WEBVTT 00:00.810 --> 00:01.310 Prof: Welcome to prefrosh [newly admitted 00:01.306 --> 00:01.916 students visiting during Yale's "Bulldog Days" program]. 00:01.920 --> 00:04.970 I'm talking about black holes at 8 o'clock this evening. 00:04.970 --> 00:07.380 Come listen to that, too, and in the meantime, 00:07.383 --> 00:09.853 we'll talk about the future of the Universe. 00:09.850 --> 00:12.420 Okay. 00:12.420 --> 00:14.980 Logistical questions? 00:14.980 --> 00:16.190 Anything? 00:16.190 --> 00:16.500 All right. 00:16.500 --> 00:20.290 00:20.290 --> 00:22.430 Where were we? 00:22.430 --> 00:25.280 We were here. 00:25.280 --> 00:29.330 This is the data that demonstrate that the Universe is 00:29.327 --> 00:33.447 filled with dark energy, a kind of anti-gravity that is 00:33.452 --> 00:35.822 pushing the Universe apart. 00:35.820 --> 00:39.140 And what this is--this is the same data on both of these 00:39.136 --> 00:41.726 plots, just plotted slightly differently. 00:41.730 --> 00:44.500 On the top plot, what they've done is they've 00:44.503 --> 00:48.413 plotted the apparent magnitude of these supernovae versus their 00:48.410 --> 00:49.230 redshift. 00:49.230 --> 00:52.650 And so, apparent magnitude--because the absolute 00:52.652 --> 00:54.912 magnitude is always the same. 00:54.910 --> 00:56.400 These are standard candles. 00:56.400 --> 00:59.060 So, from the apparent magnitude, you can figure out 00:59.060 --> 01:00.710 what the distance modulus is. 01:00.710 --> 01:02.190 That gives you a measure of the distance. 01:02.189 --> 01:04.459 So, this is just distance versus velocity. 01:04.459 --> 01:07.599 Now, we've plotted distance versus velocity of bunch of 01:07.595 --> 01:08.055 times. 01:08.060 --> 01:09.100 That's the Hubble Diagram. 01:09.099 --> 01:12.519 Most of the times we've plotted it, it's come out on a straight 01:12.523 --> 01:12.913 line. 01:12.909 --> 01:16.399 Do you understand why this plot isn't on a straight line? 01:16.400 --> 01:18.990 The top one, I'm talking about, 01:18.992 --> 01:21.932 now--why those lines are curved? 01:21.930 --> 01:23.710 What's the y-axis? 01:23.710 --> 01:25.320 The y-axis is--yes? 01:25.319 --> 01:26.189 Student: It's logarithmic. 01:26.190 --> 01:27.120 Prof: It's logarithmic. 01:27.120 --> 01:28.220 Thank you very much. 01:28.220 --> 01:30.210 Yes, it's magnitude. 01:30.209 --> 01:32.569 Magnitudes are upside down and logarithmic, right? 01:32.569 --> 01:37.579 That's why faint stars have high numbers up at the top. 01:37.580 --> 01:41.000 And because one axis is logarithmic and the other axis 01:40.996 --> 01:42.926 isn't, of course, it curves. 01:42.930 --> 01:46.090 You could--the way--if you want a nice straight line, 01:46.086 --> 01:48.936 you just make this axis logarithmic, as well. 01:48.940 --> 01:53.210 What we've done down on the bottom is just subtracted off 01:53.207 --> 01:57.857 the empty Universe--a Universe with no matter and no energy in 01:57.855 --> 02:02.045 it--so that you can see more clearly the way these three 02:02.046 --> 02:03.566 lines diverge. 02:03.569 --> 02:07.829 And these three lines are three different models of the 02:07.831 --> 02:08.701 Universe. 02:08.699 --> 02:12.439 And they're denoted by these Ω factors. 02:12.439 --> 02:14.859 Ω _matter, that's the density of matter 02:14.860 --> 02:16.540 divided by the critical density. 02:16.539 --> 02:20.129 Ω_λ, that's the energy density of 02:20.130 --> 02:24.700 the dark energy divided by that same critical density. 02:24.699 --> 02:28.829 And down here is an Ω _matter of 1. 02:28.830 --> 02:31.330 That's the dividing line between a Universe that 02:31.328 --> 02:34.038 re-collapses and a Universe that expands forever. 02:34.039 --> 02:37.129 So, if the Universe were--if the points that we studied were 02:37.133 --> 02:39.443 down here, the Universe would re-collapse. 02:39.440 --> 02:41.130 If they're up here, it wouldn't. 02:41.129 --> 02:45.499 This dotted line here is 1/4 and 0. 02:45.500 --> 02:50.660 1/4 in Ω_matter is the amount of matter that we 02:50.662 --> 02:54.922 actually observe in dark matter and galaxies. 02:54.919 --> 02:57.699 If you go out and count up all the dark matter in the galaxies, 02:57.699 --> 02:59.539 add it all up, you get to about 1/4 of the 02:59.538 --> 03:00.478 critical density. 03:00.479 --> 03:04.919 So, what people were kind of expecting to see was something 03:04.921 --> 03:06.761 between here and here. 03:06.759 --> 03:08.689 And, of course, that wasn't what happened, 03:08.685 --> 03:09.995 as we discussed last time. 03:10.000 --> 03:13.650 Turns out, all the points are too high, and therefore, 03:13.645 --> 03:17.625 you end with a current best fit--the best guess for the way 03:17.633 --> 03:20.663 of the Universe is this solid line here. 03:20.659 --> 03:25.309 This is called the standard model or the concordance model, 03:25.314 --> 03:30.134 where you've got a 1/4 of--the Ω_matter is 1/4, 03:30.129 --> 03:32.469 but there's a whole bunch of dark energy. 03:32.470 --> 03:35.660 3/4 of the Universe is in this mysterious form of dark energy, 03:35.664 --> 03:38.444 which tends to push things apart rather than pull them 03:38.439 --> 03:39.119 together. 03:39.120 --> 03:41.730 That's why these points are above the 0 line, 03:41.726 --> 03:43.026 instead of below it. 03:43.030 --> 03:47.460 And that's the current best idea for what the Universe is. 03:47.460 --> 03:52.040 So, by virtue of the fact that these points lie on the solid 03:52.044 --> 03:56.944 line rather than on somewhere between these two dotted lines, 03:56.940 --> 03:59.640 or perhaps even below, we make this remarkable 03:59.643 --> 04:03.013 conclusion: that the Universe is 3/4 full of something we 04:03.007 --> 04:06.207 absolutely don't understand, called dark energy, 04:06.212 --> 04:08.982 which has the effect of an anti-gravity. 04:08.979 --> 04:12.559 And then, it turns out that Einstein's biggest mistake is 04:12.559 --> 04:13.709 right after all. 04:13.710 --> 04:18.790 Pretty hefty conclusion to lay on the basis of two dozen points 04:18.789 --> 04:22.889 with, let it be said, pretty sizeable error bars on 04:22.886 --> 04:25.176 any one of those points. 04:25.180 --> 04:27.810 And so, I thought, at the start of today, 04:27.811 --> 04:30.641 I would talk about what these points are, 04:30.639 --> 04:33.349 how they are measured, and what could go wrong with 04:33.347 --> 04:34.807 this kind of measurement. 04:34.810 --> 04:39.240 Because, you know, we've transformed what we think 04:39.237 --> 04:42.397 about the Universe based on this. 04:42.399 --> 04:47.769 And so, it behooves one to actually try and understand 04:47.774 --> 04:49.604 what's going on. 04:49.600 --> 04:52.060 I'll come back to that in a minute. 04:52.060 --> 04:53.980 So, what are these points? 04:53.980 --> 04:55.570 What are we measuring? 04:55.569 --> 05:00.449 And why do we think it might even work? 05:00.449 --> 05:03.979 What we are measuring is Type Ia Supernovae. 05:03.980 --> 05:09.000 05:09.000 --> 05:11.270 So, this is typically astronomical nomenclature, 05:11.273 --> 05:11.663 right? 05:11.660 --> 05:12.870 We go out. 05:12.870 --> 05:13.880 We find a bunch of things. 05:13.880 --> 05:15.750 We divide them into categories. 05:15.750 --> 05:18.220 We call them Type I, Type 2. 05:18.220 --> 05:21.680 It then turns out that each of those categories has 05:21.683 --> 05:23.973 sub-categories, Type Ia. 05:23.970 --> 05:28.460 The joke is when astronomers find three objects, 05:28.461 --> 05:32.381 that's two categories and an exception. 05:32.379 --> 05:35.689 Type Ia Supernovae, though, are by now a fairly 05:35.692 --> 05:38.882 well-defined category, and here's what we think they 05:38.879 --> 05:39.379 are. 05:39.379 --> 05:42.689 Think back to the middle part of the class--to the black hole 05:42.687 --> 05:45.327 section of the class, where we were talking about 05:45.332 --> 05:46.382 x-ray binaries. 05:46.379 --> 05:48.059 X-ray binary, you'll recall, 05:48.056 --> 05:51.776 is a black hole in orbit around something--some other kind of 05:51.781 --> 05:54.431 star, and it pulls material from that 05:54.431 --> 05:56.051 other star onto itself. 05:56.050 --> 05:59.500 So, Type I Supernovae come from a very similar category of 05:59.504 --> 06:00.114 objects. 06:00.110 --> 06:03.470 Here's a normal star, except it's pulled out of shape 06:03.466 --> 06:05.916 a little bit, and it's in a double star 06:05.919 --> 06:06.629 system. 06:06.630 --> 06:08.660 Here's something else. 06:08.660 --> 06:11.650 This is a white dwarf. 06:11.649 --> 06:13.379 In this case, you will remember, 06:13.383 --> 06:16.353 white dwarfs are these very compact stars--not compact 06:16.348 --> 06:19.928 enough to be black holes, but fairly compact--that are 06:19.926 --> 06:23.976 created at the end of the lifetime of stars like the Sun. 06:23.980 --> 06:25.270 So, a fairly dense object. 06:25.269 --> 06:28.949 And just as in the x-ray binaries, stuff is being pulled 06:28.951 --> 06:32.031 off of the normal star onto the white dwarf. 06:32.029 --> 06:34.169 So, then, what happens to this stuff? 06:34.170 --> 06:37.130 First of all, the white dwarf has had all its 06:37.125 --> 06:40.945 hydrogen and helium fused together, so there's no hydrogen 06:40.953 --> 06:42.233 or helium left. 06:42.230 --> 06:46.410 So, this white dwarf is composed of elements like carbon 06:46.413 --> 06:49.683 and oxygen and nitrogen and neon, and so on, 06:49.683 --> 06:53.033 up the line, but no hydrogen and helium. 06:53.029 --> 06:55.349 So, the material that comes from the normal stars, 06:55.350 --> 06:57.620 full of hydrogen and helium--it's pretty much all 06:57.623 --> 06:58.763 hydrogen and helium. 06:58.759 --> 07:03.069 So, the accreted material, what does it do? 07:03.070 --> 07:10.360 Lands on the white dwarf. 07:10.360 --> 07:12.540 And as it lands, it heats up. 07:12.540 --> 07:13.330 It falls down. 07:13.329 --> 07:14.569 It heats up, gets very hot, 07:14.570 --> 07:15.430 gets very dense. 07:15.430 --> 07:19.590 And so, it undergoes nuclear fusion, just like the material 07:19.586 --> 07:23.376 in the middle of the Sun or in the middle, presumably, 07:23.384 --> 07:25.754 of this normal star, as well. 07:25.750 --> 07:27.200 So, there's all this fusion going on. 07:27.199 --> 07:31.499 One of the features of the way this works on a white dwarf is 07:31.498 --> 07:35.648 it is usually true that what happens is hydrogen and helium 07:35.653 --> 07:38.733 piles up for a while, and then, it has a big 07:38.733 --> 07:39.883 explosion. 07:39.879 --> 07:42.649 It doesn't usually burn steadily. 07:42.649 --> 07:50.419 And so, what actually happens is, you have occasional 07:50.420 --> 07:58.190 thermonuclear explosions of the accreted material. 07:58.190 --> 08:01.650 08:01.649 --> 08:05.999 And so, you pile up all this hydrogen and you wait some 08:06.000 --> 08:09.550 amount of time, somewhere between 10 days and 08:09.545 --> 08:12.925 10^(5) years, depending on the object. 08:12.930 --> 08:15.930 You pile up all this hydrogen and helium and finally it gets 08:15.931 --> 08:18.931 dense and hot enough to explode, and then it explodes all at 08:18.932 --> 08:19.392 once. 08:19.389 --> 08:22.279 Huge hydrogen bomb on the surface of this white dwarf. 08:22.279 --> 08:24.939 And that makes the system much, much brighter, 08:24.939 --> 08:27.479 because there's all this stuff exploding. 08:27.480 --> 08:32.360 This is the phenomenon we call a nova, because it looked to the 08:32.361 --> 08:37.091 ancients as if a new star had appeared, because the thing had 08:37.085 --> 08:39.285 gotten so much brighter. 08:39.290 --> 08:39.960 Okay. 08:39.960 --> 08:42.380 So, stuff piles up. 08:42.380 --> 08:43.390 Novae occur. 08:43.390 --> 08:44.590 More stuff piles up. 08:44.590 --> 08:46.310 More novae occur. 08:46.309 --> 08:50.229 And one of the things that's happening while this is going on 08:50.225 --> 08:54.135 is that the white dwarf is gradually getting more massive, 08:54.139 --> 08:57.979 because it's piling up all this extra material. 08:57.980 --> 09:01.800 Oh, the consequence of the nova is that all the hydrogen and 09:01.798 --> 09:04.838 helium gets fused into carbon, oxygen, nitrogen, 09:04.841 --> 09:06.331 neon, and so forth. 09:06.330 --> 09:09.430 So then, it looks just like the rest of the white dwarf, 09:09.431 --> 09:12.981 gets assimilated into the white dwarf, except the white dwarf is 09:12.984 --> 09:13.834 bigger now. 09:13.830 --> 09:19.190 So, the white dwarf gets more massive and gradually more, 09:19.192 --> 09:21.972 and more, and more massive. 09:21.970 --> 09:24.530 But, you may recall, there's a limit to how this 09:24.533 --> 09:25.573 long could go on. 09:25.570 --> 09:30.050 The reason there's a limit to how long this can go on is 09:30.048 --> 09:35.018 because of something we talked about before that Chandrasekhar 09:35.015 --> 09:38.605 Limit, which says that white dwarfs 09:38.610 --> 09:44.470 cannot be more massive than 1.4 times the mass of the Sun. 09:44.470 --> 09:48.600 So, what happens when this white dwarf, which starts out at 09:48.603 --> 09:51.033 some perfectly respectable mass, 0. 09:51.026 --> 09:53.446 6 of the Sun, or 1 solar mass. 09:53.450 --> 09:56.910 And it's piling up all this material from its friend, 09:56.909 --> 09:59.969 and gradually getting more and more massive, 09:59.970 --> 10:02.850 and then, it reaches this limit, this Chandrasekhar limit. 10:02.850 --> 10:03.800 So then, what happens? 10:03.799 --> 10:06.509 What happens--remember what the Chandrasekhar limit is. 10:06.509 --> 10:09.819 If you've got a white dwarf that's bigger than the 10:09.820 --> 10:13.000 Chandrasekhar limit, then the white dwarf cannot 10:12.995 --> 10:17.045 hold itself up against gravity, and so, the whole thing 10:17.049 --> 10:18.739 collapses all at once. 10:18.740 --> 10:23.000 10:23.000 --> 10:25.590 And, as is generally the case, when it collapses, 10:25.593 --> 10:26.353 it gets hot. 10:26.350 --> 10:27.680 It gets dense. 10:27.679 --> 10:30.959 That's what generally happens in a collapse. 10:30.960 --> 10:35.210 And so, the carbon, in particular, 10:35.207 --> 10:42.287 but all the other elements as well--so, carbon and other 10:42.287 --> 10:47.047 elements in the white dwarf fuse, 10:47.050 --> 10:50.040 and that generates energy. 10:50.039 --> 10:56.319 And they fuse together to form heavy elements such as iron, 10:56.316 --> 11:00.316 and heavier than that, all at once. 11:00.320 --> 11:04.270 11:04.269 --> 11:07.209 So what happens is, every time this occurs, 11:07.214 --> 11:10.304 you have exactly the same amount of stuff. 11:10.299 --> 11:13.769 This always happens when you have 1.4 solar mass white 11:13.769 --> 11:16.059 dwarfs, because that's the limit. 11:16.059 --> 11:18.529 You've gradually built up to that limit. 11:18.529 --> 11:23.349 And so, you have what you might refer to as a standard bomb. 11:23.350 --> 11:25.500 We've talked about standard candles. 11:25.500 --> 11:30.240 This is a standard bomb. 11:30.240 --> 11:41.700 You always have the same amount of material and it all explodes 11:41.701 --> 11:43.551 at once. 11:43.550 --> 11:46.760 11:46.759 --> 11:48.909 Well, actually, it takes about, 11:48.908 --> 11:49.408 what? 11:49.409 --> 11:52.029 A hundred milliseconds, something like that, 11:52.025 --> 11:53.785 but basically, all at once. 11:53.789 --> 11:57.069 So, you blow up 1.4 solar masses of carbon all at once. 11:57.070 --> 11:59.610 Now, the advantage of standard things is that if you have a 11:59.609 --> 12:01.579 standard bomb with the same amount of fuel, 12:01.580 --> 12:04.950 every one of them should be exactly as bright as every other 12:04.946 --> 12:07.796 one, and that's what we need to make these distance 12:07.799 --> 12:08.769 measurements. 12:08.770 --> 12:09.600 Remember? 12:09.600 --> 12:15.210 So, if you look at these things, you see that they're 12:15.207 --> 12:21.247 always the same brightness, so, they're terrific standard 12:21.245 --> 12:22.535 candles. 12:22.539 --> 12:26.089 And so, one of the things that happens is that you look at 12:26.087 --> 12:29.567 these things and you can tell, from how bright they look, 12:29.573 --> 12:31.693 exactly how far away they are. 12:31.690 --> 12:37.690 You also measure their redshift when they blow up in this way, 12:37.685 --> 12:43.385 and you get to put a point on that redshift versus distance 12:43.385 --> 12:44.265 plot. 12:44.270 --> 12:46.800 And they're stupendously bright. 12:46.799 --> 12:50.889 These things have an absolute magnitude of -19.5. 12:50.889 --> 12:54.509 They outshine whole galaxies, for about a week or two, 12:54.506 --> 12:55.936 until they go away. 12:55.940 --> 12:57.940 And so, you can see them at enormous distances. 12:57.940 --> 13:02.290 So, they're just about the perfect thing for exploring 13:02.285 --> 13:03.265 cosmology. 13:03.269 --> 13:07.199 But we were only really able to do this in the--starting in the 13:07.201 --> 13:11.131 early 1990s, because there were two key advances that were made 13:11.132 --> 13:12.212 at that time. 13:12.210 --> 13:18.900 One is that the Hubble Space Telescope measured things like 13:18.904 --> 13:23.064 Cepheids and other kinds of stars, 13:23.059 --> 13:27.509 other kinds of distance measurements, 13:27.512 --> 13:35.182 in galaxies that historically had Type Ia Supernovae. 13:35.179 --> 13:39.199 These things don't occur very often, once every couple of 100 13:39.197 --> 13:40.467 years per galaxy. 13:40.470 --> 13:43.720 There hasn't been one in our own galaxy since before they 13:43.719 --> 13:45.169 invented the telescope. 13:45.170 --> 13:47.350 We're kind of overdue, actually. 13:47.350 --> 13:50.190 One of the worrying things– You know, it would be great to 13:50.192 --> 13:52.362 have one of these supernovae in our galaxy. 13:52.360 --> 13:54.250 We could study it enormously carefully. 13:54.250 --> 13:56.930 The problem is, all the telescopes are too big 13:56.931 --> 14:00.091 and--because it would burn out all the instruments. 14:00.090 --> 14:02.390 You put one of these big research telescopes pointing to 14:02.390 --> 14:02.600 it. 14:02.600 --> 14:05.440 So, one of the things that we have, just in case, 14:05.439 --> 14:09.049 sort of, for emergencies in the telescopes I've worked with in 14:09.048 --> 14:11.138 Chile, is we have a big thing you can 14:11.139 --> 14:13.839 put over the front of the telescope and stop it down to 14:13.840 --> 14:17.070 about a couple of inches across, just in case there's a Type 14:17.071 --> 14:20.311 Ia super--any kind of supernovae in our own galaxy. 14:20.309 --> 14:23.529 But when these--we do have supernovae in the historical 14:23.532 --> 14:24.072 record. 14:24.070 --> 14:26.560 Kepler and Tycho saw one. 14:26.559 --> 14:30.039 And then, back in the eleventh century, there was a famous one 14:30.039 --> 14:32.719 observed by the Chinese and Arab astronomers. 14:32.720 --> 14:35.990 The Europeans were, of course, in barbarity at the 14:35.994 --> 14:38.004 time and didn't even notice. 14:38.000 --> 14:40.620 And--which, now, we see the Crab Nebula, 14:40.617 --> 14:43.367 which is a big outward-going explosion. 14:43.370 --> 14:46.070 And these things become the brightest objects in the sky. 14:46.070 --> 14:47.130 You can see them in the daytime. 14:47.129 --> 14:49.949 Pretty amazing, but it hasn't happened for 400 14:49.950 --> 14:52.270 years, at least, in our own galaxy. 14:52.269 --> 14:53.819 Student: How long did you say they lasted? 14:53.820 --> 14:56.680 Prof: They last--well, I'll show you in a minute what 14:56.676 --> 14:58.076 the light curve looks like. 14:58.080 --> 15:00.650 They take a couple weeks to rise to their maximum 15:00.652 --> 15:03.442 brightness, and then they decay over a few months. 15:03.440 --> 15:08.360 So, you can see them for a little while. 15:08.360 --> 15:11.120 So, it just--measured Cepheids. 15:11.120 --> 15:13.630 This meant that we could calibrate them. 15:13.630 --> 15:15.120 Remember the distance ladder? 15:15.120 --> 15:20.220 So, you could calibrate these things – calibration. 15:20.220 --> 15:24.600 And this, in particular, meant that we know the absolute 15:24.596 --> 15:29.526 magnitude, which is crucial for determining these distances. 15:29.529 --> 15:33.019 What, then, came out of that and other things, 15:33.020 --> 15:36.050 mostly, actually, done with ground-based 15:36.046 --> 15:41.226 telescopes--so, ground-based telescopes 15:41.232 --> 15:48.332 discovered and compared many of these things, 15:48.333 --> 15:54.773 many of these Type Ias, and discovered that, 15:54.768 --> 15:58.038 you know, it isn't actually quite true that they all look to 15:58.038 --> 15:59.478 be the same brightness. 15:59.480 --> 16:03.640 Because, it would be true, if you could measure all of the 16:03.642 --> 16:06.492 energy that came out of these things. 16:06.490 --> 16:08.750 But that isn't actually what you measure. 16:08.750 --> 16:12.440 What you measure is all of the photons in a certain 16:12.443 --> 16:16.363 range--depending on your detector and how you set your 16:16.357 --> 16:20.937 telescope up--all photons within a certain range of wavelengths 16:20.937 --> 16:22.707 at a certain time. 16:22.710 --> 16:26.520 And that is not the same thing as measuring all the energy that 16:26.518 --> 16:27.868 the thing gives out. 16:27.870 --> 16:37.670 And so, it turns out that if you measure all photons in some 16:37.665 --> 16:47.625 wavelength region at some time, that actually varies from one 16:47.627 --> 16:51.277 object to another. 16:51.279 --> 16:54.009 This can vary by, oh, I don't know, 16:54.005 --> 16:58.815 15 - 20%, but that's enough to cause you some real trouble in 16:58.815 --> 17:01.215 making these measurements. 17:01.220 --> 17:04.080 But what they discovered was that you can correct for this. 17:04.080 --> 17:08.320 17:08.319 --> 17:14.839 If you measure the color and the decay rate--that is to say, 17:14.837 --> 17:17.817 how fast it gets fainter. 17:17.819 --> 17:19.809 So, your question turns out to be very important. 17:19.809 --> 17:24.979 These things behave differently depending on how fast they go 17:24.977 --> 17:25.577 away. 17:25.579 --> 17:30.089 If you measure the color and the decay rate, 17:30.085 --> 17:35.845 you can correct for some of these deviations and turn it 17:35.848 --> 17:40.038 back it into a good standard candle. 17:40.039 --> 17:44.789 And I'll show you how this is done in just a second, 17:44.788 --> 17:45.438 okay? 17:45.440 --> 17:49.640 How we doing? 17:49.640 --> 17:57.320 Okay, let me turn this off for a second and go back to here. 17:57.320 --> 17:58.610 All right. 17:58.609 --> 18:03.959 This is the key thing that was found out in the early 1990s. 18:03.960 --> 18:07.670 Up on the top, you have observations from a 18:07.673 --> 18:10.153 whole bunch of supernovae. 18:10.150 --> 18:11.340 This is time. 18:11.339 --> 18:14.729 So, this is 0,20 days, 40 days, 60 days. 18:14.730 --> 18:16.880 So, this is time, counting from the peak 18:16.882 --> 18:17.602 brightness. 18:17.599 --> 18:19.949 And most of the time you can observe these things before they 18:19.950 --> 18:20.930 get to peak brightness. 18:20.930 --> 18:23.630 You watch them get brighter and then you watch them get fainter. 18:23.630 --> 18:26.170 In the top plot there, we're plotting, 18:26.173 --> 18:28.583 more or less, absolute magnitude. 18:28.579 --> 18:31.039 Think of it--it's a complicated thing, but think of it as 18:31.038 --> 18:31.958 absolute magnitude. 18:31.960 --> 18:34.630 So -19.5, as I said, is a typical 18:34.625 --> 18:37.285 magnitude--absolute magnitude. 18:37.289 --> 18:39.899 And each color is a different supernova. 18:39.900 --> 18:42.890 So, they've made repeated observations of a large number 18:42.890 --> 18:43.760 of supernovae. 18:43.759 --> 18:46.619 And then, the line is just connecting the dots, 18:46.622 --> 18:48.492 connecting the observations. 18:48.490 --> 18:52.040 And you can see from that top plot that it is not true, 18:52.039 --> 18:54.929 that every supernova has the same brightness, 18:54.931 --> 18:57.101 at peak or at any other time. 18:57.099 --> 19:01.639 And so, the green supernova on the bottom there gets up to 19:01.637 --> 19:05.697 about -18.8, whereas, the orange one on the top gets 19:05.697 --> 19:07.287 up to about -20. 19:07.289 --> 19:11.559 That's almost a factor of 3 in difference of peak brightness. 19:11.559 --> 19:14.629 But then you can make this correction. 19:14.630 --> 19:17.170 They measure the color of the thing, which is not apparent on 19:17.174 --> 19:18.154 this particular plot. 19:18.150 --> 19:21.020 They measure the rate of decay, and that is apparent. 19:21.019 --> 19:23.629 You can tell the green ones, the ones at the bottom, 19:23.630 --> 19:26.240 tend to fall off faster than the ones at the top. 19:26.240 --> 19:29.930 And they came up with a correction formula that allows 19:29.927 --> 19:33.747 the absolute magnitudes of these things to be corrected, 19:33.754 --> 19:36.194 and that's what they plot here. 19:36.190 --> 19:40.850 These are these same exact data points as they have on the top 19:40.847 --> 19:45.347 line, except corrected for the differences in observed color 19:45.352 --> 19:47.492 and observed decay rate. 19:47.490 --> 19:49.920 And you can see, now, you've got a very 19:49.920 --> 19:53.690 beautiful combined light curve where everything does exactly 19:53.693 --> 19:56.063 the same thing as all the others. 19:56.059 --> 19:59.469 And, in particular, the maximum brightness of these 19:59.469 --> 20:02.469 things is always the same at around -19.5. 20:02.470 --> 20:06.960 So, you have to make this correction in order to be able 20:06.960 --> 20:11.370 to use these things effectively as standard candles. 20:11.369 --> 20:14.409 And so, when that was done, and we had calibrated this, 20:14.411 --> 20:15.821 and they thought, well, 20:15.819 --> 20:18.479 now we know, every time we see one of these 20:18.478 --> 20:21.818 things, we'll just follow it up, follow it down, 20:21.817 --> 20:25.847 make this correction, and then we have--we know what 20:25.854 --> 20:28.154 the absolute magnitude is. 20:28.150 --> 20:29.760 We measure the apparent magnitude. 20:29.760 --> 20:30.950 We determine the distance. 20:30.950 --> 20:34.540 We get a spectrum along the way so that we can get a redshift. 20:34.539 --> 20:38.509 And then, we can make these plots for distant objects. 20:38.509 --> 20:41.459 These guys aren't particularly distant, because you want to be 20:41.461 --> 20:43.931 able to get really accurate measurements of them. 20:43.930 --> 20:47.780 And so, if this set were the ones that were observed so close 20:47.778 --> 20:51.628 to us at such low redshifts that you can't tell the different 20:51.625 --> 20:53.545 cosmological models apart. 20:53.549 --> 20:56.329 So then, people got very fired up. 20:56.329 --> 20:57.879 They said, aha, we're going to figure out 20:57.879 --> 21:00.319 everything that is happening in the Universe by looking at these 21:00.319 --> 21:00.899 supernovae. 21:00.900 --> 21:05.710 And they started up big observational projects to find 21:05.713 --> 21:08.623 many high redshift supernovae. 21:08.619 --> 21:11.399 So, these things are going to be quite faint. 21:11.400 --> 21:16.490 They're going to be--they have distance moduluses of close to 21:16.485 --> 21:21.735 45, and so, they'll have an apparent magnitude as low as 25, 21:21.740 --> 21:23.960 which is really very hard to see. 21:23.960 --> 21:26.020 So here's what they do. 21:26.019 --> 21:28.599 First of all, let me just show you this 21:28.600 --> 21:29.280 picture. 21:29.280 --> 21:33.070 This is just fun. 21:33.070 --> 21:34.120 Let's see, here. 21:34.119 --> 21:37.629 If I do this, that will be good, 21:37.628 --> 21:40.908 except I think I want this. 21:40.910 --> 21:44.160 There we go--all right. 21:44.160 --> 21:48.940 This is a photograph from the Hubble Space Telescope of empty 21:48.942 --> 21:49.582 space. 21:49.579 --> 21:52.709 They picked a part of the sky in which there was nothing. 21:52.710 --> 21:54.620 Actually, that's not true. 21:54.619 --> 21:57.759 There was one star, one faint star that they knew 21:57.759 --> 21:59.459 about, and nothing else. 21:59.460 --> 22:02.080 And they took the space telescope and they looked at it 22:02.079 --> 22:03.679 for about three weeks in a row. 22:03.680 --> 22:06.700 And this is the picture they got. 22:06.700 --> 22:10.220 You can see two or three stars in this picture. 22:10.220 --> 22:12.460 This is one, and there are a couple of 22:12.463 --> 22:14.043 others scattered around. 22:14.039 --> 22:16.349 You can tell they're stars because they have this, 22:16.352 --> 22:19.092 sort of, spike pattern from the optics of the telescope. 22:19.089 --> 22:23.789 Everything else that you see in this picture is a galaxy. 22:23.789 --> 22:27.319 There's a whole galaxy, each one of them with billions 22:27.317 --> 22:28.047 of stars. 22:28.049 --> 22:30.519 There are, I think, 13,000 of them? 22:30.520 --> 22:31.290 8,000? 22:31.289 --> 22:32.609 How many in the ultra deep field? 22:32.610 --> 22:33.540 I don't remember. 22:33.540 --> 22:34.350 Huh? 22:34.349 --> 22:37.329 Student: Are any of them lensed? 22:37.329 --> 22:39.629 Prof: A couple of them are lensed, but most of them, 22:39.631 --> 22:39.871 not. 22:39.869 --> 22:43.949 So, most of them are just straight-up images of galaxies. 22:43.950 --> 22:46.250 You could see, in the bigger ones, 22:46.249 --> 22:50.499 some nice spirals and all the usual kinds of galaxy shapes. 22:50.500 --> 22:53.240 This is a really small piece of the sky. 22:53.240 --> 22:58.280 This is a piece of the sky about 1% of the area of the full 22:58.281 --> 22:58.891 Moon. 22:58.890 --> 23:02.050 So, if you looked at the whole area covered by the full 23:02.048 --> 23:05.438 Moon--picture the full Moon up in the sky--and you did this 23:05.440 --> 23:08.170 kind of picture, you would discover literally 23:08.173 --> 23:09.963 millions of different galaxies. 23:09.960 --> 23:14.330 So, this means that you can discover supernovae in the--so, 23:14.333 --> 23:17.353 there are thousands of galaxies, here. 23:17.349 --> 23:21.729 And if supernovae occur once per every 100 years per galaxy, 23:21.730 --> 23:26.180 there ought to be about ten or twenty supernovae going off in 23:26.184 --> 23:29.084 this tiny piece of space right now. 23:29.079 --> 23:32.339 Or any other such tiny piece of space. 23:32.339 --> 23:35.649 And so, if you're looking for high redshift supernovae, 23:35.654 --> 23:37.684 you don't care where you point. 23:37.680 --> 23:38.990 They're everywhere. 23:38.990 --> 23:42.330 And so, you just pick out some nice blank piece of space, 23:42.330 --> 23:45.310 take really deep pictures of them, and wait for the 23:45.312 --> 23:47.402 supernovae to start showing up. 23:47.400 --> 23:52.090 And this is what people have done. 23:52.089 --> 23:56.759 So, here's a little bit of data from the Supernova Cosmology 23:56.755 --> 24:01.495 Project, which is one of the groups that was attempting to do 24:01.500 --> 24:03.240 this in the 1990s. 24:03.240 --> 24:06.240 So, in the background, here, is just a huge field of 24:06.235 --> 24:08.815 stars that they happened to be looking at. 24:08.819 --> 24:14.839 Then, they've taken this tiny piece of the sky and blown it 24:14.840 --> 24:15.360 up. 24:15.359 --> 24:17.179 So, here's their first image of it. 24:17.180 --> 24:19.380 By the way, this, and this, and this--these are 24:19.375 --> 24:22.335 galaxies, but they're taken from the ground instead of with the 24:22.335 --> 24:23.285 space telescope. 24:23.289 --> 24:24.949 And so, they look like blobby things. 24:24.950 --> 24:26.600 You can't see any of the structure. 24:26.599 --> 24:30.019 And then, three weeks later they take another picture, 24:30.015 --> 24:33.105 and it turns out, there's a little extra light on 24:33.109 --> 24:35.429 the side of one of the galaxies. 24:35.430 --> 24:39.860 Now, imagine taking something maybe 100 times bigger than this 24:39.862 --> 24:44.152 whole background picture and looking for that difference. 24:44.150 --> 24:48.840 You would make your graduate students completely cross-eyed 24:48.839 --> 24:49.889 doing this. 24:49.890 --> 24:51.600 And so, they do it digitally. 24:51.600 --> 24:52.480 They do it differently. 24:52.480 --> 24:55.760 What you do is you take this picture, each one of these 24:55.761 --> 24:58.381 pixels, you know, tells you exactly how many 24:58.375 --> 24:59.525 photons hit it. 24:59.530 --> 25:00.910 So, it's all digitized. 25:00.910 --> 25:02.500 Each one of these is a number. 25:02.500 --> 25:05.930 And you just take this number and subtract this number. 25:05.930 --> 25:09.780 And you take the number from each pixel, subtract the number 25:09.776 --> 25:13.686 that you got in the previous thing and get a subtracted image 25:13.688 --> 25:17.328 of how much light there is, minus the light there was the 25:17.327 --> 25:18.887 last time you looked at it. 25:18.890 --> 25:20.840 Here's the subtracted picture. 25:20.839 --> 25:24.549 Now this, even a blind old professor can see, 25:24.550 --> 25:27.670 has something interesting going on. 25:27.670 --> 25:30.930 There's a new object that has appeared between the first 25:30.926 --> 25:32.876 picture and the second picture. 25:32.880 --> 25:35.700 Now, up at the top, in the upper right-hand corner 25:35.695 --> 25:39.025 there, that's a Hubble Space Telescope picture taken of the 25:39.028 --> 25:41.598 same field, while the supernova was in 25:41.601 --> 25:42.261 outburst. 25:42.259 --> 25:45.049 And you can see, this galaxy, 25:45.051 --> 25:45.751 here. 25:45.750 --> 25:48.600 That's the galaxy, you know, below the arrow 25:48.599 --> 25:49.129 there. 25:49.130 --> 25:53.430 And then, those two arrows are placed in exactly the same 25:53.427 --> 25:56.647 relative position in these two pictures. 25:56.650 --> 25:59.420 And so, in the Hubble Space Telescope picture, 25:59.423 --> 26:03.123 you can see that the additional light comes from a particular 26:03.122 --> 26:05.652 point in the outskirts of the galaxy. 26:05.650 --> 26:08.570 But it wasn't discovered with the Hubble Space Telescope, 26:08.567 --> 26:11.587 because the HST doesn't cover enough of the sky at once. 26:11.589 --> 26:14.729 So, you try and discover these things from the ground, 26:14.733 --> 26:17.583 because you can cover so much more of the sky. 26:17.579 --> 26:19.259 And so, this is a discovery image. 26:19.259 --> 26:21.959 And then, if you want more precise imaging, 26:21.956 --> 26:25.226 then you have to tell Hubble, or go and look at this 26:25.231 --> 26:26.581 particular place. 26:26.579 --> 26:29.009 Anyway, what they do is they keep at it. 26:29.010 --> 26:30.550 They keep at it. 26:30.549 --> 26:32.129 Every three days, they make one of these 26:32.125 --> 26:32.565 pictures. 26:32.569 --> 26:34.689 They make these difference pictures, and they get these 26:34.686 --> 26:35.466 nice light curves. 26:35.470 --> 26:38.530 And out of those light curves, they can then do the correction 26:38.528 --> 26:38.978 factor. 26:38.980 --> 26:42.790 And then, once you've done that--you also take a spectrum 26:42.791 --> 26:45.791 along the way for two purposes: first of all, 26:45.786 --> 26:48.266 to get the redshift; second of all, 26:48.272 --> 26:51.252 to make sure that it's a Type Ia Supernova, 26:51.254 --> 26:54.484 rather than any of the other five or six subtypes. 26:54.480 --> 27:00.250 And then, you put them on this plot and you plot their apparent 27:00.252 --> 27:04.442 magnitude, corrected by these various factors, 27:04.442 --> 27:06.772 against the redshift. 27:06.769 --> 27:11.949 And that's how you come up with these kinds of data. 27:11.950 --> 27:17.530 So, that's where this information comes from. 27:17.530 --> 27:25.260 27:25.259 --> 27:27.989 And there is, as you see, a kind of 27:27.990 --> 27:32.650 theoretical--both a theoretical reason and an observational 27:32.649 --> 27:35.379 reason to trust these results. 27:35.380 --> 27:45.520 So, there is a theoretical basis for thinking these things 27:45.523 --> 27:52.393 are standard candles--namely, that it's the same amount of 27:52.386 --> 27:54.546 fuel each time one of these things goes off. 27:54.549 --> 28:03.939 And there's also an empirical basis, which is that after some 28:03.944 --> 28:11.934 corrections, the nearby ones line up beautifully. 28:11.930 --> 28:15.510 The nearby ones, for which you know the answer 28:15.512 --> 28:20.132 in advance by other means--the nearby ones line up well. 28:20.130 --> 28:23.920 And where by "well", I mean less than 5% difference 28:23.922 --> 28:25.062 between them. 28:25.059 --> 28:30.699 And there still is about a few percent difference. 28:30.700 --> 28:34.100 But if we observe enough of them, we can average over that 28:34.102 --> 28:36.372 and we think we're going to be okay. 28:36.369 --> 28:40.399 So, if you want to come up with some kind of explanation for 28:40.395 --> 28:44.685 this that does not involve dark energy, you've got to get around 28:44.694 --> 28:48.314 both of these points; namely, the fact that we expect 28:48.305 --> 28:51.925 them to look like each other, and the fact that they do look 28:51.932 --> 28:53.102 like each other. 28:53.099 --> 28:55.479 Now, it's possible to do that and, in fact, 28:55.477 --> 28:58.697 one of the problems on the problem set addresses just this 28:58.703 --> 28:59.273 issue. 28:59.269 --> 29:04.489 If you can invent some way that all of the supernovae at a 29:04.485 --> 29:08.415 redshift of .8, high redshifts like that, 29:08.420 --> 29:13.180 are all systematically fainter than otherwise identical-looking 29:13.177 --> 29:15.937 supernovae in the nearby Universe, 29:15.940 --> 29:18.090 then you can get around this problem. 29:18.089 --> 29:20.639 But they have to be identical-looking in the sense 29:20.639 --> 29:22.929 that they have the same color and decay rate, 29:22.929 --> 29:23.969 but are fainter. 29:23.970 --> 29:27.200 We don't see that in the local Universe. 29:27.200 --> 29:30.580 We don't see a category of things, which have the same 29:30.580 --> 29:33.640 color and decay rate, but one is fainter than the 29:33.642 --> 29:34.282 other. 29:34.280 --> 29:36.440 But, who knows? 29:36.440 --> 29:39.170 The Universe was, you know, half its size back 29:39.165 --> 29:39.585 then. 29:39.589 --> 29:40.759 All sorts of things were different. 29:40.759 --> 29:44.019 Maybe there's some way that supernovae then were 29:44.015 --> 29:47.405 systematically different from how they are now, 29:47.410 --> 29:52.250 except that they don't show it in these particular ways. 29:52.250 --> 29:54.230 They only show it in the overall brightness. 29:54.230 --> 29:55.410 That's tough. 29:55.410 --> 29:56.800 That's tough, theoretically. 29:56.800 --> 29:58.130 It's tough empirically. 29:58.130 --> 30:00.340 You know, you would expect that if that were true, 30:00.336 --> 30:02.626 then there would be intermediate cases that we could 30:02.633 --> 30:04.033 see, and we don't see them. 30:04.029 --> 30:06.579 But, you know, shortly after this result was 30:06.580 --> 30:10.140 announced, I used to--when I was at conferences and stuff, 30:10.140 --> 30:12.470 I would try and take the supernovae people off in a 30:12.469 --> 30:14.239 corner and give them beer and stuff, 30:14.240 --> 30:15.860 until they would, you know--and then, 30:15.858 --> 30:18.328 after you give them four beers, you ask the question, 30:18.330 --> 30:19.910 what could be going wrong? 30:19.910 --> 30:23.230 Do you really believe in dark energy? 30:23.230 --> 30:26.880 And then, they start mumbling stuff about all the different 30:26.884 --> 30:29.094 weirdnesses that supernovae have. 30:29.089 --> 30:30.989 And, of course, these are people who have 30:30.994 --> 30:33.904 devoted their life to studying the weirdness of supernovae, 30:33.900 --> 30:37.970 and so, they have many things that they will tell you under 30:37.967 --> 30:39.367 cover of darkness. 30:39.369 --> 30:43.739 Which, of course, then, everybody went out to try 30:43.738 --> 30:44.828 and check. 30:44.829 --> 30:48.779 And none of these things have turned out to be able to provide 30:48.780 --> 30:51.500 a satisfactory explanation for the data, 30:51.500 --> 30:55.520 except the idea that there's something very significant, 30:55.524 --> 30:57.504 cosmologically, going on. 30:57.500 --> 31:04.830 Okay, so, from that point of view, it's kind of hard to avoid 31:04.830 --> 31:09.600 believing this, which disturbed a lot of 31:09.596 --> 31:10.936 people. 31:10.940 --> 31:14.100 And, in fact, one of the reasons people 31:14.104 --> 31:19.104 believed this as quickly as they did was that in the late--in 31:19.100 --> 31:21.590 1998, when this was first announced, 31:21.593 --> 31:24.913 it was not announced by one group, it was announced by two 31:24.907 --> 31:26.067 different groups. 31:26.069 --> 31:33.129 There were two groups trying to do the same thing--doing the 31:33.128 --> 31:36.978 same thing and theyso, they were sort of spying on 31:36.981 --> 31:38.801 each other, because this was an important result. 31:38.799 --> 31:41.369 And they both found out, at a certain point, 31:41.371 --> 31:44.421 that the other guys had been spending a year driving 31:44.422 --> 31:48.192 themselves crazy because they didn't believe their results. 31:48.190 --> 31:49.270 They were saying, look at this, 31:49.266 --> 31:51.486 these things are getting--these things are going totally in the 31:51.492 --> 31:52.212 wrong direction. 31:52.210 --> 31:53.600 We must be wrong somehow. 31:53.599 --> 31:56.559 And it turned out that both of these groups had been spending 31:56.559 --> 31:59.469 the past year trying to figure out why their results were so 31:59.470 --> 32:00.210 screwed up. 32:00.210 --> 32:02.550 But then, they spied on each other and they found out that 32:02.547 --> 32:04.677 the other guys were having the exact same problem, 32:04.680 --> 32:07.810 having taken their data and dealt with it in quite a 32:07.808 --> 32:08.788 different way. 32:08.789 --> 32:11.089 And so, then, miraculously enough, 32:11.087 --> 32:15.197 they kind of submitted their papers within twenty-four hours 32:15.195 --> 32:18.185 of each other, so they both got credit. 32:18.190 --> 32:22.390 And so, the two groups doing the same things, 32:22.391 --> 32:25.161 but doing them differently. 32:25.160 --> 32:29.540 Different approaches, in some ways, 32:29.537 --> 32:32.367 got the same result. 32:32.369 --> 32:34.619 And in particular, one group were a bunch of 32:34.617 --> 32:36.967 particle physicists led by Saul Perlmutter, 32:36.970 --> 32:40.330 who had gotten depressed by the fact that the Super Collider was 32:40.327 --> 32:43.657 cancelled in the early 1990s, and had decided--somebody 32:43.661 --> 32:47.831 described this as "adult onset cosmology," where you used to be 32:47.832 --> 32:51.442 interested in particle physics, but then, they didn't build 32:51.437 --> 32:53.387 your machine, so now you're interested in 32:53.389 --> 32:54.169 astrophysics. 32:54.170 --> 33:00.420 And those guys took a very particle physics approach to it. 33:00.420 --> 33:04.070 They had a big team, with a team leader and a whole 33:04.065 --> 33:04.935 hierarchy. 33:04.940 --> 33:08.650 The other guys were a bunch of supernova--and they were very 33:08.651 --> 33:11.231 expert in the cosmology side of things, 33:11.230 --> 33:13.160 and in the dark energy explanations, 33:13.164 --> 33:14.384 and stuff like that. 33:14.380 --> 33:16.950 The supernova experts, the sort of guys who knew all 33:16.950 --> 33:19.320 the weirdnesses about supernovae, formed another 33:19.319 --> 33:21.939 group, but it was totally differently organized. 33:21.940 --> 33:24.890 It was kind of a loose confederation of small research 33:24.892 --> 33:26.232 groups here and there. 33:26.230 --> 33:30.820 They had done this interesting work with the correction factors 33:30.821 --> 33:35.161 on supernovae some years before, and they approached it as, 33:35.160 --> 33:38.380 you know, my group will do this little piece. 33:38.380 --> 33:40.030 My group will do this other little piece. 33:40.029 --> 33:42.259 We'll get together over lunch and we'll figure out what's 33:42.263 --> 33:43.303 going on, kind of thing. 33:43.299 --> 33:45.829 And they both got the same kinds of answers. 33:45.829 --> 33:48.049 They both basically got the same answers. 33:48.049 --> 33:51.469 And so, this is one of the fables. 33:51.470 --> 33:55.800 So, fable: discovery of dark energy. 33:55.800 --> 33:59.540 33:59.539 --> 34:06.139 And I would say that the moral here is that replicating 34:06.142 --> 34:13.232 important results is one of the things that leads people to 34:13.233 --> 34:19.593 actually believe what you're saying--leads to greater 34:19.591 --> 34:21.671 acceptance. 34:21.670 --> 34:24.730 And it was particularly nice in this particular case, 34:24.731 --> 34:27.911 because neither of them were replicating the others. 34:27.909 --> 34:30.699 They both made the discovery independently, 34:30.697 --> 34:33.817 at the same time, using a very different kind of 34:33.815 --> 34:37.925 organizational structure and a very different approach to their 34:37.930 --> 34:38.660 data. 34:38.660 --> 34:41.100 So, this was kind of compelling. 34:41.100 --> 34:43.860 Okay. 34:43.860 --> 34:48.970 So, here we are, Δ (m – M), 34:48.970 --> 34:51.110 versus redshift. 34:51.110 --> 34:55.190 Here's Ω _matter = 0. 34:55.190 --> 34:58.280 Ω_λ = 0, except that, 34:58.284 --> 35:03.994 in fact, the data--you know, they kind of look like this. 35:03.989 --> 35:10.049 So, this is Ω _matter = 1/4 and 35:10.051 --> 35:13.601 Ω_λ = 3/4. 35:13.599 --> 35:17.069 And, as you will recall, the explanation for this--or, 35:17.074 --> 35:20.684 the first explanation that was offered was the fact that 35:20.679 --> 35:24.219 Einstein had this figured out eighty years before, 35:24.220 --> 35:26.250 except he decided he was wrong. 35:26.250 --> 35:32.430 And so, the first explanation of this was Einstein's 35:32.430 --> 35:38.980 Cosmological Constant--that's this symbol, lambda [λ], 35:38.975 --> 35:42.485 that I keep writing down. 35:42.489 --> 35:45.739 And so, once people believed this result, you had to start 35:45.740 --> 35:49.220 worrying about what the heck this actually is in real life. 35:49.219 --> 35:54.409 And it has some very peculiar properties. 35:54.409 --> 35:57.399 In particular, there is the issue of what is 35:57.396 --> 36:00.866 constant about Einstein's Cosmological Constant? 36:00.869 --> 36:02.999 So, let me first tell you what it is, and then, 36:03.001 --> 36:04.671 I'll tell you why it's so bizarre. 36:04.670 --> 36:13.230 The energy density – remember, that's the crucial 36:13.227 --> 36:22.467 quantity--of λ is constant as the Universe expands. 36:22.469 --> 36:25.399 So, if you take 1 cubic meter of space, and you say, 36:25.397 --> 36:28.897 how much dark energy is there in this cubic meter of space? 36:28.900 --> 36:31.070 We take an average cubic meter of space. 36:31.070 --> 36:34.750 You figure that out by how fast the Universe is being pushed 36:34.750 --> 36:35.250 apart. 36:35.250 --> 36:37.350 And then, you know, you wait 10 billion years, 36:37.352 --> 36:39.882 or something like that, until the Universe is very much 36:39.876 --> 36:40.386 bigger. 36:40.389 --> 36:43.169 And then, you take a cubic meter of space, 36:43.172 --> 36:47.042 and you ask yourself how much dark energy is in this cubic 36:47.041 --> 36:49.421 meter, and you get the same answer, 36:49.421 --> 36:50.881 10 billion years later. 36:50.880 --> 36:53.650 And you got the same answer now, and you would have gotten 36:53.646 --> 36:55.536 the same answer 10 billion years ago. 36:55.540 --> 36:59.400 Very peculiar, right? 36:59.400 --> 37:00.930 Do you see why? 37:00.930 --> 37:02.540 Think about matter. 37:02.539 --> 37:04.869 You know, the Universe also has a bunch of matter in it. 37:04.869 --> 37:08.979 All right, so I measure the average density of the Universe 37:08.981 --> 37:12.811 in the way we've discussed, and you get some answer. 37:12.809 --> 37:19.809 So, for matter, you can get some density to the 37:19.808 --> 37:22.088 Universe now. 37:22.090 --> 37:24.880 And then, supposing you imagine in your mind, 37:24.877 --> 37:28.547 you go back in time when--to the time when the scale factor 37:28.552 --> 37:34.542 of the Universe, when a was half its 37:34.543 --> 37:40.723 present size, its present amount. 37:40.719 --> 37:42.519 But, of course, you have the same amount of 37:42.519 --> 37:43.589 matter in the Universe. 37:43.590 --> 37:45.600 Matter doesn't--you know, in general, it doesn't get 37:45.596 --> 37:45.986 created. 37:45.989 --> 37:47.559 Or, at least, you have the same amount of 37:47.557 --> 37:48.377 matter plus energy. 37:48.380 --> 37:53.200 So, you go back to when you have the same amount of matter, 37:53.204 --> 37:56.704 but it's in half the size, by which I mean, 37:56.697 --> 37:58.857 1/8 the volume, right? 37:58.860 --> 38:02.670 Half squared--half cubed is 1/8. 38:02.670 --> 38:06.560 And so, if I reduce the linear scale of the Universe by a 38:06.562 --> 38:09.062 factor of two, I have 1/8 the volume, 38:09.064 --> 38:11.154 but same amount of matter. 38:11.150 --> 38:15.090 38:15.090 --> 38:19.690 So rho_then, which is equal to mass, 38:19.690 --> 38:25.010 which doesn't change, because there's the same amount 38:25.007 --> 38:30.647 of mass in the Universe, which doesn't change, 38:30.646 --> 38:35.666 divided by volume, which does change. 38:35.670 --> 38:41.270 So, it has to equal eight times the density_now. 38:41.269 --> 38:42.889 We've talked about this before, right? 38:42.889 --> 38:45.699 The whole deal with the Big Bang is that if you go back into 38:45.701 --> 38:48.181 the past, things were denser than they were today. 38:48.179 --> 38:52.839 Also hotter, which is a by-product of the 38:52.835 --> 38:53.995 density. 38:54.000 --> 38:56.250 You take a big balloon full of stuff. 38:56.250 --> 38:57.320 You make it smaller. 38:57.320 --> 38:58.820 The same amount of stuff is in there. 38:58.820 --> 39:01.230 It's got to be denser inside the balloon after you've 39:01.229 --> 39:02.109 squashed it down. 39:02.110 --> 39:04.180 You take a balloon and you stretch it out. 39:04.179 --> 39:07.769 If you don't let stuff come in or out, then it has to be less 39:07.769 --> 39:11.179 dense--the stuff inside, after you've stretched it out. 39:11.179 --> 39:13.649 And then, you get into all these nice little thermodynamics 39:13.651 --> 39:16.461 problems where you have, pressure is equal to density 39:16.460 --> 39:18.950 times temperature, and things like that. 39:18.949 --> 39:24.549 So, all of familiar gas physics comes into play. 39:24.550 --> 39:27.610 And so, you expect that the density of the Universe is 39:27.608 --> 39:30.958 constantly getting smaller, because the Universe is getting 39:30.955 --> 39:31.585 bigger. 39:31.590 --> 39:33.480 And, in fact, there's extremely good 39:33.478 --> 39:36.498 empirical evidence of that, because you look back in time 39:36.499 --> 39:38.279 by looking at distant things. 39:38.280 --> 39:41.150 Sure enough, it's denser back then. 39:41.150 --> 39:44.870 But not the dark energy. 39:44.869 --> 39:51.329 Dark energy density, at least in Einstein's 39:51.330 --> 39:55.330 conception, is constant. 39:55.329 --> 39:59.729 So, a cubic meter of the Universe has the same amount of 39:59.726 --> 40:04.676 dark energy in it now as a cubic meter of the Universe did when 40:04.683 --> 40:08.043 the Universe was only a cubic meter across, 40:08.040 --> 40:09.000 right? 40:09.000 --> 40:12.680 Where the whole observable Universe was packed down into a 40:12.680 --> 40:16.550 cubic meter, that cubic meter had only as much dark energy in 40:16.554 --> 40:18.924 it as, you know, this part of the 40:18.916 --> 40:20.166 Universe does now. 40:20.170 --> 40:25.510 Very odd behavior, but this is what Einstein's 40:25.514 --> 40:27.894 equations predict. 40:27.889 --> 40:32.419 Now, the thing is, we don't know that Einstein 40:32.418 --> 40:34.328 really was right. 40:34.329 --> 40:37.149 We don't, because we don't have a clue what the dark energy 40:37.149 --> 40:37.829 actually is. 40:37.829 --> 40:46.569 So let me--so, λ, the Cosmological Constant, 40:46.568 --> 40:56.298 suggests that dark energy has constant density. 40:56.300 --> 40:59.490 But, since we don't know what the heck this stuff is, 40:59.491 --> 41:00.781 maybe that's wrong. 41:00.780 --> 41:03.460 Or maybe not. 41:03.460 --> 41:10.020 If it's not, we don't call it λ anymore. 41:10.019 --> 41:15.419 But if you allow for changes in the density, you can get very 41:15.420 --> 41:18.300 interesting potential effects. 41:18.300 --> 41:20.480 And let me--we'll talk about this more next time, 41:20.479 --> 41:23.159 but let me just describe one of the very strange things that 41:23.158 --> 41:23.928 could happen. 41:23.929 --> 41:28.539 Suppose it is true--and this is not ruled out by the data we 41:28.536 --> 41:29.626 have so far. 41:29.630 --> 41:43.210 Suppose the dark energy density increases as the Universe gets 41:43.206 --> 41:45.206 bigger. 41:45.210 --> 41:47.600 And since we don't have any idea what this stuff is, 41:47.599 --> 41:49.659 it might do that, and we can't rule it out by 41:49.661 --> 41:50.881 observations just yet. 41:50.880 --> 41:53.740 And so, the Universe gets bigger and bigger. 41:53.739 --> 41:57.179 The density of the matter is going down, because you have the 41:57.175 --> 41:59.575 same amount of matter in a bigger space. 41:59.579 --> 42:02.759 But, supposing we invent some kind of dark energy where the 42:02.758 --> 42:06.318 density actually gets bigger as the Universe increases in size. 42:06.320 --> 42:16.390 Then, a cubic meter of volume has increasing dark energy as 42:16.393 --> 42:19.523 time goes along. 42:19.519 --> 42:25.039 That, of course, pushes the Universe out faster, 42:25.041 --> 42:28.801 so the acceleration increases. 42:28.800 --> 42:37.790 That makes the size increase and you get a feedback as the 42:37.793 --> 42:43.003 Universe exponentially expands. 42:43.000 --> 42:47.840 42:47.840 --> 42:50.400 You get an exponential expansion. 42:50.400 --> 42:55.170 And as that exponential expansion increases, 42:55.174 --> 43:01.724 the amount of dark energy in any particular cubic meter gets 43:01.724 --> 43:03.394 bigger too. 43:03.390 --> 43:04.670 And so, what happens? 43:04.670 --> 43:07.540 After a while, the dark energy in any cubic 43:07.539 --> 43:11.569 galaxy has become so much that it blows the galaxy apart. 43:11.570 --> 43:14.120 Gravity can't hold the galaxy together. 43:14.119 --> 43:16.359 And then, the expansion continues. 43:16.360 --> 43:20.100 And then, after a while, the amount of dark energy in 43:20.100 --> 43:23.050 one cubic star, if I can use that term, 43:23.050 --> 43:26.320 in one star becomes so great that it overcomes the gravity of 43:26.322 --> 43:28.452 the star and it blows the star apart. 43:28.449 --> 43:30.859 And then, the expansion continues even faster. 43:30.860 --> 43:34.390 And after a while, the amount of dark energy in a 43:34.394 --> 43:37.564 cubic meter--that would be a human being. 43:37.559 --> 43:42.049 Remember, human beings are exactly a cubic meter and 43:42.051 --> 43:44.871 exactly 100 kilograms in mass. 43:44.869 --> 43:47.889 The amount of dark energy in a human being overcomes the 43:47.894 --> 43:51.144 chemical bonds that hold your body together and human beings 43:51.139 --> 43:52.239 get blown apart. 43:52.239 --> 43:54.529 And eventually, you have so much dark matter 43:54.534 --> 43:57.154 that whole atoms--that atoms get blown to bits, 43:57.150 --> 44:00.580 and even the sub-atomic particles that are within them 44:00.582 --> 44:02.592 eventually get blown to bits. 44:02.590 --> 44:06.090 And so, dark energy conquers all. 44:06.090 --> 44:11.510 This is described as the Big Rip, and it is kind of an 44:11.505 --> 44:17.835 alternative hypothesis of what might happen to the Universe, 44:17.840 --> 44:21.950 that stems from an alternative hypothesis of what the dark 44:21.948 --> 44:26.128 energy is, that there's no particular reason to believe, 44:26.130 --> 44:28.150 but that hasn't been disproved. 44:28.150 --> 44:31.140 And since there's no particular reason to believe anything else, 44:31.143 --> 44:33.523 you can amuse your students by talking about it. 44:33.519 --> 44:38.779 So, to summarize this, here is--it's all a question of 44:38.782 --> 44:41.862 the scale factor versus time. 44:41.860 --> 44:43.040 Here is now. 44:43.040 --> 44:44.140 Here is 1. 44:44.140 --> 44:46.830 Here is an empty Universe. 44:46.829 --> 44:49.939 We thought that what would happen is that it would look 44:49.944 --> 44:52.314 like this, and either collapse, or not. 44:52.309 --> 44:57.339 What actually happened is, it turns out, 44:57.342 --> 45:00.442 things look like this. 45:00.440 --> 45:02.920 We only really observe it in the past, so there's a whole 45:02.924 --> 45:05.014 bunch of supernovae proving that that's true. 45:05.010 --> 45:08.590 And you can extrapolate a kind of gentle expansion that looks 45:08.585 --> 45:09.295 like this. 45:09.300 --> 45:17.590 This is the standard model with a Cosmological Constant. 45:17.590 --> 45:22.300 But if you assume that things get even bigger--that the dark 45:22.298 --> 45:25.488 energy increases per volume with time, 45:25.489 --> 45:29.169 then you asymptotically go to infinity at some time in the 45:29.165 --> 45:31.675 future and you blow everything apart. 45:31.680 --> 45:34.360 Not ruled out. 45:34.360 --> 45:37.760 And so, people are anxious to discover whether that, 45:37.763 --> 45:41.103 or some other set of crazy ideas, might be true. 45:41.099 --> 45:45.439 And we'll talk about how people are going about trying to nail 45:45.436 --> 45:46.996 this down next time.