1 00:00:01,181 --> 00:00:06,057 Finally, let us address the question of, is the universe really expanding? 2 00:00:06,057 --> 00:00:12,366 The reason we think its expanding is the existence of Hubble's Law, and this is 3 00:00:12,366 --> 00:00:17,532 generally accepted to be true. However, there are other possibilities, 4 00:00:17,532 --> 00:00:22,530 hence there is a so-called Tired Light theory, which states that for some reason 5 00:00:22,530 --> 00:00:27,089 that as yet is completely unknown, photons coming from very far away lose 6 00:00:27,089 --> 00:00:31,673 their energy on the way here in a way that's proportional to their travel 7 00:00:31,673 --> 00:00:34,871 distance. There is no physics behind it, but it's a 8 00:00:34,871 --> 00:00:38,442 possibility. So, several tests have been actually 9 00:00:38,442 --> 00:00:42,801 designed to demonstrate that universe actually is expanding. 10 00:00:42,801 --> 00:00:48,037 The first of those is so called Tolman Test, which Tolman and Hubble came up 11 00:00:48,037 --> 00:00:53,170 with in 1930s, and it uses behavior as surface brightness as a function of 12 00:00:53,170 --> 00:00:55,812 distance. And here is how it works. 13 00:00:55,812 --> 00:00:59,847 If the Universe wasn't expanding at all, nothing else funny was going on. 14 00:00:59,847 --> 00:01:04,072 Surface brightness will be constant, not depending on the distance because 15 00:01:04,072 --> 00:01:08,022 remember, the luminosity of the clients was the square of the distance, 16 00:01:08,022 --> 00:01:12,887 but so does the area of the angular areal over which its distributed so the ratio 17 00:01:12,887 --> 00:01:17,132 of the two remains constant. In Tired Light Theory, the brightness 18 00:01:17,132 --> 00:01:20,792 will decline with redshift as first power of one plus redshift. 19 00:01:20,792 --> 00:01:25,482 And finally, in an expanding Universe, it will decline as the fourth power of 20 00:01:25,482 --> 00:01:29,797 stretch factor one plus redshift. The second method uses time dilation of 21 00:01:29,797 --> 00:01:33,522 Supernova light curves. Recall that those can be standardized for 22 00:01:33,522 --> 00:01:38,823 type 1A Supernova to the same shape. Now, these Supernova or rather their host 23 00:01:38,823 --> 00:01:44,229 galaxies are receiving from us with relativistic speeds, and so clocks are 24 00:01:44,229 --> 00:01:48,504 ticking slower there. So, we have to compensate for the time 25 00:01:48,504 --> 00:01:54,014 dilation. So, in addition to the stretch factor that brings them all together, 26 00:01:54,014 --> 00:01:59,934 light curves have to be compensated for time dilation that's proportional to the 27 00:01:59,934 --> 00:02:05,145 first power of, of the stretch factor 1 + z And finally, somewhat indirect 28 00:02:05,145 --> 00:02:10,072 argument, is the black body nature and temperature of the cosmic 29 00:02:10,072 --> 00:02:13,676 micro-background. In an expanding Universe, the shape of 30 00:02:13,676 --> 00:02:19,532 the black body curve is preserved and the energy density has to scale as the fourth 31 00:02:19,532 --> 00:02:23,915 power of temperature. If the Universe wasn't expanding, that 32 00:02:23,915 --> 00:02:27,142 relationship would not be exactly power of four. 33 00:02:27,142 --> 00:02:31,105 But we do see essentially perfect black body radiation, 34 00:02:31,105 --> 00:02:35,452 which is perfectly consistent with an expanding Universe. 35 00:02:35,452 --> 00:02:40,527 So, here's how Tolman Test works. In non expanding Euclidian space, surface 36 00:02:40,527 --> 00:02:45,452 brightness is constant and does not depend distance. Because luminosity 37 00:02:45,452 --> 00:02:50,677 declines a second power distance and so does the angular area over which we're 38 00:02:50,677 --> 00:02:55,983 dividing it to get surface brightness. However, in an expanding Universe, we 39 00:02:55,983 --> 00:03:00,860 have to deal with angular diameter distance and luminosity distance. 40 00:03:00,860 --> 00:03:05,528 As you recall, the angular diameter distance is equal to the physical 41 00:03:05,528 --> 00:03:11,356 distance divided by one plus redshift because of the objects fixed and proper 42 00:03:11,356 --> 00:03:16,793 coordinates do not expand with co-moving coordinates. And luminosity distance is 43 00:03:16,793 --> 00:03:21,654 bigger than co-moving distance by factor one plus redshift because the photons 44 00:03:21,654 --> 00:03:25,882 lose energy and the rate of the photon emission is also direct. 45 00:03:25,882 --> 00:03:31,017 So the upshot of this is that surface brightness will decline as one plus 46 00:03:31,017 --> 00:03:36,127 redshift to the 4th power relative to what it would be if the Universe wasn't 47 00:03:36,127 --> 00:03:39,771 expanding. Note, that this has nothing to do with 48 00:03:39,771 --> 00:03:44,244 curvature of space or anything else. It simply tests whether universe is 49 00:03:44,244 --> 00:03:48,921 expanding or not, and assumes that special relativity is valid and nobody's 50 00:03:48,921 --> 00:03:51,866 doubting that. So, in some sense, it's completely 51 00:03:51,866 --> 00:03:56,812 independent of cosmology of Hubble constant or all cosmological paramaters. 52 00:03:56,812 --> 00:04:02,165 In order to perform this test, we need something that can be seen far away that 53 00:04:02,165 --> 00:04:06,802 has a constant surface brightness, what we may call standard fuzz. 54 00:04:06,802 --> 00:04:12,107 One good choice is the surface brightness intercept of the fundamental plane 55 00:04:12,107 --> 00:04:16,028 correlations. Remember, they connect things like radii, 56 00:04:16,028 --> 00:04:20,503 velocity dispersion, and means surface brightness of galaxies 57 00:04:20,503 --> 00:04:25,577 in what's essentially perfect correlation module of the Earth, module of measument 58 00:04:25,577 --> 00:04:29,188 of the Earth. So, we can reproject it in such a way 59 00:04:29,188 --> 00:04:34,593 that one axis has surface brightness on it, and the intecept on that axis will be 60 00:04:34,593 --> 00:04:39,255 defining the standard fuzz. So, if we have two clusters of galaxies, 61 00:04:39,255 --> 00:04:44,457 one larger distance than the other, and we compare the intercepts for their 62 00:04:44,457 --> 00:04:48,966 own fundamental plane solutions, they should shift according to the 63 00:04:48,966 --> 00:04:51,283 expansion law. This test was done, 64 00:04:51,283 --> 00:04:55,358 and here is the result. This is a log log plot so the power law 65 00:04:55,358 --> 00:04:59,089 is a straight line, and the line that's drawn through the 66 00:04:59,089 --> 00:05:02,281 points here is exactly one plus redshift to the -4 power. 67 00:05:02,281 --> 00:05:07,175 So, the Universe does really seem to be expanding exactly as Tolman Test would 68 00:05:07,175 --> 00:05:10,265 say it would. Now, the time dilation of Supernova light 69 00:05:10,265 --> 00:05:13,810 curves. On, shown on the left here is a set of 70 00:05:13,810 --> 00:05:18,512 light curves as observed for the normalized to the same peak brightness 71 00:05:18,512 --> 00:05:21,562 for Supernova of type 1A, a different redshift. 72 00:05:21,562 --> 00:05:26,926 On the right, we apply the stretch factor to, that's normally used to standardize 73 00:05:26,926 --> 00:05:29,706 them. However, no correction was made for 74 00:05:29,706 --> 00:05:33,754 realistic time dilation. In the lower left now, we see what 75 00:05:33,754 --> 00:05:38,872 happens when we apply the relativistic time dilation correction, the scatter 76 00:05:38,872 --> 00:05:42,044 goes way down. And then, if we, of course, bend the 77 00:05:42,044 --> 00:05:47,492 points, it becomes very obvious. Thus, Supernova light curves a sense of 78 00:05:47,492 --> 00:05:52,747 giant clocks, do behave exactly in the way that should if the Universe was 79 00:05:52,747 --> 00:05:56,302 expanding. Another way to show this result is to 80 00:05:56,302 --> 00:06:01,777 plot this characteristic width of Supernova light curves before and after 81 00:06:01,777 --> 00:06:07,402 relativistic correction and before you can see there is a residual trend, 82 00:06:07,402 --> 00:06:12,002 after the distribution is flat. Which means that is the way it should be. 83 00:06:12,002 --> 00:06:15,797 So, next week, we'll start talking about cosmological tests. 84 00:06:15,797 --> 00:06:19,775 How do we actually figure out in what kind of Universe do we live?