1 00:00:00 --> 00:00:03,533 2 00:00:03,533 --> 00:00:07,953 Today I want to talk with you about Doppler effect, 3 00:00:07,953 --> 00:00:12,728 and I will start with the Doppler effect of sound which 4 00:00:12,728 --> 00:00:17,856 many of you perhaps remember from your high school physics. 5 00:00:17,856 --> 00:00:22,454 If a source of sound moves towards you or if you move 6 00:00:22,454 --> 00:00:27,14 towards a source of sound, you hear an increase in the 7 00:00:27,14 --> 00:00:30,324 pitch. And if you move away from each 8 00:00:30,324 --> 00:00:34,745 other you hear a decrease of a pitch. 9 00:00:34,745 --> 00:00:40,703 Let this be the transmitter of sounds and this is the receiver 10 00:00:40,703 --> 00:00:44,22 of sound, it could be you, your ears. 11 00:00:44,22 --> 00:00:49,495 And suppose this is the velocity of the transmitter and 12 00:00:49,495 --> 00:00:53,012 this is the velocity of the receiver. 13 00:00:53,012 --> 00:00:58,58 And V should be larger than zero if the velocity is in the 14 00:00:58,58 --> 00:01:01,999 direction. And in the equations what 15 00:01:01,999 --> 00:01:08,153 follow, smaller than zero it is in this direction. 16 00:01:08,153 --> 00:01:12,386 The frequency that the receiver will experience, 17 00:01:12,386 --> 00:01:17,34 will hear if you like that word, that frequency I call F 18 00:01:17,34 --> 00:01:20,672 prime. And F is the frequency as it is 19 00:01:20,672 --> 00:01:26,256 transmitted by the transmitter. And that F prime is F times the 20 00:01:26,256 --> 00:01:31,66 speed of sound minus V receiver divided by the speed of sound 21 00:01:31,66 --> 00:01:36,884 minus V of the transmitter. So this is known as the Doppler 22 00:01:36,884 --> 00:01:41,569 shift equation. If you have Volume one of 23 00:01:41,569 --> 00:01:45,117 Giancoli you can look it up there as well. 24 00:01:45,117 --> 00:01:47,973 Suppose you are not moving at all. 25 00:01:47,973 --> 00:01:51,781 You are sitting still. So V receiver is zero. 26 00:01:51,781 --> 00:01:55,935 But I move towards you with one meter per second. 27 00:01:55,935 --> 00:02:00,781 If I move towards you then F prime will be larger than F. 28 00:02:00,781 --> 00:02:05,541 If I move away from you with one meter per second then F 29 00:02:05,541 --> 00:02:11,576 prime will be smaller than F. The speed of sound is three 30 00:02:11,576 --> 00:02:16,887 hundred forty meters per second. So if F which is the frequency 31 00:02:16,887 --> 00:02:20,485 that I will produce is four thousand hertz, 32 00:02:20,485 --> 00:02:24,512 then if I move to you with one meter per second, 33 00:02:24,512 --> 00:02:29,309 which I'm going to try to do, then the frequency that you 34 00:02:29,309 --> 00:02:33,679 will experience is about four thousand twelve hertz. 35 00:02:33,679 --> 00:02:36,506 It's up by oh point three percent. 36 00:02:36,506 --> 00:02:41,732 Which is that ratio one divided by three forty. 37 00:02:41,732 --> 00:02:45,605 And if I move away from you with one meter per second, 38 00:02:45,605 --> 00:02:49,844 then the frequency that you will hear is about twelve hertz 39 00:02:49,844 --> 00:02:52,183 lower. So you hear a lower pitch. 40 00:02:52,183 --> 00:02:54,668 About oh point three percent lower. 41 00:02:54,668 --> 00:02:58,615 I have here a tuning fork. Tuning fork is four thousand 42 00:02:58,615 --> 00:03:01,173 hertz. I will bang it and I will try 43 00:03:01,173 --> 00:03:05,266 to move my hand towards you one meter per second roughly. 44 00:03:05,266 --> 00:03:08,044 That's what I calculated it roughly is. 45 00:03:08,044 --> 00:03:10,529 Move it away from you, towards you, 46 00:03:10,529 --> 00:03:13,526 away from you, as long 47 00:03:13,526 --> 00:03:17,916 as the sound lasts. You will hear the pitch change 48 00:03:17,916 --> 00:03:22,843 from four thousand twelve to three thousand nine hundred 49 00:03:22,843 --> 00:03:25,352 eight-eight. Very noticeable. 50 00:03:25,352 --> 00:03:29,205 Have you heard it? Who has heard clearly the 51 00:03:29,205 --> 00:03:31,982 Doppler shift, raise your hands, 52 00:03:31,982 --> 00:03:32,878 please? OK. 53 00:03:32,878 --> 00:03:36,014 Chee chee chee chee it's very clear. 54 00:03:36,014 --> 00:03:41,389 Increased fre- frequency and then when I move my hands away a 55 00:03:41,389 --> 00:03:43,817 lower pitch. 56 00:03:43,817 --> 00:03:48,308 Now you may think that it makes no difference whether I move 57 00:03:48,308 --> 00:03:51,504 towards you or whether you move towards me. 58 00:03:51,504 --> 00:03:56,071 And that is indeed true if the speeds are very small compared 59 00:03:56,071 --> 00:04:00,104 to the speed of sound. But it is not true anymore when 60 00:04:00,104 --> 00:04:03,529 we approach the speed of sound. As an example, 61 00:04:03,529 --> 00:04:07,182 if you move away from me with the speed of sound, 62 00:04:07,182 --> 00:04:11,064 you will never hear me. Because the sound will never 63 00:04:11,064 --> 00:04:14,184 catch up with you, and so F prime is zero. 64 00:04:14,184 --> 00:04:18,772 And you can indeed confirm that with this 65 00:04:18,772 --> 00:04:21,808 equation. But if I moved away from you 66 00:04:21,808 --> 00:04:26,158 with the speed of sound, for sure the sound will reach 67 00:04:26,158 --> 00:04:29,441 with you. And the frequency that you will 68 00:04:29,441 --> 00:04:32,97 hear is only half of the one that I produce. 69 00:04:32,97 --> 00:04:37,649 So there's a huge asymmetry. Big difference whether I move 70 00:04:37,649 --> 00:04:41,67 or whether you move. So I now want to turn towards 71 00:04:41,67 --> 00:04:46,184 electromagnetic radiation. There is also a Doppler shift 72 00:04:46,184 --> 00:04:52,354 in electromagnetic radiation. If you see a traffic light red 73 00:04:52,354 --> 00:04:57,391 and you approach it with high enough speed you will experience 74 00:04:57,391 --> 00:05:02,592 a higher frequency and then you will see the wavelengths shorter 75 00:05:02,592 --> 00:05:06,06 than red and you may even think it's green. 76 00:05:06,06 --> 00:05:09,528 You may even go through that traffic light. 77 00:05:09,528 --> 00:05:13,904 To calculate the proper relation between F prime and F 78 00:05:13,904 --> 00:05:18,362 requires special relativity. And so I will give you the 79 00:05:18,362 --> 00:05:21,665 final result. F prime is the one that you 80 00:05:21,665 --> 00:05:27,268 receive. F is the one that is emitted by 81 00:05:27,268 --> 00:05:32,642 the transmitter. And we get here then one minus 82 00:05:32,642 --> 00:05:38,6 beta divided by one plus beta to the power one-half. 83 00:05:38,6 --> 00:05:44,207 And beta is V over C, C being the speed of light, 84 00:05:44,207 --> 00:05:50,633 and V being the s- speed, the relative speed between the 85 00:05:50,633 --> 00:05:56,741 transmitter and you. If beta is larger than zero you 86 00:05:56,741 --> 00:06:00,52 are receding from each other in this equation. 87 00:06:00,52 --> 00:06:05,474 If beta is smaller than zero you are approaching each other. 88 00:06:05,474 --> 00:06:10,261 You may wonder why we don't make a distinction now between 89 00:06:10,261 --> 00:06:14,039 the transmitter on the one hand, the velocity, 90 00:06:14,039 --> 00:06:16,895 and the receiver on the other hand. 91 00:06:16,895 --> 00:06:20,841 There's only one beta. Well, that is typical for 92 00:06:20,841 --> 00:06:24,788 special relativity. What counts is only relative 93 00:06:24,788 --> 00:06:28,691 motion. There is no such thing as 94 00:06:28,691 --> 00:06:32,083 absolute motion. The question are you moving 95 00:06:32,083 --> 00:06:36,815 relative to me or I relative to you is an illegal question in 96 00:06:36,815 --> 00:06:40,522 special relativity. What counts is only relative 97 00:06:40,522 --> 00:06:43,519 motion. If we are in vacuum then lambda 98 00:06:43,519 --> 00:06:48,251 equals C divided by F and so lambda prime equals C divided by 99 00:06:48,251 --> 00:06:50,696 F prime. Lambda prime is now the 100 00:06:50,696 --> 00:06:55,428 wavelength that you receive and lambda is the wavelength that 101 00:06:55,428 --> 00:06:59,706 was emitted by the -- by the source. 102 00:06:59,706 --> 00:07:05,336 So I can substitute in here, in this F, C divided by lambda 103 00:07:05,336 --> 00:07:10,966 which is more commonly done. So this Doppler shift equation 104 00:07:10,966 --> 00:07:16,888 for electromagnetic radiation is more common given in terms of 105 00:07:16,888 --> 00:07:19,994 lambda. But of course the two are 106 00:07:19,994 --> 00:07:23,78 identical. And then you get now one plus 107 00:07:23,78 --> 00:07:28,731 beta upstairs divided by one minus beta to the power 108 00:07:28,731 --> 00:07:33,488 one-half. The velocity there if I'm 109 00:07:33,488 --> 00:07:38,646 completely honest with you is the radial velocity. 110 00:07:38,646 --> 00:07:44,963 If you are here and here is the source of emission and if the 111 00:07:44,963 --> 00:07:50,227 relative velocity between the two of you were this, 112 00:07:50,227 --> 00:07:55,07 then it is this component, this angle is theta, 113 00:07:55,07 --> 00:07:59,071 this component which is V cosine theta, 114 00:07:59,071 --> 00:08:03,809 which we call the radial velocity, 115 00:08:03,809 --> 00:08:08,561 that is really the velocity which is in that equation. 116 00:08:08,561 --> 00:08:12,237 Police cars measure your speed with radar. 117 00:08:12,237 --> 00:08:17,796 They reflect the radar off your car and they measure the change 118 00:08:17,796 --> 00:08:21,203 in frequency as the radar is reflected. 119 00:08:21,203 --> 00:08:26,404 That gives a Doppler shift because of your speed and that's 120 00:08:26,404 --> 00:08:31,605 the way they determine the speed of your car to a very high 121 00:08:31,605 --> 00:08:35,371 degree of accuracy. You can imagine that in 122 00:08:35,371 --> 00:08:40,199 astronomy Doppler shift plays a key role. 123 00:08:40,199 --> 00:08:44,688 Because we can measure the radial velocities of stars 124 00:08:44,688 --> 00:08:48,142 relative to us. Most stellar spectra show 125 00:08:48,142 --> 00:08:51,681 discrete frequencies, discrete wavelength, 126 00:08:51,681 --> 00:08:56,603 which result from atoms and molecules in the atmosphere of 127 00:08:56,603 --> 00:09:00,056 the stars. Last lecture I showed you with 128 00:09:00,056 --> 00:09:05,322 your own gradings a neon light source and I convinced you that 129 00:09:05,322 --> 00:09:10,393 there were discrete frequencies and discrete 130 00:09:10,393 --> 00:09:15,576 wavelengths emitted by the neon. If a particular discrete 131 00:09:15,576 --> 00:09:19,834 wavelength, for instance in our own laboratory, 132 00:09:19,834 --> 00:09:24,739 would be five thousand Angstrom, and look at the star, 133 00:09:24,739 --> 00:09:29,922 and I see that that wavelength is longer, lambda prime is 134 00:09:29,922 --> 00:09:34,55 larger than lambda, then I conclude -- lambda prime 135 00:09:34,55 --> 00:09:39,271 is larger than lambda, that means the wavelength the 136 00:09:39,271 --> 00:09:45,285 way I observe it is shifted towards longer wavelength, 137 00:09:45,285 --> 00:09:50,322 is shifted in the direction of the red, and we call that red 138 00:09:50,322 --> 00:09:53,311 shift. It means that we are receding 139 00:09:53,311 --> 00:09:56,982 from each other. If however I measure lambda 140 00:09:56,982 --> 00:10:02,104 prime to be smaller than lambda, so lambda prime smaller than 141 00:10:02,104 --> 00:10:05,861 lambda, we call that blue shift in astronomy, 142 00:10:05,861 --> 00:10:09,874 and it means that we are approaching each other. 143 00:10:09,874 --> 00:10:17,191 And so we make reference to the direction in the spectrum where 144 00:10:17,191 --> 00:10:22,125 the lines are moving. I can give you a simple 145 00:10:22,125 --> 00:10:26,386 example. I looked up for the star Delta 146 00:10:26,386 --> 00:10:33,225 Leporis what the red shift is. There is a line that most stars 147 00:10:33,225 --> 00:10:38,383 show in their spectrum which is due to calcium, 148 00:10:38,383 --> 00:10:45,223 it even has a particular name, I think it's called the calcium 149 00:10:45,223 --> 00:10:48,891 K line, but that's not so 150 00:10:48,891 --> 00:10:53,794 important, the name. In our own laboratory lambda is 151 00:10:53,794 --> 00:10:58,985 known to a high degree of accuracy, is three nine three 152 00:10:58,985 --> 00:11:02,253 three point six six four Angstroms. 153 00:11:02,253 --> 00:11:07,636 We look at the star and we recognize without a doubt that 154 00:11:07,636 --> 00:11:13,116 that's due to calcium in the atmosphere of the star and we 155 00:11:13,116 --> 00:11:19,076 find that lambda prime is one point two nine eight 156 00:11:19,076 --> 00:11:24,094 Angstroms higher than lambda. So lambda prime is larger than 157 00:11:24,094 --> 00:11:27,326 lambda. So there is red shift and so we 158 00:11:27,326 --> 00:11:31,664 are receding from each other. I go to that equation. 159 00:11:31,664 --> 00:11:36,768 I substitute lambda prime and lambda in there and I find that 160 00:11:36,768 --> 00:11:41,531 beta equals plus three point three times ten to the minus 161 00:11:41,531 --> 00:11:43,998 four. The plus for beta indeed 162 00:11:43,998 --> 00:11:49,016 confirms that we are receding, that our relative velocity is 163 00:11:49,016 --> 00:11:54,201 away from each other, and I find therefore that the 164 00:11:54,201 --> 00:11:58,593 radial velocity -- I stress it is the radial component of our 165 00:11:58,593 --> 00:12:02,472 velocity is then beta times C and that turns out to be 166 00:12:02,472 --> 00:12:05,912 approximately ninety-nine kilometers per second. 167 00:12:05,912 --> 00:12:09,132 So I have measured now the relative velocity, 168 00:12:09,132 --> 00:12:12,06 radial velocity, between the star and me, 169 00:12:12,06 --> 00:12:16,451 and the question whether the star is moving away from me or I 170 00:12:16,451 --> 00:12:20,038 move away from the star is an irrelevant question, 171 00:12:20,038 --> 00:12:24,722 this is always a relative velocity that matters. 172 00:12:24,722 --> 00:12:28,703 How can I measure the wavelength shifts so accurately 173 00:12:28,703 --> 00:12:33,448 that we can see the difference of one point three Angstroms out 174 00:12:33,448 --> 00:12:37,046 of four thousand? The way that it's done is that 175 00:12:37,046 --> 00:12:41,562 you observe the starlight and you make a spectrum and at the 176 00:12:41,562 --> 00:12:46,384 same time you make a spectrum of light sources in the laboratory 177 00:12:46,384 --> 00:12:49,905 with well-known and well-calibrated wavelength. 178 00:12:49,905 --> 00:12:55,34 Suppose there were some neon in the atmosphere of a star. 179 00:12:55,34 --> 00:12:59,509 Then you could compare the neon light the way we looked at it 180 00:12:59,509 --> 00:13:02,428 last lecture. You could compare it with the 181 00:13:02,428 --> 00:13:06,737 wavelength that you see from the star and you can see very very 182 00:13:06,737 --> 00:13:08,961 small shifts. You make a relative 183 00:13:08,961 --> 00:13:11,88 measurement. So you need spectrometers with 184 00:13:11,88 --> 00:13:16,05 very high spectral resolution. So there was a big industry in 185 00:13:16,05 --> 00:13:19,663 the early twentieth century to measure these relative 186 00:13:19,663 --> 00:13:23,208 velocities of stars. And their speeds were typically 187 00:13:23,208 --> 00:13:26,961 a hundred, two hundred kilometers per 188 00:13:26,961 --> 00:13:29,775 second. Not unlike the star that I just 189 00:13:29,775 --> 00:13:33,477 calculated for you. Some of those stars relative to 190 00:13:33,477 --> 00:13:37,18 us are approaching. Other stars are receding in our 191 00:13:37,18 --> 00:13:39,55 galaxy. But it was Slipher in the 192 00:13:39,55 --> 00:13:43,919 nineteen twenties who observed the red shift of some nebulae 193 00:13:43,919 --> 00:13:48,436 which were believed at the time to be in our own galaxy and he 194 00:13:48,436 --> 00:13:52,583 found that they were -- had a very high velocity of up to 195 00:13:52,583 --> 00:13:58,063 fifteen hundred kilometers per second, and they were always 196 00:13:58,063 --> 00:14:01,531 moving away from us. And it was found shortly after 197 00:14:01,531 --> 00:14:05,9 that that these nebulae were not in our own galaxy but that they 198 00:14:05,9 --> 00:14:08,12 were galaxies in their own right. 199 00:14:08,12 --> 00:14:11,934 So they were collections of about ten billion stars just 200 00:14:11,934 --> 00:14:15,471 like our own galaxy. And so when you take a spectrum 201 00:14:15,471 --> 00:14:18,523 of those galaxies, then of course you get the 202 00:14:18,523 --> 00:14:22,823 average of millions and millions of stars, but that still would 203 00:14:22,823 --> 00:14:26,776 allow you then to calculate the red shift, the average red 204 00:14:26,776 --> 00:14:31,577 shift, of the galaxy, and therefore uh its velocity. 205 00:14:31,577 --> 00:14:35,043 And Hubble, the famous astronomer after which the 206 00:14:35,043 --> 00:14:39,014 Hubble space telescope is named, and Humason made a very 207 00:14:39,014 --> 00:14:42,984 courageous attempt to measure also the distance to these 208 00:14:42,984 --> 00:14:45,439 galaxies. They knew the velocities. 209 00:14:45,439 --> 00:14:48,76 That was easy because they knew the red shifts. 210 00:14:48,76 --> 00:14:52,948 The distance determinations in astronomy is a can of worms. 211 00:14:52,948 --> 00:14:56,557 And I will spare you the details about the distance 212 00:14:56,557 --> 00:15:00,961 determinations. But Hubble made a spectacular 213 00:15:00,961 --> 00:15:04,242 discovery. He found a linear relation 214 00:15:04,242 --> 00:15:07,705 between the velocity and the distances. 215 00:15:07,705 --> 00:15:10,621 And we know this as Hubble's law. 216 00:15:10,621 --> 00:15:15,998 And Hubble's law is that the velocity is a constant which is 217 00:15:15,998 --> 00:15:19,825 now named after Hubble, capital H, times D. 218 00:15:19,825 --> 00:15:24,564 And the modern value for H, the modern value for H is 219 00:15:24,564 --> 00:15:30,214 seventy-two kilometers per second per megaparsec. 220 00:15:30,214 --> 00:15:35,627 What is a megaparsec? A megaparsec is a distance. 221 00:15:35,627 --> 00:15:42,055 In astronomy we don't deal with inches, we don't deal with 222 00:15:42,055 --> 00:15:49,272 kilometers, that is just not big enough, we deal with parsecs and 223 00:15:49,272 --> 00:15:53,67 megaparsecs. And one megaparsec is three 224 00:15:53,67 --> 00:15:58,858 point two six times ten to the six light-years. 225 00:15:58,858 --> 00:16:04,046 And if you want that in kilometers, 226 00:16:04,046 --> 00:16:11,748 it's not unreasonable question, it's about three point one 227 00:16:11,748 --> 00:16:16,613 times ten to the nineteen kilometers. 228 00:16:16,613 --> 00:16:24,18 So I could calculate for a specific galaxy that I have in 229 00:16:24,18 --> 00:16:31,072 mind, I can calculate the distance if I know the red 230 00:16:31,072 --> 00:16:35,802 shift. I have a particular galaxy in 231 00:16:35,802 --> 00:16:44,034 mind for which lambda prime -- for which lambda prime is one 232 00:16:44,034 --> 00:16:47,746 point zero zero three three times lambda. 233 00:16:47,746 --> 00:16:52,571 So notice again that the wavelength that I receive is 234 00:16:52,571 --> 00:16:57,211 indeed longer than lambda, so there is a red shift. 235 00:16:57,211 --> 00:17:01,944 I go to my Doppler shift equation which is this one. 236 00:17:01,944 --> 00:17:06,306 I calculate beta. One equation with one unknown, 237 00:17:06,306 --> 00:17:10,76 can solve for beta. And I find now that V is five 238 00:17:10,76 --> 00:17:16,739 thousand kilometers per second. Very straightforward, 239 00:17:16,739 --> 00:17:20,001 nothing special, very easy calculation. 240 00:17:20,001 --> 00:17:24,379 But now with Hubble's law I can calculate what D is. 241 00:17:24,379 --> 00:17:28,757 Because D now is the velocity which is five thousand 242 00:17:28,757 --> 00:17:34,079 kilometers per second divided by that seventy-two and that then 243 00:17:34,079 --> 00:17:37,341 is approximately sixty-nine megaparsec. 244 00:17:37,341 --> 00:17:42,062 Again we have the distance if we do it in these units in 245 00:17:42,062 --> 00:17:46,27 megaparsecs. That's about two hundred and 246 00:17:46,27 --> 00:17:50,648 twenty-five million light-years. And so the object is about two 247 00:17:50,648 --> 00:17:54,602 hundred and twenty-five million light-years away from us. 248 00:17:54,602 --> 00:17:58,486 So it took the light two hundred and twenty-five million 249 00:17:58,486 --> 00:18:01,945 years to reach us. So when you see light from this 250 00:18:01,945 --> 00:18:04,346 object you're looking back in time. 251 00:18:04,346 --> 00:18:08,441 And if you have a galaxy which is twice as far away as this 252 00:18:08,441 --> 00:18:11,618 one, then the velocity would be twice as high. 253 00:18:11,618 --> 00:18:16,745 And they're always receding relative to us. 254 00:18:16,745 --> 00:18:24,411 I'd like to show you now some spectra of three galaxies. 255 00:18:24,411 --> 00:18:28,872 Can I have the first slide, John? 256 00:18:28,872 --> 00:18:36,12 All right, you see here a galaxy and here you see the 257 00:18:36,12 --> 00:18:43,786 spectrum of that galaxy. That may not be very impressive 258 00:18:43,786 --> 00:18:45,734 to you. 259 00:18:45,734 --> 00:18:49,527 The lines that are being recognized to be due to calcium 260 00:18:49,527 --> 00:18:52,56 K and calcium eight are these two dark lines. 261 00:18:52,56 --> 00:18:55,594 Some of you may not even be able to see them. 262 00:18:55,594 --> 00:18:59,593 And this is the comparison spectra taken in the laboratory. 263 00:18:59,593 --> 00:19:03,386 These lines are seen as dark lines, not as bright lines. 264 00:19:03,386 --> 00:19:06,971 We call them absorption lines. They are formed in the 265 00:19:06,971 --> 00:19:10,626 atmosphere of the star. Why they show up as dark lines 266 00:19:10,626 --> 00:19:13,659 and not as bright lines is not important now. 267 00:19:13,659 --> 00:19:17,452 I don't want to go into that. That's too much astronomy. 268 00:19:17,452 --> 00:19:21,19 But they are lines and that's what 269 00:19:21,19 --> 00:19:23,629 counts. And these lines are shifted 270 00:19:23,629 --> 00:19:27,861 towards the red part of the spectrum by a teeny weeny little 271 00:19:27,861 --> 00:19:30,372 bit. You see here this little arrow. 272 00:19:30,372 --> 00:19:34,605 And the conclusion then is that in this case the velocity of 273 00:19:34,605 --> 00:19:38,909 that galaxy is t- seven hundred twenty miles per second which 274 00:19:38,909 --> 00:19:43,07 translates into eleven hundred fifty kilometers per second, 275 00:19:43,07 --> 00:19:47,446 and so that brings this object if you believe the modern value 276 00:19:47,446 --> 00:19:52,038 for Hubble constant at about sixteen megaparsec. 277 00:19:52,038 --> 00:19:55,056 This galaxy is substantially farther away. 278 00:19:55,056 --> 00:19:59,178 No surprise that it therefore also looks smaller in size, 279 00:19:59,178 --> 00:20:02,344 and notice that here the lines have shifted. 280 00:20:02,344 --> 00:20:05,73 These lines have shifted substantially further. 281 00:20:05,73 --> 00:20:10,073 And if I did my homework using the velocity that they claim, 282 00:20:10,073 --> 00:20:14,269 which they can do with high degree of accuracy because you 283 00:20:14,269 --> 00:20:17,508 can calculate lambda prime divided by lambda, 284 00:20:17,508 --> 00:20:22,441 those measurements can be made with enorm- accuracy, 285 00:20:22,441 --> 00:20:26,038 I find that this object is about three hundred five 286 00:20:26,038 --> 00:20:29,852 megaparsecs away from us, so that's about twenty times 287 00:20:29,852 --> 00:20:33,881 further away than this object. So the speed is also about 288 00:20:33,881 --> 00:20:37,694 twenty times higher of course because there's a linear 289 00:20:37,694 --> 00:20:40,572 relationship. And if you look at this one 290 00:20:40,572 --> 00:20:44,53 which is even further away, then notice that these lines 291 00:20:44,53 --> 00:20:48,415 have shifted even more. The next slide shows you what I 292 00:20:48,415 --> 00:20:52,229 would call Hubble diagram. It was kindly sent to me by 293 00:20:52,229 --> 00:20:55,85 Wendy Freedman and her coworkers. 294 00:20:55,85 --> 00:21:00,077 Wendy is the leader of a large team of scientists who are 295 00:21:00,077 --> 00:21:03,926 making observations with the Hubble space telescope. 296 00:21:03,926 --> 00:21:08,38 You see here distance and you see here velocity in the units 297 00:21:08,38 --> 00:21:11,701 that we used in class, kilometers per second. 298 00:21:11,701 --> 00:21:14,796 Forget this part. That's not so important. 299 00:21:14,796 --> 00:21:18,268 But you see the incredible linear relationship. 300 00:21:18,268 --> 00:21:22,117 And Wendy concluded that Hubble's constant is around 301 00:21:22,117 --> 00:21:26,345 seventy-two. It could be a little lower, 302 00:21:26,345 --> 00:21:30,8 it could be a little higher. She goes out all the way to 303 00:21:30,8 --> 00:21:35,58 four hundred megaparsecs with associated velocities of about 304 00:21:35,58 --> 00:21:38,901 twenty-six thousand kilometers per second. 305 00:21:38,901 --> 00:21:42,709 That's about nine percent of the speed of light. 306 00:21:42,709 --> 00:21:47,407 So beta is about one-tenth. So for this object lambda prime 307 00:21:47,407 --> 00:21:51,134 divided by lambda would be about one point one. 308 00:21:51,134 --> 00:21:54,536 With a ten percent shift in the wavelength. 309 00:21:54,536 --> 00:21:58,424 Hubble, who published his data in 310 00:21:58,424 --> 00:22:01,027 the twenties, his whole data set when he 311 00:22:01,027 --> 00:22:04,898 concluded that there was a linear relation had only objects 312 00:22:04,898 --> 00:22:09,036 with velocities less than eleven hundred kilometers per second. 313 00:22:09,036 --> 00:22:12,973 And eleven hundred kilometers per second is this point here. 314 00:22:12,973 --> 00:22:16,511 So Hubble had only points -- there are not even any in 315 00:22:16,511 --> 00:22:18,579 Wendy's diagram, which are here. 316 00:22:18,579 --> 00:22:22,25 And he concluded courageously that there was this linear 317 00:22:22,25 --> 00:22:24,986 relationship. And you see it has stood the 318 00:22:24,986 --> 00:22:27,656 acid test. We still believe it is linear. 319 00:22:27,656 --> 00:22:33,198 The only difference was that Hubble's distances were very 320 00:22:33,198 --> 00:22:36,29 different from what we believe today. 321 00:22:36,29 --> 00:22:39,296 They were about seven times smaller. 322 00:22:39,296 --> 00:22:43,934 So Hubble constant was different for him but the linear 323 00:22:43,934 --> 00:22:48,143 relationship was there. OK, that's enough for this 324 00:22:48,143 --> 00:22:50,806 slide. So now comes a sixty-four 325 00:22:50,806 --> 00:22:54,671 dollar question, why do all galaxies which are 326 00:22:54,671 --> 00:22:58,279 far away, why w- do they move away from us? 327 00:22:58,279 --> 00:23:02,383 Well, I can uh suggest a very simple 328 00:23:02,383 --> 00:23:05,603 picture to you. We are at the center of the 329 00:23:05,603 --> 00:23:09,821 universe and there was a huge explosion a long time ago. 330 00:23:09,821 --> 00:23:13,041 We refer to that explosion as the Big Bang. 331 00:23:13,041 --> 00:23:17,566 And since we are at the center where the explosion occurred, 332 00:23:17,566 --> 00:23:22,243 the galaxies which obtained the largest speed in the explosion 333 00:23:22,243 --> 00:23:24,773 are now the farthest away from us. 334 00:23:24,773 --> 00:23:28,607 Now assume that this explosion is the correct idea. 335 00:23:28,607 --> 00:23:31,061 Assume that there was a Big Bang. 336 00:23:31,061 --> 00:23:36,457 Then I can ask the question now when did it occur? 337 00:23:36,457 --> 00:23:41,555 I can now turn the clock back and I can do the following. 338 00:23:41,555 --> 00:23:47,016 I can take two objects which are a distance D apart today but 339 00:23:47,016 --> 00:23:52,023 they were together when the universe was born at the Big 340 00:23:52,023 --> 00:23:55,3 Bang. And let's assume that they have 341 00:23:55,3 --> 00:24:00,852 been going away from each other always with the same velocity. 342 00:24:00,852 --> 00:24:05,037 Let's assume that now for simplicity. 343 00:24:05,037 --> 00:24:09,419 So if they always went away with the same velocity from each 344 00:24:09,419 --> 00:24:13,503 other then the distance that they are now today is their 345 00:24:13,503 --> 00:24:18,181 velocity times the time T which is then the age of the universe. 346 00:24:18,181 --> 00:24:22,488 But we also know with Hubble's law that the velocity V is H 347 00:24:22,488 --> 00:24:24,864 times D. And we assume that these 348 00:24:24,864 --> 00:24:27,983 velocities are the same now for simplicity. 349 00:24:27,983 --> 00:24:31,77 You multiply these two equations with each other and 350 00:24:31,77 --> 00:24:35,929 you find immediately that the age of the 351 00:24:35,929 --> 00:24:41,409 universe is one over H. And that indeed has the unit of 352 00:24:41,409 --> 00:24:43,337 time. If you take H, 353 00:24:43,337 --> 00:24:49,122 the one that we believe in nowadays, and you calculate one 354 00:24:49,122 --> 00:24:55,109 over H, and you work in M K S units, you'll find that T H is 355 00:24:55,109 --> 00:25:00,894 about fourteen billion years, I'll first give it to you in 356 00:25:00,894 --> 00:25:07,186 seconds, it's about four point three times ten to the seventeen 357 00:25:07,186 --> 00:25:11,293 seconds. And that is about fourteen 358 00:25:11,293 --> 00:25:14,56 billion years. So with this picture in mind, 359 00:25:14,56 --> 00:25:18,663 the universe would be about fourteen billion years old, 360 00:25:18,663 --> 00:25:22,083 but because of the gravitational attraction of 361 00:25:22,083 --> 00:25:25,046 these galaxies, they attract each other, 362 00:25:25,046 --> 00:25:29,453 you may expect that the speed of the galaxies was larger in 363 00:25:29,453 --> 00:25:33,86 the past, and therefore the speed that we have -- we assume 364 00:25:33,86 --> 00:25:37,735 that the speed doesn't change is not quite accurate, 365 00:25:37,735 --> 00:25:42,209 and so maybe the universe is a little younger, 366 00:25:42,209 --> 00:25:44,296 maybe twelve billion years or so. 367 00:25:44,296 --> 00:25:47,687 We know from theoretical calculations that the oldest 368 00:25:47,687 --> 00:25:51,273 stars in our own galaxy are about ten billion years old. 369 00:25:51,273 --> 00:25:54,925 Therefore the universe cannot be younger than ten billion 370 00:25:54,925 --> 00:25:57,273 years. And there is general consensus 371 00:25:57,273 --> 00:26:00,86 in the community that our universe is probably twelve to 372 00:26:00,86 --> 00:26:04,381 fourteen billion years old. Now the whole issue of this 373 00:26:04,381 --> 00:26:08,294 deceleration that I mentioned as the galaxies moved away from 374 00:26:08,294 --> 00:26:12,142 each other is at the heart of research in 375 00:26:12,142 --> 00:26:15,419 cosmology. And in fact it is now believed 376 00:26:15,419 --> 00:26:19,433 that very early on in the universe there was first 377 00:26:19,433 --> 00:26:22,465 acceleration followed by deceleration, 378 00:26:22,465 --> 00:26:26,889 and maybe again acceleration. That is quite mysterious. 379 00:26:26,889 --> 00:26:30,33 Frontier research is going on in this area. 380 00:26:30,33 --> 00:26:34,919 At MIT we have three world experts, Professors Alan Guth, 381 00:26:34,919 --> 00:26:38,442 w- made major contributions to this concept, 382 00:26:38,442 --> 00:26:42,62 cosmology, we have Ed Bertschinger and we have Scott 383 00:26:42,62 --> 00:26:47,209 Burles. If we take Hubble's law at face 384 00:26:47,209 --> 00:26:52,338 value, I can calculate how far the edge of our visible universe 385 00:26:52,338 --> 00:26:54,323 is. Which is the horizon. 386 00:26:54,323 --> 00:26:58,377 We call that the horizon. I can calculate what the 387 00:26:58,377 --> 00:27:01,356 maximum distance is that we can look. 388 00:27:01,356 --> 00:27:05,244 D maximum can be found by making the velocity C. 389 00:27:05,244 --> 00:27:10,291 So that the galaxies are moving -- we are moving away from the 390 00:27:10,291 --> 00:27:15,007 galaxies, the galaxies are moving away from us -- with the 391 00:27:15,007 --> 00:27:18,812 speed of light. And so you would find then that 392 00:27:18,812 --> 00:27:22,345 D max is C divided by H. 393 00:27:22,345 --> 00:27:26,246 That is a distance. And you will find then, 394 00:27:26,246 --> 00:27:30,055 no surprise, if you use the modern number, 395 00:27:30,055 --> 00:27:34,699 that that distance is fourteen billion light-years. 396 00:27:34,699 --> 00:27:40,273 We can never see beyond that. Because if V equals C then beta 397 00:27:40,273 --> 00:27:45,382 becomes one and if beta becomes one lambda prime becomes 398 00:27:45,382 --> 00:27:50,676 infinitely large, you have an infinite amount 399 00:27:50,676 --> 00:27:54,389 of red shift, and F prime becomes zero. 400 00:27:54,389 --> 00:27:59,078 So the electromagnetic radiation has no frequency 401 00:27:59,078 --> 00:28:04,452 anymore and so there's no energy anymore in the photons. 402 00:28:04,452 --> 00:28:09,825 So that is then the edge of our universe, of our visible 403 00:28:09,825 --> 00:28:13,635 universe. You can never see beyond that. 404 00:28:13,635 --> 00:28:16,957 So now comes a reasonable question. 405 00:28:16,957 --> 00:28:23,21 How far have we been able to see into the universe? 406 00:28:23,21 --> 00:28:28,147 And to my knowledge the record holder is a galaxy for which 407 00:28:28,147 --> 00:28:32,232 lambda prime over lambda is seven point five six. 408 00:28:32,232 --> 00:28:35,041 Was published only two months ago. 409 00:28:35,041 --> 00:28:39,297 Seven point five six. Now at such very large values 410 00:28:39,297 --> 00:28:43,043 of red shift, general relativity becomes very 411 00:28:43,043 --> 00:28:45,937 important. And the equation that we 412 00:28:45,937 --> 00:28:49,937 derived here was derived for special relativity. 413 00:28:49,937 --> 00:28:54,193 And so with very high values of red 414 00:28:54,193 --> 00:28:58,975 shift like lambda prime over lambda seven point five six you 415 00:28:58,975 --> 00:29:03,838 cannot reliably calculate the velocities using that equation. 416 00:29:03,838 --> 00:29:08,458 And so you cannot use that velocity then and shove it into 417 00:29:08,458 --> 00:29:11,781 Hubble's law and find the -- the distance. 418 00:29:11,781 --> 00:29:16,563 But there is no question that the -- that object is probably 419 00:29:16,563 --> 00:29:21,426 at a distance of something like thirteen billion light-years. 420 00:29:21,426 --> 00:29:27,181 Very very far away from us, near the edge of our universe. 421 00:29:27,181 --> 00:29:32,424 I will show you an object that is also believed to be near the 422 00:29:32,424 --> 00:29:36,808 edge of the universe. It comes up in the next slide. 423 00:29:36,808 --> 00:29:41,107 The distance is roughly twelve billion light-years. 424 00:29:41,107 --> 00:29:46,093 So for one, when you look at that object, there it is -- it 425 00:29:46,093 --> 00:29:51,079 doesn't look very impressive but what do you expect from an 426 00:29:51,079 --> 00:29:55,721 object that is twelve billion light-years away from us? 427 00:29:55,721 --> 00:29:58,987 It's a quasar, which is a very peculiar 428 00:29:58,987 --> 00:30:03,261 galaxy. It uh emits emission lines, 429 00:30:03,261 --> 00:30:08,291 the spectra do not show these dark lines that I showed you 430 00:30:08,291 --> 00:30:12,35 earlier, but they actually have emission lines, 431 00:30:12,35 --> 00:30:17,821 and the light that you see here was emitted some twelve billion 432 00:30:17,821 --> 00:30:21,44 years ago. And now comes the spectrum from 433 00:30:21,44 --> 00:30:26,822 this object in the next slide. This was published last year by 434 00:30:26,822 --> 00:30:30,882 Scott Anderson and his coworkers, University of 435 00:30:30,882 --> 00:30:36,586 Washington in Seattle. I have collaborated with Scott 436 00:30:36,586 --> 00:30:40,631 on many projects. So here you see the spectrum of 437 00:30:40,631 --> 00:30:45,181 that quasar that you just saw. And here you see a line, 438 00:30:45,181 --> 00:30:48,214 an emission line, at roughly seven -- 439 00:30:48,214 --> 00:30:53,269 seventy-eight hundred Angstroms. And there are all reasons to 440 00:30:53,269 --> 00:30:58,409 believe that this in the frame of reference of that quasar was 441 00:30:58,409 --> 00:31:02,538 the Lyman alpha line which is emitted by hydrogen, 442 00:31:02,538 --> 00:31:06,666 which is twelve hundred and sixteen 443 00:31:06,666 --> 00:31:10,165 Angstroms. Now we have here five thousand, 444 00:31:10,165 --> 00:31:12,639 four thousand, three thousand, 445 00:31:12,639 --> 00:31:14,857 two thousand, one thousand, 446 00:31:14,857 --> 00:31:19,038 so here is roughly where the wavelength lambda is, 447 00:31:19,038 --> 00:31:23,731 and here is lambda prime. Lambda prime is six point four 448 00:31:23,731 --> 00:31:28,509 one times larger than lambda. He mentions five point four 449 00:31:28,509 --> 00:31:33,799 one, but Z is what astronomers in general quote is lambda prime 450 00:31:33,799 --> 00:31:40,113 divided by lambda minus one, so the ratio lambda prime over 451 00:31:40,113 --> 00:31:44,538 lambda is six point four one. Absolutely amazing that you can 452 00:31:44,538 --> 00:31:49,186 make such accurate measurements, such incredible beautiful data, 453 00:31:49,186 --> 00:31:52,431 and this line is all the way in the infrared, 454 00:31:52,431 --> 00:31:55,898 you cannot see this with your naked eye anymore, 455 00:31:55,898 --> 00:31:59,882 our eyes I think can only see up to sixty-five hundred. 456 00:31:59,882 --> 00:32:04,234 So the twelve sixteen line was in the UV, shifts all the way 457 00:32:04,234 --> 00:32:07,553 into the infrared, and this allows astronomers 458 00:32:07,553 --> 00:32:11,832 then to measure the value lambda prime over 459 00:32:11,832 --> 00:32:16,821 lambda, and there is little doubt that this object is also 460 00:32:16,821 --> 00:32:20,06 near the edge of our visible universe. 461 00:32:20,06 --> 00:32:22,686 That's enough, John, thank you. 462 00:32:22,686 --> 00:32:27,588 I'd like to return to the Big Bang, to the explosion some 463 00:32:27,588 --> 00:32:30,652 twelve or fifteen billion years ago. 464 00:32:30,652 --> 00:32:35,467 And I'd like to raise the question, are we at the center 465 00:32:35,467 --> 00:32:39,668 of that explosion? Are we really at the center of 466 00:32:39,668 --> 00:32:44,395 our universe? That cannot be of course. 467 00:32:44,395 --> 00:32:48,882 It's an incredible arrogance. It would be too egocentric. 468 00:32:48,882 --> 00:32:52,807 I know that we all think very highly of ourselves, 469 00:32:52,807 --> 00:32:56,813 but this cannot be. We are nothing in the framework 470 00:32:56,813 --> 00:33:00,818 of the total universe. We cannot possibly be at the 471 00:33:00,818 --> 00:33:03,863 center. So how do we reconcile this now 472 00:33:03,863 --> 00:33:07,948 with what we observe? Imagine that you were a raisin 473 00:33:07,948 --> 00:33:10,832 in a raisin bread. Quite a promotion, 474 00:33:10,832 --> 00:33:14,678 from a human being to a raisin in a raisin bread. 475 00:33:14,678 --> 00:33:19,686 And I put you in an oven. And the raisin bread, 476 00:33:19,686 --> 00:33:23,99 the dough is going to expand. All raisins will see other 477 00:33:23,99 --> 00:33:27,981 raisins move away from each other and the larger the 478 00:33:27,981 --> 00:33:32,129 distance to your raisins the larger the speed will be. 479 00:33:32,129 --> 00:33:36,276 And each raisin will think that they are very special. 480 00:33:36,276 --> 00:33:40,581 Suppose here this is you, one raisin, and here's another 481 00:33:40,581 --> 00:33:43,163 raisin, and here's another raisin. 482 00:33:43,163 --> 00:33:48,798 After a certain amount of time all distances have doubled. 483 00:33:48,798 --> 00:33:51,737 So this one is here. And this one is here. 484 00:33:51,737 --> 00:33:55,824 So you can immediately see that when you look at this one, 485 00:33:55,824 --> 00:33:59,337 that its velocity is substantially lower than that 486 00:33:59,337 --> 00:34:01,488 one. This is twice as far away, 487 00:34:01,488 --> 00:34:03,926 you will see twice as high a speed. 488 00:34:03,926 --> 00:34:06,579 But this raisin will look at this one. 489 00:34:06,579 --> 00:34:11,024 And it will also conclude that this raisin relative to this one 490 00:34:11,024 --> 00:34:15,542 has a higher velocity than this raisin has relative to this one. 491 00:34:15,542 --> 00:34:19,772 So all of them will think that they are special and you as a 492 00:34:19,772 --> 00:34:24,011 raisin would come up with Hubble's law. 493 00:34:24,011 --> 00:34:28,433 You would conclude that the velocity of your other raisins 494 00:34:28,433 --> 00:34:31,613 are linearly proportional to the distance. 495 00:34:31,613 --> 00:34:36,034 There is an analogy which is even nicer than raisin bread, 496 00:34:36,034 --> 00:34:38,827 and that analogy is with Flatlanders. 497 00:34:38,827 --> 00:34:42,938 A Flatlander is someone who lives on a two-dimensional 498 00:34:42,938 --> 00:34:45,342 world. He happens to live on the 499 00:34:45,342 --> 00:34:49,143 surface of a balloon. And light travels only along 500 00:34:49,143 --> 00:34:55,197 the surface of the balloon. So the two-dimensional world is 501 00:34:55,197 --> 00:35:00,46 curved in the third dimension, but the Flatlanders cannot see 502 00:35:00,46 --> 00:35:04,933 in the third dimension. They can only see the second 503 00:35:04,933 --> 00:35:08,441 dimension. So here you have such a world. 504 00:35:08,441 --> 00:35:11,599 So here are the galaxies. Flat world. 505 00:35:11,599 --> 00:35:16,861 And the universe is curved in the third dimension which these 506 00:35:16,861 --> 00:35:21,509 Flatlanders cannot see. And when you blow this balloon 507 00:35:21,509 --> 00:35:26,217 up, the galaxies move away from 508 00:35:26,217 --> 00:35:33,128 each other, and the farther the galaxies are away from each 509 00:35:33,128 --> 00:35:40,515 other, the higher the velocity. This model works actually quite 510 00:35:40,515 --> 00:35:46,949 well and I want to pursue that in my next calculations. 511 00:35:46,949 --> 00:35:52,787 Let me first try to bring this universe to a halt. 512 00:35:52,787 --> 00:35:57,911 Because I don't want the universe 513 00:35:57,911 --> 00:36:00,404 to collapse again. Ooh. 514 00:36:00,404 --> 00:36:02,104 OK. I succeeded. 515 00:36:02,104 --> 00:36:08,791 So you can pursue this idea very nicely and you can see that 516 00:36:08,791 --> 00:36:14,684 the Flatlanders would draw quite amazing conclusions. 517 00:36:14,684 --> 00:36:20,124 Here is that balloon. The balloon has a radius R. 518 00:36:20,124 --> 00:36:25,337 Here is one galaxy. And here is another galaxy. 519 00:36:25,337 --> 00:36:30,438 And they are a distance S apart. 520 00:36:30,438 --> 00:36:35,392 I will call that later D. But now I want to call it S. 521 00:36:35,392 --> 00:36:39,13 You will see why. A little later in time, 522 00:36:39,13 --> 00:36:44,178 the universe has expanded, this galaxy is here and this 523 00:36:44,178 --> 00:36:48,478 galaxy is here. And this distance now is R plus 524 00:36:48,478 --> 00:36:53,712 dR and so this distance now between the two galaxies is S 525 00:36:53,712 --> 00:36:57,358 plus dS. And it follows immediately from 526 00:36:57,358 --> 00:37:04,8 the geometry that S plus dS divided by S is R plus dR 527 00:37:04,8 --> 00:37:10,875 divided by R. Simple high school geometry. 528 00:37:10,875 --> 00:37:18,283 I can work this out. I get S R plus R dS is SR plus 529 00:37:18,283 --> 00:37:21,246 S dR. I lose this SR. 530 00:37:21,246 --> 00:37:27,321 I divide by dT. dS dT is the velocity with 531 00:37:27,321 --> 00:37:34,432 which these two galaxies move away from each 532 00:37:34,432 --> 00:37:38,448 other. That's they what they would 533 00:37:38,448 --> 00:37:44,169 measure in their universe. So there is a V here. 534 00:37:44,169 --> 00:37:49,767 It's clear that S is the distance between them. 535 00:37:49,767 --> 00:37:54,879 I will call that D again now. So that is D. 536 00:37:54,879 --> 00:37:59,503 And then I have one over R times dR dT. 537 00:37:59,503 --> 00:38:06,44 One over R I will write this a little higher. 538 00:38:06,44 --> 00:38:09,402 dR over R. No no no we had dR dT. 539 00:38:09,402 --> 00:38:13,844 So now I have one over R dR dT. And look at this. 540 00:38:13,844 --> 00:38:16,897 I have V equals D times something. 541 00:38:16,897 --> 00:38:22,079 And that something at a given moment in time has a unique 542 00:38:22,079 --> 00:38:25,318 value. R of the balloon has a unique 543 00:38:25,318 --> 00:38:27,909 value. And dR dT which is the 544 00:38:27,909 --> 00:38:31,796 expansion velocity also has a unique value. 545 00:38:31,796 --> 00:38:38,121 And so it's immediately obvious that in this universe this is 546 00:38:38,121 --> 00:38:41,617 Hubble's constant. And this Hubble's constant is a 547 00:38:41,617 --> 00:38:44,614 function of time. It is changing with time. 548 00:38:44,614 --> 00:38:47,895 And it's obvious that it should change in time. 549 00:38:47,895 --> 00:38:51,891 No reason why it shouldn't do the same in our own galaxy. 550 00:38:51,891 --> 00:38:54,602 Because R in the past was much smaller. 551 00:38:54,602 --> 00:38:58,097 So even if you take an expansion velocity which is 552 00:38:58,097 --> 00:39:02,521 constant, if R is smaller in the past, then H was larger in the 553 00:39:02,521 --> 00:39:04,946 past. And that is the reason why if 554 00:39:04,946 --> 00:39:08,586 you ever see a quote of H to be 555 00:39:08,586 --> 00:39:12,394 seventy-two kilometers per second per megaparsec, 556 00:39:12,394 --> 00:39:15,012 there's always a little zero here. 557 00:39:15,012 --> 00:39:19,058 And the zero means now. The zero means not a billion 558 00:39:19,058 --> 00:39:22,39 years from now and not a billion years ago. 559 00:39:22,39 --> 00:39:26,515 We really don't know what it was a billion years ago. 560 00:39:26,515 --> 00:39:31,116 Now don't get -- don't carry this analogy between the two-D 561 00:39:31,116 --> 00:39:34,527 balloon and the -- our own universe too far. 562 00:39:34,527 --> 00:39:37,541 But it gives some interesting insights. 563 00:39:37,541 --> 00:39:41,96 It is suggestive of the idea that our own 564 00:39:41,96 --> 00:39:46,265 three-dimensional space may be curved in the fourth dimension 565 00:39:46,265 --> 00:39:49,78 that we cannot see. This is very fascinating and I 566 00:39:49,78 --> 00:39:54,012 would advise you if you are interested in this area that you 567 00:39:54,012 --> 00:39:57,886 take a course in cosmology. You should also take one in 568 00:39:57,886 --> 00:40:01,401 general relativity. It will open a whole new world 569 00:40:01,401 --> 00:40:03,841 for you. And both Allen Guth and Ed 570 00:40:03,841 --> 00:40:07,93 Bertschinger and also Scott Burles are the experts in this 571 00:40:07,93 --> 00:40:12,09 area and they happen to be one of our best 572 00:40:12,09 --> 00:40:14,628 teachers. So you can't lose there. 573 00:40:14,628 --> 00:40:19,241 Now comes a key question and that is will our universe expand 574 00:40:19,241 --> 00:40:21,624 forever? If the universe expands 575 00:40:21,624 --> 00:40:26,083 forever, we call that an open universe, that's just a name. 576 00:40:26,083 --> 00:40:30,389 It's also possible that our universe will come to a halt. 577 00:40:30,389 --> 00:40:33,157 That means that H, Hubble's constant, 578 00:40:33,157 --> 00:40:36,463 will become zero, that everything will stand 579 00:40:36,463 --> 00:40:40,461 still, no relative motion anymore, which then will be 580 00:40:40,461 --> 00:40:43,26 followed by collapse. 581 00:40:43,26 --> 00:40:47,643 And so all the red shifts will then come to zero and will turn 582 00:40:47,643 --> 00:40:50,086 to blue shifts. It's the same idea, 583 00:40:50,086 --> 00:40:53,32 the same question, when you throw up an apple, 584 00:40:53,32 --> 00:40:57,344 will the apple come back or will the apple not come back. 585 00:40:57,344 --> 00:41:01,655 It depends on the speed of the apple and on the gravitational 586 00:41:01,655 --> 00:41:04,96 field of the earth, and we all know that if you 587 00:41:04,96 --> 00:41:08,409 throw it fast enough, about eleven kilometers per 588 00:41:08,409 --> 00:41:12,362 second in the absence of atmosphere the 589 00:41:12,362 --> 00:41:16,503 apple would never come back. Now if only gravity played the 590 00:41:16,503 --> 00:41:20,288 key role in our universe, then we can do a very simple 591 00:41:20,288 --> 00:41:23,144 calculation. And the answer to whether or 592 00:41:23,144 --> 00:41:27,286 not our universe is open or closed would then depend on the 593 00:41:27,286 --> 00:41:31,713 average density of the universe. And when I say average density 594 00:41:31,713 --> 00:41:34,998 then you have to think in terms of a big scale. 595 00:41:34,998 --> 00:41:37,64 You don't think in terms of Cambridge. 596 00:41:37,64 --> 00:41:41,568 That's not representative for the average density of the 597 00:41:41,568 --> 00:41:45,833 universe. Nor is our solar system. 598 00:41:45,833 --> 00:41:50,649 Nor is our galaxy. But you have to think probably 599 00:41:50,649 --> 00:41:55,164 on the scale of a few hundred million parsecs. 600 00:41:55,164 --> 00:42:01,385 Maybe five hundred megaparsecs. And so I bring you out now into 601 00:42:01,385 --> 00:42:04,797 the universe. Here is the universe. 602 00:42:04,797 --> 00:42:10,115 And these are galaxies. And here is a sphere which has 603 00:42:10,115 --> 00:42:15,433 a radius R and that's on a scale of about five hundred 604 00:42:15,433 --> 00:42:20,679 megaparsecs. So rho, the average density, 605 00:42:20,679 --> 00:42:23,882 is representative for the universe. 606 00:42:23,882 --> 00:42:29,723 And here let's suppose you were here, or I can take any part in 607 00:42:29,723 --> 00:42:33,68 the universe, there's nothing special about 608 00:42:33,68 --> 00:42:39,332 it, and you see here a galaxy and that galaxy moves away from 609 00:42:39,332 --> 00:42:44,137 you with a velocity V. That galaxy has a mass little 610 00:42:44,137 --> 00:42:46,304 M. The mass inside here, 611 00:42:46,304 --> 00:42:52,05 capital M, inside this sphere, is four-thirds pi R cubed times 612 00:42:52,05 --> 00:42:56,212 rho. It's the average density, 613 00:42:56,212 --> 00:42:59,31 right? Now we know from Newton that 614 00:42:59,31 --> 00:43:05,051 the force that this galaxy will experience is only determined by 615 00:43:05,051 --> 00:43:10,336 the mass inside this sphere and not by the mass outside the 616 00:43:10,336 --> 00:43:13,616 sphere. And so if I want to calculate 617 00:43:13,616 --> 00:43:18,81 whether these two objects will forever move away from each 618 00:43:18,81 --> 00:43:23,456 other or whether they will fall back to 619 00:43:23,456 --> 00:43:28,878 each other then all I have to make sure that I make the total 620 00:43:28,878 --> 00:43:34,21 energy zero, the sum of the kinetic energy and the potential 621 00:43:34,21 --> 00:43:38,728 energy must be zero. So one-half MV squared of this 622 00:43:38,728 --> 00:43:42,071 object, it must be M M G divided by R. 623 00:43:42,071 --> 00:43:45,414 That is when the total energy is zero. 624 00:43:45,414 --> 00:43:51,017 We will expand forever and ever and ever and it will never come 625 00:43:51,017 --> 00:43:53,366 back. Little M cancels out. 626 00:43:53,366 --> 00:43:57,704 Capital M I can write four-thirds 627 00:43:57,704 --> 00:44:03,125 pi R cubed rho. Here comes my G and here comes 628 00:44:03,125 --> 00:44:06,137 R. Notice that the R cubed 629 00:44:06,137 --> 00:44:12,884 upstairs becomes R squared. And so if I have an R squared 630 00:44:12,884 --> 00:44:19,992 here and I have a V squared here, remember that V divided by 631 00:44:19,992 --> 00:44:25,293 R, that is Hubble's constant. Because R is D, 632 00:44:25,293 --> 00:44:31,92 it's the distance between us and the galaxy. 633 00:44:31,92 --> 00:44:38,36 And so V squared divided by R squared is the Hubble constant 634 00:44:38,36 --> 00:44:44,8 as we measure it today squared. And so you'll find then from 635 00:44:44,8 --> 00:44:50,148 this simple result that rho as it should be today, 636 00:44:50,148 --> 00:44:56,916 that's why I put a little zero there, is three divided by eight 637 00:44:56,916 --> 00:45:03,137 pi -- I get a G there, and I get H zero squared. 638 00:45:03,137 --> 00:45:08,719 And so this tells me that if the density, the average density 639 00:45:08,719 --> 00:45:12,625 of our universe, is larger than this value, 640 00:45:12,625 --> 00:45:17,741 then our universe will come to a halt and will collapse. 641 00:45:17,741 --> 00:45:20,625 And we can calculate that value. 642 00:45:20,625 --> 00:45:24,345 Because we know H zero, we think we know, 643 00:45:24,345 --> 00:45:30,206 we know G, and so you will find then -- I'll write it down here, 644 00:45:30,206 --> 00:45:35,043 that rho zero is about ten to the minus 645 00:45:35,043 --> 00:45:38,542 twenty-six kilograms per cubic meter. 646 00:45:38,542 --> 00:45:43,693 And so if rho is smaller than this amount then we will 647 00:45:43,693 --> 00:45:48,942 continue to expand forever, the universe would be open. 648 00:45:48,942 --> 00:45:54,385 If the mean density right now is larger than that amount, 649 00:45:54,385 --> 00:45:59,148 then we will -- the expansion will come to a halt, 650 00:45:59,148 --> 00:46:04,397 red shift will become blue shifts, and we will collapse 651 00:46:04,397 --> 00:46:06,535 again. The matter here, 652 00:46:06,535 --> 00:46:12,417 this matter density, doesn't have to be tomatoes or 653 00:46:12,417 --> 00:46:15,393 potatoes. It could be electromagnetic 654 00:46:15,393 --> 00:46:18,782 radiation. Because according to Einstein E 655 00:46:18,782 --> 00:46:22,006 equals MC squared. So any form of energy 656 00:46:22,006 --> 00:46:24,982 represents mass. So don't think of it 657 00:46:24,982 --> 00:46:30,025 necessarily as this being the stars and galaxies and tomatoes. 658 00:46:30,025 --> 00:46:34,571 It is generally believed today that the expansion of our 659 00:46:34,571 --> 00:46:38,291 universe will not come to a halt and collapse. 660 00:46:38,291 --> 00:46:43,676 But our views could change. Enormous development has been 661 00:46:43,676 --> 00:46:47,463 going on in the last ten years and you can read about that in 662 00:46:47,463 --> 00:46:50,367 the New York Times. Almost every month you will 663 00:46:50,367 --> 00:46:53,775 read something about the enormous progress that's being 664 00:46:53,775 --> 00:46:56,489 made in cosmology. And of course the idea of 665 00:46:56,489 --> 00:46:59,456 whether or not the universe will expand forever, 666 00:46:59,456 --> 00:47:03,306 whether it's open or whether it is closed, is something that's 667 00:47:03,306 --> 00:47:05,642 emotionally an important issue for us. 668 00:47:05,642 --> 00:47:09,429 If the universe is open and it will expand forever then stars 669 00:47:09,429 --> 00:47:13,027 will all burn out and the universe will 670 00:47:13,027 --> 00:47:16,114 become a cold, dead and boring place. 671 00:47:16,114 --> 00:47:21,001 If however the universe is closed, the expansion will come 672 00:47:21,001 --> 00:47:26,061 to a halt, it will collapse, and it will end up with what we 673 00:47:26,061 --> 00:47:30,005 call the Big Crunch as opposed to the Big Bang. 674 00:47:30,005 --> 00:47:33,692 And it will be hot, there will be fireworks, 675 00:47:33,692 --> 00:47:37,637 it will be like the early days of the Big Bang. 676 00:47:37,637 --> 00:47:40,638 Temperatures of billions of degrees. 677 00:47:40,638 --> 00:47:45,612 I'd like to read a poem from Robert Frost which he wrote in 678 00:47:45,612 --> 00:47:48,289 nineteen twenty. 679 00:47:48,289 --> 00:47:52,478 It's called Fire and Ice. Some say the world will end in 680 00:47:52,478 --> 00:47:55,981 fire, some say in ice. From what I've tasted of 681 00:47:55,981 --> 00:47:59,028 desire, I hold with those who favor fire. 682 00:47:59,028 --> 00:48:03,522 But if it had to perish twice, I think I know enough of hate 683 00:48:03,522 --> 00:48:07,026 to know that for destruction ice is also great. 684 00:48:07,026 --> 00:48:10,682 And would suffice. There are many people who want 685 00:48:10,682 --> 00:48:15,023 our universe to be closed, probably for emotional reasons, 686 00:48:15,023 --> 00:48:18,831 maybe for religious reasons, maybe 687 00:48:18,831 --> 00:48:22,391 it's more esthetic, maybe it's more reassuring, 688 00:48:22,391 --> 00:48:25,332 maybe it's more romantic. I don't know. 689 00:48:25,332 --> 00:48:29,046 But if it's open the end is not very spectacular. 690 00:48:29,046 --> 00:48:29,356 T. S. 691 00:48:29,356 --> 00:48:32,684 Eliot wrote, "This is the way the world ends 692 00:48:32,684 --> 00:48:37,404 not with a bang but a whimper." Now it is conceivable that the 693 00:48:37,404 --> 00:48:41,815 expansion of the universe will come to a halt and that the 694 00:48:41,815 --> 00:48:44,369 universe will ultimately collapse. 695 00:48:44,369 --> 00:48:48,78 We will have a big crunch. And it is even conceivable that 696 00:48:48,78 --> 00:48:52,634 a new universe will then be born 697 00:48:52,634 --> 00:48:55,632 afterwards. That there will be a new Big 698 00:48:55,632 --> 00:48:58,169 Bang. And if the evolution of that 699 00:48:58,169 --> 00:49:02,166 universe were a carbon copy, exact carbon copy of the 700 00:49:02,166 --> 00:49:05,626 present universe, a few thousand billion years 701 00:49:05,626 --> 00:49:09,393 from now we may have a great eight oh two reunion. 702 00:49:09,393 --> 49:14 Same place same time same people, perhaps see you then.