Nobel Lecture: Roger Penrose, Nobel Prize in Physics 2020

this year's nobel prize in physics celebrates one of the great triumphs of mankind's thinking and exploration the formation of black holes was predicted on theoretical grounds these are objects that by definition cannot be observed directly astronomers took up the challenge and thanks to great innovations and by pushing the boundaries of technology were able to show firm evidence for their existence these bizarre regions of space time where gravity is so strong that even light is trapped have captivated the interest of both scientists and laymen alike among physicists many resisted the idea that such beasts could arise in the universe as they involve a so-called gravitational singularity at their center a point where gravity becomes infinitely strong albert einstein was arguably the most notable skeptic simply put the notion shared by many of the sharpest minds of the first half of the 20th century was that it would take unphysically perfect symmetry for collapsing matter to become a black hole thus in a real universe natural imperfections would prevent such objects from ever forming this year's nobel laureates have drastically changed that perception roger penrose receiving one half of this year's nobel prize used ingenious mathematical tools to demonstrate that the formation of black holes is in fact a robust prediction of the theory of general relativity regardless of the geometry of the mass being pulled gravitationally the other half of the prize is shared by reinhard gensel and andrea guess for their spectacular detective work examining the orbits of stars around the milky way center with exquisite precision circumventing formidable observational challenges to disclose the nature of the invisible object in the galactic center harboring over 4 million times more mass than our sun with that i would like to invite our first speaker roger penrose to talk about black holes cosmology and space-time singularities roger penrose earned his ph.d from cambridge in 1957 in the late 50s and in the 60s he held positions in prestigious institutions in the us and in the uk and in 1973 he became the rose bowl professor of mathematics at the university of oxford turning into emeritus in 1998 there are numerous mathematical and physical findings that carry his name including penrose tilings parents hawking singularity theorems and of course penrose diagrams he is also exceptionally gifted as a popularizer of science and has written several best-selling books please join me in welcoming sir roger penrose in 1908 herman minkowski introduced the idea of space-time which was a four-dimensional space which encapsulated pretty well all of einstein's 1905 theory of special relativity at first einstein didn't like the idea very much he thought it was mathematical so history or something but then he picked up on it and it was central to his generalization to his general theory of relativity now in the first picture i've imagined three axes for a three-dimensional space and then we can move on to introduce a time axis to see our axes four axis four dimensional space now the important most important thing of this is to represent the speed of light here we have a light ray and this we want to see it so that it doesn't sort of lie on the floor so we want to have units so that it can be seen as maybe 45 degrees or some reasonable angle so that you have your space and time unit so they're comparable now here we have the nalcone which represents the directions of all the null rays so the light rays in all directions are represented by this cone it's very important in fact we don't really need the light ray there because we've got them all in the cone we don't need the axes so the important thing is this null cone now in general relativity you see there's a null cone at each point representing the local speed of light but the cones can be more or less all over the place now you can imagine a point and the light rays coming out of that point and that's the light cone if you like the narcons can be tangent to it wherever it goes but you can see at the back at the top and right hand side where the light rays start to cross each other and this sort of thing makes it like cones complicated but it's important for what i i'm going to talk about later that you understand these things you certainly are going to get crossovers crossing points caustics and things like that and they're a central feature of what i'm going to discuss okay now let's consider the following picture in this picture we see basically the oppenheimer snyder collapse of a dust cloud to what we now call a black hole this was in 1939 when they studied a collapse of what they called a dust cloud this has no pressure what what you call dust is simply a fluid or something with no pressure and the thing was spherically symmetrical so the fact that you fell inwards and it focused itself into the central point and you see as you move up the picture you see this singularity in the middle where the dust cloud gets itself focused to and you find that since the density goes infinite the space-time curvature becomes infinite and this is what's called a singularity now this was known and at the time that quasars were discovered people do people started to wonder whether there wasn't something like the oppenheimer schneider collapse involved now i wasn't aware of this openstack schneider paper in the i think it was in 1958 when i went to a lecture in london in king's college london my good friend and mentor dennis shaw drove me there he said it would be interesting to me and this was a talk describing how you get through what was then thought of as as the schwarzschild singularity now the top part of this picture is what finkelstein described you see schwarzschild shortly after einstein introduced his general theory of relativity solve the equations for a spherically symmetrical body now he also solved it sort of for the interior of the body but that wasn't a very realistic model wasn't important so much what was important was the solution for the exterior of the body spherically symmetrical vacuum now the thing about this is if you imagine squashing the body down smaller and smaller and smaller you get to a point which is called the schwarzschild singularity often it was called that because the equations all go crazy and things go infinite and people used to think this was a singularity which means you simply have some physical nastiness which you can't extend beyond but the model as i'm showing you here well at least the top part of it was described to me by david finkelstein at king's college where he gave a talk in in i think it was 1958 and i came away thinking gosh you've got the singularity still in the middle where you got right rid of the one on the outside but you still have that one in the middle so i wondered whether there was a theorem or something which showed that whatever you did if you had it complicated irregular in some way you would still get a singularity i had no idea of how you might prove such a thing so i started to think to myself what do i know about general relativity that maybe other people don't know and possibly this will be helpful to me to do something that people aren't familiar with what i settled on was two components spinners now here we have in the next picture a picture on the right hand side of a two-spinner i learned really about these things from the great physicist paul dirac um i think it was earlier in the same year when he gave he sort of deviated from his normal course and talked about two spinners he he was famous for discovering the equation for the electron but these use four spinners four component spinners and you can break them down into these two spinners and direct was well aware of that and i was familiar with the idea but i simply didn't understand them and iraq's lecture made it absolutely clear to me and so i began thinking okay this is something comply to general relativity and maybe it will give me an insight that perhaps isn't familiar to people in the picture you see now on the left hand side you see the celestial fear sphere and that's the different directions in which the two spinner can point in the two spinners it points along the like cone but it's also got a little flag attached to it i won't go into that at the moment but it was important to have an understanding of the geometry of two spinners now the important thing mainly for me was that you can understand the curvature much better in two spinners in particular the part of the curvature which is called the vile curvature now in this picture you see the curvature splits into two parts one is called the richie curvature and that is what matter directly influences einstein's theory tells you that the matter density the energy density the pressure and all that stuff tells you what the richie tensor is directly but what's left that's ten components what's left is another ten components which describe the way the gravitational field behaves so that the free gravitational field in the gravitational wave say is described by the vial coach and you see it gives you a distortion in the field of vision so somebody's looking back and you see the focusing effect due to the richie curvature and then you see the effect due to the distortion due to the vowel curvature now um the vodka which is satisfied very nice equation when you rise in two spinners and it really attracted me very much but getting used to how light roads behaved it was something that i felt at home with and how they focused and how caustics behaved and crossing surfaces behaved and all that sort of thing so i got familiar with all that but at the time this was when the quasars were being seen this was in 1962 63 64 that sort of time when these bodies which were producing enormous amounts of energy and they seem to be very small so they had a an energy which was i forget 100 times an entire galaxy but yet they seem to vary in a few wows or days or something like that which meant they had to be very small and they had to be very big to emit such energy very massive to such energy so how could all that energy be squashed into that small volume and people started to speculate speculate on whether something like the oppenheimer schneider model might be relevant but then you think just collapses radially inwards and doesn't give you anything so if you want to have radiation coming out you need to have at least a quadrupole structure or something complicated not just a radial collapse so i started thinking about it partly at the instigation of john wheeler and at the time there was a paper by two russians liftshits kolatnikov which seemed to have proved that in general you would not get singularities and only very special situations so if you had a generic collapse it would just swish around and come swirling out again so i started to worry about this problem i had a look at their paper i didn't notice the mistake there was a mistake in the paper i didn't see that but what i did see was the methods they were using i didn't feel altogether convincing and that it was worth trying to see whether you could get singularities in a generic situation and i remember walking in the woods and trying to think about this and i came to the conclusion that it couldn't be a local thing it had to be something non-local some kind of criterion which tells you the point of no return in some sense has been reached and i then devised the idea of a trapped surface the picture you see here is the picture that appeared in my paper a paper that i published in 1965 i gave a talk at king's college london in 1964 about it and the argument was that if you have a collapse which is generic that you might still have problems even though it wouldn't be focused right into the central central region and i developed this idea of a trapped surface you can see that's this little ring in the sort of middle of the picture you have to imagine that it's not a ring because i'm only depicting two dimensions and the whole thing should be four dimensional and that ring is really a two-dimensional surface like a sphere but you can imagine it might be distorted not like that now what is a trap surface you have to imagine that there is a flash of light emitted all along that surface here on the top left you see a picture of a little surface and you imagine suppose there's a flash of light occurring on that surface and if it's convex well on the concave side the flash will be converging on the convex side it will be diverging and that will be the normal thing for a surface now on the top right you have something which is sort of you might imagine that it can converge on both sides on the bottom you see a much more general situation which doesn't depend on any kind of curvature you get this in flat space the intersection of two parts like cones you get this property of a locally trapped surface now the trouble is that when you have a surface like this which is global all the way around such as in the in the in the picture that i have on the uh the central ring which is really a two surface and i'm imagining that a flash of light occurring on that it's converging on both sides and that's what a trap surface is and one i was able to show that if you have energy which is locally positive and you look at the behavior of the future of that surface that you must run into a contradiction that is to say you get a singularity so this was a proof in general circumstances that you couldn't have irregularity as something swishing around in a complicated way and come swirling out again you would always get a singularity and this was the central theorem that i proved which eventually seems to have won me the nobel prize okay now let's think about the universe as a whole now you see stephen hawking was not that talk but dennis sharma got me to give a repeat talk in cambridge and stephen was at that talk in cambridge and we held quite a long chat afterwards about the methods i was using george ellis was there also and uh steven picked up on it very quickly and developed these ideas uh by generalizing my arguments to apply to a cosmonaut cosmological model i won't go into the details of this but the main point was that you could also show using the arguments that he developed and also we got together eventually and wrote a paper together uh which more or less encompassed the things that we've done before and this showed on the under very general circumstances in the past now if you have some kind of diverging ray some kind of expansion in the universe then you couldn't avoid having this singular state in the very early universe now this was fine that you seem to prove these singularities but i remember being uh very puzzled by why cosmologists didn't study all the different kinds of singularity you could have because they're very common there are many many solutions known genuine relativists where you could get very complicated singularities and i remember this was an occasion when i think i was at princeton and we were about to go to a conference at stevens institute in hoboken and we used to drive up in several cars i noticed in the car in the back of one of these cars was jim peebles this was last year's nobel prize winner in physics this was long before that of course but um i noticed he was there and i asked him i said why don't you cosmologists ever consider all these complicated possible singularities that you could have and you just look at this simple case why don't you look at these other cases and he looked at me and says because the universe is not like that and i thought my gosh it's not is it i presume that he was looking at the microwave background radiation which is very uniform over the whole sky and it tells you that the universe really is very uniform so it tells me that there's something very strange about these singularities that the big bang singularity is utterly different from the kinds that you see in the future in the collapses in black holes and i was very puzzled by this and since everybody seemed to think that the solution of the singularity problem was the that you had to combine general relativity with quantum mechanics you had to find a quantum gravity theory uh it must be a very peculiar quantum gravity theory which is grossly asymmetrical in time which gives you a theory which makes the singularities quite different in the past and the future well i had this view for quite a long time until i think i started to worry more about well well i thought you worried about the singularities in relation to the entropy in the universe i'll come to that in a minute but first of all let me talk about what the universe is actually like according to what people think you see what they think is that the big bang was not just like this and if you have a magnifying glass you can have a good look at it there's something called inflation now inflation according to the theory is another exponential expansion which took place with a tiny tiny tiny fraction 10 to the minus 30 something or other second of a second and that is supposed to have taken place this exponential expansion and it was supposed to smooth out the universe and do various other things to the microwave background make it look as though scale and variance and things like that so it had role to play but i didn't see that it would scale up you smooth out the universe well the reasoning i was using is suppose you imagine a collapsing universe so here we have a collapsing universe and this collapsing universe suppose we put the inflitan field which is supposed to give you inflation well it just doesn't do anything if you have not irregularities black holes or congealing together the picture would look more like this a great mess with your vowel curvature diverging like mad in then you imagine well that is much more likely thing and you can work out how much more likely it is something like the probability of finding this is 10 to the 10 to the 100 something 10 to the power of 120 or something that you get that more likely than the isometrical model that we seem to see at least in the big bang but in the big crunch if you have the universe collapsing into a mess like this this is what you get but the question is why wasn't it like this in the past this is a very strange kind of quantum gravity theory which is what i thought for a while now another this is connected with another problem which is the problem of the second law of thermodynamics now let me describe the picture of the second law of thermodynamics people often talk about a gas in the box so the top three pictures on the left hand side we see a gas in the tucked up into the corner in a little box you open the box and it spreads out through the through the big box if you like so as the gas spreads out it gets more and more uniform the entropy or the randomness increases in accordance with the second law now that's what you you see that the right hand side stage of this picture you see matter which is very very uniform in the beginning which would be a maximum entropy state in fact the microwave background where you see it it looks like a maximum entropy state so there's something very funny going on how can it start off at a maximum but then when you think about gravity it works the opposite way because gravity is uniformly attractive so here i have a picture on the left of a lot of stars running around and then they tend to clump and then they finally get black holes and the entropy goes shooting up enormously by the bekenstein hawking formula which tells you what the entropy in a black hole is and it completely utterly dominates the entropy in the universe right now almost the entire entropy in our current universe is in black holes by an enormous factor so we see that what's special about the universe is that the gravitational degrees of freedom were not activated somehow and i tend to postulate just that maybe quantum gravity tells us in some mysterious theory that somehow the vial curvature had to be zero in a past singularity and it could be infinite in the future singularity just sort of waving hands around and no theory which tells you that and i thought that for a long time but then after i became persuaded and i think i want to go back now look at this picture that the universe this was a another nobel prize saw palmetto mutter and uh and uh schmidt and rhys discovered the distant supernovae stars seem to be accelerating away from us and i had to be persuaded of that and when i came around to believe it i had some wrong reason for disbelieving it but when i came around to believing it i thought gosh this means this is interesting it tells you that the future infinity is space-like now let's talk about infinity you see people think how do you talk about infinity well now you aisha has a very nice way of describing infinity this is a conformal representation of what's called hyperbolic geometry don't worry about the geometry but the boundary of this represents infinity now it's a conformal picture that means that angles are preserved but sizes can be big or small and the the fish as they get closer to the edge they don't really realize that they're more according to them they're the same size as the ones in the middle so this is a conformal represent representation you can squash or stretch as long as you don't alter the the small shapes and that's that's conformal geometry now the importance of control conformal geometry i'll come to in a minute but let me think about the light cone again the space-time structure means not not just the light cone you need to know these little surfaces within it which are the surfaces of equal time from the origin point so if you have some light rays that these aren't right here so you have two massive particles and there i'm having two different ones going at different speeds going through the central point and the ticks of a clock at the top you see a little clock sees and the clock registers the time as the as the light as the world line of that particle intersects the these various bowl shaped surfaces the first tick the second take the first stick and by the two formula at the bottom we have the two most famous formula of 20th century physics and size equals m3 squared and max planck's equals h nu you put the two together and you see that energy and frequency are equivalent from the planck and energy and mass equivalent from einstein put the two together and you get that mass and frequency are equivalent which tells you that a massive particle is a very perfect clock so this is where you get the metric structure but what about light rays but you see the light ray doesn't even hit the surfaces so light ray doesn't register the passage of time at all and here we have we'll forget about the the light ray the light cone or the null cone is itself gives you the structure of space time so if you only got no cones and not the scale then you have a good picture of infinity and in fact you can do this and not only you can you have a picture of infinity but you can stretch out the big bang as well and this is you see i was trying to say as a sort of criterion that the big bang or initial singularity sort of vanishing vial curvature my student paul todd had a better way of doing it to say okay let's say that it's extendable to something you see you could imagine the escher picture you could extend the little fish to beyond the bounding circle to something outside they don't experience that but you could imagine there was a world continuing beyond infinity and here i imagine there might be a world continuing beyond infinity and there might be a world continuing before the big bang now is this physic does this make physical sense it makes geometrical sense but what about physical sense well you see the big the remote future is very rarefied very cold and the density is very very low when you scale things to squash it to make it a finite boundary this makes the energies go up and the temperature go up and if you stretch out the big bang that makes the energy go down and the temperature go down and you might imagine that physically they are similar so would they match that's a possibility you need the space-like nature of infinity and that comes from the cosmological constant the space-like nature of the big bang comes about automatically you also get something more if you do what i'm now going to suggest which is to imagine not just that you have a finite boundary the two ends but you continue our big bang was the continuation of something before and our remote future is a continuous will continue to something beyond it now does this make physical sense which it only really makes physical sense if you've got massless things around what about the remote future well the main things running around will be photons and they're massless so let's say there's something more you've got mass as well i have to sort of suggest that the mass does fade out eventually but let's say it's dominated by the photons what about the big bang well it's the opposite reason here the einstein z equals m c squared you'll find that the energy in the mass is pretty well completely dominated by the energy in the motion so the kinetic energy when the mass when the motions get so big the energy gets so great then it's almost entirely in the kinetic energy and not in the mass so you might as well consider that the mass is zero and the physics relevant to the two ends is the physics of zero massless particles in fact in the remote future the photons that's maxwell's equations maxwell's equations don't even note notice the metric they're conformally invariant and in fact you can consider that you could actually if you have electromagnetic things or masses things or gravitational wave things they could get across from one side to the other so i can imagine that the crossing over from one side to the other makes sense if you are you are if your physics is sufficiently conformal and you're not worrying too much about the mass okay now i'm going to now finish this talk by talking about two classes of observation the first one was an idea i had about maybe you would see in the previous eon if it's like ours i'm calling the different sections the different eons so if i go back to this picture our eon is this initial cylinder it's not really a cylinder you see the back there's some curly stuff it may not close up at the back so i don't mind whether the universe is closed spatially or open now here i have the join from one to the next and you might imagine light rays getting cross but what else might get across we'll hear the previous eon i'm calling all those different what we previously called the universe was our eon there was an eon prior to ours and eon after rs and so on now the big bang of our eon was the remote future of the previous eon now they might have been in that previous eon black holes supermassive black holes running each into each other as they run into each other they would emit gravitational wave signals these would get through and make a signal that we might observe in our eon moreover if you imagine what the big really super duper massive black holes which ultimately swallow clusters of galaxies they will be the result of many many supermassive black hole collisions and they will be maybe one two three four five six several of them so you might see not just a signal of one of these but several of them now what you would expect to see according to this theory would be rings in the in the cosmic microwave background where the temperature is slightly lower variance as you go around or higher or lower temperature but my colleague vaheguru zidane who looked at this he looked at concentric sets of at least three rings of low variance uh low temperature variance and he plotted these things out and then the next picture i'm going to show you which is rather remarkable to me he didn't select these things from the color which is the temperature he didn't select it for that tally selected just for the low variance and these are plotted out in the planck data centers of three at least three concentric low variance rings now whatever you believe the origin of the signal is what is very remarkable is the extreme anisotropy of the picture or inhomogeneity of of the apparent universe here on the lower right you see a very large collection of red points now in the color coding and in the theory i won't go into the details here the red means distant so these would according to the theory be a collection of very distant supermassive black holes clumped together in some super duper cluster on the top right you see a bluish region that would be closer to us within our past light cone so you probably could see that of uh something which again some not quite so big and super duper but pretty super duper and a little on the lower slightly lower left you see something intermediate the red ones would be distant according to my theory the blue ones but what's remarkable is not just they're clumping they're clumped together in where you see them but they're clumped together in the color which means according to the theory in the distance so if you don't believe my theory you have to think of another explanation for this but it's very much at odds with the current view where the inflation is supposed to stretch things out and flatten everything out another possible observation of events in the previous eon would be the evaporation of supermassive black holes according to stephen hawking's hawking evaporation where the entire mass ultimately it would may take something like 10 to 100 years or more for a supermassive black hole finally to disappear in form of radiation now this radiation would get through into the pre next eon so here i have a picture taken from a paper written by christophe meisner pavlo nirovsky daniel ann and myself in the monthly notices of royal astronomical society and we see the crossover is the lowest horizontal line in the picture and the vertical line just meeting it is the world's line of a supermassive black hole which finally evaporates right at the crossover almost into the next eon really squashed up into that little point it spreads out through 380 000 years until you finally see it when it reaches the last scattering or decoupling surface and according to the work of james peeble and his colleagues you uh have a good knowledge of what happens in that previous 380 000 years but what we actually see is the spread of that point to about eight times the diameter moon so this would be a heated point which is hotter in the middle by about something like 15 times it could be as much as that times the background variations in temperature the normal variations and we seem to see in both the wmap and planck satellite data these points in the planck data we see it with a confidence in some something like 99.98 percent confidence level so this is a very very strong signal these points are there of the five strongest points in the planck data these are also seen as exactly the same places in the wmap data there's another one in wrap which is seen the same point in blank data so these six points i think are pretty i have pretty great confidence that they are genuine hawking points if not i think somebody else will have to come up with an explanation for this effect and explain how we can have a confidence of the level we seem to see on the basis of some other theory thank you very much

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Length: 34min 3sec (2043 seconds)

Published: Thu Jan 28 2021