What are Hawking points? | Sir Roger Penrose | Mathematical physicist and Nobel Prize

Many of the things I want to say will be difficult to understand. I apologize because I'm talking to experts tomorrow and I think they'll find it harder to understand than you because some of the things I want to say are unconventional when I say them. something unconventional I will explain that it is unconventional now a minute I have to know how I move things here yes, it's okay red and green now the title has to do with Hawking

points

, that is already unconventional because in standard cosmology I will be talking about cosmology in standard cosmology, now they have no such things to tell you

what

they would look like if you had eyes that saw, could see microwave radiation, not ordinary light, but microwave radiation, and you are in space.

I claim that you would see certain

points

in the sky. which are approximately eight times the diameter of the full moon so it is not very big but the full moon does seem big to you but only because we are used to it but eight times the discharge of the moon sometimes a little smaller but never bigger than that Now these points are not part of conventional cosmology, however, they are an expectation of the scheme I wish to describe. Now, first of all, I want to show you a picture of the universe. This is an image of the universe.

It is an image of space-time. Everyone who attended the previous talk will understand about space-time images. Time is the dimension that rises in the image. Space rotates now. To get the image, the complete image, I have to remove two dimensions of space. we have a dimension that goes horizontally, in fact, maybe I'll show you the next image, it doesn't move exactly when I mean it, but that's okay, the blue section shows you about once so you can imagine that blue section moving up. . the image and at any time you have a section through this image of the universe as you see at the bottom let me go back.

I have to get used to the time. Yeah, oh no, no, that was meant to be the other way around. I was told that if I press the red button it goes backwards and the green button goes forwards, but it doesn't seem to do that, okay, yeah, so the Big Bang is at the bottom, which is supposed to be the beginning, and then the universe expands outward. and as time goes by it slows down and works a little and then begins to accelerate in its expansion. This is a fairly recent discovery. This acceleration of expansion is often called the dark energy effect.

I call it the Einstein effect. Cosmological constant, which is a term that Einstein introduced into his equations of general relativity for the wrong reason: he wanted a static universe, but when he discovered that the Universe expanded, he retracted the cosmological constant from it. He calls himself Lambda term, but unfortunately or fortunately he should say that his introduction of this term describes the way the universe has this expansion in the remote future. Now there is another feature of this image that may seem disconcerting at heart, it became a bit complicated, that's because I don't want to prejudge the subject as such. about whether the universe really is closed and especially closed or maybe it's open and does complicated things, so I won't worry about that, except I'll describe all three.

Sorry, there is a time delay. In my gratitude, I want the next image, maybe if I say the next image please, this doesn't seem to be of much use, the next image, please, yes, now you see, these are some images of the Dutch artist M.C Escher and they describe the three types. of uniform geometry in the upper left we see an image, these are all in terms of angels and demons. It's very clever how he does everything. At the top left we see ordinary Euclidean geometry, which is a plane geometry. At the top right we have the positively curved geometry that you can think of as the surface of a sphere, except you have to think in more dimensions.

This is just two-dimensional geometry in three dimensions. It is something similar but with one more dimension, but the positive curvature is the one in the top right, the bottom one is the negative curvature image, which is the third type of geometry. Cosmologists tend to believe that it is more or less flat. The one on the top left, however, doesn't make much difference and

what

I mean is that I don't care much which one it is, but the reason I have the Free Geometry on the back is simply so as not to hurt the problem. The image at the bottom will be important to us later and I'll come back.

Getting back to that now I want to move on to the next image, if I may, which I should talk about if I could remember what it is, it's just the one we just had, so this is our universe. Now I want to say something about the Big Bang, some people would say that this picture is inadequate because it does not describe the very early stage of the universe which is called inflation or cosmic inflation. Now there are two reasons why I don't describe it in the picture, one of them is that maybe I do it because it's actually in the little spot at the bottom completely squashed at that point and you wouldn't see it.

The other reason it's not in the picture is that I don't believe it, so this is something that's different from standard cosmology. I just don't believe in the initial inflationary phase. Now I want to show you what inflation looks like. If it is there, we need a very powerful magnifying glass to see it correctly and the following image shows you what you would see. You will see something that looks very similar to the distant future. It has this exponential expansion, which is what we're again starting to see on a completely different scale in the remote future.

However, it is assumed that there was such a phase in the early universe. Now what I am going to assert is that there was no such phase after the Big Bang, but in a sense there was before the Big Bang, so inflation is needed to explain certain characteristics of this radiation that arrives in the future. cosmic microwave background radiation which is microwaves and this is in this radiation. I claim that you would see these points that are eight times the diameter of the moon, a little warmer than the temperature around people, why haven't they seen this well?

The reason is nobody. look and the reason no one looks is because they believe that inflation smoothes out the universe and makes it uniform. I will affirm that it is not as uniform as we think. Now let's move on to the next image. The following image is the same one I had. before, but with time going in the opposite direction, I am going to try to explain why I do not believe that the unity of the Universe causes the inflationary phase to make the universe uniform. I don't think I should spend too much time on this because I don't have much time, but you see, suppose the Universe was collapsing and we had the inflation field, as it's called, which explains inflation.

You put it in and now I want to make it a little irregular. I'm going to put it. irregularities in it, inflation is supposed to eliminate the irregularities, let's put them in and what happens is that they produce black holes, all these black holes freeze into a big mess and that would be the most likely type of final future of this inflationary universe, which inflationary. field or not now if we consider that the other way around now this is the most probable initial state, the universe was not like that and inflation, the inflation field would not solve this initial mess, but why wasn't it like that?

Well, I want to try to explain something about that, but it's not like that, it's more like this looks a lot like the picture that we actually see in the universe now. I want to say now something about this is an image of Escher that is not exactly the same. He had done it before, but it is another image of Asher that describes the same type of geometry. Now this is an image in what is called conformal geometry. Now in Geometry you are used to thinking only in distances, it can be a curved geometry or where the distances are.

They are not uniform but, on the other hand, we think in distances. Now there is a more general type of geometry called conformal geometry. Now conformal geometry is the geometry of angles, so if you have a triangle, the triangle will have certain angles and you can have a large triangle and a small triangle and the geometry I'm interested in is the geometry of angles of the triangle now you can have a geometry that is not like Euclidean geometry and this is what we are describing here the negative geometry but the point What I mean is not that this could be the geometry of the Universe.

I guess I'm not sure it is. I don't necessarily expect it to be, but it illustrates an interesting feature in this type of geometry: you can represent infinity. You see that Infinity is that circle around the outside and you see that the little fish or whatever they are are very, very small, but they believe that they are the same size and the geometry describes the whites and the blacks, each one thinks that They are exactly the same size. same size and shape no matter how close to the boundary they are, but from our perspective we can make a conformal map that crosses the entire image downwards so that Infinity is represented by a finite boundary.

This is a very useful trick in relativity and I'm going to use this trick in space-time, not just in this two-dimensional space but in four-dimensional space-time. Now, to describe the geometry of space-time, it is really better to talk about light. cones or null cones that you see in the image above on the left side, we have a light cone or a null cone and this describes a flash of light, so imagine at the vertex that little dot in the middle. Suppose there is a flash of light on the right side you see a spatial description and that has all the dimensions on the left side.

I had to pull one of the dimensions and when the light comes out first, it's a dot in the middle and then it hits the red sphere, I think it's red and then the blue one. I can't see the colors very well, so you'll have to correct me on that, the blue on the outside and those are sections through the cone on the left, so I have to pull the cone down one dimension but it really represents what you see in the right side is the story of a flash of light now the story of the flash of light has a bottom inward cone and that is light.

Focusing on that point, this tells you most of the geometry of spacetime. If you know where those cones are, you know most of the geometry of spacetime. A special relativity. I think the previous talk was mainly about special relativity. Look, the cones are generally relatively evenly distributed, they can be all over the place in one way or another. The important thing is that the flash of light or the particle of a photon of light is described by a line that is along the cones. all the time, while a particle, a massive particle, would always be inside the cones, so that's the important part of Relativity, you can't travel faster than light, but your world line, which is the history of a period, it would be inside the cones, okay, so that's the main part of the geometry and what I'm trying to say is conformal geometry.

It's not all geometry. Now you see the image above and I have on the left side the two most famous physics of the 20th century. Of them, the second, I think, is Einstein's E equal to m c squared which tells you that C is a constant tells you that e that is, energy and mass are equivalent, so energy and mass are equivalent. The top formula is even older, early 20th century physics. quantum theory, while Max Planck's formula E is equal to H nu nu is a frequency which is the Greek letter Nu H is again a constant, so it tells you that energy and frequency are equivalent, so if Putting the two formulas together tells you that mass and frequency are equivalent, so if you have a massive particle, a stable massive particle, it's a clock, it's an incredibly precise clock and a lot of amazing things you can do in physics today depend on that fact.

The fact that we have such accurate clocks ultimately depends on the fact that mass gives you frequency, so that's the top image, the bottom image tells you what would happen. You see, I have introduced, in addition to the cones, what the mass gives you and shows you how the clocks behave, so I have two clocks working. At the point you see, I imagine you have two clocks whizzing past each other very close to each other at that point and they are identical clocks, but the first tick is represented by the first small bowl-shaped surface, the second tick is the second surface. so now we have the geometry of spacetime, if we not only have the cones, I should say the cones to describe the geometry, you need 10 numbers per point, the cones give you nine numbers, that's really the ratio of those 10 numbers to the tenth number is the scale certain things in physics only need those nine numbers certain things need the ten numbers the difference is that if you have mass then you need the 10 numbers if you don't have mass you only need the geometry as you only need the cones of light, you don't need the scale and the love of physics does not need mass and the main part of physics that does not need mass is light, photons do not have mass and in the image below you see a photon that goes along the cone it is not even meets the first cone, the first bone surface, so photons don't need mass, they just needconformal geometry, so this is an important point in the diagrams that I want to describe to you now here. it's a little trick it's just a trick but it's a big trick what I've done at the top is like the image we just had, the image of Asher.

I have crushed Infinity to be a limit, so the purple line on the left, well, it is a Divinity, you don't see it, but on the right I have crushed it, just like in Escher's image, that limit is at the top, like this that I crushed Infinity and while we are only talking about massless things, it describes the physics very well now, in the distant future, most of the particles that will be around by a huge factor will be photons and the photons that we see in the image I described here they came about because I was worrying about the future that you see and I'll explain a little bit why I was worrying about the future that comes after. but let me also talk about the beginning, the Big Bang.

I've done the opposite trick. I've extended it and that's another limit, so there's nothing unconventional about this image. Cosmologists generally don't draw it this way, but it's perfectly reasonable. The way I draw it now what I want to say here is that in the remote future we have massless things, so even the physics is pretty well described in this image and in the past it is the other way around as seen in the remote future. you have very rarefied cold in the distant past and the Big Bang is the opposite you have very very hot and very dense but in a sense they are very very similar and if you didn't have mathematics they would be extremely similar And that is the important point I want to make now , you see, why do I say that in the distant past, a little close to the Big Bang, it is good enough not to ignore mass, but it is a different argument?

Things are getting very hot. everything moves so fast that the energy in its emotion is much greater than the energy in its mass and that is why particles are very well described as a particle that has no mass at all because the mass it has is completely flooded by the energy in its motion and again you can legitimately describe physics by massless things, so the image is also a good physics image. Now I want to dig a little deeper into this first of all in the past, now you see why the image doesn't have that big mess that I described, it's much more likely to be the beginning of the universe, why do I say much more likely?

Well, if the universe were chosen at random, it would be like that big mess at the beginning, not just the very nice, fluid image we seem to see now. This is a feature of the second law of thermodynamics. What does the second law of thermodynamics say? He says that randomness increases well. It's called entropy, which broadly speaking is a measure of randomness and says. you as time goes forward the randomness increases now this tells you that if you go back in time the randomness should be very very small so the universe was not random. Now this is something that people have trouble accepting and they try. make inflation remove all the irregularities, but it doesn't and I'm trying to say that in the description above I don't think I need to say much more about that, but let me say something about this image.

Up here, now you see that you go back and forth in time. Another way of saying the second law is that they go back in time. Things become less and less random. Entropy goes down and down. What is the first thing you see? I can see directly what is the origin of this microwave background, this radiation coming in all directions, it was discovered that Christ got the Nobel Prize, once he got the

prize

nowhere for his Discovery, second, more or less he got the Nobel Prize because of this image here. This image describes in more detail what the radiation is like, it tells you that at the bottom we see the horizontal line at the bottom, the x axis if you will is the frequency and the y axis going up is the intensity and that tells you indicates the what you see in this radiation and then you see these lines that are error bars and you are exaggerated by a factor of 500, so you have to consider that the error bars hug that inclination, so it is a very good image of What is that radiation like now?

There's a bit of a paradox there because what is this? An image of this is the famous Planck curve that describes maximum entropy well. It tells you what the state of maximum entropy is. What radiation and matter in balance with each other, the radiation would follow that curve. What do we see that you go back and back and back in time? The entropy should be going down and down and down until the first point where you see that the entropy is at a maximum because this curve tells us that it is at a maximum and that seems like a paradox.

I consider that to be the mammoth in the room. Why don't cosmologists worry about that? Because it should be a very low entropy state, whereas now we see a high entropy state. It is not a paradox. Why is it not a model? because what we are seeing is radiation and matter in balance and that is fine, the universe is expanding, but that is a minor point, that is not the point of the argument, the point of the argument is that what you are not seeing in that image is the entropy is low in gravity and this is a crucial point of the image.

Now you see the top image here. I just have a cartoon, let's say you have a box and you have a gas in the box and initially it is hidden in a corner and remove the partial partition if you want and the gas then spreads evenly. The state represents high entropy for a gas in a box. Now what about the bottom image? These are gravitating bodies that you imagine, let's say, a galactic scale box and these are stars or something like that. then you will see that you could start with a uniform state and as the entropy increases it becomes more and more lumpy, then what you are seeing in the universe is a combination of the top right image and the bottom left image of the uniform sky, this is from done you see, this microwave background is extremely uniform across the sky, which is consistent with a low entropy in gravity and a high entropy in matter, and that's what we see, so the puzzle we have to explain is why gravity wasn't exactly what it was.

Why was something like always increasing entropy? Well, you see, it is also important how we live because we live from the Sun and people say that we get energy from the Sun. That is not really correct. I think Schrodinger was the first to point out. What we really get from the Sun is energy in a low entropy state. The Sun is a hot spot and a dark sky and, due to Planck's formula, energy comes to us in a small number of photons and disappears in a large number of photons. photons I don't want to talk about that in particular, but it is an illustration that we are living from the fact that the Universe has condemned and the matter in the universe is condensed in these hot spots that are stars and that is what we live from. that's how we don't do it, our entropy is kept low because the sun is a hot spot in the dark sky, so okay, this is consistent with a picture I've shown you here, but the gravitational degrees of freedom don't They are excited.

They are very uniform and one way to say it is in this image. He had another complicated way of saying it that I won't describe to you, but my student, my former student Paul Todd, had a much better way of saying it and that's just this picture. It's saying that you can just stretch the big bang and make it into a nice soft boundary that's not unconventional. That's not the way you normally hear it from cosmologists. It's a picture of what the universe is like. That's not unconventional. It is not conventional is my next image What I am saying is that our Aeon (the one in the middle) is meant to be us, that is our universe.

I do not call it our universe because our universe, what I say, is this continuous succession of eons with which our Aeon began. our big bang and it will end in a sense with this exponential expansion and when we extend our big bang and flatten our remote Affinity we find that it seems to fit very well, the squashed remote future seems to fit very well with an extended big bang with this very special condition that the Universe was very uniform and it gives you that if this model is correct then you have an elimination of all those very complicated and messy Big Bangs that might otherwise have taken place, so it is a very nice model.

I think and this is what I want to try to describe to you, so this universe consists of a succession of eons, each of which has its own Big Bang. Each of which is a very nice and uniform big bang that is the continuation of a previous remote. future, as I said before, they don't look very similar if you think about the geometry that involves distances and mass, because you have a dense and very hot initial state in the big bang, you have a very sparse, very rarefied, um cold remote future, but From the conformal point of view, if you flatten the cold Universe, it becomes hotter, if you spread the hot Universe, it becomes colder and therefore even the physics coincides very, very beautifully.

Now I want to say something else that I haven't described yet and that I haven't described yet. It is an important feature about the remote future and they are black holes, it is very important because it is where all the entropy goes in the remote future. This is a space-time image of a black hole that people usually represent by a black spot that doesn't tell you much, but if you put the light cones in, you really see a lot of what's going on. I'm not going to spend too much on this image, but you see that the cones are tilted in such a way that it becomes the outer side of the cone and it becomes tangential to this cylinder at the top which is the Event Horizon and you can see that A falling particle is trapped and cannot escape, so this is a conventional image of a black hole collapsing.

And now that? happens with black holes in the distant future, what happens is good, first of all, I put the black holes in the image now so that it is no longer to scale, but it doesn't matter, now those are the lines that represent the singularity as I should have. He said that the Big Bang is considered a singularity, so we cut where the curvatures become infinite and the black holes have singularities in the middle, which is where the curvatures become infinite. That's where Mark thinks red, but he doesn't care too much about that, now what happens?

Well, black holes, according to Stephen Hawking, if you wait long enough, these black holes will start to radiate. They will radiate to get an idea of ​​this. There are many black holes that are very, very big. Supermassive black holes are galactic. The galaxy has a black hole at its center that is approximately four million times the mass of the Sun. It is relatively small compared to other galaxies. uh, uh, we're, there's the Andromeda galaxy, which you can see in the night sky. The Andromeda galaxy has a black hole that I think is about 40 times bigger than ours, never mind the bigger ones, which we seem to see, how long would you have to wait, you see, the universe has to expand and become larger and colder, and colder, this radiation is very very, very, very cold.

If you have to think about the highest temperature you've ever reached in these things, you have to compare it to the coldest temperature ever reached on Earth, but when the universe expands and expands and expands, it gets very, very cold. and then the The black hole becomes the hottest thing ever and then it evaporates Away by Stephen Hawkings uh black hole evaporation now the biggest ones actually probably aren't the biggest they would even be longer than this, but how long How long would it last? Think about Google years, what is Google? It's not a very scientific term, but think of one followed by a hundred zeros, that's a Google.

Write everything in ordinary notation. That would be a Google now. If you wait that many years, some of these supermassive black holes will have exploded. pop or whatever, some of them won't have to take very long, but we're talking about infinity, infinity is much longer than an awfully long time, so all these things will disappear. Now, the crux of this in my image. is that although that radiation spreads and spreads and spreads, if you remember that image, I don't know if I have it here, you see, I have them exploding here, the actual final disappearance of them is relatively boring thing I called it pop okay, you can think of it as a nuclear explosion or something because cosmologically it's really very, very trivial, almost all the mass of that black hole, which could be the entire mass of a galaxy, will probably ultimately be all the mass. mass of a galaxy cluster galaxies tend to be in clusters ours is relatively small there are many larger galaxy clusters out there and they are supermassive black holes that eventually swallowed each other we are on a collision course our supermassive black holes on course of collision with the black hole of the dramatic Andromeda galaxies and they will smile at each other and there will be an explosion when that happens.

I talk a little bit about that, but I really want to talk about the Hawking effect, which is really what I'm talking about, so let me go to the next image that you see. Can you observe?I used to talk about this and where I'm thinking someone will probably tell me how much time I have left in five minutes. Is it thanks? I used to think I gave a lot of talks for a while. I think no one will be able to prove me wrong, so I can talk about this forever, however, then I thought, well, maybe there are observational effects now that this image shows. you, one of them, these are a collision between supermassive black cards, the horizontal plane in the middle is the union between the previous Aeon that is before that thing and our Aeon that is above it and this is us, just above, Looking back, that is our light. cone and see the effect of supermassive black holes in the previous Eon colliding and I'm not really one to talk about that, but this is a photo from my colleague Valhi, again plotted, uh, a lot of these things in the sky and they are very uniform , simply with a non-uniform distribution.

You see these things in the sky. Nobody believes me because heaven should not be. You're not supposed to see regular irregularities like that. A Polish group led by Christophe Meisner, Pavil Nirosky. and another survey and later a Korean named Daniel Anne did some analysis. This is the first one, I should say, was the Planck data. Sorry, the map data W. It was a satellite sent. This is a more sophisticated satellite called Planck. data and you see that it is still very, very non-uniform. People didn't like that because they didn't link the non-uniform. I didn't want to move on.

Can we back up just a second? Please, that showed. The concentration of prayer, well, let's move on to this image. Now this is something else. Now below that plane, you see the bottom. The red plane is the crossover between one eon and the next, so we are seeing supermassive black holes that eventually evaporate. and you have to imagine that Google years if you want, but remember the picture of Asher that I showed you right at the edge, you see those angels and demons or the fish or whatever they are, they become very, very, very small so that everything what happens even though it is a long time is crushed into a small point, so the supermassive black hole all the radiation from that supermassive black hole will be concentrated in one point and now just vahi low and I using an analysis method and the polish The group using another method of analysis seems to see these points.

Now I talk mainly about the Polish analysis because they give it a figure. They first looked at the W map analysis and found a level of confidence that this is. a real effect of 99.4 confidence now we look again um this is maybe a good picture of let me explain what I was saying, I mean today they looked again and found these Hawking points with a confidence of 99.98, so it's pretty clear that they are there you see both on a w map and in the Planck data the five most prominent points are in exactly the same places this image is just to give you a cartoon the conclusion is the crossover between the previous Aeon and ours and Hawking is seen evaporating back home producing a huge explosion as all the energy from the black holes passes through it and spreads.

The next line is what you see, it is the cosmic microwave background that is 380,000 years after the Big Bang and one point extends to four degrees. in the sky, so when I look, you see these dots that are eight times the diameter of the moon, that's what you see, you look back, you don't see the dot, the Hawking dot is the dot at the bottom, it What you see is the extended point. at four degrees in the sky that the recovery is the result of a Hawking point now maybe there is some other explanation than someone present to tell us that you can't have inflation in this image, it would ruin the whole image that would have to be explained some other way I haven't heard of any other explanation so I'll leave you with this this is what I claim we're actually seeing we're seeing the stretch at 380,000 years where a point at the Big Bang becomes what you see in the microwave background extended to four degrees.

Thank you very much, foreigner.