:00:24.350 --> 00:00:29.290 PROFESSOR: So I want to begin by reviewing a little bit what 00:00:29.290 --> 00:00:31.920 I said last time in terms of this overview lecture. 00:00:31.920 --> 00:00:35.580 And then we'll finish the overview lecture. 00:00:35.580 --> 00:00:38.240 So summary of last lecture is actually on five slides. 00:00:38.240 --> 00:00:41.359 It's not all on this one slide. 00:00:41.359 --> 00:00:43.900 We started by talking about the standard Big Bang, by which I 00:00:43.900 --> 00:00:47.590 mean the Big Bang without thinking about inflation. 00:00:47.590 --> 00:00:49.340 And I pointed out that it really describes 00:00:49.340 --> 00:00:51.730 only the aftermath of a bang. 00:00:51.730 --> 00:00:54.890 It begins with the description of the universe 00:00:54.890 --> 00:00:59.870 as a hot, dense soup of particles which more or less 00:00:59.870 --> 00:01:02.500 uniformly fills the entire available space, 00:01:02.500 --> 00:01:07.150 and the entire system is already expanding. 00:01:07.150 --> 00:01:13.140 Cosmic inflation is a prequel to the conventional Big Bang 00:01:13.140 --> 00:01:14.770 story. 00:01:14.770 --> 00:01:18.250 It describes how repulsive gravity, which 00:01:18.250 --> 00:01:19.870 in the context of general relativity, 00:01:19.870 --> 00:01:24.136 can happen as a consequence of negative pressure. 00:01:24.136 --> 00:01:25.510 This repulsive gravity could have 00:01:25.510 --> 00:01:28.310 driven a tiny patch of the early universe 00:01:28.310 --> 00:01:32.800 into a gigantic burst of exponential expansion. 00:01:32.800 --> 00:01:34.750 And our visible universe would then 00:01:34.750 --> 00:01:38.930 be the aftermath of that event. 00:01:38.930 --> 00:01:42.530 As this happened, the total energy of this patch 00:01:42.530 --> 00:01:45.810 would be very small and could even be identically 0. 00:01:45.810 --> 00:01:49.870 And the way that's possible is caused by the fact 00:01:49.870 --> 00:01:53.380 that the gravitational field that fills the space 00:01:53.380 --> 00:01:55.580 has a negative contribution to the energy. 00:01:55.580 --> 00:01:57.710 And as far as we can tell in our real universe, 00:01:57.710 --> 00:01:59.209 there are about equal to each other. 00:01:59.209 --> 00:02:02.250 They could cancel each other exactly as far as we can tell. 00:02:02.250 --> 00:02:03.790 So the total energy could in fact 00:02:03.790 --> 00:02:06.000 be exactly zero, which is what allows 00:02:06.000 --> 00:02:07.950 one to build a huge universe starting 00:02:07.950 --> 00:02:10.130 from either nothing or almost nothing. 00:02:13.330 --> 00:02:14.040 Inflation. 00:02:14.040 --> 00:02:16.660 The next item is evidence for inflation. 00:02:16.660 --> 00:02:18.700 Why do we think there's at least a good chance 00:02:18.700 --> 00:02:20.700 that our universe underwent inflation? 00:02:20.700 --> 00:02:23.290 And I pointed out three items. 00:02:23.290 --> 00:02:26.270 The first was that inflation could explain the large scale 00:02:26.270 --> 00:02:29.180 uniformity that we observe in the universe 00:02:29.180 --> 00:02:31.760 and that large scale uniformity is 00:02:31.760 --> 00:02:35.230 seen most clearly in the cosmic microwave background 00:02:35.230 --> 00:02:38.700 radiation, which is observed to be uniform to one 00:02:38.700 --> 00:02:42.280 part in $100,000, that is same intensity all across the sky 00:02:42.280 --> 00:02:44.490 no matter what direction you look, once you account 00:02:44.490 --> 00:02:48.085 for the Earth's motion, to an accuracy of one part 00:02:48.085 --> 00:02:50.300 in 100,000. 00:02:50.300 --> 00:02:53.920 Secondly, inflation can explain a rather remarkable fact 00:02:53.920 --> 00:02:56.860 about this quantity omega, where omega 00:02:56.860 --> 00:02:59.730 is defined as the actual mass density of the universe 00:02:59.730 --> 00:03:03.500 rho divided by rho critical, the critical mass density which 00:03:03.500 --> 00:03:08.330 is the density that would make the universe precisely flat. 00:03:08.330 --> 00:03:11.520 The statement that that ratio is equal to 1 we know 00:03:11.520 --> 00:03:14.880 is accurate to about 15 decimal places at one second 00:03:14.880 --> 00:03:16.150 after the Big Bang. 00:03:16.150 --> 00:03:18.960 And prior to inflation, we didn't really 00:03:18.960 --> 00:03:21.460 have any explanation for that at all. 00:03:21.460 --> 00:03:23.770 But inflation drives omega to one 00:03:23.770 --> 00:03:26.670 and gives us an explanation for why, therefore, 00:03:26.670 --> 00:03:29.232 started out so extraordinarily close to 1. 00:03:29.232 --> 00:03:30.690 And in fact, it makes a prediction. 00:03:30.690 --> 00:03:32.580 We'd expect that if inflation is right, 00:03:32.580 --> 00:03:35.160 omega should still be one today. 00:03:35.160 --> 00:03:39.900 And we now have measured omega to be 1.0010 plus or minus 00:03:39.900 --> 00:03:43.730 0.0065, which I think is fabulous. 00:03:43.730 --> 00:03:48.110 Finally, inflation gives an explanation 00:03:48.110 --> 00:03:52.440 for the inhomogeneities that we see in the universe. 00:03:52.440 --> 00:03:54.550 It explains them as quantum fluctuations which 00:03:54.550 --> 00:03:57.860 happened during the inflationary process and, most importantly 00:03:57.860 --> 00:04:01.690 really, as inflation was ending, the quantum fluctuations 00:04:01.690 --> 00:04:03.810 cause inflation to go on for a little bit 00:04:03.810 --> 00:04:06.110 longer in some regions than others. 00:04:06.110 --> 00:04:09.890 And that sets up these inhomogeneities. 00:04:09.890 --> 00:04:13.150 Today, we can see these inhomogeneities 00:04:13.150 --> 00:04:14.996 most accurately. 00:04:14.996 --> 00:04:17.579 inhomogeneities, of course, are huge at the level of galaxies, 00:04:17.579 --> 00:04:18.470 so they're obvious. 00:04:18.470 --> 00:04:21.339 But it's hard to connect them to the early universe. 00:04:21.339 --> 00:04:24.620 So we can make our most precise comparison between what 00:04:24.620 --> 00:04:27.870 we observe and theories of the early universe 00:04:27.870 --> 00:04:30.350 by making careful observations of the cosmic background 00:04:30.350 --> 00:04:33.890 radiation itself, which has these ripples in the intensity, 00:04:33.890 --> 00:04:36.450 It is not quite uniform. 00:04:36.450 --> 00:04:39.830 There really are ripples at the level of one part in 100,000, 00:04:39.830 --> 00:04:42.030 which can now be observed. 00:04:42.030 --> 00:04:44.110 And inflation makes a clear prediction 00:04:44.110 --> 00:04:46.310 for the spectrum of those ripples, 00:04:46.310 --> 00:04:49.590 how the intensity should vary with wavelength. 00:04:49.590 --> 00:04:53.540 And I showed you this graph last time from the Planck satellite. 00:04:53.540 --> 00:04:56.300 The agreement between the prediction and the theory 00:04:56.300 --> 00:04:59.080 is really marvelous. 00:04:59.080 --> 00:05:03.860 So we'll be coming back to that near the end of the course. 00:05:03.860 --> 00:05:06.960 Finally, in the last lecture, I began 00:05:06.960 --> 00:05:11.970 to talk about inflation and the possible implications 00:05:11.970 --> 00:05:17.650 for a multiverse, the idea that our universe might be embedded 00:05:17.650 --> 00:05:19.470 in a much larger thing consisting 00:05:19.470 --> 00:05:23.920 of many universes, which we call a multiverse. 00:05:23.920 --> 00:05:26.810 And the key point is that most inflation models 00:05:26.810 --> 00:05:28.440 tend to become eternal. 00:05:28.440 --> 00:05:32.000 And that is once inflation starts, it never stops. 00:05:32.000 --> 00:05:33.650 And the reason for that, basically, 00:05:33.650 --> 00:05:37.500 is that the metastable material, this repulsive gravity 00:05:37.500 --> 00:05:42.780 material that's causing the inflation, decays, 00:05:42.780 --> 00:05:45.480 but it also exponentially expands. 00:05:45.480 --> 00:05:48.970 And for typical models, the exponential expansion 00:05:48.970 --> 00:05:51.060 completely overpowers the decay. 00:05:51.060 --> 00:05:54.590 So even though it's an unstable material that decays, 00:05:54.590 --> 00:05:57.290 the total volume of it actually increases exponentially 00:05:57.290 --> 00:06:01.030 with time rather than decreases. 00:06:01.030 --> 00:06:03.540 Decays happen however, and wherever decay happen, 00:06:03.540 --> 00:06:06.100 it forms what we call a pocket universe. 00:06:06.100 --> 00:06:10.100 We would be living in one of those pocket universes. 00:06:10.100 --> 00:06:12.690 And the number of pocket universes 00:06:12.690 --> 00:06:16.040 grows exponentially with time as the whole system grows and goes 00:06:16.040 --> 00:06:18.240 on, as far as we can tell, forever. 00:06:18.240 --> 00:06:21.060 And that is the picture of the multiverse 00:06:21.060 --> 00:06:23.550 that inflation tends to lead to. 00:06:27.830 --> 00:06:29.630 Finally, this is my last summary slide 00:06:29.630 --> 00:06:31.880 and then we'll start new material. 00:06:31.880 --> 00:06:33.620 At the very end of lecture, I talked 00:06:33.620 --> 00:06:38.460 about a problem, which is very important in our present day 00:06:38.460 --> 00:06:41.130 thinking about physics and cosmology, 00:06:41.130 --> 00:06:45.650 and that is the nightmare that this discovery of dark energy 00:06:45.650 --> 00:06:46.250 leads to. 00:06:49.300 --> 00:06:52.050 What was discovered at about 1998 00:06:52.050 --> 00:06:53.820 is that the expansion of the universe 00:06:53.820 --> 00:06:56.450 is not slowing down under the influence of gravity 00:06:56.450 --> 00:06:59.090 as one might expect, but Instead, it's 00:06:59.090 --> 00:07:00.380 actually accelerating. 00:07:00.380 --> 00:07:03.520 The universe is expanding faster and faster. 00:07:03.520 --> 00:07:05.430 And that indicates that space today 00:07:05.430 --> 00:07:09.190 is filled with some repulsive gravity material, which 00:07:09.190 --> 00:07:11.380 we call the dark energy. 00:07:11.380 --> 00:07:14.170 And the simplest interpretation of the dark energy 00:07:14.170 --> 00:07:18.570 is that it simply vacuum energy, the energy of empty space. 00:07:18.570 --> 00:07:20.600 Space does have an energy density that 00:07:20.600 --> 00:07:22.630 have exactly the properties that we observe, 00:07:22.630 --> 00:07:24.495 so it seems natural to draw that connection. 00:07:27.070 --> 00:07:29.300 Vacuum energy, at first, might seem surprising. 00:07:29.300 --> 00:07:33.030 If a vacuum's empty, why should it have any mass density? 00:07:33.030 --> 00:07:36.584 But in a quantum field theory, it's really not surprising 00:07:36.584 --> 00:07:38.000 because in a quantum field theory, 00:07:38.000 --> 00:07:39.974 the vacuum is really not empty. 00:07:39.974 --> 00:07:41.390 In a quantum field theory, there's 00:07:41.390 --> 00:07:44.330 no such thing as actual emptiness. 00:07:44.330 --> 00:07:48.440 Instead, in the vacuum, one has constant quantum fluctuations 00:07:48.440 --> 00:07:49.580 of fields. 00:07:49.580 --> 00:07:54.160 And in our current theory of particle physics, 00:07:54.160 --> 00:07:56.040 the standard model of particle physics, 00:07:56.040 --> 00:07:58.660 there's even one particular field called the Higgs field, 00:07:58.660 --> 00:08:01.510 which has a non-zero mean value in the vacuum 00:08:01.510 --> 00:08:04.160 besides fluctuations. 00:08:04.160 --> 00:08:06.010 So the vacuum is a very complicated state. 00:08:06.010 --> 00:08:07.720 What makes it the vacuum is simply 00:08:07.720 --> 00:08:10.620 that it's alleged to be the state of lowest possible energy 00:08:10.620 --> 00:08:12.474 density, but that doesn't have to be zero 00:08:12.474 --> 00:08:13.890 and doesn't even look like there's 00:08:13.890 --> 00:08:16.210 any reason why it should be zero. 00:08:16.210 --> 00:08:19.550 So there's no problem buying the fact 00:08:19.550 --> 00:08:23.040 that maybe the vacuum does have a non-zero energy density. 00:08:23.040 --> 00:08:25.290 The problem comes about though when 00:08:25.290 --> 00:08:28.230 we try to understand the magnitude of this vacuum 00:08:28.230 --> 00:08:29.250 energy. 00:08:29.250 --> 00:08:31.250 If it was going to have a vacuum energy density, 00:08:31.250 --> 00:08:34.190 we'd expect it to be vastly larger than what 00:08:34.190 --> 00:08:37.090 is observed in the form of the expansion 00:08:37.090 --> 00:08:39.929 acceleration of the universe. 00:08:39.929 --> 00:08:42.610 So a typical order of magnitude in the particle physics 00:08:42.610 --> 00:08:45.400 model for the vacuum energy is, in fact, 00:08:45.400 --> 00:08:47.980 about a full 120 orders of magnitude 00:08:47.980 --> 00:08:51.260 larger than the number that's implied 00:08:51.260 --> 00:08:53.590 by the acceleration of the universe. 00:08:53.590 --> 00:08:56.990 So that is a big problem. 00:08:56.990 --> 00:08:59.940 I began to talk about a possible resolution to that problem. 00:08:59.940 --> 00:09:01.330 It's only a possible resolution. 00:09:01.330 --> 00:09:03.765 Nobody has really settled on this. 00:09:03.765 --> 00:09:05.140 But there's a possible resolution 00:09:05.140 --> 00:09:07.080 which comes out of String theory, 00:09:07.080 --> 00:09:09.685 and in particular from this idea, which 00:09:09.685 --> 00:09:12.510 is called the landscape of String theory. 00:09:12.510 --> 00:09:15.970 Most String theorists believe that String theory has 00:09:15.970 --> 00:09:19.140 no unique vacuum, but instead, there's 00:09:19.140 --> 00:09:23.650 a colossal number, perhaps something like 10 to the 500, 00:09:23.650 --> 00:09:26.990 different metastable states, which 00:09:26.990 --> 00:09:30.230 even though they are metastable, are incredibly long-lived, 00:09:30.230 --> 00:09:34.120 long-lived compared to the age of the universe as we know it. 00:09:34.120 --> 00:09:37.790 So any one of these 10 to the 500 different states 00:09:37.790 --> 00:09:41.390 could serve as effectively the vacuum for one 00:09:41.390 --> 00:09:42.774 of these pocket universes. 00:09:42.774 --> 00:09:44.190 And the different pocket universes 00:09:44.190 --> 00:09:51.310 would presumably fill the whole set of possible vacua 00:09:51.310 --> 00:09:55.880 in the landscape, giving reality to all these possibilities 00:09:55.880 --> 00:09:58.080 that come about in String theory. 00:09:58.080 --> 00:10:03.050 And in particular, each different type of vacuum 00:10:03.050 --> 00:10:05.910 would have its own vacuum energy density. 00:10:05.910 --> 00:10:08.050 And because there are both positive and negative 00:10:08.050 --> 00:10:10.330 contributions-- I think I didn't read that out loud-- 00:10:10.330 --> 00:10:12.579 but there are both positive and negative contributions 00:10:12.579 --> 00:10:14.700 that arise in quantum field theories. 00:10:14.700 --> 00:10:16.830 So the vacuum energy of a typical state 00:10:16.830 --> 00:10:18.750 could be either positive or negative. 00:10:18.750 --> 00:10:20.910 And what we would expect of these 10 00:10:20.910 --> 00:10:23.380 to the 500 different vacua is that they 00:10:23.380 --> 00:10:26.010 would have a range of energy densities 00:10:26.010 --> 00:10:29.610 that would range from something like minus 10 to the 120 00:10:29.610 --> 00:10:34.264 to plus 10 to the 120 times the observed value. 00:10:34.264 --> 00:10:35.930 So the observed value would be in there, 00:10:35.930 --> 00:10:38.700 but would be an incredibly small fraction of the universes. 00:10:38.700 --> 00:10:39.200 Yes? 00:10:39.200 --> 00:10:42.518 AUDIENCE: Does this mean that so many pocket universes could 00:10:42.518 --> 00:10:46.073 be closed and opened as well in terms of their geometry? 00:10:46.073 --> 00:10:47.769 Or-- 00:10:47.769 --> 00:10:49.310 PROFESSOR: They're actually predicted 00:10:49.310 --> 00:10:52.130 to be open due to complications about how they form, 00:10:52.130 --> 00:10:54.350 which I'm not going to go into. 00:10:54.350 --> 00:10:57.510 But they should all be open, but very close to flat for the ones 00:10:57.510 --> 00:10:59.200 that under a lot of inflation. 00:10:59.200 --> 00:11:00.930 So they'd be indistinguishable from flat, 00:11:00.930 --> 00:11:03.710 but technically, they'd be open. 00:11:03.710 --> 00:11:04.533 Yes? 00:11:04.533 --> 00:11:08.397 AUDIENCE: Is the minus 10 to the 120 plus 10 to the 120 just 00:11:08.397 --> 00:11:10.812 chosen because we're off 520 orders of magnitude, 00:11:10.812 --> 00:11:13.612 or is it predicted somewhere else? 00:11:13.612 --> 00:11:15.195 PROFESSOR: Well, when we say we're off 00:11:15.195 --> 00:11:17.940 by 120 orders of magnitude, the more precise statement 00:11:17.940 --> 00:11:21.740 is that the estimate of what a typical range of the energy 00:11:21.740 --> 00:11:26.150 should be is 10 to 120 times the observed value. 00:11:26.150 --> 00:11:29.320 So this is basically just a restatement of that. 00:11:29.320 --> 00:11:31.280 And you might wonder why I didn't 00:11:31.280 --> 00:11:35.150 put 5 times 10 to the 120, but in fact, the 120 00:11:35.150 --> 00:11:37.230 itself is only accurate to within a few orders 00:11:37.230 --> 00:11:39.220 of magnitude, so 5 times that wouldn't 00:11:39.220 --> 00:11:40.850 have made any difference in the way one 00:11:40.850 --> 00:11:42.320 actually interprets those numbers. 00:11:46.490 --> 00:11:49.280 10 to the 123 is probably slightly more accurate number 00:11:49.280 --> 00:11:50.390 actually. 00:11:50.390 --> 00:11:52.381 But this is good enough for our purposes. 00:11:52.381 --> 00:11:52.880 Yes? 00:11:52.880 --> 00:11:53.852 AUDIENCE: Just a general question 00:11:53.852 --> 00:11:55.310 about inflation properties. 00:11:55.310 --> 00:11:58.226 We think of attractive gravity as driving 00:11:58.226 --> 00:12:01.110 the motion of objects through space. 00:12:01.110 --> 00:12:03.372 So why do we think of repulsive gravity 00:12:03.372 --> 00:12:07.150 like to drive the expanse of space itself? 00:12:07.150 --> 00:12:09.150 PROFESSOR: Well, for one thing, it does actually 00:12:09.150 --> 00:12:10.200 behave differently. 00:12:10.200 --> 00:12:12.420 Repulsive gravity, repulsive gravity 00:12:12.420 --> 00:12:14.000 that appears in general relativity, 00:12:14.000 --> 00:12:17.170 is not just ordinary gravity with the opposite sign. 00:12:17.170 --> 00:12:18.620 Ordinary gravity has the property 00:12:18.620 --> 00:12:21.950 that if I have two objects to attract each other with a force 00:12:21.950 --> 00:12:25.390 proportional to the masses of those objects. 00:12:25.390 --> 00:12:26.850 This repulsive gravity is actually 00:12:26.850 --> 00:12:31.140 an effect caused by the negative pressure in the space between. 00:12:31.140 --> 00:12:33.020 So if I have two objects, they will 00:12:33.020 --> 00:12:35.990 start to accelerate apart by the amount that's 00:12:35.990 --> 00:12:38.150 totally independent of the masses. 00:12:38.150 --> 00:12:40.680 This is not really the masses that's causing it. 00:12:40.680 --> 00:12:43.450 So the whole force was completely different, 00:12:43.450 --> 00:12:47.010 so we can't really just compare them. 00:12:47.010 --> 00:12:50.280 In either case, when everything is moving apart, 00:12:50.280 --> 00:12:53.080 it's really a matter of viewpoint 00:12:53.080 --> 00:12:55.069 when you think of the whole space as expanding 00:12:55.069 --> 00:12:56.610 or whether you think of the particles 00:12:56.610 --> 00:12:58.620 as moving through space. 00:12:58.620 --> 00:13:01.830 In relativity, there's no way to put a needle on space, 00:13:01.830 --> 00:13:05.170 put a pen in it and say this is stationary. 00:13:05.170 --> 00:13:08.520 So we really can't say that the space is moving or not. 00:13:08.520 --> 00:13:11.660 In cosmology, we usually find that the simpler picture 00:13:11.660 --> 00:13:13.850 and the one that we will generally use 00:13:13.850 --> 00:13:15.922 is that space expands with the matter. 00:13:15.922 --> 00:13:17.380 It gives a much simpler description 00:13:17.380 --> 00:13:18.255 of how things behave. 00:13:21.480 --> 00:13:22.470 Good question. 00:13:22.470 --> 00:13:23.660 Yes? 00:13:23.660 --> 00:13:26.380 AUDIENCE: I have a question going back a few slides. 00:13:26.380 --> 00:13:28.440 PROFESSOR: Sure, you want me to go back. 00:13:28.440 --> 00:13:31.410 AUDIENCE: How the energy of the early universe 00:13:31.410 --> 00:13:34.400 seemed to be close to zero. 00:13:34.400 --> 00:13:36.750 Are there theoretical models that would explain 00:13:36.750 --> 00:13:39.645 or that would say it should be exactly 0? 00:13:39.645 --> 00:13:40.770 PROFESSOR: Yeah, there are. 00:13:40.770 --> 00:13:42.050 I didn't mention it. 00:13:42.050 --> 00:13:45.940 But if the universe is closed, which is a possibility. 00:13:45.940 --> 00:13:48.602 Even if it's very nearly flat, it could still be closed. 00:13:48.602 --> 00:13:50.810 If it were closed, it would have exactly zero energy. 00:13:55.220 --> 00:13:56.120 Yes? 00:13:56.120 --> 00:13:58.334 AUDIENCE: So the cosmic background, 00:13:58.334 --> 00:14:00.636 microwave background, picks ups that it's 00:14:00.636 --> 00:14:03.480 pretty similar in all directions once correct for it. 00:14:03.480 --> 00:14:06.210 And this leads to the thought that the cosmological principle 00:14:06.210 --> 00:14:09.270 all over the universe is pretty identical. 00:14:09.270 --> 00:14:11.640 Is it possible that we are actually 00:14:11.640 --> 00:14:15.316 located in just a smaller like circular pathway 00:14:15.316 --> 00:14:19.244 and it may be different than [? allowed. ?] 00:14:19.244 --> 00:14:20.660 And there's many of these patches, 00:14:20.660 --> 00:14:24.760 so we-- there's actually like a speckled form. 00:14:24.760 --> 00:14:25.580 PROFESSOR: OK. 00:14:25.580 --> 00:14:27.038 So if you didn't hear the question, 00:14:27.038 --> 00:14:29.820 I was asked if it's possible that the universe is not 00:14:29.820 --> 00:14:32.120 really homogeneous on a very large scales, 00:14:32.120 --> 00:14:35.142 but really speckled, just that speckles are large 00:14:35.142 --> 00:14:36.850 and our speckle might look very different 00:14:36.850 --> 00:14:38.580 from other speckles that are far away. 00:14:38.580 --> 00:14:40.030 And that was the question. 00:14:40.030 --> 00:14:41.595 And the answer is certainly if the multiverse picture 00:14:41.595 --> 00:14:42.040 is right. 00:14:42.040 --> 00:14:44.090 That is exactly the case that's being predicted. 00:14:44.090 --> 00:14:45.770 These other pocket universes could 00:14:45.770 --> 00:14:48.540 be viewed as other speckles in your language, 00:14:48.540 --> 00:14:51.420 and they'd be very different from what we've observed. 00:14:51.420 --> 00:14:55.820 So inflation actually changes one's attitude 00:14:55.820 --> 00:14:57.870 about this particular question. 00:14:57.870 --> 00:15:00.840 Back in the old days, before inflation, 00:15:00.840 --> 00:15:04.180 the uniformity of the universe had no explanation, 00:15:04.180 --> 00:15:06.420 so it became a postulate. 00:15:06.420 --> 00:15:08.750 And nobody postulates that something 00:15:08.750 --> 00:15:09.792 is uniform on that scale. 00:15:09.792 --> 00:15:11.333 If you are going to make a postulate, 00:15:11.333 --> 00:15:14.040 you just postulate that the universe is uniform. 00:15:14.040 --> 00:15:16.950 So that was the postulate that was in use. 00:15:16.950 --> 00:15:19.350 But now that we think of the homogeneity of the universe 00:15:19.350 --> 00:15:24.260 as being generated by a dynamical process, inflation, 00:15:24.260 --> 00:15:26.180 then, it's a natural question to ask, 00:15:26.180 --> 00:15:27.900 what is the scale of the homogeneity 00:15:27.900 --> 00:15:29.950 that that generates. 00:15:29.950 --> 00:15:31.470 And it's certainly a scale that's 00:15:31.470 --> 00:15:33.140 much larger than what we can observe. 00:15:33.140 --> 00:15:35.280 So we don't really expect to see inhomogeneity 00:15:35.280 --> 00:15:38.860 as caused by different pockets of inflation, 00:15:38.860 --> 00:15:42.700 but the model seems to make it very plausible that 00:15:42.700 --> 00:15:45.070 is what we would see if we could see far enough. 00:15:49.880 --> 00:15:54.250 Any other questions while we're on a little break here? 00:15:54.250 --> 00:15:55.130 Yes? 00:15:55.130 --> 00:15:56.755 AUDIENCE: If the universe is expanding, 00:15:56.755 --> 00:16:00.105 then I think like we are expanding as well, so how can 00:16:00.105 --> 00:16:01.775 we observe the change from a distance, 00:16:01.775 --> 00:16:04.327 in particular everything is increasing scale? 00:16:04.327 --> 00:16:04.910 PROFESSOR: OK. 00:16:04.910 --> 00:16:07.020 That's a very good question. 00:16:07.020 --> 00:16:09.430 The question was if the universe is expanding, 00:16:09.430 --> 00:16:10.890 then the universe is everything. 00:16:10.890 --> 00:16:12.340 So everything is expanding. 00:16:12.340 --> 00:16:14.590 And if everything's expanding, when you compare things 00:16:14.590 --> 00:16:16.950 with rulers, they have the same length. 00:16:16.950 --> 00:16:20.590 So how would you even observe that everything was expanding? 00:16:20.590 --> 00:16:22.660 And the answer to that is that when 00:16:22.660 --> 00:16:24.470 we say the universe is expanding, 00:16:24.470 --> 00:16:27.717 we're not really saying that everything is expanding. 00:16:27.717 --> 00:16:29.300 When we say the universe is expanding, 00:16:29.300 --> 00:16:31.716 we really are saying that the galaxies are getting further 00:16:31.716 --> 00:16:34.840 apart from each other, but individual atoms 00:16:34.840 --> 00:16:36.080 are not getting bigger. 00:16:36.080 --> 00:16:38.270 The length of a ruler, determined 00:16:38.270 --> 00:16:40.440 by the number of atoms and how those atoms move 00:16:40.440 --> 00:16:43.980 to ground state, does not expand with the universe. 00:16:43.980 --> 00:16:47.040 So the expansion is now partially driven 00:16:47.040 --> 00:16:48.880 by the repulsive gravity that exists 00:16:48.880 --> 00:16:51.360 now, which is causing the universe to accelerate. 00:16:51.360 --> 00:16:54.580 But most of the expansion is really just a residual velocity 00:16:54.580 --> 00:16:57.770 from the Big Bang, whatever caused it then. 00:16:57.770 --> 00:16:59.390 I would assert inflation. 00:16:59.390 --> 00:17:01.425 And it's just a matter of coasting outward, not 00:17:01.425 --> 00:17:03.980 being pulled outward, and that coasting outward 00:17:03.980 --> 00:17:07.626 does not cause atoms to get bigger. 00:17:07.626 --> 00:17:08.126 Yes? 00:17:08.126 --> 00:17:10.771 AUDIENCE: Is the current idea that the expansion, 00:17:10.771 --> 00:17:13.699 like the acceleration, is indefinite or are we 00:17:13.699 --> 00:17:16.827 going to reach a stop point? 00:17:16.827 --> 00:17:17.410 PROFESSOR: OK. 00:17:17.410 --> 00:17:20.839 What will be the ultimate future, I'm being asked here. 00:17:20.839 --> 00:17:25.220 And the answer, as you might guess, is nobody really knows. 00:17:25.220 --> 00:17:28.230 But in the context of the kind of models I'm talking about, 00:17:28.230 --> 00:17:30.620 there is a pretty definite answer, 00:17:30.620 --> 00:17:33.782 which is that our pocket universe-- 00:17:33.782 --> 00:17:35.740 I'll answer at the level of our pocket universe 00:17:35.740 --> 00:17:38.930 and I'll answer at the level of the multiverse as a hole. 00:17:38.930 --> 00:17:40.970 At the level of our pocket universe, 00:17:40.970 --> 00:17:43.770 our pocket universe will thin out. 00:17:43.770 --> 00:17:45.790 Life will eventually become impossible 00:17:45.790 --> 00:17:48.465 because matter density will be too low. 00:17:50.990 --> 00:17:53.000 It will probably decay. 00:17:53.000 --> 00:17:55.530 Our vacuum is probably not absolutely stable. 00:17:55.530 --> 00:17:57.690 Very few things 2 String theory are, 00:17:57.690 --> 00:18:00.530 if something like String theory is the right theory. 00:18:00.530 --> 00:18:02.050 But even though it will be decaying, 00:18:02.050 --> 00:18:04.910 it will be expanding still faster than it decays. 00:18:04.910 --> 00:18:07.260 So the decay will cause holes in our universe. 00:18:07.260 --> 00:18:09.256 It will become like Swiss cheese. 00:18:09.256 --> 00:18:10.880 But the universe, as a whole, will just 00:18:10.880 --> 00:18:13.090 go on exponentially expanding, perhaps 00:18:13.090 --> 00:18:15.860 forever, as far as we can tell, forever. 00:18:15.860 --> 00:18:18.710 The multiverse is a more vibrant object. 00:18:18.710 --> 00:18:20.440 The multiverse, as I always said, 00:18:20.440 --> 00:18:24.060 would continue to generate new pocket universes forever. 00:18:24.060 --> 00:18:26.230 So the multiverse would forever be alive 00:18:26.230 --> 00:18:29.620 even though each pocket universe in the multiverse 00:18:29.620 --> 00:18:33.640 would form at some time and then ultimately die, 00:18:33.640 --> 00:18:38.610 die of thinning out into nothingness. 00:18:38.610 --> 00:18:39.473 Yes? 00:18:39.473 --> 00:18:41.405 AUDIENCE: Just to add to that. 00:18:41.405 --> 00:18:44.786 Do you believe that maybe it's a cyclic process? 00:18:44.786 --> 00:18:49.616 So it expand and decay and then come back [? yet again ?] 00:18:49.616 --> 00:18:51.777 and then happen all over again? 00:18:51.777 --> 00:18:52.360 PROFESSOR: OK. 00:18:52.360 --> 00:18:54.820 The question is could it be a cyclic process that 00:18:54.820 --> 00:18:57.090 expands, reaches maximum, comes back and crunches, 00:18:57.090 --> 00:18:58.410 and expands again. 00:18:58.410 --> 00:19:00.490 That is certainly a possibility, and there 00:19:00.490 --> 00:19:03.240 is some people who take it very seriously. 00:19:03.240 --> 00:19:05.480 I don't see any evidence for it. 00:19:05.480 --> 00:19:08.520 And furthermore, there never really was and still 00:19:08.520 --> 00:19:11.720 really isn't a reasonable theory of the bounce 00:19:11.720 --> 00:19:16.165 that would have to be a part of that theory. 00:19:16.165 --> 00:19:16.665 Yeah? 00:19:16.665 --> 00:19:18.778 AUDIENCE: But would it be the expansion overtaking 00:19:18.778 --> 00:19:23.640 the decay in our own vacuum that our universe exists 00:19:23.640 --> 00:19:29.350 in, our own little pocket vacuums of ultimate decay 00:19:29.350 --> 00:19:33.246 within our system create more little pocket universes-- 00:19:33.246 --> 00:19:34.220 [INTERPOSING VOICES] 00:19:34.220 --> 00:19:34.640 PROFESSOR: Within. 00:19:34.640 --> 00:19:35.139 Yes. 00:19:35.139 --> 00:19:37.670 Yeah, that's correct. 00:19:37.670 --> 00:19:42.120 They would not be a big fraction of the volume of our universe, 00:19:42.120 --> 00:19:43.200 but, yes. 00:19:43.200 --> 00:19:46.210 The pieces in our universe that might decay in the future 00:19:46.210 --> 00:19:48.442 would produce new pocket universes. 00:19:48.442 --> 00:19:50.900 Most of them would be very low energy pocket universes that 00:19:50.900 --> 00:19:53.930 would presumably not create life, but some of them 00:19:53.930 --> 00:19:57.920 could nonetheless have a high enough energy to create life. 00:19:57.920 --> 00:20:03.080 So we would expect new, thriving universes 00:20:03.080 --> 00:20:06.010 to appear out of our own pocket universe 00:20:06.010 --> 00:20:11.800 as it reaches this expansion death. 00:20:11.800 --> 00:20:12.300 Yes? 00:20:12.300 --> 00:20:14.750 AUDIENCE: What does distinguishes different vacua 00:20:14.750 --> 00:20:17.735 besides the cosmological constant? 00:20:17.735 --> 00:20:19.610 PROFESSOR: The question is what distinguishes 00:20:19.610 --> 00:20:23.260 the different vacua besides the cosmological constant. 00:20:23.260 --> 00:20:28.200 And the answer is that they can distinguish in many, many ways. 00:20:28.200 --> 00:20:30.360 What fundamentally distinguishes them 00:20:30.360 --> 00:20:32.910 is the rearrangement of the innards 00:20:32.910 --> 00:20:37.160 within the space, maybe a little bit more precise without trying 00:20:37.160 --> 00:20:38.770 to get into details which I probably 00:20:38.770 --> 00:20:40.510 don't understand either. 00:20:40.510 --> 00:20:43.960 But what's going on is that String theory fundamentally 00:20:43.960 --> 00:20:46.500 says that space has nine dimensions, not the three 00:20:46.500 --> 00:20:47.730 that we observe. 00:20:47.730 --> 00:20:50.220 And the way the nine becomes three 00:20:50.220 --> 00:20:52.370 is that the extra dimensions get twisted up 00:20:52.370 --> 00:20:56.420 into tiny little knots, so they occupy too small a length 00:20:56.420 --> 00:20:57.665 to ever be seen. 00:20:57.665 --> 00:20:59.040 But there are many different ways 00:20:59.040 --> 00:21:00.677 of twisting up those extra dimensions, 00:21:00.677 --> 00:21:03.010 and that's really what leads to these very large numbers 00:21:03.010 --> 00:21:04.730 of possible vacua. 00:21:04.730 --> 00:21:08.060 The extra dimensions are twisted up differently. 00:21:08.060 --> 00:21:13.260 So that means that as far as the low energy 00:21:13.260 --> 00:21:14.890 physics in these different vacua-- 00:21:14.890 --> 00:21:16.640 practically everything could be different, 00:21:16.640 --> 00:21:18.598 even the dimension of space could be different. 00:21:18.598 --> 00:21:23.300 You could have different numbers of dimensions compactified. 00:21:23.300 --> 00:21:24.970 And the whole particle spectrum would 00:21:24.970 --> 00:21:28.590 be different because what we view as a particle is really 00:21:28.590 --> 00:21:30.890 just the fluctuation of vacuum. 00:21:30.890 --> 00:21:33.656 And if you have a different structure to the vacuum itself, 00:21:33.656 --> 00:21:35.280 the kinds of particles that exist in it 00:21:35.280 --> 00:21:37.180 could be totally different. 00:21:37.180 --> 00:21:39.919 So the physics inside these pocket universe 00:21:39.919 --> 00:21:41.710 could look tremendously different from what 00:21:41.710 --> 00:21:44.240 we observe even though that we're predicating 00:21:44.240 --> 00:21:46.190 the whole description on the idea 00:21:46.190 --> 00:21:48.160 that, ultimately, it's the same laws of physics 00:21:48.160 --> 00:21:49.076 that apply everywhere. 00:21:55.421 --> 00:21:56.900 Other questions? 00:21:56.900 --> 00:21:57.400 Yes? 00:21:57.400 --> 00:21:58.316 AUDIENCE: [INAUDIBLE]? 00:22:38.807 --> 00:22:39.390 PROFESSOR: OK. 00:22:39.390 --> 00:22:43.640 I think you're asking about if we have a small patch, then 00:22:43.640 --> 00:22:47.110 that goes inflation and the rest doesn't, how does the patch end 00:22:47.110 --> 00:22:49.740 up dominating because it started out 00:22:49.740 --> 00:22:51.630 with just a small fraction of the particles. 00:22:51.630 --> 00:22:54.088 Doesn't it still have the same small fraction of particles? 00:22:54.088 --> 00:22:57.042 Is that what you're asking? 00:22:57.042 --> 00:22:58.042 AUDIENCE: Well, I guess. 00:22:58.042 --> 00:23:01.938 If you start out with the smooth particles being 00:23:01.938 --> 00:23:05.347 the excessive matter, and one of the particles 00:23:05.347 --> 00:23:07.782 behaves and the other two particles [INAUDIBLE] 00:23:07.782 --> 00:23:11.200 even if it's still just two particles? 00:23:11.200 --> 00:23:11.990 PROFESSOR: Right. 00:23:11.990 --> 00:23:14.346 It isn't the number of particles conserved, basically, 00:23:14.346 --> 00:23:16.470 as all this happens, is I think what you're asking. 00:23:16.470 --> 00:23:18.960 AUDIENCE: Well, even if it eventually [? is called ?] 00:23:18.960 --> 00:23:26.365 expanded wave because the second part will [INAUDIBLE] 00:23:26.365 --> 00:23:27.490 PROFESSOR: Well, let's see. 00:23:27.490 --> 00:23:28.780 I'm having a little trouble hearing you. 00:23:28.780 --> 00:23:30.570 But let me make a definite-- let me make a broader statement, 00:23:30.570 --> 00:23:32.070 and you can tell me if I've answered 00:23:32.070 --> 00:23:34.520 what you're asking about or not. 00:23:34.520 --> 00:23:36.960 When one of these patches undergoes 00:23:36.960 --> 00:23:40.140 the exponential expansion of inflation, 00:23:40.140 --> 00:23:42.490 the energy is really not very well described 00:23:42.490 --> 00:23:43.490 as particles at all. 00:23:43.490 --> 00:23:45.700 It's really described in terms of fields. 00:23:45.700 --> 00:23:48.800 And fields sometimes behave like particles, but not always. 00:23:48.800 --> 00:23:52.290 And in this case-- in principle, there's a particle description 00:23:52.290 --> 00:23:54.540 too, but it's not nearly as obvious 00:23:54.540 --> 00:23:56.260 as the field description. 00:23:56.260 --> 00:23:59.365 So you have energy stored in fields and the region grows. 00:23:59.365 --> 00:24:00.740 The energy stored in those fields 00:24:00.740 --> 00:24:02.770 actually increases as the region goes. 00:24:02.770 --> 00:24:05.430 The energy density remains approximately constant. 00:24:05.430 --> 00:24:07.130 And that sounds like it would violate 00:24:07.130 --> 00:24:09.600 the conservation of energy, but we discussed the fact 00:24:09.600 --> 00:24:12.410 that what saves conservation of energy 00:24:12.410 --> 00:24:15.680 and allows this to happen in spite of conservation of energy 00:24:15.680 --> 00:24:17.770 is that as the region expands, it 00:24:17.770 --> 00:24:21.420 is filled by a gravitational field, which is now occupying 00:24:21.420 --> 00:24:24.540 a larger and larger volume, and that gravitational field has 00:24:24.540 --> 00:24:26.650 a negative energy density. 00:24:26.650 --> 00:24:29.370 So the total energy, which is what has to be conserved, 00:24:29.370 --> 00:24:32.120 remains very small and perhaps zero, 00:24:32.120 --> 00:24:35.100 and the region can grow without limit 00:24:35.100 --> 00:24:39.370 while still having this very small or zero total energy. 00:24:39.370 --> 00:24:41.690 Then, eventually it decays and when it decays, 00:24:41.690 --> 00:24:44.814 it produces new particles, and the colossal number 00:24:44.814 --> 00:24:46.730 of new particles, and those would be the stuff 00:24:46.730 --> 00:24:48.920 that we would be made out of. 00:24:48.920 --> 00:24:51.740 And that number is vastly larger than the number of particles 00:24:51.740 --> 00:24:53.210 that may have been in this region 00:24:53.210 --> 00:24:55.491 when the inflation started. 00:24:55.491 --> 00:24:55.990 Yes? 00:24:55.990 --> 00:24:59.894 AUDIENCE: So does the emergence of [INAUDIBLE] just purely 00:24:59.894 --> 00:25:02.334 a conservation of energy? 00:25:02.334 --> 00:25:05.262 Like, what do you need to make these [? an organism ?], 00:25:05.262 --> 00:25:09.574 the negative energy, zero [INAUDIBLE] I guess. 00:25:09.574 --> 00:25:11.740 PROFESSOR: Are you saying the conservation of energy 00:25:11.740 --> 00:25:15.420 maybe controls the whole show, and that this is really 00:25:15.420 --> 00:25:18.540 the only thing consistent with conservation of energy? 00:25:18.540 --> 00:25:21.890 I think that's probably an exaggeration 00:25:21.890 --> 00:25:25.780 because if nothing happened, that would conserve energy too. 00:25:25.780 --> 00:25:29.330 So I think one needs more than just the conservation of energy 00:25:29.330 --> 00:25:33.120 to be able to describe how the universe is going to evolve. 00:25:37.621 --> 00:25:38.120 OK. 00:25:38.120 --> 00:25:39.215 Let me continue. 00:25:46.284 --> 00:25:49.270 Get back to the beginning there, back to the end. 00:25:49.270 --> 00:25:49.770 OK. 00:25:49.770 --> 00:25:52.420 So I just finished talking about the landscape of String theory 00:25:52.420 --> 00:25:54.530 and how it offers all these possible vacua. 00:25:54.530 --> 00:25:58.960 So in particular, and this is now the new stuff, if there 00:25:58.960 --> 00:26:02.340 are 10 to the 500 vacua of String theory, for example. 00:26:02.340 --> 00:26:05.950 We don't really know the number, but something crazy like that. 00:26:05.950 --> 00:26:09.770 And if only one part in 10 to the 120 of them 00:26:09.770 --> 00:26:12.680 have this very small energy, thus the energy densities 00:26:12.680 --> 00:26:17.750 are spread from plus 10 to the 120 times 00:26:17.750 --> 00:26:22.429 what we observe to minus 10 to the 120 times what we observe. 00:26:22.429 --> 00:26:23.970 That would mean that what we observed 00:26:23.970 --> 00:26:27.990 would be a narrow slice in the middle there occupying about 10 00:26:27.990 --> 00:26:32.382 to the minus 120th of the length of that spread. 00:26:32.382 --> 00:26:34.340 We would then expect-- and all this, of course, 00:26:34.340 --> 00:26:36.675 is very crude estimates. 00:26:36.675 --> 00:26:38.550 It's not really the numbers that's important, 00:26:38.550 --> 00:26:41.406 it's whether or not you believe the ideas. 00:26:41.406 --> 00:26:44.640 But we'd expect then that about 10 to the minus 120 00:26:44.640 --> 00:26:48.610 of the different vacua would have an acceptably low vacuum 00:26:48.610 --> 00:26:50.486 energy density. 00:26:50.486 --> 00:26:52.360 But that's still a colossal number because 10 00:26:52.360 --> 00:26:55.160 to the minus 120 times 10 to the 500-- 00:26:55.160 --> 00:26:58.540 you add the exponents-- is 10 to the 380. 00:26:58.540 --> 00:27:01.000 So we would still predict that even though they'd 00:27:01.000 --> 00:27:05.320 be very rare, there might be 10 to the 380 different kinds 00:27:05.320 --> 00:27:08.470 of vacua, all which would have a vacuum energy density 00:27:08.470 --> 00:27:10.580 as well as what we observe. 00:27:10.580 --> 00:27:15.290 So there's no problem finding, in the landscape, vacua 00:27:15.290 --> 00:27:18.160 whose energy density is as low as what we observe. 00:27:18.160 --> 00:27:21.780 But then there's the question if they're so incredibly rare, 00:27:21.780 --> 00:27:23.260 wouldn't it take a miracle for us 00:27:23.260 --> 00:27:27.070 to be living in one of these incredibly unusual vacua 00:27:27.070 --> 00:27:30.520 with such an extraordinarily low vacuum energy density. 00:27:30.520 --> 00:27:33.250 That then leads to what is sometimes 00:27:33.250 --> 00:27:38.490 called Anthropic considerations or perhaps a selection effect. 00:27:38.490 --> 00:27:41.920 And to see how that works and make it sound not as crazy 00:27:41.920 --> 00:27:43.890 as it might sound otherwise, I want 00:27:43.890 --> 00:27:46.620 to begin by giving an example where I think one could really 00:27:46.620 --> 00:27:48.560 say that this effect happens. 00:27:48.560 --> 00:27:53.820 And that is suppose we just look at our own position 00:27:53.820 --> 00:27:56.770 in our own visible universe and look at, 00:27:56.770 --> 00:27:59.432 for example, the mass density. 00:27:59.432 --> 00:28:01.140 Where we're actually living is incredibly 00:28:01.140 --> 00:28:03.723 unusual in many ways, but one of the ways we could talk about, 00:28:03.723 --> 00:28:05.740 which is just simple and quantitative, 00:28:05.740 --> 00:28:07.050 is the mass density. 00:28:07.050 --> 00:28:09.990 The mass density of the things around this room 00:28:09.990 --> 00:28:14.200 is on the order of one gram per centimeter cubed give or take 00:28:14.200 --> 00:28:15.217 a factor of 10. 00:28:15.217 --> 00:28:16.800 The factor of 10 is not very important 00:28:16.800 --> 00:28:18.144 for I'm talking about here. 00:28:18.144 --> 00:28:19.560 The point is that the average mass 00:28:19.560 --> 00:28:22.890 density of the universe, the visible universe, is about 10 00:28:22.890 --> 00:28:25.610 to the minus 30 grams per centimeter cubed. 00:28:25.610 --> 00:28:30.000 It's really unbelievable how empty the universe is. 00:28:30.000 --> 00:28:33.630 It's actually a far lower mass density than is possible for us 00:28:33.630 --> 00:28:36.990 to achieve in laboratories on Earth with the best vacua 00:28:36.990 --> 00:28:40.130 that we can make in our laboratories. 00:28:40.130 --> 00:28:43.720 So where we're living has a mass density of 10 00:28:43.720 --> 00:28:48.360 to the 30 times the average of the visible universe. 00:28:48.360 --> 00:28:51.070 So we're not living in a typical place in our visible universe. 00:28:51.070 --> 00:28:54.470 We're living in an extraordinarily atypical place 00:28:54.470 --> 00:28:56.160 within our visible universe. 00:28:56.160 --> 00:28:59.224 And we can ask how would we explain that. 00:28:59.224 --> 00:29:00.890 Is it just a matter of chance that we're 00:29:00.890 --> 00:29:03.550 living in a place that's such a high mass density? 00:29:03.550 --> 00:29:05.805 Doesn't seem very likely if it's a matter of chance. 00:29:05.805 --> 00:29:06.500 Is it luck? 00:29:06.500 --> 00:29:08.560 Is it divine providence, whatever? 00:29:08.560 --> 00:29:11.460 I think most of us would admit that it's probably a selection 00:29:11.460 --> 00:29:12.450 effect. 00:29:12.450 --> 00:29:15.020 That that's where life happens. 00:29:15.020 --> 00:29:18.740 Life doesn't happen throughout most of the visible universe, 00:29:18.740 --> 00:29:20.930 but in these rare places, like the surface 00:29:20.930 --> 00:29:23.280 of our planet, which is special in more ways than just 00:29:23.280 --> 00:29:25.370 the mass density, but the mass density alone 00:29:25.370 --> 00:29:28.950 is enough to make it extraordinarily special. 00:29:28.950 --> 00:29:31.020 We're off by a factor of 10 to the 30 00:29:31.020 --> 00:29:33.890 from the average of our environment. 00:29:33.890 --> 00:29:36.420 So if we're willing to explain why 00:29:36.420 --> 00:29:40.560 we live in such an unusual place within our visible universe 00:29:40.560 --> 00:29:44.000 and explain that as simply a requirement for life, 00:29:44.000 --> 00:29:47.450 then it doesn't seem to be such a stretch to maybe imagine-- 00:29:47.450 --> 00:29:51.542 and it was Steve Weinberg who first emphasized this in 1987. 00:29:51.542 --> 00:29:53.250 Certainly not the first person to say it, 00:29:53.250 --> 00:29:56.310 but the first person to say it and have people 00:29:56.310 --> 00:29:58.670 sometimes believe him. 00:29:58.670 --> 00:30:01.940 He pointed out that may be the low energy-- the low vacuum 00:30:01.940 --> 00:30:05.190 energy density could be explained the same way. 00:30:05.190 --> 00:30:07.490 If we're not living in a typical place 00:30:07.490 --> 00:30:10.090 within our visible universe, there's 00:30:10.090 --> 00:30:14.410 no reason for similar ideas to expect 00:30:14.410 --> 00:30:16.370 that we should be living in a typical place 00:30:16.370 --> 00:30:18.150 in the multiverse. 00:30:18.150 --> 00:30:21.720 Maybe only a small fraction of these different types 00:30:21.720 --> 00:30:24.820 of pocket universe's can support life. 00:30:24.820 --> 00:30:27.290 And maybe the only way to have life 00:30:27.290 --> 00:30:31.170 is to have a very small value for the vacuum energy density. 00:30:31.170 --> 00:30:33.700 And there is some physics behind that. 00:30:33.700 --> 00:30:38.050 Remember this vacuum energy density drives expansion-- 00:30:38.050 --> 00:30:41.000 acceleration, I should say. 00:30:41.000 --> 00:30:46.210 So if the vacuum energy density were significantly larger 00:30:46.210 --> 00:30:48.070 than what we observe, the universe 00:30:48.070 --> 00:30:49.594 would accelerate incredibly rapidly 00:30:49.594 --> 00:30:51.010 and would fly apart before there'd 00:30:51.010 --> 00:30:53.280 be any time for anything interesting to happen 00:30:53.280 --> 00:30:55.306 like galaxies forming. 00:30:55.306 --> 00:30:57.430 Weinberg based his arguments here on the assumption 00:30:57.430 --> 00:31:00.340 that galaxies are a necessity for life. 00:31:00.340 --> 00:31:00.840 Yes? 00:31:00.840 --> 00:31:02.820 AUDIENCE: So that's what I was going to ask. 00:31:02.820 --> 00:31:05.112 Why do we assume that our universe is the only one that 00:31:05.112 --> 00:31:07.570 could have like-- why couldn't just all the multi-universes 00:31:07.570 --> 00:31:08.162 have like-- 00:31:08.162 --> 00:31:08.870 PROFESSOR: Right. 00:31:08.870 --> 00:31:09.090 Right. 00:31:09.090 --> 00:31:09.800 Well, that's OK. 00:31:09.800 --> 00:31:11.430 That is what I am talking about. 00:31:11.430 --> 00:31:13.540 I'm trying to answer it. 00:31:13.540 --> 00:31:16.430 So if the vacuum energy density were significantly larger 00:31:16.430 --> 00:31:18.424 than what we observe, the universes 00:31:18.424 --> 00:31:20.340 would fly apart so fast that there could never 00:31:20.340 --> 00:31:24.085 be galaxies and therefore never planets, none of things 00:31:24.085 --> 00:31:26.460 that we think of as being associated with life as we know 00:31:26.460 --> 00:31:27.670 it. 00:31:27.670 --> 00:31:31.820 Conversely, if the vacuum energy density were negative, but had 00:31:31.820 --> 00:31:34.530 a magnitude large compared to what we observed, 00:31:34.530 --> 00:31:37.550 that would be a large negative acceleration, an implosion. 00:31:37.550 --> 00:31:40.050 And those universes would just implode, collapse, 00:31:40.050 --> 00:31:44.840 in an incredibly short amount of time, much too fast for life, 00:31:44.840 --> 00:31:47.750 of any type that we know of, to form. 00:31:47.750 --> 00:31:51.780 So there is a physical argument which suggests that life only 00:31:51.780 --> 00:31:56.040 forms when the vacuum energy density is very low. 00:31:56.040 --> 00:31:58.392 And Weinberg and his collaborators-- and this 00:31:58.392 --> 00:32:00.892 is the same Steve Weinberg who wrote the First Three Minutes 00:32:00.892 --> 00:32:04.860 that we're reading-- calculated what the requirements would 00:32:04.860 --> 00:32:06.220 be for galaxy formation. 00:32:06.220 --> 00:32:09.710 And they decided that, within about a factor of 5 or so, 00:32:09.710 --> 00:32:11.260 the vacuum energy density would have 00:32:11.260 --> 00:32:14.430 to be about the same as what we observe or less 00:32:14.430 --> 00:32:17.300 in order for galaxies to form. 00:32:17.300 --> 00:32:19.354 So it seems like a possible explanation. 00:32:19.354 --> 00:32:21.520 It's certainly not a generally accepted explanation. 00:32:21.520 --> 00:32:22.820 These things are very controversial one. 00:32:22.820 --> 00:32:24.278 I guess that's, in fact, what I was 00:32:24.278 --> 00:32:26.940 going to talk about on my next slide. 00:32:26.940 --> 00:32:30.910 Some physicists by this selection effect idea. 00:32:30.910 --> 00:32:33.720 I tend to buy it. 00:32:33.720 --> 00:32:35.791 But a number of physicists regard it as totally 00:32:35.791 --> 00:32:37.665 ridiculous, saying you could explain anything 00:32:37.665 --> 00:32:40.680 if you except arguments like that. 00:32:40.680 --> 00:32:42.960 And there's some truth to that. 00:32:42.960 --> 00:32:44.730 You can explain a lot of things if you're 00:32:44.730 --> 00:32:46.800 willing to just say, well, maybe that's needed 00:32:46.800 --> 00:32:49.050 for life to happen. 00:32:49.050 --> 00:32:52.840 So because of that, I would say that these selection effect 00:32:52.840 --> 00:32:55.530 arguments or anthropic arguments should always 00:32:55.530 --> 00:32:59.200 be viewed as the arguments of last resort. 00:32:59.200 --> 00:33:01.659 That is, unless we actually understand 00:33:01.659 --> 00:33:03.200 the landscape of String theory, which 00:33:03.200 --> 00:33:05.660 we do not in detail, and once we actually 00:33:05.660 --> 00:33:08.640 understand what it takes to create life, 00:33:08.640 --> 00:33:12.510 we really can't do more than give plausibility arguments 00:33:12.510 --> 00:33:17.190 to justify these anthropic explanations. 00:33:17.190 --> 00:33:22.620 But these anthropic arguments do sound sensible. 00:33:22.620 --> 00:33:24.670 I think there's nothing illogical about them, 00:33:24.670 --> 00:33:28.060 and they could very well be the explanations for some things. 00:33:28.060 --> 00:33:31.070 As I pointed out, I think it is the explanation for why 00:33:31.070 --> 00:33:33.270 we are living in such an unusual place 00:33:33.270 --> 00:33:36.580 within our own visible universe. 00:33:36.580 --> 00:33:41.310 And it means that these selection effect arguments 00:33:41.310 --> 00:33:44.760 become very attractive when the search for more deterministic 00:33:44.760 --> 00:33:46.800 explanations have failed. 00:33:46.800 --> 00:33:50.370 And in the case of trying to explain the very small vacuum 00:33:50.370 --> 00:33:52.770 energy density, I think other attempts have failed. 00:33:52.770 --> 00:33:58.270 We don't have any calculational, deterministic understanding 00:33:58.270 --> 00:34:03.040 for why the vacuum energy should be so small. 00:34:03.040 --> 00:34:07.900 So is it time to accept this explanation of last resort 00:34:07.900 --> 00:34:10.090 that the vacuum energy density is small 00:34:10.090 --> 00:34:13.665 because it has to be for life to the evolve? 00:34:13.665 --> 00:34:15.320 Your guess is as good as mine. 00:34:15.320 --> 00:34:17.380 I don't really know. 00:34:17.380 --> 00:34:20.520 But I would say that, in the case of the vacuum energy 00:34:20.520 --> 00:34:22.929 density, people have been trying very, very 00:34:22.929 --> 00:34:24.760 hard for quite a few years now to try 00:34:24.760 --> 00:34:28.610 to find a particle physics explanation for why the vacuum 00:34:28.610 --> 00:34:32.872 energy has to be small, and nobody's really found anything 00:34:32.872 --> 00:34:35.205 that anybody has found-- that any large number of people 00:34:35.205 --> 00:34:37.770 have found to be acceptable. 00:34:37.770 --> 00:34:39.520 So it is certainly a very serious problem. 00:34:39.520 --> 00:34:41.900 And I think it is time to take seriously 00:34:41.900 --> 00:34:45.770 the argument of last resort, that maybe it's that way only 00:34:45.770 --> 00:34:49.120 because in the parts of the multiverse where it's not 00:34:49.120 --> 00:34:51.139 that way, nobody lives there. 00:34:53.576 --> 00:34:55.409 So I would say it's hard to deny, as of now, 00:34:55.409 --> 00:34:58.720 that the selection effect explanation is 00:34:58.720 --> 00:35:00.930 the most plausible of any explanation that 00:35:00.930 --> 00:35:04.440 is known at the present time. 00:35:04.440 --> 00:35:06.570 To summarize things-- I'm actually done now, 00:35:06.570 --> 00:35:09.410 but let me just summarize what I said 00:35:09.410 --> 00:35:12.856 to remind you where we're at. 00:35:12.856 --> 00:35:14.605 I've argued that the inflationary paradigm 00:35:14.605 --> 00:35:16.790 is in great shape. 00:35:16.790 --> 00:35:20.007 It explains the large scale uniformity. 00:35:20.007 --> 00:35:21.840 It predicts the mass density of the universe 00:35:21.840 --> 00:35:26.180 to better than about 1% accuracy and explains the ripples 00:35:26.180 --> 00:35:29.260 that we see in the cosmic background radiation, 00:35:29.260 --> 00:35:32.010 explaining them as a result of quantum fluctuations 00:35:32.010 --> 00:35:36.590 that took place in the very early universe. 00:35:36.590 --> 00:35:39.560 The picture leads to three ideas that 00:35:39.560 --> 00:35:42.610 at least point towards the idea of a multiverse. 00:35:42.610 --> 00:35:45.560 It certainly doesn't prove that we're living in a multiverse. 00:35:45.560 --> 00:35:47.800 But the three ideas that point in that direction 00:35:47.800 --> 00:35:50.610 are, first of all, the statement that almost 00:35:50.610 --> 00:35:53.230 all inflationary models lead to this feature 00:35:53.230 --> 00:35:57.030 of eternal inflation, that the exponential expansion 00:35:57.030 --> 00:35:59.630 of the inflating material, generally speaking, 00:35:59.630 --> 00:36:02.530 out runs the decay of that material 00:36:02.530 --> 00:36:07.490 so that the volume grows exponentially forever. 00:36:07.490 --> 00:36:12.030 Second point is that, in 1998, the astronomers discovered 00:36:12.030 --> 00:36:15.290 this rather amazing fact that the universe is not 00:36:15.290 --> 00:36:21.420 slowing down as it expands, but in fact, is accelerating. 00:36:21.420 --> 00:36:23.380 And that indicates that there has 00:36:23.380 --> 00:36:26.560 to be some peculiar material in the universe other than what 00:36:26.560 --> 00:36:29.510 we already knew was here, and that peculiar material is 00:36:29.510 --> 00:36:31.780 called the dark energy. 00:36:31.780 --> 00:36:35.410 And we don't have any simple interpretation of what it is, 00:36:35.410 --> 00:36:37.970 but it seems to most likely be vacuum energy. 00:36:37.970 --> 00:36:40.800 And if it is, it leads immediately 00:36:40.800 --> 00:36:43.470 to the important question of can we 00:36:43.470 --> 00:36:47.420 understand why it has a value that it has. 00:36:47.420 --> 00:36:50.810 It seems to be much smaller than what we would expect. 00:36:50.810 --> 00:36:54.370 And then three, the String theorists 00:36:54.370 --> 00:36:57.172 give us an interesting way out here. 00:36:57.172 --> 00:36:59.130 The String theorists tell us that maybe there's 00:36:59.130 --> 00:37:01.780 not unique vacuum to the laws of physics, 00:37:01.780 --> 00:37:03.410 but maybe there's a huge number, which 00:37:03.410 --> 00:37:06.410 seems to be in fact what String theory predicts. 00:37:06.410 --> 00:37:11.910 And if there is, then of the many different vacua 00:37:11.910 --> 00:37:14.070 you expect there to be, in fact perhaps even 00:37:14.070 --> 00:37:17.460 a large number, that would have this very small vacuum energy 00:37:17.460 --> 00:37:22.680 density, a tiny fraction of the total different vacua, 00:37:22.680 --> 00:37:24.820 but nonetheless a large number of vacua 00:37:24.820 --> 00:37:26.740 that would have this property. 00:37:26.740 --> 00:37:29.170 And then this selection effect idea 00:37:29.170 --> 00:37:30.620 can provide a possible explanation 00:37:30.620 --> 00:37:35.230 for why we are living in one of those very unusual vacua which 00:37:35.230 --> 00:37:39.630 has this incredibly tiny vacuum energy density. 00:37:39.630 --> 00:37:42.040 So finally, I'd just like to close 00:37:42.040 --> 00:37:45.460 with a little sociological discussion here. 00:37:45.460 --> 00:37:48.130 Do physicists really take this seriously? 00:37:48.130 --> 00:37:50.810 And I'd like to tell you about a conversation that took place 00:37:50.810 --> 00:37:52.670 at a conference a few years ago. 00:37:52.670 --> 00:37:56.260 Starting with Martin Rees, who I don't know if you know the name 00:37:56.260 --> 00:37:58.850 or not, but he's an Astronomer Royal of Great Britain, 00:37:58.850 --> 00:38:00.590 former president of Royal Society, 00:38:00.590 --> 00:38:02.810 former master of Trinity College as well, 00:38:02.810 --> 00:38:06.082 a very distinguished person, nice guy, too, by the way. 00:38:06.082 --> 00:38:07.540 And he said that he is sufficiently 00:38:07.540 --> 00:38:12.340 confident in the multiverse to bet his dog's life on it. 00:38:12.340 --> 00:38:16.490 Andrei Linde, from Stanford, a real enthusiastic person 00:38:16.490 --> 00:38:21.410 about the multiverse, one of the founders of inflation as well, 00:38:21.410 --> 00:38:23.227 said that he's so confident that he 00:38:23.227 --> 00:38:25.801 would bet his own life on it. 00:38:25.801 --> 00:38:27.550 Steve Weinberg was not at this conference, 00:38:27.550 --> 00:38:29.758 but he wrote an article commenting on this discussion 00:38:29.758 --> 00:38:31.467 later which became known. 00:38:31.467 --> 00:38:33.050 And I always considered Steve Weinberg 00:38:33.050 --> 00:38:34.827 the voice of reason, which is why we're 00:38:34.827 --> 00:38:36.160 reading the First Three Minutes. 00:38:36.160 --> 00:38:38.076 And he said that I have just enough confidence 00:38:38.076 --> 00:38:40.130 in the multiverse to bet-- guess what's 00:38:40.130 --> 00:38:43.556 coming-- the lives of both Andrei Linde and Martin Rees' 00:38:43.556 --> 00:38:44.055 dog. 00:38:49.730 --> 00:38:52.870 That's it for the summary, or the overview. 00:38:52.870 --> 00:38:56.000 Anymore overview type questions before we get back 00:38:56.000 --> 00:38:59.140 to the beginning, actual beginning of the class? 00:39:05.810 --> 00:39:07.066 Yes? 00:39:07.066 --> 00:39:13.345 AUDIENCE: You said-- so selection effect argument says 00:39:13.345 --> 00:39:19.668 that it's because life exists within these certain 00:39:19.668 --> 00:39:24.150 constraints, omega being one and low energy larger than it 00:39:24.150 --> 00:39:29.130 generally is allowed, that life could exist in this way. 00:39:29.130 --> 00:39:32.118 But we're considering carbon-based life. 00:39:32.118 --> 00:39:36.351 What if there's some other [INAUDIBLE] life 00:39:36.351 --> 00:39:39.588 forms out there that gives us different energies 00:39:39.588 --> 00:39:41.997 and radiation and stuff like that? 00:39:41.997 --> 00:39:43.830 PROFESSOR: Yeah, what you're pointing toward 00:39:43.830 --> 00:39:47.720 is certainly a severe weakness of these selection effect 00:39:47.720 --> 00:39:51.760 arguments, that we really know about carbon-based life, life 00:39:51.760 --> 00:39:54.600 that's like us, and we can talk about what conditions 00:39:54.600 --> 00:39:58.090 are needed to make life like us, but maybe there's 00:39:58.090 --> 00:39:59.860 life that's totally different from us 00:39:59.860 --> 00:40:01.490 that we don't know anything about that 00:40:01.490 --> 00:40:02.970 might be able to live under totally 00:40:02.970 --> 00:40:04.485 different circumstances. 00:40:08.160 --> 00:40:10.590 That is a real weakness. 00:40:10.590 --> 00:40:14.240 However, I would argue-- and this is also controversial. 00:40:14.240 --> 00:40:17.110 Not everybody would agree with what I'm about to say. 00:40:17.110 --> 00:40:21.830 But I would argue that if we're willing to explain 00:40:21.830 --> 00:40:25.990 the unusual features of the piece of the universe 00:40:25.990 --> 00:40:29.350 that we live in by selection effect arguments-- 00:40:29.350 --> 00:40:32.140 the fact I used, the example is simply 00:40:32.140 --> 00:40:34.580 that we're living a place where the mass density is 00:40:34.580 --> 00:40:37.060 10 to the 30 times larger than the mean. 00:40:37.060 --> 00:40:39.790 If we're willing to use the anthropic arguments to explain 00:40:39.790 --> 00:40:43.930 that, then I think all those same issues arise there also. 00:40:43.930 --> 00:40:46.210 If life was really teem-- if the universe was really 00:40:46.210 --> 00:40:49.040 teeming with a different kind of life that 00:40:49.040 --> 00:40:51.290 thrived in vacua, then we'd be much more 00:40:51.290 --> 00:40:54.020 likely to be one of them, extremely unusual creatures 00:40:54.020 --> 00:40:56.690 living on the surfaces of planets. 00:40:56.690 --> 00:41:00.010 So I think it's a possible weakness 00:41:00.010 --> 00:41:01.874 that one has to keep in mind, but I 00:41:01.874 --> 00:41:03.540 don't think it should stop us from using 00:41:03.540 --> 00:41:04.720 those arguments completely. 00:41:04.720 --> 00:41:07.940 But it is certainly a cause for skepticism. 00:41:07.940 --> 00:41:08.440 Yes? 00:41:08.440 --> 00:41:10.606 AUDIENCE: Isn't the point of the selection principle 00:41:10.606 --> 00:41:16.376 just the fact that exist-- the universe selected for us. 00:41:16.376 --> 00:41:19.352 Does it matter for the general of just for like carbon-based 00:41:19.352 --> 00:41:21.832 [? organisms? ?] Is the fact that we exist [INAUDIBLE] 00:41:21.832 --> 00:41:24.312 that we've been selected for [INAUDIBLE]? 00:41:28.310 --> 00:41:29.710 PROFESSOR: You're asking about, I 00:41:29.710 --> 00:41:32.750 think, how peculiar to carbon-based life 00:41:32.750 --> 00:41:35.353 should we expect these selection effect arguments to be. 00:41:35.353 --> 00:41:37.728 AUDIENCE: Doesn't the selection affect where [INAUDIBLE]? 00:41:46.262 --> 00:41:47.970 PROFESSOR: Now that's an important point, 00:41:47.970 --> 00:41:51.550 and certainly one that's not settled among philosophers, 00:41:51.550 --> 00:41:54.170 probabilist, physicists, or anybody. 00:41:54.170 --> 00:41:56.680 What you're asking-- if I'm summarizing it right-- 00:41:56.680 --> 00:41:59.300 is when we're thinking of the selection effects, 00:41:59.300 --> 00:42:01.554 should we may be only talk about carbon-based life 00:42:01.554 --> 00:42:03.970 because, after all, we know that we are carbon-based life. 00:42:03.970 --> 00:42:06.178 So what does it matter if there's other kinds of life 00:42:06.178 --> 00:42:07.180 out there? 00:42:07.180 --> 00:42:09.390 That's one way of looking at it, certainly. 00:42:09.390 --> 00:42:12.420 Or, maybe we should think about all kinds of life. 00:42:12.420 --> 00:42:14.550 That's something else that people say. 00:42:18.560 --> 00:42:21.085 The problem I would-- I tend to be by the way 00:42:21.085 --> 00:42:23.460 the kind of person that thinks that all life is relevant, 00:42:23.460 --> 00:42:25.210 not just carbon-based life. 00:42:25.210 --> 00:42:26.876 Because we happen to be carbon-based, 00:42:26.876 --> 00:42:28.250 and we happen to have fingernails 00:42:28.250 --> 00:42:29.330 that have a certain length, and we 00:42:29.330 --> 00:42:31.230 happen to have hair that's a certain length 00:42:31.230 --> 00:42:32.990 or a certain thickness, does that 00:42:32.990 --> 00:42:34.930 mean we should only think of those things 00:42:34.930 --> 00:42:36.471 as being relevant when we're thinking 00:42:36.471 --> 00:42:38.066 about selection effects? 00:42:38.066 --> 00:42:39.440 And I would say that they're not. 00:42:39.440 --> 00:42:42.100 If our hair had a different thicknesses, 00:42:42.100 --> 00:42:46.870 we would still be able to make measurements and so on. 00:42:46.870 --> 00:42:49.890 So from my point of view, when one 00:42:49.890 --> 00:42:53.680 thinks about these issues of selection effects, 00:42:53.680 --> 00:42:57.350 one should precondition only on the elements that 00:42:57.350 --> 00:43:00.000 are necessary to ask the question in the first place. 00:43:00.000 --> 00:43:03.200 And what I would like to think-- and as I point out, 00:43:03.200 --> 00:43:04.920 this is controversial, not everybody 00:43:04.920 --> 00:43:08.060 agrees with me-- is that a good theory should 00:43:08.060 --> 00:43:11.550 be a theory in which you could say that most of the people who 00:43:11.550 --> 00:43:14.440 ask this particular question will get the answer that we 00:43:14.440 --> 00:43:15.420 say. 00:43:15.420 --> 00:43:18.380 If only a tiny fraction of people who ask that question 00:43:18.380 --> 00:43:20.525 will get that answer, but that same tiny fraction 00:43:20.525 --> 00:43:22.150 happens to have hair of a certain color 00:43:22.150 --> 00:43:23.767 and you have hair of that color, to me 00:43:23.767 --> 00:43:26.350 that's still not an explanation because you don't know why you 00:43:26.350 --> 00:43:27.891 have hair of that color or why you're 00:43:27.891 --> 00:43:30.700 living in such an unusual place. 00:43:30.700 --> 00:43:33.190 OK that strikes up a lot of conversations. 00:43:33.190 --> 00:43:33.690 Yes? 00:43:33.690 --> 00:43:35.065 AUDIENCE: You mentioned last time 00:43:35.065 --> 00:43:36.540 that the different pocket universes 00:43:36.540 --> 00:43:39.460 that comprise the multiverse are disconnected from each other 00:43:39.460 --> 00:43:44.460 though they start out as patches within the preceding vacua. 00:43:44.460 --> 00:43:46.630 What starts to disconnect them fundamentally 00:43:46.630 --> 00:43:50.850 from the vacuum which they formed? 00:43:50.850 --> 00:43:53.540 PROFESSOR: The question is what is it that separates these 00:43:53.540 --> 00:43:55.410 different pocket universe's. 00:43:55.410 --> 00:43:57.200 If they start out all in the same space, 00:43:57.200 --> 00:43:59.520 don't they remain all in the same space? 00:43:59.520 --> 00:44:02.250 And the answer is they do, but the space they started out in 00:44:02.250 --> 00:44:04.660 was expanding at a very rapid rate. 00:44:04.660 --> 00:44:08.130 So in most cases, but not all actually, 00:44:08.130 --> 00:44:10.480 two pocket universes will form far enough apart 00:44:10.480 --> 00:44:12.040 from each other that they will never 00:44:12.040 --> 00:44:14.460 touch each other as they grow because the space in between 00:44:14.460 --> 00:44:17.820 will expand to fast to ever allow them to meet. 00:44:17.820 --> 00:44:21.010 However, collisions of pocket universities 00:44:21.010 --> 00:44:24.710 will occur if two pocket universes form close enough 00:44:24.710 --> 00:44:27.240 to each other, the expansion of space in between 00:44:27.240 --> 00:44:31.620 will not be enough to keep them apart, and they will glide. 00:44:31.620 --> 00:44:33.940 How frequent one should think of that as being 00:44:33.940 --> 00:44:36.380 is an incredibly tough question to which 00:44:36.380 --> 00:44:38.440 nobody knows the answer. 00:44:38.440 --> 00:44:40.680 There are actually-- at least there 00:44:40.680 --> 00:44:42.650 is at least one astronomical paper 00:44:42.650 --> 00:44:44.610 in the literature by a group of astronomers 00:44:44.610 --> 00:44:49.160 who have looked for possible signs of a collision of bubbles 00:44:49.160 --> 00:44:50.410 in our past. 00:44:50.410 --> 00:44:53.380 They did not find anything definitive. 00:44:53.380 --> 00:44:55.860 But it is something to think about, 00:44:55.860 --> 00:44:57.882 and it's something people are thinking about. 00:44:57.882 --> 00:44:59.340 There really are quite a few papers 00:44:59.340 --> 00:45:03.760 about collisions of bubbles in the literature. 00:45:03.760 --> 00:45:04.260 Yes? 00:45:04.260 --> 00:45:06.260 AUDIENCE: How long is long-lived? 00:45:06.260 --> 00:45:10.760 So if the energy density was too large and too negative 00:45:10.760 --> 00:45:13.092 would that still be long-lived if it 00:45:13.092 --> 00:45:15.777 were to collide upon itself? 00:45:15.777 --> 00:45:18.110 PROFESSOR: Talking about the lifetime of these universes 00:45:18.110 --> 00:45:20.250 that I said would collapse very quickly. 00:45:20.250 --> 00:45:21.630 How quickly do I mean? 00:45:21.630 --> 00:45:25.429 AUDIENCE: Like the metastable long-lived. 00:45:25.429 --> 00:45:26.970 PROFESSOR: I used the word long-lived 00:45:26.970 --> 00:45:29.095 at least twice in what I've talked about-- I talked 00:45:29.095 --> 00:45:31.280 about the long-lived metastable vacua. 00:45:31.280 --> 00:45:33.600 And there, by long-lived I mean anything 00:45:33.600 --> 00:45:37.250 that's long compared to the age of our universe since the Big 00:45:37.250 --> 00:45:38.080 Bang. 00:45:38.080 --> 00:45:40.170 Long means long compared to 10 to the 10 00:45:40.170 --> 00:45:42.980 years in that context. 00:45:42.980 --> 00:45:47.640 I also said that if the vacuum energy of a universe 00:45:47.640 --> 00:45:51.220 were large and negative, it would very rapidly collapse. 00:45:51.220 --> 00:45:54.890 That could be as fast as 10 to the minus 20 seconds. 00:45:54.890 --> 00:45:57.110 It could be very fast depending on how large 00:45:57.110 --> 00:45:59.860 the cosmological constant was. 00:45:59.860 --> 00:46:00.705 Yes? 00:46:00.705 --> 00:46:04.330 AUDIENCE: So I have read that there's an effect such 00:46:04.330 --> 00:46:07.180 that if you're vacuum can be seen differently 00:46:07.180 --> 00:46:08.180 by different observers. 00:46:08.180 --> 00:46:10.090 For example, inertial-- there's something 00:46:10.090 --> 00:46:13.710 that I read in effect it says that if one inertial observer 00:46:13.710 --> 00:46:15.860 sees vacuum, another observer that's 00:46:15.860 --> 00:46:17.930 accelerating with respect to that observer 00:46:17.930 --> 00:46:21.140 would see like a number of particles [INAUDIBLE] 00:46:21.140 --> 00:46:22.140 a warm gas. 00:46:22.140 --> 00:46:25.800 So how much of the effect we observe are due to the fact 00:46:25.800 --> 00:46:28.490 that perhaps we believe the universe is accelerating, 00:46:28.490 --> 00:46:31.580 and we're accelerating perhaps with respect to some vacuum 00:46:31.580 --> 00:46:32.830 and we're just observing that. 00:46:32.830 --> 00:46:36.115 That's just a fact of our motion not necessarily the-- 00:46:36.115 --> 00:46:37.740 PROFESSOR: You're touching on something 00:46:37.740 --> 00:46:40.920 that is in fact very confusing. 00:46:43.640 --> 00:46:44.390 What is your name? 00:46:44.390 --> 00:46:45.110 AUDIENCE: Hani. 00:46:45.110 --> 00:46:46.060 PROFESSOR: Hani? 00:46:46.060 --> 00:46:48.920 What Hani said was that he had heard-- 00:46:48.920 --> 00:46:52.810 and this is correct-- that if one had simply 00:46:52.810 --> 00:46:55.602 a region of ordinary vacuum-- and I am now 00:46:55.602 --> 00:46:57.560 going to talk about special [INAUDIBLE] vacuum. 00:46:57.560 --> 00:46:59.650 You don't even need relativity. 00:46:59.650 --> 00:47:01.810 You don't general relativity, you just need this. 00:47:01.810 --> 00:47:03.870 If you had an accelerating observer moving 00:47:03.870 --> 00:47:06.250 through that vacuum, the accelerating observer 00:47:06.250 --> 00:47:08.380 would not see something that looked like vacuum, 00:47:08.380 --> 00:47:10.630 but rather would see particles that in fact would look 00:47:10.630 --> 00:47:12.629 like they had a finite temperature which you can 00:47:12.629 --> 00:47:16.200 calculate, a temperature that's determined by the acceleration. 00:47:16.200 --> 00:47:17.750 So the question is, how much of what 00:47:17.750 --> 00:47:20.590 we see should we think of as really being there 00:47:20.590 --> 00:47:24.780 and how much might be caused just by our own motion. 00:47:24.780 --> 00:47:29.175 And there's not a terribly great answer to that question 00:47:29.175 --> 00:47:34.600 that I know of except that we-- when these questions come up, 00:47:34.600 --> 00:47:38.190 we tend to just adopt the philosophy 00:47:38.190 --> 00:47:41.060 that an observer who's freely moving, 00:47:41.060 --> 00:47:44.290 which really means moving with the gravitational field, 00:47:44.290 --> 00:47:49.280 a geodesic observer as the word phrase is sometimes used, 00:47:49.280 --> 00:47:51.362 essentially defines what you might call reality 00:47:51.362 --> 00:47:53.820 and then if you calculate what accelerating observers might 00:47:53.820 --> 00:47:57.160 see in terms of that reality. 00:47:57.160 --> 00:48:00.620 And we are almost geodesic observers. 00:48:00.620 --> 00:48:02.620 The Earth is exerting a force on our feet, which 00:48:02.620 --> 00:48:05.115 violates that a little bit, but by the overall cosmic scale 00:48:05.115 --> 00:48:06.531 of things where the speed of light 00:48:06.531 --> 00:48:08.960 is what determines what's significant, 00:48:08.960 --> 00:48:14.590 we are essentially inertial or geodesic observers. 00:48:14.590 --> 00:48:17.230 Yes, Aviv? 00:48:17.230 --> 00:48:18.900 Aviv first and then the one in front. 00:48:18.900 --> 00:48:21.358 AUDIENCE: So I'm wondering about the philosophical approach 00:48:21.358 --> 00:48:26.232 to this discussion and why the very-- by the definition, 00:48:26.232 --> 00:48:28.420 we can't possibly observe another universe. 00:48:28.420 --> 00:48:31.125 And so maybe we have a theory that 00:48:31.125 --> 00:48:33.125 makes a lot of great predictions like inflation. 00:48:33.125 --> 00:48:36.618 But it may also make predictions about multiverse. 00:48:36.618 --> 00:48:39.778 We can't possibly empirically determine whether that's true 00:48:39.778 --> 00:48:41.770 or not, so a nonfalsifiable question. 00:48:41.770 --> 00:48:46.740 And so I feel like [INAUDIBLE] who [INAUDIBLE] 00:48:46.740 --> 00:48:49.728 essentially never going to be answered. 00:48:49.728 --> 00:48:52.192 And if we're going to be strict empiricists, 00:48:52.192 --> 00:48:55.720 should we not be concerned with this question? 00:48:55.720 --> 00:48:58.350 PROFESSOR: The question is if we could never see another pocket 00:48:58.350 --> 00:49:01.210 universe, is it even a valid question 00:49:01.210 --> 00:49:03.825 to discuss whether or not they exist, 00:49:03.825 --> 00:49:06.770 a valid scientific question. 00:49:06.770 --> 00:49:09.210 That is also a question which is generally 00:49:09.210 --> 00:49:13.420 debated in the community, and people have taken both sides. 00:49:13.420 --> 00:49:14.970 There certainly is a point of view, 00:49:14.970 --> 00:49:18.110 which I think I tend to take, which 00:49:18.110 --> 00:49:21.150 is that we never really insist that every aspect 00:49:21.150 --> 00:49:23.540 of our theories can be tested. 00:49:23.540 --> 00:49:27.560 If you think about any theory, even Newtonian gravity, 00:49:27.560 --> 00:49:30.105 you can certainly imagine implications 00:49:30.105 --> 00:49:31.480 of Newtonian gravity that you can 00:49:31.480 --> 00:49:34.440 calculate that nobody's ever measured. 00:49:34.440 --> 00:49:38.686 So I think in practice we tend to accept theories 00:49:38.686 --> 00:49:41.060 when they have made enough measurements that we've tested 00:49:41.060 --> 00:49:44.910 so that the theory becomes persuasive. 00:49:44.910 --> 00:49:47.970 And when that happens, I think we should, at the same time, 00:49:47.970 --> 00:49:50.420 take seriously whatever those words mean, 00:49:50.420 --> 00:49:54.670 the implications that the theory has for things that cannot be 00:49:54.670 --> 00:49:56.270 directly tested. 00:49:56.270 --> 00:49:58.010 As far as the other pocket universes, 00:49:58.010 --> 00:49:59.385 some people think it's important, 00:49:59.385 --> 00:50:03.280 and maybe I do too, that even though it's 00:50:03.280 --> 00:50:06.880 highly unlikely, incredibly unlikely, unbelievably unlikely 00:50:06.880 --> 00:50:09.800 that we'll ever acquire direct observational evidence 00:50:09.800 --> 00:50:12.830 for another pocket universe, it's not really in principle 00:50:12.830 --> 00:50:16.180 impossible because of the fact that pocket universes can, 00:50:16.180 --> 00:50:18.210 in principle, collide. 00:50:18.210 --> 00:50:21.020 So we could, in principle, describe with evidence 00:50:21.020 --> 00:50:23.865 that our universe has had contact with another pocket 00:50:23.865 --> 00:50:24.740 universe in the past. 00:50:27.250 --> 00:50:28.170 Yes. 00:50:28.170 --> 00:50:29.840 AUDIENCE: What determines the stability 00:50:29.840 --> 00:50:33.190 of a particular vacuum state? 00:50:33.190 --> 00:50:36.785 Is it simply things with higher vacuum energies are less stable 00:50:36.785 --> 00:50:39.035 and things with lower vacuum energies are more stable? 00:50:42.000 --> 00:50:43.750 PROFESSOR: The question is what determines 00:50:43.750 --> 00:50:47.260 the stability of the different vacua. 00:50:47.260 --> 00:50:48.940 Is it simply that higher energy ones 00:50:48.940 --> 00:50:51.990 are more unstable and lower energy ones are more stable 00:50:51.990 --> 00:50:54.630 or is it more complicated than that? 00:50:54.630 --> 00:50:56.140 And the answer, as far as I know, 00:50:56.140 --> 00:50:59.450 is that there is a trend for higher energy ones 00:50:59.450 --> 00:51:02.639 to be more unstable and lower energy ones to be more stable. 00:51:02.639 --> 00:51:03.930 But it's not as simple as that. 00:51:03.930 --> 00:51:06.450 There are also wide variations that 00:51:06.450 --> 00:51:08.390 are independent of the energy density. 00:51:08.390 --> 00:51:10.410 AUDIENCE: If the one that we're living in 00:51:10.410 --> 00:51:14.800 is incredibly is really ridiculously close to zero 00:51:14.800 --> 00:51:19.400 in a city that seems to make it incredibly unlikely that we 00:51:19.400 --> 00:51:25.910 would pay anything else I soon 00:51:25.910 --> 00:51:27.570 PROFESSOR: Right. 00:51:27.570 --> 00:51:29.330 The question is if our universe has 00:51:29.330 --> 00:51:31.310 such has such a small energy density 00:51:31.310 --> 00:51:33.460 relative to the average. 00:51:33.460 --> 00:51:35.980 Wouldn't that mean that we should also 00:51:35.980 --> 00:51:39.040 expect to be much more long-lived than average? 00:51:39.040 --> 00:51:41.140 And the answer is I guess so. 00:51:41.140 --> 00:51:43.920 But as far as the effect on the Swiss cheese 00:51:43.920 --> 00:51:46.579 picture that I described for the ultimate future, 00:51:46.579 --> 00:51:48.245 it doesn't change the words that I used. 00:51:48.245 --> 00:51:52.320 It just changes how frequent those decays would be. 00:51:52.320 --> 00:51:55.470 But since the future of this pocket universe, 00:51:55.470 --> 00:51:58.280 if this picture is right, will be infinite, 00:51:58.280 --> 00:52:02.280 decays will happen no matter how small the probability is. 00:52:02.280 --> 00:52:05.550 An infinite number of decays will happen in fact. 00:52:05.550 --> 00:52:07.050 OK we should probably go on now even 00:52:07.050 --> 00:52:08.380 if there are more questions. 00:52:08.380 --> 00:52:12.960 We have a whole term to discuss things like this. 00:52:12.960 --> 00:52:15.120 The next thing I want to do is handle 00:52:15.120 --> 00:52:17.170 some housekeeping details. 00:52:17.170 --> 00:52:19.700 I'd like to arrange office hours. 00:52:19.700 --> 00:52:23.220 And the problem sets are due on Friday, 00:52:23.220 --> 00:52:25.730 so what [? Tsingtao ?] and I thought 00:52:25.730 --> 00:52:28.220 was that a good time for office hours 00:52:28.220 --> 00:52:30.740 would be on Wednesdays and Thursdays. 00:52:30.740 --> 00:52:33.480 One of us on each of those days. 00:52:33.480 --> 00:52:35.470 It turns out that I can't really do Thursdays, 00:52:35.470 --> 00:52:37.870 so one of us on each of those days 00:52:37.870 --> 00:52:39.430 ends up meaning that I'll probably 00:52:39.430 --> 00:52:41.290 be having office hours on Wednesdays. 00:52:41.290 --> 00:52:42.790 This is all provisional depending 00:52:42.790 --> 00:52:45.202 on how it works with you folks. 00:52:45.202 --> 00:52:46.660 And [? Tsingtao ?] will probably be 00:52:46.660 --> 00:52:49.660 having office hours on Thursdays. 00:52:49.660 --> 00:52:51.784 Generally speaking, if one wants to have an office 00:52:51.784 --> 00:52:53.200 hour that most people can come to, 00:52:53.200 --> 00:52:56.520 I think it should be in the late afternoon. 00:52:56.520 --> 00:52:59.350 So maybe we'll start by discussing my office hours 00:52:59.350 --> 00:53:01.500 since it comes before [? Tsingtao's, ?] Wednesday 00:53:01.500 --> 00:53:03.300 versus Thursday. 00:53:03.300 --> 00:53:07.450 So on Wednesday, I can do an office hour 00:53:07.450 --> 00:53:13.220 in the late, normal afternoon, which might mean 4:00 to 5:00 00:53:13.220 --> 00:53:16.590 I think after five some people have sports activities 00:53:16.590 --> 00:53:17.090 and things. 00:53:17.090 --> 00:53:20.224 We're told to try to avoid those hours. 00:53:20.224 --> 00:53:22.265 So 4:00 to 5:00 would be a reasonable possibility 00:53:22.265 --> 00:53:24.610 for my office hour on Wednesday. 00:53:24.610 --> 00:53:26.464 If that doesn't work, I could stay 00:53:26.464 --> 00:53:28.130 and have the office hour in the evening. 00:53:28.130 --> 00:53:30.290 That's actually what I did two years ago. 00:53:30.290 --> 00:53:33.140 I had an office hour from 7:30 to 8:30. 00:53:33.140 --> 00:53:35.030 It was also Wednesdays-- I forget. 00:53:35.030 --> 00:53:38.130 But it was in the evening, and that's a possibility. 00:53:38.130 --> 00:53:44.200 So let me ask if I have my office hour from 4:00 to 5:00 00:53:44.200 --> 00:53:47.490 on Wednesdays, how many of you who 00:53:47.490 --> 00:53:50.090 might be interested in coming would not be able to come? 00:53:53.150 --> 00:53:57.500 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 00:53:57.500 --> 00:54:02.970 A significant number, but most of you can come at least. 00:54:02.970 --> 00:54:06.760 Let me ask the corresponding question for the evening. 00:54:06.760 --> 00:54:10.490 Suppose I made the office hour from 7:30 to 8:30 00:54:10.490 --> 00:54:12.690 in the evening on Wednesdays. 00:54:12.690 --> 00:54:17.120 In that case, how many of you who might want to come 00:54:17.120 --> 00:54:18.230 would not be able to come? 00:54:21.158 --> 00:54:28.170 1, 2, 3 5, 6, so it's a smaller number, but not vastly smaller. 00:54:33.100 --> 00:54:35.760 OK I think I'll do it in the evening for the benefit 00:54:35.760 --> 00:54:37.780 of the difference between those two groups. 00:54:37.780 --> 00:54:40.480 And the evening also has the little slight advantage 00:54:40.480 --> 00:54:43.220 that it can be a little more open-ended if people still 00:54:43.220 --> 00:54:46.270 have questions after the normal time is over. 00:54:46.270 --> 00:54:56.270 So I will make my office hour on Wednesday's from 7:30 to 8:30. 00:54:56.270 --> 00:54:58.990 Is that particular hour as good an hour as any on Wednesday 00:54:58.990 --> 00:54:59.554 evening. 00:54:59.554 --> 00:55:01.470 Would people want to move it earlier or later? 00:55:05.410 --> 00:55:08.651 Any suggestions for moving it earlier or later? 00:55:08.651 --> 00:55:11.151 AUDIENCE: I know people have sports til technically at least 00:55:11.151 --> 00:55:17.354 7:00, but if it's 6:30 to 7:30 might be a little-- 00:55:17.354 --> 00:55:18.020 PROFESSOR: 6:30? 00:55:18.020 --> 00:55:21.400 You'll be starting at 6-- starting at 6:30 versus-- 6:30 00:55:21.400 --> 00:55:24.480 to 7:30, starting at 6:30. 00:55:24.480 --> 00:55:26.884 Well, I'd be happy to do that, but I 00:55:26.884 --> 00:55:28.800 suspect we might run into problems with people 00:55:28.800 --> 00:55:30.940 who have sport activities, but let's see. 00:55:30.940 --> 00:55:34.290 How many of you would be inconvenienced 00:55:34.290 --> 00:55:36.277 if I started at 6:30 instead of 7:30? 00:55:39.079 --> 00:55:42.780 3, 4, 5, 6, a number. 00:55:42.780 --> 00:55:47.440 So I think we'll honor that and start at 7:30. 00:55:47.440 --> 00:55:49.910 I assume 7 is also a bit of a problem for those people. 00:55:55.225 --> 00:55:55.850 We'll say 7:30. 00:56:22.287 --> 00:56:24.245 Now, I have to announce that this week is going 00:56:24.245 --> 00:56:26.661 to unfortunately have to be an exception because I already 00:56:26.661 --> 00:56:28.670 have plans for Wednesday night. 00:56:28.670 --> 00:56:32.030 So for this week, I think the best thing-- 00:56:32.030 --> 00:56:33.730 the only possible thing, probably 00:56:33.730 --> 00:56:35.810 the best-- it's almost the only possible thing 00:56:35.810 --> 00:56:38.700 would be 4:00 to 5:00 on Wednesday. 00:56:38.700 --> 00:56:40.040 Wednesday's bit tomorrow. 00:56:40.040 --> 00:56:42.412 I'll send you all an email when I find a room for that. 00:56:42.412 --> 00:56:44.370 I think I'll probably not have it in my office, 00:56:44.370 --> 00:56:46.850 but maybe it will be in my office. 00:56:46.850 --> 00:56:47.680 Comment up there? 00:56:47.680 --> 00:56:49.930 AUDIENCE: Oh, I was just going to ask where, but you-- 00:56:49.930 --> 00:56:51.132 PROFESSOR: Where? 00:56:51.132 --> 00:56:53.090 OK, I guess then the fourth option's my office. 00:56:53.090 --> 00:56:54.714 I was hoping to put a sign of my office 00:56:54.714 --> 00:56:56.950 if we're someplace other than my office. 00:56:56.950 --> 00:57:00.260 So should put this on the board too. 00:57:00.260 --> 00:57:07.110 Tomorrow 4:00 to 5:00 PM. 00:57:15.790 --> 00:57:17.770 So be at my office or I'll send email. 00:57:27.470 --> 00:57:28.416 Yes? 00:57:28.416 --> 00:57:32.280 AUDIENCE: How will we be turning in the Thursday problem set? 00:57:32.280 --> 00:57:35.910 PROFESSOR: We're going to talk about that now. 00:57:35.910 --> 00:57:38.819 For Thursday, for [? Tsingtao, ?] I remember 00:57:38.819 --> 00:57:39.860 you had some constraints. 00:57:39.860 --> 00:57:41.026 So what was possible? 00:57:41.026 --> 00:57:41.760 TSINGTAO: Yeah. 00:57:41.760 --> 00:57:44.215 So I usually leave around 7:00 PM, 00:57:44.215 --> 00:57:47.652 so I have appointment [? meeting ?], 00:57:47.652 --> 00:57:52.562 and today is probably not very good at 4:00 PM. 00:57:56.090 --> 00:57:58.800 PROFESSOR: So 4:00 to 5:00 is a possibility for [? Tsingtao ?] 00:57:58.800 --> 00:58:02.290 on Thursday, and I guess later than that. 00:58:02.290 --> 00:58:04.422 But should be over by 5:00-- by 7:00 either 00:58:04.422 --> 00:58:06.130 or do you want it to be over before then. 00:58:06.130 --> 00:58:08.380 TSINGTAO: Oh, 6:00 to 7:002 Oh, 6:00 to 7:002 I guess. 00:58:08.380 --> 00:58:10.412 PROFESSOR: 6:00 to 7:00 would be OK? 00:58:10.412 --> 00:58:11.495 TSINGTAO: Yeah, that's OK. 00:58:17.540 --> 00:58:20.587 PROFESSOR: OK, so let's start with 4:00 to 5:00. 00:58:20.587 --> 00:58:23.170 If [? Tsingtao ?] was to have an office hour from 4:00 to 5:00 00:58:23.170 --> 00:58:26.990 on Thursdays, how many of you think you might want to go 00:58:26.990 --> 00:58:29.640 would be unable to? 00:58:29.640 --> 00:58:31.100 Wow, tons! 00:58:31.100 --> 00:58:34.750 OK, that seems more than half of you I think. 00:58:34.750 --> 00:58:36.400 So I guess we try to avoid that. 00:58:36.400 --> 00:58:40.235 This impact's probably an athletic region, 00:58:40.235 --> 00:58:44.250 but maybe we'll have to do that for lack of an alternative. 00:58:44.250 --> 00:58:46.240 Suppose it were 5:00 to 6:00. 00:58:46.240 --> 00:58:48.907 How many of you who would be interesting in coming-- who 00:58:48.907 --> 00:58:50.740 might be interesting in coming, I should say 00:58:50.740 --> 00:58:52.180 I guess because it'll vary from week to week-- 00:58:52.180 --> 00:58:53.190 but how many of you who think you might 00:58:53.190 --> 00:58:54.780 be interested in coming would not 00:58:54.780 --> 00:58:58.620 be able to come from 5:00 to 6:00 on Thursdays. 00:58:58.620 --> 00:58:59.660 OK, a small group. 00:58:59.660 --> 00:59:03.872 1, 2, 3, 4, 5, 6, 7. 00:59:03.872 --> 00:59:06.810 Looks to me like 7. 00:59:06.810 --> 00:59:10.090 And let's say, I said 4:00-- That 00:59:10.090 --> 00:59:13.850 was at 6:00-- that was 5:00 to 6:00. 00:59:13.850 --> 00:59:17.170 So maybe we should next try 5:30 to 6:30 in smaller increments 00:59:17.170 --> 00:59:17.850 here. 00:59:17.850 --> 00:59:20.100 If we're 5:30 to 6:30, how many of you 00:59:20.100 --> 00:59:21.210 would not be able to come? 00:59:24.745 --> 00:59:27.800 Looks like pretty much the same people. 00:59:27.800 --> 00:59:30.330 And if it were 6:00 to 7:00, how many of you 00:59:30.330 --> 00:59:33.050 would not be able to come? 00:59:33.050 --> 00:59:36.810 Same people, I think it is literally the same people. 00:59:36.810 --> 00:59:37.680 OK. 00:59:37.680 --> 00:59:40.450 So it looks like 4:00 to 5:00 is very bad. 00:59:40.450 --> 00:59:44.200 And all other times are about equivalent. 00:59:44.200 --> 00:59:46.695 So I think if all other times are bad equivalently, 00:59:46.695 --> 00:59:50.930 we probably might as well make it 5:00 to 6:00. 00:59:50.930 --> 00:59:53.313 And that way [? Tsingtao ?] can get off 00:59:53.313 --> 00:59:57.670 to an earliest possible start to wherever he's going at 7:00, 00:59:57.670 --> 01:00:00.620 and it also means a little more flexibility in the end 01:00:00.620 --> 01:00:02.005 if there are more questions. 01:00:34.969 --> 01:00:36.752 AUDIENCE: Where is that located? 01:00:36.752 --> 01:00:38.210 PROFESSOR: That also, I think, will 01:00:38.210 --> 01:00:40.685 require us to get a room which will be announced. 01:00:54.860 --> 01:00:56.980 So I will try to arrange rooms tomorrow 01:00:56.980 --> 01:00:59.390 morning and send it by email, and I 01:00:59.390 --> 01:01:01.140 guess I'll post it on the website as well. 01:01:04.360 --> 01:01:07.900 Any other organizational-- and questions 01:01:07.900 --> 01:01:10.080 limited to organizational questions now? 01:01:10.080 --> 01:01:12.130 Get back to physics later. 01:01:12.130 --> 01:01:13.880 Any organizational questions before we 01:01:13.880 --> 01:01:16.340 start on Doppler shifts? 01:01:16.340 --> 01:01:17.612 Yes? 01:01:17.612 --> 01:01:20.067 AUDIENCE: If I can't make a single office hour, 01:01:20.067 --> 01:01:23.020 how should I field questions when I have questions? 01:01:23.020 --> 01:01:25.409 PROFESSOR: A good question. 01:01:25.409 --> 01:01:27.700 Yeah, there may be some people, and apparently there is 01:01:27.700 --> 01:01:29.825 at least one who cannot make either of these times, 01:01:29.825 --> 01:01:31.700 even though we tried to optimize things. 01:01:31.700 --> 01:01:34.582 So by all means, don't feel like you 01:01:34.582 --> 01:01:36.040 don't have a channel for questions. 01:01:36.040 --> 01:01:37.715 If you have a question, send an email to 01:01:37.715 --> 01:01:39.250 either me, or [? Tsingtao, ?] or both. 01:01:39.250 --> 01:01:40.930 And we'll either answer it together with you 01:01:40.930 --> 01:01:43.360 or answer you by email depending on what the question is 01:01:43.360 --> 01:01:46.484 and what seems useful. 01:01:46.484 --> 01:01:47.650 And that goes for everybody. 01:01:54.720 --> 01:01:57.600 In that case, if everybody's on board, 01:01:57.600 --> 01:02:02.060 we will now start the actual material for the term. 01:02:02.060 --> 01:02:03.599 Well, the overview is an overview 01:02:03.599 --> 01:02:06.015 of the material for the term, but not at the standard pace 01:02:06.015 --> 01:02:08.880 and the standard level of detail. 01:02:08.880 --> 01:02:11.200 So what I want to talk about this week-- 01:02:11.200 --> 01:02:13.430 and I guess I'll only get to start today and finish 01:02:13.430 --> 01:02:15.106 on Thursday-- I had planned to tell you 01:02:15.106 --> 01:02:17.480 everything you need to know for the problem set by today, 01:02:17.480 --> 01:02:20.160 but that's not going to happen. 01:02:20.160 --> 01:02:24.240 So I don't-- if people complain, we could consider postponing 01:02:24.240 --> 01:02:28.321 the due date of the problem set, so consider that an option. 01:02:28.321 --> 01:02:30.320 But probably you could do the problem set anyway 01:02:30.320 --> 01:02:32.970 because it is all described in lecture notes. 01:02:32.970 --> 01:02:35.670 But if any of you have difficulties meeting 01:02:35.670 --> 01:02:38.360 that deadline, it will be a somewhat flexible deadline 01:02:38.360 --> 01:02:40.110 this week because of the fact that I'm not 01:02:40.110 --> 01:02:43.270 covering the material today as I had planned. 01:02:43.270 --> 01:02:47.080 And I'll admit that's not necessarily a good thing 01:02:47.080 --> 01:02:50.680 to do in terms of problem set. 01:02:50.680 --> 01:02:54.420 So we're going to begin the course, in principle, 01:02:54.420 --> 01:02:58.490 by talking about Hubble's law, although Hubble's law will 01:02:58.490 --> 01:03:01.050 rapidly lead us to the question of the Doppler shift, 01:03:01.050 --> 01:03:03.150 which is what I'll mainly be talking 01:03:03.150 --> 01:03:07.650 about for the rest of today and for most of Thursday. 01:03:07.650 --> 01:03:17.920 Hubble's law itself is a simple equation 01:03:17.920 --> 01:03:24.810 that v is equal to h r, where v is the recession 01:03:24.810 --> 01:03:33.365 velocity of any typical galaxy. 01:03:38.126 --> 01:03:39.500 Hubble's law is not an exact law, 01:03:39.500 --> 01:03:42.754 so individual galaxies will deviate from Hubble's law. 01:03:42.754 --> 01:03:44.420 But in principle, Hubble's law tells you 01:03:44.420 --> 01:03:48.000 what the recession velocity is of a galaxy, at least 01:03:48.000 --> 01:03:50.160 to reasonable accuracy. 01:03:50.160 --> 01:04:00.880 Where h is what is often called Hubble's constant. 01:04:00.880 --> 01:04:04.290 Sometimes, it is called the Hubble parameter. 01:04:04.290 --> 01:04:08.410 I like actually-- it's called the Hubble expansion rate. 01:04:08.410 --> 01:04:10.720 The problem with calling Hubble's constant 01:04:10.720 --> 01:04:12.310 is that it's not really a constant 01:04:12.310 --> 01:04:13.970 over the lifetime of the universe. 01:04:13.970 --> 01:04:17.202 It's a constant over the lifetime of an astronomer, 01:04:17.202 --> 01:04:19.410 but not a constant over the lifetime of the universe? 01:04:19.410 --> 01:04:21.720 And we'll be talking about universes, not astronomers, 01:04:21.720 --> 01:04:23.550 at least for the most part. 01:04:23.550 --> 01:04:26.302 And even over history, it's not a constant 01:04:26.302 --> 01:04:28.010 because the estimate of Hubble's constant 01:04:28.010 --> 01:04:31.160 has actually changed by a factor of about 10 or so 01:04:31.160 --> 01:04:33.730 since Hubble's original estimate. 01:04:33.730 --> 01:04:37.500 And the r that appears here is the distance to the galaxy. 01:04:48.360 --> 01:04:51.250 And if you look at the lecture notes from two years ago, 01:04:51.250 --> 01:04:53.230 they start out by saying that Hubble's law was 01:04:53.230 --> 01:04:56.150 discovered by Hubble in 1929. 01:04:56.150 --> 01:04:59.430 When I looked at that first sentence in my notes, 01:04:59.430 --> 01:05:01.430 and when I started to revise them for this year, 01:05:01.430 --> 01:05:03.980 I realized that I heard that that statement has 01:05:03.980 --> 01:05:05.525 become controversial. 01:05:05.525 --> 01:05:07.525 Almost everything in cosmology is controversial, 01:05:07.525 --> 01:05:09.720 so even that statement is controversial. 01:05:09.720 --> 01:05:12.650 There are claims that Lemaitre really 01:05:12.650 --> 01:05:15.280 deserves credit for Hubble's law rather than Hubble. 01:05:15.280 --> 01:05:17.412 And there's some validity to that claim. 01:05:17.412 --> 01:05:19.370 There's also some [? intrigued ?] that happens, 01:05:19.370 --> 01:05:21.320 if you want to read about this. 01:05:21.320 --> 01:05:23.794 It was discovered by several of-- I think 01:05:23.794 --> 01:05:26.210 amateur historians I think is what they are often referred 01:05:26.210 --> 01:05:32.277 to in the press-- that we know mainly of Lemaitre's work-- we 01:05:32.277 --> 01:05:34.610 being the Western speaking, the Western English speaking 01:05:34.610 --> 01:05:37.490 world-- know mainly of a Lemaitre's work 01:05:37.490 --> 01:05:41.830 through a 1931 translation in a 1927 paper 01:05:41.830 --> 01:05:45.270 he wrote about the foundations of cosmology. 01:05:45.270 --> 01:05:50.140 And it turned out that several significant seeming paragraphs 01:05:50.140 --> 01:05:52.950 in the 1927 French article somehow 01:05:52.950 --> 01:05:57.090 didn't make it to the 1931 English translation, paragraphs 01:05:57.090 --> 01:06:00.970 about the Hubble constant. 01:06:00.970 --> 01:06:03.739 And for a while, that seemed like dirty play 01:06:03.739 --> 01:06:06.280 and there were accusations that Hubble, or friends of Hubble, 01:06:06.280 --> 01:06:09.260 had suppressed those paragraphs when 01:06:09.260 --> 01:06:11.700 the article was translated. 01:06:11.700 --> 01:06:15.330 The truth finally was discovered a couple years ago 01:06:15.330 --> 01:06:19.710 by a physicist named Mario Livio who actually was on the Daily 01:06:19.710 --> 01:06:21.210 Show a couple nights ago by the way. 01:06:21.210 --> 01:06:25.540 He has a book out now, not about this, but about other things. 01:06:25.540 --> 01:06:26.990 But anyway, he discovered by going 01:06:26.990 --> 01:06:34.470 through the archives of the monthly notices of astronomy, 01:06:34.470 --> 01:06:36.660 which is where the article was published in English. 01:06:36.660 --> 01:06:38.243 And turned out it was Lemaitre himself 01:06:38.243 --> 01:06:40.590 he removed those paragraphs. 01:06:40.590 --> 01:06:42.880 The paragraphs basically gave a numerical estimate 01:06:42.880 --> 01:06:47.250 of the Hubble constant, but by 1931 Hubble's papered already 01:06:47.250 --> 01:06:50.110 been published, so Lemaitre felt that it was only 01:06:50.110 --> 01:06:52.900 a less accurate estimate of the same quantity 01:06:52.900 --> 01:06:58.240 that Hubble had estimated, so he cut it out of his translation. 01:06:58.240 --> 01:07:00.500 What certainly is true is that Lemaitre 01:07:00.500 --> 01:07:02.880 knew about Hubble's law on theoretical grounds. 01:07:02.880 --> 01:07:06.465 Lemaitre was building a model of an expanding universe. 01:07:06.465 --> 01:07:08.340 I don't know if he is really the first person 01:07:08.340 --> 01:07:11.330 to know that an expanding universe model gave rise 01:07:11.330 --> 01:07:15.870 to a linear relationship between velocity and distance, 01:07:15.870 --> 01:07:20.930 but he certainly did know about it and understood Hubble's law 01:07:20.930 --> 01:07:24.350 and give an estimate of it based on data. 01:07:24.350 --> 01:07:26.440 What he did not do, however, is try 01:07:26.440 --> 01:07:28.150 to use data to actually show that there 01:07:28.150 --> 01:07:29.850 was a linear relationship. 01:07:29.850 --> 01:07:32.670 What Lemaitre did, in those paragraphs 01:07:32.670 --> 01:07:35.010 that were not translated, was simply 01:07:35.010 --> 01:07:38.690 to look at a large group of galaxies, 01:07:38.690 --> 01:07:41.840 figure an average value for v and an average value of r 01:07:41.840 --> 01:07:44.704 and determine h from dividing those two averages. 01:07:44.704 --> 01:07:46.120 And he admitted that there was not 01:07:46.120 --> 01:07:48.450 really good enough data to tell if the relationship is linear 01:07:48.450 --> 01:07:49.050 or not. 01:07:52.430 --> 01:07:54.880 I think it is definitely fair to say that Hubble 01:07:54.880 --> 01:08:00.380 is the person who deserves credit for arguing first really 01:08:00.380 --> 01:08:03.620 with a fairly weak argument, but then got stronger over time, 01:08:03.620 --> 01:08:05.510 that there really is astronomical evidence 01:08:05.510 --> 01:08:12.689 for this linear relationship between velocity and distance. 01:08:12.689 --> 01:08:14.980 So probably it will continue to be called Hubble's law. 01:08:14.980 --> 01:08:16.563 If you look in Wikipedia, it tells you 01:08:16.563 --> 01:08:19.170 either one is acceptable at the moment, 01:08:19.170 --> 01:08:20.810 but Wikipedia articles change rapidly, 01:08:20.810 --> 01:08:25.170 so we'll see what it says next year. 01:08:25.170 --> 01:08:27.140 It's also mentioned that we should probably 01:08:27.140 --> 01:08:30.170 root for Lemaitre since Lemaitre, it turns out-- well, 01:08:30.170 --> 01:08:32.210 he was a Belgian priest, it was often described, 01:08:32.210 --> 01:08:35.569 but he was also an MIT student, had a Ph.D. for MIT, 01:08:35.569 --> 01:08:37.060 which he received in 1927. 01:08:37.060 --> 01:08:38.765 You can actually read his thesis. 01:08:38.765 --> 01:08:40.389 When I was writing my [INAUDIBLE] book, 01:08:40.389 --> 01:08:42.189 I remember going to the MIT archives 01:08:42.189 --> 01:08:44.939 and actually picking up his thesis and reading it. 01:08:44.939 --> 01:08:47.355 It's not that well-written actually, but it's interesting. 01:08:53.540 --> 01:08:55.559 Although he got his Ph.D. from MIT, 01:08:55.559 --> 01:08:57.979 it also turns out that he did most of his work 01:08:57.979 --> 01:09:02.859 down Mass Ave at the Harvard College Observatory, 01:09:02.859 --> 01:09:04.340 but the Harvard College Observatory 01:09:04.340 --> 01:09:06.130 did not give degrees in those days. 01:09:06.130 --> 01:09:07.550 It was just an observatory. 01:09:07.550 --> 01:09:09.540 So he wanted to get a degree, so he signed up 01:09:09.540 --> 01:09:13.670 at MIT for the Ph.D. Program and wrote a thesis, 01:09:13.670 --> 01:09:17.060 received a Ph.D. 01:09:17.060 --> 01:09:20.029 Onward, what I really want to talk about 01:09:20.029 --> 01:09:23.140 is, after mentioning Hubble's law-- 01:09:23.140 --> 01:09:26.220 so Hubble's law as an indication that the universe is expanding. 01:09:26.220 --> 01:09:29.312 And we'll talk more about the history of all this later, 01:09:29.312 --> 01:09:31.270 and it actually is very well-described in Steve 01:09:31.270 --> 01:09:33.729 Weinberg's book. 01:09:33.729 --> 01:09:36.597 But initially, Einstein proposed a model 01:09:36.597 --> 01:09:38.680 of the universe that was static, and it was really 01:09:38.680 --> 01:09:42.210 Hubble who convinced Einstein that observationally 01:09:42.210 --> 01:09:46.350 the universe does not appear to be static, but does 01:09:46.350 --> 01:09:50.399 appear instead to obey this expansion law. 01:09:50.399 --> 01:09:54.060 So that gave rise to the theory of the expanding universe. 01:09:54.060 --> 01:09:57.040 But what I want to talk about today 01:09:57.040 --> 01:10:03.666 is how one measures the v that appears here. 01:10:03.666 --> 01:10:05.290 There's also a big discussion about how 01:10:05.290 --> 01:10:07.890 one measures r, the distance. 01:10:07.890 --> 01:10:11.460 And that is, I think, rather well-done in Steve Weinberg's 01:10:11.460 --> 01:10:15.070 book, and I'm going to pretty much leave it 01:10:15.070 --> 01:10:17.350 to your reading of Steve Weinberg's book 01:10:17.350 --> 01:10:22.340 to learn about how distances to distant galaxies are estimated. 01:10:22.340 --> 01:10:24.610 Roughly-speaking, I might just say 01:10:24.610 --> 01:10:27.600 that they are estimated by finding objects 01:10:27.600 --> 01:10:30.580 in those distant galaxies whose brightnesses you think 01:10:30.580 --> 01:10:32.520 you know, by one means or another. 01:10:32.520 --> 01:10:35.110 And a complicated story is what objects are there 01:10:35.110 --> 01:10:37.320 in brightnesses we think we know. 01:10:37.320 --> 01:10:39.230 But once you find an object whose brightness 01:10:39.230 --> 01:10:42.130 you think you know, those go by the general name 01:10:42.130 --> 01:10:45.490 of standard candles, a standard candle 01:10:45.490 --> 01:10:48.450 being an object whose brightness you know, 01:10:48.450 --> 01:10:50.460 then you can tell how far the object is 01:10:50.460 --> 01:10:51.720 by how bright it appears. 01:10:51.720 --> 01:10:54.120 And that becomes a very straightforward way 01:10:54.120 --> 01:10:57.370 of estimating distances, and that is the only way 01:10:57.370 --> 01:11:01.569 we really have of estimating distances of distant galaxies. 01:11:01.569 --> 01:11:04.110 So it's a much longer story than what I just said, and you'll 01:11:04.110 --> 01:11:07.000 read about it in Weinberg's book. 01:11:07.000 --> 01:11:09.540 The velocity is measured by the Doppler shift, 01:11:09.540 --> 01:11:11.950 and that's what lecture notes one are mainly about, 01:11:11.950 --> 01:11:14.910 and that's what I'll be talking about for the remaining 01:11:14.910 --> 01:11:19.120 few minutes of today's class. 01:11:19.120 --> 01:11:24.560 And what we want to do in the course of this set of lecture 01:11:24.560 --> 01:11:27.560 notes, this week of class I guess it will be, 01:11:27.560 --> 01:11:30.980 is understand how to calculate the Doppler 01:11:30.980 --> 01:11:35.690 shift both non-relativistically and relativistically, 01:11:35.690 --> 01:11:40.440 and we'll just work out the primary cases of observer 01:11:40.440 --> 01:11:44.690 stationary source moving, source stationary observer moving, 01:11:44.690 --> 01:11:48.380 and all in a line, for both the relativistic and 01:11:48.380 --> 01:11:51.590 non-relativistic cases. 01:11:51.590 --> 01:11:54.960 So I think I'll launch into the first calculation, which 01:11:54.960 --> 01:11:57.790 you might even have time to finish. 01:11:57.790 --> 01:11:59.600 I'd like to consider a case where 01:11:59.600 --> 01:12:02.610 the observer is stationary and the source is moving, 01:12:02.610 --> 01:12:05.357 which is normally how we think of the distant galaxies. 01:12:05.357 --> 01:12:07.690 We work in our own reference frame, so we're stationary, 01:12:07.690 --> 01:12:09.180 the galaxy is moving. 01:12:09.180 --> 01:12:11.280 How do we calculate this redshift 01:12:11.280 --> 01:12:13.420 I should say at the asset here, however-- 01:12:13.420 --> 01:12:15.420 I don't know if I said it in the lecture notes-- 01:12:15.420 --> 01:12:18.090 that the cosmological redshift is actually 01:12:18.090 --> 01:12:21.170 a little bit different from what we're calculating this week. 01:12:21.170 --> 01:12:26.830 This week, we're calculating the special relativity redshift. 01:12:26.830 --> 01:12:31.020 But cosmology is not controlled by special relativity 01:12:31.020 --> 01:12:34.040 because special relativity does not describe gravity, 01:12:34.040 --> 01:12:38.910 and gravity plays a major role in cosmology. 01:12:38.910 --> 01:12:41.990 So the cosmological redshift, we will talk about a little 01:12:41.990 --> 01:12:44.730 later in the course, in a more precise way. 01:12:44.730 --> 01:12:48.700 But for now, we, like Hubble-- Hubble didn't know any better-- 01:12:48.700 --> 01:12:52.779 are ignoring gravity, which is OK for the nearby stars, 01:12:52.779 --> 01:12:54.820 and the further away they are, the more important 01:12:54.820 --> 01:12:58.810 these gravitational influences are, and ignoring gravity one 01:12:58.810 --> 01:13:03.400 could just use special relativity or even 01:13:03.400 --> 01:13:07.750 Newtonian kinematics to calculate 01:13:07.750 --> 01:13:12.020 the relationship between v and the redshift. 01:13:12.020 --> 01:13:15.309 And that's what we'll be talking about. 01:13:15.309 --> 01:13:17.350 So the first problem that we want to talk about-- 01:13:17.350 --> 01:13:22.220 and I guess I'll just set it up and that's as far as we get-- 01:13:22.220 --> 01:13:31.970 will be a problem where there's a source of radiation, which 01:13:31.970 --> 01:13:37.910 is moving to the right in our diagram with a velocity, v, 01:13:37.910 --> 01:13:46.115 and an observer who is stationary. 01:13:49.180 --> 01:13:51.960 Now of course, all these are frame dependent statements, 01:13:51.960 --> 01:13:53.410 but we're working in a frame where 01:13:53.410 --> 01:13:55.540 the observer is stationary. 01:13:55.540 --> 01:13:58.420 And we're also going to assume for the non-relativistic case, 01:13:58.420 --> 01:14:02.385 that the air-- we'll be talking about sound waves-- but the air 01:14:02.385 --> 01:14:03.970 is stationary in this frame. 01:14:03.970 --> 01:14:06.940 So the frame of backboard is not only the frame of the observer, 01:14:06.940 --> 01:14:09.040 but it's also the frame of the air 01:14:09.040 --> 01:14:12.740 when we're talking about the non-relativistic sound wave 01:14:12.740 --> 01:14:14.890 calculation. 01:14:14.890 --> 01:14:16.920 So to define our notation, we're going 01:14:16.920 --> 01:14:22.580 to let u be equal the velocity of the sound wave. 01:14:26.580 --> 01:14:29.317 And that would normally be measured relative to the air, 01:14:29.317 --> 01:14:31.150 but the air will be at rest in this picture, 01:14:31.150 --> 01:14:33.200 so u will be the velocity of the sound wave 01:14:33.200 --> 01:14:35.870 relative to the diagram. 01:14:35.870 --> 01:14:39.420 v is the velocity of the source already shown. 01:14:46.020 --> 01:14:48.930 And we'll be interested in two time periods, 01:14:48.930 --> 01:14:53.720 delta t sub s where s stands for source, 01:14:53.720 --> 01:15:07.115 which will be the period of the wave at the source, which 01:15:07.115 --> 01:15:09.240 is the same as talking about the period of the wave 01:15:09.240 --> 01:15:12.660 as it would be measured by the source. 01:15:12.660 --> 01:15:18.710 And delta t sub O-- that's supposed 01:15:18.710 --> 01:15:21.700 to be a capital O, not a zero. 01:15:21.700 --> 01:15:34.605 It is the period of the wave at the observer or as observed. 01:15:40.260 --> 01:15:44.470 And the important point, which is maybe obvious qualitatively, 01:15:44.470 --> 01:15:48.010 is that these two times, or time intervals, 01:15:48.010 --> 01:15:50.040 will not be equal to each other. 01:15:50.040 --> 01:15:54.170 And the reason, basically, is that because the source is 01:15:54.170 --> 01:15:57.080 moving-- and I've defined positive v the way 01:15:57.080 --> 01:16:01.170 astronomers would as moving away from us-- because the source is 01:16:01.170 --> 01:16:04.270 moving away from us, each successive wave that 01:16:04.270 --> 01:16:07.690 goes from the source to us has to travel a little bit further. 01:16:07.690 --> 01:16:10.272 And that means that each wave crest is slightly delayed 01:16:10.272 --> 01:16:11.730 from when it would have gotten here 01:16:11.730 --> 01:16:13.650 if everything were stationary. 01:16:13.650 --> 01:16:15.230 And if you delay each wave crest, 01:16:15.230 --> 01:16:18.130 it means the time between crests is larger. 01:16:18.130 --> 01:16:20.880 And that means that we expect here 01:16:20.880 --> 01:16:25.390 that delta t sub O will be larger than delta t sub s 01:16:25.390 --> 01:16:28.160 because of this extra distance that each wave crest has 01:16:28.160 --> 01:16:29.310 to travel. 01:16:29.310 --> 01:16:31.120 And what we'll be doing next time-- 01:16:31.120 --> 01:16:32.870 I think I will just leave the calculations 01:16:32.870 --> 01:16:34.820 for next time-- is calculating that. 01:16:34.820 --> 01:16:36.820 And then doing the same thing for the case where 01:16:36.820 --> 01:16:38.903 the observers moving and the source is stationary, 01:16:38.903 --> 01:16:41.200 and then talking a little bit about special relativity, 01:16:41.200 --> 01:16:43.050 and then repeating both calculations 01:16:43.050 --> 01:16:44.980 with a special relativity situation where 01:16:44.980 --> 01:16:48.150 we'll be talking about light rays and velocities that 01:16:48.150 --> 01:16:50.380 might be comparable to the speed of light. 01:16:50.380 --> 01:16:53.189 So see you folks on Thursday, but maybe I'll 01:16:53.189 --> 01:16:54.980 see some of you at my office hour tomorrow. 01:16:54.980 --> 01:16:58.035 And I will send an email about where exactly that office 01:16:58.035 --> 01:17:00.030 hour will take place.