1 00:00:00,012 --> 00:00:04,828 Edwin Hubble discovered that Andromeda is not a part of the Milky Way, and expanded 2 00:00:04,828 --> 00:00:08,879 our universe exponentially. He classified galaxy types, and neither 3 00:00:08,879 --> 00:00:13,489 of those is what he's really known for. What he's really known for had to do with 4 00:00:13,489 --> 00:00:18,247 measuring distances to galaxies. Again like he did to Andromeda, but to 5 00:00:18,247 --> 00:00:22,977 galaxies at a larger distances. so we're starting to measure distances at 6 00:00:22,977 --> 00:00:25,673 which finding cepheides becomes difficult. 7 00:00:25,673 --> 00:00:30,574 With todays' technology we can measure cepheides out to, as I say Maybe 10 8 00:00:30,574 --> 00:00:34,777 million parsecs or 20 million parsecs. But at the time, this was still 9 00:00:34,777 --> 00:00:37,592 difficult. Astronomers needed ways to measure 10 00:00:37,592 --> 00:00:41,522 distances to galaxies. Galaxies are easier to see than Cepheids, 11 00:00:41,522 --> 00:00:45,229 they're more luminous. What you'd like is a period luminosity 12 00:00:45,229 --> 00:00:48,854 relation for galaxies. And indeed, there are such, at least 13 00:00:48,854 --> 00:00:53,082 approximate relations. For spiral galaxies the Tully-Fisher 14 00:00:53,082 --> 00:00:58,031 relation relates the rotation velocity in a galaxy to it's luminosity. 15 00:00:58,031 --> 00:01:03,347 and there's a Tully-Fisher relation for every kind of, every type of galaxy. 16 00:01:03,347 --> 00:01:07,872 So S B galaxies have a different Tully-Fisher relation than SA. 17 00:01:07,872 --> 00:01:11,672 Galaxies and so on. And roughly, the idea is that, larger 18 00:01:11,672 --> 00:01:15,798 galaxies are more luminous and have larger rotational velocities. 19 00:01:15,798 --> 00:01:20,768 And you see here the accuracy with which this is relation holds. 20 00:01:20,768 --> 00:01:25,359 It's not a very accurate distance measurement, but it tells you that if you 21 00:01:25,359 --> 00:01:30,269 can measure with Doppler shifts, the rotational velocity of a galaxy You can 22 00:01:30,269 --> 00:01:34,164 classify its type from its shape. You can now figure out the luminosity of 23 00:01:34,164 --> 00:01:36,693 the galaxy. You have galaxies as standard candles. 24 00:01:36,693 --> 00:01:40,460 This are very brilliant standard candles indeed you can see them out, to very 25 00:01:40,460 --> 00:01:44,414 large distances and you can measure distances because if you have luminosity 26 00:01:44,414 --> 00:01:48,050 and you measure brightness, you can figure out the distance to something. 27 00:01:48,050 --> 00:01:52,587 There's an analogous relationship for elliptical galaxies which allows the 28 00:01:52,587 --> 00:01:57,522 distance to ellipticals, to be measured, today at larger distances yet, we can 29 00:01:57,522 --> 00:02:01,927 measure with type 1a supernovae. But remember, that if you want to measure 30 00:02:01,927 --> 00:02:06,447 the distance to a galaxy in which alas, there is not a type 1a supernovae that 31 00:02:06,447 --> 00:02:09,842 has been observed. Then you have been reduced to variable 32 00:02:09,842 --> 00:02:13,482 stars or these kind of methods and refinements thereof. 33 00:02:13,482 --> 00:02:18,051 So, using all these methods Hubble goes around and he measures the distances to 34 00:02:18,051 --> 00:02:22,362 many of the galaxies and, of course, try to understand how they work and measures 35 00:02:22,362 --> 00:02:26,706 their spectra, and this spectra take a while to identify because galaxies are 36 00:02:26,706 --> 00:02:30,859 moving at rather high velocities relative to each other and therefore some are 37 00:02:30,859 --> 00:02:34,999 approaching us at high velocity. Some are receding at high velocity, and 38 00:02:34,999 --> 00:02:39,418 you have a case of big red shifts or big blue shifts, and you need to figure out 39 00:02:39,418 --> 00:02:43,358 which spectral lines are which. Astronomers, as I said, are very good at 40 00:02:43,358 --> 00:02:46,347 spectrometry. And what Hubble finds when he starts 41 00:02:46,347 --> 00:02:51,074 working through these spectra Is that is, it looks farther and farther out into the 42 00:02:51,074 --> 00:02:55,570 universe, and galaxies that are more distant, less and less of them appear to 43 00:02:55,570 --> 00:03:00,130 be having negative radio velocity. Moving towards the Milky Way, more and 44 00:03:00,130 --> 00:03:04,473 more of them appear to receding and furthermore, the farther they get, the 45 00:03:04,473 --> 00:03:08,994 faster they appear to be receding, and so, here's a nice plate with an example 46 00:03:08,994 --> 00:03:13,851 of the The shifted spectra that Doppler is, that Hubble is measuring, so here are 47 00:03:13,851 --> 00:03:18,678 four images of four galaxies they become smaller, appear smaller as they get more 48 00:03:18,678 --> 00:03:22,450 distance in these negatives. And here are their spectra, compared 49 00:03:22,450 --> 00:03:25,282 against some standard spectrum above and below. 50 00:03:25,282 --> 00:03:29,512 And we're looking for some particular line of potassium here. 51 00:03:29,512 --> 00:03:34,364 And what we see is that the farther the galaxy is, the farther to the red this 52 00:03:34,364 --> 00:03:38,360 line has shifted. And the bottom image gives you a sense of 53 00:03:38,360 --> 00:03:43,826 how good these guys were with spectra graphs because it's not totally obvious 54 00:03:43,826 --> 00:03:48,603 that this little gap right here is a spectra line and furthermore that it is 55 00:03:48,603 --> 00:03:51,818 the potassium line. And it turns out that it was. 56 00:03:51,818 --> 00:03:57,214 And so, with these Hubble can relate that known wavelength of the sode, of the 57 00:03:57,214 --> 00:04:01,017 potasium line to the wavelength that which he measures it. 58 00:04:01,017 --> 00:04:06,047 He can use the relativistic version of the doppler shift formula or the Newton 59 00:04:06,047 --> 00:04:08,775 approximation. Non-realistic expression. 60 00:04:08,775 --> 00:04:11,468 Both of those are things we are familiar by now. 61 00:04:11,468 --> 00:04:16,009 And ye can convert the observed redshift into an observed recessional velocity. 62 00:04:16,009 --> 00:04:20,488 And the statement that the redshift is increasing with distant is the statement 63 00:04:20,488 --> 00:04:24,645 that the farther the galaxy is, the faster he observes it moving away from 64 00:04:24,645 --> 00:04:27,065 us. And so, here is Hubble's collection of 65 00:04:27,065 --> 00:04:31,612 data from the paper. that he published, and what we see here 66 00:04:31,612 --> 00:04:35,527 the horizontal axis is distance. The vertical axis is recessional 67 00:04:35,527 --> 00:04:39,207 velocity, radial velocity. We see that here's a galaxy that's 68 00:04:39,207 --> 00:04:44,250 actually approaching the Milky Way. That is fine, but that the farther You 69 00:04:44,250 --> 00:04:49,745 get the more the galaxies are all receding, and Hubble very bravely draws a 70 00:04:49,745 --> 00:04:54,806 straight line through this bit of data, and declares that he's found a relation 71 00:04:54,806 --> 00:05:00,155 between distance and relational velocity. Notice the Hubble Law, this is what he's 72 00:05:00,155 --> 00:05:04,622 famous for, the recessional velocity of the galaxy is given by a constant, 73 00:05:04,622 --> 00:05:09,246 Hubble's Constant, times its distance from the Milky Way or the Sun, it's the 74 00:05:09,246 --> 00:05:12,086 same thing. And Hubble's Constant is therefore, 75 00:05:12,086 --> 00:05:16,974 conversion of distance to velocity, so 1 way to express its units, because that's 76 00:05:16,974 --> 00:05:20,792 the way we measure it, is a kilometer per second recession. 77 00:05:20,792 --> 00:05:25,709 Per megapersec distance, and Hubble has an estimate for the value. 78 00:05:25,709 --> 00:05:31,646 he this estimate has been refined over the years, we have a lot more data. 79 00:05:31,646 --> 00:05:37,376 but this consant is of such importance that long before its exact value was 80 00:05:37,376 --> 00:05:41,938 known Astronomers needed to use it in their expressions and so they developed a 81 00:05:41,938 --> 00:05:44,761 method of sort or parameterizing their ignorance. 82 00:05:44,761 --> 00:05:49,295 The Hubble constant is characteristically writen and as 100 times h kilometer per 83 00:05:49,295 --> 00:05:52,889 second per megaparsec. In other words if someone were to measure 84 00:05:52,889 --> 00:05:57,290 the Hubble constant and its value were to be discovered to be 100 kilometers per 85 00:05:57,290 --> 00:06:01,893 second per megaparsec, we'd say h is 1. And we'd go around into all the formulas, 86 00:06:01,893 --> 00:06:06,085 and all the books and papers that have various powers of H in them, and set H to 87 00:06:06,085 --> 00:06:10,454 1 and get an answer, but at the moment, until we're absolutely certain of the 88 00:06:10,454 --> 00:06:14,622 value of the Hubble constant, people use this little h to parameterize. 89 00:06:14,622 --> 00:06:19,425 The dependence on that measurement because so much depends on this, as we 90 00:06:19,425 --> 00:06:24,305 shall see, but the value of h is not too far from one, We now have far better 91 00:06:24,305 --> 00:06:29,473 measurements that hubble had, we have measured much more statistics, the most 92 00:06:29,473 --> 00:06:34,789 recent measurements suggest a value of H on the order of point seventy one, and as 93 00:06:34,789 --> 00:06:40,914 you see we know it quite accurately, We have here a plot of recent measurements 94 00:06:40,914 --> 00:06:47,498 in the vein of Hubble of recessional velocities, a function of distance out to 95 00:06:47,498 --> 00:06:51,641 1.6 billion light years away, so 500 megaparsecs. 96 00:06:51,641 --> 00:06:57,405 We see that Hubble's relation, linear relationship Holds up very, very well 97 00:06:57,405 --> 00:07:02,269 what's exciting about this plot is that little rectangle at the lower left, that 98 00:07:02,269 --> 00:07:05,082 represents the data that Hubble actually had. 99 00:07:05,082 --> 00:07:09,812 So he was predicting the straight line velocity on the base, the straight line 100 00:07:09,812 --> 00:07:14,056 plot, and it's slope on the basis of a very small amount of data and was 101 00:07:14,056 --> 00:07:19,711 gloriously vindicated. Now typically in astronomy we write the 102 00:07:19,711 --> 00:07:23,771 Doppler shift as lamda is 1 + z * lamda 0. 103 00:07:23,771 --> 00:07:28,704 And we call z the red shift, so z is a positive number. 104 00:07:28,704 --> 00:07:36,462 And assuming something is red shifted and z = 0 is a red shift of 0, in other words 105 00:07:36,462 --> 00:07:41,935 lamda = lamda 0. And so clearly z is related to velocity. 106 00:07:41,935 --> 00:07:46,841 The expression is written down here, lets figure it out. 107 00:07:46,841 --> 00:07:52,683 So, lamda / by lamda 0 is 1 + z. And lamda / by lamda 0, remember we had 108 00:07:52,683 --> 00:07:56,709 lamda / by lamda 0 is the square root of 1 + v / c. 109 00:07:56,709 --> 00:08:02,452 This is the completely Relativistic formula, and this is supposed to be 1+z. 110 00:08:02,452 --> 00:08:07,627 So, the first thing I do, of course, is I, I want to figure out how z determines 111 00:08:07,627 --> 00:08:12,777 v, and so I want to solve this for v over c, and the first thing I do, of course, 112 00:08:12,777 --> 00:08:20,877 is I square both sides. And I write that, 1+z^2=1+vC/1-vC. 113 00:08:20,877 --> 00:08:30,802 Then I multiply both sides by 1-v/C, and I find 1-v/C. 114 00:08:30,802 --> 00:08:41,837 *(1+z)²=1+V/C and then, I move all the V/C over here, so I have V/C * (1+(1+z) ^ 115 00:08:41,837 --> 00:08:51,260 2) and then everything without V/C goes over here and that (1+z)²-1. 116 00:08:51,260 --> 00:08:59,155 So, I solve for V/C and I get that V/C = (1+z)²-1 /(1 + z)² + 1 and again if z is 117 00:08:59,155 --> 00:09:07,851 small, if the red-shift is small, you can use Newton's approximation to show that 118 00:09:07,851 --> 00:09:12,542 this is approximately z. Which is indeed when this is 119 00:09:12,542 --> 00:09:18,297 approximately 1+v over c, lambda 0, then z is approximately v over c, but this is 120 00:09:18,297 --> 00:09:23,952 the exact relativistic expression. So, astronomers will rarely tell you, 121 00:09:23,952 --> 00:09:29,707 unless they're talking to, you know, the Hoi polloi like us, that an object is at 122 00:09:29,707 --> 00:09:36,767 a distance of 2.8 billion parsecs, they will tell you that it has a redshift of 123 00:09:36,767 --> 00:09:40,587 .3. The reason is that we'll see next week 124 00:09:40,587 --> 00:09:47,057 that distances are ill defined but certainly redshifts are measured, 125 00:09:47,057 --> 00:09:55,062 observable quantities and The larger H redshift and so we basically can speak 126 00:09:55,062 --> 00:10:00,967 about redshift as a surrogate for distance and indeed the Hubble Law tells 127 00:10:00,967 --> 00:10:06,957 us, remember we solve for v over c as a function of z here, but the Hubble Law 128 00:10:06,957 --> 00:10:10,662 tells us that v over c is the same as H0 D over c. 129 00:10:10,662 --> 00:10:14,782 So if you know z you can figure out D as well as v, so. 130 00:10:14,782 --> 00:10:20,325 Knowing the red shift tells you not only the speed obviously with which the galaxy 131 00:10:20,325 --> 00:10:24,576 is receding, but also its distance. So we have to digest this. 132 00:10:24,576 --> 00:10:28,828 In whatever direction we look, galaxies are receding from us. 133 00:10:28,828 --> 00:10:33,692 At the rate of recession does not depend on the direction of the galaxy. 134 00:10:33,692 --> 00:10:37,737 Galaxies at the same distant at all directions are receding with a equal 135 00:10:37,737 --> 00:10:41,410 velocity, but the farther they are the faster they are receding. 136 00:10:41,410 --> 00:10:45,815 Now, depending on your taste, you could either conclude that were not popular 137 00:10:45,815 --> 00:10:50,282 galaxy, or more technically that we're in the center of some cosmic expansion, 138 00:10:50,282 --> 00:10:54,863 everything is moving away from us. It turns out that this is not exactly 139 00:10:54,863 --> 00:10:57,876 correct. Your intuition is in this case actually 140 00:10:57,876 --> 00:11:01,780 misleading you. Imagine this, collection of galaxies here 141 00:11:01,780 --> 00:11:05,004 they are all going to be moving away from each other. 142 00:11:05,004 --> 00:11:09,577 The center of expansion could be the center of the screen, or if I take this 143 00:11:09,577 --> 00:11:14,354 and add to it a motion of everybody to the right, the center of expansion could 144 00:11:14,354 --> 00:11:18,191 be way over to our left. Each galaxy, as it observes each of the 145 00:11:18,191 --> 00:11:23,055 others will see that each of of the other galaxies is growing farther and farther 146 00:11:23,055 --> 00:11:26,219 away from it. So all that is going on is that as these 147 00:11:26,219 --> 00:11:31,192 galaxies grow farther and farther away, all of their distances are increasing and 148 00:11:31,192 --> 00:11:35,746 the fact that in this case. It looks like the expansion is about the 149 00:11:35,746 --> 00:11:39,921 point of the center of the screen is completely irrelevant. 150 00:11:39,921 --> 00:11:45,338 They are all moving away and the farther they are, the faster they are moving. 151 00:11:45,338 --> 00:11:49,612 There is no centrality involved, this is just the way it is. 152 00:11:49,612 --> 00:11:54,986 So we need not invoke some particular central location for ourselves. 153 00:11:54,986 --> 00:12:01,270 Everything is moving away from everything else, all distances are growing, every 154 00:12:01,270 --> 00:12:06,805 observer as he looks around him or she looks around her will see all other 155 00:12:06,805 --> 00:12:12,437 observers receding and the mathematical expression of this is that if you 156 00:12:12,437 --> 00:12:16,297 measure. Any distance in the universe at time t*0, 157 00:12:16,297 --> 00:12:21,177 by t*0 I mean now and then you measure it either later or earlier. 158 00:12:21,177 --> 00:12:26,872 If you measure it later, it will have grown by a factor which depends on time 159 00:12:26,872 --> 00:12:31,132 in this fashion. What this tells you is that over a time, 160 00:12:31,132 --> 00:12:34,848 t Distances grow, by an amount that is H*D, oh, yeah. 161 00:12:34,848 --> 00:12:39,678 The speed of recession is H*D. Now this is valid both into the future 162 00:12:39,678 --> 00:12:44,506 and of course this didn't just start happening now, so it's valid into the 163 00:12:44,506 --> 00:12:47,434 past. If T is less T0, if you're looking into 164 00:12:47,434 --> 00:12:52,462 the past, then this is a negative number, distance in the past were smaller. 165 00:12:52,462 --> 00:12:53,797 Than they are now. Fine. 166 00:12:53,797 --> 00:12:57,917 If everything is receding, that means everything used to be closer together. 167 00:12:57,917 --> 00:13:02,087 I should point out immediately that what we're seeing is the galaxies, all 168 00:13:02,087 --> 00:13:04,922 distances between all galaxies appear to be growing. 169 00:13:04,922 --> 00:13:08,802 This does not mean that the distance between say, the sun and the Earth is 170 00:13:08,802 --> 00:13:13,030 growing, first of all, or that my belly's growing That's not cosmic expansion. 171 00:13:13,030 --> 00:13:16,454 This is a description that is valid for objects too far away to be 172 00:13:16,454 --> 00:13:19,806 gravitationally bound. The Earth and the Sun and the Milky way 173 00:13:19,806 --> 00:13:23,106 are all moving as one object. The Milky is not in particular. 174 00:13:23,106 --> 00:13:27,384 Expanding this is the motion of distant galaxies, that are not gravitationally 175 00:13:27,384 --> 00:13:30,541 bound to each other. It's to that case the Hubble applies. 176 00:13:30,541 --> 00:13:35,019 The other point, Point is that of course, there are still peculiar motions, 177 00:13:35,019 --> 00:13:39,426 galaxies and are still orbiting various things and that they do on top of this 178 00:13:39,426 --> 00:13:42,549 global expansion. So everything is expanding but that 179 00:13:42,549 --> 00:13:47,183 doesn't necessarily the only motion that galaxies do so for example one could ask 180 00:13:47,183 --> 00:13:51,947 everything is expanding how do galaxies collide that is, That is a case where the 181 00:13:51,947 --> 00:13:56,277 parculiar, are larger than the Hubble expansion for the relatively small 182 00:13:56,277 --> 00:14:00,257 distance between them and that usually happens in cases where their 183 00:14:00,257 --> 00:14:03,137 gravitationally strongly interacting or bound. 184 00:14:03,137 --> 00:14:05,882 Okay. So, Hubble gives us this picture, where 185 00:14:05,882 --> 00:14:10,237 the entire universe is growing, every galaxy is receding from every other 186 00:14:10,237 --> 00:14:12,958 galaxy. What's it growing into? What is beyond 187 00:14:12,958 --> 00:14:17,453 the place where these galaxies are now? More of the universe, the galaxies are 188 00:14:17,453 --> 00:14:20,777 receding into the universe. We'll talk about the, sort of 189 00:14:20,777 --> 00:14:24,303 mathematical implications of this expansion a lot next week. 190 00:14:24,303 --> 00:14:28,747 But at the moment there need not be an edge to the universe in order for all 191 00:14:28,747 --> 00:14:31,885 distances to grow. All we have is a bunch of galaxies that 192 00:14:31,885 --> 00:14:36,204 are receding from each other, and beyond them are probably more galaxies that are 193 00:14:36,204 --> 00:14:40,341 receding even faster from where we sit, and no matter which galaxy you sit on, 194 00:14:40,341 --> 00:14:44,743 everything recedes at a rate proportional to its distance, because all distances 195 00:14:44,743 --> 00:14:47,962 grow by the same factor. This is the symmetric picture. 196 00:14:47,962 --> 00:14:51,590 Okay, so Hubble teaches us that all distances are increasing. 197 00:14:51,590 --> 00:14:54,144 Right from there, you have a big discovery. 198 00:14:54,144 --> 00:14:56,762 Look, this can't have been going on forever. 199 00:14:56,762 --> 00:15:01,422 Because, if in the future, distances are going to bigger, as I said in the past, 200 00:15:01,422 --> 00:15:05,125 they are going to be smaller. And, farther in the past they were 201 00:15:05,125 --> 00:15:08,752 smaller yet, And farther in the past they were smaller yet. 202 00:15:08,752 --> 00:15:13,860 At, oh, and at some point in the past you can solve the equation that says D(t) = 203 00:15:13,860 --> 00:15:15,475 0. The distance is zero. 204 00:15:15,475 --> 00:15:20,940 Which distance? It doesn't really matter. If I make this factor zero, all distances 205 00:15:20,940 --> 00:15:24,048 are zero. All of the galaxies that we see and the 206 00:15:24,048 --> 00:15:26,412 ones that are too far for us to see. 207 00:15:26,412 --> 00:15:45,742 208 00:15:45,742 --> 00:15:54,113 What is that time well solve the equation, one plus H times t minus t0 is 209 00:15:54,113 --> 00:16:02,142 zero, move the one over to there you find that H t minus Hto equal. 210 00:16:02,142 --> 00:16:11,677 To -1, and so what does that tell me? That tells me dividing by H, I call that 211 00:16:11,677 --> 00:16:19,647 H0 ^ -1 and cross out the H's over here and I find that t = t0 - H0 ^ -1. 212 00:16:19,647 --> 00:16:27,785 Wait, so H0 ^ -1 is a time? I thought H was something in a kilometer per second 213 00:16:27,785 --> 00:16:31,392 per megaparsec. Well, once you remember that a megaparsec 214 00:16:31,392 --> 00:16:36,144 and a kilometer are both distance, you realize that you can convert one to the 215 00:16:36,144 --> 00:16:38,885 other. And indeed, kilometer per second per 216 00:16:38,885 --> 00:16:44,038 megaparsec is one over seconds times some small number or megaparsecs per kilometer 217 00:16:44,038 --> 00:16:48,052 per second The units of Ho inverse are indeed the units of time. 218 00:16:48,052 --> 00:16:51,552 So what is this time? This is the so called Hubble Time. 219 00:16:51,552 --> 00:16:55,377 It's very important. This is the time where if you imagine if 220 00:16:55,377 --> 00:17:00,377 this equation governs the universe, this is the time in the past of go, the time 221 00:17:00,377 --> 00:17:04,272 in the past in which everything was on top of everything else. 222 00:17:04,272 --> 00:17:07,871 So let's compute it, the 100 gets converted to .01. 223 00:17:07,871 --> 00:17:12,968 H converted to H inverse, this is the inverse of a kilometer per second per 224 00:17:12,968 --> 00:17:16,504 megaparsec. A megaparsec is how many kilometer's? 225 00:17:16,504 --> 00:17:21,447 Well a megaparsec is this many Au. And then Au is this many kilometer's, 226 00:17:21,447 --> 00:17:26,701 except, I also, while I was at it, Introduced the mega parsecs. 227 00:17:26,701 --> 00:17:33,389 So, there's 10 ^ 11, this is how many, a mega, a mega parsec is and the seconds 228 00:17:33,389 --> 00:17:37,724 come out. I plug in all the numbers, I get this 229 00:17:37,724 --> 00:17:42,331 number. If I allow multiply through, I get 9.8h 230 00:17:42,331 --> 00:17:47,854 inverse, plug in the most Recent value for H of .71 I get finally my result for 231 00:17:47,854 --> 00:17:52,681 the Hubble time, 13.8 billion years. What is this? Well this is the maximum 232 00:17:52,681 --> 00:17:57,220 amount of time the universe can exist because before that, at that time 233 00:17:57,220 --> 00:18:01,662 everything was on top of everything else and I can't go farther back. 234 00:18:01,662 --> 00:18:05,101 [UNKNOWN]. So we have a finite age for the universe, 235 00:18:05,101 --> 00:18:09,489 given Hubble's expansion. And this is our rough and ready estimage 236 00:18:09,489 --> 00:18:13,806 for how old the universe is. It turns out to be surprisingly good. 237 00:18:13,806 --> 00:18:17,806 We will need to improve it. It will turn out that this precise 238 00:18:17,806 --> 00:18:23,554 behavior is a Newton approximation to some More complicated time dependents of 239 00:18:23,554 --> 00:18:27,110 distances, that'll be the topic of next week. 240 00:18:27,110 --> 00:18:30,716 But first, we can get even more out this story. 241 00:18:30,716 --> 00:18:36,311 Remember that the red shift, z, determines distance, at least for small 242 00:18:36,311 --> 00:18:43,517 z, where the Newton Approximation holds, as, v/ c is 1 +, z/ c is z Remember that 243 00:18:43,517 --> 00:18:51,324 V/C was supposed to be Z and V/C is therefore H0/C, D/C and so D is ZC/H0. 244 00:18:51,324 --> 00:18:58,504 So if you know the red-shift you can figure out the number, the distance. 245 00:18:58,504 --> 00:19:04,002 This, allows you to figure out something else though. 246 00:19:04,002 --> 00:19:08,783 Someting called the look back time. If a galaxy is a distance d away, then, 247 00:19:08,783 --> 00:19:13,777 what I am seeing is the light that left that galaxy a while ago, and the farther 248 00:19:13,777 --> 00:19:17,464 the galaxy is, the longer the light has taken to get here. 249 00:19:17,464 --> 00:19:21,132 The Andromed galaxy is 2 1/2 million light years away. 250 00:19:21,132 --> 00:19:24,997 We see the Andromeda galaxy as it was 2 and a half million years ago. 251 00:19:24,997 --> 00:19:28,371 The farther an object is the farther back in time we see it. 252 00:19:28,371 --> 00:19:32,765 The look back time is simply the time that the light was emitted is t0 which is 253 00:19:32,765 --> 00:19:37,398 our notation for the present minus D over c, this is how long it takes light at the 254 00:19:37,398 --> 00:19:42,255 speed c to cover that distance. PLUGGING IN THE VALUE FOR D WE GET THAT 255 00:19:42,255 --> 00:19:47,696 THE TIME WE SEE A GALAXY ACT IS T ZERO MINUS Z TIMES EIGHT ZERO INVERSE. 256 00:19:47,696 --> 00:19:53,602 AGAIN Z IS THE FRACTION OF THE HUBBLE TIME IF YOU WANT A FRACTION OF THE AGE OF 257 00:19:53,602 --> 00:19:59,652 THE UNIVERSE, THAT HAS PASSED SINCE THE LIGHT WAS EMITTED FROM THIS GALAXY. 258 00:19:59,652 --> 00:20:04,052 [INAUDIBLE] us another exciting way to think about things. 259 00:20:04,052 --> 00:20:10,055 let's think about it this way. So, remember that I'm going to compute 260 00:20:10,055 --> 00:20:15,908 the wavelength at which light was emitted / the wavelength at which I'm going to 261 00:20:15,908 --> 00:20:19,586 observe it. This is kind of backwards to the usual 262 00:20:19,586 --> 00:20:25,881 calculation of the Redshift, the redshift is lambda observed divided by lambda 263 00:20:25,881 --> 00:20:29,335 emitted, so this is actually 1+z, inverse. 264 00:20:29,335 --> 00:20:36,254 it'll be clear why I'm doing it this way. Now I'm going to assume that I'm in the 265 00:20:36,254 --> 00:20:42,627 small And that, reasonably small redshift neighborhood of non relativistic motion 266 00:20:42,627 --> 00:20:48,332 so that this expression is correct, first of all and second of all that because I 267 00:20:48,332 --> 00:20:53,692 can use Newton's approximation because z is much less than 1, then I can use 268 00:20:53,692 --> 00:20:57,722 Newton's approximation to approximate 1 + z to the -1. 269 00:20:57,722 --> 00:21:03,548 As one minus z. Ok, and then from here i have an 270 00:21:03,548 --> 00:21:13,445 expression for minus z which says that this is equal to one minus to get minus z 271 00:21:13,445 --> 00:21:22,254 i take h zero times minus z is plus H 0 times T emission minus T 0. 272 00:21:22,254 --> 00:21:28,341 Oh, but I know what 1 plus H 0 times T minus T 0 is. 273 00:21:28,341 --> 00:21:38,799 Remember that our expression for the Hubble change in distances, was D of T, 274 00:21:38,799 --> 00:21:43,652 is D of T 0. Times 1 + H zero T - T zero. 275 00:21:43,652 --> 00:21:54,512 Oh good, so this is exactly D at the time of emission, for any distance / that 276 00:21:54,512 --> 00:21:57,677 distance at T zero. Okay. 277 00:21:57,677 --> 00:22:02,849 So what do we have? That, the wavelength at the time of omission, / by the light 278 00:22:02,849 --> 00:22:07,825 wave length that we observe, is the, which is 1 - Z approximately is the same 279 00:22:07,825 --> 00:22:11,410 as distance at the time of emission, and distance now. 280 00:22:11,410 --> 00:22:15,848 Which distance? Doesn't matter. They all scale by the same factor. 281 00:22:15,848 --> 00:22:20,077 Write that out cleanly. And now you see, that it's telling me 282 00:22:20,077 --> 00:22:23,609 something, What is this? This is a distance, the 283 00:22:23,609 --> 00:22:27,140 wave length. This is telling me, that the wavelength 284 00:22:27,140 --> 00:22:32,918 over the time between emission and observation or absorption has scaled the 285 00:22:32,918 --> 00:22:37,738 same way any other distance would. So the red, Hubble's redshift formula is 286 00:22:37,738 --> 00:22:42,209 basically telling me that the wave length of a light wave grows along with the 287 00:22:42,209 --> 00:22:46,221 distances between galaxies. That's a very strange way to think about 288 00:22:46,221 --> 00:22:48,430 it. We'll see next week that it's very 289 00:22:48,430 --> 00:22:52,325 natural, this is thinking of the redshift, of the redshift not as a 290 00:22:52,325 --> 00:22:54,829 Doppler shift but as a cosmological shift. 291 00:22:54,829 --> 00:22:59,428 The wave lengths of light stretch just like any other distance, we'll come back 292 00:22:59,428 --> 00:23:00,412 to this next week.