1 00:00:02,120 --> 00:00:12,080 They did not think it over. So the legal discussion about polls in 1970 and beyond the outlying peaceful 2 00:00:12,110 --> 00:00:17,540 and personal reminders of intensity and vigilante response time by people, 3 00:00:17,540 --> 00:00:21,860 opinions and rhetoric. We'll talk about quantifying this relationship. 4 00:00:22,160 --> 00:00:24,120 And that brings us suppose. 5 00:00:24,770 --> 00:00:31,760 Then we'll discuss the most fundamental solutions of general relativity, such as washing, first, personal notes, the tests on human efforts. 6 00:00:32,090 --> 00:00:38,440 And then we'll come to political discussion of that crisis discussed in this article versus course, the literature. 7 00:00:38,930 --> 00:00:49,549 Before coming to the more advanced topic that involves loss of mental mechanics, then lost in terms of the likes of the real system hawking radiation. 8 00:00:49,550 --> 00:00:56,350 But whole entropy then will come more smoothly to focus such as holographic principle, which you. 9 00:00:58,710 --> 00:01:04,830 So first of all, we all go to some extent some people from high school, some people from popular movies, 10 00:01:04,900 --> 00:01:13,470 or else we all know the problems of general relativity, momentum and energy curve spacetime. 11 00:01:13,860 --> 00:01:20,439 They distort the science. And because of this distortion motion of other questions. 12 00:01:20,440 --> 00:01:27,390 So exoplanets, libraries around the object that first spacetime change, 13 00:01:27,630 --> 00:01:34,170 I mean different basically if you have like great synergy and so large quantities of space time, 14 00:01:34,170 --> 00:01:38,390 the delay train will look up to get slightly more it will be disrupted by the for 15 00:01:38,400 --> 00:01:42,060 simply the fact that the drug is still in the property will throw things curves. 16 00:01:43,050 --> 00:01:48,440 So this is the quality to future discussion is over. Quantify this and quantify this. 17 00:01:48,450 --> 00:01:54,930 We need like old equations before the question to fulfil general relativity or even above 100 years ago. 18 00:01:55,110 --> 00:02:00,330 And they are Einstein's equations written here and discussing some to behold. 19 00:02:01,110 --> 00:02:11,400 So basically the context of general relativity is the geometry, which is metric will be affected by energy for mass and vice versa. 20 00:02:12,480 --> 00:02:16,230 So what are the ingredients of Einstein's equations of motion? 21 00:02:16,980 --> 00:02:20,640 The main hero of his discussion? The beauty of the magic. 22 00:02:21,150 --> 00:02:25,660 So let me remind you the simplest facts, such as in front of us, 23 00:02:26,380 --> 00:02:32,280 we have a two dimensional flat space and it will take the measure difference between points B and C, 24 00:02:32,280 --> 00:02:41,580 for example, distance built S, then the distance is given by the firm to see the distance of a square you simply equal to the x squared plus no force. 25 00:02:42,870 --> 00:02:49,079 Then we can take the distances to be small, and then the same line, but no difference. 26 00:02:49,080 --> 00:02:56,340 And it doesn't. The small elements applies. We have here squared is a small element is equal to x squared plus twice square. 27 00:02:56,790 --> 00:03:00,600 This is the metric of two dimensional space time. 28 00:03:00,990 --> 00:03:07,830 We can generalise this for three dimensions. Here squared is equal to the squared white squared plus none of work is that squared. 29 00:03:08,190 --> 00:03:15,270 If in fact, Weisskopf is contentious with the headlines in the last four or five six dimensions if necessary. 30 00:03:15,540 --> 00:03:20,400 And so you get dimensional, you get dimensional flat Euclidean spacetime. 31 00:03:20,600 --> 00:03:24,450 The light element squared is equal to the sample squares. 32 00:03:24,630 --> 00:03:26,260 Obviously he doesn't want these displacement. 33 00:03:27,300 --> 00:03:35,129 We can put this in the more elegant form metric square by right controlling the threshold need a squared is equal to g i g. 34 00:03:35,130 --> 00:03:40,290 He explained the energy where summation over energy is assumed. 35 00:03:40,740 --> 00:03:42,990 So this example is given equal dimensions. 36 00:03:43,170 --> 00:03:52,410 So I'm saying go from one end to issue because one and two, and in the end you should get 53 just like the x squared plus the iceberg. 37 00:03:52,800 --> 00:03:58,310 So explicitly this relationship is given here in this line we have four elements already. 38 00:03:58,320 --> 00:04:01,110 We saw over 83 that are for energy, 39 00:04:01,110 --> 00:04:08,550 one long if you include you want energy pool and these four elements you'll be unable to put into numerical metrics such as you here. 40 00:04:08,820 --> 00:04:14,280 And we can compare this line to this line and we see that these two of the elements are 41 00:04:14,280 --> 00:04:18,870 equal to zero and g one is a good one and should have at least in this one as well. 42 00:04:19,470 --> 00:04:27,360 So this is a metric comes up in fifth dimensional space, so most of which is like this. 43 00:04:28,380 --> 00:04:35,850 So in the previous example, G was independent of absolute just in metric cost of metric six one and 100, 44 00:04:36,300 --> 00:04:40,530 but in principle it means about four points in space for this time. 45 00:04:41,610 --> 00:04:48,750 So for example, we didn't have to name the three dimensional space, the square in which three can use a square. 46 00:04:49,410 --> 00:04:52,890 But another one important thing. But we can use different coordinates. 47 00:04:53,130 --> 00:04:59,440 We can use for the same three dimensional space. We can use either official coordinates or circles. 48 00:04:59,460 --> 00:05:04,440 Origins are shown in this picture, and then the left element will change physically from this. 49 00:05:04,440 --> 00:05:10,620 Look, it's just not surprising because if we change versions of the discussion with this, the squared will not change. 50 00:05:10,860 --> 00:05:16,890 But of course these orbits change and therefore the metric itself does a must change. 51 00:05:17,490 --> 00:05:28,469 So in this form it means that in the first case, which is 3.33, we with the last one on the yellow in the second case receive a symmetric no. 52 00:05:28,470 --> 00:05:33,480 Depends on the point in space why the exclusive dependence on space? 53 00:05:33,600 --> 00:05:36,670 It will be important to discuss equals. 54 00:05:38,720 --> 00:05:45,020 So some examples of the metrics here. 55 00:05:45,350 --> 00:05:47,980 So this is a metric in the field of admissions. 56 00:05:48,800 --> 00:05:57,830 Now we can generalise this more, and this is the performance of a social media, which is scholarly, getting made by inside and others. 57 00:05:58,130 --> 00:06:05,420 That's the reaction at least, at least locally in four dimensional spacetime where this is a spatial can't get a squared away. 58 00:06:05,420 --> 00:06:09,110 Squared is indeed so squared. But the thing is not an independent spectrum. 59 00:06:09,740 --> 00:06:13,280 They need to put also the time elements into the metric. 60 00:06:13,490 --> 00:06:21,180 And essentially the cosmos of special relativity is that our spacetime is locally in cost, is beside the dimension given here. 61 00:06:21,660 --> 00:06:26,299 Again, you can write this metric avoidance, for example, in circle coordinates. 62 00:06:26,300 --> 00:06:29,300 And again, the same 11 point is two squared squared. 63 00:06:29,570 --> 00:06:37,640 But this part is written in certain importance. How do we know that our space spacetime is actually current? 64 00:06:38,540 --> 00:06:43,220 What kind of local experiments and vocalisations can we do to determine the curvature? 65 00:06:43,520 --> 00:06:47,810 Oh, so it's like this. Well, some people talk about this whole time. 66 00:06:48,140 --> 00:06:53,850 In particular it goes and then it's actually one of the local experiments is the law is 67 00:06:54,050 --> 00:06:57,770 that you can draw triangles and try to measure to solve the angles in the triangle. 68 00:06:58,250 --> 00:07:02,780 You just based on the set, you discover that to some of the angles is equal to 100 degrees. 69 00:07:03,140 --> 00:07:06,170 If it is not, for example, which handles here, 70 00:07:06,380 --> 00:07:13,310 you can measure bicycles and discover that the sun exceeds all other places if your space happens to be the cell is one thing, 71 00:07:13,640 --> 00:07:19,430 this one, but just the charge and then the triangle, the sum of the angles of 300 degrees. 72 00:07:19,850 --> 00:07:26,690 So this is a test. One of them, you can do this, for example, do the same central point figure, which is on the public space, 73 00:07:26,810 --> 00:07:30,990 the but just the space you can do the whole only you can draw a circle and measurements of 74 00:07:31,010 --> 00:07:35,239 difference and you discover that in the secondary space discovery is greater than to pay. 75 00:07:35,240 --> 00:07:41,510 Ah, this is where were in the prestige, which is also price a little bit to measure light elements in fact. 76 00:07:41,510 --> 00:07:44,899 But what he sees is even less discretion with Weisler downstairs. 77 00:07:44,900 --> 00:07:48,110 So this is all to Mexico City. 78 00:07:49,100 --> 00:07:54,080 But then you only ask one. So how do you know for sure if somebody gives me this lecture? 79 00:07:54,920 --> 00:08:02,999 Is it surely the fact that the space is curved or you can do some important information like in the previous slide from circle for just 80 00:08:03,000 --> 00:08:10,040 to partition apartments and actually being the centre for some complicated information back to the flat space is impossible enough. 81 00:08:10,310 --> 00:08:17,450 So we need to have some local test of possible lots of space is correct and such a local test is provided by three mountains. 82 00:08:18,320 --> 00:08:25,610 So what will believe that? Explain what this object is. It's the dirty dom so you can only know it is two fold. 83 00:08:25,610 --> 00:08:33,770 In fact, it's not very well done. So the thing are derivative of some object which is known as the free stuff and connection is not the simple dharma. 84 00:08:34,370 --> 00:08:37,370 And this is such a simple domain itself. Depends on the metric. 85 00:08:37,670 --> 00:08:41,610 So ultimately remote answer is inexpressible in terms of derivatives. 86 00:08:41,780 --> 00:08:47,600 Actually the second image, because it's one third of the way here and then on top of that there is another derivative for God. 87 00:08:48,020 --> 00:08:50,150 So it is a second value, which is called the metric, 88 00:08:50,480 --> 00:08:58,400 which reminds us of all the human desire you can build other important ingredients such as nature comes up and reach stellar. 89 00:08:58,730 --> 00:09:05,570 And the important local statement is that the space is slept even only if its human presence is identical as you. 90 00:09:06,500 --> 00:09:10,660 So you somebody goes to and tries to sell a very complicated poetic statement. 91 00:09:10,670 --> 00:09:17,120 I found a wonderful solution of Einstein's equation. The space is curved and this is a solution which would be named after me. 92 00:09:17,630 --> 00:09:25,100 So you should not. Belief is first, if once. First of all, you should check that the optimal design of this metric is you by holding these formulas. 93 00:09:25,310 --> 00:09:33,830 And if you discover that the human does zero, then that is the existence mission which brings this complicated entity back into the vertical space. 94 00:09:33,830 --> 00:09:42,040 And therefore the claim just in this so the even and it's the images will play a very important role in general energy. 95 00:09:42,360 --> 00:09:46,819 Of course as we saw already you as on the basis of the piece begins in alcohol. 96 00:09:46,820 --> 00:09:50,450 And here's what I don't think we should send you to the equations. 97 00:09:50,780 --> 00:10:01,250 You already are. So let us have you. On the left hand side is basically the second order partial differential equations for the metric. 98 00:10:01,640 --> 00:10:06,430 On the right hand side, there is an object which is known as the stress energy density. 99 00:10:06,980 --> 00:10:10,400 This encodes energy and matter contained in space. 100 00:10:11,990 --> 00:10:15,080 So important statement is the following. 101 00:10:15,080 --> 00:10:18,560 Despite the fact that you don't see any of the images explicitly entering here, 102 00:10:18,650 --> 00:10:24,340 the equations the oh is this all the previous like the are second order nonlinear coupled 103 00:10:24,350 --> 00:10:28,970 partial differential equations for the components of achieving you which by the Mexicans. 104 00:10:29,450 --> 00:10:35,570 Okay, so you can I tries to magically carry the expression of what you're saying is equations of the left hand side. 105 00:10:35,780 --> 00:10:42,880 So you could see that indeed. The second order of operations and the source of these equations. 106 00:10:42,890 --> 00:10:53,150 On the right hand side, you can compare it his muscles equations where he has a point to support the distribution of charges and currents in space, 107 00:10:53,570 --> 00:10:57,530 and he would like to find electrical magnetic field generated by those studies. 108 00:10:57,920 --> 00:11:04,930 Then write the muscle equations. And these are also partial differential equations with respect to the for potential a new from Amy. 109 00:11:04,940 --> 00:11:08,330 We can cultivate EMV electrical within the field in more space. 110 00:11:08,900 --> 00:11:16,690 So the velocity is the same. The electrical magnetic fields here are sourced by distribution of charges of cards. 111 00:11:17,000 --> 00:11:22,910 Here the method to renew is source by distribution of matter and energy in space. 112 00:11:23,510 --> 00:11:26,560 There is no fundamental difference in these equations. 113 00:11:26,900 --> 00:11:35,370 Lots of situations are linear. This means that we can find the generic solution, if not explicitly done in the form of some integrals immediately. 114 00:11:35,420 --> 00:11:42,499 And people in 19th century did exactly that. However, here I'm saying equations are possible. 115 00:11:42,500 --> 00:11:45,830 Moving their differential equations. Generic solution is not known. 116 00:11:46,040 --> 00:11:49,219 It is not unique. It is very, very complicated. 117 00:11:49,220 --> 00:11:58,040 Set of differential equations. So you are in a similar piece because you decide you will consider zero metric sources supposedly. 118 00:11:58,040 --> 00:12:05,210 Tell us what you. We don't have any sources that I can cite generic solutions to non and you're going to call them yes. 119 00:12:05,330 --> 00:12:10,190 Situations for theories, which is also a very complicated set of equations and solutions. 120 00:12:10,190 --> 00:12:19,519 Will you? However, solutions into highly symmetric species can be solved by making assumptions about ultimately, for example, 121 00:12:19,520 --> 00:12:24,140 if the source is surplus emission, we can assume that the solution will be strictly symmetric as well. 122 00:12:24,530 --> 00:12:33,620 If the source of the left hand side will be strictly symmetric, such as the distribution of mass and uniform distribution of press and surplus. 123 00:12:33,620 --> 00:12:37,550 Maybe we can make an assumption about the light elements. 124 00:12:37,910 --> 00:12:41,149 We can think that it will be certainly symmetric. 125 00:12:41,150 --> 00:12:48,650 That means that the ends A and B here will depend only on the radial distance from the centre, 126 00:12:48,800 --> 00:12:54,260 but they will not depend on the angles because it is a surplus energy and this is a possible assumption. 127 00:12:54,530 --> 00:13:02,540 So look at the next to substitute the solution. This answers to the equations, emotion and so forth a and B with appropriate public positions. 128 00:13:02,900 --> 00:13:07,310 And you discover so that Moscow Schwarzschild did in 1916. 129 00:13:07,550 --> 00:13:12,230 You just tell and we'll just all just dishwashers. But one of the most important solutions of journalism. 130 00:13:13,010 --> 00:13:21,650 So be sure to read this you'll hear it describes this magical spacetime outside of the point of mass, just outside is extremely important. 131 00:13:22,160 --> 00:13:25,740 So if you look at the message, it's not so different, different from this. 132 00:13:26,100 --> 00:13:30,350 I mean, of course, you are breaking similar to this little element here. You jam over a C squared. 133 00:13:30,350 --> 00:13:36,230 Ha, it does a circle here. If you've got just a zero this vessel, then you're back to the boss dimension. 134 00:13:37,070 --> 00:13:40,760 This element is actually just these is actually not very large. 135 00:13:41,030 --> 00:13:44,089 So corrections to this one is very small. 136 00:13:44,090 --> 00:13:51,140 Four stars is limits. So you can think I mean, if you think of Earth as a start to symmetric body, then even estimate what this action is. 137 00:13:51,350 --> 00:13:55,729 How much is based on your skirt? All right, here. I'm sending you, don't you? 138 00:13:55,730 --> 00:14:01,370 Because what you are and you calculate the selection, what actually will be on the order of total minus nine. 139 00:14:01,790 --> 00:14:09,260 So it's a rather small distortions based on colour and it's still sufficiently large to affect, for example, justification specifications. 140 00:14:10,490 --> 00:14:18,059 What the thought of this very simple. Derek So this is about the logical it seems at a certain point, but this whole bracket becomes you. 141 00:14:18,060 --> 00:14:21,709 What happens? It's a so-called short term reduced and part is equal. 142 00:14:21,710 --> 00:14:26,330 Each question squared. Then this becomes you and this becomes you as well. 143 00:14:26,330 --> 00:14:31,069 Therefore this term pulls up. Well, something happens specific and we need to investigate. 144 00:14:31,070 --> 00:14:42,260 Look, exactly. Well, remember that the graphic describes this based on outside of the body of Miss M so for most object this pathology this is clarity 145 00:14:42,470 --> 00:14:49,130 is not is of no consequence is of significance the most object the shortest Regulus is located deep inside the object itself, 146 00:14:49,430 --> 00:14:54,470 and therefore is not an element of a solution because the solution is on the very top side, but it's from the earth. 147 00:14:54,890 --> 00:15:01,340 You Schwarzenberg This is about one centimetre, so this is the whole issue and a solution is so of this is, this is, this is the earth. 148 00:15:01,940 --> 00:15:07,190 The shore surface from the British is somewhere deep inside and the solution is hold it outside. 149 00:15:07,430 --> 00:15:12,560 So you don't, you don't worry about the house inside. There is a different solution that they want you to write inside. 150 00:15:12,740 --> 00:15:17,870 Inside this inside the solution of the sun, the shortest radius is kilometres. 151 00:15:17,990 --> 00:15:21,010 And again, this is a tiny, tiny distance deep inside the song. 152 00:15:21,020 --> 00:15:24,290 You don't worry about the solution there because the solution is very complex. 153 00:15:25,220 --> 00:15:37,870 However, something comes if some violent forces will squeeze all the matter of the star or split in two inside dishwasher days in the case of. 154 00:15:37,940 --> 00:15:41,630 We'll get some political indications from the logic yourself. 155 00:15:42,830 --> 00:15:48,090 So you remember this piece Inside Dishwasher videos, for example, in the process of the rotation of Pop Superstar. 156 00:15:48,530 --> 00:15:53,240 Then we got the bullet hole and this is where our problems start. 157 00:15:53,960 --> 00:15:58,100 So then we have to take the spectacle of this kid celebrities very seriously. 158 00:15:58,520 --> 00:16:03,730 First of all, you have this well, there's all this events item that are equal to our forces. 159 00:16:03,740 --> 00:16:10,520 Then this thing becomes zero. And then there's another singularity in the metric, not just scared of you are close to zero. 160 00:16:10,790 --> 00:16:16,760 Then this whole term goes up and the same happens here. So there's another singularity in the metric that are equal to zero. 161 00:16:18,050 --> 00:16:25,130 Well, we need to remember that the metric is actually, in terms of issues differently in different partner systems. 162 00:16:25,370 --> 00:16:29,390 You change the importance of words. And you can think of something here. 163 00:16:29,630 --> 00:16:33,610 For example, in two dimensions you have the addition words, light elements. 164 00:16:33,740 --> 00:16:41,330 Let's face the x squared plus y squared. You can write the same line element in polar ordnance and you can see all bets are equal. 165 00:16:41,330 --> 00:16:44,899 Zero. We have a pathology similar to what happens for schedules. 166 00:16:44,900 --> 00:16:46,580 Right? This whole term does appear historical. 167 00:16:46,590 --> 00:16:52,160 So but we know that going can make it more automation back to the properties of space and points of origin. 168 00:16:52,340 --> 00:16:54,440 Zero is no different from any other point in space. 169 00:16:54,800 --> 00:17:01,670 So this is a board, this is military, this is this is a single entity that we can get rid of by changing the change in performance. 170 00:17:02,870 --> 00:17:04,090 So in a similar way, 171 00:17:04,160 --> 00:17:12,180 we'll get breakfast Russian Federation different board does a couple of things is violence and the vegetable is equal to our s law. 172 00:17:12,230 --> 00:17:15,050 Population of Baltimore boiling up a little curve. 173 00:17:15,320 --> 00:17:23,480 However, something will happen as we discuss in the next slide in general to check the story coordinate similarity, 174 00:17:23,630 --> 00:17:28,160 we need to compute something to see some variation coordinates a change because we need 175 00:17:28,160 --> 00:17:32,450 something that does not change for the change in system or just a couple of competitions. 176 00:17:32,450 --> 00:17:35,989 The polar analysers and special variants. 177 00:17:35,990 --> 00:17:41,930 One of them is called differential variant. It is it is basically a product of three methods of reporting. 178 00:17:41,930 --> 00:17:46,490 This is support for a first metric. 179 00:17:46,850 --> 00:17:51,470 This special variance is a version of the one or 2 to 6. 180 00:17:51,800 --> 00:17:59,090 So this is completely normal people. There are people who are pushing these similar laws up as far as possible. 181 00:17:59,390 --> 00:18:06,530 So after that, this encourages what we want is a truly nonpartisan letter, an article to see what we don't know. 182 00:18:06,980 --> 00:18:10,510 We need to modify physics in order to understand what these articles yield. 183 00:18:10,700 --> 00:18:16,020 But we don't need the money. If I just focus on the central problems that are economical solutions. 184 00:18:16,940 --> 00:18:20,210 So what happens at such a high speed? 185 00:18:20,600 --> 00:18:25,969 Something isn't covered. Sadly, the president began to study emotional particles. 186 00:18:25,970 --> 00:18:33,650 Light rays got all black holes, just like to study the orbits around the star or or any other source. 187 00:18:34,370 --> 00:18:40,309 So let's think about what comes to light. So curious what happens to special abilities, right? 188 00:18:40,310 --> 00:18:45,470 The special relativity. If the observer is looking at this here, it's going to be right somewhere in the centre. 189 00:18:45,890 --> 00:18:55,459 Then of course it must light forth. And the future light cone, which means yes to particle for example, a massive particle does not propagate, 190 00:18:55,460 --> 00:18:58,700 does not mean in the natural cycle this observer just stays there. 191 00:18:59,000 --> 00:19:02,150 Then it simply propagates along with that next plane goes up. 192 00:19:02,780 --> 00:19:08,130 If this particle has some velocity, no matter how small, it will not stay on the same space point. 193 00:19:08,360 --> 00:19:11,720 It will move in space and therefore it will move on this graph, 194 00:19:11,990 --> 00:19:17,360 the sum endless flow and the slope will be equal to the speed of the motion of this particle. 195 00:19:17,900 --> 00:19:21,320 So the maximal speed, the consensus, will be the speed of light. 196 00:19:21,440 --> 00:19:26,080 And this response to this, they are going to they are going to motion along the surface of the light pole. 197 00:19:26,360 --> 00:19:33,830 So problems like trains will move in the future along the surface of this well, this small and therefore usually. 198 00:19:34,640 --> 00:19:38,990 So let's see what happens to problems in the vicinity of the black hole in the centre ties. 199 00:19:39,530 --> 00:19:44,900 So here are these light poles drawn locally like poles outside of the prison. 200 00:19:45,200 --> 00:19:47,600 They look more or less like in the special relativity. 201 00:19:47,810 --> 00:19:52,700 But then you come closer to the horizon with ideas of these, become a little bit squeezed and a little bit delivered. 202 00:19:53,750 --> 00:19:55,880 This is a property, the virtue of spacetime. 203 00:19:56,330 --> 00:20:04,400 And then so you can follow these, this, this and a little bit like and the light from this point, for example, 204 00:20:04,520 --> 00:20:09,680 will only propagate inside the light forms and let them only propagate inside this little, 205 00:20:10,070 --> 00:20:13,190 little region here which emanates from this from this point. 206 00:20:13,700 --> 00:20:16,700 But now it's coming through the glass horizon. 207 00:20:17,000 --> 00:20:22,100 You can see the table, the fish use light bulb to comfort the garden. 208 00:20:22,100 --> 00:20:30,669 See, our axis becomes what you find. It is a third for all photons which which emanates from really begin to look like from here. 209 00:20:30,670 --> 00:20:37,730 In here they will only propagate inside this region which is bounded by the event horizon little. 210 00:20:37,910 --> 00:20:44,479 Never come outside. They can only come inside the inside the size of and eventually they will end up and are 211 00:20:44,480 --> 00:20:48,890 equal to zero 30 similarities and where we don't know what kind of physics this had. 212 00:20:49,700 --> 00:20:58,370 So this is the property of the event horizon which is compatible with our understanding of the black hole in sort of the normal terms. 213 00:20:58,370 --> 00:21:04,440 Right. That separates the body is very strong. There's nothing even like the whole scheme just doesn't work. 214 00:21:06,100 --> 00:21:12,430 So let's see what happens in terms of the more advanced physics and the limits of quantum physics. 215 00:21:12,680 --> 00:21:16,129 But of course, so again, this is a question magic. And you may ask why? 216 00:21:16,130 --> 00:21:24,320 So what do we go? Well, this is very genius. The answer is, unfortunately, after a hundred years of Jha, not so much. 217 00:21:24,650 --> 00:21:32,390 We know a great deal about the behaviour of particles in fields around horizon, but we don't really know that it's happening inside some literature. 218 00:21:32,720 --> 00:21:37,490 One thing to remember is that general relativity is an approximate field. 219 00:21:37,880 --> 00:21:47,000 It's not the last word, it is. So here's an example of a branch of general relativity where Einstein's equations go from these two terms, 220 00:21:48,350 --> 00:21:53,530 but you can easily write down all the terms which are ends and therefore they can handle the action. 221 00:21:53,550 --> 00:21:58,280 And at one level they must enter the action according to the quantum democracy. 222 00:21:58,700 --> 00:22:04,880 And if you observe these these until you discover connections between science equations, 223 00:22:05,450 --> 00:22:09,950 we don't know at the moment what kind of conditions enter these directions. 224 00:22:10,280 --> 00:22:15,050 But generically we can see but you can actually see are expected. 225 00:22:15,350 --> 00:22:20,000 So sure. But it does not give us more than a little bit corrections to the message coming from the 226 00:22:20,060 --> 00:22:26,360 so-called Holy Week first and also coming from quantum quantum groups like Constellations. 227 00:22:26,540 --> 00:22:34,070 Again, we don't know the future with it at the moment. You can think of unity as the fact effective theory if large distances some time. 228 00:22:34,940 --> 00:22:36,800 Compare this again to students. 229 00:22:37,490 --> 00:22:45,200 Yes, situation describes the motion of essentially any truth, but we know that for a very short distance the fluid is discrete. 230 00:22:45,200 --> 00:22:53,030 We have molecules, you other pseudo and so on. So it has a very complicated structure which is not captured by not just those equations. 231 00:22:53,540 --> 00:22:54,829 In fact, you can generalise them. 232 00:22:54,830 --> 00:23:02,870 Just those equations become closer and closer to this, to this distribution of these molecules and discrete just of fluid. 233 00:23:03,500 --> 00:23:09,329 So similarly, gravity, if you want, you can think of energy as a simple equation equations. 234 00:23:09,330 --> 00:23:18,770 And some of the equations which describe this fluid is sort of looking through the spacetime without looking at the fine details at a very, 235 00:23:18,770 --> 00:23:23,570 very short distance. We don't know what it is. This is the frontline of the modern particle physics. 236 00:23:24,920 --> 00:23:30,380 So let's briefly discuss all the solutions of intense equations. 237 00:23:30,710 --> 00:23:35,960 One of them is relational, not observation. This is a surplus distribution of mass ethanol. 238 00:23:35,960 --> 00:23:40,310 No charge. Q So look at the metric. It is all the Schwarzschild metric. 239 00:23:40,310 --> 00:23:43,580 This is an example of this traditional term here, which depends on the charge. 240 00:23:43,820 --> 00:23:48,379 So now all this ball is, is, is my system is also has an integral charge. 241 00:23:48,380 --> 00:23:51,410 Q And so we have this term here and this term here. 242 00:23:51,590 --> 00:23:55,860 It's a good chance to go back to first metric. If not, then it is a generalisation. 243 00:23:55,870 --> 00:24:01,489 The not just something has to be closely held while the r squared square equation 244 00:24:01,490 --> 00:24:06,020 will give us the Horizons presence inside the solutions for the extreme solution. 245 00:24:06,320 --> 00:24:09,800 And it's very important to think theory of issues. 246 00:24:11,150 --> 00:24:17,690 All right, then another solution is even more important. It will solve by Roy Care in 1963, not so long time ago. 247 00:24:18,230 --> 00:24:23,360 It is a solution which discussed danger, excellent symmetrical charge, distribution of mass. 248 00:24:23,750 --> 00:24:31,910 Its parameters are mass angular momentum. J So there's is a complicated metric also that comprises and the reason for that is you're in between them. 249 00:24:32,390 --> 00:24:36,260 I'm not going to tell the kind of metric, just notice that is not a solution. 250 00:24:36,260 --> 00:24:40,880 So you can say while taking charge that the solution will solve. 251 00:24:41,120 --> 00:24:44,239 So you're going to have to take an absolute symmetric charge. 252 00:24:44,240 --> 00:24:52,240 Distribution of mass, but only does not completely dislodge just the whole loop in mass charge from the governmental j. 253 00:24:53,970 --> 00:24:56,490 Now let's go to more advanced topics. 254 00:24:57,810 --> 00:25:08,490 The portable Civil War games started by Jemmy Carter in 1973, after studying the metrics such as questions, graphics, cards and quantitative graphics. 255 00:25:09,330 --> 00:25:13,710 But he does support the decision of law that says the horizons of a station in the pool. 256 00:25:13,960 --> 00:25:20,400 It's also surface take. You can see the surface reality as the analogue concentration of people. 257 00:25:20,400 --> 00:25:25,200 G nine point basically 4 seconds square. But no, no. Here, look at the eyes of the black flesh. 258 00:25:25,270 --> 00:25:28,530 That's the kinds of issues important for description of the police. 259 00:25:28,860 --> 00:25:35,130 The first law tells us, but the valuation sufficient must post the change at best is related to the change of charge. 260 00:25:35,340 --> 00:25:40,000 At the moment, the change in size is area by default in quantity equation. 261 00:25:40,350 --> 00:25:47,850 So if you if you look at five of the whole symbol, you think it's to the whole increase the mass and all of a sudden it just will increase. 262 00:25:48,680 --> 00:25:57,870 However, the second law tells us that the crisis area is a long, decreasing function of the volume of the piece and the third law. 263 00:25:58,080 --> 00:26:01,480 It is impossible to achieve zero circles, very focussed costs. 264 00:26:02,790 --> 00:26:10,200 So what you can do is to compare these four laws of level against the laws of thermodynamics, 265 00:26:11,340 --> 00:26:18,400 and you find the remarkable, remarkable coincidence if you want. 266 00:26:18,420 --> 00:26:24,120 Or maybe it's not the constant. So the zero 400 X tells us that the system to solve the problem has a constant 267 00:26:24,120 --> 00:26:29,489 temperature gene that is very similar to the zero four but negates the first of all, 268 00:26:29,490 --> 00:26:35,790 from the nexus of all conservation terminology. It tells us that if you change the energy of that whole, the entropy of the system changes. 269 00:26:35,910 --> 00:26:44,940 And the Russian work serves on the second law, which is an important work that tells us that the entropy officer of the system does not used style. 270 00:26:45,660 --> 00:26:51,470 And the third law says that it's impossible to achieve too much. But if this whole process is just a coincidence, well, 271 00:26:51,480 --> 00:26:56,130 if you just there's a deeper connection between the laws of platform against the laws of thermodynamics. 272 00:26:56,610 --> 00:27:06,150 You are tempted, perhaps, to identify a couple to some conditions of departure and area and areas of the entropy of some of some system. 273 00:27:06,390 --> 00:27:10,860 But it's not clear how in 1972, 274 00:27:11,040 --> 00:27:17,700 just a big baseline suggested that the black holes should count as well defined entropy proportional to the horizon area as in the previous slide, 275 00:27:18,550 --> 00:27:24,570 and was actually lost in very many of the searches because black holes are left with lots 276 00:27:24,960 --> 00:27:28,610 and lots of information and therefore can also have a temperature associated with them. 277 00:27:28,710 --> 00:27:30,570 So lot of it is false. 278 00:27:31,380 --> 00:27:39,900 However, in 1974, Hawking demonstrated that the black holes actually borders on the Asian quantum level and so one in fact associated temperature cut. 279 00:27:40,350 --> 00:27:44,340 So that was a rather dramatic advance. So here are some formulas. 280 00:27:44,580 --> 00:27:48,239 So Hawking showed basically black holes can get radiation, a play for you. 281 00:27:48,240 --> 00:27:52,470 Spectrum of the temperature given by this expression not is the presence of the H bar. 282 00:27:52,710 --> 00:27:54,990 So it is a process which happens at the normal level. 283 00:27:55,380 --> 00:28:00,570 And you can see from this formula that the Hawking temperature is inversely proportional to the mass of the black hole. 284 00:28:00,930 --> 00:28:05,190 So if you have a supermassive black hole, its temperature conduction will be very small. 285 00:28:05,400 --> 00:28:11,880 You can look at these numbers and hopefully for some, however, it's in black holes that are extremely small with all primordial black holes. 286 00:28:12,810 --> 00:28:18,820 But the temperature will be sufficiently sluggish. So, for example, black hole of one solar masses of hawking. 287 00:28:18,820 --> 00:28:27,050 So much of the ball is. So this fixes the additional analogy between science conjecture and the baking soda 288 00:28:27,370 --> 00:28:32,450 entropy estimate is indeed proportional to the kinds of areas in Horizon area, 289 00:28:32,540 --> 00:28:35,810 and I didn't notice the presence of each far downstairs. 290 00:28:36,560 --> 00:28:41,670 So that's the immediate consequences and immediate problems which are related to this piece. 291 00:28:42,560 --> 00:28:48,710 First of all, that whole elaborate the stuff you see from this expression, it's almost obvious that they have negative specific heat. 292 00:28:49,200 --> 00:28:54,110 Right? So what happens if this is temperature? The black cold is suppose it's released. 293 00:28:54,440 --> 00:28:58,520 Some of its mass masses decreases masterpieces. 294 00:28:58,700 --> 00:29:03,050 This end becomes smaller than for a temperature becomes large, right? 295 00:29:03,260 --> 00:29:10,469 And eventually this black hole will evaporate. The question is what comes after it lies in its liquid. 296 00:29:10,470 --> 00:29:19,040 The spectrum is completely features. There are no imprints of any information which was ever thrown into a black hole. 297 00:29:19,040 --> 00:29:24,710 So you can throw you black holes and you start to complicated systems, which some books. 298 00:29:27,910 --> 00:29:33,670 So although some political systems contain some some obscure information and in the end, 299 00:29:33,670 --> 00:29:42,160 the windfall of all the irrigation future distribution remains, it seems maybe we don't understand something in the very end of this process. 300 00:29:42,460 --> 00:29:48,500 But it seems to me this is not just information lost, folks, which has been developed until until until now. 301 00:29:48,500 --> 00:29:54,670 In fact, it's not going to clear, you know, what is happening then. But that doesn't mean I don't at all. 302 00:29:56,050 --> 00:30:02,830 The most important question, however, is often what form the microscopic degrees of freedom underlined by most governments? 303 00:30:03,370 --> 00:30:10,890 Remember, the thermodynamics is also, in effect, your theory. But in the usual systems we have normally microscopic level. 304 00:30:11,160 --> 00:30:19,510 We go to statistical mechanics, this notion of temperature, entropy and so on, emerging from the dynamics of the microscopic quantum systems. 305 00:30:19,960 --> 00:30:25,660 So the example of this, the simple example of this is the system of particles, the spin. 306 00:30:25,910 --> 00:30:34,690 So suppose we have we have one particle. The spin has to make a state system can be up with up a few particles as a form of particles. 307 00:30:34,960 --> 00:30:42,010 Then there are more options, Wolf. You just come down for a spin up for four the in the opposite direction so 308 00:30:42,070 --> 00:30:46,629 that all together in one particle we have to like a states for two particles, 309 00:30:46,630 --> 00:30:47,770 you know, for microstates. 310 00:30:47,950 --> 00:30:56,139 Generically, if you have any particles to spin, the number of microstates is equal to the power and and also borders that the entropy, 311 00:30:56,140 --> 00:31:04,540 the usual thermodynamic entropy on this preferential level can be completed as the location of the number of microstates and in this case the entropy. 312 00:31:04,780 --> 00:31:09,500 You can easily calculate just proportional to the number of degrees of freedom of this composite. 313 00:31:10,540 --> 00:31:15,120 What happens? A black hole with all the black holes, entropy, because I'm hoping to calculate the percentages. 314 00:31:15,610 --> 00:31:20,740 But this entropy looks nothing like the states which we want to count in a similar fashion. 315 00:31:20,790 --> 00:31:26,500 Maybe to get to get the centre to be in the lack of force can be called to make up this black hole. 316 00:31:26,650 --> 00:31:29,920 And the problem that we can start talking is what are the microstates? 317 00:31:30,400 --> 00:31:40,180 This is a fundamental question and people are tend to go for many years to solve this problem and there is a partial progress in this direction. 318 00:31:40,420 --> 00:31:45,000 In particular, the strongest one probably is by strange involving 1996, 319 00:31:45,370 --> 00:31:52,360 we're able to count the microstates of a very special supersymmetric black hole in five dimensions. 320 00:31:52,660 --> 00:31:57,330 Yeah, it's a far cry from misfortune. Black call since in the middle of our galaxy ensemble. 321 00:31:57,950 --> 00:32:02,710 But nonetheless it is. It is a model which achieves this success. 322 00:32:03,100 --> 00:32:06,280 But the result translates exactly the defects that took it from. 323 00:32:07,090 --> 00:32:13,060 The reason why they had to resort to the special repulsive magic level is the following. 324 00:32:13,630 --> 00:32:22,570 What they do basically is it is a construction of things and the orginal object, the feeling, all the things you can count it to be complete. 325 00:32:22,750 --> 00:32:27,340 You can go to microscopic states of the system, just like in statistical mechanics system of spin. 326 00:32:28,090 --> 00:32:34,719 Then you squeeze this whole thing beyond this short radius, it becomes a whole and you can get the a sense, I mean, 327 00:32:34,720 --> 00:32:43,060 entropy is easy to do and then you compare this to results, but you must be sure that in the process of reasoning you don't lose Einstein's. 328 00:32:43,630 --> 00:32:49,660 So this is affected by supersymmetry and this other special problems, the bulk of special properties. 329 00:32:49,660 --> 00:32:54,040 You cannot be sure you hope this is not the case, but they are not serious exactly. 330 00:32:54,160 --> 00:33:00,670 But this is a major difficulty here. So strong and powerful results is the general life in many ways to find the right physics. 331 00:33:01,030 --> 00:33:04,510 However, you still do not know how to find the manifestation of the normal level. 332 00:33:04,630 --> 00:33:09,160 For example, the symbols that hold important dimensions moving less. 333 00:33:09,520 --> 00:33:13,690 It does profound consequences of relations. Well, let's talk about this. 334 00:33:13,690 --> 00:33:22,090 What about the principles for the learning systems and identity? The other is extensive proportion to what you think of the gas or some fluid, 335 00:33:22,360 --> 00:33:26,320 and the entirety of the system will be proportional to the what is this gas such question. 336 00:33:26,800 --> 00:33:28,959 But notice that because I'm talking entropy, 337 00:33:28,960 --> 00:33:40,180 which we just discussed is proportional to the area because I is an area called not volume control system before you just proportional to the area. 338 00:33:40,420 --> 00:33:45,220 And it seems that the gravitational degrees of freedom in dimensions generically 339 00:33:45,550 --> 00:33:50,380 are effectively described by some theory you might have some dimensions. 340 00:33:50,680 --> 00:33:56,110 This is known as the chemical principle, which was first discussed by Fulton Susskind in 1992. 341 00:33:56,530 --> 00:34:00,370 So again, very clear. This is a great occupied in some way. 342 00:34:00,700 --> 00:34:07,890 The effective degrees of freedom seems to be of the boundary of this of this region and move over initially. 343 00:34:08,890 --> 00:34:13,690 So this development resulted in what is known as the eastern gravity, 344 00:34:13,870 --> 00:34:19,600 sometimes also is known as few correspondence and is basically the same statement. 345 00:34:19,840 --> 00:34:24,940 And he grew up. It's important to understand the Eastern principle as kind of those who are open of them. 346 00:34:25,120 --> 00:34:26,160 This. On the calendar. 347 00:34:27,000 --> 00:34:35,820 So in the open sea creature you have the of grains of low energy and it is the highest described by quantum computing development. 348 00:34:36,150 --> 00:34:44,130 Some of you or someone, you squeezed this whole thing beyond the coastal radius and now you've got a closing feature that makes the strings. 349 00:34:44,220 --> 00:34:48,090 Grains of low energy is described by very thin molecules in higher dimensions. 350 00:34:48,450 --> 00:34:56,550 And you conjecture, the ideas people have on this is that the conjunction is by the fact that it survives many, many, many discs of it is just proven. 351 00:34:57,300 --> 00:35:02,640 The conjecture is that this site is exactly equivalent to decide to do it in a session forward. 352 00:35:02,640 --> 00:35:06,810 Like, well, the sentiment goes by looks profitable and we don't imagine that the solve. 353 00:35:08,780 --> 00:35:12,700 So that's all good. So we know that's what I saw. 354 00:35:12,710 --> 00:35:15,110 But it's a microscopic system that describes all black holes. 355 00:35:16,040 --> 00:35:20,779 It describes some internal equilibrium because we saw what was a black hole for many stores, 356 00:35:20,780 --> 00:35:25,260 and therefore these are identified as being cytokines, entropy and temperature. 357 00:35:25,880 --> 00:35:34,370 But what about black holes beyond the people so uncertain because they're characterised completely by global charges such as mass, 358 00:35:34,730 --> 00:35:36,860 both electric charge and those forms of momentum. 359 00:35:37,850 --> 00:35:45,250 And so licensing, if you will, is also characterised by control charges, total energy, total electric charge, total environment. 360 00:35:45,290 --> 00:35:52,880 So this is not surprising. Now, what happens if one tracks movement, visual system, for example, to spring pendulum like this one. 361 00:35:53,600 --> 00:35:58,220 It's a oscillate to find efficiencies in all its normal loads and blow things up. 362 00:35:58,400 --> 00:36:02,430 And this opens legal system, but it depends on the system itself. 363 00:36:02,480 --> 00:36:06,049 So for example, for this object here, the idea will disappear. 364 00:36:06,050 --> 00:36:13,880 So obviously it to the mess and of course the local TV stations, it will be not just one frequency, it will be the full spectrum of the spectrum just. 365 00:36:14,000 --> 00:36:17,100 But this can be found and what is crucial to the best of this. 366 00:36:17,360 --> 00:36:20,560 The system itself does not depend on the forces in terms of the system. 367 00:36:20,840 --> 00:36:24,650 It is a intrinsic of systems. So what happens to black holes? 368 00:36:24,670 --> 00:36:29,900 Because to do the same with black holes, I want to return to the cold. I don't want to throw some stuff and it'll make it oscillate. 369 00:36:30,200 --> 00:36:38,270 Give me find the spectrum. What happens if you find the spectrum which characterises black holes and how the spectrum is encoded into this microscope? 370 00:36:41,120 --> 00:36:41,830 So yes, 371 00:36:41,840 --> 00:36:51,510 if you correspondence of biology gives a quantitative way of comparing and studying the spectrum and identifying the ingredients of discrepancies. 372 00:36:51,980 --> 00:36:53,840 So look at the left side of this slide. 373 00:36:54,350 --> 00:37:01,150 So you have some black hole of the brain talk, try to listen to charges and it has done, which is the constant problem entropy. 374 00:37:01,700 --> 00:37:09,500 Now suppose to control that all the original metric is observed by H.M. and his Einsteins equations. 375 00:37:09,650 --> 00:37:17,180 You can write down precise equations which describes these operations h new developments, the properties of the conditions, 376 00:37:17,720 --> 00:37:25,490 the important difference between the normal moles like a bubble and so on, and the black hole oscillations is the presence of the horizon. 377 00:37:26,090 --> 00:37:30,050 Classically, we don't think about qualification like qualification. 378 00:37:30,440 --> 00:37:34,850 Classically, any stuff that shows inside the present disappears forever. 379 00:37:35,330 --> 00:37:44,150 And therefore our system is not a normal mode system anymore because information part of information of the system is lost. 380 00:37:44,330 --> 00:37:50,120 Once the quantum device, you can think of some quantum, but well for example Reddington as well. 381 00:37:50,600 --> 00:37:56,030 So constant walls and parking of information which not so simple as the horizon, but the dimension will not. 382 00:37:56,540 --> 00:38:02,780 So the spectrum will not be real in this case, it will reflect the fact that a very the problem is on the mission. 383 00:38:03,050 --> 00:38:06,920 It is known as the normal spectrum. It will acquire some zero imaginary. 384 00:38:06,920 --> 00:38:10,760 But this is exactly the same. What happened is the digital. 385 00:38:10,800 --> 00:38:18,440 This is the same as happens. If you take the usual no gravitational system and deviate from equilibrium, what will happen? 386 00:38:18,440 --> 00:38:24,290 Give it from within. A system most likely to interact will be some diffusion of it will be Soundwave for example, right? 387 00:38:24,470 --> 00:38:30,110 If in return the air in this room some more important offers will be absolutely. 388 00:38:30,110 --> 00:38:33,319 The something will not propagate, for it will actually it will die. 389 00:38:33,320 --> 00:38:38,299 Eventually it will die because the dispersion relation from is only has an optical emission. 390 00:38:38,300 --> 00:38:45,350 The reverse version of the discourse. We see the resurrection here and here is this first relation of a sound. 391 00:38:45,680 --> 00:38:48,860 You can see the part that describes the propagation of sound. 392 00:38:49,160 --> 00:38:53,810 And then there is a creation part which is proportional to the viscosity integration. 393 00:38:54,680 --> 00:39:06,889 So from this in the slide, it is clear that if you identify the microscopic system which describes all the whole, we must find the quantity. 394 00:39:06,890 --> 00:39:15,140 The condition is in question almost spectrum of black holes and the spectrum of microscopic system, and this has been done. 395 00:39:15,500 --> 00:39:24,980 So one simple example is the following. This is the spectrum of the black hole, the honest completion from from from the official site. 396 00:39:25,550 --> 00:39:32,390 And this is the expression of relation which is expected from the point of view of the fuel theory practice, which is pretty. 397 00:39:32,960 --> 00:39:38,440 So I compare the two, you can see that the speed of sound is still the flight going by the School of Free. 398 00:39:38,750 --> 00:39:44,330 And you can compare these two terms and leads of the ratio, distortions of the ratio. 399 00:39:44,660 --> 00:39:52,280 I don't want to just mention this. Moreover, one people and the relation of just spoke situations of this fluid of the spectrum. 400 00:39:52,280 --> 00:39:58,340 So the beauties of freedom and I size equations want to take this has done around 2007 2000 custody. 401 00:39:58,730 --> 00:40:01,800 So this is very recent stuff. All right. 402 00:40:02,060 --> 00:40:06,110 Coming to the end. So we have some black holes. 403 00:40:07,010 --> 00:40:13,250 Both. You also believe this makes all Jews from the first point of view of this, 404 00:40:14,030 --> 00:40:21,260 the destitute of knowledge, any decent credit for if you really must be able to explain the problems. 405 00:40:21,560 --> 00:40:25,140 This is not left for liberals offensively. 406 00:40:25,160 --> 00:40:28,360 A double helix, I think. 407 00:40:28,580 --> 00:40:33,590 You know why? Because we talk about the principles. We know that in some models, in some cases, 408 00:40:33,830 --> 00:40:40,900 we are able to identify but decided to be the political to guard the behaviour of the whole little spectrum of conservation. 409 00:40:40,910 --> 00:40:45,270 Some call it non-equilibrium properties of this will because viscosity, 410 00:40:45,800 --> 00:40:51,440 like in many other problems, we do not know how to resolve the black similarity. 411 00:40:51,590 --> 00:40:56,140 This is a puzzle with us for many, many years. This is like smoking, breaking. 412 00:40:56,720 --> 00:41:06,140 I sense there is an approximation if you remember this analogy, just in case we do not know the whole theory at the global level. 413 00:41:07,220 --> 00:41:16,820 This is what's frustrating and it's also interesting, and we should also not forget the first publication, 414 00:41:16,820 --> 00:41:20,970 because all this stuff was about the theoretical concept of We're hopeful but realised. 415 00:41:21,960 --> 00:41:29,100 The problem is often the theoretical form, the fuel. But we should not forget about practical applications and real black holes, for example, 416 00:41:29,110 --> 00:41:38,390 real black holes in our very own universe and quite a lot of damage to see the next level inside these real black holes.