Hawking Radiation First Anniversary — Part I

0:00 What would happen near those similarities in which you have a singularity in the literature or not a singularity in the literature? Well, I'm assuming that the density doesn't have to be part of the density. Yes, but if you don't, then you're not supposed to stick back up here. Yes, I'm not going to sit with that, or we're not going to do that. If there were a lot of superbaryotes around with maximum 15 grams, Now, you said that would have an effect on helium formation. We don't hear about it tomorrow, but what would you do with helium formation? Well, a lot of the matter would be locked up in these very massive particles, which would decay very slowly. I mean, they would decay at times much later. It would decay at times much later than 200 seconds. So it would simply remove them from the nuclear atmosphere that makes it easier, so that it would make a low density universe, in effect, even if it weren't really. So who got in that way reconciled the deuterium problem, which of course we'll hear about tomorrow, with the, to guess a low abundance, a low density universe, reconciled that with a high density universe. We could also do this with black holes that formed up between the horizon at that time, is it? We could do what's next? Well, anything well above 15 grand up to the stage. Which, of course, could be very well performed if one had the soft equation of the stage of the stage. Any other questions? Well, let's now press on to the program. Those of us who went to the last point in the series a year ago, recall that probably the most of the highlights were Stevie Hawking's paper, where he presented his latest results on particle creation around black holes. and the way Caltech all this year, Gary Gibbons is going to report on recent work which he and others will be doing on this demo project.

2:30 Thank you. So I immediately want you to name out the list of things to be done, I apologise, and I would be grateful for anybody to let me know what we're trying to overlook. Again, to some extent in the view, I'd like to excuse myself, I'd like to say that it will no doubt be a bias. That's a real question. I had American Mental Science put in a great deal this morning. I'm going to page out the book of the United Mental Science. His name hasn't been mentioned, which we asked Skinner and his Behaviourist Psychologist. I'll give you my quiz. I'm going to page out the book of the United Mental Science. in the other universe. And I have a list of possible reasons, not necessarily the rule that you might yourself be the most important. Firstly, for somewhat intellectual reasons, that seeks to be here the chance of understanding some new aspects of fundamental physics. There's something here which I'm saying to you the case of quantum theory and general relativity, and you get to show the net, and Professor Penrose will talk a little bit more about that. Here's a very practical reason, and that's the following. If you look back at things you see around us, trying to understand the beginnings of the universe, where there's a possible curtain that comes down as a combination. If you can't see anything through the back, you look via metafetal. You can see via neutrinos, but that's a difficult thing. You can see via gravitons, but that's a difficult thing. Another way you can see is the factors, because they just hang around from a forced recombination, which would be they were very off. So they are only looking way back

5:00 into the event. The big problem is the cognitive matter problem. This is a problem for some and not for others. by Chatham. The only point I wish to add is that Chatham, as has been pointed out today, by numbers, because the results of Deuterium do not imply necessarily an own low density of matter. They only imply an own low density of three new films at the time in the history of the universe when Deuterium was made. You could also post the other words out of that thing using the cube or hex or whatever. So this could be a problem if you want. Another notion version is a galaxy formulation. A number of people have written on this using the idea of grass holes as some sort of seeds for galaxies. There are three references by Orion and Osiris. I'm not going to talk greatly about this, but this is really a reason you'd want to let the holes around. Now, this is a published by Edmonton, and that is the executive production. I should talk a bit about this in paper. If this idea won't work if you use black holes, then it's still a problem in the quantum field. So I'll talk about the other way of talking about it as well. So, that's the motivation. And I've gone to formation at origin, intellectual and physical. to point out that black holes need not necessarily have the mass in excess of the chunk of sacrum and the zoldovish, which is actually pretty critical has small black holes and the sort of energy barrier to making them. They say, if you compress matter, there will be tremendous barrier with pressure from the exposure. What's very critical you can do. Subsequently, and I think totally dependently, Paul King, in an article in monthly notices, pointed out, in fact, if we put it this way, that the necessary high pressures are available in the early universe. And currently, what it says is that if you look at the early universe, if you believe, as was perhaps reasonable at that time, maybe still reasonable, chaotic,

7:30 the MISLA chaos of cosmology program, then you might expect black holes to be formed, to work on the gene plant, it turns out to be roughly equal to the particle horizon there, and so you'll find that you're talking about rather small black holes, but early epochs, and they could indeed be as small as 10 to minus 5 grams, the number of when quantum effects become important in the landscape and graphs and the set codes. He's postulated a number of things which I think Naughty would not agree with, the idea that these little holes can be charged and have atomic systems around them. I'll talk about that later. After that, Kyra Hawking looked in detail at this formation process, in a paper, it might be a nervous system, and the effect arguing against the LHU's panel by WMG, in the State of the General of Astronomy, that if you had a little black hole like this, it would have grown by an ounce of gigantic size, as it is to say, it would have grown with the horizon to reach an egg mass, at the end of the radiation of the order of 10 to 15 these are masses, this would be an embarrassment because some scandals advantage of that such mass are called Dark and Brown. And they argued that Seldovich and Novikov were incorrect in their assertions, and that the black hole wouldn't grow. Now, the next section I want to describe, to some extent, how the reasoning behind this, in a qualitative fashion, by asking him to consider the accretion problem from black hole amongst the mediums, very schematically. The first one is just stationary accretion from the initial stationary black hole. And basically, what you start off with is to do it on the other side, the type of sub-sonic moving regularly inwards. As it goes to the horizon, it has to become supersonic, pressure that should be fallen. And there's a transition radius, a little bumpy radios, which the sound speed is, when the outgoing sound radios are dragged backwards by the fluid. In fact, this is an acoustic black hole. We have the radios there. Now, in an expanding universe, you don't quite have the same setup, but you have almost the same setup.

10:00 It's easier to see. you have basically a high-pressure region, a low-pressure region. The high-pressure region here is expanding, it's part of the expanding universe. The low-pressure region is falling in. This is around the ground, which is moving out of the blast of light. And separating the low-pressure and high-pressure region is a decompression wave. and the decompression wave moves it up and it's through that that the whole creek. Now, as I said, Dr. Short pointed out that it's powered by Doug Lynn and others who have been working for my core of him on this creek. But then it becomes fairly clear, you see, that you wouldn't expect these things to grow very fast, because the particle horizon moves out of the velocity of light, but the decompression weight can't keep up the horizon, and so black holes do not grow very rapidly. That is, of course, unless the sound is too much of a light speed, and with work by Douglas Jess, but it's not completely Jess, so I shouldn't have to stress this, Then if you had a hard equation of stakes, if it was Rome, maybe it could be a new wave, that's what it was. So we then are the, this is our situation, I guess it was about two years ago, there was some reason to believe you could have rather tall glass holes around, come against me for what may have to be kept Rome. I think that given that 10 grams is 5 grams, the lactose has got a small, given that these results implied at the beginning of the Hagon area, we have a lactose 10 to 15 grams with the size of one family, the quantum effects were obviously something to look at. And, roughly, in order of the, I would expect his opinion. First of all, the fact that flatulence has associated with them a simple plastic and super radius is part of something which was suggested, pointed out by Professor Penrose, that you can extract energy from a black hole by reflecting off particles always, which extract the rotational energy,

12:30 implied, at least on the new physical reading, that there should be a spontaneous loss of angle of momentum of charge, just sort of thinking vaguely about the general principles of quantum mechanics. People have looked into this, but I had a first suggestion of Odovich, Mr. Stavritsky is in some detail calculations, and Unruh in great room detail. It became obvious also that charge should be lost by this process, according to myself due to some calculations, and a bit more detailed calculations show that this is the case, but we also have people back up. Basically, what is happening here is that the black hole is going to contain to lose those parameters which make it most detectable, its angular momentum and its charge. timescales evolved from the angular dimension, we find that the time scale from the dimensional ground is given by a particular one that should be mq, not one point mq. And then we'll be a very curious coincidence. Let's just say, if we make it out a couple of times, we find that every two 10 to 50 grand and the Schwarzschild radius of the centre line's 30 centimetres are precisely waiting for the dimension possible because this becomes an import charge. Also, it is lost spontaneously, providing the mass as great as one of the mass of the electron, which is likely to say in order of magnitude, again, related to cosmological coincidence. In both cases, the process becomes interesting when A.M. is a mover or whatever else. All right. Well, that's how the Matthew Stewart took. Steve Hawking investigated further the implications of... ...and he came up with an idea which we talked about last year, which is a nature of the frequency on this, that not only these easily-handled rounds of charge and momentum can be radiated, but in fact the total mass can be radiated because the black core behaves like a black body with a temperature T, which was given by real

15:00 form of this, under a high end. The unit of the T is going to be for you at a 10-70 degree in A, since they're a rare. There was a clear from that, that the process is called not important. So, very much physical black holes. Again, by these curious questions, if you were asked for a lifetime, you'd find this to be acute. So again, these black holes become important. So the process will take the time shorter than the Hubble time, if their masses are less intensively grounded. I'm not going to say greatly about this whole explosion process, but I don't want to get into the details, but what I have thought to mention is one of the many of my mentors in some recent work, which there are a brand new company that I did, I can carry myself to be considering, we have the type of creeper that we have. These calculations of all x were on the assumption that you could trick the particles independently. The quantum fields that represent the particles could just interact with the gravitational field but not with their cells. So it's clear that that is sort of interesting size. and so what we have attempted to do is try to see what we can say about the effect of strong interactions without, it must be admitting, it must be a great deal about strong interactions. and what we did to do that was to work the model. You can't do anything. Go, properly. And the model, we adopted an additive model, sometimes you give time and end-bar delusions, the hydrodynamical model, this was a model of a crystal that has a lambda but basically the point of the idea is to say that if you have a strongly interactive region strongly interacting with the matter, then at least one will have an approximation to that

17:30 is fluid approximation, in regards to fluid. Now what sort of fluid are we talking about? We're talking about a neutral fluid, we're talking about heat radiation. Now, there are a number of candidates for equations to state this. One of them is, of course, picked the third row, diagonal compared to the second row, so it's a stiff matter. This is certainly true at low temperatures, we just have a total of gas, and high temperatures we don't really know. But let's assume we have some sort of pressure settings of gamma law, depending on the number T. Now the implication of talking to the results is what you'd like to extrapolate, but of course you might not extrapolate more to prove yet, is that if you have a black belt here in the heat bath, then of course the black belt is in this heat bath, so the black belt will treat from this heat bath, the fluid around it, in the way that I've described it before. Despite the responsibility of equilibrium, there must be a ripple process, fluid emitted at the same rate. Imbalanced. As to say, whereas before we were dealing with a creaking problem, So, what we should see now, beginning with is a wind problem. The black hole is to claim it's sending out fluid from here. The black hole is rather like a stellar wind with a stokes at a wind. Go back to the expression and reverse all the arrows.

20:00 In this simple accretion problem, there's a unique solution given that you've got a certain temperature density. Basically, there is only one solution which from a certain temperature outside, in this case a certain pressure, can smoothly make this transition from the high pressure region to the low pressure region, which is the transition from subsonic to supersonic. And you get the inverse problem and you ask if you're coming out, and similarly, there are a whole range of solutions. Sorry, there's a unique solution which creates a transition from subsonic to supersonic outside, which goes to the arrow and the arrow and the arrow and the arrow. Now, that one is specified by a certain accretion rate, M dot, and certain parameter, T, excuse me, where the temperature falls along the circuit. So what we've done is to use for those, the signs you get from the accretion process. And to the pure depth, but it all looks like it all works out. So you've done that, you can then represent your outgaining fluid as your outgaining part of the fluid, And you ask at what stage does the fluid approximation break down, does the fluid become transparent, or the optical depth become large, then you would have to guard the non-interactive particles. In conclusion, is that for equations of state whose velocity of sound x is greater than 1 over the other side, this fluid approximation is never anything. That means that in some sense we ought to regard the particles as non-interacting, even though they're at very high densities. The reason for this thing is coming up so fast. For equations to stay less than that, we find that you can really be regarded as an interactive fluid. The hangover would be great for states that comes down to the wall, reaching quite large dimensions because it becomes transparent. What this means is, if I am clear, and I'm not going to tell you, perhaps somebody who knows more about strong interactions,

22:30 one possibility is that these three particles are not the three particles that we know of, and can be seen in the laboratory, but it requires, if you believe, some sort of sparking. Which then recombines for the vegetable particles that we know about and any of it can give us just a string of gamers and protons, essentially. And that you have to colour them and charl them in fashion. And after that... Well, that's the work that's heavy done. And now I want to try and talk about observations. I'll kind of make a few statements from the observations. Not very many. The first observations are a daunting one, because it's a very obvious mimic. You ask how many of these things could be around, who will go to the identification of the magnetism, and that immediately derives the following daunting statement. you know, that even that less than one black hole in Max Grace's intensity is granted to Hitler and to nine years. Which, at least to my mind, is a very meter right. This limit might be much stronger than it looks, for the reasons I pointed out by the Lodonians. If you say that now the density is less than the magic gas, you can extrapolate the fact because of course the density of the lactose falls off or increases as one ever arcued so the density of the photon gas is one ever arcued for, is rationed as one ever arcued That means at the very time, you can say that the density of black holes is very small. So you write it down and try to get that many positive. So that, at the end, the behavior here of us is less than 10 to minus 5. So there weren't very many black holes going on. Now that, you can say without being any kind of theory, and I think the rest of it is in fact. we're slowly going, what do we need to do? This is just the ratio against motion ratio. This is a retrospective fact, and would indicate that the self-position that the universe was in the beginning of the world, was chaotic, really on, is probably not true.

25:00 And it would also argue against, to some extent, the self-equation of the state of the sort that paganism could be a rather large number of black holes in the world. Already we have found out that there is something about the universe It's a way-way for recombination. Given also that there is this black hole emission process going on, one can ask what that has had for observation. It's relatively easy to tell that the only interesting background is in the gamma wave background. And when you look at this, this has been done, I think, by Hawkeye Page, and you've also looked at it, you've come to the conclusion If masses are around 10 to 15 grams, so they're all relevant and they're still around, then their density is less than 10 to minus 5 of romanticization. Which again tells you that really, if you believe the story, the universe is not up to. Another observation, I just mentioned to some extent, of the gamma reversing too long, if you want that sort of explosion. Another observation, we once thought that we could get away with the constant ray background, but that turns out not to be. The reason for that is that you get so many gamma-through-topic rays that the gamma-through-topic wave gives you a limit, and that's the 10th minus 5, which is not very much of a particular equation by the next wave. The final topic I really want to talk about is net-through-production, which I think goes towards the arguing, saying, that's rather true. The main question, then, with entropy structure, is can black-courts be used to generate entropy of the variance of psi from about ten to the nine to the ten to the plus of eight, ten to the plus of nine, to the cost of zero. What this process does is to take the code of matter and press the candidate's profile.

27:30 And the major flag here is that the process is only a coping-native producer for large these holds not to change it. What you can do, if you really are persistent, and you can insist almost all of the universe at some early time with processing this work. And if you do it during the arithmetic, you find that all for the fractions, something about 10 to the minus 9, I think, or maybe that's the former number, tends to have been fractured. So it was very efficient, really, honestly. That's a bit of plausible, maybe you can believe that it's a proof of proof of proof. So, then, to conclude from that, is that probably this process will not create entropy, but of course, that's a proof of proof of proof of proof of proof of proof of proof of proof of proof of proof. One, not many back holes, pretty optimal that size for congenation. Two, entropy. The variable probably still remains unknown. A weak argument against Haggadorn. In the first part, it still remains unexplained, and to some extent requires more related matter and more anti-matter. But even if it did make the process become an important and efficient process earlier on, As Stephen Hawking pointed it out to be, it really doesn't care whether it was matter or anti-matter, so if you start off with matter, you'll rapidly turn it into a mixture of matter and anti-matter equally, which means it's very difficult to make pure matter or pure anti-matter. So, this could raise rather grave problems if you want to use,

30:00 Thank you very much. in the literature by Bekenstein, which I'd like your opinion of, which again is a non-teriproductive argument. You couldn't spontaneously make a black hole of less than 10 to 15 grams, because that's the mass for which the lowest entropy in the macroscopic body would be equal to the black hole entropy if you insert the surface area of entropy into a conversion of the area of the macroscopic body. Now, what's your opinion on that? Well, I think the danger with all of the pseudonymic arguments is that you can rapidly commit yourself, as very obvious in the universe, as very well as in actual middle of any state was affecting these processes. So, at the time scale, these so-called pseudonymic processes, that seems naturally all that makes sense to get. It's very long to have this super-expansion. So that you really are looking at, and knowledge is a problem, and you are looking at the formation of that color. You mean, you'd imagine you would pull a smaller black color as long as you produce some entropy somewhere else in the process. It simply wouldn't occur by a straight collapse, if you believe it actually happened, that's all. by having it somewhere else. So is that what you're having? Well, I would say that the typical time scale for the new president to go on, to do this, is still an average. If you get to the end of the argument, it's still an average. It seems a time scale to do the order of n to be effective, where we're using that to use it. But by that, the time scale expansion of the universe to know the order than the square in the universe. Now, to end in the series, it's a number of regs in xs1, and from the next time to go,

32:30 very strongly than the expansion time to go to the universe. It seems to me to try that a-tent with entropy arguments discuss the origin of that total noun universe, and the dv values. Thank you. If I remember correctly, car's calculations uh perturbations spectrum perturbations if you if you've been set these I don't think that's enough room to make up room and be compatible with the observation. He has, I believe he has. But not very much, I don't understand. If black hole form in the other stage of the chaotic universe, then the conditions indicated to be proof of this theorem were not exactly satisfied because he had an empty space around him, I think. I'd like to ask, firstly, is everyone confident that the results would hold in that situation? And secondly, if that's true and the results don't hold, is these results potentially another way of looking at what the data we get out and already said happens, if you were to share it earlier? I think the problem is, too, one indication is that you have to understand Thank you, the first question, I, again, I would not be honest with you to say that everyone agrees that I'd like to look at the geometric reasons that happen, particularly in the imagination of human life, will be equally present in the current universe, and will be in the conventional class, and that's what we are going to say about. But then, I'd like to say, What are all the objectives of having atomic systems around 5.5?

35:00 Well, it's up on 10 to 16. Just to look. I mean, the lifetime goes as a... Already their temperature, they're looking like a black body of temperature, while it's in the order of 6 to 10 to 10. You can split it. You may well, you can split it half enough. I mean, I suppose then you'll get more involved to that. The next problem is, if you want to have a system, you'll find it no more than the west-land electrons, and rather less as you make it bigger. So, you can find it much smaller than the energy of the photons. I was wondering if I was spinning it and cooling it down, Why does a soft collision state in Paris transformation have a doctorate, but in the university of Paris, it is very soft on large terms. and the fact that it's dead for precisely for this reason there's nothing to stand out in the emotions making this around or whatever and also, it's precisely an issue of pressure which is required to form something like a star to effectively coordinate the last channel to an organized point what prevents the last of the policy is that the other thing is that the other thing is that the other thing is doing Thank you. I think the point is that if you have a hard equation of strength, then a problem is stabilized by a pressure almost as soon as it comes to the horizon, and there will be the curvature of the equation of all the units in order to collapse.

37:30 If you have a soft equation today, then the beam mass is much smaller than the horizon mass. And therefore you can have a small actually curvature population, which can grow in density contrast for a long time when you're in the horizon. In that sense, the soft equation is going to be easier to form lactose or balance your swings from small amplitude. If not, let's go on to the trial contribution where since we couldn't get John Wheeler to kind of talk in the session I think colleagues tried to persuade me to say something, and I'm afraid that I felt that all I could say was, well, I could speak about what I don't know about cosmology, and you'll notice that these titles are rather sweet translations there. In fact, I'm not the appropriate person to talk about what I didn't know about cosmology. So, it seems to me that since I was going to see Stephen Hawking in the meantime, there was at least a chance that I had an interesting conversation with him before coming here. And in fact, one of the things I want to talk about is a conversation I've had with Stephen Hawking. In fact, the main area I want to discuss is the question of singularities in cosmology and singularities in general relativity in general, and the relation between singularities and the question of time's error. It seems to me that there are some interesting questions for investigation here. If one takes the view that, as one normally does when discussing the question of time error, that local physical laws are symmetrical in time, then we have to explain the gross a symmetry in time that we see about this, which is normally, I mean, this is the question

40:00 of the fact that entropy is going in one direction, and we associate that with a normal feeling of direction of time, and then we ask the question, what's the blame for the credit for this gross asymmetry in the way the statistics goes? And always, if we have some isolated is something outside the system. But if we're talking about the universe as a whole, then the blame for the asymmetry has to be traced back to the place where the universe as a whole ends, namely the singularities. So the question of the asymmetry of the statistics, that time's arrow, it appears then must be attributed to the nature or something to do with the singularities that occur. in space-time models. Well, I think I want to say a little bit about just one particular view of singularities. This is one that was just briefly mentioned by Barry Collins but I couldn't say much about it. I just want to say perhaps it depends upon at least one way of looking at singularities. I can imagine if you're one way of looking at singularities. This is a suggestion of what I've originally used as Eifert, and independently by Gerrard, Trondheim and myself, as to how one might identify or define extra points for a space-time manifold which might be singularity or they might be points to infinity. At first, the construction doesn't distinguish between the two, and these objects are called well, let me describe the construction. We consider, first of all, two time-like curves with the same future endpoints. Now, if we think of the past of these two curves, then if we have a space-time which has normal sort of causality properties, what's called past distinguishing, then if you simply that set, which is the path of that curve, then you can associate that with this point. And any two curves which have the same past will in fact end at the same point.

42:30 And that's quite straightforward if we're talking about ordinary points in space-time. But we can also use the same idea associating certain sets with points. But now these are not actual points in the space-time, but extra points called ideal points that we add to the space-time. You might consider a curve that just goes on forever, goes on indefinitely. It might be because this curve is going off to infinity. It might be because it's going into a singularity. That would be the view. And if you have two such curves, the question is, when do you say that they get to the same point either at infinity or the same singularity? Well, the definition is, if these two curves are at the same cost, then you say they have the same point at infinity or the same singular cost. So you can simply create new points which you add to the space-time, which may be points to infinity, which may be singular points, simply add these steps, you identify them or associate them with these steps, which are the paths of time-like curves. So time-like curves are the future end-point, giving nothing new, it passes that curve into the surface to identify that end-point, whereas the time-like curve which goes off to infinity or goes into singularity, supplies you with new kinds of points, which you add to the same time now. You can distinguish between the ones which you would call singular points and the ones which you would call points of infinity by saying the point of infinity is one for which So the step, the question, is the path of a curve of infinite length? And then we call that a point of infinity, otherwise we can call it a c-point. We can do this construction one way up or the other way up, and the other way up we call the tips or tips or either a path in decomposable, sorry, properly decomposable futures and terminally decomposable futures. Now, we can ask how do we classify different types of singular points. Let's talk about singular points. We can consider the question of naked singularities or otherwise. And this is still one of the great unsolved problems of general relativity. If you have a collapse of some sort, is one likely to get a naked singularity or other singularities necessarily hidden inside that hole?

45:00 Well, I'll say something about this in relation to the Hawking process shortly, but for the moment let's just consider a definition of a naked singularity. As I said, you might recognize one if you can see one, I'll point about one if you can see it. As I said, the time-mark singularity, that's an example of the name of the time-mark. And what I've drawn here is the blue star that's been here is one of these singular points. If you consider a time-like curve, which is a particular point, then identify that particular singular point. And the thing that takes its naked is that it can be seen by this chap up here, put another way. This particular tip lies to the past of this particular point. If you have that situation occurring, then you call this to make a singularity. One of the reasons for using such a definition rather than just something that you can see But I want to exclude the big band singularity as a naked singularity in this definition. The big band singularity, well I've got this now in the bottom. This is the big band singularity here. You can see it, but the thing is you can't get underneath it. So that's a modified naked singularity. And just to illustrate what this sort of way of looking at singularity does, is if you consider the normal freedom models, the Big Bang and the normal freedom models, what one has in a situation where you have powerful horizons, and this means that you can have several of these tips, all going down to the same initial Big Bang singular point. And if we define these singular points, or I should say we identify these singular points with these particular tips, as to say these are, you have to say some particle which comes out there, and you look at the future of that particle, then that blue region is the future of that particle, and another particle coming out here, the blue region is the future of particles, so they don't get into communication later on. Initially, they can't communicate one another with one another. And this is another way of saying that you have, in fact, distinct

47:30 tips, so you have distinct points of infinity. So we shouldn't say, in this picture, the Big Bang is a singular point, one singular point. What we say is the Big Bang is many singular points. It's, in fact, a whole three-dimensional region of singular points. Each one of these with one of these tips. And the existence of particle horizons is associated with facts, for example, the same thing, right? The fact that we have more than one past singularity according to this definition. If we look at the thing the other way up and consider the type of singularity in the future it's normally considered. Again, we take a black hole, and I've got one here which is a new start to collapse. Then we have, again, several of those types of tips. These curves, these particles that fall into the singularity, they fall into the black hole, and it gets destroyed on the singularity. We've got a blue one here, a green one there, and the other one there. And you see there's many different tips associated with this singular line, the way one draws this, it looks like a singular line. But if you look and see how many tips there are, tips, sorry, you find that there is in fact a three-dimensional set of these three-dimensional tips. So again, we have a situation where we have space-like three-dimensional irregularity. It looks very much like the situation we have in the case of the Big Bang. So, here we have big man, black hole similarities, and so far they've run similar. We might consider white holes, which would be just this picture upside down. Or we might consider a universe, which, say, freedom model, which freedom collapses. And then again we have this picture upside down. And the question again is whether there is some qualitative difference between the black hole, the singularity, and the singularity which arises in the re-collapse of the treatment model. I hope to come back to that question in a moment.

50:00 First of all, I want to mention one thing that is a slight digression, but seems to be rather interesting. This is some work done by Sachs and Lubitsch on this question of horizons, coming back to the Big Bang. And if we take the point of view that I think Wisner held for originally, that the reason one has this large-scale anthology that one deserves is something to do due to the fact that the universe has to step out, and what one likes to have is a situation in which you don't have these horizons here in which you can have them all mixing up appropriately. There's a mixed master model that was, there's point of view anyway, that's a gift of a new man. Perhaps if one doesn't have a horizon, you can use everything to get mixed up, you wouldn't have this problem, if you go near enough to find out what is very good at that, you wouldn't have this problem of having causally disconnected events in the mission of Japan. Well, I think what's interesting about the work that they've done, Saps and Budi, is that, well, how restrictive the assumption is that one says that there is no, that there's only one shift. What they call a deterministic space-time is a space-time in which there is exactly one tick. Another way of putting this is that if you know the past, then in principle you can predict the future. What this means is that you have some observer, and you consider this past, first he's allowed to know everything goes on in there. And then suppose that the physics is completely causal. The question is, can you predict his future? If this is future, that means that, well, one way of looking at this is that the future domain of dependence or Cauchy development of his light cone is the whole space.

52:30 Another way of saying this is that there aren't points here with the probability that there are time-like curves going indefinitely into the past, going to dissect his light cone. So if you say every one of these curves finally does accept the light curve, then this is what they call a deterministic space-time, and one can see quite easily the fact that the difference is exactly one thing. No horizon again in this case. So this is what they call deterministic. And this is the implications of this Big Master point of view. But one of the implications, which seems to me to be very striking, is that the universe has to be compact. That if, in fact, one has reason to believe that the universe is open, is non-compact, there is no compact kosher surface. What about that? One is no compact... Well, this is even stronger, not if it is compact, but there is a compact kosher surface. If one has reason to give this is not true, then once the implication is that we don't have this sense of space-time, we don't have this mixing, we do therefore have horizons. It would be rather a striking conclusion. Well now, I want to say something about the conversation that I had with Stephen Hawking. It has to do with this black hole explosion we've been hearing about, and here we are. I just drew a rather rough picture, I'm afraid I did these rather hastily, a rough picture of what happens to a black hole according to Hawking. this is just a situation where you initially have a creation of some matter collapses together and form an event horizon, event horizon being defined by, well, the boundary between those points, well, actually depends on what context you're talking about these things, but let's Let's say event horizon is defined as the boundary between those points for which all time-like curves into the future are finite length, and those points through which there

55:00 exist time-like curves into the future of infinite length. And this will supply you with a definition which works in the universe which is ever expanding between the acid types of flat. Now we therefore have the cement horizon, we have matter collapsing into it, and the light cones are all tipped over in that familiar fashion. Somewhere in the middle we've got singularity, and then suppose the matter falls in, and the thing settles down, and after a long while, the radiation density gets low enough outside like this in Hawking radiation process is fishing, of course, could be enormously long time. I should say that I'm not going to do any figures in my calculations, I've just been waving my hand. So, what would have been 20, I shouldn't have been 20 other times, but my figure would all be wrong. Anyway, this thing collapses, gradually reduces in size, you have these particles, And finally, a great verse disappears on you, and, well, the view seems to be that one ends up with a nice, smooth stretch after that, but one doesn't have to handle this point here. It is, in fact, an Aki-Singularity according to the definition I've given. You have some chap sitting here above that point. You can see there will be a tip. A tip, sorry, responding to that point itself. And that will line the path to this chap up here. So it would be an Aki-Singularity. Well, we'll be worried about that. We'll see if we're facing this problem if we are considering the Hawking first-day experiences. Well, I should indicate what this discussion was. I should say it wasn't quite an easy discussion, it was also partly an argument, which is sometimes unusual, because I normally find that I'd be in agreement this evening, and this time, I don't think we really came to agreement by the time I had to leave, and so I'd better do my best to present both of our points of view,

57:30 The situation that Hawking was considering was a box. Of course, they have to be rather big. I'm not going to consider the details of the nature of this box, which may be a problem. This is a box with reflecting walls, and all you're given is the size of that box, it's supposed to be pictures in volume, and the total energy of the material in this box, and you just leave it. You leave it for forever and a day, whatever you need it for. And the question is, what are the equilibrium states? What is the state of the maximum entropy of that box? I think Gary was touching on this question. One thing is that if the box is sufficiently large, then you will find that the state of, back to the mention, a lot of radiation running around, if the box is smaller, then there will be a situation which consists of a black hole in equilibrium with with a little bit of radiation running around the outside of it. So this was the picture that Hawking was considering. Now, what he says is that this is a state in thermal equilibrium, and according to general principles of thermodynamics, that situation ought to be symmetrical in time. As I say, if you check this and run the clock backwards, ought to be physically indistinguishable from what you have when you run the clock forward. Now this to me was a very alarming statement to make because what he said is, you may think you've got a black hole in the box, but he said that's equivalent to having a white hole in the box. He says then that the process of emission, of radiation here, is physically in a sense indistinguishable from the process of material falling into a black hole here. The idea is that one has thermal radiation here coming out, and you might have a situation where you throw all sorts of junk in here, to begin with trying to throw a television set into a black hole, and the question is, why don't you get television sets coming out?

1:00:00 But he says, the only reason he's okay telling me to talk about is that unless he's a servant who had a question, he might, if you wait, just hurry up my phone. So I couldn't argue with that. It's quite a reasonable statement. One tends to be talking about things which are extraordinary and improbable in this whole discussion. Never mind, this is not the exact same experiment, which one is allowed to do that kind of thing. But the thing that really worries me more about this is that the space-time geometry in the situation where a black hole is quite different from the space-time geometry for a white hole. And here you have to turn the picture upside down, and I'm all allowed to have it pointing the other way around, and it just isn't the same thing at all from the point of view of space-time geometry. And we were each accusing each other of being a reactionary or fuzzy band, because I was hanging on to the concept of space-time, whereas he was hanging on to certain dynamical considerations. And what seemed to be very interesting was that there really seems to be a conflict between these thermodynamic considerations and the space-time picture. So I think Hawking's idea was that somehow the space-time geometry becomes quantum-mechanical, and that one really led into considering real quantum gravity, and that one can't really attribute as classical space-time to what the situation when the flagpole sits in the box forever and a day. Yes, thank you.