1 00:00:17,860 --> 00:00:22,720 Well, thank you very much. I should warn you that I have other talks which I might go back to. 2 00:00:23,890 --> 00:00:29,740 I've had projectors. You see, I had all these pictures from the book so I can show them, but it's not always like that. 3 00:00:30,760 --> 00:00:32,890 In fact, I should explain a bit about the title. 4 00:00:33,220 --> 00:00:43,270 I think it's the Princeton University Press is publishing the book, and it was based on three lectures that I gave about 13 years ago. 5 00:00:43,480 --> 00:00:49,630 You can see how quick I am about the write up, and I think they woke me up too early in the morning and I. 6 00:00:50,440 --> 00:00:55,800 I just gave them this title, which was a bit rash because well, you'll see why. 7 00:00:56,250 --> 00:01:01,960 But in fact, I do think that the words are appropriate to. 8 00:01:02,070 --> 00:01:07,320 I'm going to talk specifically about three different major topics in physics. 9 00:01:07,770 --> 00:01:11,999 And, one, I'm using the word fashion, four, and the other, an excellent faith. 10 00:01:12,000 --> 00:01:19,049 And the third one, fantasy, the fashion one has to do with, well, let me give you an old fashion. 11 00:01:19,050 --> 00:01:22,860 Islington doesn't have to be modern fashion if I can get this thing to work. 12 00:01:23,350 --> 00:01:26,510 There we go. This is a really old fashioned the time of Plato. 13 00:01:26,520 --> 00:01:32,040 So there were four elements, and then the dodecahedron was discovered. 14 00:01:32,040 --> 00:01:37,679 So they had to think of another element, which was the the the aether or something. 15 00:01:37,680 --> 00:01:41,579 It's the planets seem to obey different laws from those on on the earth. 16 00:01:41,580 --> 00:01:49,200 So they had to think of another element to figure out that the another regular polyhedron had been discovered. 17 00:01:49,650 --> 00:01:53,280 It's not just the beauty of these things, which is certainly clear. 18 00:01:53,610 --> 00:02:03,600 And I think we regard physical theories as likely to be if the deep fundamental theories, they're likely to be beautiful theories. 19 00:02:03,900 --> 00:02:07,860 And so you see these beautiful polyhedra which satisfy that particular criterion. 20 00:02:08,520 --> 00:02:10,920 The other thing is they've got to explain things in the world. 21 00:02:11,160 --> 00:02:17,450 And actually I didn't know this originally, but there is and it does explain certain things. 22 00:02:18,510 --> 00:02:27,010 For example, you can take. I'm going to get this thing pointing to cubes and that represents Earth. 23 00:02:27,040 --> 00:02:36,730 You see, the accused represent Earth. The tetrahedron far air was the octahedron and water, the icosahedron, and then the aether was the dodecahedron. 24 00:02:37,600 --> 00:02:45,850 But if you take two cubes, you can cut them up. And create two tetrahedra and one octahedron. 25 00:02:46,050 --> 00:02:49,800 And that expands if you take two sticks. That's made of sort of solid things. 26 00:02:49,800 --> 00:02:54,450 So they're obviously the cubes and you rub them together, you can get well, you see, 27 00:02:54,450 --> 00:02:59,670 you take two cubes, you cut them up and you can produce far two sticks, produce fire and smoke. 28 00:03:00,060 --> 00:03:08,280 So that's an explanation in terms of this whole theory, and I'm not going to say much about that, although fire, of course, 29 00:03:08,280 --> 00:03:15,090 had many different explanations which were fashionable at the times that they were thought of phlogiston theory, 30 00:03:15,660 --> 00:03:18,810 which was disproved basically by Lavoisier. 31 00:03:19,140 --> 00:03:26,040 And then he had a different theory, which is caloric theory, which was disproved a little bit later by Lord Rutherford and so on. 32 00:03:26,460 --> 00:03:32,790 We have better ideas now having to do with molecules running around in oxygen and things like that. 33 00:03:32,790 --> 00:03:39,510 And I'm not going to say anything about that really, but I do want to talk about there is a certain fashionable theory. 34 00:03:42,450 --> 00:03:46,100 This. This is not it yet. These are fine man diagrams. 35 00:03:46,110 --> 00:03:50,370 I should explain what they are, basically. You have to think of the time as going upwards. 36 00:03:50,730 --> 00:03:53,760 Particle physicists think of time going from left to right. 37 00:03:54,180 --> 00:03:59,910 But since I'm more relevant to relativistic the particle physics first, I think my time goes upwards. 38 00:04:00,480 --> 00:04:05,400 And so you think here of this, these lines representing particles, the first one, 39 00:04:05,400 --> 00:04:10,170 two particles come together, together, make another one, and then they split up to make two more and so on. 40 00:04:10,650 --> 00:04:14,700 All these things are possible, things that particles can do. 41 00:04:14,880 --> 00:04:18,330 Each one of them stands for a particular mathematical expression. 42 00:04:18,600 --> 00:04:22,500 And then you're supposed to add all these things up in complicated ways to see what really happens. 43 00:04:23,700 --> 00:04:33,000 The trouble arises when you have these ones with closed loops, because the answers tend to be infinity, and infinity isn't much good as an answer. 44 00:04:33,150 --> 00:04:38,820 Now there are all sorts of clever ways of getting around the infinities, but it was thought of originally, 45 00:04:38,820 --> 00:04:45,630 I think by the Japanese American physicist Nambu that a good idea was to think of. 46 00:04:46,800 --> 00:04:50,610 You see, these are particles were thought of as points you see. 47 00:04:50,620 --> 00:04:54,779 And so when you think of the time progressing, they trace out lines. 48 00:04:54,780 --> 00:04:59,550 And that's what these lines are basically is a little bit more than that, but that's basically what they are. 49 00:04:59,820 --> 00:05:04,260 But if you think of the basic ingredients, not as points, but as loops. 50 00:05:04,830 --> 00:05:11,100 And that was the idea of string theory. Then you can have things which don't have those awkward corners and so on, 51 00:05:11,430 --> 00:05:15,960 and the things can loop around and produce these things with holes in them instead of loops. 52 00:05:16,260 --> 00:05:23,430 And the answers turn out to be fine art. So this was a wonderful idea and I think an extremely impressive and beautiful idea. 53 00:05:25,140 --> 00:05:32,280 They relate to very attractive mathematical ideas called Riemann Surfaces, which are one of the most beautiful things in mathematics. 54 00:05:32,280 --> 00:05:37,740 So, yes, incredible ideas. I was very taken by this when I first heard about them, 55 00:05:38,070 --> 00:05:46,350 but then they people working in these theories found that it didn't really work unless space had 25 dimensions. 56 00:05:47,220 --> 00:05:55,310 When I heard about that, I thought, Well, that's the end of it. That just shows how wrong I was because people thought, well, these idea, 57 00:05:55,320 --> 00:05:59,730 these extra dimensions are kind of hidden and maybe you can make sense of it. 58 00:05:59,970 --> 00:06:07,590 And then the theory works and all sorts of wonderful ideas, I may say, but the mathematics is extremely beautiful attached to these things. 59 00:06:08,620 --> 00:06:13,740 Whether it makes a sense of a physical theory is, to my mind, more questionable. 60 00:06:13,920 --> 00:06:21,510 Now, you might say, surely space doesn't have 25 dimensions, which it doesn't 26 altogether, because time gives you another dimension. 61 00:06:23,310 --> 00:06:29,639 But then what was the point? Well, let me before I go into that, I want to explain a little bit of mathematics. 62 00:06:29,640 --> 00:06:32,910 This is really the only serious mathematics I'm going to do here. 63 00:06:34,230 --> 00:06:38,130 It's very basic elementary mathematics that's a little bit unusual. 64 00:06:38,700 --> 00:06:46,170 First of all, I want to talk about a come back to the string thing in a minute, but this is a sort of interlude which is needed. 65 00:06:46,200 --> 00:06:56,430 What I want to say later, if you want to raise a number to a par at the top, we have eight to the B, except time is the wrong thing to the B. 66 00:06:57,670 --> 00:07:02,020 My press there again. There you go. Hmm. 67 00:07:02,350 --> 00:07:06,549 That means multiplying a batch of B times. Now you can do this again. 68 00:07:06,550 --> 00:07:15,700 H is the C. And by that I mean A to the base, the C to the B to C, because as we did see, it could be written as H of the VC. 69 00:07:15,700 --> 00:07:22,780 So we won't worry about that. But age of the base of the C means a magpies but a base of the C times. 70 00:07:22,990 --> 00:07:26,380 In other words, B multiplied by C times. Times. 71 00:07:27,280 --> 00:07:33,580 So that's a pretty big number. Usually if these numbers are sizeable, in fact, there's a thing called a Google, 72 00:07:33,970 --> 00:07:38,960 which was, I believe, a name introduced by the nephew of a mathematician, Kastner. 73 00:07:39,990 --> 00:07:43,149 And this is he was just trying to think of big numbers. 74 00:07:43,150 --> 00:07:44,740 He was nine years old at the time. 75 00:07:45,070 --> 00:07:54,460 And he invented this name as well, that if you multiplied ten by itself 100 times, in other words, it's one zero 0 to 100 zeros. 76 00:07:54,790 --> 00:07:57,940 That's a pretty big number. And that's ten to the hundred. 77 00:07:58,600 --> 00:08:01,839 Well, it's the sort of number you might think. Well, what's that going to come into? 78 00:08:01,840 --> 00:08:11,770 Physics? Well, it comes in to physics in one particular respect, because it's about the length of time that the biggest black hole will last for. 79 00:08:11,860 --> 00:08:17,110 You see, black holes will eventually radiate away by hawking evaporation. 80 00:08:17,110 --> 00:08:25,420 If you wait long enough and the universe cools down enough that you have to wait for about a Google years before the biggest one disappears. 81 00:08:25,780 --> 00:08:29,890 So there is a number which has relevance to the sorts of things I talk about in my book. 82 00:08:31,480 --> 00:08:37,810 Now, that number, I think the nephew of Karsner wasn't happy with the size of that number. 83 00:08:37,850 --> 00:08:47,680 He thought of even bigger numbers. And Karsner settled on the idea of a number which was has one and Google Zeros. 84 00:08:48,070 --> 00:08:52,030 So you see that's a double exponent thing, ten to the 10 to 100. 85 00:08:52,950 --> 00:08:57,839 That also comes in in what I will say in a minute. So these numbers are the huge. 86 00:08:57,840 --> 00:09:02,400 They are, though. They are. They have some relevance to the things that I talk about in my book. 87 00:09:03,810 --> 00:09:07,650 Now, I want to say one thing here is this. 88 00:09:07,770 --> 00:09:11,220 You have aged agency and these are fairly large numbers. 89 00:09:12,090 --> 00:09:17,130 It doesn't matter much what A is at all. C is the all important number. 90 00:09:17,370 --> 00:09:25,080 And just to illustrate that, I'm going to write down a number ten to the power, ten to the power 124. 91 00:09:25,800 --> 00:09:33,720 And the reason I'm thinking about that number here is it represents how unlikely the Big Bang was. 92 00:09:33,750 --> 00:09:38,520 Now, what I mean by that is they're all possible different big banks that could have taken place. 93 00:09:38,760 --> 00:09:43,380 So the thing about the Big Bang is it was what's called a singular initial state. 94 00:09:43,710 --> 00:09:49,230 It's something where everything went to infinity, curvatures densities, everything went to infinity. 95 00:09:49,590 --> 00:09:52,649 And all your equations then break down. 96 00:09:52,650 --> 00:09:57,959 So it's called a singularity for that kind of reason. And you might say, well, 97 00:09:57,960 --> 00:10:06,600 they're all possible different versions of the singularity and the very particular one that we seem to have had we so improbable. 98 00:10:06,750 --> 00:10:11,250 The improbability is about one in ten to the ten to the 124. 99 00:10:12,290 --> 00:10:14,810 Well, I say a little bit more about that later, 100 00:10:15,140 --> 00:10:22,640 but the point I just want to make here is if you change that bottom ten to a two, it makes hardly any difference. 101 00:10:22,940 --> 00:10:26,990 The number at the top is now 124.52 or something like that. 102 00:10:28,010 --> 00:10:31,880 And since we don't really know how big that 124 is to that kind of accuracy, 103 00:10:32,300 --> 00:10:35,390 it doesn't really matter whether you put a ten or a two down at the bottom. 104 00:10:35,960 --> 00:10:42,320 So it's quite striking how irrelevant that number at the bottom is and how all important the one at the top is. 105 00:10:42,530 --> 00:10:43,850 So that's the point I want to make. 106 00:10:44,390 --> 00:10:50,390 Now, the real thing I want to say about these large numbers, I want to talk about them when they're actually infinite. 107 00:10:50,420 --> 00:10:54,770 Now, you might say, can we talk about infinite numbers where you certainly can. 108 00:10:55,220 --> 00:11:04,160 And there's a theory. There's a cantor. Perhaps I'll skip to that first, which tells you that you can talk about different sized infinities. 109 00:11:05,090 --> 00:11:08,300 And this is a way you can talk in a number of. 110 00:11:09,320 --> 00:11:13,730 Discrete points on the plane, if you like, is no bigger than the number on the line. 111 00:11:14,120 --> 00:11:19,640 And maybe some of you are familiar with that. I'm only showing you the slide, really, to show that's not what I'm talking about, 112 00:11:19,820 --> 00:11:25,460 because many of you may have seen Qantas theory and how you can talk about infinite numbers and some are bigger than others. 113 00:11:26,180 --> 00:11:34,220 This is just to show that if you have numbers and it's in a lattice in a plane, it's no bigger than the number of points on the line. 114 00:11:34,580 --> 00:11:38,900 And you can win the line backwards and forwards and count all the points on the plane, the lattice points. 115 00:11:39,260 --> 00:11:45,140 But the trouble here is it's not continuous because right o keep pointing to first pressing the wrong number. 116 00:11:45,490 --> 00:11:53,000 Then you can see that that when the numbers get fairly large, they can be very close on the on the grid, 117 00:11:53,000 --> 00:11:58,310 on the lattice, but very far away on the actual counting scheme. 118 00:11:58,520 --> 00:12:00,740 So it's not what's called continuous. 119 00:12:01,280 --> 00:12:09,829 If you want now you want to count in a continuous way, then this Cantor idea isn't quite powerful enough for what I want to say. 120 00:12:09,830 --> 00:12:14,989 So let's now go back and talk about these numbers. 121 00:12:14,990 --> 00:12:24,190 I'm going to call them infinity to a power, infinity to the one that will be basically the number of points on the line. 122 00:12:24,200 --> 00:12:27,259 Infinity squared will be the number of points in the plane, 123 00:12:27,260 --> 00:12:33,470 and infinity cubed will be the number of points in a solid space or curve, could be a curved line or whatever. 124 00:12:33,860 --> 00:12:37,130 And for an end space it's infinity to the end. 125 00:12:38,150 --> 00:12:43,790 So these numbers, you can make mathematical sense of them and. 126 00:12:46,790 --> 00:13:00,530 The great French mathematician educator who sort of early in the 20th century analysed all sorts of things and understood these things very well. 127 00:13:02,360 --> 00:13:08,400 Uh. Okay? No. Now I'm going to talk about functions. 128 00:13:08,760 --> 00:13:13,020 Now you see the top left hand picture here. Sorry. 129 00:13:13,470 --> 00:13:15,600 Top left hand picture here, 130 00:13:16,530 --> 00:13:27,000 you might say how many functions where the number of values they can take a that's goes up the y axis and the x axis goes horizontally. 131 00:13:27,330 --> 00:13:31,680 It's discrete in each case, and you want to know how many different functions that is. 132 00:13:31,680 --> 00:13:37,770 How many graphs can you have altogether when you see the first value could be a different possibilities. 133 00:13:37,770 --> 00:13:42,930 The second could be a different third a different sense eight times, eight times, eight times, a B times. 134 00:13:43,110 --> 00:13:47,190 So that age of the B, different graphs. Now suppose. 135 00:13:49,120 --> 00:13:53,350 These were not discrete. But you had a. 136 00:13:54,270 --> 00:14:02,070 At the bottom some space which had a B dimensions and which went up, we would have a dimensions. 137 00:14:02,370 --> 00:14:08,620 Then the number of these. The functions that you could have is a to the. 138 00:14:10,470 --> 00:14:19,380 Age of the sorry infinity to infinity to va to the infinity to the B because infinity va is the number of things going horizontally. 139 00:14:19,740 --> 00:14:23,160 Infinity the B is going horizontally. Infinity va is going vertically. 140 00:14:23,430 --> 00:14:30,690 And so it is infinity to which the infinity to be. In other words, infinity to a infinity to the B, if you can. 141 00:14:31,680 --> 00:14:35,040 See, I should get pointed, pressing the wrong thing again. Sorry about that. 142 00:14:37,650 --> 00:14:42,360 Here we go. Trying to fit down the vintage that introduces me now. 143 00:14:42,720 --> 00:14:49,620 The bottom line here is an example. So an example would be so as you have electric fields in three space. 144 00:14:49,770 --> 00:14:56,250 So that's meant to be a picture of an electric field. At every point you've got the field points in some direction with a certain strength, 145 00:14:56,700 --> 00:15:02,760 and there's three dimensions worth of different possible electric fields, and the space is three dimensions. 146 00:15:02,910 --> 00:15:08,030 So the number of possible electric fields would be infinity. 147 00:15:08,040 --> 00:15:14,549 The bottom line here. Infinity to the A, infinity to the B, which is now infinity the three. 148 00:15:14,550 --> 00:15:21,000 Infinity to the three. But what I want to say is that it's the three at the top, which is the number of dimensions. 149 00:15:21,180 --> 00:15:23,790 The three at the bottom fortuitously happens to be three as well. 150 00:15:23,940 --> 00:15:28,259 But it could have been, say, the number of possible temperatures, temperatures just one parameters, 151 00:15:28,260 --> 00:15:32,670 then it would be infinity to the infinity to the three and it would be only one. 152 00:15:33,180 --> 00:15:38,160 So this is just showing you how this notation works. 153 00:15:38,490 --> 00:15:42,150 If I want to talk about fields, that's the idea. Okay. 154 00:15:42,420 --> 00:15:44,250 So that's counting the electric fields. 155 00:15:45,240 --> 00:15:53,670 The point I want to make is, well, infinity is a lot bigger than finishes would be if a is bigger than infinity would be. 156 00:15:54,000 --> 00:15:58,319 But as I said before, with the finite numbers, it's really the top exponent. 157 00:15:58,320 --> 00:16:03,180 When you got double exponents, it's the top number, which is important, and that's the dimension of the space. 158 00:16:03,450 --> 00:16:11,400 So infinity edge to the A, infinity to the B is much, much, much greater than infinity to the C, infinity to the D. 159 00:16:11,580 --> 00:16:17,700 If P is greater than D, and it doesn't matter a hoot whether A and see which one is bigger there. 160 00:16:18,390 --> 00:16:26,460 The point is that if you have fields in space of a certain number of dimensions, if that dimension is larger than three, 161 00:16:27,000 --> 00:16:33,930 then the number of fields will completely swamp those in in the ordinary in the ordinary ones we're used to. 162 00:16:34,230 --> 00:16:39,180 And that's the point I want to make. So if you have a space which has more than three dimensions, 163 00:16:39,390 --> 00:16:47,350 then potentially you're going to have huge numbers of fields which swamp everything else that you might be familiar with. 164 00:16:47,370 --> 00:16:55,230 So that's a real problem. Now, this kind of problem always seemed to me with a problem with these high dimensional theories. 165 00:16:55,680 --> 00:16:59,160 I want to say how people sort of try to deal with it. 166 00:16:59,460 --> 00:17:08,070 Now, the main argument, I think that people who I should say that when I'm objecting to string theory, 167 00:17:08,190 --> 00:17:16,020 I'm not objecting to it as a piece of mathematics is wonderful mathematics, which has implications in all sorts of other fields in mathematics. 168 00:17:16,440 --> 00:17:21,870 I'm not objecting to the idea of a string as a serious prospect for physical theory. 169 00:17:22,050 --> 00:17:26,520 What I am objecting to is that having these extra space dimensions. 170 00:17:26,730 --> 00:17:30,000 Now one of the arguments that people said, well, 171 00:17:30,180 --> 00:17:36,669 there's a good theory that was produced not that long after Einstein produced his general theory of relativity, 172 00:17:36,670 --> 00:17:44,760 a wonderful theory in which the gravity within explained in terms of curvature of space this time, space time. 173 00:17:44,910 --> 00:17:52,080 So four dimensional space time and but it was his theory of gravity a little while later. 174 00:17:53,990 --> 00:17:58,160 Kaluza, who was a German mathematician living in what is now part of Poland. 175 00:17:58,190 --> 00:18:03,799 I don't know what you call it this Polish German mathematician who introduced a beautiful idea where 176 00:18:03,800 --> 00:18:10,580 you could incorporate not just gravity but electromagnetism into the geometry of the space time. 177 00:18:10,850 --> 00:18:17,150 But the space time now had to be a five dimensional space, but it was a very special kind of five dimensional space. 178 00:18:17,390 --> 00:18:22,370 The five dimensional space is one, which is a thing which you can call a bundle. 179 00:18:22,550 --> 00:18:27,740 Now, you see, this is meant to be a picture of a bundle. I'll give you another picture of a bundle in a minute. 180 00:18:28,430 --> 00:18:34,370 Here we go. You see, it's a general idea in mathematics, which is a very fruitful idea that you can have. 181 00:18:35,480 --> 00:18:41,150 Think of the picture on the picture on the left is just showing you how that bundle idea generalises the idea of a graph, 182 00:18:41,450 --> 00:18:52,190 which is what I showed you before, where you can have the the x axis in the initial case on the left there, they're just ordinary axes, 183 00:18:52,370 --> 00:18:58,249 but they could each be high dimensional spaces and the bottom one could be four dimensional space time. 184 00:18:58,250 --> 00:19:03,469 In other words, three dimensional space amount of time. And the vertical axis could be then all sorts of things. 185 00:19:03,470 --> 00:19:07,190 It could be some complicated manifold. And what a bundle is. 186 00:19:07,190 --> 00:19:12,709 Basically, we call B the whole thing F is what's called the fibre. 187 00:19:12,710 --> 00:19:18,440 So that's the space, those little doughnut, little things which you see at the top what the bundle is. 188 00:19:18,440 --> 00:19:28,070 It's an M's worth of S, so you have a whole space, which is a lot of F so stuck together and it's emsworth of them and that's what a bundle is. 189 00:19:29,150 --> 00:19:35,720 Now, the thing is that if Mr. Space Time, that would be well from space is concerned, it's just three dimensional. 190 00:19:36,110 --> 00:19:39,379 And so that would incidentally, why wouldn't I say four dimensional? 191 00:19:39,380 --> 00:19:45,980 The thing is that usually you have in physics you have equations which carry your information away from the initial three space, 192 00:19:46,220 --> 00:19:53,900 and those equations fix what happens in the threes in the four dimensional space once you know what it is on three dimensional space. 193 00:19:54,020 --> 00:19:57,440 So when I'm talking about how much freedom there is, I'm talking about the space. 194 00:19:57,890 --> 00:20:02,060 The temporal evolution is then determined by what happens in space. 195 00:20:02,060 --> 00:20:06,200 So there's no more freedom in the time it's the freedom is in space. 196 00:20:06,860 --> 00:20:12,170 So three dimensions for the ordinary physics, we know. But you could imagine that was larger. 197 00:20:12,740 --> 00:20:20,030 And the thing is that the Kaluza Klein idea, the bundle, it was a bundle of circles. 198 00:20:20,030 --> 00:20:24,079 And these circles were originally it was it didn't have to be circles. 199 00:20:24,080 --> 00:20:30,710 But I think the Klein idea is that that these were circles and they could be imagined to be very small circles. 200 00:20:31,610 --> 00:20:37,220 I'll come back to that in a minute. But the thing is that the the circles up there at the top, 201 00:20:37,790 --> 00:20:41,600 there's no more freedom in there because you're not your functions are supposed to be all down here. 202 00:20:41,870 --> 00:20:47,870 And these things represent a symmetry. The the, the, the in the Kaluza Klein idea. 203 00:20:48,410 --> 00:20:53,990 Klein was a Swedish physicist who came along later and introduced the idea that there should be little loops. 204 00:20:55,910 --> 00:21:01,879 But the thing is that there in the original theory, there is no freedom in those extra dimensions. 205 00:21:01,880 --> 00:21:05,959 The freedom is all in the base space and in the space time. 206 00:21:05,960 --> 00:21:15,060 That's the same thing at the bottom. Now. The idea with string theory was that you did have freedom all over the space. 207 00:21:15,180 --> 00:21:18,770 So they were saying that the whole five dimensional space, 208 00:21:18,770 --> 00:21:26,790 so in this case 25 dimensional space or 26 dimensional space time was meant to be like space time where you have freedom all over the place. 209 00:21:26,790 --> 00:21:29,820 You can wiggle these things all over as much as you like. 210 00:21:31,080 --> 00:21:39,980 And the argument was that you still is, I should say that those extra dimensions don't show themselves because they're very small. 211 00:21:39,990 --> 00:21:45,300 Well, what is small mean? And this is the sort of analogy that people tend to point to. 212 00:21:45,660 --> 00:21:49,980 You could imagine a hosepipe, and if you're a long way away from that hosepipe, 213 00:21:50,100 --> 00:21:54,720 it looks one dimensional, looks like this, this look, it's just this one dimensional line. 214 00:21:54,930 --> 00:21:58,470 And that's the idea, like ordinary three space, that's the analogue, only three space. 215 00:21:58,740 --> 00:22:02,520 But if you look closely, you see this tiny little loop. 216 00:22:03,030 --> 00:22:06,780 Now you see the hosepipe. You're just supposed to think of the surface of a hosepipe. 217 00:22:06,780 --> 00:22:13,410 So that's an extra one, one extra dimension, just the move which gives you two dimensional space time. 218 00:22:13,830 --> 00:22:17,100 And since it's so small, the argument is you don't notice it. 219 00:22:17,820 --> 00:22:22,920 Well, it seems to me that that is a difficult argument to maintain. 220 00:22:23,190 --> 00:22:29,520 Usually the argument is presented in the form. Well, okay, classically classified of classical physics. 221 00:22:29,670 --> 00:22:34,229 Yes, you could with all those extra dimensions and those might wiggle and they would disturb everything else. 222 00:22:34,230 --> 00:22:41,940 And yes, it would be chaos. But because of quantum mechanics, you need a certain energy to excite those extra dimensions. 223 00:22:42,240 --> 00:22:48,270 And that amount of energy has to do with the dimension of that extra little loop that goes round the hosepipe. 224 00:22:48,570 --> 00:22:55,620 And if the hose part is that hosepipe is small enough, then that energy would be ridiculously large. 225 00:22:56,580 --> 00:23:00,870 Energy goes in the opposite direction from the size of the time. 226 00:23:00,870 --> 00:23:03,030 It would take like to go around the little loop. That's the point. 227 00:23:03,750 --> 00:23:07,440 It would take an enormous amount of energy and what they mean by an enormous amount of energy. 228 00:23:07,650 --> 00:23:14,640 They're thinking in terms of, say, an accelerator where you would try and inject that energy into particle creations. 229 00:23:14,850 --> 00:23:23,549 Like in the LHC, where we had this wonderful news last year or whenever it was about the discovery of the Higgs particle and things like that. 230 00:23:23,550 --> 00:23:24,600 You need a lot of energy, 231 00:23:24,870 --> 00:23:32,250 but the amount of energy that the accelerators that we have today would be just totally by comparison what you would seem to need here, 232 00:23:32,610 --> 00:23:38,460 you would need. So the argument goes, an energy is comparable to something like a sizeable artillery shell, 233 00:23:39,090 --> 00:23:46,350 but in one single particle, and that's way beyond what they could do at the particle accelerators that exist. 234 00:23:46,350 --> 00:23:49,409 You need something, say maybe the size of a solar system. 235 00:23:49,410 --> 00:23:55,379 I dunno what the exact figure would be, some huge accelerator in order to get energies up to that scale. 236 00:23:55,380 --> 00:23:58,950 So it's quite safe. They say you couldn't excite these extra dimensions, 237 00:23:59,370 --> 00:24:09,300 but it seems to me that that's the argument is just wrong because you don't need to see just like that, extra dimensions for the entire universe. 238 00:24:09,990 --> 00:24:13,890 It's that extra dimension extends to the whole universe. 239 00:24:14,010 --> 00:24:19,319 So if you could excite that extra dimension, you would be doing it for the entire universe. 240 00:24:19,320 --> 00:24:23,910 And an artillery shell is absolutely trivial for the entire universe. 241 00:24:24,240 --> 00:24:28,740 In fact, I have a picture in my book which is this one here which I hope I can make sense of. 242 00:24:29,730 --> 00:24:36,959 The top you see the earth going around the sun and the amount of energy that there is in the Earth's motion around the sun is, 243 00:24:36,960 --> 00:24:44,040 I don't know, a million, many. I forget how many millions it is more than the energy that you would need to excite these extra dimensions. 244 00:24:44,250 --> 00:24:50,550 And if that is spread over a distance, which could be, say, the earth, sun orbit, which it would be, 245 00:24:50,670 --> 00:24:55,709 I mean, you've only got to excite that thing just a little bit by disturbing the space time. 246 00:24:55,710 --> 00:24:59,640 Just a bit. It's trivial. 247 00:25:00,750 --> 00:25:03,540 It's a tiny, tiny proportion of an amount of energy. 248 00:25:04,140 --> 00:25:11,500 So if you are going to excite that stretch of the extra dimensions that way, if that little hosepipe thing is going across the middle, 249 00:25:11,520 --> 00:25:18,030 it's supposed to represent that those extra dimensions is the loop being around and the space time is the horizontal lines. 250 00:25:18,930 --> 00:25:28,430 Then you could. Hmm. You would need to have enormous millions and millions and millions of quanta in order to excite it. 251 00:25:28,440 --> 00:25:33,210 And so when you've got lots and lots of quote quanta, people say, well, you must think of it as a classical problem. 252 00:25:33,600 --> 00:25:42,629 So classically, yeah, you could excite these things. So I really don't know why people don't take this argument seriously. 253 00:25:42,630 --> 00:25:54,459 And I say that. I did actually present this argument at a conference which was honouring Stephen Hawking's whatever it was, 254 00:25:54,460 --> 00:26:01,240 birthday, and I think 2002, which was before I gave the lectures at Princeton. 255 00:26:01,660 --> 00:26:04,690 And there were a number of expert string theorists there. 256 00:26:05,110 --> 00:26:10,290 And the thing was published and I never got anybody complaining about this argument. 257 00:26:10,300 --> 00:26:14,320 They just ignored it, which I'm afraid is what seems to happen. 258 00:26:14,620 --> 00:26:18,909 Anyway, let me move on, because that's enough about that particular thing. 259 00:26:18,910 --> 00:26:19,479 That's fashion. 260 00:26:19,480 --> 00:26:28,720 Anyway, so I was a little bit nervous that since it took me 13 years to write the book, that what was fashionable then might not be fashionable here. 261 00:26:28,870 --> 00:26:35,890 I was rather relieved to know that although the fashion in string theory has tapered off a bit, it's still pretty fashionable. 262 00:26:36,420 --> 00:26:42,270 Uh. So anyway. This is quantum mechanics. 263 00:26:42,660 --> 00:26:49,440 Why am I talking about quantum mechanics? Well, you see, that's the faith now is completely different from string theory. 264 00:26:49,440 --> 00:26:50,100 String theory? 265 00:26:50,250 --> 00:26:59,400 See, some people object to string theory because it doesn't have any implications in observed experiments or experiments that one can think of. 266 00:26:59,940 --> 00:27:03,720 That's the trouble. Okay, it may be a wonderful theory, but how do you test it? 267 00:27:03,840 --> 00:27:08,940 That's not my objection. I'm saying that that is a good objection, but it's not the one I'm trying to make. 268 00:27:08,970 --> 00:27:13,470 I'm trying to say that it actually doesn't hang together as a physical theory. 269 00:27:14,340 --> 00:27:21,450 It makes a lot of mathematical sense in many ways, but it doesn't seem to hang together as a plausible theory for the physics of the world. 270 00:27:22,170 --> 00:27:25,680 Quantum mechanics is a completely different kettle of fish, 271 00:27:26,040 --> 00:27:32,370 because quantum mechanics has absolutely enormous numbers of experiments supporting it at it. 272 00:27:32,850 --> 00:27:39,630 Nobody would have thought of it. It weren't for the fact that there were experimental facts which simply do not fit in with our classical picture. 273 00:27:39,960 --> 00:27:44,950 This is one of the examples which is often presented as a. 274 00:27:46,080 --> 00:27:49,260 Sort of a typical archetypical experiment. 275 00:27:49,410 --> 00:27:56,640 You say here we have an electron gun or something which fires particles as a screen behind. 276 00:27:56,970 --> 00:28:04,110 And there are a couple of little slits here. Now, the thing is. Every time a particle goes through, look at the next picture. 277 00:28:04,160 --> 00:28:08,580 This is the B part. One of the slits is now closed and the other slit is open. 278 00:28:08,820 --> 00:28:15,540 And as you follow these electrons through, they make individual points, particle like behaviour on the screen. 279 00:28:16,020 --> 00:28:22,320 But these points are sort of concentrated more or less in the middle where the straight line through the slit would be, 280 00:28:22,500 --> 00:28:24,760 but with a bit of scatter from one way or the other. 281 00:28:25,050 --> 00:28:30,209 If you close that slit and open the other one, you've got a very similar picture slightly shifted to the left, 282 00:28:30,210 --> 00:28:34,890 to the right, but nevertheless very similar particle like behaviour. 283 00:28:35,250 --> 00:28:37,980 If you open both slits, you get magic. 284 00:28:38,490 --> 00:28:45,360 Suddenly the two possible things that the electron might do, each one seems to interfere with the other possibility. 285 00:28:45,630 --> 00:28:49,800 And in some places you find where it's not p. I think I've got the right one. 286 00:28:50,370 --> 00:28:53,430 You find that they sort of cancel out the two different possibilities. 287 00:28:53,440 --> 00:28:57,000 Little places they enhance each other, which is very, very strange. 288 00:28:57,450 --> 00:29:01,229 And so you have to attribute wavelike behaviour to the particles and they now 289 00:29:01,230 --> 00:29:04,860 behave like waves and it's as though they have to pass through both slits at once. 290 00:29:05,250 --> 00:29:10,829 So it's very much part of standard quantum mechanics, it's part of the the Feynman diagrams, 291 00:29:10,830 --> 00:29:15,510 things like playing before you need to add them together because that means all these different things might happen. 292 00:29:15,600 --> 00:29:21,900 It's not just one process, it's all the possible processes have to be considered as somehow coexisting. 293 00:29:22,380 --> 00:29:27,610 So the particles and this is what happens with individual particles, they can be in two places at once. 294 00:29:28,050 --> 00:29:35,520 Ridiculous idea. If you have a, you know, old fashioned Newtonian and so on, way of thinking, classical way of thinking about particles. 295 00:29:35,730 --> 00:29:41,310 They have individual locations, but quantum mechanically, they can cohabit in different well, that's the wrong word. 296 00:29:41,430 --> 00:29:47,280 They can co-exist in different places. And that's certainly the way you understand quantum mechanics. 297 00:29:47,850 --> 00:29:53,790 It works fine for particles. It even works fine for big things like buckyballs. 298 00:29:53,800 --> 00:30:00,030 These are molecules which involved 60 or 70 carbon atoms, but still they're not that big. 299 00:30:00,270 --> 00:30:06,930 You can't see them. But Schrödinger was worried about these things and he introduced his cat and he said, 300 00:30:07,230 --> 00:30:14,580 If you follow my career that's treating this equation, you would have to consider that a cat could be alive and dead, same time. 301 00:30:14,700 --> 00:30:18,330 Well, this is my version of the cat. It's a little bit more humane than Schrödinger's version. 302 00:30:18,820 --> 00:30:24,750 Yeah, the cat. You see, I have a room, and in this room there are some nice tempting food. 303 00:30:24,930 --> 00:30:31,739 And the cat wants to get in and have some food. It's a bit more like John Bell's version, meaning he had the full cat in the empty cat. 304 00:30:31,740 --> 00:30:40,570 But that's a different version. Here. Here. What I've got is up at the top, a thing called a beam splitter that sends individual. 305 00:30:41,260 --> 00:30:45,000 Well, there's a laser at the top that's marked. I think it's a laser. 306 00:30:45,360 --> 00:30:52,200 And then you see, oh, sorry, I still can't get hang of her with pressing the right, but here we go. 307 00:30:52,260 --> 00:30:56,489 That's it. And then there's a mirror here. I think of that as a half silvered mirror. 308 00:30:56,490 --> 00:31:01,410 So every time we've just emits a single photon, single photon, 309 00:31:01,650 --> 00:31:08,520 it hits the beam splitter and the photon now shares its existence between being reflected and transmitted. 310 00:31:08,910 --> 00:31:16,049 That's the way you have to understand quantum mechanics. So this thing goes both ways, and if it goes one way, it opens the door. 311 00:31:16,050 --> 00:31:21,900 If it goes the other way, it opens the door. If it's reflected overspeed or you go straight through, it is open to be a door. 312 00:31:22,380 --> 00:31:28,320 And therefore, because the particle was in superposition of being in those two positions. 313 00:31:28,320 --> 00:31:36,330 Schrodinger's equation if you follow this equation along, you say, yes, the doors have to be one open superimposed with the other open. 314 00:31:36,660 --> 00:31:40,240 They're both. It's sort of both at once happening. What does a cat do? 315 00:31:40,260 --> 00:31:45,180 Well, the cat becomes superimposed between going through one door and the other door, and it goes and gets its food. 316 00:31:45,360 --> 00:31:52,580 It's like the particle going through the two slits, and you have to consider that both alternatives are coexist, 317 00:31:52,590 --> 00:31:57,210 even if the cat gets happily eating its food at the other end as one single cat is 318 00:31:57,450 --> 00:32:02,210 free is its history would have been shared between those two doors and shutting. 319 00:32:02,220 --> 00:32:05,730 We say that's a load of nonsense. That's the implication of his equation. 320 00:32:06,180 --> 00:32:12,540 And well, he said he complained about say what he complained about in the minute. 321 00:32:12,900 --> 00:32:16,890 And I wanted to explain a little bit more about quantum mechanics. 322 00:32:17,910 --> 00:32:27,450 You might ask what on earth this has got to do with it? Well, you see, I was invited to give a lecture by the Hans Christian Andersen Society. 323 00:32:28,710 --> 00:32:35,820 It was coming up to Hans Christian Andersen's 100th 200th anniversary, and they had various people giving lectures. 324 00:32:35,820 --> 00:32:40,950 And they asked me to give a lecture, and I wondered why on earth they'd asked me to give a lecture on fairy tales or something. 325 00:32:41,540 --> 00:32:48,120 And then I thought, Well, I've had used the title The Emperor's New Mind, which was a play on the Emperor's New Clothes. 326 00:32:48,480 --> 00:32:51,450 And I thought maybe that was what they wanted to hear about, 327 00:32:51,450 --> 00:32:56,549 but I didn't think I would talk about that because I was more interested in foundations of quantum mechanics at the time. 328 00:32:56,550 --> 00:33:00,300 And I went through and thought about all different Hans Christian Andersen stories. 329 00:33:00,630 --> 00:33:07,300 And occurred to me that the story of The Little Mermaid in various different respects would illustrate very well what I meant. 330 00:33:07,320 --> 00:33:12,210 So this is what this is. It's The Little Mermaid. And what's she doing? 331 00:33:12,870 --> 00:33:21,000 Well, I did talk about this in this lecture, but then I had to give another picture, which is what it's about. 332 00:33:21,480 --> 00:33:26,100 So the bottom part of the picture is the quantum world, in a sense. 333 00:33:26,490 --> 00:33:31,200 This is where Schrodinger's equation holds. Well, it's an interesting question. 334 00:33:31,200 --> 00:33:38,040 Does it hold always or not? You see, Schrodinger's equation is describes how the quantum world behaves. 335 00:33:38,370 --> 00:33:42,270 And I use the word letter U for that. It stands for unitary evolution. 336 00:33:42,570 --> 00:33:46,980 This writing equation is an unitary evolution of more or less interchangeable for our purposes. 337 00:33:47,370 --> 00:33:53,429 So unitary evolution is the way in which the state, the quantum state evolves. 338 00:33:53,430 --> 00:33:57,540 It evolves in this very particular way, deterministic way. 339 00:33:57,690 --> 00:34:01,080 The state, which describes the quantum world, evolves in this way. 340 00:34:01,830 --> 00:34:07,500 And that is a mysterious way with things all sort of entangled up with each other and things that we don't understand. 341 00:34:07,650 --> 00:34:13,020 So I've illustrated that with strange sea creatures and all tangled up in various ways, and that's the quantum world. 342 00:34:13,350 --> 00:34:22,290 At the top we have the classical world. I use the word sea for classical world classical equations, and that includes Newton's equations. 343 00:34:22,290 --> 00:34:26,460 Einstein's equations. Max was the wonderful equations for electromagnetism. 344 00:34:26,940 --> 00:34:30,180 And that's the classical world at the top. The mermaid. 345 00:34:30,280 --> 00:34:33,420 She shares both worlds. She's the magic part. 346 00:34:33,660 --> 00:34:37,830 And that is what the letter R is being used for. That's the reduction of the states. 347 00:34:38,310 --> 00:34:41,610 And I want to explain what the reduction of the state means. 348 00:34:41,910 --> 00:34:48,180 There is also a feature of this picture, which is slightly oddly drawn deliberately, 349 00:34:48,510 --> 00:34:55,380 that the not only is the mermaid sharing these two worlds, but somehow she if you look at the top part, 350 00:34:55,530 --> 00:35:03,389 she's looking down on on the classical world from a new height, which is the experience she gains from the quantum world, 351 00:35:03,390 --> 00:35:07,920 which sheds light on the classical world that people didn't appreciate before. 352 00:35:08,250 --> 00:35:12,090 But anyway, let me explain how we do quantum mechanics. 353 00:35:12,810 --> 00:35:16,530 You see, this is the way quantum mechanics is used in practice. 354 00:35:17,130 --> 00:35:23,370 The letter U. Or Quantum States is the thing, the upward line on the left. 355 00:35:23,880 --> 00:35:28,050 That's the quantum state. And this is time, not horizontal in the particle physics way of writing. 356 00:35:28,050 --> 00:35:28,410 Fine. 357 00:35:28,740 --> 00:35:37,290 And here we have the state represented by this graph, and it evolves in this deterministic way, according to you, according to this writing equation. 358 00:35:37,530 --> 00:35:41,940 And then every now and again, you do what's called, well, making a measurement or something, 359 00:35:42,240 --> 00:35:46,350 which is the reduction of the quantum state or the collapse of the wave function. 360 00:35:46,650 --> 00:35:53,850 And suddenly we reinterpret the state as a set of alternatives, depending on what measurement you're doing a very crazy thing to do, 361 00:35:54,180 --> 00:35:56,490 but nevertheless, that's what you have to do in quantum mechanics. 362 00:35:56,760 --> 00:36:04,799 And one of these alternatives seems to be what comes out, and that's probabilistically you have this deterministic evolution, 363 00:36:04,800 --> 00:36:10,080 and then suddenly a probabilistic, probabilistic decision is made by the universe. 364 00:36:10,080 --> 00:36:13,860 It chooses one or the other or the other, and that now evolves according to you. 365 00:36:14,070 --> 00:36:17,280 And then again, one of these is chosen and then evolves according to you. 366 00:36:17,280 --> 00:36:19,620 And so I'm like, that very strange. 367 00:36:19,980 --> 00:36:27,450 And Schrödinger made this comment, went to Niels Bohr, and I think he was staying with Bjorn Heisenberg was there and he said, 368 00:36:27,450 --> 00:36:35,430 well, if, if it weren't for if this dam jumping, if we catch the jumping with it suddenly jumps to one of these individual states. 369 00:36:35,700 --> 00:36:40,920 If this random jumping is here to stay. I'd wish I'd had never had anything to do with quantum mechanics. 370 00:36:41,370 --> 00:36:46,500 Well, the other to try to encourage him and get him out of his misery state. 371 00:36:46,800 --> 00:36:51,600 Nevertheless, he appreciated that there's something very strange about what this going on. 372 00:36:51,600 --> 00:36:54,840 It's not the way the world that we perceive behaves. 373 00:36:55,170 --> 00:36:58,440 Some people say, well, you know, the world really does behave according to you. 374 00:36:58,440 --> 00:37:02,310 And all these two alternatives coexist. I'm not taking that view. 375 00:37:02,640 --> 00:37:09,630 Well, that's quite popular here in Oxford. And I'm not saying that's called the many worlds or many universes view or something. 376 00:37:09,930 --> 00:37:14,340 I'm not taking that view. I'm just I want to describe the world we actually see about us. 377 00:37:14,640 --> 00:37:20,470 And that does behave according to this strange thing. And that is not explained by the unity. 378 00:37:20,610 --> 00:37:25,110 Many people try to get this picture as a sort of approximation thing, but I don't think any of it works. 379 00:37:25,590 --> 00:37:34,140 If the unitary evolution is all that happens, you don't get this picture that we seem to observe. 380 00:37:34,680 --> 00:37:41,700 See, this is the faith, if you like. Quantum mechanics works so well, does works extraordinarily well for small things. 381 00:37:42,570 --> 00:37:45,780 And you have problems when you have large things like cats or black holes. 382 00:37:45,780 --> 00:37:51,600 You have bad things there, too. But people, they build up this quantum faith. 383 00:37:51,990 --> 00:37:57,059 And faith is that you must hold at all levels. And I'm arguing, no, that can't be true. 384 00:37:57,060 --> 00:38:00,960 There must be a bigger theory. And it certainly. Is that not the truth? 385 00:38:01,020 --> 00:38:04,169 Just writing a thought this. Einstein certainly thought this. 386 00:38:04,170 --> 00:38:10,560 Debray thought this. Who introduced the idea of particles having a having behaving like ways and so on. 387 00:38:11,010 --> 00:38:20,730 And even more surprisingly, Dirac, who is the person who really introduced the formalism that all quantum mechanics experts use pretty well. 388 00:38:21,210 --> 00:38:28,050 And there's a nice quote in my book which shows that Dirac also thought that this quantum mechanics is provisional theory. 389 00:38:28,240 --> 00:38:33,450 Someday there will have to be a better theory in which this picture is made sense of. 390 00:38:34,050 --> 00:38:39,310 Now, my view is that it will only be made sense of when we bring general relativity into the picture. 391 00:38:39,330 --> 00:38:42,720 You have to combine quantum mechanics with general relativity. 392 00:38:43,020 --> 00:38:46,050 And by that I don't mean what people call quantum gravity, 393 00:38:46,170 --> 00:38:53,640 because quantum gravity means the rules of quantum mechanics applied to gravitational theory, in particular general relativity. 394 00:38:54,120 --> 00:39:00,870 But I think what one needs is a more evenhanded marriage, where there is a back reaction onto quantum mechanics itself. 395 00:39:01,290 --> 00:39:04,080 So it must be that there's give on both sides. 396 00:39:04,320 --> 00:39:10,710 Quantum mechanics has to give, as well as no doubt general relativity will give at some stage that quantum mechanics, 397 00:39:11,130 --> 00:39:15,570 in fact, is the more important, given my view is that quantum mechanics will have to change. 398 00:39:15,720 --> 00:39:20,430 This picture here is a space time picture. So that is my time going upwards. 399 00:39:20,880 --> 00:39:24,960 Oh, except happened. I've got jumped again. I really can't master this thing, I'm afraid. 400 00:39:25,470 --> 00:39:34,620 Here we go. At the bottom, you see two sizeable lumps of material which are put into a superposition of two places at once. 401 00:39:34,620 --> 00:39:40,590 You can do that with a beam. Splitters and things wouldn't be hard to do so that it would be here and here at the same time. 402 00:39:41,220 --> 00:39:45,600 Now, the question is, that's what the unitary evolution. 403 00:39:45,600 --> 00:39:49,170 The other thing would tell us, the Schrödinger equation that tells us, yes, it could be like that. 404 00:39:50,050 --> 00:39:53,220 I'm agreeing with that. But that wouldn't last. 405 00:39:53,430 --> 00:39:59,310 It would be unstable. And the thing is, the picture top here is the distortion of the space time. 406 00:39:59,460 --> 00:40:02,940 So if it's in one place, you can see the space time, a little wrinkle and it goes up. 407 00:40:03,270 --> 00:40:06,240 If it's in the other place, it's got a different little wrinkle which goes up. 408 00:40:06,600 --> 00:40:11,550 And these little curves at the side represent how the acceleration of freefall goes. 409 00:40:11,880 --> 00:40:19,470 And once you try to superimpose these ideas, you run into inconsistency with quantum mechanics, 410 00:40:19,860 --> 00:40:26,130 which is not normally recognised, but there is an inconsistency which begins to show up after a certain time. 411 00:40:26,370 --> 00:40:30,420 So there's a time scale that relates to how much mass is displaced. 412 00:40:30,990 --> 00:40:33,990 If it's more mass displaced, the timescale would be much shorter. 413 00:40:34,290 --> 00:40:37,500 If this there's a cat, it would be ridiculous. It would be instantaneous. 414 00:40:37,980 --> 00:40:45,960 If it's a very tiny thing, like protons, neutrons or something, then it would last a long time, probably longer than the age of the universe. 415 00:40:46,380 --> 00:40:49,530 So it's a huge difference depending on how big those things are. 416 00:40:50,690 --> 00:40:52,129 And here's the picture. 417 00:40:52,130 --> 00:41:00,500 I have probably a bit hard to see what's going on here, but basically it's a bit like the picture we just had, but it's evolving. 418 00:41:00,500 --> 00:41:05,080 So the bottom you have the to the the lamp is in one location. 419 00:41:05,090 --> 00:41:07,430 That's the thing at the bottom distorting the space time. 420 00:41:07,430 --> 00:41:16,370 You can see a little bit of a wrinkle in it and then it gets moved apart and you see the two space times then get different from each other. 421 00:41:16,670 --> 00:41:23,780 And when the whole difference, the region of difference becomes an order unity in what's called absolute units, 422 00:41:23,780 --> 00:41:31,340 absolute units of the units, when you take Planck's constant, basically equal to one speed of light one and the. 423 00:41:32,390 --> 00:41:40,280 Newton's gravitational constant equal to one, then that's the size, the units that you use, the crazy units to use in practice. 424 00:41:40,700 --> 00:41:48,800 But it does give you the sort of picture that in that sort of scale of time, a choice has to be made one or the other. 425 00:41:49,040 --> 00:41:54,679 So that's the way the world seems to behave. And you don't get the coexistence of different alternatives. 426 00:41:54,680 --> 00:42:02,960 You just get one or the other. In fact, they're one of the nice things about this sort of scheme is that it is open to potential experiment. 427 00:42:03,140 --> 00:42:10,459 You don't have to have accelerators bigger than the solar system, which you might have to to test the effect of quantum mechanics on gravity. 428 00:42:10,460 --> 00:42:15,140 But if it's gravity and quantum mechanics, this sort of thing might give an answer to it. 429 00:42:15,530 --> 00:42:21,530 And this is a sort of cartoon of an experiment which is being explored for, oh, 430 00:42:22,470 --> 00:42:30,800 couple of decades by now by Dirk Baumeister and his colleagues in Santa Barbara in the US and in Leiden in the Netherlands. 431 00:42:31,130 --> 00:42:34,430 And this is the cartoon, this picture of what how this is done. 432 00:42:34,640 --> 00:42:43,250 You have a laser at the left beam splitter in the middle, and the photon coming from the laser is split into two possible existences. 433 00:42:43,580 --> 00:42:48,200 One is caught in the in a in a cavity, which is up at the right here. 434 00:42:49,510 --> 00:42:55,419 That one. The other one is in another kind of cavity, a funny one which reflects backwards and forwards about a million. 435 00:42:55,420 --> 00:43:03,730 This goes a million times to about a million times. It hits this little tiny mirror, which is about a 10th of the thickness of a human hair. 436 00:43:04,300 --> 00:43:09,220 You just can't see it. And it hits it bangs about a million times. 437 00:43:09,220 --> 00:43:12,730 That's about enough to displace it by about the diameter of a nucleus. 438 00:43:12,850 --> 00:43:17,079 That's just about big enough that in seconds or minutes, the thing should, 439 00:43:17,080 --> 00:43:22,600 according to the scheme I just told you, become one or the other, and this would be detectable. 440 00:43:23,080 --> 00:43:27,430 And as I say, it's likely within within the next decade, maybe within the next five years, 441 00:43:27,790 --> 00:43:31,089 this experiment will determine whether or not this is correct. 442 00:43:31,090 --> 00:43:34,420 So watch this space. Okay. What about fantasy? 443 00:43:35,170 --> 00:43:41,110 When I talk about fantasy, I was aiming the thing at one particular thing. 444 00:43:41,110 --> 00:43:45,579 I'll tell you about that in a minute. The picture here is not the fantasy. 445 00:43:45,580 --> 00:43:51,489 This is more or less what we believe and what I believe also about the history of the universe. 446 00:43:51,490 --> 00:43:53,890 According to current theory and observation, 447 00:43:54,310 --> 00:44:05,200 what we seem to have the time is now going upwards as in that previous few pictures and this is the history of the universe. 448 00:44:05,200 --> 00:44:09,700 They think of sections through it, giving the space lectures. They can't draw the three dimensions. 449 00:44:09,700 --> 00:44:14,080 You just think of space as one dimension of this picture. You might ask what all this really stuff is at the back. 450 00:44:14,320 --> 00:44:18,190 That's just because I'm not trying to say the universe is open or closed. 451 00:44:18,190 --> 00:44:22,120 It might be closed up. It might be open. It doesn't matter for what I want to say here. 452 00:44:22,720 --> 00:44:26,950 We don't know. It's pretty close to being open, but that's not good enough. 453 00:44:26,950 --> 00:44:33,580 Might possibly be closed up. Now this you see there's an expansion which takes place. 454 00:44:34,750 --> 00:44:39,760 That's the big bang right at the bottom. It's fairly sedate expansion and then it starts accelerating. 455 00:44:40,000 --> 00:44:43,329 This is the accelerated expansion that seems to be observed. 456 00:44:43,330 --> 00:44:48,129 It's referred to as the mysterious dark energy. Sometimes it's in all the cosmology books. 457 00:44:48,130 --> 00:44:56,020 Since 1917, Einstein introduced an extra term into his equations for what actually turned out to be the wrong reason. 458 00:44:56,020 --> 00:45:03,670 Never mind, he did introduce it, and it is, as far as I know, in all cosmology books, all serious ones since that time. 459 00:45:04,330 --> 00:45:06,040 It's called The Cosmological Constant. 460 00:45:06,460 --> 00:45:14,770 And this does give this accelerated expansion, which was observed remarkable observations made at the end of the 20th century. 461 00:45:15,340 --> 00:45:18,910 And fine, that seems to be what's going on. 462 00:45:19,450 --> 00:45:25,240 And this expansion will presumably, according to Einstein's equations, will continue indefinitely. 463 00:45:25,660 --> 00:45:31,660 I'll come back to that later, which is a bit of a worry in some respects, but that's the picture that we get. 464 00:45:32,320 --> 00:45:37,540 But I want to worry about something slightly different here, namely that right at the very bottom, 465 00:45:37,540 --> 00:45:44,409 at the Big Bang itself, current cosmology says tucked into that little black spot which represents the Big Bang. 466 00:45:44,410 --> 00:45:48,010 Here is another version of this whole universe. 467 00:45:48,220 --> 00:45:51,640 Imagine this expansion going on far more than in this picture. 468 00:45:52,060 --> 00:45:58,660 I don't know how many more times, 60 times or something, and squashed into that little tiny point. 469 00:45:58,990 --> 00:46:02,950 And that's what's called inflation. And inflation was introduced for various reasons. 470 00:46:03,580 --> 00:46:13,270 Most of them, in my view, are not correct, although subsequently some of the reason, some new reasons came out which are supportive of inflation. 471 00:46:14,050 --> 00:46:18,970 Just show you how good my predictions are here. When I first heard of inflation, I thought it wouldn't last a week. 472 00:46:19,750 --> 00:46:25,510 It's now, of course, fundamental to cosmology, and I was wrong again. 473 00:46:26,650 --> 00:46:35,320 But nevertheless, I don't have a great deal of faith talking about faith in the inflationary scheme. 474 00:46:35,680 --> 00:46:41,409 And one of the reasons, one of the big reasons is that I don't believe that it explains one of the early things. 475 00:46:41,410 --> 00:46:48,219 It was therefore see one of the strange things about the universe is its very, very great uniformity in many respects. 476 00:46:48,220 --> 00:46:54,160 It's very, very uniform and the idea of inflation was that somehow it could have been very irregular to begin with, 477 00:46:54,370 --> 00:47:00,850 but it kind of got stretched out by this inflationary phase and produced this very uniform universe. 478 00:47:01,210 --> 00:47:06,190 Now, I want to explain a bit why I don't believe that. But first of all, let me just give you some hint. 479 00:47:06,430 --> 00:47:10,450 You see, you have to introduce an extra field, which is called the inflation field. 480 00:47:10,720 --> 00:47:15,190 This is some funny particle which is not part of current particle physics. 481 00:47:15,580 --> 00:47:19,120 But nevertheless, people need to introduce this. 482 00:47:19,450 --> 00:47:25,899 And these curves here are taken from various books and articles which are just to show that this curve, 483 00:47:25,900 --> 00:47:35,410 which represents the sort of potential function, the important thing that this field has and they are drawn just to make it have the right properties. 484 00:47:35,650 --> 00:47:38,830 And you see the different people have different ideas for the shape of the curve. 485 00:47:39,140 --> 00:47:46,270 The good reason being that there is no good theory which gives you a shape that they want, so you more or less draw it by hand. 486 00:47:46,450 --> 00:47:52,080 So that's just to show you that there is. No real acceptance of exactly what's going on. 487 00:47:52,590 --> 00:47:58,050 But if it has these various things, the claim is it does produce this expansion over these pictures. 488 00:47:58,380 --> 00:48:04,780 These pictures are just to indicate one of my problems with inflation actually earning the universe out. 489 00:48:04,800 --> 00:48:12,200 I should say that the inflation field is like other fields in physics in that it's symmetrical in time. 490 00:48:12,210 --> 00:48:15,990 If you run the clock backwards, it works just as well as running the clock forwards. 491 00:48:16,410 --> 00:48:25,200 So what's happened if you run it backwards? Well, let's imagine the first two pictures represent a collapsing universe, but it collapses at the end. 492 00:48:25,200 --> 00:48:28,770 It might start by expanding the first one and then expand and then starts to collapse. 493 00:48:29,010 --> 00:48:35,880 Or it might be collapsing all the time. Doesn't make any difference. And all the possible things which might happen are that great mess at the end. 494 00:48:36,600 --> 00:48:40,440 That great mess at the end is really a congealing of all sorts of black holes and things. 495 00:48:40,920 --> 00:48:44,700 And when I gave you this number ten to the 10th of 124 at the beginning, 496 00:48:45,090 --> 00:48:51,930 that is how improbable it is that you get something which is nice and smooth at the end of a collapse. 497 00:48:52,410 --> 00:49:00,930 Now, that would apply just as much at the beginning. This shows you how improbable this very smooth thing beginning would be. 498 00:49:00,960 --> 00:49:05,970 And because the information field doesn't smooth out, that meant a great mess at the end. 499 00:49:06,120 --> 00:49:11,790 We're running the clock backwards. You get you could start off with something very irregular and you would still get this messes. 500 00:49:12,240 --> 00:49:18,300 It doesn't it explains that you can't answer all those irregularities. 501 00:49:18,540 --> 00:49:22,230 Basically, it's like if you have a fractal picture, you probably see as you expand them out. 502 00:49:22,380 --> 00:49:26,370 It still stays fractional no matter how much you expand it. And that's the sort of thing you've got to expect. 503 00:49:26,700 --> 00:49:29,370 That's the most likely thing in something like that. 504 00:49:29,760 --> 00:49:36,000 We had a very, very special initial stage, which was very smooth indeed, but not because of inflation. 505 00:49:36,150 --> 00:49:39,790 Inflation does not do that. However, it does do other things. 506 00:49:39,810 --> 00:49:42,960 Let me see where I am here. There's this is just explaining. 507 00:49:43,650 --> 00:49:48,210 Yes, inflation does do other things. And it's the reason it didn't die in a week. 508 00:49:48,300 --> 00:49:55,550 I think it's because of the other things it does and it does do things which let me not get into them now, I should say. 509 00:49:55,560 --> 00:50:02,280 But there are three good reasons two or three, and there are about four or five bad reasons, which I don't. 510 00:50:02,790 --> 00:50:08,849 Anyway, the two or three good reasons are good. So if you don't have inflation and I say I don't want inflation, if you don't have it, 511 00:50:08,850 --> 00:50:13,860 you've got to have another theory which gives the same explanations as inflation does. 512 00:50:14,130 --> 00:50:21,240 Now, I told you that this is the fantasy chapter, and I was regarding inflation and very many other more fantastical theories. 513 00:50:21,660 --> 00:50:30,030 And by the time between giving this title to the Princeton University Press and starting to write my book, I had my own fantastical theory. 514 00:50:30,330 --> 00:50:33,930 So I have a different point of view about fantasies. Now you say fantasy. 515 00:50:33,930 --> 00:50:36,660 We need fantasy. The world is so extraordinary. 516 00:50:36,810 --> 00:50:43,890 And it is when you think about quantum mechanics, so extraordinary that we need a fantastical theory, it's just got to be the right fantasy. 517 00:50:44,280 --> 00:50:47,970 So I'm trying to say inflation is a fantastical theory. 518 00:50:48,240 --> 00:50:53,280 It's not quite the right fantastical theory, but maybe it is in a certain sense. 519 00:50:53,310 --> 00:50:57,030 And what I'm trying to say, this is a picture of a black hole, which I'll come back to in a minute. 520 00:50:57,690 --> 00:51:04,050 Let me go back first. So what I am trying to say is that instead of tucked in right at the beginning, 521 00:51:04,560 --> 00:51:09,510 which is where inflation is, there is a sort of inflation, but it was before the big bang. 522 00:51:09,900 --> 00:51:13,180 Now, that's a very fantastical idea. I didn't think of that. 523 00:51:13,200 --> 00:51:19,920 That idea was, well, way back into the old cosmology models that were pretty big bang theories, but more recently, 524 00:51:20,580 --> 00:51:26,820 a theory due to veneziano, which also had an inflationary phase which was before the Big Bang. 525 00:51:26,880 --> 00:51:31,740 So I'm going to give you a scheme of that nature, but it's little different from any of those. 526 00:51:32,220 --> 00:51:36,720 And to explain the idea, let me first go back to the black hole. 527 00:51:36,720 --> 00:51:41,100 Well, I don't really want the black hole except to explain what all those little cones are. 528 00:51:41,610 --> 00:51:44,970 Those cones are to tell you causal behaviour. 529 00:51:45,150 --> 00:51:51,860 So this is a spacetime. And the first thing in order to get the spacetime to look like general relativity, you've got to put these cones on it. 530 00:51:52,440 --> 00:51:56,370 And what do the cones represent? Were they represent how light would behave? 531 00:51:56,760 --> 00:52:00,809 Think of the middle picture here. Light flash at the bottom. 532 00:52:00,810 --> 00:52:07,140 This is time going up the picture in the middle one. So that is time going up again. 533 00:52:07,530 --> 00:52:11,339 The flash of light spreads out. Here we have a three dimensional picture flash here. 534 00:52:11,340 --> 00:52:14,760 And the next moment is the sphere around the next moment, a sphere bigger than that. 535 00:52:14,760 --> 00:52:20,190 That's the flash coming out. These are different sections of this car. And of course, you have to add another dimension to get that picture. 536 00:52:20,370 --> 00:52:24,630 Now, I hope you're used to that manner. You have the passcode, which is a flash coming in. 537 00:52:25,140 --> 00:52:31,290 And what does this represent? It represents the speed of light. At any point, ordinary particles have got to have world lives. 538 00:52:31,290 --> 00:52:35,609 That's histories which are within the cone. And at every point you've got to have one of these cones. 539 00:52:35,610 --> 00:52:43,049 So that's what the pictures that I've been showing you here represent and a little bit more you see here is a a particle. 540 00:52:43,050 --> 00:52:48,150 And you can see its world line. Its history must be within the cone now. 541 00:52:48,720 --> 00:52:53,700 The picture that we have here. I'm sorry. I'm in the wrong way of having that minute. 542 00:52:54,270 --> 00:52:58,200 That is not quite the full kind of geometry you need. 543 00:52:58,350 --> 00:53:03,270 You want to have a scale as well. Now a scale is given by clocks. 544 00:53:04,330 --> 00:53:12,040 We know that there are extraordinary precise clocks now that, well, your GPS wouldn't work with if it weren't for extraordinary, precise clocks. 545 00:53:12,250 --> 00:53:18,040 But even a general relativity, you know, clocks more slowly if they're down there than if they're up there. 546 00:53:18,340 --> 00:53:23,230 But it doesn't have to be that much. It can be only a few. Only about a centimetre, maybe less than that. 547 00:53:23,500 --> 00:53:28,690 That people can measure the difference in clock rates that tiny distance. 548 00:53:28,930 --> 00:53:34,450 It's extraordinary. Why are clocks so precise? Well, there's a good reason why they're so precise. 549 00:53:34,870 --> 00:53:42,340 And that is that they the ordinary particles, massive particle stable, massive particles are clocks. 550 00:53:42,760 --> 00:53:52,480 This comes basically from the two most fundamental laws of physics or equations of physics of 20th century Einstein equals. 551 00:53:52,840 --> 00:53:56,140 And C squared, of course, is one of them. That's one of these two here. 552 00:53:56,350 --> 00:53:59,360 The other one is max planck's equals h new news. 553 00:53:59,360 --> 00:54:02,800 The frequency. Frequency is equivalent to mass. 554 00:54:03,310 --> 00:54:10,810 H is just a constant. Energy is equivalent to mass according to Einstein. 555 00:54:11,200 --> 00:54:16,040 So therefore, electric energy could. It's equivalent to Mars. 556 00:54:16,250 --> 00:54:20,690 So therefore, Mars sort of cancelling mass up between those two frequency. 557 00:54:22,320 --> 00:54:25,690 Is it? Sorry. Cancelling energy out between those two. 558 00:54:26,890 --> 00:54:31,240 Frequency is equivalent to mass. 559 00:54:31,630 --> 00:54:39,010 So any massive particle which is a stable, massive particle is a clock by these fundamental laws, very, very precise laws. 560 00:54:39,670 --> 00:54:42,729 Of course, the clocks that you actually have in practice aren't single particles. 561 00:54:42,730 --> 00:54:47,380 You've got to you've got to magnify that somewhere to make a clock that you can actually read the time off. 562 00:54:47,710 --> 00:54:55,120 But basically, it's because of this very fundamental nature of time which comes from these two basic equations. 563 00:54:55,480 --> 00:54:58,720 So clocks basically the mass of particles. 564 00:54:59,920 --> 00:55:06,399 Okay. So this is what I want to say. And the final thing here that okay, that is the picture. 565 00:55:06,400 --> 00:55:11,920 If you don't have clocks, if you have the clocks, then you have the full scheme that Einstein has. 566 00:55:12,220 --> 00:55:16,750 But you don't need the clock part for most of physics. 567 00:55:17,110 --> 00:55:25,239 Maxwell's beautiful equations electromagnetic equations describe electricity, magnetic magnetism and light doesn't need it. 568 00:55:25,240 --> 00:55:28,840 In fact, all it needs is the cones. You don't need the scaling given by the clocks. 569 00:55:29,650 --> 00:55:32,950 I should say that distances and times are equivalent because of the speed of light. 570 00:55:33,190 --> 00:55:36,310 The metre rule in Paris used to be the definition of metre. 571 00:55:36,520 --> 00:55:42,579 Now the definition of metre is just in terms of light seconds because that thing isn't good enough for current you. 572 00:55:42,580 --> 00:55:46,180 Just time measurements of what you use and speed of light gets you distances. 573 00:55:46,570 --> 00:55:51,190 So it's the time measurements which give you the scaling that you need in addition to these cones. 574 00:55:51,610 --> 00:55:56,080 But certain things in physics don't need that. Maxwell's equations don't. 575 00:55:56,230 --> 00:56:05,470 In fact, the strong and weak forces. Of particle physics don't need either, so they don't require the scaling. 576 00:56:05,770 --> 00:56:10,150 This geometry with the light cones is good enough. Now, when I say that. 577 00:56:11,240 --> 00:56:20,630 That's what's called conformal geometry. Now, if you didn't have any massive particles and in the very remote future, mostly it'll be photons. 578 00:56:20,750 --> 00:56:24,860 I remember you had this picture of the universe expanding, and it does expands and expands. 579 00:56:25,220 --> 00:56:27,900 And I was worried about this one time. It's an emotional argument. 580 00:56:27,920 --> 00:56:34,580 I admit that I was there thinking, goodness, if this universe is going to go on and on and on and on, and it's going to be incredibly boring. 581 00:56:35,000 --> 00:56:38,540 It's already pretty boring by the time there's nothing left but black holes. 582 00:56:38,690 --> 00:56:43,910 It's even more boring when the black holes finally evaporate after a Google years and there's nothing left. 583 00:56:44,210 --> 00:56:48,380 That's the very boring era. And then I thought, Well, who's going to be bored by that? 584 00:56:48,380 --> 00:56:51,470 Not us. But mainly it's going to be photons around. 585 00:56:51,470 --> 00:56:57,920 It's very hard to borrow a photon, partly, of course, because photons probably feel anything, but never mind. 586 00:56:58,100 --> 00:57:03,410 The real reason is because photons don't measure time if they travel along the light cone. 587 00:57:04,430 --> 00:57:10,460 The time between the creation of a photon and its reception somewhere else is zero as far as that photon is concerned. 588 00:57:11,180 --> 00:57:17,600 So right out to infinity is zero. So the end of the universe comes zapped like that if you're a photon. 589 00:57:18,260 --> 00:57:23,390 Well, you see, this ties in with something else, which I illustrate here. 590 00:57:24,500 --> 00:57:31,340 Those are the different clocks going on. And if they get up to lose the light cone, they don't experience any time. 591 00:57:32,540 --> 00:57:39,260 This is a wonderful picture by the Dutch artist M.C. Escher, and it illustrates a kind of geometry. 592 00:57:42,010 --> 00:57:48,100 Called hyperbolic geometry. Don't worry about that too much. But you see, this is what's called a conformal picture. 593 00:57:48,340 --> 00:57:53,200 These fish, I think they're fish. As you get closer and closer to the edge, they get smaller and smaller. 594 00:57:53,650 --> 00:57:58,900 But they are. It's a conformal picture. So you see the eyes of a fish that exact circles. 595 00:57:59,140 --> 00:58:01,480 They remain exact circles right up to the edge. 596 00:58:01,870 --> 00:58:09,460 So although that is infinity as far as the fish are concerned, if you look at it from this picture where large and small and equivalent, 597 00:58:09,790 --> 00:58:15,489 but as long as you squash uniformly in each direction, that's what's going to conformal in space time. 598 00:58:15,490 --> 00:58:20,140 It means you keep your light cones, you squash the space in the time by the same amount. 599 00:58:20,530 --> 00:58:27,310 Then the most of physics doesn't notice the difference. The only in physics which does notice the difference is where mass comes into it. 600 00:58:27,800 --> 00:58:32,200 Remote future photons. They don't care about mass. What about the Big Bang? 601 00:58:32,500 --> 00:58:38,140 That doesn't care about mass either? Because the energies get so big that mass becomes irrelevant. 602 00:58:38,740 --> 00:58:45,280 You may have heard people talking about the Higgs particle and when temperatures get higher than the fact of mass of the Higgs particle, 603 00:58:45,280 --> 00:58:49,000 then particles become massless. So they're massless at both ends. 604 00:58:49,240 --> 00:58:56,260 If they're masses at both ends, the physics which is relevant is the physics of this conformal geometry. 605 00:58:56,290 --> 00:59:00,220 So think about this Escher picture. Infinity is a nice, finite place. 606 00:59:00,670 --> 00:59:06,280 So if you were a conformal person, somebody who didn't have mass, then that would just be a boundary like everywhere else. 607 00:59:06,910 --> 00:59:16,330 Well, it's just a boundary. So here is the picture I have and you see the line across the middle if you're below it. 608 00:59:17,260 --> 00:59:22,090 That is. Their remote future. That line represents your remote future. 609 00:59:22,510 --> 00:59:27,630 If you are above it, that represents somebody else's big bang and you see it, 610 00:59:27,640 --> 00:59:35,440 the squashing down of infinity gives you a finite boundary and the stretching out of the Big Bang gives you a finite boundary. 611 00:59:35,920 --> 00:59:41,770 And the idea is that that would give you a cosmology, which is my crazy cosmology. 612 00:59:42,430 --> 00:59:47,260 You see here on the left, we see a picture more as I had before, which is. 613 00:59:48,820 --> 00:59:55,450 I think that's meant to be. Ah. Ian, I'm calling. That's Ari on a picture of the universe before it. 614 00:59:56,460 --> 01:00:02,460 Which instead of being tapped into its big bang before it was this entire aeon, before that was another aeon. 615 01:00:02,610 --> 01:00:05,810 After I's will be another one and so on. And these are stuck together. 616 01:00:05,820 --> 01:00:10,120 If you stretch out the big bang and squish down infinity, then they all fit nice and smoothly. 617 01:00:10,440 --> 01:00:17,430 And so this is the crazy scheme. I call it conformal cyclic cosmology, which I think explains the thing for inflation. 618 01:00:17,700 --> 01:00:20,440 It does also explain the smoothness of the Big Bang. 619 01:00:20,820 --> 01:00:27,630 It's a nice way of looking at how to describe the smooth as the Big Bang, which is due to Paul Todd, my colleague here in Oxford. 620 01:00:28,050 --> 01:00:33,480 And this was a way of characterising the way in which the Big Bang was special. 621 01:00:33,480 --> 01:00:37,140 That's the ten to the ten 224. I told you the one. 622 01:00:38,120 --> 01:00:45,770 Thing or the one the few which are the one out of that 110 to 104 will be the smooth ones that we seem to have. 623 01:00:46,160 --> 01:00:53,690 And to have those ones you get automatically with this scheme because it's got to fit smoothly onto the remote future of the previous one. 624 01:00:53,870 --> 01:00:57,380 Well, I think I probably mystified you enough in calling an end to this. 625 01:00:57,530 --> 01:00:58,780 Thank you very much. Thank you.