The End of Space and Time

Gresham College presents The End of Space and Time by Professor Robert Dijkgraaf, the University of Amsterdam. My name is Michael Minelli. I'm the Emeritus Professor of Commerce and one of the fellows and trustees of Gresham. And I'm here really to welcome Robert Dijkgraaf to the UK today and to give his talk on the end of space and time. You wonder what a mere businessman has to say about physics, and the answer is not a lot, but I did do a little bit of post-grad physics at one point, so I was very interested when we contacted Robert about coming over and talking to us about some of the more exciting things that are going on in the boundaries of physics. And as you'll gather, over the last year, it's only gotten more and more interesting. Now, Willie Whitelaw famously famously said at one point I do not intend to prejudge the past but I do intend to prejudge this lecture. Gresham College has been built over many years on an openness towards overseas learning and in particular a very strong relationship with the Low Countries because Sir Thomas Gresham himself maintained a residence in Antwerp during his life and was trading. The Royal Exchange is really just a mimic of the Antwerp Bourse. The Royal Society, founded here in 1660, had lectures on botany, physics, mathematics and linguistics, all delivered by Dutchmen. And we continue today with recent lectures, including one on Gresham College in Antwerp, given by Guido Marneffe a few years back. In one of my lectures, I rather arrogantly said, or used, a quote from John Archibald Weaver, time is nature's way of keeping everything from happening at once, and space is what prevents everything happening to me and I use that actually to talk about the concept of a great timeless and spaceless trading force and what that might mean but I think what we're seeing today is Roberts come over to explain to us about what space and time might really mean Roberts is a distinguished distinguished university professor, as you well know, mathematical physics at the University of Amsterdam. From 2008, he's been president of the Royal Netherlands Academy of Arts and Sciences. Robert studied theoretical physics and mathematics in Utrecht, where after an interlude studying painting, I hear, he obtained his PhD under the supervision of Gerard Tuft in 1989. And Gerard Tuft's daughter happens to be with us today. Robert's a member of a research group that works in string theory, quantum gravity, and the interface of mathematics and particle physics. He won the 2001 Physica Prize of the Dutch Physical Society and the 2003 Spinoza Prize, the highest scientific award in the Netherlands. Earlier this month he was also awarded the prestigious Comenius Prize for creating more public awareness of mathematics and science and bridging the gap with the arts and humanities as a columnist for Handelsblatt and Folia. And finally in July Robert will become the director of the renowned Institute for Advanced Study at Princeton. I commend you, Robert Dijkraaf. Thank you so much, Michael, for this very kind introduction and for the wonderful opportunity to speak here in an institution that has such a long history in public outreach of the sciences. I think something that we cannot do enough. Today I will tell you kind of a grand story, which is our thinking of space and time, and in some sense what is the role of geometry, mathematics, and understanding the universe. And this goes back certainly to the beginning of modern science. This is a wonderful image of Galileo, of a book of nature that is being read. But before to read it, you have to know basically the language in which it's written. And for Galileo, this was the language of Euclidean mathematics, triangles, circles, and other geometrical figures. And I think this is a long tradition. If you go back in more recent history, for instance, Richard Feynman, a famous particle physicist, he has said that if you really do not know mathematics, don't be worried, there won't be many equations today, but if you don't really know mathematics, you can't get across the real feeling of the beauty of nature now Feynman is also famous for having said that if all mathematics disappear today physics would be set back exactly one week so uh and i always thought this was a very clever remark until a famous mathematician gave the right response to this and said well this was the week that God created the world. So I say two to one, mathematics to physics. The amazing thing is that the kind of mathematics that we're talking about today is in some sense very far away from our everyday intuition. We talk about the very large scale structures in the universe, the theory of relativity and the very small scale structures, the quantum theory. And I think we live in an amazing time where these two concepts are actually coming together. It's really this snake biting its own tail. And it's actually happening right in that time that we are now in the history of science. Now if you see space and time, which I will at the end proclaim to be kind of near to their end, of course had quite an evolution of themselves. Space started among the Greeks as basically something infinitely rigid, basically like a big stage on which the natural phenomena would play their parts. And time, according to Newton, was this kind of big clock that would tick and actually would set the stage directions. Now this image of this kind of directed play kind of really changed very much with a hundred years ago when Einstein came and he famously said, of course, that time is the fourth dimension. Now it's very difficult to visualize four dimensions, but let me just help you to get across this image of this extra dimension. The best way to do this is think of a movie. So if you............................ Now it's very difficult to visualize four dimensions, but let me just help you to get across this image of this extra dimension. The best way to do this is think of a movie. So if you think of this movie, it's called two-dimensional, and think of the individual pictures that make up the movie real. And now put these pictures on top of each other so that you basically get a stack of pictures. Now if you follow that, you see that a single particle will actually become a line in this so-called space-time. And that's what Einstein said, kind of mysteriously all of this form one continuum, which is pictured here on the right-hand side, and everything that moves, or not move, will have these kind of spaghetti strands that you see here on the right-hand side. So we're all now kind of moving in this kind of space-time continuum, and Einstein said basically this is the object that we want to study. So anything you have to say about space, you're basically also saying about time. And this went on. Not only we had this kind of unification of space and time, but the next ingredient was that space, this stage, so to say, is not rigid, it's flexible. It can curve, it can shape, and it does so under the influence of energy and mass. And that's the phenomena that we call gravitation. So anything that carries mass or energy will curve the space and time around, and thereby space and time became no longer a stage, but an active player in the game. Space and time are something which have physical properties and that feature in physical laws and in fact it's the influence of this curvature that describes the motion of particles under the influence of gravity and this was kind of the grand scheme that einstein had that basically all of physics and his persuasion was geometry and i think his claim of, his intent in life, particularly in the latter parts of his life, was to put everything in this geometrical form. Also the theory of elementary particles, which in some sense was a very fruitless effort. And one of my conclusions today, well, this is also not the line of argument that you want to follow, because in some sense, quantum theory will kind of probably be victorious over the underlying ideas of geometry that were so dear to Einstein and all of us, I think. Of course, Einstein was the first one that actually was able to do a computation that nobody did before, again in the history of science, namely compute what happens to the universe. He could put the universe in his equations and he saw that the universe was expanding and he could also conclude that the Debra in the past would be contracting and getting basically an inconsistent conclusion. Namely, there should be a moment where space and time started. And when he discovered this, he said, there's such a bad thing, the only thing that I now have to do is to change my theory. So famously, he took his equations with roughly in words Thank you. and when he discovered this he said there's such a bad thing the only thing that i now have to do is to change my theory so famously he took his equations with roughly in words say that the expansion of the universe is driven by the matter and energy and the curvature of space and time and he added a so-called correction to it which you call the cosmological constant with the greek letter lambda to just stop the expansion of the universe. Well, later he called this intervention his biggest blunder because this was something that at that time he could have made a wonderful prediction, namely, I predict that the universe is expanding. And please, astronomers, look and see this phenomena. He did not. But with Einstein, anything he did was brilliant, so even his biggest blunder was brilliant. We'll see this in a moment. Of course, so ten years later, roughly, the astronomers, Hubble in particular, sees that indeed the galaxies that we see in the sky are expanding, the universe expanding, and the first proof of this so-called Big Bang theory finally comes in the 1960s when these two engineers with a microwave telescope or receiver, Penzias and Wilson, discovered the first, so to say, light emitted at the Big Bang. That's the famous cosmic microwave background radiation. And I never really did the calculation myself. Apparently if you take your television set and disconnect it and you see this kind of static on your screen, then one in hundreds of these pixels is actually turned white because of a cosmic background radiation. So actually it's the cosmos influencing with your television reception and it's amazing that these are photons, particles, that traveled for 13.7 billion years to hit your television screen. Which is, of course, a very special effect. But now, I think the evolving universe, the Big Bang, is part of our culture. And, in fact, these images and the discoveries that are made are getting more and more exact and precise. We're living in the age of precision cosmology. And for instance, satellites like this WMAP satellite make these very beautiful pictures which are kind of celestial globes as they made in the 16th and 17th century where you had the zodiac. But now it shows the very early universe, the first light that was emitted by the universe when 400,000 after the big bang it became transparent and you see these small fluctuations here they in some sense led to everything we see around just like a parentalistic painting and i have to say here that you know it's science it's sh it says for stephen hawking i think we have noticed this uh and you see once you you see this, you can never unsee it anymore, I think that's the point, here it is, and in fact, you can now make a beautiful animation, I think, I hope this will work, where you actually can take this, sorry, this 13.7 years of evolution, in a few seconds, you see how the first small variations of energy distribution come together they form beginning very violent galaxies then these galaxies form and a lot of stars modern forms of stars and finally you see also that these structure in the universe is very as a very particular nature the kind of strands going through space and now we have a beautiful I'm going to pause here for a minute. And finally, you see also that this structure in the universe has a very particular nature, the kind of strands going through space. And now we have a beautiful position that we can kind of reconstruct these 13.7 billion years of history. And we have a very precise, in the order of 0.01 sometimes percent of the description of this particular cosmological evolution. Now, of course, this is a wonderful statement. It actually shows the power, in some sense, of all of Einstein's ideas. I think now, a hundred years later, we are in a position to make experimental verifications of all the initial concepts that he introduced. Now, there are still lots of questions. For instance, there's this question of why is the universe so flat? It's basically a flat universe. Why is it so large and full of structure? And also here we have some good ideas why this is actually the case. And this has to do with the fact that before, at the very, very beginning of the Big Bang, just after the Big Bang, there was a period where the universe was also expanding, but was it actually in a very kind of violent rate. This is the so-called inflation, cosmological inflation, which is something very different from the economic inflation in the sense that it adds roughly 26 zeros to the size of the universe in a very brief period. So we believe that the universe, in the very, very, very beginning, and then we talk about really fractions of a second, expanded gigantically and produced, so to say, this kind of random pattern that we now can follow very beautifully through the equations of cosmology to see how it shaped our universe. Now, the amazing thing of this picture is that it, in some sense, is a gigantic microscope. It takes the world of the universe as a kind of a magnification of a very small patch of something that was there before. And this thing that's there before, this kind of randomness, is something that really belongs to the theory of quantum mechanics. So we feel that in order to understand the very beginning of the universe, we have to understand the laws of the very small elementary particles quantum theory to describe the structures that we find there. So to find any kind of solution to the kind of grand picture of the universe, we have to study the very small, the quantum world. Now, in the quantum world, it was not obvious for a long time that the intuition that physicists have had for many, many centuries, that namely mathematics is the appropriate question to understand structure, actually is working. In fact, if you see pictures like this that are coming out of particle accelerators look like a big mess so is there any kind of beauty is there mathematics behind this and in fact if you go to for instance the 1960s there was a period where people were actually arguing there's no such thing kind of the elementary particle physics is like a black box something you cannot open something comes in, something comes out you can study the correlation between the two at that time it was kind of the hippie period people were thinking kind of a holistic point of view and declared in principle that this black box could not be opened now this was historically speaking a kind of famous last word so to say because not only could this box be opened, it turned out, inside it was in fact quite a small formula. So this is my way of writing the so-called formula for the standard model, which is our description of the fundamental laws of particle physics. And this is all written in formulas that you could give a lecture to a mathematician who would know a single thing of mathematics but would understand that these are natural geometrical objects so again it's geometry that's in a very deep way responsible for it, of course if you take an actual physics course then you get something like this which is, the first equation is a compact way to write this big mess, but it's even much better, because in some, so to say, the standard model of particle physics is something that kind of fits on the t-shirt, right, there's a handful of particles, there's a very natural way in which they interact, and I think it's one of the great triumphs of modern physics, that In fact, this single equation or this T-shirt is able to describe all the physics that we see around us here, all the matter, all the forces, all the radiation. And, of course, if you look at that, you look at that T-shirt, look at this distribution of particles, there are basically two feelings that a physicist has. One is absolute beauty and elegance. Amazing that the world works like this. And the second feeling is what was once expressed when one of these particles was discovered. A physicist, a rabbi, famously said, who ordered this? So you look at this and you say, why? Why quarks? Why this funny phenomena that anything in nature seems to come in three so-called families, small, medium, large? Why are there three colors of quarks? There are lots of questions. Why questions? Questions that typically a child would ask. And of course, these are good questions in the sense they have questions that basically do not have an answer. Physicists are basically at a loss. And they try to figure out whether this fits in a grander pattern. So if you start to rearrange the pieces of the puzzle, then for instance you can see that you can rearrange them in more symmetric patterns, I've pictured here one, which seem to suggest that this is just part of a bigger story, there are bigger symmetries here that we can't see in nature, but that perhaps are behind the physical phenomena that we see. Now, nature has given us a few clues that, indeed, this is not the end of the story. And perhaps the most famous one is, again, coming from cosmology. You definitely must have heard about this, the existence of dark matter. If you look at the way in which gravity is acting on the stars in a galaxy, then astronomers have discovered that in order to count this in terms of matter, there's a huge cloud of matter which is dark, invisible, and not made out of the particles that we know surrounding each galaxy. And by indirect measurements, you can actually determine the structure of this dark matter distribution. Roughly six times more of that dark matter than there is original matter. And for instance, all this thing which is shaded blue is artificially added, say, to this picture. You can't see it, but it seems to be there. And it's enormously important because of the structure of the universe. If you... Cosmologists, they look at the structure of the universe. So each of the little dots you see here is a galaxy and as we saw in the small animation these galaxies are not uniformly distributed to the universe they clumped together in some kind of large-scale structure these kind of strands that fly basically through through space and by studying the dynamics of of matter and dark matter, actually get a very clear model that seems to fit very well the observed structure of the universe. So we know there's lots and lots of more matter around that we can't encode at this moment in our physical models. And even it's worse, the last couple of years there has been a great survey of cosmological phenomena, particularly also of supernovae, which are stars exploding in galaxies. The moment such a supernova explodes, it's roughly as bright as a whole galaxy. And there are large surveys here, each of these pictures is a supernova that's been found the last few years. And by looking at these supernovae, you basically, there are kind of little bombs, well little, they're enormous bombs that go off with kind of a fixed amount of energy that gets released. So by knowing where the supernova is and you know basically how much light it would produce, you can get a very good measurement of distances in the universe. And the great conclusion of this is that the universe is not only expanding, it's expanding in an accelerating way. So it's like it's only getting faster and faster, and there's a force that actually is pushing the universe apart. Now this force, which cosmologists call dark energy, is exactly this parameter that Einstein introduced, the so-called biggest blunder, the extra physical phenomena that he conjectured to hold back the universe. In fact, it's there, but it's working just the opposite way that Einstein figured. It's not slowing down the expansion, it's actually adding to the expansion, and in fact this has dramatic consequences in the sense that in the end the universe will be expanding so fast that most of the galaxies that we see now will actually be far, far away and we will actually sometimes look in a really a dark void. Now this was of course an equation and the result has got lots of attention. Last year's Nobel Prize was, in fact, awarded to this phenomenon. And I guess you also know the consequence of this, which is that physicists are in this wonderful position that they know exactly what they don't know. So 96%, according to these computations, of the universe is either in the form of the dark matter or dark energy, which is just a fancy way of saying there's some physical phenomena that we don't understand, but we see its presence. And only four percent of the universe consists of the particles that we describe in our textbooks and that we teach in our lectures about. I often ask people in other fields, you know, what's your percentage of dark matter? How much do you know that you don't know? It would be very interesting to ask this question in economics. Of course, there's also the so-called unknown unknowns, which are things that you even know, don't even know that you don't know them. And that, for instance, this dark energy was in that category ten years ago. Because basically every cosmologist at that time would have claimed that this 4% was everything. So only now we come in this kind of very modest position that we only have to find this another 96%. So I always feel that cosmologists and physicists are a little bit like these old people making map makers who charted some part of the territory, because there was a large part which was unknown, and of course they're very difficult to leave that empty, so they sketched all these kind of sea monsters there to be there. So these are kind of dark energy and dark matter, are kind of the sea monsters, I think, of present-day physics, and perhaps the physicists are in this little boat trying to figure out whether these monsters are really there, but we're still mapping it out. Now, what could be the possible explanation of these effects, these big question marks that are, so to say, in the sky? And to answer that, I want to go back to a completely different question that perhaps some of you have asked once. So if you learn about elementary particles or molecules, you are told what the property, for instance, of an electron is. So how come that every electron has exactly the same properties? If there's a machine making this, if there's a factory, then actually it's a perfect factory. It makes these individual particles exactly the same. Now there's a good answer to this, and this answer was actually by John Miller. You just mentioned him In a telephone conversation to his then graduate student Richard Feynman and Feynman describes this in his Nobel lecture Feynman would win the Nobel Prize Basically because of this idea we look also up in the middle of the night Ask him this question and ask you I know the answer because there's only one electron in the whole universe. Now, I always feel that if your thesis advisor is calling you in the middle of the night, you know, you have to be wondering what he was drinking, but actually, this is typically Wheeler, this is a crazy idea that is kind of crazy enough to be true. Here's Wheeler, so this is this little particle, This is space. Time is going upwards. And Wheeler was saying, suppose this particle could only go up in time, like we are now doing, but could go back in time. If I could go back in time, I could re-enter this room, stand next to myself, and would be an exact copy of myself. Exact, really, to the last digit. And I could do it another time. So Wheeler was saying, suppose this particle could go up and down in space and time, and make a big knot. What would it signify? Well, if you think of this as a stack of pictures, on the bottom you would have a single particle, but in the middle you would have many, many particles, going up and going down, which have exactly the same property, because it's basically, it is the same particle. So I think it's a very clever idea. Feynman immediately said, well, then you would have as many particles as antiparticles, but now these pictures are known as Feynman diagrams, so Feynman really took full advantage of this so-called paste-time picture of particles, which he how we described it. And in fact, reality is even more strange. For instance, a particle can do the following thing. According to these rules, it can split in two particles for a very brief time, and then these two particles are combining again to another particle. These intermediate particles are so-called virtual particles. You can only see them indirectly. It's basically this rule of quantum mechanics that anything is allowed as long as you do it fast enough before it can detect it. I always feel this is something very typical to the Dutch mentality, I think, because basically our whole society is based on this description, our so-called tolerance. But these things happen. In fact, they are measured in particle accelerators. And there's the ultimate result of this, which is that for a brief moment of time, two particles can appear out of nothing, of course, violating every rule in the book. And then they combine again. Or if you wish and you want to think like Wheeler, it's a single particle that goes up in time and down in time and keeps on going round and round and round. This is not some kind of science fiction phenomena. This is something that's happening right now here in this room and can be measured in the laboratory. In fact, the Dutch physicist Casimir, after which this effect is named, measured this in between two electric plates in a slightly different context. So empty space, according to quantum theory, this is my own kind of visualization of empty space. It's kind of this boiling pot of particles and antiparticles appearing and disappearing. So space-time is not only can be curved, can be shaped, it's also full of life, so to say. It has really a physical material that you can study. And if you take a chunk of this quantum space-time, because of all these phenomena, there's energy in it. And this energy, according to quantum theory, that's this dark energy. That's the phenomena that cosmologists measure. So I like to joke that kind of empty space, the vacuum, is the most fascinating thing to study in physics. But of course writing big grand proposals to study nothing might actually not come across very clear, but in fact it's what we're doing. The big mystery is really, so to say, the old-fashioned ether studying nothing, studying space and time itself. And as we see, it's really the place where these two theories come together so what we are studying is a thing called quantum gravity how does space and time behave in the quantum world and we know there is such a thing because if you look at the various forces of nature the three forces that are there in the standard model and you compare them to gravity you see that when the energy scale goes up and up and up and up, that gravity basically gets the same kind of weak, of the same strength as the other forces. So there should be a moment, even before this very brief split of a second in which inflation starts, where space-time itself becomes a quantum phenomenon. So not only are the particles themselves allowed to do anything they want, space-time itself is allowed to do this. And therefore it basically stops. Max Planck, the father of quantum mechanics, in his first paper ever written on quantum theory immediately realized this. He realized that if quantum mechanics was there, the ultimate consequence would be that there is a smaller size in physics, a smaller size to space and time. It's a little bit like you take this picture, which, as you know, consists of pixels on a computer screen, so if you zoom in and zoom in, you see at some point you get to see these pixels. And basically what physics is telling us is that space itself should have this property. If you put it on a gigantic microscope, there's no longer space, there are little bits, there are pixels, there are quantum bits roughly the size of this Planck length. Now this Planck length is incredibly small. If you look at the various scales in physics, there's a smaller scale, which is the Planck scale. There's a larger scale, which is the size of the visible universe, the Hubble scale. And if you go from left to right, from the smallest to the largest structure imaginable, there are 60 steps of a factor of 10. And one way to kind of visualize this is right, very convenient in the middle, the geometrical mean of the two, is the scale, it's roughly 10 micron, it's the scale of a human cell. So if you want to think of how small the Planck scale is, take the whole universe, make a scale model of it as small as a bacteria, and now think of a bacteria inside the scale model of the universe it's incredible because the most incredible thing is that this stops there's a larger scale and there's a smaller scale that means that in some sense putting this under the microscope won't help anymore there is there's no way in which we could get to smaller structures now where do we see these phenomena is this relevant to physics and then i come i I think the amazing thing is that there's a kind of a laboratory where you can test these ideas, and it's again a cosmological laboratory, and it's black holes. So black holes are something that really, you know, were in science fiction books twenty years ago, but now are part of the standard description of our universe. For instance, there are black holes inside every galaxy we see, often millions and millions of suns with a weight, a mass of millions and millions of suns. And if you see, they're extremely violent. This is a galaxy, and you see these big radio plumes coming off, which are hundreds of thousands of light years big, are coming out of this galactic black hole. And for instance, look and zoom in the the center of our own galaxy you see that the nearby stars are moving around quite violently and fast at speeds which are percentages of the speed of light all surrounding this intergalactic this galactic black hole now for a theoretical physics system like myself i would draw the so so-called space-time picture and then the galaxy, and then black holes, something very particular. It's something, you all know, it's a star that's kind of imploding. Its own gravitational force is pulling everything together in this so-called singularity, where the gravitational force becomes incredibly strong, and then remarkably, this very violent area of the universe is protected by a so-called horizon. There's an area around the black hole, a sphere, if you would draw a three-dimensional, that has this property that once you're inside, you're doomed, but once you stay outside, you're fine. And the reason that you're doomed inside the horizon has to do with a completely crazy phenomenon that in all these pictures, I had time flowing upward. Inside the black hole, time is flowing inward. That is, it's a spatial direction. It's flowing from the boundary of the horizon towards the center of the black hole. So if you're inside, you would typically say, well, there's like one meter distance to the center. I'm going to show minutes distance to the center. That is to say, you know, you're watching a movie, you know, you have only three minutes to go, so you will know it will end when you hit the singularity. Now, there's a famous set of laws that black holes obey and that are very famous in some sense, or very familiar from a standard physics perspective. The first law is the so-called second law of black hole thermodynamics, that if you have two of these black holes and they merge together, the area of their horizons of the new black hole is larger than the sum of the two original ones. And this is something that we know in some sense from standard thermal physics, where we call this the second law of thermodynamics, which is the phenomenon that entropy always increases. So black hole physicists, Bekenstein and Hawking and others, introduced the notion of so-called geometrical entropy, which is a kind of gravitational version, which is equal to the area of the horizon. And then there was the famous discovery of Hawking, that if you introduce an entropy, perhaps you can also introduce a temperature. And indeed he he discovered something quite phenomenal. That if you have these funny laws of quantum mechanics that say that particles can be created out of nothing for a very brief time, if the same phenomena happens in the neighborhood of a black hole, you could have like two particles just here at the edge of the origin. One particle being inside, the other particle being outside. The particle inside is basically doomed and will be pulled by the gravitational force to the singularity, while the other particle is now kind of liberated and can escape to infinity. So one of the places where quantum mechanics and relativity interact in a very strong way is in the neighborhood of a black hole, where it leads to so-called spontaneous radiation out of the black hole. This is called Hawking radiation, and the amazing thing, if you do the computation, you find that the temperature of this thermal radiation, in fact, is given by the surface gravity of the black hole. So not only we have entropy, we have energy, we have temperature, it looks like there's something like thermodynamics going on in black hole physics. In fact, if you look at a very tiny black hole, you might say, well, it could form by matter colliding, it would live for some time, and then it would radiate out particles by this Hawking process. So if you look at a very small black hole, it would almost be like a small particle, you know, particle as they are formed in our usual accelerators. Two particles collide, they make a new particle, could be something like a radioactive particle, so it will decay and after some time it will disappear. So it means that if you want to make a little black hole at a certain spot, and put a lot of energy in a certain space, then at some point that black hole will evaporate. So there will actually be some kind of uncertainty into the time during which this particle will live. So this already tells you that space and time are interacting in a very strange way with black hole physics. In fact, this led to a kind of a line of reasoning, which I'm actually talking about, which goes again back to John Wheeler, who put a wonderful, he was very good in slogans, and he called this phenomena it from bit. Namely, what is it? It is the universe. And what is bit? Bit is the entropy that's there. Entropy is information. So he had this image that if you think of the horizon of a black hole, there's some kind of information inside the black hole, and you can compute the amount of information, and you find actually that that amount of information, it's like you filled the black hole with zeros and ones, with little bits of information, where you use one bit per square Planck length. So think of this horizon of the black hole as this kind of pixel of the picture of Max Planck that I had. And you can see how much information can you store in a black hole, well, basically by putting one bit of information of every kind of square plunk length that you can subdivide, in which you can subdivide the horizon of the black hole. So this leads to what the physicists now call the holographic principle. Perhaps the physics of the black hole, and anything outside it at least, can be encoded in all putting this information on the surface of this horizon, which is, in some sense, the edge of space. We already argued that inside the black hole, space and time come to an end. But so it doesn't really end, but basically this theory says that just cut it off, create a screen, which is the thing that surrounds the black hole, forget anything inside, and project all of physics in terms of the information on that black hole horizon the zeros and ones that are sitting there there's a rather radical idea because the basic would tells you that in some sense information is the underlying layer of understanding all of quantum geometrical physics now can this idea be tested it can be tested in some kind of a theoretical way. And one way is in string theory. I'm not giving a course in string theory here. But, of course, you all must have heard that string theory is something where the notion of an elementary particle is, so to say, generalized to a one-dimensional object, a little bit of string. But one thing that the last, say, 10 years, a lot of research has been devoted to is studying how does string theory encode for black holes. String theory is supposedly a theory of quantum gravity, combining gravity and quantum physics in a unique way. So what does it tell us about black holes? Well, here's the cartoon version of what black holes look like in string theory. Here's the horizon of the black hole. Outside, you have gravitation. And gravitation is described in string theory in terms of these so-called closed strings, these little loops of elementary loops that are running around and basically are forming the shape of space and time, the curvature of space. So we can kind of replace these closed strings by Einstein's description of space-time. Now, what happens to these strings when they're very close to the black hole? Well, this is really a cartoon version, quite remarkable. You can make this cartoon into an exact mathematical formula. What happens is that these kind of strings halfway fall through. So you see here there's a half of a string sticking out, almost like somebody in the sea waving his hands, you know, help. So there are these kind of so-called open strings that are, you can think of, are kind of attached to this horizon, to the surface of the black hole. So they are like tethered to the open pieces of string that are kind of, the two endpoints are fixed on the horizon. And you can describe this system. It's a very complicated system, but you can describe it. In fact, the mathematical description of this, of this neighborhood of the horizon, quite remarkable in string theory, is in terms of a well-known physical theory. It's a so-called Yang-Mills theory. It's the theories that are described in the standard model. So in a kind of very roundabout way, the physical theories that we developed to study our elementary particles seem to be relevant also to describe black holes, but then we really have to apply them in this quantum gravity regime. So there's some kind of theory of so-called open strings, matrices of strings. I have no time to explain the details of it, but the important thing is that this is a working model, an exact mathematical model, that describes to you the physics of quantum black holes. And in fact, out of this, the conclusion is that in some sense, what we call the fundamental layer of physics, namely space and time, gets replaced at very small distances by something more involved, and in the case of string theory, actually you have a very precise candidate for this more fundamental theory, which is the so-called large N-gay theory. So there's this description, which is kind of here, it's known under the technical name of ADS-CFT correspondence, but it's very, in the caricature version, it basically tells you that all physics in this particular model is equivalent to a theory living only on the boundary of the black hole. So in some sense, the three-dimensional physics, or if you include time, four-dimensional physics, is something which actually all comes down to this area of the black hole. And that's, of course, quite an amazing thing, because that means that one of the space dimensions, the distance that you go off the black hole, is something which is not really there in the fundamental description. It's what's called an emergent phenomena, something that comes up only in a limit, a particular limiting structure. In fact, if you look what this extra dimension is in terms of the original, the kind of the quantum description living on the surface of the black hole, you find the fact that this is the holographic principle, so it's really like a hologram, which is also a two-dimensional picture that gives you three-dimensional reality. The extra dimension, so to say, that has to be constructed is related to the energy scale in which you probe this kind of two-dimensional system. Well, I prepared some slides how this will look in a very concrete detail. This is all called ADS-CFT, but let me just skip that. Perhaps the most important thing to be said is that this gives you, so to say, a dictionary that translates questions in terms of geometry and gravity in terms of a completely different set of notions, namely quantum theory and elementary particles. Finally, I want to say something about the most radical way in which this is implemented, which is a theory that got quite a lot of attention two years ago by my direct colleague and friend, we wrote many papers together, Eric Verlinde. And he took the ultimate consequence of this idea. He said, if really gravity is not a fundamental force, if what we call curvature of space and time is in some sense just an illusion because underlying is this more quantum description, perhaps we should stop looking for a fundamental description of gravity. And he noticed there's such a thing as entropic forces, which are there in space, are just in everyday physics. And there's a famous example of an entropic force, which is, for instance, if you take a large molecule, like a polymer or something, you know, it can be, or think of it, you can even think of a protein or something, it can be folded in many, many different ways. And if you pick a pincer and you pull on the molecule, you'll find a certain I don't know. You can even think of a protein or something. It can be folded in many, many different ways. And if you pick a pincer and you pull on the molecule, you'll find a certain force. That's basically, I mean, the technical description is that because of thermal effects, this molecule can be in all kinds of different shapes. And there's a technical description that the force that you feel has to do with the entropy into the system. So there are many forces in nature that are not fundamental forces. That means that there's not a little particle like the photon for the electromagnetic force or the gluon for the strong force, the quantum chromodynamics, that's responsible for this. We shouldn't look for an elementary description. We should look for an emergent description. There should be an entropic way to reformulate all of gravity. And he made a very interesting start in this project. For instance, he had a kind of embarrassingly simple derivation of Newton's law. So it's always nice to tell about Newton's law here, I would say, so close to home. But if you look at this paper, he has a very element, he looks what happens to a particle if it's in the neighborhood of a black hole. You can see basically by throwing in a single particle what happens to the entropy. You can look at the temperature of the black hole, which is in some sense a thermal temperature. And again, I won't go into the mathematical details. I'm not sure that everybody could follow. But if you combine these three equations in a clever way, you get F as MLA. So he basically is doing something, I would say, very complicated, taking these most fancy new ideas from physics and out of it producing, I would say, the very bedrock in which you would think everything was based. So he's really turning things around. But I think he has a very principal point here because if we take these ideas from string theory from quantum gravity from his entropic description series space and time should not be the basis of any of our arguments. Space and time should emerge from what we are doing. So there should be something under it. For instance, if you ask the question, what was the very beginning of time? Or what's at the very end of time? It's a little bit like asking, where is the beginning of a river? You can follow it up, you get a little mountain stream, and then at a certain point there are a few drops of water lying on the stone. Is this the beginning of the river? Well, the whole concept of a river doesn't make sense anymore. What is the temperature of a gas if it only has two or three molecules? The thermodynamical concepts stop. So perhaps there should be a more basic description of space and time, or out of which these emerge. And this goes down to a very deep argument that runs among physicists, which often is phrased as, what is garbage and what is beauty? So what do physicists like? Often the word you use describing a physical theory is beautiful or it's elegant. And where do we find beauty in science? And there are basically two schools here. The first school is that, I would say that's the reductionist school, and most particle physicists belong to that school. They say, well, we see basically a big mess around us, you know, the chaos of life. But if you really go down to the fundamental laws of elementary particles, they're very elegant and simple. Only you have to start describing everything in terms of electrons and quarks, etc. So that's very neat if you have two or three of these particles, become pretty hopeless if you have billions and billions and billions. But so then the idea is you shouldn't look at beauty at the large scale, beauty is at the smaller scales. And in fact, we hope, along that line of argument, that if there is even something more fundamental than the standard model, it will be even more beautiful. And Feynman described this in a very nice way. He said, you know, often in physics, you have a beautiful theory, and then some measurements don't fit, and you lose this beautiful picture, and you go through a kind of chaotic period of transition. And and certainly there's a bigger picture that comes into mind that's even more beautiful because it explains more things in terms of a smaller number of ingredients. Now that's one half of the physics community, the other half, it's just the opposite way. Take this glass of water, now it has very beautiful properties, you know, it has a temperature. You can do hydrodynamics. It's transparent. You can drink it. But if you want to describe it as a chemist in terms of 10 to the 26 H2O molecules, it's extremely complicated. So the big mass is actually in the small details, and the beauty is in the large scale. The laws of hydrodynamics are beautiful equations, but of course only in approximation to this large collection of elementary molecules. So for instance, thermodynamics is one of the most beautiful theories in physics. Statistical mechanics is a big mass. So beauty is at the larger end, the larger scale. Now you see these two are kind of in conflict. And I think something, the lesson that we are now learning is that, well, if you really want to understand the full picture of the universe, we already see we are forced by experiments and results to combine the largest and the smallest. So in some sense, we need some kind of synthesis of these points of view of life. And in some sense, the two are competing here I would say is geometry which is the large scale structure and quantum theory which is very different it's much more abstract, it's more algebraic than geometry and both have their own qualities but I think if you see in some sense what is the best way to understand these structures I I think right now all the evidence, the theoretical evidence, is pointing that in some sense quantum theory, quantum information to be more precise, is a more fundamental concept than space-time geometry. And so in some sense the lesson that we go from the individual molecules to the properties of materials is very similar in which that we go through the individual spacetime bits, the bits of Wheeler, to kind of the spacetime it, namely the spacetime geometry, emerging with beautiful equations. In fact, Einstein always said that his two favorite parts of physics were thermodynamics, which are just a few lines and you describe basically all the properties of all materials, and his own theory of general relativity. And I think what we are leading to, that these two things are not only both beautiful and they are kind of analogous, they might be actually equivalent. There might be an equal sign connecting the two. And I think that it would be an astonishing fact. I think Einstein would probably be very happy with these conclusions. But, of course, it also leaves you with the enormous question, what is this thing on the left? And it might be actually comforting in some sense that the basic phenomena out of which everything is made consists of these kind of zeros and ones, which I think is also a good metaphor, I think, of our present life. But information might, in some sense, according to this argument, be, in some sense, the very basic layer of our understanding of the universe. Well, this needs, so to say, a lot of details. I'm very much aware this is a very general lecture. I have to remind of an anecdote of Pauli. Pauli, of course, a famous co-discoverer of quantum theory. And there are two quotes I want to mention of Pauli to his friend Werner Heisenberg. The first one, when Heisenberg discovered the first uncertainty principle, that an electron can sometimes be a particle and sometimes be a wave, he wrote very enthusiastically to Wolfgang Pauli, and Pauli wrote back, this is one week after the discovery of quantum theory, and Pauli says well, I think I understand it if I look with my left eye, I see a particle, if I look with my right eye I see a wave, if I open both eyes, I become crazy. You might feel like this. Or you might feel that there's another anecdote, which when both are grand men of physics, Heisenberg, in fact, has a universal theory of the world. And Pauli is in the audience and he listens to the lecture and clearly he's not very impressed with the amount of details of the theory. So he sends Heisenberg a postcard and just has a square, an empty square. And he says, dear Heisenberg, just to show that I can paint like Titian, details will follow later. Thank you very much. For all information, please visit www.gresham.ac.uk