Sir Roger Penrose - From Cosmology to Consciousness - Conformal Cyclic Cosmology

Well, Roger, it's very nice to talk to you in this strange interview format because I've been talking to someone for 42 years, a long time, so we're rehearsing all sorts of things that came up during that period and I guess my thinking goes from immediate. in time I mean that you are everything you have done seems to be like defeating time in one way or another being defeated by it normal well I don't think so I think you have defeated it more than this is for any exam that I I don't know if you remember my office where I used to have a clock that went backwards, I think it would be a good reason if we wanted one in the background, but we are certainly thinking about the second law of thermodynamics and the mystery of the direction of time and our

consciousness

and our

consciousness

of the past and that's why we can only talk about the past unfortunately it's a major disadvantage that we have but I was thinking that maybe you would like to say something about how your first mathematical work in the maybe In Cambridge Spanish, I'm sure you started before, but in Cambridge in the 1950s it seems to me that a lot of things came out of that and there are still some puzzles for you that still exist today.

Well, I started out solving algebraic geometry in Cambridge as a graduate student at st. John's College and I think I was misled into thinking that algebraic geometry was geometric and very quickly I learned that it was basically algebra, where geometry was what I liked the most and I found that I could do it more easily, so one thing I did was develop a notation. Hodge was my supervisor originally and Michael Attea was one of the people at the time, which is quite scary because I thought all graduate students were like that and it took me a while to learn that there was something particular about Michael, but I used to.

I initially developed a notation to handle Hodges's lectures because he gave lectures on differential geometry and he had these indices all over the board and they weren't the easiest to follow and partly stimulated by that I developed this notation. where tensors could be represented by blobs with arms and legs and could be put together to form contractions etc., it turned geometric algebraic problems involving tensors into images that I could understand much more easily, that's a whole motif that was actually I'll ask later about the ways in which you develop ways of seeing things on the page and in the mind, which are quite different from the usual way of formal notation, but I'm also surprised that I mean you didn't.

Not following the kind of algebraic geometry of more abstract notes that has been so huge since that period. I mean, tremendous things were happening with the abstraction of mathematics. For you, you maintained a geometric point of view that must be very old-fashioned actually. Cambridge of that period, I think it was very old-fashioned, although if you look at my thesis, there is not a single diagram in it, but everything was done using, I mean, there were diagrams because I did algebra by doing these tensor drawings and drawing lines and having notations for symmetries ations and displacements relationships of images and things and how you manipulated these things and although it was very algebraic what I was doing was done in a very geometric way, but I think this is one of the most important things that was important in how it was things developed.

With me I developed this general tensor formalism that went beyond the normal idea and you could include things like negative dimensional tensors and these turned out to have relevance to spin in quantum mechanics, but one of the things was that I was very puzzled by the spinners because they seemed to be fractional things where there was a square root of a vector or something and I couldn't understand how you could do that and Dennis Sharma, who was a great friend of mine when I was at Cambridge from the beginning, he kind of made good friends and he was a cosmologist who very much followed the Cambridge line at the time, which was the steady state model of

cosmology

which was Bondi and gold and Hoyle, they were all there, these being the creators of this idea and Dennis .

I was a big fan of it, which I found very interesting and intriguing and philosophically a satisfying picture where the universe was there all along, it didn't have a beginning and the expansion of the universe was offset by new material being created. continuously, which I had trouble with later because it was hard to see how it could be combined with the rules of general relativity and if I had to choose between general relativity in the steady state model, I would choose general relativity, but my friendship with Dennis It was very important. for me because I learned a lot of physics from him, you see, I was doing pure mathematics as a graduate student, but I attended at least three lecture courses and I attended a lot of pure courses that were important to him.

I remember the courses by Philip Halls, Sean Sean Wiley, he gave a very good course on topology and things like that, but then I also went on to other things that weren't really obvious and had nothing to do with my research project. A beautifully done course by Bondi at his home in Bondi on

cosmology

, general relativity and cosmology, which was done with great brilliance and a wonderful course and another equally brilliant course in a completely different way was Dirac's course on quantum mechanics, which was all very logical and very beautifully organized many of my colleagues said oh well that's the same as this book you see so I said well I hadn't read this book so the elegant victim of what he did came out at this conference, but it was also important to me. because for some reason I don't know if Denis had been talking to him or something, I'm not really sure, but there was a standard quantum mechanics course, which was the first quarter and then the next quarter. on quantum field theory and in this course he took a week off to talk about two-component spinners and I had been trying to understand by reading several incomprehensible books on two-component minutes and they didn't make any sense to me, but I think these are probably two lectures that Dirac gave and they were just perfect, the whole topic was completely clear, which is a bit ironic because people think of Dirac as a four-piece spinner, but in fact he understood not only about two-piece spinners components, but he developed his higher spin versions of his own equation using this zhim formula and it seemed to me to be absolutely the right way to do it so you already mentioned it.

I mean, I'm thinking that when he was at Cambridge he was very divided and he applied and people barely talked to each other. I mean, in my day they were in separate departments and as a college student you were supposed to choose which one you were and you just stuck to that, there was a real cultural block there, but you just ignored that, oh that's it, I think I ignored it, Yes, well, Denis was all the time trying to get me interested in physics. I had a conversation before I went to Cambridge about the wonderful steady state lectures given by Fred Hoyle, who there.

There were some issues I couldn't understand and I started talking to Dennis, who was a friend of my brothers. I annoyed Oliver, who was at Cambridge a couple or several years before me, so we struck up a friendship with Dennis. At the time he was trying to get me to do physics all the time and get me interested in physics and maybe convert my subject to physics, which I never did because there was too much of it and there was too much in math that I was very involved with. an interest in tensor systems in ideas of general geometry, etc., and a lot of these ideas I should have learned, so you see, one of them in particular was about the Co homology of sheaf because well, they used to call them batteries in those days.

Stack theory, you see, I think the stack still means something, but at the time it's what became what was called the Chiefs sheaves, I guess, and I was taken aback by the whole thing and it was just many, many years later when Michel Lotito made all these things clear, but at that moment I realized that there were things that would have been very useful to me later if I had paid proper attention, so what was it? William Hodge thinks you're studying all these different things that he knows. I mean, I think too. Many postgraduate students would now be horrified at the thought of completely different studies or courses that could not publish the papers in the correct issue, and although it was different then, there was something strange about that too.

You see, I started with Hodge and well. There were two other students, one of them gave up quite early, another was Michael Huskin, who did his PhD but then went into the history of science and the other was Michael Attea and they were all more or less like that and it was quite because Hodge suggested at one point, well, if he felt that I was a little unhappy with the algebra problem he had set for me, and then he said, well, maybe you would like to sit in one of the classes at another school, so that was it.

I didn't understand a word of what was going on, but that was Michael Michael too, you see, and I think I became very good friends with him later. There was another course that I attended when I was at Cambridge at the same time as when I went to the De Rax and Bondi course, this was a course taught by a logician called Steen and I went to one that I also found to be very influential and what made me It happened later because I learned about the girl theorem, I had vaguely heard about it. before and I find it quite disturbing you say I think before I went to Cambridge I would have believed you know we're all computers and that's what it thinks, it's computing or something, mainly because I couldn't think about anything else and girl. or ceramide vaguely heard and was touted as something that showed that there were things in mathematics that could not be proven and then when I went to this course for teenagers it became quite clear that although they could not be proven using some particular system the mere fact of that you trusted that system is something that you could give reliable and trustworthy conclusions from that mere belief in the system allowed you to transcend the system and you were able to find statements that had to be true based on your trust in the system even though it couldn't be proven using the system, so I found it very surprising if even at that time you had any idea that there should be some connection with the physical description of the brain and matter in general.

I think so. but it wasn't very well formulated, you see, I think I probably did it as a result of Steen's course, because I also learned about Turing machines, that was all part of the course, so the Turing machine theorem and the girdles and the fact therefore. Because of this understanding that seems to transcend any particular formal system, there must be something else going on in the brain that is not computational in nature and I probably learned from Dirac's course on quad Kanaks; again, there's a bit of irony because I remember the first lecture I attended, he had a little piece of chalk, I think he broke the talking piece or something, he's talking about superpositions, you know, in quantum mechanics, and If we could do one thing or another, then we could have overlays of the two and then he said you could have an overlay of a piece of chalk here and here and my mind wandered to that point, you see, and I remember him saying something about energy or something, but I couldn't understand why this.

It was an explanation of whatever I thought it must be because my mind had wandered at that point and I missed the point, but it bothered me ever since and I think I formulated the idea that there was a huge gap in our understanding of the world in quantum mechanics. specifically and that there was probably some link between that and what must be happening in our conscious thought, but it was quite vague and it was only much later that I heard a talk on the radio in which Marvin Minsky and Redken were talking from a point of view very computational and I could see well from that perspective, so I see why they are taking that view, but it seemed ridiculous to me to extrapolate to that degree and this is what made me realize that I had something to say about this topic, which seemed to be different from what other people had been saying, so I had this idea that in the very distant future I would write some book about trying to get people excited about math and physics, but I didn't really have a focus, but then this He said, well, silence, I will try to describe my ideas about what is happening in the mind.

I guess we should do that in case people aren't as familiar with the time scale we're talking about because this is really the only thing you're talking about now was the work that emerged in the emperor's new mind. I was ahead of it, yeah, and you actually started publishing about this in the mid-'80s and the book was what yeah and the browsers remind people that the cosmological images that you were studying by Dennis Sharma, I mean, almost nothing was known at all, so it was really just the comparatively local expansion of neighboring galaxies and well, I think people considered

conformal

infinite and I think in the mid 60s and early 60s it became clear from Martin Schmidt's observations that those were the first observations of quasars and I remember Wheeler getting very excited about this and saying look this tells us that there are objects that are really on the scale of their shrapnel singularity before we always thought, well, this shot, the so-called singularity, this little thing would not be real, that relevance is the physical at all, but here it became It was clear that There was a funny thing going on where there were really things that varied.

They must be large enough because they have this energy and they must be small enough because they vary in weeks or days of weeks or something like that. They cannot be too large and therefore they must be the size of their Schwarzschild radius which was what we now we call a black hole and called a black hole and it emerged at that stage, but Wheeler was very interested in this idea about where singularities were generic or not, are we aware of that, I mean, are you aware of Oppenheimer's? Yes 39 yes, well, this was something that was brought to our attention a lot, you see, with all the various articles that Oppenheimer was involved in, particularly Oppenheimer Schneider. paper forms just before the war where you have this very artificial material collapse, kind of dusty and very artificial and it was exactly symmetrical and then you had this collapsing model thick to a point, but many people considered it as highly artificial, these idealizations No applies in general, particularly because the Russians were delightful and collecting seemed to have shown that singularities were something very special and wouldn't happen in general now that I had seen a little about their proof and couldn't imagine it.

You could really try something like this the way they were doing it, so I started trying to think about this and other ways, geometrically visualizing what it would be like inside a collapsing star and trying to convince myself that it had to be a star. not local. argument that nothing could be proven from purely local considerations and then this idea came up about what's called a trapped surface which came about in a rather curious way, well I was talking to him, yes I have a Robinson in which I was at that moment. Once I was at Backbit College in London and I had an ensign who was a friend of mine, I learned a lot about spinners and self-purchase things etc. which became important later in Twista theory and he was talking about something completely It was probably different than politics and we got to a street and we crossed the street and the conversation stopped and then we got to the other side.

He started talking again. You see? And then, when he left, he walked back home. You see? When Murray was going. Thinking at the end of this, a feeling of euphoria and I couldn't put my finger on it now, why do I feel like this? You see? So I went back to all the things I had been thinking about during the day and then I remembered crossing the street. and when I was halfway down the street a thought occurred to me and this was evidently this characterization of a collapse of what we call a trapped surface that this characterization that was a global condition and I would tell you that this star has reached a point of no return, so when I realized that idea, I developed quite well on the same day a proof that you had to get singularities, but that's misleading in the sense that the techniques were things I had developed a little earlier. partly though I never posted it as an argument for going back to the steady state level because I was interested in the steady state, but I was also interested in general relativity and I was trying to see if it's possible that you can have something like consistent steady state with general relativity if it was in an exactly symmetrical case, you could see big energy problems, but if it's irregular maybe you can get away with it, but then I developed an Ag mixture with these cones and concentrated, and so on, to Realize that it wouldn't help you.

I would still be in trouble. I never published that, but there was a discussion that something else at the Royal Society had to try to prove something about asymptotics, which I wasted a lot of time on, but I developed these techniques. I thought I was wasting a lot of time. She spent a lot of time developing the techniques that became just what was needed in the case of the collapse of those ideas in differential geometry in topology that were needed there, they were developed for the problem of the 50s, yes, state that was where she exploded, I mean, as soon as Big Bang was just a thing for black holes that were a fantasy in this in the 50s, yes, but far from fantasy, no, I mean, no, that's right, well, It was purely how it went because the first time I went a lot.

Initial boredom called for the Texas conferences on relativistic astrophysics and I went to the first one, which was about a lot of things about quasars, these things that Mars Martin Schmidt had seen and Wheeler was so excited about, etc., and Roy Kerr. At that time I had discovered that a solution known as the Kerr solution, which can be interpreted as a rotating black hole, it was not entirely clear at the time whether it could be interpreted that way, but this became clear and the knowledge of these things. was important and in what I did at that stage they show that you had to get extremely general singularities and segments, so it's not symmetry, there are not supposed to be particular stage equations, you didn't have to assume the dust that Oppenheimer and Schneider had for you .

You could have fairly general material as long as the positive energy here wasn't violated, so the obvious thing to do in the late sixties was to fully enter the new realm of general relativity that modern astronomy and cosmology opened up, and was that so? ? I started thinking about elementary particle physics at the same time, yes, it was okay, yes, they were definitely at the same time, but you see, these were things that were bothering me for a long time. I just couldn't. I have to give an angle, but cook a lot of credit here because on my trip before this is the first trip to the United States where I went after two, first to work with John Wheeler at Princeton and then I went to Syracuse and shared an office with such a shocking angle and he went on about talking about

conformal

maps and the importance of conformal transformations and how Maxwell's equations were invariant and why he wasn't sure at the time, but another thing he emphasized was the importance in quantum theory of fields of the notion of positive frequency and these things.

They stayed with me and were very important in the development of Twister theory. Partly conformal staff to represent radiation crushing infinity creating a conformal boundary, just base time, that was one of the ideas, but the idea of ​​positive frequency was very crucial to Tricity I remember I made a new one. I wanted some kind of geometry that was complex in some fundamental sense, but I was really trying to describe the world as we know it and I had to try to incorporate quantum theory and I made a huge table. with all kinds of themes and arrows between them and things like this and but the pasta frequency angle that nobody in quantum field theory tends to emphasize that at the time it wasn't, I think they consider it as physics.

This is very, very analysis, yes, so it's something trivial, it's just more or not. I think it was the combination and yes of burst analysis and the fact that if conformal things were important to the analysis it is not appropriate because it is not even a formal variant anyway. the fact that you're choosing a positive frequency instead of a negative one is a confirmatory event and this idea of ​​extending it so that you have your Riemann sphere again, you have your function at the equator, a real-valued function which is the real numbers at the equator and then If you can extend your function to the holomorphic Li towards the north or south, this gives you a positive or negative frequency now, because it is such a beautiful idea, can it be extended in some global way to all of spacetime and Was this bothering me?

Look and I wanted something where you see if you complexify you don't have division into two halves you see this Riemann sphere you complexify that circle you have the Riemann sphere which is the real part divide it into two halves and the ticket are positive and the frequencies are negative or maybe I think which are negative and positive, but it doesn't matter, so I kept thinking, well, what about Minkowski space? What are you making complex? It doesn't spit anything in two halves, see, but then I remember I got kicked out of it, I think. It was shortly after Kennedy's assassination.

I was in the United States, you saw it, and in Austin, Texas, and the family is the respective families. These were the parts of Rindler Santosh that had come down to San Antonio. I don't remember where I was exactly and in the car on the way back. It was very dark and he's not very talkative, so it's very quiet, you see, and I started thinking about what Robinson had about how you can take a ray of light and somehow push it into the complex. and then you get these funny solutions to Maxwell's equations that are non-singular and twisted, so I tried to understand what was going on and then I realized this stuff about Clifford's parallels that I can't quite remember, I realized that Yeah. that these solutions of Maxwell's equations must have been directions of the Nile together with these Clifford parallels.

I vaguely knew that I already knew the dangers of Clifford, but the fact that this is what you got, I realize that this must be what you got, this configuration, so this is the twisting of the lines around these tours in the nested tour I and that setup I knew from Clifford's parallels when I got home I just translated everything into two component spinners and somehow it disappeared and that was the tornado theory and then you see you had both, the thing was split into two halves, a kind of metal, you heard that the real space of light rays and then a kind of slight complexity in these two halves, the ones on the right and the ones on the left, and that this was the analogue of the division of the Riemann sphere in two halves, it took a long time before we realized what it really looked like, that's how it was because it needed the G comala, but it's so amazing, I mean, now physicists use tornado variables. but they send a call, it's a half Fourier transform and I think it's a completely linear shape, actually nothing like this geometric characterization and yet, let's stop doing everything in Mycoskie space, we really need to have an idea of ​​what which is a particle.

It's an antiparticle it's and so it doesn't depend on I mean, I don't know if we can be getting to this there are really things from that period that concern you and that I think are still very open Well, it's very interesting, I mean, and as You know, we had this group developing tornado theory ideas and these meetings every Friday pretty well and pretty extensive discussions about tariff issues and then you almost single-handedly developed these ideas, they're twisted diagrams and and I'll always admire you how much you know. , you felt like this was something you should do, you held on to it, well, they were your diagrams, but I kept them alive until they were signed with other people's.

I was thinking about this. You've always wondered what a wave function really is, yes, and many people don't care about this, they just write down the formalism of quantum mechanics, yes, linear, etc., but do you like the things that we can see in certain sense? I mean, I think so, seeing is very important to everything you do, whether it's notation or just the business of light or the action of consciousness and seeing the truth of your girdle's statement. I mean, this is a very important thing and I feel like I don't think we can see you in a wave function is that what always worried me is that people would say, well, quantum mechanics just tell him that his images are useless, more fantasies. , just calculate them and forget about the pictures, but I was never happy that I didn't want to try to imagine anything that I could certainly with ideas of spin, spin, etc., but it sure seems to be very important to develop the geometric ideas as much as possible, but There are some very strange things about quantum mechanics.

I think, as I wrote in one of my books, shadows are a mind, just like their quantum mechanics has two kinds of mysteries. I think people tend to confuse them, so what I call Zen mysteries, which are the puzzle mysteries, which are things that are true of the world and it's baffling that you can understand them, I mean, we, is not exactly the way What we used to think was the world. Spin doesn't behave like a small cricket ball or something that spins around a well-defined axis, it's something much more. It happens subtly, but it can be understood and it is consistent and it makes sense, it often makes beautiful sense and there are the ex mysteries, the exes were the ones that were paradoxes and, like Schrodinger's cat, quantum mechanics tells you without a doubt. a very difficult explanation. experiment, although it wasn't as nice with the cat, it couldn't be put into a superposition of being alive and dead, so Schrodinger was basically showing or look, this is whatthat my shredding shreds, this equation tells you that you could have this cat that is dead. and I live at the same time that's nonsense you don't see cats like that so although he never expressed it like that it seemed to me that he was saying look there's something missing there's something in the theory that's not adequate and Einstein felt the same and Dirac is on it because that's one of the reasons I was interested in hearing it, but he got more, you can see it on the web, there are some lectures there anyway, it says this explicitly and I'm having trouble finding the original quotes because I know that there are some quotes where he clearly says that the theory, well, yeah, he says in the Bohr and Einstein debates, he says, well, you know, Bohr is usually thought to have one of these and I think maybe time will tell. which Einstein perhaps you understood.

Skepticism on his part is not true, no, that was not a characteristic of what he was very reluctant to do. I think it is very difficult to express your opinions in his opinions. I had a curious experience once when the philosophy department at Boston University asked me if philosophers like it. Do you know a talk given by someone and then there will be someone who contradicts or measures? Then they asked me if I would like to do this. See who I was? It was supposed to contradict, well, I think they had heard of Dirac, he commented on how projective geometry had been useful in his thinking, you see, so they had it and I rationally said, oh, well, okay. , I will make some comment, you can't refute that because That's absolutely yes, so he gave this talk, she led his talk and she was not very elegant during the talk on projective geometry, just some projects they don't know physics, they didn't read, they didn't influence his own thinking or anything, it was just a talk about projective. geometry, so I'm afraid I got it a little right.

I think some of the owners were hoping that they might reveal something about you in a thought and then I gave a little talk, as I took a leaf out of her book and gave a little talk about Twista theory. I did my version of - geometric physics, but that was a bit curious, but well, projective geometry had a big influence on me because, oh yeah, actually that's going back a bit, but that would have really seen an outdated theme there, you know, it's something that Victoriano, yeah, I mean people just abandoned the curriculum at that time.

I think almost all the units here, I just understood them, you see, I went to when I was at University College London, that's where I did my university work, in fact, there was geometry. a lot of the curriculum you had applied mathematics, you had a kind of algebra, no, primary mathematics analysis and then algebra and geometry. I think that's right, but geometry was a big part of it and there wasn't any complete type, ren TL ren, who was a great purist, started, you know, there were only two axioms, you know anything, there's a line that goes through any two points and if there is a line that goes through these two points and through these and satisfies the needs that must be met here, thank you very much.

Could you prove it? You see that from time to time you need another axiom later, but that's something everyone knows. I hated it, but I quite liked the course. I thought it was very nice to see these kinds of very primitive ideas developing. in a geometry, so there was some projective geometry that I learned there, which was very important, my own knowledge here, well, you brought it back to the endurance contest, yeah, and I was just thinking that it came from your own experience of a way that was quite unusual, yes. so he got caught up in the end, well, I think there was another gentleman who came in later, but then he kind of faded away and he almost dropped out of the syllabus completely and then he kind of regressed a little bit, but but. it was considered old-fashioned and even when you did what was called algebraic geometry there was very little geometry and sense and what you could really see in it, so I didn't like it very much, although I tried to put as much in as possible.

I could, but a lot of that came when I translated my diagrams into some incomprehensible notation, which is, I'm afraid, what my thesis ended up with, but geometry was always important to me, but somehow it meant more in physics like geometry. of quantum mechanics and relativity, well, Roger, we've talked about how in the early days you were starting to think about cosmology, when people really knew absolutely nothing about cosmology, there was almost nothing about the stars that people could see now , it's completely different. There are absolutely gigantic amounts of data, huge numbers of people poring over it every which way, but I think you would feel that some pretty fundamental things haven't really been answered at all.

I mean the role of the cosmological constant and then the origin of the Tell me how you think things are right. I guess I have to think about things differently because issues I've considered important over the years get just as little attention these days. Well, I have always been very puzzled by the second law. of thermodynamics and the direction of time and all that and well, there are several things that it has to do with that can be ramifications and in one way or another, as if it were in conscious perception, it relates to that, but let's leave that aside for the moment, the main thing. something that's pretty obvious in some ways but almost completely ignored now, we're supposed to have this Big Bang origin of the universe and if entropy, which is this measure of disorder, increases with time, that's what the second The law tells us that that means well, okay, it's understandable that if I take a glass of water and I splash it, it falls to the ground and you don't see the opposite, that is, the entropy increases, you don't see the entropy decrease, but if You say this, backwards, it's the same statement, but expressed in the opposite direction, it means that as you go back in time, things become more and more ordered, entropy goes down and down and down and where do you get to? this thing called the Big Bang and what's the best evidence of the Big Bang, well, it's this microwave.

Do you see this radiation coming from all directions? This microwave background has a very important characteristic. Note that it is very early in the Cobie mission that thermal energy is seen. equilibrium, you see this beautiful spectrum, the Planck spectrum, which indicates that what you're seeing was in thermal equilibrium, which is not real equilibrium because it was expanding, but taking that into account and that expansion is not an expansion that increases the entropy, is an adiabatic expansion and Tolman the American. Cosmologists and physicists fully appreciated that they were observing something that was, in fact, thermal equilibrium, which at first glance is a paradox because surely when you go back in time, if the entropy decreases and decreases, it should be quite small, but what You see it's something that tells you that entropy was at its maximum now, it's never been said, you know, this is a big enigma, who says that, well, I've been saying it, but hardly anyone else, not only that, they don't say that. but they said this is what you expect in standard cosmological models if you take a completely random initial state, that's what you get and that's what you expect and yeah, right, and that when they saw Penzias and Wilson they saw this, Dickie and people would say Yes, well, that's what we expected to see.

It's just the flash of the Big Bang. What you're seeing, what about entropy? How can that be? Well, I think this is viral here because people tried to solve the answer in cosmology equations and how do they solve well? Symmetry is assumed because otherwise the equation is too difficult to solve and Friedman did this. He simply assumed that he has a very homogeneous isotropic universe and now he was able to solve the equations. Einstein was quite unhappy with his equations initially. but he still did it right and Sunny agreed with his math, but he thought there must be something wrong somewhere, but he's curious that these are the models that we have that people have used since then and since they use them , you just think this is cosmology and the fact that this is such an incredible assumption doesn't affect people and this is where the entropy is low, it's because all the ripples in spacetime that could have been there weren't there and initially it was assumed that they aren't there because that's the only way they could solve the equations, but then you get used to the idea that they aren't there because those are the models, but why weren't they there?

All of these degrees of freedom in the gravitational free field could have been there and to see how extraordinary this assumption is, think of a collapsing universe that has all the irregularities that could be its shapes. black holes these black holes freeze the entropy skyrockets incredibly now that we have this bekenstein Hawking formula for the entropy in a black hole we can now make an estimate of how big that entropy is and how unlikely the universe is in which it actually we meet. I don't see, you may have had that puzzle even before the big, microwave background was discovered because that attracted you to Hoyle's steady state model as a way out of the Freedman.

It's really that thought about UC. I thought a lot about the second law issue in relation to the steady state model, but yes, there was something. I've already learned that, but then it seemed like the problem could be solved with the picture they have with hydrogen evenly distributed and then when it collapses it turns into stars, which gives it an increase in energy, is the right idea, because but it's with the wrong model, you see that you have a model with the hydrogen produced uniformly and as it builds up, it produces these hot spots. It's great, the action of gravity, yes, gravity reaches hot spots and the Sun is a hot spot in the dark sky and it's not the.

The sun is hot, the sun is bright and it gives us life on earth because yes, the entire sky had the same temperatures as the sun, because it is totally useless, it is the combination of the hot sun and the dark sky and that is where it resides low entropy and that. it occurs through gravity, so it was a crucial thing that yes, already when I was thinking about the steady state I must have been thinking about that, although I can't pinpoint that, but it's true, I did. I worried about the second law then, but the The fact that Hajin was Dennis Sciama think about that too because that's the kind of thing I don't remember, yeah, you should have, but well, I wrote this article for Hawking Hawking Israel with the editors of the Einstein centenary volume and this was me.

I put up this long article about the study of the second law of thermodynamics. I don't think I discussed all of those things with Dennis beforehand, but I didn't have a particular idea that I had subsequently, yeah, I didn't know how to do it. characterize the particular way in which the Big Bang was special and that really comes out of the study of conformal structure. I mean, that's one thing, yeah, in the old days, I don't think I would have given it as much thought as you do too. There were a number of things that I noticed very early and that played very important roles later, but I couldn't understand them early.

One of them is this fact, just a curious fact in mathematics, we are talking about four dimensions and we are talking about space-time times free space of a time and we are talking about via curvature, none of our curvatures are conformal curvature, so that if you have a metric you don't know what the scale of things is, but you know what angles are or if you know what results, that is another way of saying the same thing, that conformal structure tells you that the light comes out but you don't distinguish what big of the small, then the characterization of the curvature is in this curvature of the Weyl vial and the barrel.

Curvature is a measure of conformal curvature, but it is also, in a sense, a measure of gravitational degrees of freedom now in connection with tornadoes, but not specifically with tornadoes. I think I was thinking about it before because I was looking at how to write on spinners. zero rest mass field equations for all the different spins, it was specifically Dirac and although he had it all, when he made the zero mass case for some reason he did it in a different way that I never fully understood, but if you follow the previous article of Dirac and I did it for zero mass, that's what you get, you have this particular way of writing the different spins and Maxwell's equations, you only have two decay rates and then you are the graviton equation, if you want, you have four rates . just the same equation neutrino equation which is just one if you consider it massless, so the gravitational field is two propagations and there is this wave equation.

It had interesting and slightly anecdotal things. Dirac never spoke much, but I was a fellow at John's College in the At the same time, his direct and a fellow at one point asked if he could chat with him about some of his stuff, you see, because they knew he was interested in the quantization of relativity and then he agreed and he left and he had this and I started to describe this turn of things to him and he had this equation, this wave equation for me, so that the turn would feel like you've seen it, I said, sighs, I was wondering Yes thisit could have something to do with quantification using the associated turn, absolutely, it did, sir.

I just don't know, no one is really you, absolutely that's true, and then he said why are quantities used. Well, I don't know, you have to have a Hamiltonian, this company is a little bit, but then the other thing, yeah, the other thing about this. equation he said where that came from he told me where that equation comes from I said well it comes from the Bianchi identities and he said what are the Bianchi identities and I thought we don't know what the fuck you see and here he had been doing all this quantization and obviously he knew them, he just didn't know that they were trapped in the great desert, he knew the contract, the hired ones, for everything and he was curious, I mean, I guess he is someone who also worked a lot on his own, so he knew all these equations, but I had no idea they were called Bianchi identities.

That's a little side story, but the point is that this came later, but he realized that he had this propagation equation that generated the gravitational equations. They look like maximal equations, but first they were... well, they were good. I mean, this was already done about Fierce Power Levy or something, but they didn't do it this way, which looks a lot more complicated if you run into spinners. It becomes completely obvious, but then I started to worry about the conformal invariants of these equations and I was struck by this curious fact that that equation is conformally invariant with a particular conformal weighting waiting for the spinner and we already have the interpretation of the file.the curvature it's conformal curvature and therefore it has another conformal interpretation, so it's a conformal object, but the weighting is different, you have two different conformal expects and it just catches my eye, there's something important here and I had no idea what it was , so it's only a long time later when I realize that it's absolutely crucial in a certain way, which gets to this point.

Yeah, well, you're asking me about the second law and what I thought was important and this big problem that you've been seeing for a long time. At that moment I thought, like everyone else, that the Big Bang, to understand it, we need quantum gravity. I mean, that's this conventional view: we need quantum gravity, maybe it's string theory, quantum gravity, maybe it's loop quantum gravity, maybe it's this kind of higher gravity or that one. a kind of gravity link or twisted quantum gravity, but it's called gravity, no, that means to me or it means to me, quantum gravity must be a very fun theory because the singularity that you see is one of the reasons why you are studying quantum gravity is to explain the Big Bang Singularity, well, see everyone, see how black hole singularities are completely different, people used to say, well, you know you have black hole singularities, listen and say that you have singularities in the big bank or sink, which is the Therefore, the Big Bang in black holes is the same, sometimes it's the other way around, but it's not completely different, but it's this entropy thing, the singularities in black holes are absolutely wild, the curvature of the vile curvature completely dominating as it oscillates all around.

Complete complete insanity in Big Bang karma, so you can imagine, think of the Big Bang as a very violent thing, but its completely regular gravitational degrees of freedom just don't kick in. Now what kind of quantum gravity will give you these two completely different ones? extremes in the black hole complete domination by the vile curvature in the Big Bang the vile curvature appears to be zero or at least very, very suppressed. Well my review then was to say oh what quantum gravity must be a very fun theory with time, not asymmetric time. and if we're going to find quantum gravity here, you have to put in the time asymmetry somewhere, so that was my opinion until well, I guess it was a long time ago, no, it was later, nine years ago, I just had this idea I was thinking about.

Well, it took me a long time to convince myself, when I say a long time, maybe about three years, that the observations of these distant supernovae by Perlmutter Perlmutter, Schmidt and Reese had convincingly shown that the universe is accelerating in its expansion and It was all promoted as something totally mysterious that no one could understand, totally unexpected and I should say, but Gunn, look at God, he seems like a cosmological constant, he's in all the cosmology books, I don't know why they thought that. it was a mistake why should I think we should explain that we are talking about dark, dark dark energy, no, it is a very bad name, but nevertheless, what people call it and apparently it fits perfectly as far as we know now with what the term which Einstein introduced in 1917 for certainly the wrong reason and wanted a static universe, well half of us are right about this, the only yes, the only modification you can make, which in general is absolutely yes, a term, no is only one term, it is the one indicated.

What you can do with generality without ruining it basically yes, without changing it in a radical way, that is correct and very often I would take into consideration in asymptotics the work that I did in trying to live it radiates. I'm crushing infinity and making infinity seem. as a finite limit and you can use the conformal there and some excellent or offi equations of this equation that is obtained through the propagation of gravitons I feel that it tells you how to study the radiation field looking at infinity and I also knew that if there was a constant cosmological constant that was positive this surface would be spaced as it would be now if it were not zero cosmological constant true time if it is negative cosmological constant fortunately it is not negative because that causes all kinds of problems even though string theorists seem to like this cosmological constant positive is a completely different class of problems.

I used to think I had bad characteristics. Upon reflection, it seemed to me that they were just unusual features, but now it was absolutely crucial because I was thinking about the very remote future and how boring it was. I will be in the remotest part, sure that all the black holes will eventually disappear due to Hawking evaporation and there will be nothing left of interest and this continues until Eternity, but for me eternity is not that long because I am used to thinking about compressing. Find out through these conformal scales. This is what defeats time. Yeah, well, your argument is basically.

I mean, I tend to use this in lectures and in jest, but it's a real argument. You know, the universe gets incredibly boring, but there won't be. any of us, any of us around, would get bored of us, mainly their photons, and it's not possible, there are more photons very easily, so the photons just go straight to this limit and I'm getting very used to the image that was having. it's the idea of ​​a boundary that if you just have massive stuff, that boundary is like everywhere else and then the cathode red for me, well you have a space like a boundary for the Big Bang Maya, don't you put them? together, so it's a scandalous thought and I lectured about it, usually being careful to mention it in that scandalous idea before someone else said it was scandalous, but as the years went by I started to think more, but I think I originally would have given a reasonable chance of being right reasonable chance maybe not 50% there are more substances in that report the odds were sweet well you see Paul is tough yeah look Paul Todd.

I had what I called the viral curvature hypothesis, which said that the curvature of the viola has only one hypothesis, one way of characterizing the Big Bang that, since you have an initial type singularity like the Big Bang, the curvature of the viola should be zero, but it's awkward to say because it's a singular state, what do you mean one tenth? So when it's singular and so So Paul had a much clearer way of expressing it, which is, you had stretched it, you had stretched the back of the Big Bang and the form factor, which is something we did all the time to , you know, the freedom of the models, which was quite a standard thing, but making V conditional on the Big Bang, I think is an important step, like Paul did originally, just makes the vowel curvature finite, not necessarily zero, but since I already knew infinity, Warka G must be zero because of how these things scale.

I said before that because there is a conformal factor in the scale, it must scale a biochemical zero, so if you put them together, the zero of our curvature must propagate to be zero in the next eon, so I started playing with these. ideas half thinking it was completely crazy I guess and now the thought is probably correct and we end up looking for circles in the sky actually something we can actually see something that has to do with the Mobius transformations in the sphere well that's it, is that it? what could be more? beautiful, okay, you see, it was just starting.

I just didn't care right away. I was trying to get people to ask me about, do you know how you would know if this is right? and I thought I'm some kind of wrong brother about gravitational radiation or something, but later it occurred to me what's the most violent thing that could happen, that we could be a transmitted signal, and then I was thinking about these collisions between supermassive black holes . You see, we are on a collision course with Andromeda, the Andromeda nebula and it has a black hole that is 20 50 times bigger than ours and we have a four million solar mass black hole it has a bigger one and they could on our course of collision could well capture each other in a spiral when they swallow each other with a huge explosion in the form almost entirely of gravitational waves and these gravitational waves, as I am used to, have the limit, they will come and hit the limit in a defined place What will they do when they arrive? well because of the scales, they cannot exist as gravitational waves on the other side, they have to be reduced to another form and the equations tell us that you have to have a new darkness again.

The word darkness is not a very good word, but I think of the conformal

cyclic

cosmology scheme, which is what I'm talking about here, the acronym or as they call it CCC, this scheme tells us that the gravitation through which darkness propagates information in gravitational waves, but in the form of disturbances in this initial one. dark matter, so dark material has been created and this rotational wave impulse will give it the impetus. Actually, they have another prediction in addition to the circular features corresponding to the outgoing radiation. Yes, that's true. I haven't shot it so well circularly because yeah, I mean, it's what I call the initial form of dark matter because it originally has no mass, it has to have mass, but the equations also tell you that you have to increase the mass so that it doesn't You can keep it massless, there is just an inconsistency, so the mass has to incur, it must be related to the Higgs mechanisms, etc., it hasn't been done correctly yet, but I think one has to understand more about the physics of particles, how is the Higgs mechanism related to the creation of mass in the early universe? appearance of mass that arises from the equations that you have here, this is another big area of ​​your thinking, it is really how conformal symmetry is broken, yes, different ways that it is broken, which we see much more clearly in expressing things in twisted geometric terms so you can I can see the breakup explicitly, but there are always different aspects that I've always had doubts about that, yeah, I saw that the cosmological constant has changed a little bit because I used to think that one of my minds was that you have If there are no cosmological constants, you have these punks, a group of tornadoes and that's it, you have a kind of exact sequence and the exact sequence plays an important role and a lot of homology and theory of tornadoes, etc., but if you have a cosmological constant , It is not like this. you have an exact sequence, you have something that is invertible and changes one's attitude, so I think it was a change because it took me a little while to get used to a lot of the constants, but with cosmology it becomes absolutely crucial, you can't, you can not.

We don't do this cosmology without a cosmological constant, so you have to have dark energy, as it's called, you have to have Dark Matter, as it's called, because there has to be new scalar material created every time you go from one Aeon to the next and, so in all of this it's not to build up, it has to decay, so it has to decay over the course of history, for example in Dark Matter, which I think there is some pretty weak evidence because I don't know how much to trust in it, I see. they should break down instead of clump together, which yes a little bit, but over time they should break down, they should break down, yeah, otherwise what a buildup, yeah, and then, you know, it just builds up for me until the morning and then it doesn't. you're going to have to have a way to spread, so I think it has a disintegration, but there are some, it's not, the evidence is not very strong, but I heard two snippets ofmagnetics or some of these things, these things seem to tell us that there is a lot more going on in biology that you just can't explain in a purely classical way some of it by chemistry, which is already quantum mechanics, but you see, I'm saying you got I have to have enough quantum mechanics to make it coherent across many neurons in a way that allows for sufficient displacement of mass according to the scheme I'm trying to develop.

What did you originally have a scheme like this with and then with different motivations? I picked up a very similar idea, which is that when insurmountable additions are made, if there is a sufficient mass displacement, we move on to classical alternatives, but this is very round: the quantum mechanics people because they think that quantum mechanics has to be maintained . durably at all levels, but all experiments to date have only been done at one level that is not investigated, this is the root area, so there are experiments hidden in the wings. Well, thank you very much Roger for taking advantage of this time.

Well, once again, time is ruling. Yes, well, it has been a great pleasure for me. It's always a pleasure to talk about these things and try to inspire and maybe inspire someone who's watching this to think that would be good, who knows.