1 00:00:00,080 --> 00:00:02,430 The following content is provided under a Creative 2 00:00:02,430 --> 00:00:03,820 Commons license. 3 00:00:03,820 --> 00:00:06,050 Your support will help MIT OpenCourseWare 4 00:00:06,050 --> 00:00:10,140 continue to offer high quality educational resources for free. 5 00:00:10,140 --> 00:00:12,690 To make a donation or to view additional materials 6 00:00:12,690 --> 00:00:18,060 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:18,060 --> 00:00:18,960 at ocw.mit.edu. 8 00:00:21,660 --> 00:00:25,650 HONG LIU: OK, so let me first summarize what we 9 00:00:25,650 --> 00:00:28,790 did at the end of last lecture. 10 00:00:35,110 --> 00:00:43,990 So we can see that the Rindler space 11 00:00:43,990 --> 00:00:50,490 can be separated from the right column 12 00:00:50,490 --> 00:00:53,960 into into four different patches. 13 00:00:53,960 --> 00:01:03,120 In particular, there's a left patch and the right patch, 14 00:01:03,120 --> 00:01:13,790 and this is a constant row slice in the Rindler. 15 00:01:13,790 --> 00:01:16,330 So what we showed is that the Minkowski vacuum, 16 00:01:16,330 --> 00:01:18,900 the standards, the vacuum we defined, 17 00:01:18,900 --> 00:01:22,990 the Minkowski quantum field theory, 18 00:01:22,990 --> 00:01:30,560 can be written as an entangled state, 19 00:01:30,560 --> 00:01:33,620 and we express it in terms of the Hilbert space of the left 20 00:01:33,620 --> 00:01:34,670 and the right patch. 21 00:01:39,960 --> 00:01:42,820 So this n sum over all possible in the [INAUDIBLE] state. 22 00:01:50,870 --> 00:02:02,780 So this n and n are eigen vectors, eigen values, 23 00:02:02,780 --> 00:02:12,079 and eigen vectors of the Rindler Hamiltonian, which 24 00:02:12,079 --> 00:02:12,620 we called HR. 25 00:02:17,800 --> 00:02:23,610 And so this, similarly, is an L. So an R 26 00:02:23,610 --> 00:02:26,700 means the eigen vector in the right patch 27 00:02:26,700 --> 00:02:29,210 and an L is the eigen vector for the left patch. 28 00:02:33,220 --> 00:02:39,780 And now when you trace out, for example, the left patch, 29 00:02:39,780 --> 00:02:44,060 suppose you're only interested in the physics 30 00:02:44,060 --> 00:03:01,390 in the right patch when you trace out the left patch, 31 00:03:01,390 --> 00:03:07,150 then you find the sum of density matrix for the right patch. 32 00:03:10,130 --> 00:03:16,500 [? Under ?] the [? sum ?] of the density matrix is the partition 33 00:03:16,500 --> 00:03:25,460 function for the full Rindler minus 2 pi h and so you 34 00:03:25,460 --> 00:03:29,440 conclude that the temperature is 1 over 2 pi. 35 00:03:34,480 --> 00:03:41,580 So that's what we did at the end of last lecture. 36 00:03:41,580 --> 00:03:45,096 So there are several key elements here. 37 00:03:45,096 --> 00:03:46,720 So there are several key elements here. 38 00:03:46,720 --> 00:03:51,910 So the first key element is that the Minkowski [? ground ?] 39 00:03:51,910 --> 00:03:54,660 state turned out to be a particular kind 40 00:03:54,660 --> 00:03:58,980 of entangled state between the left and the right patch. 41 00:03:58,980 --> 00:04:02,510 And then you get the [? sum ?] of density matrix 42 00:04:02,510 --> 00:04:05,030 when you have a Lorenz above the left patch. 43 00:04:05,030 --> 00:04:08,670 So these are two of the basic elements. 44 00:04:08,670 --> 00:04:11,140 So any questions on this? 45 00:04:11,140 --> 00:04:11,640 Yes. 46 00:04:11,640 --> 00:04:14,105 AUDIENCE: [INAUDIBLE] left patch. 47 00:04:14,105 --> 00:04:17,141 Is there any physical meaning to the left patch? 48 00:04:17,141 --> 00:04:19,640 HONG LIU: It's the same physical meaning to the right patch. 49 00:04:29,160 --> 00:04:32,030 For the observer in the right patch, of course, 50 00:04:32,030 --> 00:04:35,269 you don't see the left patch, and so that's 51 00:04:35,269 --> 00:04:37,560 why you get the [? sum ?] of density-- yeah, that's why 52 00:04:37,560 --> 00:04:39,370 you have to integrate them out. 53 00:04:39,370 --> 00:04:43,585 Yeah, they play a very important physical role. 54 00:04:43,585 --> 00:04:46,435 AUDIENCE: [INAUDIBLE] observable [INAUDIBLE] 55 00:04:49,770 --> 00:04:52,300 HONG LIU: This is just pure Minkowski space. 56 00:04:52,300 --> 00:04:54,800 Yeah, this is just pure Minkowski space. 57 00:04:54,800 --> 00:04:58,500 This is Minkowski space. 58 00:04:58,500 --> 00:05:01,600 So this kind observer can only observe the right patch, 59 00:05:01,600 --> 00:05:04,980 so to this kind of observer then you 60 00:05:04,980 --> 00:05:08,650 must integrate out all the physics in the left patch. 61 00:05:08,650 --> 00:05:12,197 So that's why they see a similar physics. 62 00:05:12,197 --> 00:05:14,030 Yeah, so this is just a physical explanation 63 00:05:14,030 --> 00:05:15,650 why this is similar physics. 64 00:05:18,210 --> 00:05:21,720 AUDIENCE: Why do we need to introduce a harmonic oscillator 65 00:05:21,720 --> 00:05:25,190 during [INAUDIBLE] HR can be anything? 66 00:05:28,440 --> 00:05:31,770 I forgot the reason why we introduced harmonic oscillator. 67 00:05:31,770 --> 00:05:33,690 HONG LIU: Oh, I just gave you a simple example 68 00:05:33,690 --> 00:05:38,110 to explain this kind of physics using a simple example. 69 00:05:38,110 --> 00:05:40,830 just in case you're not familiar with this kind physics 70 00:05:40,830 --> 00:05:43,220 I gave you a simple example to build up your intuition. 71 00:05:51,781 --> 00:05:53,780 the reason we considered the harmonic oscillator 72 00:05:53,780 --> 00:05:57,360 is not an important reason. 73 00:05:57,360 --> 00:06:00,240 Say if you [? quantize ?] the scalar field theory-- so 74 00:06:00,240 --> 00:06:03,520 any theory on this space, say if you [? quantize ?] 75 00:06:03,520 --> 00:06:06,590 a free quantum field theory, that just reduce the harmonic 76 00:06:06,590 --> 00:06:07,860 oscillator. 77 00:06:07,860 --> 00:06:09,780 So the harmonic oscillator in fact 78 00:06:09,780 --> 00:06:12,924 have the exact same physics as general quantum field theory 79 00:06:12,924 --> 00:06:13,465 you consider. 80 00:06:17,304 --> 00:06:18,265 Any other questions? 81 00:06:20,970 --> 00:06:23,614 AUDIENCE: May I repeat my question? 82 00:06:23,614 --> 00:06:25,452 The right patch, the [INAUDIBLE] patch, 83 00:06:25,452 --> 00:06:27,660 corresponds to the exterior of the black hole, right? 84 00:06:32,740 --> 00:06:34,390 HONG LIU: In the black hole problem, 85 00:06:34,390 --> 00:06:36,290 the counterpart of the right patch 86 00:06:36,290 --> 00:06:37,970 is exterior over the black hole. 87 00:06:37,970 --> 00:06:38,650 That's right. 88 00:06:38,650 --> 00:06:40,526 AUDIENCE: So the upper patch is the interior? 89 00:06:40,526 --> 00:06:41,483 HONG LIU: That's right. 90 00:06:41,483 --> 00:06:43,410 AUDIENCE: So what are the kind of [INAUDIBLE]? 91 00:06:43,410 --> 00:06:46,230 HONG LIU: The left patch is [INAUDIBLE] asymptotical region 92 00:06:46,230 --> 00:06:49,930 over the black hole, which is also outside the horizon. 93 00:06:49,930 --> 00:06:53,785 So the extended black hole has two asymptotical regions. 94 00:06:53,785 --> 00:06:54,284 Yeah. 95 00:06:54,284 --> 00:06:57,303 AUDIENCE: So is there any kind of [INAUDIBLE] way 96 00:06:57,303 --> 00:06:59,187 with the left patch [INAUDIBLE]? 97 00:07:02,510 --> 00:07:04,130 HONG LIU: Yeah, as I said. 98 00:07:04,130 --> 00:07:06,340 Yeah, I'm going to talk about this a little bit. 99 00:07:06,340 --> 00:07:08,464 I'm going to talk about black hole in a little bit. 100 00:07:11,390 --> 00:07:12,260 Any other questions? 101 00:07:14,860 --> 00:07:15,360 Good? 102 00:07:22,330 --> 00:07:24,160 So let me make some further remarks. 103 00:07:37,240 --> 00:07:44,910 The first is that this Minkowski vacuum-- this entangled 104 00:07:44,910 --> 00:07:48,710 state between the left and the right-- is 105 00:07:48,710 --> 00:08:03,000 invariant under the [? axim-- ?] Or maybe 106 00:08:03,000 --> 00:08:07,720 I should say-- let me just say it. 107 00:08:07,720 --> 00:08:18,040 It's invariant under HR R minus HR left. 108 00:08:25,320 --> 00:08:29,080 By invariant under this I mean-- so this state 109 00:08:29,080 --> 00:08:34,570 is [INAUDIBLE] by this, and this invariant under any translation 110 00:08:34,570 --> 00:08:37,740 generated by this combination. 111 00:08:37,740 --> 00:08:39,360 I'm not using very precise English, 112 00:08:39,360 --> 00:08:41,610 but I think you understand what I mean. 113 00:08:41,610 --> 00:08:44,450 Anyway, so this you can see immediately from there. 114 00:08:47,220 --> 00:08:51,840 I just [INAUDIBLE] this harmonic oscillator example, 115 00:08:51,840 --> 00:08:55,990 and if you act this on that-- so this R means Rindler, 116 00:08:55,990 --> 00:08:59,410 and this R means the right patch and left patch. 117 00:08:59,410 --> 00:09:04,230 So act this on that state, then they just get 118 00:09:04,230 --> 00:09:05,650 an E because of the minus sign. 119 00:09:05,650 --> 00:09:08,660 They just canceled. 120 00:09:08,660 --> 00:09:14,360 And so this minus sign is related. 121 00:09:14,360 --> 00:09:18,437 What I said last time is that you can think of the left patch 122 00:09:18,437 --> 00:09:20,145 half the time running over the direction. 123 00:09:24,700 --> 00:09:26,830 By time I mean this [INAUDIBLE], OK? 124 00:09:46,560 --> 00:09:48,640 So what this operator gener-- it does 125 00:09:48,640 --> 00:09:55,860 is the generator flow-- there's a generate flow in eta. 126 00:09:55,860 --> 00:09:58,372 So the eta goes running to so this 127 00:09:58,372 --> 00:10:00,330 goes running to [? comes ?] in the low surface. 128 00:10:09,250 --> 00:10:12,620 And the flow in the right quadrant is going up, 129 00:10:12,620 --> 00:10:14,370 but in the left quadrant it should go down 130 00:10:14,370 --> 00:10:16,660 so the time should be moving [? normally ?] direction, 131 00:10:16,660 --> 00:10:18,243 and that's what this minus sign means. 132 00:10:21,760 --> 00:10:24,130 And then this transformation, we'll 133 00:10:24,130 --> 00:10:25,275 leave this state invariant. 134 00:10:27,850 --> 00:10:29,270 And you [? graph ?] the same thing 135 00:10:29,270 --> 00:10:31,228 like we did before for the harmonic oscillator. 136 00:10:33,640 --> 00:10:36,120 Any questions on this? 137 00:10:36,120 --> 00:10:39,010 So you can immediately see from that equation 138 00:10:39,010 --> 00:10:40,955 this operator [INAUDIBLE] that state. 139 00:10:46,150 --> 00:10:52,840 So this can also be-- so do you have 140 00:10:52,840 --> 00:10:55,820 any problems saying that the HR generated translation 141 00:10:55,820 --> 00:10:56,470 along this? 142 00:11:02,080 --> 00:11:03,802 Is this clear to you? 143 00:11:03,802 --> 00:11:06,658 AUDIENCE: So the [INAUDIBLE], the time [INAUDIBLE] 144 00:11:06,658 --> 00:11:08,042 are opposite. 145 00:11:08,042 --> 00:11:13,625 Does it mean that any other physical is the opposite time 146 00:11:13,625 --> 00:11:15,050 and [? changing weight ?]? 147 00:11:15,050 --> 00:11:18,020 HONG LIU: It doesn't matter what you mean. 148 00:11:18,020 --> 00:11:20,757 It doesn't matter how you interplay, physically. 149 00:11:20,757 --> 00:11:23,090 Right now, I'm talking about the mathematical statement. 150 00:11:23,090 --> 00:11:26,380 I want to first understand the mathematical statement. 151 00:11:26,380 --> 00:11:29,610 So this mathematical statement has two layers. 152 00:11:29,610 --> 00:11:31,780 Let me write explicitly. 153 00:11:31,780 --> 00:11:53,770 This means i HR R minus HL, HR left acting on 0N with reach 154 00:11:53,770 --> 00:11:58,020 any eta this is invariant. 155 00:11:58,020 --> 00:11:58,770 This is invariant. 156 00:12:02,860 --> 00:12:06,030 This, you can just see directly from that 157 00:12:06,030 --> 00:12:09,850 the fact this [INAUDIBLE] that state. 158 00:12:09,850 --> 00:12:13,520 And then that means that this thing 159 00:12:13,520 --> 00:12:16,240 leaves this thing invariant. 160 00:12:16,240 --> 00:12:22,410 Under the action of this guy, this operator, 161 00:12:22,410 --> 00:12:25,360 from the point of view of the red patch because one thing, 162 00:12:25,360 --> 00:12:28,150 you generate the translation in the eta 163 00:12:28,150 --> 00:12:31,700 because HR is the [INAUDIBLE] for the eta, 164 00:12:31,700 --> 00:12:35,340 so this just generates the translation in eta, 165 00:12:35,340 --> 00:12:37,530 which leaves rho invariant. 166 00:12:37,530 --> 00:12:41,450 And this slice I'm showing here is the constant, the rho slice, 167 00:12:41,450 --> 00:12:44,410 so that means this generates a translation along that arrow 168 00:12:44,410 --> 00:12:49,500 direction, moving to positive time. 169 00:12:49,500 --> 00:12:53,030 And this minus sign means that, in the left patch-- 170 00:12:53,030 --> 00:12:54,660 because [INAUDIBLE] transformation 171 00:12:54,660 --> 00:12:57,450 we are moving [? in the only ?] direction. 172 00:12:57,450 --> 00:13:01,820 And then that operation, we will leave this state invariant. 173 00:13:01,820 --> 00:13:02,340 Yes. 174 00:13:02,340 --> 00:13:03,010 AUDIENCE: So one question. 175 00:13:03,010 --> 00:13:04,730 So sometimes people have this interpretation-- 176 00:13:04,730 --> 00:13:06,430 I'm not sure if this picture is correct-- but in the black hole 177 00:13:06,430 --> 00:13:08,040 picture, we interpret the bottom thing 178 00:13:08,040 --> 00:13:10,560 as being some sort of white hole, which sort of spews out 179 00:13:10,560 --> 00:13:11,550 things. 180 00:13:11,550 --> 00:13:14,290 So if we reverse time, then does it sort of become a black hole 181 00:13:14,290 --> 00:13:15,780 again because now it's-- 182 00:13:15,780 --> 00:13:16,520 HONG LIU: No, no. 183 00:13:16,520 --> 00:13:18,561 We are talking about completely different things. 184 00:13:18,561 --> 00:13:21,750 Here, I'm just talking about-- in the left and in the right 185 00:13:21,750 --> 00:13:25,280 you can choose whatever time direction you want. 186 00:13:25,280 --> 00:13:28,080 I'm just making a statement that said, 187 00:13:28,080 --> 00:13:33,800 if I make this kind of operation-- 188 00:13:33,800 --> 00:13:38,250 do a time translation in the positive time direction, 189 00:13:38,250 --> 00:13:41,280 but in the opposite time direction in the left-- 190 00:13:41,280 --> 00:13:46,565 that particular operation leaves the this state invariant. 191 00:13:50,640 --> 00:13:53,030 For physical applications you can choose whatever time 192 00:13:53,030 --> 00:13:55,550 direction you want. 193 00:13:55,550 --> 00:13:57,620 You can choose whatever time direction you want. 194 00:13:57,620 --> 00:13:59,330 And this is a mathematical statement 195 00:13:59,330 --> 00:14:03,330 saying this particular operator leaves this state invariant, 196 00:14:03,330 --> 00:14:05,445 and this particular operator half 197 00:14:05,445 --> 00:14:08,800 of the interpretation of generate opposite time 198 00:14:08,800 --> 00:14:11,410 translation in the left and the right patch. 199 00:14:15,190 --> 00:14:18,200 So this is an algebraic statement, 200 00:14:18,200 --> 00:14:21,931 but this can also be seen geometrically. 201 00:14:21,931 --> 00:14:23,430 This can also be seen geometrically. 202 00:14:25,950 --> 00:14:32,500 So if you work out the relation between the Minkowski's 203 00:14:32,500 --> 00:14:44,680 coordinates and the Rindler coordinates, 204 00:14:44,680 --> 00:14:48,650 you can actually immediately just see 205 00:14:48,650 --> 00:15:03,230 is that, geometrically, eta translation is a boost. 206 00:15:07,820 --> 00:15:15,720 in x, T. So what that does, it just generates a boost. 207 00:15:15,720 --> 00:15:17,800 So if this is not immediately clear to you, 208 00:15:17,800 --> 00:15:22,920 just go back and try to look at a translation between the two 209 00:15:22,920 --> 00:15:23,420 coordinates. 210 00:15:23,420 --> 00:15:26,360 Then you will see it immediately. 211 00:15:26,360 --> 00:15:31,960 So in other words, this HR actually generates a boost. 212 00:15:31,960 --> 00:15:37,160 This Hamiltonian essentially generates a boost. 213 00:15:37,160 --> 00:15:39,190 This Rindler Hamiltonian generates a boost. 214 00:15:43,470 --> 00:15:43,970 One second. 215 00:15:43,970 --> 00:15:45,660 Let me finish. 216 00:15:45,660 --> 00:15:53,140 So, clearly, by definition, the Minkowski vacuum 217 00:15:53,140 --> 00:15:54,500 is invariant on the boost. 218 00:16:04,230 --> 00:16:06,540 So this statement is essentially the statement 219 00:16:06,540 --> 00:16:11,190 that this thing is invariant on the boost. 220 00:16:11,190 --> 00:16:15,210 And then you can see this negative sign. 221 00:16:15,210 --> 00:16:18,750 Then you can see the negative sign from the fact 222 00:16:18,750 --> 00:16:22,990 that if you make a Lorenz boost-- 223 00:16:22,990 --> 00:16:25,890 and this is the trajectory of the Lorenz boost, 224 00:16:25,890 --> 00:16:29,629 and it acts off the direction in the left and in the right. 225 00:16:29,629 --> 00:16:31,420 So that's why there's a negative sign here. 226 00:16:35,020 --> 00:16:37,100 So this negative sign goes [? bonds, ?] 227 00:16:37,100 --> 00:16:39,120 so the geometric statement that when 228 00:16:39,120 --> 00:16:42,190 you make a Lorentz boost in the Minkowski plane, 229 00:16:42,190 --> 00:16:44,430 and the action on the left and on the right 230 00:16:44,430 --> 00:16:47,830 is in the opposite direction, so the same boost 231 00:16:47,830 --> 00:16:52,920 will take a point here to there, but we'll take a point here 232 00:16:52,920 --> 00:16:54,850 to here. 233 00:16:54,850 --> 00:16:57,100 And you can check yourself. 234 00:16:57,100 --> 00:16:59,440 And this translates into an algebraic statement-- 235 00:16:59,440 --> 00:17:01,010 just become this statement. 236 00:17:01,010 --> 00:17:04,079 And this statement is the same-- that this 237 00:17:04,079 --> 00:17:07,079 is invariant on the boost. 238 00:17:07,079 --> 00:17:10,290 So this is the first remark. 239 00:17:13,530 --> 00:17:23,344 And the second remark is that, if we expand the field phi 240 00:17:23,344 --> 00:17:33,387 R in the right patch in terms of a complete set of modes, 241 00:17:33,387 --> 00:17:34,970 just ask, what do you normally do when 242 00:17:34,970 --> 00:17:36,178 you do canonical [INAUDIBLE]? 243 00:17:52,990 --> 00:18:18,680 In the right patch, say-- so this 244 00:18:18,680 --> 00:18:20,470 defines a [INAUDIBLE] and the creation 245 00:18:20,470 --> 00:18:27,830 operators for the theory in the right patch. 246 00:18:27,830 --> 00:18:31,290 And, similarly, you can do it in the left patch. 247 00:18:31,290 --> 00:18:35,460 And then you can show, just based on that relation-- 248 00:18:35,460 --> 00:18:37,654 just based on that relation, you can show-- 249 00:18:37,654 --> 00:18:39,820 so let's consider the freescale [? of ?] [? field ?] 250 00:18:39,820 --> 00:18:44,110 [? series ?] so you can show that this-- 251 00:18:44,110 --> 00:18:48,920 just as the harmonic oscillator example we discussed before-- 252 00:18:48,920 --> 00:18:55,340 and this Minkowski state can be written as a [? squeezed ?] 253 00:18:55,340 --> 00:19:01,470 state in terms of [? their ?] vacuum. 254 00:19:01,470 --> 00:19:07,780 And now you have to take the product of all possible modes, 255 00:19:07,780 --> 00:19:10,010 and only the j is the frequency for each mode. 256 00:19:22,310 --> 00:19:25,510 So this is a precise analog of the harmonic oscillator 257 00:19:25,510 --> 00:19:29,820 example, just because each set of modes 258 00:19:29,820 --> 00:19:31,470 gives you a harmonic oscillator. 259 00:19:31,470 --> 00:19:33,136 So you just take the [INAUDIBLE] product 260 00:19:33,136 --> 00:19:35,130 of all these harmonic oscillators, 261 00:19:35,130 --> 00:19:38,600 and then you have this relation. 262 00:19:38,600 --> 00:19:53,510 Also, very similarly, the usual Minkowski 263 00:19:53,510 --> 00:20:06,210 creation and the relation operators are related. 264 00:20:18,160 --> 00:20:39,010 So this ajr, ajl by Bogoliubov transformations, just 265 00:20:39,010 --> 00:20:45,740 as the harmonic oscillator example. 266 00:20:50,640 --> 00:20:54,110 So we are allowed to write this transformation explicitly. 267 00:20:57,990 --> 00:21:00,330 But he's saying here, just direct generalize 268 00:21:00,330 --> 00:21:02,634 of the harmonic oscillator example 269 00:21:02,634 --> 00:21:04,300 because the field series is just a bunch 270 00:21:04,300 --> 00:21:05,300 of harmonic oscillators. 271 00:21:07,439 --> 00:21:09,730 A field series is just a bunch of harmonic oscillators. 272 00:21:12,302 --> 00:21:13,760 Any questions regarding this point? 273 00:21:19,320 --> 00:21:21,180 Yes. 274 00:21:21,180 --> 00:21:26,776 AUDIENCE: So, just to check-- so the right only 275 00:21:26,776 --> 00:21:29,150 affects the right patch and its identity everywhere else. 276 00:21:29,150 --> 00:21:29,870 HONG LIU: Sure. 277 00:21:29,870 --> 00:21:32,752 AUDIENCE: So that the combination leaves the bottom 278 00:21:32,752 --> 00:21:36,222 and the top portion just fixed. 279 00:21:36,222 --> 00:21:38,040 So the combination leaves the bottom 280 00:21:38,040 --> 00:21:40,520 and the top quarter fixed? 281 00:21:43,680 --> 00:21:48,010 HONG LIU: You don't get back to the-- yeah, when we-- yeah, 282 00:21:48,010 --> 00:21:54,160 so this is-- so this operation itself does not 283 00:21:54,160 --> 00:21:58,160 direct-- so this operation itself does not direct access 284 00:21:58,160 --> 00:22:00,970 to the top and bottom portion. 285 00:22:00,970 --> 00:22:03,054 And this is a [? trajectoral ?] for them. 286 00:22:03,054 --> 00:22:04,470 So if you have a point there, just 287 00:22:04,470 --> 00:22:06,490 take them to the [? hyperbolic ?] trajectory. 288 00:22:06,490 --> 00:22:07,854 So we're not taking to there. 289 00:22:07,854 --> 00:22:08,520 AUDIENCE: Right. 290 00:22:08,520 --> 00:22:11,244 And the top and the bottom are just-- it's [INAUDIBLE]. 291 00:22:14,180 --> 00:22:15,239 So it keeps them fixed? 292 00:22:15,239 --> 00:22:15,780 HONG LIU: No. 293 00:22:18,500 --> 00:22:20,550 When you define the Hilbert space, 294 00:22:20,550 --> 00:22:22,440 you only define for the left and the right 295 00:22:22,440 --> 00:22:24,660 because they don't define Hilbert space. 296 00:22:24,660 --> 00:22:30,850 The Hilbert space defines the given time slice, 297 00:22:30,850 --> 00:22:33,460 so that only includes the left and the right. 298 00:22:33,460 --> 00:22:36,600 And those particles run into future evolution, 299 00:22:36,600 --> 00:22:41,070 and that evolution is not controlled by them 300 00:22:41,070 --> 00:22:44,720 because they only take you along the hyperbolic trajectory. 301 00:22:51,160 --> 00:22:52,000 Any other questions? 302 00:22:54,910 --> 00:22:56,770 Good? 303 00:22:56,770 --> 00:23:08,350 So the third remark is that all of the discussions 304 00:23:08,350 --> 00:23:41,770 generalizes in complete parallel to Schwarzschild space time 305 00:23:41,770 --> 00:23:51,410 In particular, we said before, the Schwarzschild time 306 00:23:51,410 --> 00:23:54,770 have the falling space time causal structure. 307 00:23:54,770 --> 00:23:58,280 You have a whole-- so this is your regional region 308 00:23:58,280 --> 00:24:07,067 outside the horizon, but then you 309 00:24:07,067 --> 00:24:11,970 can extend this part of the space time into four regions. 310 00:24:11,970 --> 00:24:14,510 In particular, you have two-- again, 311 00:24:14,510 --> 00:24:18,890 you have R and L-- two asymptotical regions. 312 00:24:18,890 --> 00:24:21,650 So this way the R goes to infinity, 313 00:24:21,650 --> 00:24:26,230 and similarly this way, also, R goes infinity. 314 00:24:26,230 --> 00:24:33,660 So, again, in this [INAUDIBLE] vacuum state, 315 00:24:33,660 --> 00:24:37,456 which it can be defined from going to create 316 00:24:37,456 --> 00:24:39,830 the [? signature ?] and the [? compact ?] [INAUDIBLE] phi 317 00:24:39,830 --> 00:24:42,300 this tau. 318 00:24:42,300 --> 00:24:44,230 Again, corresponding to an entangled state 319 00:24:44,230 --> 00:24:47,070 between the left and the right. 320 00:24:47,070 --> 00:24:49,270 And if you ignore the left, again, you'll 321 00:24:49,270 --> 00:24:51,937 get a similar state from the right. 322 00:24:51,937 --> 00:24:53,520 So the story's completely in parallel. 323 00:24:56,460 --> 00:24:57,840 It's what we discussed before. 324 00:25:00,550 --> 00:25:03,930 The only different thing is the technicalities 325 00:25:03,930 --> 00:25:06,585 that, of course, in the specific metric are different. 326 00:25:06,585 --> 00:25:08,185 The specific metric are different. 327 00:25:10,850 --> 00:25:13,960 And in particular, this [INAUDIBLE] vacuum 328 00:25:13,960 --> 00:25:17,535 can be obtained by doing Euclidean paths integral. 329 00:25:20,150 --> 00:25:26,570 Again, will be the half space, so this is the tau direction. 330 00:25:26,570 --> 00:25:32,480 Again, you do the half space, and the times S2. 331 00:25:32,480 --> 00:25:37,450 It's the same thing exactly as we did for the Rindler. 332 00:25:42,330 --> 00:25:46,717 You do the half space and when you're 333 00:25:46,717 --> 00:25:49,050 interpreting in terms of this tau [? foliation ?], which 334 00:25:49,050 --> 00:25:53,612 is angle, then you get this entangled state. 335 00:25:53,612 --> 00:25:54,820 You get this entangled state. 336 00:25:57,520 --> 00:25:58,740 So any questions on this? 337 00:25:58,740 --> 00:25:59,360 Yes. 338 00:25:59,360 --> 00:26:00,443 AUDIENCE: Just to clarify. 339 00:26:00,443 --> 00:26:02,450 So this entangled state is really 340 00:26:02,450 --> 00:26:05,170 nothing more than a mathematical trick to help us? 341 00:26:05,170 --> 00:26:07,010 Or should I think about it physically? 342 00:26:07,010 --> 00:26:08,218 HONG LIU: No, this is a fact. 343 00:26:08,218 --> 00:26:11,190 This is not a mathematical trick. 344 00:26:11,190 --> 00:26:16,920 If we're grabbing that case, the Minkowski vacuum 345 00:26:16,920 --> 00:26:19,580 is entangled state. 346 00:26:19,580 --> 00:26:22,710 If you write it in terms of the Hilbert space over the left 347 00:26:22,710 --> 00:26:24,170 and the right patch. 348 00:26:24,170 --> 00:26:25,930 This is a mathematical fact. 349 00:26:25,930 --> 00:26:29,260 This is not a mathematical trick. 350 00:26:29,260 --> 00:26:31,860 AUDIENCE: Well in the sense that I'm perfectly also allowed, 351 00:26:31,860 --> 00:26:34,174 I can create something which, in my patch, 352 00:26:34,174 --> 00:26:35,882 gives me the same description-- if I just 353 00:26:35,882 --> 00:26:37,480 think of a perfectly thermal state, 354 00:26:37,480 --> 00:26:38,660 and I don't even have to think about that being 355 00:26:38,660 --> 00:26:40,070 en entangled with anything. 356 00:26:40,070 --> 00:26:41,810 Is that also OK? 357 00:26:41,810 --> 00:26:43,690 HONG LIU: Oh, sure. 358 00:26:43,690 --> 00:26:48,360 Yeah, but I'm just telling you-- if you 359 00:26:48,360 --> 00:26:50,920 are observer in the right patch, of course 360 00:26:50,920 --> 00:26:53,920 you will never see anything on the left patch. 361 00:26:53,920 --> 00:26:56,220 I'm just giving you a physical explanation. 362 00:26:56,220 --> 00:26:57,732 Where does that physically-- where 363 00:26:57,732 --> 00:26:59,440 does that thermal [? nature ?] come from? 364 00:26:59,440 --> 00:27:00,272 AUDIENCE: Sure, OK. 365 00:27:00,272 --> 00:27:00,690 Yeah. 366 00:27:00,690 --> 00:27:01,940 I just wanted to clarify that. 367 00:27:03,955 --> 00:27:05,580 AUDIENCE: Is this Minkowski [INAUDIBLE] 368 00:27:05,580 --> 00:27:08,520 defined in the upper patch? 369 00:27:08,520 --> 00:27:09,830 HONG LIU: Sorry? 370 00:27:09,830 --> 00:27:10,860 Yeah. 371 00:27:10,860 --> 00:27:14,766 So you're talking about this upper patch? 372 00:27:14,766 --> 00:27:16,550 AUDIENCE: Yeah. 373 00:27:16,550 --> 00:27:20,670 HONG LIU: So the stories are [? falling. ?] In the standard 374 00:27:20,670 --> 00:27:23,500 [? QFT, ?] in the Minkowski spacetime, 375 00:27:23,500 --> 00:27:28,080 you define whatever your states at [INAUDIBLE] equal to 0, 376 00:27:28,080 --> 00:27:30,410 then you move this time. 377 00:27:30,410 --> 00:27:34,400 Then, of course, that will include this part. 378 00:27:34,400 --> 00:27:37,080 And then the standard Minkowski time evolution, 379 00:27:37,080 --> 00:27:40,800 in terms of capital T, will include this part. 380 00:27:40,800 --> 00:27:44,430 But if you do the Rindler time evolution, 381 00:27:44,430 --> 00:27:47,580 then you will not involve that part. 382 00:27:47,580 --> 00:27:48,080 Yeah. 383 00:27:48,080 --> 00:27:48,850 Is that what you are asking? 384 00:27:48,850 --> 00:27:50,891 AUDIENCE: So it's not defined in the upper patch? 385 00:27:50,891 --> 00:27:51,638 HONG LIU: Hmm? 386 00:27:51,638 --> 00:27:53,659 AUDIENCE: So it's not defined in upper patch? 387 00:27:53,659 --> 00:27:54,200 HONG LIU: No. 388 00:27:54,200 --> 00:27:58,910 It's not-- it just does not access those informations, 389 00:27:58,910 --> 00:28:03,550 because the time translation is always like this. 390 00:28:03,550 --> 00:28:05,570 The time translation will always-- 391 00:28:05,570 --> 00:28:09,040 will never take you there. 392 00:28:09,040 --> 00:28:13,460 You have to ask, what is your time translation? 393 00:28:13,460 --> 00:28:18,550 So in quantum mechanics, you define an initial state 394 00:28:18,550 --> 00:28:20,860 and then you have a [? tone ?] intake 395 00:28:20,860 --> 00:28:24,200 you wove into future time. 396 00:28:24,200 --> 00:28:28,700 And in-- then, depend on which time 397 00:28:28,700 --> 00:28:33,260 you use, then cover different regions of the Minkowski 398 00:28:33,260 --> 00:28:34,640 spacetime. 399 00:28:34,640 --> 00:28:36,830 If you use the standard Minkowski time, 400 00:28:36,830 --> 00:28:39,460 capital T, then that will cover everything. 401 00:28:39,460 --> 00:28:42,340 If you only use the Rindler time, 402 00:28:42,340 --> 00:28:45,200 then that only covers this region or this region. 403 00:28:51,312 --> 00:28:52,145 Any other questions? 404 00:28:56,701 --> 00:28:57,200 Good. 405 00:28:59,930 --> 00:29:00,700 The fourth remark. 406 00:29:06,480 --> 00:29:09,740 So now, let me call this-- so this is r and l and then 407 00:29:09,740 --> 00:29:11,176 this f. 408 00:29:11,176 --> 00:29:12,710 OK? 409 00:29:12,710 --> 00:29:15,910 So let me call this region f. 410 00:29:15,910 --> 00:29:22,840 So this story, experienced perfectly in this Schwarzschild 411 00:29:22,840 --> 00:29:28,750 spacetime, why an observer in infinity 412 00:29:28,750 --> 00:29:33,905 will see, say, thermal radiation. 413 00:29:36,600 --> 00:29:38,440 But actually, this does not apply 414 00:29:38,440 --> 00:29:46,340 to the real-life black holes, because the black hole formed 415 00:29:46,340 --> 00:30:04,074 by gravitational collapse only have the right 416 00:30:04,074 --> 00:30:04,990 and the future region. 417 00:30:08,650 --> 00:30:12,290 You don't have the left region. 418 00:30:12,290 --> 00:30:14,710 You don't have the left region. 419 00:30:14,710 --> 00:30:15,210 OK? 420 00:30:22,230 --> 00:30:24,730 So this discussion does not apply. 421 00:30:24,730 --> 00:30:26,320 OK? 422 00:30:26,320 --> 00:30:29,510 This discussion does not apply. 423 00:30:29,510 --> 00:30:33,700 But this is only one of the ways to derive that the black hole 424 00:30:33,700 --> 00:30:35,620 have a finite temperature. 425 00:30:35,620 --> 00:30:38,280 In fact, the Hawkings original derivation, 426 00:30:38,280 --> 00:30:42,510 just by considering scalar field, 427 00:30:42,510 --> 00:30:45,720 just by considering quantizing scalar field alone, 428 00:30:45,720 --> 00:30:47,970 in the right patch, and he already 429 00:30:47,970 --> 00:30:53,112 did deduce the thermal nature. 430 00:30:53,112 --> 00:30:54,820 So even though this particular discussion 431 00:30:54,820 --> 00:31:01,140 does not apply, all our conclusion, 432 00:31:01,140 --> 00:31:03,380 all our conclusion does apply. 433 00:31:03,380 --> 00:31:03,880 OK? 434 00:31:07,640 --> 00:31:09,830 Our conclusion does apply, including 435 00:31:09,830 --> 00:31:12,020 the finite temperature, et cetera. 436 00:31:15,620 --> 00:31:16,120 OK? 437 00:31:18,640 --> 00:31:24,747 So now, to interpret, where does this temperature come from? 438 00:31:24,747 --> 00:31:27,080 And later we will say, actually, the black hole not only 439 00:31:27,080 --> 00:31:31,330 have a temperature, it can satisfy all the thermodynamics. 440 00:31:31,330 --> 00:31:33,250 So in this case, to interpret where 441 00:31:33,250 --> 00:31:37,390 this temperature come from is physically more intricate. 442 00:31:37,390 --> 00:31:37,890 OK? 443 00:31:37,890 --> 00:31:40,030 So I will not try to do it now. 444 00:31:40,030 --> 00:31:44,950 But later, when we talk about the duality, and then 445 00:31:44,950 --> 00:31:48,270 that will be a better place to go back to this question. 446 00:31:48,270 --> 00:31:51,830 And then we can ask the precise difference between these two 447 00:31:51,830 --> 00:31:52,330 cases. 448 00:31:52,330 --> 00:31:57,370 Between the case which you have all patches, 449 00:31:57,370 --> 00:31:59,290 and the case which you only have two 450 00:31:59,290 --> 00:32:01,400 pat-- only have two regions. 451 00:32:01,400 --> 00:32:04,870 And that they are, actually, physically fundamentally 452 00:32:04,870 --> 00:32:06,230 different. 453 00:32:06,230 --> 00:32:08,380 Physically fundamentally different. 454 00:32:08,380 --> 00:32:11,960 But the reason those conclusion applies 455 00:32:11,960 --> 00:32:15,510 is because the temperature, in fact, 456 00:32:15,510 --> 00:32:18,570 is a state that can be made by the local observer. 457 00:32:18,570 --> 00:32:22,070 For local observer, outside the horizon, 458 00:32:22,070 --> 00:32:25,890 he's not going to tell the difference between this metric 459 00:32:25,890 --> 00:32:30,090 and the exac-- and the almost identical metric 460 00:32:30,090 --> 00:32:30,990 in outside horizon. 461 00:32:30,990 --> 00:32:32,830 Outside the horizon, Schwarzschild metric 462 00:32:32,830 --> 00:32:34,547 is a perfect one. 463 00:32:34,547 --> 00:32:36,380 So locally, he will not tell any difference. 464 00:32:36,380 --> 00:32:38,820 So that's why the local observer should always 465 00:32:38,820 --> 00:32:40,170 see the temperature. 466 00:32:40,170 --> 00:32:44,400 If you see it in one case, you will see it in the other case. 467 00:32:44,400 --> 00:32:45,770 OK? 468 00:32:45,770 --> 00:32:48,791 But the underlying physics will turn out to be very different. 469 00:32:48,791 --> 00:32:49,290 Yes? 470 00:32:49,290 --> 00:32:51,882 AUDIENCE: How are we defining temperature here? 471 00:32:51,882 --> 00:32:54,875 Are we defining it by means of energy, like we do [INAUDIBLE]? 472 00:32:54,875 --> 00:32:55,500 HONG LIU: Yeah. 473 00:32:55,500 --> 00:32:55,860 Yeah. 474 00:32:55,860 --> 00:32:56,360 Yeah. 475 00:32:56,360 --> 00:33:00,147 Yeah, here, we define it in terms of the density matrix. 476 00:33:00,147 --> 00:33:01,980 AUDIENCE: Oh, it's defined by that equation? 477 00:33:01,980 --> 00:33:02,646 HONG LIU: Right. 478 00:33:02,646 --> 00:33:03,420 Yeah. 479 00:33:03,420 --> 00:33:08,500 So the density matrix-- so if you have a density matrix like 480 00:33:08,500 --> 00:33:16,600 this, which z is traced explain [? to ?] [? matters ?] beta h, 481 00:33:16,600 --> 00:33:19,740 then you say the temperature is one over beta. 482 00:33:19,740 --> 00:33:21,460 So that's how we define temperature 483 00:33:21,460 --> 00:33:23,710 in quantum statistical physics. 484 00:33:23,710 --> 00:33:24,210 Yeah. 485 00:33:24,210 --> 00:33:24,550 Yeah. 486 00:33:24,550 --> 00:33:25,110 Yeah. 487 00:33:25,110 --> 00:33:28,370 So this defines a canonical example for you. 488 00:33:28,370 --> 00:33:31,397 And this beta is the temperature, the [INAUDIBLE] 489 00:33:31,397 --> 00:33:31,897 temperature. 490 00:33:35,240 --> 00:33:35,910 OK. 491 00:33:35,910 --> 00:33:36,995 So any questions on this? 492 00:33:39,740 --> 00:33:43,590 I hope not, because I want to discuss this later, not now. 493 00:33:48,367 --> 00:33:48,950 AUDIENCE: Sir? 494 00:33:48,950 --> 00:33:50,100 HONG LIU: Yes? 495 00:33:50,100 --> 00:33:54,944 AUDIENCE: If we hold up a thermometer like this, 496 00:33:54,944 --> 00:33:57,510 should we get some different temperature 497 00:33:57,510 --> 00:33:59,810 than if we let it fall? 498 00:33:59,810 --> 00:34:02,430 It's accelerated right now. 499 00:34:02,430 --> 00:34:04,520 Can this has been measured? 500 00:34:04,520 --> 00:34:06,590 HONG LIU: No. 501 00:34:06,590 --> 00:34:08,929 Because it's too low, the temperature. 502 00:34:08,929 --> 00:34:10,310 Right. 503 00:34:10,310 --> 00:34:12,122 Yeah. 504 00:34:12,122 --> 00:34:13,580 Yeah, because our temperature would 505 00:34:13,580 --> 00:34:16,699 be much bigger than this temperature 506 00:34:16,699 --> 00:34:18,530 you are able to-- yeah. 507 00:34:18,530 --> 00:34:23,880 Just the fluctuation of air in this room 508 00:34:23,880 --> 00:34:27,019 will create fluctuations in temperature which much higher 509 00:34:27,019 --> 00:34:28,269 than that kind of temperature. 510 00:34:28,269 --> 00:34:30,519 AUDIENCE: In space, can be a vacuum. 511 00:34:30,519 --> 00:34:32,060 HONG LIU: In the space, you also have 512 00:34:32,060 --> 00:34:34,179 to do very precise measurement. 513 00:34:34,179 --> 00:34:37,060 It's-- yeah, you have to calculate it. 514 00:34:37,060 --> 00:34:39,870 h bar is very small. 515 00:34:39,870 --> 00:34:42,929 AUDIENCE: Divide by the mass. 516 00:34:42,929 --> 00:34:44,440 HONG LIU: Yes? 517 00:34:44,440 --> 00:34:47,400 AUDIENCE: To-- constructing on that same question. 518 00:34:47,400 --> 00:34:51,040 So the same thermometer that is being held in position. 519 00:34:51,040 --> 00:34:54,370 So if I observe it while sitting down here, 520 00:34:54,370 --> 00:34:58,950 so I'm accelerating with it, I'm like the Rindler observer, 521 00:34:58,950 --> 00:35:01,502 and I would see it at a certain temperature, right? 522 00:35:01,502 --> 00:35:03,335 Although it's very small, so we haven't been 523 00:35:03,335 --> 00:35:04,830 able to measure everything. 524 00:35:04,830 --> 00:35:07,010 But if I am, instead, free-falling 525 00:35:07,010 --> 00:35:09,890 while the thermometer is being held in place, 526 00:35:09,890 --> 00:35:13,504 would I then not see-- would I then not measure a temperature? 527 00:35:13,504 --> 00:35:14,670 Would I measure temperature? 528 00:35:14,670 --> 00:35:15,030 HONG LIU: Yeah. 529 00:35:15,030 --> 00:35:15,529 Yeah. 530 00:35:15,529 --> 00:35:17,340 You wouldn't be able to see a temperature. 531 00:35:17,340 --> 00:35:17,840 Yeah. 532 00:35:17,840 --> 00:35:18,842 Free-falling. 533 00:35:18,842 --> 00:35:19,675 Although won't see-- 534 00:35:19,675 --> 00:35:21,216 AUDIENCE: So the thermometer is being 535 00:35:21,216 --> 00:35:22,989 held-- so the thermometer is accelerating? 536 00:35:22,989 --> 00:35:23,530 HONG LIU: No. 537 00:35:23,530 --> 00:35:25,732 Thermometer is also free-falling. 538 00:35:25,732 --> 00:35:27,940 No, if you free-fall, the thermometer also free-fall. 539 00:35:27,940 --> 00:35:30,106 AUDIENCE: No, no, I mean-- he holds the thermometer, 540 00:35:30,106 --> 00:35:32,753 and he is sitting in his chair, but I'm 541 00:35:32,753 --> 00:35:36,484 the one who measures the reading on the thermometer, 542 00:35:36,484 --> 00:35:37,448 and I'm free-falling. 543 00:35:40,830 --> 00:35:43,960 HONG LIU: Yeah, that's an intricate experiment. 544 00:35:43,960 --> 00:35:47,500 Then we have to analyze that. 545 00:35:47,500 --> 00:35:50,310 So the photon from his thermometer 546 00:35:50,310 --> 00:35:54,250 then will somehow go into your eyes, and you will analyze it. 547 00:35:54,250 --> 00:35:57,080 Then whatever is the reading on his thermometer, 548 00:35:57,080 --> 00:35:58,450 you will see it. 549 00:35:58,450 --> 00:36:00,459 Yeah. 550 00:36:00,459 --> 00:36:02,000 No, you're not doing any measurement. 551 00:36:02,000 --> 00:36:03,805 You just see the reading on his thermometer. 552 00:36:03,805 --> 00:36:05,346 If his thermometer has a temperature, 553 00:36:05,346 --> 00:36:06,706 then you will see a temperature. 554 00:36:06,706 --> 00:36:08,956 AUDIENCE: Right. 555 00:36:08,956 --> 00:36:11,330 HONG LIU: Yeah, you are not doing a measurement yourself. 556 00:36:11,330 --> 00:36:12,050 AUDIENCE: So, OK. 557 00:36:12,050 --> 00:36:15,360 So now, bringing it back to non-gravitational physics, 558 00:36:15,360 --> 00:36:16,940 flat spacetime. 559 00:36:16,940 --> 00:36:19,650 I'm a [? neutral ?] observer, and I see a thermometer 560 00:36:19,650 --> 00:36:21,030 accelerating by me. 561 00:36:21,030 --> 00:36:26,350 I would therefore see it as reading a certain temperature? 562 00:36:26,350 --> 00:36:29,592 The thermometer itself isn't a measurement. 563 00:36:29,592 --> 00:36:31,550 You need to have something to measure yourself. 564 00:36:31,550 --> 00:36:33,990 HONG LIU: Yeah, it's not [INAUDIBLE]. 565 00:36:33,990 --> 00:36:34,800 AUDIENCE: Sorry? 566 00:36:34,800 --> 00:36:35,530 HONG LIU: No. 567 00:36:35,530 --> 00:36:38,000 No, the thermometer-- whatever thermometer 568 00:36:38,000 --> 00:36:44,090 is doing, what you are doing-- you just read the thermometer. 569 00:36:44,090 --> 00:36:47,320 And it has nothing to do whether the thermometer has 570 00:36:47,320 --> 00:36:48,040 a temperature. 571 00:36:48,040 --> 00:36:49,350 Thermometer maybe have a temperature 572 00:36:49,350 --> 00:36:50,391 due to some other reason. 573 00:36:50,391 --> 00:36:52,085 Whether you have-- what you could do 574 00:36:52,085 --> 00:36:54,770 is just read that thing. 575 00:36:54,770 --> 00:36:55,270 Yeah. 576 00:36:59,160 --> 00:37:00,490 HONG LIU: OK. 577 00:37:00,490 --> 00:37:01,935 So let me continue. 578 00:37:24,060 --> 00:37:25,361 OK. 579 00:37:25,361 --> 00:37:27,360 So now, we found a black hole has a temperature. 580 00:37:30,580 --> 00:37:37,240 So then, you only need to take a very small leap of faith. 581 00:37:37,240 --> 00:37:41,190 Saying, if this guy has a temperature, 582 00:37:41,190 --> 00:37:43,350 then it should satisfy thermodynamics. 583 00:37:43,350 --> 00:37:45,100 OK? 584 00:37:45,100 --> 00:37:52,040 Then we say, this must obey thermodynamics. 585 00:38:01,130 --> 00:38:01,787 OK? 586 00:38:01,787 --> 00:38:02,870 Also obeys thermodynamics. 587 00:38:02,870 --> 00:38:03,369 Black hole. 588 00:38:08,277 --> 00:38:09,860 And then, you immediately deduce there 589 00:38:09,860 --> 00:38:13,740 should be entropy, because now you 590 00:38:13,740 --> 00:38:16,550 can just apply the first law. 591 00:38:16,550 --> 00:38:21,580 For example, we have the thermodynamical relation dSdE 592 00:38:21,580 --> 00:38:24,220 should be 1 over t. 593 00:38:24,220 --> 00:38:25,180 OK? 594 00:38:25,180 --> 00:38:28,604 Say, if we think of t as a function of e, 595 00:38:28,604 --> 00:38:30,020 then by integrating this equation, 596 00:38:30,020 --> 00:38:35,190 we should deduce what is the entropy of the black hole. 597 00:38:35,190 --> 00:38:40,920 So remember the t of the black hole is 1 over-- remember, 598 00:38:40,920 --> 00:38:46,780 the t of the black hole, the t of the black hole. 599 00:38:46,780 --> 00:38:49,550 Yeah, let me do it here. 600 00:38:49,550 --> 00:38:53,380 t b h of the black hole is h bar kappa 601 00:38:53,380 --> 00:39:00,155 divided by 2 pi, which is the h bar divided by 8 pi g n times 602 00:39:00,155 --> 00:39:00,655 m. 603 00:39:03,540 --> 00:39:12,380 So this would be just 8 pi g n times m h bar. 604 00:39:12,380 --> 00:39:14,970 Of course, you identify the mass of the black hole 605 00:39:14,970 --> 00:39:20,430 with its [? image. ?] So you identify them. 606 00:39:20,430 --> 00:39:23,890 So now, you can just integrate this. 607 00:39:23,890 --> 00:39:27,840 You can just now become a trivial exercise. 608 00:39:27,840 --> 00:39:33,870 Then you find s e is equal to 4 pi 609 00:39:33,870 --> 00:39:38,470 g n e square divided by h bar. 610 00:39:38,470 --> 00:39:42,240 And the plus integration constant. 611 00:39:42,240 --> 00:39:44,740 OK? 612 00:39:44,740 --> 00:39:47,140 And this integration constant we can 613 00:39:47,140 --> 00:39:50,830 say to be zero, because if the black hole have 614 00:39:50,830 --> 00:39:53,600 zero mass, of course there's nothing there. 615 00:39:53,600 --> 00:40:00,370 And so then, we just have this formula. 616 00:40:00,370 --> 00:40:03,480 So this formula can be written a little bit more geometrically. 617 00:40:03,480 --> 00:40:08,330 So also remember, the black hole-- the Schwarzschild radius 618 00:40:08,330 --> 00:40:11,255 is 2 g n m. 619 00:40:11,255 --> 00:40:13,030 OK? 620 00:40:13,030 --> 00:40:17,130 So this can be written a little bit in the geometric way. 621 00:40:17,130 --> 00:40:24,630 So this can be written in terms of s 4 pi r s square divided 622 00:40:24,630 --> 00:40:28,160 by 4 h bar g n. 623 00:40:28,160 --> 00:40:28,660 OK? 624 00:40:28,660 --> 00:40:32,410 Now g n goes to the downstairs, because the r s 625 00:40:32,410 --> 00:40:34,680 contain two powers of g n. 626 00:40:34,680 --> 00:40:41,110 So this is given by the horizon area of the black hole, divided 627 00:40:41,110 --> 00:40:44,390 by 4 h bar g n. 628 00:40:44,390 --> 00:40:44,890 OK? 629 00:40:47,510 --> 00:40:52,990 So now we conclude-- we conclude just 630 00:40:52,990 --> 00:40:56,660 a bit-- let's connect these two formulas together. 631 00:40:56,660 --> 00:40:58,200 The temperature of the black hole 632 00:40:58,200 --> 00:41:02,740 is h bar times the surface gravity divided by 2 pi. 633 00:41:02,740 --> 00:41:08,580 And the entropy of a black hole is the area of the black hole, 634 00:41:08,580 --> 00:41:13,700 area of the horizon of the black hole, divided by 4 h bar g m. 635 00:41:13,700 --> 00:41:15,670 So as I said before, for the black hole, 636 00:41:15,670 --> 00:41:19,930 there are two very important geometric quantities. 637 00:41:19,930 --> 00:41:22,730 One is kappa, surface gravity. 638 00:41:22,730 --> 00:41:24,790 The other is the horizon area. 639 00:41:24,790 --> 00:41:28,970 And then they enter in a very-- in a nice and simple way, 640 00:41:28,970 --> 00:41:31,880 into the temperature and the horizon-- 641 00:41:31,880 --> 00:41:34,930 the entropy of a black hole. 642 00:41:34,930 --> 00:41:36,410 And let me call this equation one. 643 00:41:36,410 --> 00:41:37,740 This is an important equation. 644 00:41:45,320 --> 00:41:49,410 So let me just note one thing. 645 00:41:49,410 --> 00:41:51,840 This temperature is rather funny, 646 00:41:51,840 --> 00:41:56,140 if you look at that formula, because the mass is 647 00:41:56,140 --> 00:41:58,800 in the downstairs. 648 00:41:58,800 --> 00:42:02,240 Say, if you increase the mass, then the temperature actually 649 00:42:02,240 --> 00:42:03,730 decrease. 650 00:42:03,730 --> 00:42:07,670 This is actually opposite to your everyday experience. 651 00:42:07,670 --> 00:42:08,700 OK? 652 00:42:08,700 --> 00:42:10,880 Because when we increase the mass, 653 00:42:10,880 --> 00:42:14,410 the black hole temperature decreases. 654 00:42:14,410 --> 00:42:14,910 OK? 655 00:42:19,680 --> 00:42:26,030 If you calculate the, say, specific heat, 656 00:42:26,030 --> 00:42:29,950 the specific heat is smaller than zero. 657 00:42:29,950 --> 00:42:31,240 OK. 658 00:42:31,240 --> 00:42:34,845 So we will later see this is actually 659 00:42:34,845 --> 00:42:39,820 an artifact of a black hole in asymptotically flat spacetime. 660 00:42:39,820 --> 00:42:42,660 So here, we're considering black holes in asymptotically flat 661 00:42:42,660 --> 00:42:44,230 spacetime. 662 00:42:44,230 --> 00:42:46,590 If you think about black holes, say, in the spacetime 663 00:42:46,590 --> 00:42:50,390 like [INAUDIBLE] space, and then actually, the temperature 664 00:42:50,390 --> 00:42:51,865 will go up with the mass. 665 00:42:54,400 --> 00:42:55,710 As in the ordinary story. 666 00:42:55,710 --> 00:42:56,300 OK? 667 00:42:56,300 --> 00:42:59,810 So this is just the third remark. 668 00:42:59,810 --> 00:43:05,460 So another third remark is that this equation, these equations 669 00:43:05,460 --> 00:43:07,940 tend not to be universal. 670 00:43:07,940 --> 00:43:13,650 So we derive it to the simplest Schwarzschild black hole, 671 00:43:13,650 --> 00:43:18,360 but actually, those relations apply to all black holes 672 00:43:18,360 --> 00:43:20,180 have been discovered. 673 00:43:20,180 --> 00:43:22,290 Just apply to every black hole. 674 00:43:22,290 --> 00:43:24,040 OK? 675 00:43:24,040 --> 00:43:27,130 So now let me talk about general black holes. 676 00:43:42,130 --> 00:43:45,750 So we are mostly just making some statements. 677 00:43:45,750 --> 00:43:47,520 Because most of the statement I make here, 678 00:43:47,520 --> 00:43:49,620 they are highly nontrivial. 679 00:43:49,620 --> 00:43:51,550 And each statement may take one lecture 680 00:43:51,550 --> 00:43:55,460 to prove, or even more, so I will not really prove them. 681 00:43:55,460 --> 00:43:57,640 I just [? coat ?] them. 682 00:43:57,640 --> 00:44:00,210 And I can also not prove it on the spot. 683 00:44:04,700 --> 00:44:08,710 So first is something called the no-hair theorem. 684 00:44:16,310 --> 00:44:24,340 So no-hair theorem says that stationary-- stationary's 685 00:44:24,340 --> 00:44:33,640 a key word-- and asymptotically flat-- this is also 686 00:44:33,640 --> 00:44:52,480 a key word-- black hole is fully characterized 687 00:44:52,480 --> 00:44:56,725 by the first, mass. 688 00:45:00,530 --> 00:45:02,430 Second, angular momentum. 689 00:45:11,560 --> 00:45:20,010 Third, conserved gauge charges. 690 00:45:24,820 --> 00:45:25,320 OK? 691 00:45:31,689 --> 00:45:34,230 So the Schwarzschild black hole we talked about corresponding 692 00:45:34,230 --> 00:45:37,850 to a special case, which angular momentum is zero, 693 00:45:37,850 --> 00:45:40,546 and the conserved charge-- yeah, conserved charge-- 694 00:45:40,546 --> 00:45:41,920 for example, the electric charge. 695 00:45:49,200 --> 00:45:50,977 For example, electric charge. 696 00:45:50,977 --> 00:45:52,470 OK? 697 00:45:52,470 --> 00:45:55,500 And so-- yeah, so let me just give 698 00:45:55,500 --> 00:46:00,310 some-- so typically we denote mass by m, 699 00:46:00,310 --> 00:46:04,754 and angular momentum by j, and the electric charge by q. 700 00:46:04,754 --> 00:46:06,420 So the Schwarzschild black hole goes one 701 00:46:06,420 --> 00:46:09,870 into the j equal to zero, and the q equal to zero, 702 00:46:09,870 --> 00:46:14,082 but more general black holes you can have both j and the q. 703 00:46:17,180 --> 00:46:21,240 So for our-- in string theory, there 704 00:46:21,240 --> 00:46:23,535 can be many, many different gauge fields. 705 00:46:23,535 --> 00:46:25,260 So in string theory, actually there 706 00:46:25,260 --> 00:46:26,935 are many, many different charges. 707 00:46:26,935 --> 00:46:28,310 So black holes, in string theory, 708 00:46:28,310 --> 00:46:32,660 can have many, many more charges than, say, just 709 00:46:32,660 --> 00:46:34,586 in the standard model. 710 00:46:34,586 --> 00:46:35,710 Just in the standard model. 711 00:46:37,960 --> 00:46:38,460 Yeah. 712 00:46:38,460 --> 00:46:43,410 Just for all those black holes, this equation one still holds. 713 00:46:43,410 --> 00:46:46,060 OK? 714 00:46:46,060 --> 00:46:46,930 Yes? 715 00:46:46,930 --> 00:46:49,520 AUDIENCE: So in proving this theorem, 716 00:46:49,520 --> 00:46:52,610 we're going to kind of start off with a certain definition 717 00:46:52,610 --> 00:46:55,880 of what is a black hole and what isn't a black hole. 718 00:46:55,880 --> 00:46:58,550 So what is the key feature that defines it? 719 00:46:58,550 --> 00:47:00,150 Because there's lots of metrics. 720 00:47:00,150 --> 00:47:02,020 And some of them are characterized 721 00:47:02,020 --> 00:47:05,380 by only these three things, and some are not, and-- 722 00:47:05,380 --> 00:47:07,810 HONG LIU: You must have an event horizon. 723 00:47:07,810 --> 00:47:09,750 AUDIENCE: Just the presence of some horizon? 724 00:47:09,750 --> 00:47:10,080 HONG LIU: Yeah. 725 00:47:10,080 --> 00:47:10,805 So event horizon. 726 00:47:10,805 --> 00:47:11,979 Yeah. 727 00:47:11,979 --> 00:47:12,520 AUDIENCE: OK. 728 00:47:12,520 --> 00:47:14,733 But in Rindler we have an event horizon. 729 00:47:14,733 --> 00:47:15,316 HONG LIU: Hmm? 730 00:47:15,316 --> 00:47:17,482 AUDIENCE: In Rindler we have an event horizon that's 731 00:47:17,482 --> 00:47:18,974 not a black hole [INAUDIBLE]. 732 00:47:18,974 --> 00:47:19,890 HONG LIU: That's true. 733 00:47:22,412 --> 00:47:23,980 You should at least have object. 734 00:47:27,100 --> 00:47:29,340 You should have some mass. 735 00:47:29,340 --> 00:47:30,840 You should have some quantum number. 736 00:47:30,840 --> 00:47:32,580 AUDIENCE: I could be accelerating next 737 00:47:32,580 --> 00:47:34,210 to the [INAUDIBLE]. 738 00:47:34,210 --> 00:47:37,310 HONG LIU: So, no, no, no, no, no. 739 00:47:37,310 --> 00:47:40,030 Rindler is called observer horizon. 740 00:47:40,030 --> 00:47:42,440 It's observer-dependent horizon. 741 00:47:42,440 --> 00:47:44,030 And in the black hole, it's not. 742 00:47:44,030 --> 00:47:46,404 AUDIENCE: So you cannot go to any frame where there is no 743 00:47:46,404 --> 00:47:46,818 [INAUDIBLE]. 744 00:47:46,818 --> 00:47:47,646 What if you are free-falling? 745 00:47:47,646 --> 00:47:48,100 HONG LIU: Hmm? 746 00:47:48,100 --> 00:47:49,724 AUDIENCE: What if you are free-falling? 747 00:47:49,724 --> 00:47:51,612 HONG LIU: No no no. 748 00:47:51,612 --> 00:47:57,730 Yeah, what I'm just saying that the-- here, here the horizon, 749 00:47:57,730 --> 00:48:01,560 you can-- different observers have different horizons. 750 00:48:01,560 --> 00:48:05,940 AUDIENCE: So you can [INAUDIBLE] the horizon out of the picture? 751 00:48:05,940 --> 00:48:08,600 HONG LIU: So here, the horizon is arbitrary. 752 00:48:08,600 --> 00:48:10,420 It depends on your observer. 753 00:48:10,420 --> 00:48:16,810 Even though I draw here, but-- this does not 754 00:48:16,810 --> 00:48:18,660 have to cross the origin. 755 00:48:18,660 --> 00:48:21,087 This can be anywhere. 756 00:48:21,087 --> 00:48:21,670 It's anywhere. 757 00:48:21,670 --> 00:48:25,654 Just here, there's no [? generating ?] a horizon. 758 00:48:25,654 --> 00:48:27,820 AUDIENCE: But if I'm free-falling into a black hole, 759 00:48:27,820 --> 00:48:29,589 I also don't have a horizon, right? 760 00:48:29,589 --> 00:48:30,130 HONG LIU: No. 761 00:48:30,130 --> 00:48:31,340 AUDIENCE: Because I'm causally connected [INAUDIBLE]. 762 00:48:31,340 --> 00:48:33,460 HONG LIU: That's true, but independent 763 00:48:33,460 --> 00:48:35,760 of that, there's the spacetime structure, 764 00:48:35,760 --> 00:48:37,980 there's a horizon there. 765 00:48:37,980 --> 00:48:40,810 In the spacetime structure of the Minkowski space, 766 00:48:40,810 --> 00:48:42,369 there's no horizon. 767 00:48:42,369 --> 00:48:44,160 In order to talk about [INAUDIBLE] horizon, 768 00:48:44,160 --> 00:48:46,170 you have to talk about specific observer 769 00:48:46,170 --> 00:48:48,035 to have specific motion. 770 00:48:51,110 --> 00:48:55,980 Yeah, I write down the Schwarzschild metric. 771 00:48:55,980 --> 00:48:58,110 And the different [INAUDIBLE] in the way. 772 00:48:58,110 --> 00:49:00,654 There is already an event horizon. 773 00:49:00,654 --> 00:49:02,320 AUDIENCE: How do you write down a metric 774 00:49:02,320 --> 00:49:03,839 in a [INAUDIBLE] invariant way? 775 00:49:03,839 --> 00:49:06,130 HONG LIU: No, I'm just saying the motion of the horizon 776 00:49:06,130 --> 00:49:07,491 is a [INAUDIBLE] variant. 777 00:49:07,491 --> 00:49:08,032 AUDIENCE: OK. 778 00:49:08,032 --> 00:49:08,532 Yeah. 779 00:49:08,532 --> 00:49:11,990 But if I'm in a frame that's free-falling, 780 00:49:11,990 --> 00:49:13,520 then I don't see a horizon, right? 781 00:49:13,520 --> 00:49:16,302 Isn't that [INAUDIBLE] which transported me to a frame 782 00:49:16,302 --> 00:49:19,290 where there is no horizon? 783 00:49:19,290 --> 00:49:21,545 HONG LIU: Maybe let me say this. 784 00:49:21,545 --> 00:49:24,330 If this can make you a little bit happier. 785 00:49:24,330 --> 00:49:27,527 To a [? symptotic ?] observer, there's a horizon. 786 00:49:27,527 --> 00:49:29,610 There's a different [INAUDIBLE] invariant horizon. 787 00:49:29,610 --> 00:49:30,360 AUDIENCE: OK. 788 00:49:30,360 --> 00:49:31,996 HONG LIU: Yeah. 789 00:49:31,996 --> 00:49:33,594 Yeah, yeah. 790 00:49:33,594 --> 00:49:35,760 Yeah, if you don't want to fall into the black hole, 791 00:49:35,760 --> 00:49:37,450 for those people, there's a horizon. 792 00:49:37,450 --> 00:49:41,087 [LAUGHTER] 793 00:49:41,087 --> 00:49:43,670 And the difference from here, if you fall through the horizon, 794 00:49:43,670 --> 00:49:44,336 nothing happens. 795 00:49:46,910 --> 00:49:51,370 So this no-hair theorem is remarkable, 796 00:49:51,370 --> 00:49:58,880 because it says if you have a star which collapsed 797 00:49:58,880 --> 00:50:02,720 to form a black hole, in this process, 798 00:50:02,720 --> 00:50:05,710 all the features of the star were lost. 799 00:50:05,710 --> 00:50:10,150 Because black hole only are characterized by those numbers. 800 00:50:10,150 --> 00:50:10,746 OK? 801 00:50:10,746 --> 00:50:12,370 But star, you can characterize in many, 802 00:50:12,370 --> 00:50:13,700 many other different ways. 803 00:50:13,700 --> 00:50:17,620 But the black hole, essentially, don't have any features. 804 00:50:17,620 --> 00:50:19,080 So this is called no-hair theorem. 805 00:50:21,824 --> 00:50:22,365 All features. 806 00:50:40,600 --> 00:50:41,423 Yes? 807 00:50:41,423 --> 00:50:43,395 AUDIENCE: What if I add something 808 00:50:43,395 --> 00:50:47,339 like [INAUDIBLE] scalar field or other field into that 809 00:50:47,339 --> 00:50:48,325 [INAUDIBLE]. 810 00:50:48,325 --> 00:50:52,270 [INAUDIBLE] theorem? 811 00:50:52,270 --> 00:50:53,880 HONG LIU: Yeah. 812 00:50:53,880 --> 00:50:54,380 Yeah. 813 00:50:54,380 --> 00:50:56,280 The story is a little bit more complicated. 814 00:50:56,280 --> 00:50:59,019 Let's try to not go into that. 815 00:50:59,019 --> 00:51:01,060 There's something called a secondary [INAUDIBLE], 816 00:51:01,060 --> 00:51:02,880 et cetera. 817 00:51:02,880 --> 00:51:04,632 Yeah. 818 00:51:04,632 --> 00:51:06,390 It can. 819 00:51:06,390 --> 00:51:08,990 It can, but this is refers to Einstein. 820 00:51:08,990 --> 00:51:13,770 But if you go to the frame of Einstein plus-- Einstein 821 00:51:13,770 --> 00:51:17,740 plus some meta-field, and then this as a statement is true. 822 00:51:21,970 --> 00:51:22,810 Any other questions? 823 00:51:26,250 --> 00:51:28,470 OK. 824 00:51:28,470 --> 00:51:32,610 So now-- so historically, of course, 825 00:51:32,610 --> 00:51:36,130 people did not discover the temperature first. 826 00:51:38,800 --> 00:51:43,070 So historically, people first have the no-hair theorem. 827 00:51:43,070 --> 00:51:45,900 So it seems like black hole is completely featureless. 828 00:51:45,900 --> 00:51:47,000 OK? 829 00:51:47,000 --> 00:51:52,770 It's a very boring object that don't have any feature. 830 00:51:52,770 --> 00:51:54,910 And then, people discovered the so-called four laws 831 00:51:54,910 --> 00:51:56,170 of black hole mechanics. 832 00:52:01,290 --> 00:52:04,520 For general black holes-- for general stationary black holes, 833 00:52:04,520 --> 00:52:05,020 again. 834 00:52:08,270 --> 00:52:12,115 So the zeroth law-- again, we just [? coat ?] them. 835 00:52:15,480 --> 00:52:16,595 [INAUDIBLE] is gravity. 836 00:52:20,690 --> 00:52:29,050 Kappa is constant over the horizon. 837 00:52:39,390 --> 00:52:45,830 The first law is that if you change 838 00:52:45,830 --> 00:52:48,535 the mass of the black hole a little bit-- OK, 839 00:52:48,535 --> 00:52:51,076 imagine you put something, throw something into a black hole, 840 00:52:51,076 --> 00:52:53,955 you change the mass of the black hole a little bit, 841 00:52:53,955 --> 00:52:55,205 then you find such a relation. 842 00:53:02,130 --> 00:53:10,580 a is the area of the horizon 843 00:53:10,580 --> 00:53:12,050 So J is the angle of momentum. 844 00:53:12,050 --> 00:53:15,955 And omega is the angle of where you can see the horizon. 845 00:53:15,955 --> 00:53:18,080 So if you have angle of momentum on the black hole, 846 00:53:18,080 --> 00:53:18,955 we would be rotating. 847 00:53:20,662 --> 00:53:22,120 So omega is the angle of frequency. 848 00:53:29,630 --> 00:53:34,900 And fie is the electric potential. 849 00:53:34,900 --> 00:53:37,660 So if you have a charge, than the back hole, all 850 00:53:37,660 --> 00:53:40,230 the current electric fields, this 851 00:53:40,230 --> 00:53:44,625 is electric potential at the horizon. 852 00:53:47,410 --> 00:53:50,470 And you always, in this old notation, 853 00:53:50,470 --> 00:53:56,690 you normalize the electric potential to infinity to be 0. 854 00:53:56,690 --> 00:53:58,330 So this is the first law. 855 00:53:58,330 --> 00:54:04,700 It just say if you change mass of a black hole, 856 00:54:04,700 --> 00:54:06,410 and change some angle of momentum 857 00:54:06,410 --> 00:54:09,170 and change some charge then to the first order they 858 00:54:09,170 --> 00:54:12,010 satisfy this relation. 859 00:54:12,010 --> 00:54:13,960 They satisfy this relation. 860 00:54:13,960 --> 00:54:17,770 So this is just purely mechanics, a classical of gr. 861 00:54:17,770 --> 00:54:19,245 This is pure, classical gr. 862 00:54:22,600 --> 00:54:29,170 And then there's a second law, which is also classical gr, 863 00:54:29,170 --> 00:54:34,625 is that horizon area never decreases. 864 00:54:46,380 --> 00:54:55,970 And the third law, says the surface gravity-- 865 00:54:55,970 --> 00:54:59,500 let me just call it kappa. 866 00:54:59,500 --> 00:55:08,840 This kappa surface gravity over black hole cannot be reduced 867 00:55:08,840 --> 00:55:16,410 to 0 in the finite number of steps. 868 00:55:26,924 --> 00:55:29,949 AUDIENCE: What do you mean by number of steps? 869 00:55:29,949 --> 00:55:31,615 HONG LIU: Find the number of procedures. 870 00:55:33,905 --> 00:55:34,530 AUDIENCE: Like? 871 00:55:37,640 --> 00:55:39,570 HONG LIU: Say if each time you throw 872 00:55:39,570 --> 00:55:42,620 a particle to a black hole, this is called a step. 873 00:55:42,620 --> 00:55:43,365 AUDIENCE: Sure. 874 00:55:43,365 --> 00:55:43,865 OK. 875 00:55:43,865 --> 00:55:45,340 Thermometer, like [INAUDIBLE]. 876 00:55:45,340 --> 00:55:46,390 HONG LIU: That's right. 877 00:55:46,390 --> 00:55:47,430 Yeah. 878 00:55:47,430 --> 00:55:48,410 This is called a step. 879 00:55:48,410 --> 00:55:48,620 Yeah. 880 00:55:48,620 --> 00:55:49,120 Right. 881 00:55:52,280 --> 00:55:52,780 OK. 882 00:55:52,780 --> 00:55:56,040 So all of these are classical statement. 883 00:55:56,040 --> 00:55:59,335 And so this tells the second law. 884 00:55:59,335 --> 00:56:01,760 For example, if you throw something to a black hole, 885 00:56:01,760 --> 00:56:03,830 the black area will increase. 886 00:56:03,830 --> 00:56:07,180 So if you collide the two black holes, 887 00:56:07,180 --> 00:56:09,710 and then if you collide two black holes, 888 00:56:09,710 --> 00:56:11,990 they will merge into a bigger black hole. 889 00:56:11,990 --> 00:56:13,830 And this bigger black hole, the area 890 00:56:13,830 --> 00:56:20,850 will be larger than the sum of the area of two black holes-- 891 00:56:20,850 --> 00:56:24,170 than the area of two black holes. 892 00:56:24,170 --> 00:56:26,500 Yeah. 893 00:56:26,500 --> 00:56:35,650 So of course this law just-- these four laws 894 00:56:35,650 --> 00:56:39,320 then become immediately just like the four laws 895 00:56:39,320 --> 00:56:41,470 of thermodynamics. 896 00:56:41,470 --> 00:56:45,280 You make this identification of one. 897 00:56:45,280 --> 00:57:02,980 This identification of one-- so if it's one, 898 00:57:02,980 --> 00:57:07,870 this just becomes the four laws of thermodynamics. 899 00:57:15,520 --> 00:57:16,020 Yeah. 900 00:57:16,020 --> 00:57:16,645 Thermodynamics. 901 00:57:25,380 --> 00:57:27,680 The four laws of thermodynamics. 902 00:57:27,680 --> 00:57:36,790 In particular, the first law, if you substitute the copper and A 903 00:57:36,790 --> 00:57:40,610 by the temperature under the entropy, than this just 904 00:57:40,610 --> 00:57:47,620 becomes the standard, the first law, in particular. 905 00:57:47,620 --> 00:57:58,470 The first law, it's just dm, sdt, tds plus omega 906 00:57:58,470 --> 00:58:02,768 dj plus 5 dq. 907 00:58:02,768 --> 00:58:06,450 So this is really the first law of thermodynamics. 908 00:58:16,000 --> 00:58:20,830 So historically, these four laws of mechanics 909 00:58:20,830 --> 00:58:25,680 actually was discovered before Hawkings radiation. 910 00:58:25,680 --> 00:58:29,640 So first they discovered this black hole law theorem. 911 00:58:29,640 --> 00:58:31,470 And then they discovered these four laws 912 00:58:31,470 --> 00:58:34,160 of black hole mechanics. 913 00:58:34,160 --> 00:58:35,690 Then they say, ah, this is really 914 00:58:35,690 --> 00:58:38,500 look like thermodynamics. 915 00:58:38,500 --> 00:58:40,630 And they even patterned these four laws 916 00:58:40,630 --> 00:58:44,750 to precisely like the four laws of thermodynamics. 917 00:58:44,750 --> 00:58:47,710 But they could not imagine the black hole 918 00:58:47,710 --> 00:58:50,860 was a thermodynamic object. 919 00:58:50,860 --> 00:58:55,400 They could not imagine the black hole was thermodynamic object. 920 00:58:55,400 --> 00:58:58,290 So they were saying, if you look at the old paper-- there 921 00:58:58,290 --> 00:59:02,430 was a very famous paper by Bardeen, Carter, and Hawking, 922 00:59:02,430 --> 00:59:07,120 which discuss these four laws of black hole mechanics. 923 00:59:07,120 --> 00:59:10,820 And they said, this four laws of black hole mechanics 924 00:59:10,820 --> 00:59:14,534 should actually transcend the standard of thermodynamics. 925 00:59:14,534 --> 00:59:16,200 The black hole actually should transcend 926 00:59:16,200 --> 00:59:18,288 all of these, our traditional physics. 927 00:59:22,670 --> 00:59:30,250 But in 1971 or 1972, a young graduate student 928 00:59:30,250 --> 00:59:36,780 called Bekenstein, so he was a graduate student at Princeton. 929 00:59:36,780 --> 00:59:40,270 So he was studying under a guy called 930 00:59:40,270 --> 00:59:44,490 Wheeler, studied under Wheeler. 931 00:59:44,490 --> 00:59:51,070 And so he was very uncomfortable with the fact 932 00:59:51,070 --> 00:59:54,830 that if you throw something into a black hole, 933 00:59:54,830 --> 00:59:57,540 than that thing is gone. 934 00:59:57,540 --> 00:59:59,620 So he was a very uncomfortable with that. 935 00:59:59,620 --> 01:00:02,520 Because if you throw something to a black hole, it's gone, 936 01:00:02,520 --> 01:00:06,920 then he concluded that's really the second law 937 01:00:06,920 --> 01:00:08,780 of thermodynamics. 938 01:00:08,780 --> 01:00:12,530 Because if you throw to a black hole, that thing is gone, 939 01:00:12,530 --> 01:00:14,950 then the entropy associated with that thing is gone. 940 01:00:14,950 --> 01:00:16,533 And the black hole is just black hole, 941 01:00:16,533 --> 01:00:18,270 have this no-hair theorem. 942 01:00:18,270 --> 01:00:21,015 And then you violate the second law of thermodynamics. 943 01:00:24,310 --> 01:00:27,960 People like Wheeler or Hawking, they say, ah, this is great. 944 01:00:27,960 --> 01:00:31,470 Black hole transcend the thermodynamics. 945 01:00:31,470 --> 01:00:33,320 But Bekenstein was uncomfortable. 946 01:00:33,320 --> 01:00:35,600 He thinks thermodynamics should transcend black hole. 947 01:00:39,070 --> 01:00:43,370 And then based on the second law of the black hole, 948 01:00:43,370 --> 01:00:53,760 then he said, so maybe-- so he wrote a series 949 01:00:53,760 --> 01:00:55,560 of papers, a few papers. 950 01:00:55,560 --> 01:00:57,200 I don't remember. 951 01:00:57,200 --> 01:01:01,530 He say, if we think black hole has entropy proportional 952 01:01:01,530 --> 01:01:08,601 to the area, then the second law of thermodynamics can be saved. 953 01:01:08,601 --> 01:01:11,749 Because this area of level decrease, 954 01:01:11,749 --> 01:01:13,540 and if you throw something to a black hole, 955 01:01:13,540 --> 01:01:16,870 even thought that, the entropy associated to that guy's lost. 956 01:01:16,870 --> 01:01:19,010 But that area also increased. 957 01:01:19,010 --> 01:01:20,460 The area also increased. 958 01:01:20,460 --> 01:01:23,090 And then you can say it's the second law of thermodynamics. 959 01:01:23,090 --> 01:01:25,540 Now, he actually proposed to generalize the second law 960 01:01:25,540 --> 01:01:26,290 of thermodynamics. 961 01:01:32,030 --> 01:01:34,370 So he proposed a generalized second law. 962 01:01:34,370 --> 01:01:36,070 He said, you take the total, if you 963 01:01:36,070 --> 01:01:38,190 take the total entropy of the system 964 01:01:38,190 --> 01:01:41,090 to be that of the black hole, and then matter 965 01:01:41,090 --> 01:01:46,440 field outside the black hole, then this ds total 966 01:01:46,440 --> 01:01:48,796 must be non-decreasing. 967 01:01:53,520 --> 01:02:01,860 Of course, now if we accept, if we take this leap of faith 968 01:02:01,860 --> 01:02:05,530 to really think black hole as a sum or object, then of course 969 01:02:05,530 --> 01:02:07,350 this generalized second law has to be 970 01:02:07,350 --> 01:02:09,555 true because the thermodymaics-- some object. 971 01:02:12,190 --> 01:02:14,650 But when Bekenstein proposed it, it 972 01:02:14,650 --> 01:02:23,460 was really bizarre to say in a nice way 973 01:02:23,460 --> 01:02:28,140 because it just sounded crazy, just outright crazy. 974 01:02:28,140 --> 01:02:32,720 Because how can black hole have entropy? 975 01:02:32,720 --> 01:02:34,350 Black hole absorb everything. 976 01:02:34,350 --> 01:02:36,080 Just how can it have entropy? 977 01:02:36,080 --> 01:02:40,510 And it just completely was disregarded by people. 978 01:02:40,510 --> 01:02:42,670 And it was discarded by people. 979 01:02:42,670 --> 01:02:46,610 And anyway, but then now that he was right, 980 01:02:46,610 --> 01:02:49,950 then of course after Hawking's discovery of a Hawking 981 01:02:49,950 --> 01:02:54,050 radiation, they become very natural for the black hole 982 01:02:54,050 --> 01:02:55,880 to have entropy. 983 01:02:55,880 --> 01:03:03,700 And in particular, this formula, after you determine 984 01:03:03,700 --> 01:03:07,140 that the black hold have this temperature, after you 985 01:03:07,140 --> 01:03:10,895 fix this pre-factor, then you can 986 01:03:10,895 --> 01:03:16,320 also, just from the first law, just from here, just from here, 987 01:03:16,320 --> 01:03:19,250 to fix that pre-factor of a black hole. 988 01:03:19,250 --> 01:03:20,800 So Bekenstein could not decide what's 989 01:03:20,800 --> 01:03:24,190 the proportional constant. 990 01:03:24,190 --> 01:03:26,010 But once you get the temperature, 991 01:03:26,010 --> 01:03:27,940 then this proportional constant just uniquely 992 01:03:27,940 --> 01:03:33,820 fixed from this equation, so without using that. 993 01:03:33,820 --> 01:03:36,270 Just using the first law of mechanics, 994 01:03:36,270 --> 01:03:41,090 then you can immediately integrate that as entropy. 995 01:03:41,090 --> 01:03:41,770 Anyway-- 996 01:03:41,770 --> 01:03:43,228 AUDIENCE: How did Bekenstein find-- 997 01:03:46,465 --> 01:03:47,590 HONG LIU: It's a postulate. 998 01:03:47,590 --> 01:03:49,470 It's a gas. 999 01:03:49,470 --> 01:03:49,970 Yeah. 1000 01:03:49,970 --> 01:03:53,640 He just postulate, if we imagine-- 1001 01:03:53,640 --> 01:03:56,780 AUDIENCE: He didn't derive it? 1002 01:03:56,780 --> 01:03:59,405 HONG LIU: No there's no way to derive it. 1003 01:03:59,405 --> 01:04:01,880 He was just saying, if you imagine 1004 01:04:01,880 --> 01:04:04,940 black hole has entropy proportion to the area, 1005 01:04:04,940 --> 01:04:07,750 than the second law of thermodynamics can be saved. 1006 01:04:07,750 --> 01:04:10,020 And he wants to save the second law of thermodynamics. 1007 01:04:10,020 --> 01:04:10,757 Yes. 1008 01:04:10,757 --> 01:04:11,840 AUDIENCE: So one question. 1009 01:04:11,840 --> 01:04:13,660 So this makes sense classically. 1010 01:04:13,660 --> 01:04:16,860 If I have a system of entropy, I throw them to a black hole. 1011 01:04:16,860 --> 01:04:17,963 Entropy is like ignorance. 1012 01:04:17,963 --> 01:04:20,140 If I throw ignorance into the black hole, 1013 01:04:20,140 --> 01:04:22,060 maybe there's somehow the black hole 1014 01:04:22,060 --> 01:04:24,032 also becomes more ignorant or something. 1015 01:04:24,032 --> 01:04:26,240 But what does this mean in terms of quantum mechanics 1016 01:04:26,240 --> 01:04:28,360 when I have a pure state? 1017 01:04:28,360 --> 01:04:30,570 From quantum statistical mechanics, 1018 01:04:30,570 --> 01:04:33,520 substance the entropy, you just don't know something 1019 01:04:33,520 --> 01:04:34,440 about your state. 1020 01:04:34,440 --> 01:04:35,860 And it's your fault. And it's not 1021 01:04:35,860 --> 01:04:38,006 like the black hole should car if it's your fault 1022 01:04:38,006 --> 01:04:38,839 or not or something. 1023 01:04:38,839 --> 01:04:41,560 So why does this makes sense quantum mechanically? 1024 01:04:41,560 --> 01:04:43,100 Maybe it doesn't. 1025 01:04:43,100 --> 01:04:46,310 HONG LIU: You mean, why does black law have entropy make 1026 01:04:46,310 --> 01:04:47,617 sense quantum mechanically? 1027 01:04:47,617 --> 01:04:48,200 AUDIENCE: Yes. 1028 01:04:48,200 --> 01:04:55,200 HONG LIU: It's the same thing as-- this room has entropy. 1029 01:04:55,200 --> 01:04:57,710 This room we use quantum statistical physics. 1030 01:04:57,710 --> 01:05:01,530 If you believe black hole is an ordinary object, then-- 1031 01:05:01,530 --> 01:05:03,530 AUDIENCE: We only quantum statistical physics 1032 01:05:03,530 --> 01:05:06,250 because we're ignorant, the full state of-- 1033 01:05:09,050 --> 01:05:09,710 HONG LIU: Yeah. 1034 01:05:09,710 --> 01:05:12,180 For a black hole, we are also ignorant. 1035 01:05:12,180 --> 01:05:12,715 Yeah. 1036 01:05:12,715 --> 01:05:16,351 This is actually something I'm going to talk about now. 1037 01:05:16,351 --> 01:05:17,730 Any other questions? 1038 01:05:17,730 --> 01:05:21,670 AUDIENCE: I have something [INAUDIBLE]. 1039 01:05:21,670 --> 01:05:26,016 So basically, I think it can be [? a healing ?] experiment. 1040 01:05:26,016 --> 01:05:29,408 So where we hear things of [INAUDIBLE]. 1041 01:05:29,408 --> 01:05:33,340 There is one unit of entropy, and it enters black hole. 1042 01:05:33,340 --> 01:05:36,650 It increased the energy of black hole, which 1043 01:05:36,650 --> 01:05:39,040 increased the mass of black hole, which 1044 01:05:39,040 --> 01:05:40,952 increased the [INAUDIBLE] of the black hole. 1045 01:05:40,952 --> 01:05:45,870 So in this way you can actually derive the semi-qualitatively 1046 01:05:45,870 --> 01:05:50,140 derived out of proportionality. 1047 01:05:50,140 --> 01:05:51,290 HONG LIU: Yeah. 1048 01:05:51,290 --> 01:05:54,854 To derive with these precise [? cohortions-- ?] no, 1049 01:05:54,854 --> 01:05:56,770 I don't think they derive the [? cohortion ?], 1050 01:05:56,770 --> 01:05:58,150 but I need to check. 1051 01:05:58,150 --> 01:05:59,950 I don't think there's any way to derive 1052 01:05:59,950 --> 01:06:06,439 the-- you can, say, put some bond on the [? cohortions ?]. 1053 01:06:06,439 --> 01:06:08,230 But you cannot derive the [? cohortions ?]. 1054 01:06:08,230 --> 01:06:10,880 I think that argument would not enable you 1055 01:06:10,880 --> 01:06:12,980 to derive the [? cohortions. ?] 1056 01:06:17,160 --> 01:06:22,880 Anyway, so let me just mention a few more things 1057 01:06:22,880 --> 01:06:24,010 about black hole. 1058 01:06:24,010 --> 01:06:32,660 This is just pure-- actually, I'm running out of time. 1059 01:06:32,660 --> 01:06:46,400 So let me just mention some paradox or paradoxes 1060 01:06:46,400 --> 01:06:47,390 for the black hole. 1061 01:06:50,600 --> 01:06:52,948 So we have shown that the black hole is some object. 1062 01:06:56,230 --> 01:06:59,830 So Jordan just asked. 1063 01:06:59,830 --> 01:07:04,480 But we know the ordinary thermodynamics has 1064 01:07:04,480 --> 01:07:07,790 statistical physics behind it. 1065 01:07:07,790 --> 01:07:09,920 So the immediate question is actually, 1066 01:07:09,920 --> 01:07:17,044 does the black hole entropy, for example, 1067 01:07:17,044 --> 01:07:18,460 have a statistical interpretation? 1068 01:07:31,750 --> 01:07:34,440 So this is one question. 1069 01:07:34,440 --> 01:07:38,970 And another question is that, does black hole actually 1070 01:07:38,970 --> 01:07:40,515 respect quantum mechanics? 1071 01:07:48,540 --> 01:07:52,750 Does black hole respect quantum mechanics? 1072 01:07:52,750 --> 01:07:59,130 So if black hole entropy have a statistical interpretation, 1073 01:07:59,130 --> 01:08:06,447 then this give you a very-- so it black hole 1074 01:08:06,447 --> 01:08:08,030 have a statistical interpretation that 1075 01:08:08,030 --> 01:08:22,370 means-- so A, if affirmative, that 1076 01:08:22,370 --> 01:08:31,569 implies that each black hole, even though black hole 1077 01:08:31,569 --> 01:08:34,670 at a macroscopic level only is characterized by these three 1078 01:08:34,670 --> 01:08:54,685 things, But macroscopically, must have internal states. 1079 01:09:01,910 --> 01:09:12,840 Or, maybe I should call it macrostate of order 1080 01:09:12,840 --> 01:09:19,260 to the entropy, which is the A of the black hole area 1081 01:09:19,260 --> 01:09:19,985 4h bar e. 1082 01:09:29,990 --> 01:09:31,939 So hidden behind this no-hair theorem 1083 01:09:31,939 --> 01:09:33,829 is actually a huge number of macrostates. 1084 01:09:37,330 --> 01:09:41,779 Just like the air in this room, even 1085 01:09:41,779 --> 01:09:44,770 though we describe the unit temperature, pressure, 1086 01:09:44,770 --> 01:09:49,270 and the energy stature, but given that macroscopic data, 1087 01:09:49,270 --> 01:09:53,370 they can be huge number of macro states. 1088 01:09:53,370 --> 01:09:56,960 And then a similar thing should happen to the black hole. 1089 01:09:56,960 --> 01:10:00,800 And in order to see that the black hole does have, 1090 01:10:00,800 --> 01:10:02,770 a statistical interpretation, then you 1091 01:10:02,770 --> 01:10:07,150 have to find so many states for a black hole and in order 1092 01:10:07,150 --> 01:10:16,640 to answer the question A. So this question 1093 01:10:16,640 --> 01:10:20,230 has to be answered in the affirmative 1094 01:10:20,230 --> 01:10:24,100 for many different type of black holes. 1095 01:10:24,100 --> 01:10:27,725 Say in string theory and also [INAUDIBLE] spacetime, 1096 01:10:27,725 --> 01:10:30,330 and they see the spacetime. 1097 01:10:30,330 --> 01:10:34,070 Using string theory method or using this holographic duality, 1098 01:10:34,070 --> 01:10:40,120 we will see examples later. 1099 01:10:40,120 --> 01:10:42,660 We will see examples later. 1100 01:10:42,660 --> 01:10:46,790 So these really confirms that the black hole is really 1101 01:10:46,790 --> 01:10:49,570 a quantum statistical system. 1102 01:10:52,140 --> 01:11:02,360 So regarding this question B, then this long time paradox-- 1103 01:11:02,360 --> 01:11:07,350 so this A has also been a paradox for many years, 1104 01:11:07,350 --> 01:11:18,430 and was only resolved-- the basic calculations were 1105 01:11:18,430 --> 01:11:25,170 able to do only in 1996, when the [INAUDIBLE], 1106 01:11:25,170 --> 01:11:28,040 they did some very special [? Schwarzschild ?] 1107 01:11:28,040 --> 01:11:32,470 black hole, which they counted this exact number of states. 1108 01:11:32,470 --> 01:11:35,760 They counted the exact, this number of states, 1109 01:11:35,760 --> 01:11:40,230 and about for a very specific type of black hole. 1110 01:11:40,230 --> 01:11:54,907 So B is rated to the so-called Hawkins information paradox, 1111 01:11:54,907 --> 01:11:55,948 information loss paradox. 1112 01:11:59,692 --> 01:12:02,100 So I will not have time to go into detail here. 1113 01:12:02,100 --> 01:12:04,620 Let me just give you a very rough version of it. 1114 01:12:08,990 --> 01:12:11,190 So you can see the pure state, could see 1115 01:12:11,190 --> 01:12:17,240 the star, a big star in the pure state. 1116 01:12:17,240 --> 01:12:21,120 So we know from gr that a sufficiently massive star 1117 01:12:21,120 --> 01:12:25,610 will eventually always collapse to form a black hole. 1118 01:12:25,610 --> 01:12:29,900 So if we imagine you have a pure star in the pure state collapse 1119 01:12:29,900 --> 01:12:35,880 to form a black hole, and if quantum mechanics is preserved 1120 01:12:35,880 --> 01:12:39,330 throughout the process, then this black hole 1121 01:12:39,330 --> 01:12:41,360 should also be a pure state. 1122 01:12:41,360 --> 01:12:43,280 So that means the black hole should 1123 01:12:43,280 --> 01:12:49,210 be just one of all those max number of possible states. 1124 01:12:49,210 --> 01:12:51,370 There should be a pure state, but only one 1125 01:12:51,370 --> 01:12:55,080 of those all possible states. 1126 01:12:55,080 --> 01:13:00,780 But then Hawkins had an argument saying this is impossible. 1127 01:13:00,780 --> 01:13:04,840 Because if black hole is a pure state, then when 1128 01:13:04,840 --> 01:13:08,720 black hole evaporates-- so the black hole evaporates, 1129 01:13:08,720 --> 01:13:11,240 eventually the black hole will be gone. 1130 01:13:11,240 --> 01:13:14,200 So the one funny thing about black hole 1131 01:13:14,200 --> 01:13:17,560 is that the temperature is inverse proportionate 1132 01:13:17,560 --> 01:13:19,370 to the mass. 1133 01:13:19,370 --> 01:13:23,630 So when the black hole is big, then the temperature is low, 1134 01:13:23,630 --> 01:13:26,200 then the radiation is small. 1135 01:13:26,200 --> 01:13:28,980 But when you start radiate, then the black hole mass 1136 01:13:28,980 --> 01:13:30,440 will decrease. 1137 01:13:30,440 --> 01:13:33,450 And then the temperature will be higher than we radiate mole. 1138 01:13:33,450 --> 01:13:36,170 So it will be acceleration process. 1139 01:13:36,170 --> 01:13:42,220 And eventually-- presumably black hole will be gone. 1140 01:13:44,990 --> 01:13:47,650 So this kind of semi-classical argument that we are given 1141 01:13:47,650 --> 01:13:49,870 applies only for a massive black hole 1142 01:13:49,870 --> 01:13:54,480 much greater than the planck mass, only much larger 1143 01:13:54,480 --> 01:13:56,380 than a planck mass. 1144 01:13:56,380 --> 01:13:59,020 So below planck mass, what happens? 1145 01:13:59,020 --> 01:14:00,400 Nobody knows. 1146 01:14:00,400 --> 01:14:04,220 But at least this radiation statement 1147 01:14:04,220 --> 01:14:06,390 should be robust for the mass much, much larger 1148 01:14:06,390 --> 01:14:08,500 than the planck mass. 1149 01:14:08,500 --> 01:14:10,770 Now Hawking then say this is a paradox 1150 01:14:10,770 --> 01:14:16,090 because according to his calculation, 1151 01:14:16,090 --> 01:14:18,319 the radiation is simple. 1152 01:14:18,319 --> 01:14:19,860 And we know that the sum of radiation 1153 01:14:19,860 --> 01:14:22,200 does not contain any information. 1154 01:14:22,200 --> 01:14:24,880 It cannot contain information but it's pure state, 1155 01:14:24,880 --> 01:14:29,130 because sum or radiation is information free. 1156 01:14:29,130 --> 01:14:32,110 And so the sum of radiation which come out, 1157 01:14:32,110 --> 01:14:36,862 come out until you reach say the mass of all the planck mass. 1158 01:14:41,110 --> 01:14:45,880 And here we reach the planck mass. 1159 01:14:45,880 --> 01:14:50,770 And then before you reach that mass, because the radiation is 1160 01:14:50,770 --> 01:14:54,240 simple, there can be no information can come out. 1161 01:14:56,960 --> 01:14:59,860 And when you reach that planck mass, 1162 01:14:59,860 --> 01:15:03,430 it just becoming possible for such a huge amount 1163 01:15:03,430 --> 01:15:09,580 of internal state to be encoded in the planck mass object. 1164 01:15:09,580 --> 01:15:13,340 So he concluded that the information must be lost, 1165 01:15:13,340 --> 01:15:17,550 and the black hole must violate mechanics. 1166 01:15:17,550 --> 01:15:21,210 So this is a very heuristic argument. 1167 01:15:21,210 --> 01:15:23,060 But I highly suggest, if you are interested, 1168 01:15:23,060 --> 01:15:27,680 to go read his original paper, which is very beautiful. 1169 01:15:27,680 --> 01:15:30,200 Because he was really trying to think of black hole 1170 01:15:30,200 --> 01:15:33,070 as a ordinary quantum mechanical object. 1171 01:15:33,070 --> 01:15:37,590 And the way he was thinking about it is really very nice. 1172 01:15:37,590 --> 01:15:41,880 And actually, it's not very different 1173 01:15:41,880 --> 01:15:44,010 from we are thinking about black hole 1174 01:15:44,010 --> 01:15:47,414 right now, from the holographic duality. 1175 01:15:47,414 --> 01:15:48,830 He was really thinking that's it's 1176 01:15:48,830 --> 01:15:50,500 a quantum mechanical object. 1177 01:15:50,500 --> 01:15:54,150 But then he reached this paradox. 1178 01:15:54,150 --> 01:15:58,960 Anyway, so this paradox had bothered the people 1179 01:15:58,960 --> 01:16:01,860 for more than 30 years. 1180 01:16:01,860 --> 01:16:05,820 So he discovered the Hawking radiation in 1974. 1181 01:16:05,820 --> 01:16:09,270 I think he proposed this paradox in 1976. 1182 01:16:09,270 --> 01:16:14,500 So for more than 30 years, people 1183 01:16:14,500 --> 01:16:18,680 argue with each other what is going to happen. 1184 01:16:18,680 --> 01:16:22,410 It's typically divided into two camps. 1185 01:16:22,410 --> 01:16:26,040 So the gr people, they think black hole is everything, 1186 01:16:26,040 --> 01:16:28,390 quantum mechanics nothing. 1187 01:16:28,390 --> 01:16:32,060 And the black hole must be able to violate quantum mechanics 1188 01:16:32,060 --> 01:16:38,440 and will bring us to a new frontier we never see before. 1189 01:16:38,440 --> 01:16:40,630 And the particle, these people are saying, 1190 01:16:40,630 --> 01:16:46,020 a black hole-- oh, we can even creating the accelerator-- 1191 01:16:46,020 --> 01:16:51,340 must obey quantum mechanics. 1192 01:16:51,340 --> 01:16:53,890 So people would just argue with each other 1193 01:16:53,890 --> 01:16:57,150 and without really setting the question in a very 1194 01:16:57,150 --> 01:17:00,810 convincing way to either camp. 1195 01:17:00,810 --> 01:17:06,940 But this holographic duality, in the context 1196 01:17:06,940 --> 01:17:09,470 of holographic duality, then the black hole [INAUDIBLE] 1197 01:17:09,470 --> 01:17:13,450 spacetime, then you can actually rephrase 1198 01:17:13,450 --> 01:17:16,290 this question about the black hole information laws. 1199 01:17:16,290 --> 01:17:19,090 And the holographic duality strongly 1200 01:17:19,090 --> 01:17:21,840 suggests-- I think it's maybe not really completely 1201 01:17:21,840 --> 01:17:25,340 proved-- strongly suggests at least that the black hole is 1202 01:17:25,340 --> 01:17:27,460 just a ordinary quantum mechanical object. 1203 01:17:31,500 --> 01:17:35,210 We are not transcend the quantum mechanics. 1204 01:17:35,210 --> 01:17:39,041 We are not transcend the quantum mechanics. 1205 01:17:39,041 --> 01:17:39,540 Yeah. 1206 01:17:39,540 --> 01:17:41,840 I am really out of time. 1207 01:17:41,840 --> 01:17:42,650 Yes? 1208 01:17:42,650 --> 01:17:45,980 AUDIENCE: So you said the star is in a pure state. 1209 01:17:45,980 --> 01:17:49,220 But how can that be, because it has a temperature 1210 01:17:49,220 --> 01:17:50,992 and it's also thermal system? 1211 01:17:50,992 --> 01:17:52,770 So how can you put it in a pure state? 1212 01:17:52,770 --> 01:17:53,311 HONG LIU: No. 1213 01:17:53,311 --> 01:17:56,508 Black hole does not have to be in the thermal state. 1214 01:17:56,508 --> 01:17:57,340 No. 1215 01:17:57,340 --> 01:18:01,710 I can certainly imagine a star, which is in the pure state. 1216 01:18:01,710 --> 01:18:05,350 In real life, maybe it's hard to construct them. 1217 01:18:05,350 --> 01:18:07,286 But on the paper, I can do it. 1218 01:18:07,286 --> 01:18:11,660 [LAUGHTER] 1219 01:18:11,660 --> 01:18:16,700 In principle, so how many atoms in the star? 1220 01:18:16,700 --> 01:18:17,840 I don't know. 1221 01:18:17,840 --> 01:18:18,630 Maybe 10 to 100? 1222 01:18:18,630 --> 01:18:20,880 Now let's imagine there's 10 to the 100 atoms. 1223 01:18:20,880 --> 01:18:23,302 AUDIENCE: But it's radiating all the time though. 1224 01:18:23,302 --> 01:18:25,790 Doesn't it entangle with things and make it not pure? 1225 01:18:25,790 --> 01:18:26,790 HONG LIU: Don't worry. 1226 01:18:26,790 --> 01:18:28,870 Don't worry. 1227 01:18:28,870 --> 01:18:31,280 I can certainly write down a wave function for 10 1228 01:18:31,280 --> 01:18:35,350 to the 100 particles, which is in the pure state. 1229 01:18:35,350 --> 01:18:37,870 And this will be a big object. 1230 01:18:37,870 --> 01:18:40,490 And according to the rule of gr, this thing 1231 01:18:40,490 --> 01:18:42,340 will collapse to form a black hole. 1232 01:18:42,340 --> 01:18:43,596 AUDIENCE: What about the light that it's emitting, 1233 01:18:43,596 --> 01:18:44,310 which it has-- 1234 01:18:44,310 --> 01:18:44,851 HONG LIU: No. 1235 01:18:44,851 --> 01:18:45,570 There's no light. 1236 01:18:45,570 --> 01:18:46,070 No. 1237 01:18:46,070 --> 01:18:48,035 We work with zero temperature, just pure state. 1238 01:18:48,035 --> 01:18:49,600 There's nothing. 1239 01:18:49,600 --> 01:18:50,531 There's nothing. 1240 01:18:50,531 --> 01:18:51,572 AUDIENCE: No temperature? 1241 01:18:51,572 --> 01:18:52,520 Zero temperature? 1242 01:18:52,520 --> 01:18:53,490 HONG LIU: Yeah. 1243 01:18:53,490 --> 01:18:57,400 In principle, I can do that. 1244 01:18:57,400 --> 01:18:59,528 AUDIENCE: In that case, will the black hole 1245 01:18:59,528 --> 01:19:02,455 have the temperature, Hawking temperature? 1246 01:19:02,455 --> 01:19:03,080 HONG LIU: Yeah. 1247 01:19:03,080 --> 01:19:05,100 The black hole will have Hawking temperature. 1248 01:19:05,100 --> 01:19:08,700 AUDIENCE: But it's still in it's first state? 1249 01:19:08,700 --> 01:19:11,360 HONG LIU: The black hole will have a Hawking temperature, 1250 01:19:11,360 --> 01:19:13,600 will have-- similar, have entropy, 1251 01:19:13,600 --> 01:19:15,640 but will be a pure state. 1252 01:19:15,640 --> 01:19:19,960 So this is the essence of the information paradox. 1253 01:19:19,960 --> 01:19:22,240 So this is the essence of the information paradox. 1254 01:19:22,240 --> 01:19:24,420 And then we will be able to explain it, 1255 01:19:24,420 --> 01:19:28,117 why this is so, using the holographic duality. 1256 01:19:28,117 --> 01:19:29,700 AUDIENCE: So as the star collapses, it 1257 01:19:29,700 --> 01:19:31,157 gains a non-zero temperature. 1258 01:19:31,157 --> 01:19:33,740 It starts at zero temperature, and then collapses, and becomes 1259 01:19:33,740 --> 01:19:34,190 [INAUDIBLE]. 1260 01:19:34,190 --> 01:19:34,470 HONG LIU: Yeah. 1261 01:19:34,470 --> 01:19:34,602 It can. 1262 01:19:34,602 --> 01:19:35,420 Yeah. 1263 01:19:35,420 --> 01:19:39,780 It seemingly have a long zero temperature. 1264 01:19:39,780 --> 01:19:41,680 Yeah. 1265 01:19:41,680 --> 01:19:42,180 Yeah. 1266 01:19:42,180 --> 01:19:44,202 Maybe let's stop here.