Origin and Fate of the Universe

0:00 So we are delighted to invite you today to this exceptional seminar by Professor Roger Penrose, who is a professor at the Mathematical Institute at the University of Oxford. In a moment, Prof. Alejandro Perez will introduce quickly his work, but first let me introduce Prof. Jean-Paul Caverni, who is Vice President of the Anidex Foundation and of Ex-Marseille University. We are very grateful with Amidex Foundation and thanks to this financing, we are able to organize this exceptional seminar. Amidex gave us a label of Academy of Excellence for our Master 2 program, which is a Master 2 label in theoretical and mathematical physics, particle physics and astrophysics. and it is thanks to Amidex and this label that we are actually able to finance such exceptional seminar as the one given today by Professor Pennell. So Professor Caverni apologizes for, due to all the obligations, he won't be able to stay for the presentation of Professor Pennell today. So, dear sir, first of all, sorry for my very badly speaking. I am delighted to have come to you in Ex-Marseille on behalf of Professor Vara, the university president, who is currently in the United States to a convention with the University of Wisconsin. Within the framework of a French programme in Destrointes for Future, Ex-Marseille has been selected as a place of scientific excellence. This label called AMDEX is granted 25 million euros a year, at least for four years and

2:30 for eternity if we perform well. One of the reasons of such a distinction is the quality of the researchers in physics, particularly but not only at the Centre for Particle Physics of Marseille and at the Centre for Theoretical Physics in alphabetical order. Congratulations and thanks to all their members. The ABIDEX means allow us to support research and teaching project after international selection. Last year the Master of Theoretical, Physics and so on has been labeled. It is one of the 23 library projects driven by physicists. 23 over 103. So, I received an instruction to be short, only two minutes. So, it is in this context that we have the honor to welcome the Renault Scientist Bureau. We thank you warmly for your presence. Thank you. Okay, so I'd like to introduce our speaker. Professor Penrose is an Emeritus Roosevelt Professor of Mathematics in the Mathematical Institute of the University of Oxford and an Emeritus Fellow of the Watham College. He is one of the most influential figures in the field of general relativity, Einstein's theory of gravity. Among many awards and honors, he has received the World Prize of Physics in 1988 together with Stephen Hawking. The World Prize is regarded by many as the most important prize after the Nobel Prize. he received the prize for his contributions to the understanding of the theory of general relativity the physics of black holes and cosmology

5:00 enlarging our comprehension of the possible origin and fate of the universe in addition to several specialized books he has written many other books aiming at a broader audience these are The Emperor's New Mind in 1989 in 1994, The Nature of Spacetime with Stephen Hawking in 1996, The Road to Reality in 2004, and more recently, Cycles of Time and Extraordinary New View of Our Universe in 2010. These books are not quite like other popularizing books in two respects. On the one hand, the use of simplified language never compromises the rigor of the scientific statements, and Within the pages one can find treasures of ideas and insights which are of great interest for the specialists. In these books one can find profound thoughts and insights into the hardest problems of contemporary physics, science in general, such as the physics of quantum reality, the nature of understanding and consciousness, and the subject of today's lecture, the origin and the fate of our universe. So to finish this short introduction, I just want to show up some pictures of Professor Penrose. Most of the results, general relativity is a theory of the geometry of space-time. So geometry and pictures are very important for the description of reality and of the gravitational theory. And most of the contributions of Professor Penrose have a sign of it that can be represented in terms of pictures. Now this has a long history, I think, of his work. and the story tells that back in the 50s he went to a conference in Amsterdam and visited by chance an exhibition by M.C. Escher the artist M.C. Escher and he was strongly influenced by his art and started to think about impossible figures geometric figures that are impossible to realize in the real world like this one that is known as the tree bar and established some communication with M.C. Escher, his father and himself,

7:30 that ended up influencing some of the art of the artist, like is the case of these very well-known waterfalls of M.C. Escher. Beautiful pictures also come up with the perostylings that some of you might be familiar with these are pavings of the two planes which are not not periodical non-periodical pavings of the plane and have also influenced other areas such as architecture this is the the mathematical institute in oxford where you can see a realization of these pavings and in the ANC University in Texas so with this let please join me in welcoming Professor Roger Fernandes Thank you very much for that very generous introduction. It's a great pleasure for me to be in Marseille and to appreciate the beauty of the city and the surroundings and these old friends as well. I was interested to hear that the funding is for eternity because eternity will play a big role in what I have to say in my talk in fact it features in the very first picture well this is the first picture here we have I almost had everything at the ready but I forgot, no this will do I need something to point with this is a portrait of the universe it's a space-time picture so we have time going up the picture which most of my diagrams will feature time going upwards and you think of space as being horizontal slices through this

10:00 and so you might like to imagine three-dimensional space of course I can't draw all the dimensions pretend that three dimensions of space is depicted in one dimension cutting across. So here there will be the Big Bang and then the universe expands and then it continues to expand and now it is starting to accelerate in its expansion. This is the observed fact which was considered to be a great surprise when observed but on the other hand it's a feature of Einstein's theory if you incorporate the cosmological constant which was something he introduced in 1917, admittedly for the wrong reason, but it's there in all the cosmology books, and so I was a bit puzzled by why people were surprised by this, because it was one of the clear alternatives. But it's nice to have a clear evidence, and it won the Nobel Prize a few years ago for the observational fact that this accelerated expansion is taking place. To me, this is just an indication that this term in Einstein's equations, which lambda, the cosmological constant, actually has a positive value. It will feature very strongly in what I want to say, so I'm glad to know that it's there. In fact, it was from the stimulus behind the small. Now, what about the slices, horizontal slices? You might wonder what all that stuff is at the back. Why is all that fruity thing at the back? Well, that is because I do not want to prejudice the issue as to whether the universe closed or spatially open. It might be closed up at the back or it might be open. That does not matter for what I want to say. It's perhaps useful to see what the different alternatives are. You mentioned, Alessandro mentioned the Escher pictures and models. This is an Escher model and these are Escher pictures illustrating the three different possibilities for a uniform have positive curvature, that's the K, and close up around itself. So you have a three-dimensional version of the sphere, or this is the Euclidean plane and a three-dimensional Euclidean plane. And this example here is what's called hyperbolic geometry. That will feature in what I want to say quite strongly, not because I believe that the universe

12:30 is necessarily negatively curved, but because this particular representation is of importance because you see all these angels and devils crowd into this finite region but it's not really finite, it's an infinite universe and you have to imagine that the devils are all the same no matter how far out they are, but they're squashed down so as to get the entire universe within this finite region and you have a nice smooth boundary to represent infinity So I'll come back to that. That would be an important feature in what I want to say is wrong. Okay, now you might ask, where are we in this picture? Well, I'm not quite sure, but some of it are up there. But I'm scared, of course. The accelerated expansion is beginning to make itself in evidence, but not hugely as yet. now there is one feature of this picture which you might think I have forgotten to put in and that is referred to as inflation well there are two reasons it's not in this picture one reason is, well maybe it is in the picture because inflation, if it took place would be right tucked up in that initial point and you wouldn't see it on the scale of this diagram, which is more or less overall for scale you would not see inflation at all it would be tucked into there on the other hand there's a second reason why it's not there which is that I don't really believe it it has some important implications in cosmology which at least one or two of them I will mention later it would be worth our while to have a look and see what it does look like so for that I need a good powerful magnifying glass and well It's not quite popular enough, but here we have a powerful magnifying glass. That's, if you want to know what that is, it's a handball. And what we see is this initial exponential expansion is very much like the exponential expansion that we see now. In fact, that is part of the inflationary scheme, is that there should be, in the very early universe, an exponential expansion. Now, there are several reasons for introducing this inflation. It was introduced mainly by Alan Root and Sardinsian people, but in my own view, some of those reasons are not correct, and there are about two good reasons.

15:00 So there are two good reasons for inflation and several not very good reasons. I'll say something about one of the not very good reasons shortly. I shall also say something about the good reasons later on. But there is a sense in which my model does have inflation in it, although it's not really tucked in there, in my view. It's something before the Big Bang. Now this is an idea which was actually put forward by Veneziano sometime before my own particular view on this, but my picture is similar to his in that respect, that there was in some sense a before the Big Bang, and in that before there was something like inflation. So let me try and explain that a little bit more. So in my view there wasn't inflation here, but it was before in some sense. Well, I want to do two things to my picture. I want to involve you with two mathematical tricks. These are tricks that have been used in cosmology for quite a long time, many decades. One of them is to squash down infinity, squash it down, to get a smooth future boundary. Well, this is actually the same thing that I was just referring to a minute ago. I should make sure I keep the experiences to hand. If you remember this picture here, here we have a universe which is very mentally uniform, but can be squashed down infinity to become a finite boundary. And this squashing is what's called a conformal squashing. So the squashing is in all directions at the same time. So if you looked at the devils close to the edge, if you magnified them up, they would look pretty well the same shape as the devils here, or the angels as well. But they would be much smaller, but stretched uniformly in all directions. And that's what's called a conformal mapping. So it's uniform in one direction as much stretch as you have in another direction. And that is what we're doing here. I'm considering squashing future infinity down to get this smooth boundary,

17:30 just like we have in the Escher picture. The second trick is to stretch the Big Bang singularity out to get the smooth initial boundary. So you stretch this out and you squash this down and there are two tricks. Those are just mathematical tricks for the moment. They will have more significance in what I want to say later on. One little thing is here that that universe has got a bit big for the picture, so let's have a little bit smaller. And you can see the tricks illustrated. Infinity squashed down to a conformal compression. They're both conformal maps. And the Big Bang stretched out to make a boundary there. Now, these tricks allow us to do... This is just mathematical tricks. Now I'm going to do something which is not so usual. I'm going to say apply those tricks but I'm going to say that in some sense they are real and that the stretched out big bang of our eon I'm calling this an eon will be the infinity of the previous eon squashed down so I'm applying to all I'm considering that our universe or I'm calling it our eon see the conventional view would be to say this is the entire history of the universe I'm saying, no, no, that's not the entire history of the universe. There was an eon prior to ours, there will be an eon subsequent to ours, there was an eon prior to that one, and subsequent there will be a succession of these eons, presumably extending indefinitely in both directions. And the join, the crossover, from each eon to the next, will be such that it is smooth. the conformal squashing of the infinity of the previous eon matches the conformal stretching of the Big Bang of the next eon. So that is the general picture, and I want to try and give reasons for, first of all, believing this is a nice thing to do, and secondly, maybe it's actually something true of the world. So, before getting on to that, I want to say something else about these tricks. And those are, the two tricks look very similar to each other, the other way around. One is squashing and the other is stretching. But logically, they are very different. Now, why do I say that? But you see, the squashing down of infinity

20:00 is something that you can do very, very generally. So there can be lots of irregularities here. There can be galaxies and so on. In the very remote future, there are general theorems, Helmut Friedrich, which tells you that if you have a positive lambda, that's the cosmological constant, a positive cosmological constant, then you can pretty well always do this trick. If you have an exponentially expanding universe, you can squash it down to form an infinity, which is a boundary, and which is completely smooth, squashing it down by this informal on out. However, the other, the stretching out of the Big Bang is an extremely strong restriction, which suppresses gravitational degrees of freedom. And I want to explain why that's a good thing too. The squashing out of the infinity is a good thing because you can always do it pretty well. The stretching out of the Big Bang is a good thing for a completely different reason. The different reason is that you can almost never do it. Now, why is that good? I'll come to that shortly. Anyway, you get the picture, the general picture. Now, the key thing which drives this picture is a very well-known principle of physics known as the second law of thermodynamics. Now, I'll say something a bit more about that in just a moment, but before doing that, let me discuss one of the main reasons for believing in the Big Bang anyway. You see, the reason originally came from solving Einstein's equations and the Russian mathematical physicist Friedman, Alexander Friedman, solved the equations for cosmology and he came to the conclusion that there was this initial singular state where everything is squashed down together and the densities become infinite and so on. Einstein didn't like that at all at first, but eventually he got converted to it from the observations, basically. didn't initially know, however, of the most important observation indicating that the Big Bang was there, namely the cosmic microwave background. Now these are, what's that mean? That is radiation which is coming in from all directions in space. A lot of things I mention here won Nobel Prizes at different times, and this one twice won the Nobel Prize at quite different times. Initially, by Penzias and Wilson, when they discovered this radiation coming in from all

22:30 It's, well, the graph that I'm, I'm going to mention two major features of this radiation. One of them is that it comes uniformly, very, very uniformly, from all directions in space at the same time, coming in in all directions, roughly the same temperature, the temperature being about three degrees above absolute zero. The second point is this curve. Now, what is this curve? Here, this is the frequency in this direction, and this is the intensity in this direction, and this curve is the famous Planck curve. I'll say something about it in a minute. But this is a theoretical curve, and what one finds is that the observations, when you see these things are error bars, but those error bars are exaggerated by a factor of 500. Probably they're better observations now, this is quite an old slide. But you see, if you squash down those error bars by 500, you will see that the observational points precisely lie on this curve to within the thickness of the incline. So we have an extremely good agreement between the theoretical curve and the observations. Now, what is the theoretical curve? It's what's known as the Planck black-body spectrum. It's what started off quantum mechanics at the beginning of the 20th century. and it's telling us. What's it telling us? Well, the curve is indication of what's called thermal equilibrium. Now, thermal equilibrium, first of all, one observed things like this, and Planck explained it and produced a mathematical formula for that curve, and this was very much based on the idea, the famous formula E equals H nu that Planck introduced. I'll come back to that. that play roles in what I want to say later. But the main point I want to say here is, well, what I want to say here is is something which is a paradox, almost a paradox. Now, I did mention the second law of thermodynamics. What does the second law of thermodynamics say? It says that entropy increases with time. Now, what is entropy? Entropy is, roughly speaking, that would be good enough for us here, a measure of randomness so it's telling us that things get more and more random as time goes on well we know this from all sorts of things if you serve a cup of coffee it gets more random we know things keep going wrong

25:00 unless things get random and so on it's a very familiar thing that things get worse all the time well that's not quite that but things get random if you just leave them alone well another way of stating the second law is that okay the entropy up with time, the entropy increases with time, but let's say the same thing in a different way. If you go back in time, the entropy goes down. So that means, if you look earlier, the entropy must be smaller and smaller and smaller and smaller until you get to the Big Bang. Well, what are we looking at in this curve? We're looking at, it isn't quite the Big Bang, but sometimes refer to this microwave background as being the sort of flash of the Big Bang cooled down by the expansion of the universe which in a sense it is but it's about 380,000 years after the Big Bang which is quite soon after the Big Bang really but the main point I'm trying to say is that we see this curve, this very close which is in very much in agreement with thermal equilibrium, what does thermal equilibrium mean? It means maximum entropy maximum entropy you go back in time entropy is supposed to be going down and down and down until it reaches a maximum something wrong with that you don't have to be a high class mathematician to see there's something funny going on there sometimes people will say well perhaps it doesn't matter because the universe was very small in those days and maybe there wasn't much room for entropy that's just wrong when you think about it that's not the right answer I want to give you what the right answer is and the right answer is something which when I say that's what the right answer is there's probably still a lot of argument about what the right answer is but it seems to me pretty clear what the right answer is it's not that the universe was small but it's the other part of the observation which I mentioned a moment ago that this radiation, the temperature as you go all the way around not only does it agree with the spectrum but it is very very uniform over the whole sky in other words you see something to one part in about 100,000 or something like that. Well, that would be... Let's imagine a situation where you're in a box and you have a gas which is sort of constrained in one corner

27:30 by some compartment here, and you release it and it spreads out over the box. Now, this would represent an increase in entropy. Time increases, entropy increases. And that, again, would be consistent with saying the sky. So again, we seem to be seeing high entropy. So that doesn't solve the problem. However, let's think of a slightly different situation. This is not a gas in a box, but it's a lot. I'm going to increase the scale, and I'm going to think of a lot of stars running around in some galactic scale box, and they are acting on one another gravitationally. Now what will gravitation do? Well, it tends to cause things to clump. So whereas the entropy from left to right, it doesn't look very much like it, because here you see it gets more and more uniform, whereas here it gets less and less uniform. So the thing about gravity here is it is universally attractive, so that if you see a uniform distribution, that actually represents a small entropy. So what are we seeing in the universe? We are seeing some combination of those two pictures. We're seeing something which, okay, is consistent with high entropy if we're just talking about ordinary matter running around, but is low entropy if we are thinking about gravity. And this, to me, is something which I don't know why cosmologists don't worry about it more. It's not a paradox, it's just a very strange feature of the Big Bang, namely that everything, pretty well, seemed to be high entropy, random, except gravity. Gravity was singled out as being the one thing which is not thermalised along with everything else. Gravity is set at a very low entropy state, and as the clumping increases, the entropy goes up. Now, an important feature of this is what happens in the limit. You see, here I have a little blob which is meant to represent a black hole. And a black hole, when it forms, represents an absolutely stupendous increase in the entropy. So the entropy is done shooting up when a black hole is formed. The clumping already makes the entropy go up, but when it makes a black hole, then it really shoots up. So this is consistent with the second law as long as you consider the gravitational effect as important.

30:00 In fact, it's vitally important. and let me explain the situation where we see it's most important well it's why we're here one of the reasons why we're here people might say why we're here well it's because the sun is there that's what gets life going and keeps it going and so on people often say well we get energy from the sun but that's not really quite right why is it not right? because energy is conserved and what really happens pouring energy into the earth and maybe in the daytime then in the night time it all goes back out again if it didn't all go back out again we would just get hotter and hotter and hotter well we're getting global warming not at the rate it would be if we didn't have anything going out at all it's because the dark it's not because the sun is there it's the combination of the sun being there and the dark sky if the whole sky was uniformly the temperature of the sun it would be completely useless What is useful is the imbalance between the hot sun and the dark sky. And it's the imbalance which gives us the low entropy. Now, you can see this more explicitly here. It's to do with the temperature difference and the energy. The photons that come from the sun are relatively high energy photons, yellow, basically. And the ones that go back are infrared. formula equals h nu, this means that the higher frequency photons here are more energetic than the lower frequency photons which go away, and therefore you need far more photons going away to carry the same energy as comes in from the sun. And since there are far more photons going out compared with the number coming in, that means there are many, many more degrees of freedom to spread the energy over, and therefore the entropy is much higher. And this is a point made by Schrodinger a long time ago in his famous book, What is Life? And he got into trouble because people complained about, you know, there wasn't energy or something, but it's an important thing. But, of course, the energy is important, but the key thing to what keeps life going is that we get the energy from the sun in a low-entropy form, or the low-entropy is the imbalance between these temperatures. Here we see the many, many low-energy photons going away and it spreads up, the degrees

32:30 of freedom and the entropy is much higher than here. And so the plants are clever enough, through photosynthesis, to make use of this to build up their substance and then we eat animals or plants, which eat plants, ultimately it's the plants, and that's what keeps us going. And the key point is that the sun is a hot spot in the dark sky, and why is that? exist, thermonuclear reactions and goodness knows what. But the key point is it's there at all. And it's only there at all because of gravitational pumping. If there were no thermonuclear reactions, the sun would still be hot rather than the rest of it. It just wouldn't last so long. It just got very hot and then it would die out. So the thermonuclear reactions keep it going and allow life to continue and so on. So it's very important to us. But the key point is that the sun is there at all and that is through gravitational pumping. And that is just the feature of what's going on here, you start off with a uniform distribution and the clumping takes place and although it hasn't got to the black hole, nevertheless, it's this reservoir of low entropy in the gravitational uniformity that we live off. And that is a key point. Now, I'm always very surprised why it is that cosmologists don't worry about this more. For example, with the inflation business there is no real explanation for why the imbalance between gravity and other things. It struck me that this is the key which needs to explain. But in order to understand this a bit more, we're going to have to think about what this limiting case is when you actually get a black hole. So what is a black hole? Well, here is a black hole. And you will see, this is an example of many of my pictures. It's a space-time picture again. Time is going up this way. Here we have some matter which is, as time evolves, clunked, and this is the case where it wasn't, the repulsive forces, the pressures weren't big enough to stop it collapsing, and so it went on collapsing until it hit this singularity in the middle. What are these little cones here? Well, those are the important features of the diagram, those are the things called light cones or null cones, and I'll need to say a bit about them. here we have a light cone technically I should call them null cones but I'll call them light cones, never mind about that depends on whether their local structures are spread out through the space

35:00 anyway, here we have a light cone and you must imagine that throughout the space-time the space-time is four-dimensional don't worry about, you can think of two space and one time, that's good enough for whatever I say and one of those dimensions is the time dimension and the other two, in this case or three, would be the space dimensions and this cone, at every point in space time there will be one of these cones theoretically there so although it's called a light cone it doesn't mean there has to be any light there it's what light would do if it were there so here we have a spatial picture and this I've got all the number of dimensions here that point represents a flash of light this is the next moment that represents that slice through the cone and this is a moment later So the history of the light flash is represented by the cone, and here we have the past light cone, which would be a light flash converging on that point. But these cones are there just as part of the structure of the space-time, they don't need light to be there, except for what light would do, the light thinking of as partibles of light here in this picture. The difference between these two pictures, this is special relativity, that's general relativity, special relativity, the cones are all uniformly arranged. When gravity is involved, the cones are not uniform. And you see that particularly in the picture for the graph hole, where the cones are sort of very non-uniformly arranged. But they represent the limit to what a massive particle can do. you see, the history of a massive particle has got to be such that it never travels faster than the speed of light and that's a local statement so what that means is that the world line that is the history of that particle must always be within the combs so that's the key point the world lines of particles must always be within the combs that means they're not perceiving the speed of light whereas a photon, a particle of light is allowed to travel the speed of light and does travel the speed of light for the cones all the time. When you go to general relativity, it just means the cones are not uniformly arranged, but the rules are the same. Massive particle must have a world line within the cones. The photon, massless particle, has its world line along the cones. And that applies in this particular picture here, where you see the thing about the black hole is that the cones get pulled in by the gravitational field,

37:30 and you have this thing called a horizon here, enough to find yourself in here, you're stuck. You see, there's no way of escaping and getting out here because your world line isn't allowed to exceed the speed of light. World lines are allowed to come in, but they can't go out. So you really are stuck. That's why it's called the event horizon. The thing in the middle is the singularity. That is a place where densities become infinite, space-time curvatures become infinite. The laws of physics go haywire as far as we know. we don't really know what happens. Quantum gravity is something which we don't fully understand happens, and everything goes wrong. But as long as you stay a safe distance, you don't have to worry too much about that. However, I do want to modify my universe so we can incorporate the picture of the black hole. And let's do that. I'm putting it on black holes. Here we are. I have the black holes. they congeal. You see here we have two black holes swallowing each other up to make one black hole. And that sort of thing will happen from time to time, and the whole universe will be inhabited by these black holes. Okay. Now, I want to say something about the second law again. And why? You see, one of the reasons that people introduce inflation was they like evidently. Maybe it was a great mess at the beginning and that mess kind of stretched out by this inflationary feature and made it all uniform. That was one of the original big arguments of inflation. I'm going to try and argue that that doesn't really work. And the way you argue that is to think of a collapsing universe. Now I'm not saying our universe will ever collapse or anything like that. It's just hypothetical. Think of a universe which is collapsing and has irregularities. So if it's like this, it has irregularities, and then it will build up and lead to black holes ultimately. So that's the sort of picture you get. But suppose we run the other way, and we'll suppose that the second law is working again in the direction of increasing entropy, well that means there's a tendency to include black holes and irregularities, and you get a thing like this. Black hole forming, and one unholy mess at the end like that. That is the general situation.

40:00 An enormous entropy at the end, and that is what one would expect in a collapsing universe state. Now, since that satisfies the Einstein equations and whatever equations you're using for the matter, and those equations are normally taken to be symmetrical in time, so that means that they would work just as well the other way up. So the question is, why wasn't the universe like that? wasn't the Big Bang like that. That's a far, far more likely situation than what we actually saw with the gravitational degrees of freedom not activated. And how much more general is this than this? Well, I'll give you a figure on that in a while. In fact, in the next slide, I've got a figure for it. Here we are. The Big Bang must have been subject to a huge constraint in the beginning. Now, the constraint is characterized by a number of something like this. I mean, how unlikely was, just by chance, how unlikely was that as compared to something like that? Well, I'll give you a figure for the amount of matter that's within the observable power of our universe in something like 1 in 10 to the power, 10 to the power, sometimes people see 123 out there doesn't make any difference in the argument it's not as though it's a small effect it's an absolutely vast effect but it doesn't affect the argument whatsoever the difference between 123 and 124 is just whether you take into consideration the dark matter previously I had taken into consideration dark matter, I'll come to that shortly dark matter, but if you do then this number goes up a bit it's a stupendous precision, whichever way you look at it well, I'm going to come to what my explanation for this is it needs an explanation, and for some reason cosmologists don't seem to bother much to produce an explanation for it's simply one of the biggest problems in cosmology and when you see a list of what the problems in cosmology are this one is never mentioned at least I've never seen it mentioned I've never mentioned it lots of times It's basically saying that gravitational freedom

42:30 are simply not excited in the early stages. Now I did have a way of saying this for a long time, which is to say the vile curvature hypothesis. But in order to explain what that means, I've got to say what the vile curvature is and that goes into more details of mathematics which I don't want to discuss here. So it's fortunate that my colleague Oxford Paul Todd produce a different scheme it's a much more elegant way of saying it, and I'm going to give you his version well, I'm going to give you his version in a minute so let's just bear with me for the moment and before giving you his version it's useful if I talk about something else first namely the other end, the future end of the universe this is to do with the Big Bang and why it happens to be special in some way but what about the future What's going to happen if you wait around in the universe? Well, it's going to be fairly boring for a while, mainly because there are black holes, things will form black holes, stars will die out, and the black holes will sit there. And what happens to them? Well, according to Stephen Hawking, and I'm agreeing with him, if you wait long enough, all the black holes will evaporate away. Now, they evaporate away because black holes have a temperature, Black holes are hot, is what Stephen said originally. And the smaller ones are the hotter ones. So the question is, what is the hottest black hole we have any reason to believe in? Well, the smallest ones, and those will be a few times the mass of the sun. How hot are they? Well, you've got to think about the coldest temperature that's ever been made on the Earth, and you won't be far wrong. So they're not very hot. They're pretty cold. The big ones are even colder. colder and colder, so you don't normally worry too much about the Hawking radiation because there's a lot of other things which are much, much hotter than that running around, and so what's that temperature but theoretically it's very interesting in sort of dynamical processes. Well, you've got this universe which is expanding exponentially and it will get colder and colder and colder and then the black holes no matter how cold they are will be the hottest things around. The little ones will go first they evaporate away the energy in the radiation that they have and then that carries mass away, e equals mc squared again,

45:00 and so the black holes will get less and less massive and disappear in what I'm calling a pop. I'm calling it a pop because on astrophysical scales it's not much of an explosion. It might be rather unpleasant around here, but never mind about that. the final pop is about sort of a big artillery shell which is astrophysically not important but then there's a big explosion which sort of goes on just before the pop how long do you have to wait for all the biggest well we don't quite know how big black holes are going to get but there are some pretty stupendous ones around something of the general order of several thousand million let's just think 4 times 10 to 10 the biggest one so far, but you must think of them around as big as, as massive as an entire galaxy, something. So how long will it take for them to disappear? Well, something like what's called a Google, yes. What's a Google? Well, it's not a very scientific term, it was entered by some mathematicians Yang San I believe it was about 6 it's what happens if you write 1, 0, 0 as opposed to 100 zeros that's a Google you have to wait about that in years which is a pretty long time and I can't think of much more which is more boring to wait than sitting around waiting for a black hole to evaporate however and here we get to the picture of the universe again This is totally not to scale, I should say, but they're going off pop one after the other. And it's pretty boring, but sitting around waiting for a black hole to go pop is about the most boring thing I can think of, except what happens after that. That's the very boring era, where there aren't even any black holes around. And I was worrying about this for a while. I don't know, that's what people do sometimes and you can't think of anything better than worry about. I was worrying about the future of the universe and how unbelievably boring it's going to be forever. I mentioned I was going to talk about eternity. This is real eternity. It was a very boring era. But then I began to think, well, who's going to be around to be born by that very, very boring universe? Not us.

47:30 But the main things that will be around will be things like photons. be around by a long shot would be photons. By far, the particles that will be around would be mainly photons. And there is something about photons which is important here. So let me say something about mass and time. In fact, we have, you see what might worry about how you make clocks in the inside? These days there are extremely precise clocks. Clocks which are so precise that the precision in them if they were around for the length of the time from the Big Bang to now, because I'm not thinking about the actual things that are going on in the universe, but that length of time, those clocks would still be accurate to some small fraction of a second. So that's pretty accurate. Now that accuracy comes from something I want to say in a moment. In fact, there are two ways you could think of building a clock. using nuclear clocks, which are extremely precise. The other is looking at dynamical closures going out in the universe. There are things like double pulsars, and so on, neutron stars running around each other, and these are gravitational things, and they are just about as accurate. So you have these two ways of making clocks, and both of them critically depend on mass. I'm not going to say too much about the black holes running each other, except that that's gravity, and gravity depends on mass, because mass, after all, is the source of gravity. So, mass has an essential role to play with gravity, but it has also an essential role to play in relation to time when we're talking about massive particles. And that really, if you want to make an atomic or nuclear clock, the precision in that depends on well, these two very fundamental formulae, the two most basic equations of 20th century physics, one, of course, is Einstein's The other is max Planck's E equals h nu, which I mentioned before. Nu is the frequency, and what these two equations tell you is that since you've got the same E on both sides here, you just eliminate that, those are the frequency and the mass are basically equivalent. Okay, there's this constant, which is the square root of the speed of light over Planck's constant. But the basic thing is, a massive particle of mass m is a clock of frequency nu. and so here we have the world line of that particle

50:00 it sort of wiggles at a very very precise frequency and that is what brings such precision in our clocks now suppose you didn't have any massive particles you'd have a bit of trouble making the clock so you can see here we have the picture here is meant to complete the pictures that I had before, I had these pictures of the light cones and light cones are most of the geometry of space-time, but they're not quite all the geometry of space-time. Most of it, you see there's a thing called a metric, and I'm not going to say much about the metric, but it's a thing which has ten independent components at each point, and Einstein's theory depends on this metric. The light cones are nine of them. So the light cones give you most of the structure. There's one other number, which is really the ratios of these, and 9mm are the ratios and the 10th gives you the scale and that scale is what gives you the metric over and above the 9 which tells you the logarithms. And how do you represent that? Well you see here I've got a theoretical clock that's a particle ticking away here and you might imagine different perfect clocks starting at some event here, ticking away and these bowl-shaped surfaces here represent what the different ticks of the clock would be. Relativity says that if you've got clocks moving at different speeds, then the first tick will be on some surface like that, the next tick there, the next tick there. The crowding of these surfaces gives you the independent number. The nine numbers give you where these orange cones are. The tenth number tells you how crowded these surfaces are. You see a photon running along here goes along the cone and never Photons don't notice the metric path. They don't notice the scaling path at all. They just notice the light turns. So now, let me rather than improve my picture of best time. Now putting in the crowdings of the surfaces here. this is a conformal structure this is the structure which is given to us when we have mass as well no mass, mass so that's the difference between the pictures in fact this shows up in the equations too

52:30 because the Maxwell equations tell us how electromagnetic fields behave tell us how light behaves and the Maxwell equations are invariant under scale change they just need to know the cones a remarkable feature of these massless equations. It's also true of the other forces of nature excluding gravity in things called Yang-Mills equations which describe weak and strong forces. They also classically don't need the scaling. So it's just a lifetime. They're good enough for that. Whereas if you've got mass around then you've got to know the rest of the matrix. So this is the important way to make. If there's no mass that's good enough. If there is mass I said there were just mainly photons around in the remote future so that means the geometry of interest to the contents of the universe is primarily simply the lightness and then you can do this trick here's the trick which says I've done it here just for the picture but it applies in space-time terms as well that conformally the step the angels and the devils know how big they are but if you just had light rays here then the edge of this universe would be of no consequence if you're just shooting out of the edge to be a little bit more precise about this you can squash down infinity that was the trick I mentioned about in the future you can squash down infinity and as far as massless particles are concerned they don't even notice the standard they're just shooting through you might say oh no you can't shoot through well, when the stars and photons are concerned it doesn't care it's just a puzzle that you stop it from going over the edge there now there is a little point here which I do want to mention is that you're not going to get rid of all the massive particles you see, the vast majority of particles in the moment future will be photons but they will be the odd-grown electrons and positrons and whatever neutrons that give a lot of protons to and you can't really get rid of all I'm going to postulate something some people say this is the weakest part of the theory maybe it is I'm going to postulate that there was a sort of anti-Higgs process we've heard about the Higgs mechanism

55:00 it's supposed to give us mass in the early universe come to that in a minute but the idea is that there's also something in the reverse sense where mass fades out and in the very remote future there is no remote mass mass in a very remote future. And so the universe carried on happily in some way after this future infinity. But then you might ask, well, what is supposed to be after the future infinity? And here we come to the argument I was making before with the Paul Todd suggestion, and I probably can't find the transparency which happens this one, which I'm trying to find. Let me see if I can find that. Well, it doesn't matter so much. I'll just say that his scheme was not to use the biocultimate hypothesis, which I suggested, but to say that the space-time can be extended conformally to something which is nice and smooth. So he's really saying that this picture that I started with, where the universe can be stretched out, the Big Bang can be stretched out to form a nice smooth initial state, that is a form of saying that the gravitational degrees of freedom stages. And if you take that picture, then you say, well, what was behind the Big Bang? Well, you might take a view, maybe it was a collapsing universe. But that doesn't work because a collapsing universe likely would be a big mess, as I showed before. So it certainly doesn't seem to work, at least. So what was it? Well, the proposal here is that it's a remote future of the previous eon. So that's the idea. And you can therefore stick one one eon on the next in the way of the picture which I started off in this whole discussion. Okay, now there are two issues I want to discuss here. I'll bring my original picture up just to remind you what it looks like. That's just one crossover from the remote future of one eon to the big band of the next. and here we have the idea that that keeps going now, two questions one is, and it might sort of occur to you what about the second law of thermodynamics?

57:30 surely, if entropy is going up and up and up and up and up and up and up how are you going to get a sequence of things which more or less look the same as each other not in detail, but in general, overall picture without the entropy somehow going up all the time Well, here we run into an issue which is very controversial in current physics that I'm going to take a particular stand on this issue. How can a second law maintain itself in a cyclic universe? Well, a point I should make is that by far the major contribution to the entropy of our universe is even now in black holes. It's way, way larger than anything else I want to think of. I'm struck by how much entropy there is in the microwave background, but it pales into utter significance when you think about the size of the black holes that are around in our universe, as far as we can tell. Our galaxy has a supermassive black hole, which is about 4 million times the mass of the sun, and that's already swamping the entropies as anything else you can think of. What happens with black holes? Well, they will eventually disappear by walking radiation, and I'm accepting that. Now, Hawking originally argued that the information, which is basically the degrees of freedom, in the black hole must be lost, in black hole evaporation. He put this forward originally, and I agree with that, I think he was right. However, later on, he changed his mind, and he, I don't think he was, he in fact agreed to lose a bet, and I think he was wrong, he should have kept his money, because I think he was right originally that information is lost now there's a good reason why people don't like that they don't like that because it disagrees with one of the fundamental principles of quantum mechanics which is known as unitarity I think I have other reasons for thinking that unitarity can't be universally true and those of you who may have been at my talk on Tuesday I get some reasons there why I believe that I must do something about unitarity in the context of general relativity so I was quite happy with the original view here not happy with this current view I think there are all sorts of problems with this but let me just say I'm adhering to the earlier view something of that general consequence that in general I don't mention

1:00:00 now if you lose degrees of freedom then the problem arises how do you work out the entropy do you take into consideration those degrees of freedom which are swallowed and then disappear by the black hole Or if you say, well, I'm not interested in those anymore, let's not use those as a good ingredient. And then you change your definition of entropy. So this is my point of view, that one in some sense renormalizes one's entropy definition when the black holes evaporate away, and in this sense you say the second law. The second law is transcended, in a sense, not violated. The thing is you say, what do you mean by the entropy of the universe as a whole? degrees of freedom swallowed by black holes or don't you? Well once they're swallowed my view is to say well forget them and then the entropy definition doesn't take those into account and then the value assigned comes down. There's never any violation of the second law but it kind of is transcended and I believe this does make sense so that it's not actually at the crossover it's one way a little bit before that where all the black holes have disappeared the entropy that you like to use now is a much smaller entropy and agrees with a lower entropy that you get in the next time. But it's always, again, the gravitational degrees of freedom which somehow are killed off by the black hole processes and you end up with a universe which is consistent with a 12 hypothesis of a very smooth, conformally smooth big bank. So that's the picture. I think it makes sense. Whether it's right or not is another question. I want to raise that question, if it's right or not. And you might say, well, how on earth are we going to know because whatever goes on in the previous eon is going to be all squashed into the Big Bang and all information will be lost. Well, I don't think that's true. And I want to try and indicate a couple of things which could be signals coming from the previous eon. Now, the first thing I want to mention is, well, I was thinking about it, the most violent thing I can think of. Now the most violent thing I can think of, which has a chance of getting through from one year to the next, is supermassive black hole collisions. You see, I did mention that our galaxy has a black hole in its centre of about 4 million

1:02:30 solar masses, 4 million times the mass of the Sun. We are on a collision course with the Andromeda Galaxy. This, apparently, the observation is the case. The Andromeda Galaxy has a black hole in its centre, which I think, if I have my figures right, is something like 20 times as big as ours. Now, when we collide, it won't be quite soon, it'll be a few thousand million years, but never mind, we're going to hit each other. Well, the black holes are not likely to hit each other head-on. But what is quite possibly going to happen is that they sense each other's presence, and after many thousands of millions of years will spiral into each other and kaboom. When they hit each other, there will be one unholy explosion. And that explosion will carry away some significant proportion, I say significant, I mean like a few percent, of the total mass energy of those black holes. So you have to think of the black hole in a 4 million solar matrix. It depends on details. But you have one whopping explosion, which is, on the scale of things I'm talking about here, almost instantaneous. So there will be one huge burst of... Well, the energy comes out mainly in the form of gravitational waves. These will be ripples in space time. And those ripples will go out. And I have a picture here which is sort of indicating what everything happens. Here we have a black hole collision. because if they miss the first time the galaxies will go through each other and then there will go several occasions where they will cross through each other and one of those, the black holes will swallow each other so that sort of ultimately happens and then there will be this burst of radiation this is a space-time picture of the previous eon I'm supposing that sort of thing is happening in the previous eon now this is the crossover into our eon this is us up here somewhere this is in the previous eon an encounter between black holes this is this great big explosion and we look back and we see maybe the effects of that explosion. a colleague, an Armenian colleague of mine, Vahe Gerzajan, had a way of looking at this. He had a lot of trouble with people accepting what he was doing, partly because this way of analyzing it was a bit unconventional. However, he looked at these things quite carefully and I think there was a case

1:05:00 and I'm going to show you in some pictures in a minute. some of the evidence that seems to indicate there may be something here. Now, the point I want to make also is that not only does this collision take place here, but it's likely to happen again. You see, once you've got a big black hole swallowing another one here, in a cluster of galaxies, it's likely that that one will swallow another one, or maybe another pair in the same cluster, it will happen several times. of proper motions here are concerned they will more or less converge on the same point here. There will be a little bit of variation but there will be basically one point in the sky here which is where all these things come together but what we're not seeing is that, but you're seeing the effect of these gravitational waves. It's a bit like, I thought I had another picture of this, it's a bit like ripples on a pond you might think of this thing would be like a ripple on a pond if you have raindrops hitting the pond then each raindrop makes a ripple another raindrop makes a ripple and at a certain point you take a photograph of a pond and you listen to lots of ripples but are these ripples made by individual impacts or not? can you work that out by doing a statistical analysis? So what you would see here, this basically is the photograph of the pond, and these are the ripples. Do you actually have evidence that this can be analyzed in terms of individual impacts? I'll come to that in just a moment. The idea is that they should also not just be ripples, but they should be ripples which are concentric. And the way Gozadan was looking at this is to say that the temperature variation around this wing is something which is more uniform. You have more uniform, less variation around the wing than there is elsewhere. And this is the way he was looking at it, and you're looking for concentric sets. And I'll say something about that in a moment, and then there will be something else, and I'll say something about also in a moment. but let me start with the slides so I need to get that working if you can I want to show you pictures here we are this is an analysis of the WMAP data there were

1:07:30 I hope you can see these things I had a lot of trouble seeing these anyway, what are these rings? The rings here are these low-variance rings that seem to be in the sky. And this is looking at a picture where you're looking at at least three concentric low-variance rings. That's the signal. So each one of these rings will be a member of a triple. I don't know if it's very easy to see all three of them often, but that's what it is. And this is the WMAP satellite, which has been up for quite some time now and the different colours are to do with the average temperature of the rings which is quite remarkable is that you see there's a lot of clustering not only of the multiple rings but also of the colours now the red ones it's always confusing because red means blue shifted and the blue means red shifted so you have to get your mind around that that's just the conventions that people use means that they are close because the signal is going away from us and that's what you're looking at and the red ones here are the blue shifted ones which are the distant ones because the signal is coming towards us. Well, I mean, that's the way it works out. But anyway, now the question is, is this a real effect or are you just looking at a random sky and it looks as though there are rings there which aren't really there? Of course, that's the argument. Well, this is the next, the previous one was the W map, and this was the newer satellite, the Planck satellite. And people often said, well, when you look at the Planck data, then these things will disappear. I should say the crowding here of the, you see here, there's a lot going on here, and not much going on over here, you see. and that's not something you expect to see in a random sky. I've got some numbers here, actually. The number of triples of rings here is actually... Sorry, jumping in here. It's not obvious from the picture, but there are 352 centres where you find these triples. And in the plant data, you find 847 of them.

1:10:00 disappear, you'd see a bigger effect and also more crowding than you said before which is sort of puzzling I didn't expect to see the crowding but the crowding is harder to explain on the basis of conventional theory because conventional theory says inflation is responsible and that you have quantum fluctuations in what's called the inflaton field and that will be a random effect and then as the inflation takes place it becomes classical irregularities. Let me go into the details of that partly because it's... I don't want to do that. But the point mainly is that you would see a random distribution. Whereas here you see... I'm sorry, I'm not very good at working this thing. Here we have a simulation sky. This sky actually where you've actually turned up the volume a bit to see anything at all. But this sky is simply a randomly created sky I think it's 15, isn't it? No, it's about 70. You see about 70 of them, whereas in the real sky you see 352. So you see far more in the real sky than you do in the simulation. Now, oh, sorry, I'm not doing well. Here we are. Okay, now what about the centers? You see, are the centers of these rings clustered? well, the points here are the red points are the blue shifted ones which on the theory would be very distant sources and you see they're extremely clustered and the blue ones, which were the close ones also would be extremely clustered now the picture on my model the conformal cyclic cosmological model, CCC is that what you're looking at is you're looking at a concentration well this red one there would be a very very distant concentration of huge numbers of galactic clusters very non-uniform distribution the blue ones would be a relatively close distribution and this is something somewhat intermediate, there's a red distribution there which is also very distant would be the idea and now when we move on to the

1:12:30 that is the plant data sorry, that's right let me tell you something else not that long ago in fact I guess it was March or so of this year there was a big announcement about from the group of people observatory at the South Pole and it was called BICEP2 and the announcement was all over I don't know whether it was here, certainly in England it was saying the smoking gun of inflation has been seen in what are called B modes these were observations of the polarization of light coming from the microwave in the microwave background, so you're looking at this radiation coming from the glass gathering surface which is when the universe cooled down temperature in which the radiation could actually escape and get to us and people were looking at the polarization of light so you've seen whether it's polarized one way or another way, as you have with polarized glasses and so on and there is a thing that people have been looking at for some time, is to see whether the polarizations that you see are consistent with the conventional explanation of where polarization comes from. You see, when you have polarized sunglasses it cuts out the light I guess it's the more horizontal light it's to do with the variation in the density in the atmosphere and so you see an effect of polarization of the light which is due to the density variations in the atmosphere and so this is argued to be the main reason why you see polarization in the microwave background now if the polarisation in the Michael Beckland is of this kind then you can only see what are called E modes now E stands for electric and these are particular arrangements of the polarisation it's a clear cut analysis of this which you can do and if you see these Alec modes which are the B modes which B stands for magnetic in the Maxwell equation B stands for magnetic and this is a different kind of polarisation pattern And if you see these B-modes, the argument was, this must be that the E-modes that would have been there originally

1:15:00 had been distorted by the presence of gravitational wave disturbances. Now, this was very disturbing to me, because I don't want any gravitational waves in the early universe. They should be cut out by the argument which I've given you. The gravitational degrees of freedom should have been killed off right at the beginning, you shouldn't have any waves like that. So I was very worried about that for a bit. something which my colleague Paul Todd again had mentioned to me earlier on. He had been at a dinner and he had been sitting next to an expert on polarisation of signals, not right from the big band, but if you look at galaxies then you see there is polarised light. And this polarisation is a conventional explanation of where this comes from, which is that it comes from magnetic fields which are stretched out by the plasma which is out there with electrons and protons running around sort of loose and they have the effect when they get stretched of strengthening the magnetic fields and that's a conventional explanation it works perfectly well however, what Paul was doing from this discussion what he was doing from the discussion was that they see these polarization effects already in voids. Now, voids are certain regions out there in space which don't contain any galaxies. So they are sort of empty regions. They seem to be empty. Now, they're not empty of dark matter, but they're empty of matter which affects electromagnetic fields. So this is a puzzling thing. How did you see magnetic fields there? And so the question is, well, if you see them there, they must have been there right from the Big Bang. In other words, primordial. And this is a big puzzle. It's a puzzle to a certain group of people. We just don't seem to talk to the groups of people who talk about demons and so on, as far as I can make up. But it is a great puzzle. And Paul asked me, I remember just casually, he said, well, I've just been talking to this lady about these polarisation effects in the voids. is it possible that you could have had magnetic fields coming through from the previous eons I said well yes of course because it's electromagnetic fields masses, photons, yeah they come right through but I didn't think any more of it until later when the B modes were mentioned here

1:17:30 and I thought well B modes magnetic fields, they are false B modes because that's what the B stands for magnetic fields, if they were there in the early universe already they will produce B modes now since all this stuff with the b-modes we announced people are worrying about other things completely different to do with dust maybe they're not really there on the observations and we have to worry about whether dust could produce these effects well I rather hope that's wrong that they are really there not because they shoot my theory down but because they are an indication that there were magnetic fields there already from the previous eons and where would they be well the picture that I have here is here is a crossover from the previous eon and there's our eon. There is a galactic cluster. This galactic cluster, the mass fades out eventually and it sort of disperses somewhere way up here. But the magnetic field will hang around. And so that magnetic field will get through into the next eon. And so as we look back, we would see that magnetic field. But in principle, we might see it as V-modes. But how do you know that it's caused by some galactic cluster? Well, that goes back to the other thing. If there was a galactic cluster here, with lots of supermassive black holes running into each other, they would produce these rings. And so you would see at the center of these rings, this is our parcel icon cutting through these rings. Each of these is a ring. I haven't got the right number of dimensions in the picture. Each one of these looks like a ring. of it, or you might see the V-mails. Moreover, the only case you would see this is when these rings are more or less tangential to our cone, and that means they're neither red nor blue in my picture. They will be sort of green in the middle. Okay, now, that's the idea. Let me go back into... I have to turn this off or I... Actually, you better do that or I won't run something. Okay, let's see if we can find the pictures. so I tried to get hold of my colleague Vahe Berzidjan this is a plank picture you see and I said where is this region and he said well the region is

1:20:00 somewhere down here and that point unfortunately he put that in that's just the centre of the circle this is the region they're looking at so that's where it is see something there, some center of rings, and in this Planck data there's nothing. So that's not much good for me. So I at least didn't get totally discouraged. I look back at the old W map picture. And lo and behold, right in the middle is indeed this is the ring, which is not a ring in the picture. It should be indicated in a different way. That's just showing the region that the bicep people are looking at. of this picture is a triple of rings, also of intermediate color, they're not red, they're not blue, they are sort of greenish, as would be expected on this picture. So then I emailed him and said, well why don't you see them in the Planck data, that's supposed to be better than the WMAT data. So he said, well let's turn up the volume a bit, in other words look at slightly weaker signals, and there it is. still there, exactly the same as before intermediate colour sort of greenish on the whole of course it's a bit of a mixture of red and blue but on the whole, greenish neither particularly red nor particularly blue and maybe that's an indication of something. So the idea is and we haven't done this yet maybe we would look for other places in the Planck data where you see triples of rings where you see the sort of intermediate green color, and do you see B modes there? Well, I don't think anybody has looked. I'm not quite sure what the Planck data people are doing. This is a picture that Vahe did for me. I'm not sure it's quite what I want, but he's taken intermediate colors. I think rather bigger than I was hoping, because this stretch of black is the sort of green region here. but these black faces then including this region here might be where you would see B-modes as far as I'm aware that when people look for B-modes in the Planck data they just look for an average over the whole sky and that wouldn't be any use for me at all but if you can pinpoint them you might be able to relate these to the places where you see the green rings

1:22:30 and that would be very exciting to see if there is an indication which combines these two proposed effects collisions in the clusters and the production of primordial magnetic fields which would come about in clusters of galaxies in a general way. And the ones you would see as B-modes would be the ones where they're just on the edge where our class-like connection fits that region, which is where you would see green colours for non-existent than the previous one. Okay, thank you very much. So we have time for questions. So, if I understand correctly, your proposal, you need a future state of the universe, which is going in its red photons, that if I would be more ranking... Yeah, sure. So I'm happy you need a future state of the universe which is populated on the right photons in order to propose that those would be a major problem for quantum physics or something like that. More or less, but you see, I'm allowing for extra particles which would have faded out. So you have charged particles going through because you cannot destroy those particles. That's right, they're not destroyed. They're still there, but they're... massless in the limit. Only in the remote limit they would be massless, would be the idea. But that's the hypothesis. The massive particles could go through, yes. Well, you see, charged particles have to do this. I've been wondering about this for a long time. Because if you have an electron, you see, and there would be rogue electrons running around out there. Those electrons have nowhere to go. You see, they can't become a neutrino because charge has to be conserved. to remain charged.

1:25:00 So the proposal I'm making, and this is somewhat unconventional, but the argument is that in very, very long timescales, the mass will actually fade out. And so they will, in the ultimate limit, be massless particles. And then they can get through. But you violate charge conservation? That's the alternative. The alternative would be to violate charge conservation. But I don't like that. Also it doesn't help, because if charge conservation is violated, that gives a mass to the photon, and if the photon has a mass, that ruins everything. So no, I would prefer the mass to fade away, which I'm not saying this is a part of a theory which I have, I'm just saying that you've got a lot of time to play with, and so that photons, sorry, charged particles, asymptotically, the mass runs, you see, and there are theories most of them I think have something where the masses do run they don't remain absolutely constant and over a few periods of time you could imagine when the temperature gets ridiculously low the mass fades out but that's a hypothesis question here so when the next eon starts what is the mechanism that fixes the value of Newton constants I should have said one thing which I didn't say it's not quite your question but let me say it now anyway in your scheme you have to have the creation of new matter every time you pass from one knee onto the next it will be a scalar matter which is uncharged and it's the way the equations work it wouldn't work without that and I'm proposing that that is the initial form of dark matter not necessarily get the appearance of dark matter, and this has to decay. That again is a hypothesis, that over the eternity, actual dark matter in each eon would fade out. Now your question was about the gravitational constant. Now if mass, you see there's an issue here about what you mean by the gravitational constant, which has to do with mass. You see, if mass is allowed to vary then you, if all masses varied at the same rate you could interpret that as

1:27:30 a change in the gravitational constant but since on this type of scheme it's likely that that wouldn't be the case that the masses fade out would be different rates for different kinds of particles so you would have to have some standard way of talking about the gravitational constant. I think I would take it to be constant but in effect it changes sign. See, when you go from one eon to the next, it's just the way conformal factors work and so on. The gravitational constant becomes, in effect, negative. Let me backfuck a little bit. So you have to go into the equations here. You have a conformal factor which, one way around goes to zero, and the other way around goes to infinity. in the end of the one eon, write it, the conformal factor goes to zero, and the beginning of the next neon, it goes to infinity, say. But then the hypothesis is that these are reciprocals of each other. So it turns upside down. Now when it turns upside down, then your effective gravitational constant changes sign. So although when you continue from one neon to the next, it looks as though the gravitational constant would have changed sign, when you go to the opposite conformal factor, it's come back of the reasons, you keep it positive but you have to combine the changeover of conformal factors I mean, it hangs together but one has to look at the equations to see that but I'm not saying that the gravitational constant changes although it would be an interpretation I think that one could make if all the masses faded out together in proportions, but if they fade out at different rates, that simply attributing that to a change in the gravitational constant would not work. You'd need more than that. There'd have to be some rules about how the masses individual particles change. I don't know if that's answering the question, but it's a slightly more complicated question, I think, than one might hope. Yes, sir. What part of known physics is preserving and go from one eon to the next? What part of the... What part of known physics is preserved? Well, pretty well all of it, yes. So the gauge group is the same on both sides?

1:30:00 Well, that's my proposal. I mean, you could have different proposals. But I would say, yes, it changes only in things which depend on... You have to worry about the gravitational constant and how you treat that. But I wouldn't expect the gauge groups to change. I wouldn't expect the large numbers to change. you could say there's a little bit of evidence from this that maybe they don't change. And that is, it's a bit of a feeble statement in a way because all sorts of things could happen, but you see there is a question of how big can these circles get. Now if the previous eon was just like ours, and overall numbers, I mean, not in detail, then black holes will only start to appear a little bit before now. Well, now in a broad sense. And now means a certain size, the size that the rings can get is only about 40 degrees diameter in the sky. They couldn't get bigger than that because that would mean black holes forming earlier than they could if the previous eel was like ours. because it might be quite different, but you do seem to see evidence that there is a cut-off on the size of the rings. So if you believe all this, then this tells you that the rings do fade out, but sometimes around about 30 degrees overall diameter, and you don't see anything bigger than that. Maybe a few, but certainly not bigger than 40 degrees. And that is consistent with the previous eon being in overall scale like ours. So that would suggest there isn't a huge difference which changes 10 to 40 to 10 to 20 or something like that which makes the constants of nature utterly different from what we see so it does suggest that at least it's not that different from our EO and if that's the case that would be what I would want to say, that the physics doesn't change grossly, it's pretty well the same, same symmetry groups, same constants, pure numbers, there will be slight modifications to do with the mass decaying over very long periods of time there will be statements maybe tying that in with Higgs mechanisms about when that happens but I don't know how you treat that in detail but that would be when mass comes back in

1:32:30 when Higgs mechanisms start to play a role and then the dark matter which starts off on the screen as being massless it acquires a mass and it needs to do for these observations some indication that you have an initial state which is massless and then it requires a mass and then that picks up the gravitational degrees of freedom. So in your gravitational waves, they hit the crossover and they're killed off as gravitational waves but they appear on the other side as a combination of two things. One is ripples in the initial dark matter and that's what we claim to be seeing here and the other is in slight alterations in the conformal curvature of the crossover surface. So there would be effects here, I have no idea how you'd see them, but other effects which in principle one might be able to see. So the physics would be the same, but the initial values? Yeah, I should say... The physics, the basic physics would be the same, yeah. there would be and the constants of nature according to this would be the same but just there would be effects over huge periods of time that would begin to show up and mass would start to disperse eventually because if it loses as a mass matter loses its mass matter would eventually break up but that would be probably way longer than of a supermassive black hole I was thinking of a ridiculously long period of time is the for the the speed of rotation of the external the speed of rotation of what? of the external stars of galaxies is the signature oh I see, you're thinking about the dark matter well I'm going to be you see this may be a fairly outrageous theory but in most respects I'm pretty conservative and I am taking the view that dark matter is out there and that the rotation curves and the question is how do you tie in the rotation

1:35:00 curves with the amount of matter that you actually see in the galaxies and the way it's explained is to say well there is most of the matter in galaxies is dark matter dark matter, there is a little bit small because you see colliding galaxies you see it's consistent with there being this dark matter and so I'm going along with that I think it's much more likely than that gravity is modified of course that's an alternative possibility but I don't think gravity is modified I think it is dark matter and the dark matter is the result of the creation of new material in the crossover and that that would contribute to the observations of the rotation curves so that's just conventional I'm not taking a different view on that one Master's student should feel free to ask the question if you observe the circle you're looking for you would say that you have a neon before but could you say that you have the multitudabillion because otherwise you have the same problem of course Well, that's true. I mean, well, I think there's a chance of seeing two rayons back, but that wouldn't solve your question. You see, in a certain sense, I'm claiming we are seeing two rayons back. Because you might ask, why on Earth is this very different density in some regions than in others? You seem to see great clumping of super clusters of galaxies. And where would that come from? irregularities in the microwave background, let's see, yeah, well, what causes the microwave background? It would be in the matter distribution in the early universe, and that would be a result of the disturbances caused by what's known on the eon before. So you have, in principle, I've no idea in detail how you look at this, but in principle, evidence for two eons back. Now, of course, you're asking a much broader question, what about 10 million eons back number and so on. That's more just, well, it's the first thing to try again, I would say, that the eons keep on going more or less the same as they are. But you could certainly raise questions. Maybe there's a general trend for constants to change from we are who we are. It's a horrible thought. But it could be, yeah.

1:37:30 And you might introduce sort of entropic arguments and say, well, not only do you need conditions when we are on the planet and so on, but maybe the eons have to be right, you see. Only this eon and the next would be right, and then after that, we're aging. I don't like that, you see. It's purely emotional at this point. I'm quite happy with the idea to have eons going on without any overall change in the content of nature and so on. And it's sort of a baby festival, you see. You could imagine testing. I would say maybe there is some change if you have the same systems and you can say that these observations are from one year back or two years and you could push back after a while you get pretty people. it's pretty limited what you can say and you're completely right if that's what you're suggesting that it's just a hypothesis the hypothesis here because it's the simplest to say in this context to say that the eons are pretty well the same indefinitely in both directions but to have an observational evidence for that would be a tall order one year at a time I have a question you did before yesterday you gave a talk to the CPM talking about the effect of radical quantum mechanics is there you just said something ridiculous is there a connection in your mind between this problem and that problem I mean, it's certainly interconnected in that I have to get rid of information in black holes, which is a violation of immunitarity. So in that respect, there is a link between what I'm speaking about today and two days ago. But there's another point which has very considerable

1:40:00 relevance, and that is what do you count as a physical situation in which quantum gravity becomes very important. The usual statements people make or I would make similar statements some years ago that when curvature of space-time the radius of curvature of space-time becomes of a plant level then you're really in a quantum gravity regime. And so you would say if the universe is that curved You can't treat it classically. It's got to be quantum gravity. Now, in this picture, I'm not saying that. But what I am trying to say, and I'm not sure how to say it in any precise way, but what I am trying to say is that it's not the radius of curvature, it's the radius of vial curvature. So the Ritchie curvature can be as curved as you like because that you can scale away. By a conformal scale, you can get rid of it. If it's just Ritchie and there's no vial curvature, you would just stretch it away, and it's not there. So I'm trying to say that Ritchie curvature of Planck radius is not evidence of quantum gravity. That quantum gravity is only when the bar of curvature, radius of curvature, gets to that scale. Now, I have a problem with actually saying that in an invariant way, because you can't talk about the radius and so on, so it's a problem. I don't quite know how to say it. But in a hand-waving sense, I would say that the Big Bang, and this is outrageous from the point of view of quantum gravity and it wouldn't have been completely outrageous to me years ago it would be classical for you yes, I'm trying to say I've said this in the introductions to books, so why are we studying quantum gravity, well one reason is so we can get a handle on the Big Bang so if we know what the quantum gravity is like that will tell us about the Big Bang now I'm saying no, I'm saying that that Big Bang is treatable by classical equations and those classical equations we have to work out a bit but we have a pretty good idea of what they are and they enable you to carry through from one eon to the next if you're only classical equations you get your reciprocal hypothesis with a conformal factor turning upside down and you get a new scalar field coming in and all that and the ripples and the gravitational wave will produce ripples in the dark matter and so on imagine being observational, which is great, I usually think it's like, you know, I lose

1:42:30 one set of friends, but I gain another set of friends. Some of my quantum gravity friends may be unhappy with me, because I'm not saying the Big Bang needs quantum gravity, you see. Of course, the black holes need quantum gravity. And quantum gravity is needed for the overall understanding of the picture as a whole, and so on. But I'm not saying we need quantum gravity for the structure of the Big Bang, so I lose those friends. But I gain those partial differential equations and carry through because then they'd come back and solve the equations for me, and that's great. Do you have any exactly solubitory model of this phenomenon? Well, some of my colleagues, my friendly colleagues, work out that usually they'd be looking at models with Friedman's type models where you have uniformity and maybe perturbations within that. So that's the sort of thing people have been looking at. And there are issues about how you treat this, which they argue about with each other. We're going to have a meeting a little bit early next year in which we hope to line all these things out. So they're not altogether, it's not ambiguous, it's altogether unambiguous what you do. There are some disputes about different ways of handling it. Do you have a coupling to conformal scalability? Yes, it's a question of, well, the coupling of the conformal, it's more a question of how do you get rid of some unwanted freedom. So you want to make the conformal factor fixed, really. You don't want too much freedom in the conformal factor, because when you take it to reciprocal, it gives you too much freedom. You don't have a unique propagation across from the end of the end. So there are ways of making this unique, which are conjectured to making it unique. We don't know for sure, but that's true. There are ways of doing this, but they do require a little bit of symmetry breaking. It's probably tied with things like this, symmetry breaking. But there are question marks. It's not definite, what we do. The question marks don't much affect the things I was saying from the observation policy, that they do affect exactly what you do and how you treat the little bit of uncertainty there is in the equations and that has to do with uniqueness in the conformal factor because the conformal factor should be fixed basically

1:45:00 so that your propagation is unique as you go across and there are some issues there which are not resolved Okay, I think it's time to thank Professor Penrose for his talk today. Thank you very much. So will we gather here for us to do a second? Oh, I think we need a second. The thoughts that we talked about, the thoughts that we said, that we don't let go of the life of the world, and that there's something to do for. And as you are saying, if there's something to do with people here, Why can't we always see them in our own view or there is no type of view? In our view? Then how do you know that this is exploding?