THOMAS HARTMAN: Welcome So it's a pleasure to introduce tonight's Bethe Lecture. This lecture series is named after Hans Bethe, who was a physicist and professor here at Cornell for nearly 70 years from 1935 to 2005. So it's now become a tradition here to begin the public lecture with this slideshow of photos from Bethe's life on the screen behind me. So I want to say a few words about his life in science before we start.
Bethe became famous for answering the question, how does the sun shine? Where does it get its energy? Well, the first guess and a guess that physicists made in 1800s is that the sun heated up when it formed from interstellar gas and dust and that this heat is just gradually radiating away, which you can-- so you can do the calculation of how much heat is generated this way. And it's only enough for the sun to burn for about 30 million years.
So this actually satisfied the physicists for a while. But the biologists of the late 1800s were not at all happy with this. They objected that this couldn't possibly be right, because it doesn't allow enough time for the evolution of species. And the biologists had this right, but the physics explanation didn't come until 1938, when Hans Bethe discovered the nuclear reactions that power the sun. That's the fusion of hydrogen nuclei into helium. And for this work, he won the Nobel Prize in 1967.
He began his career in the late 1920s. In 1932, he was forced out of his job in Germany for his Jewish heritage. After some brief stops, he moved to Cornell in 1935, and he helped build this into a world-class department over the next few decades.
Bethe also played an early role in the development of nuclear weapons at Los Alamos and later became known as the conscience of nuclear physics for his decisive role in advocating for peaceful applications of nuclear energy and advocating for limits on nuclear weapons testing and development.
Throughout his career, Bethe continued to calculate. He was known as an incredible calculator. And he loved his slide rules, as you saw in some of the photos here. He continued to calculate and to make discoveries. In 1947, he famously calculated the Lamb shift while on a train, before the train-- the story is, before the train had gone 100 miles.
In 1985, at the age of 80, he wrote a major paper on solving the solar neutrino problem. This was nearly 50 years after discovering the nuclear reactions that produced those neutrinos, which I think is incredible. So Hans Bethe was a great physicist and a great man. And he had a wonderful positive impact on Cornell.
Turning now to tonight's lecture, it's my honor to introduce the Bethe lecturer, Andy Strominger. Professor Strominger is the York Professor of Physics and the Director of the Center for the Fundamental Laws of Nature at Harvard University. He's a renowned theoretical physicist who has made seminal contributions to relativity, quantum gravity, quantum field theory, and string theory.
Among as many discoveries, he showed that string theory has the potential to be a unified theory of nature. He discovered new connections between physics and geometry. He showed how string theory explains the microscopic physics of black holes. And in the process, he discovered that spacetime itself can emerge from something more fundamental at very short distances. Recently, he's uncovered surprising new symmetries in gravity and particle physics.
He's been recognized by numerous prizes and Awards, including the 2017 Breakthrough Prize in Fundamental Physics, the 2016 Heineman Prize from the American Physical Society, the 2014 Oscar Klein Medal and 2014 Dirac Medal, and the 2008 Eisenbud Prize from the American Mathematical Society. He's a member of the American Academy of Arts and Sciences, the American Physical Society, the National Academy of Science, and a Senior Fellow at the Harvard Society of Fellows.
In tonight's lecture, Andy will tell us about the edges of the universe, black holes, horizons, and strings. Let's welcome Andy Strominger.
ANDREW STROMINGER: OK, is-- my mic is on? Yeah, thank you. Thank you for the introduction, Tom. And let me just start by saying, it's a special honor for me to be giving this lecture. I'm honored to be Bethe's academic grandson. And I did meet him a few times when he used to escape the Cornell winters out to Santa Barbara.
So today, I'm going to be talking about black holes. And black holes are a subject which have emerged to the forefront of modern science in many different areas. Many people are interested in them for different reasons. So first of all, people who want to understand how Einstein's theory of general relativity can be unified with quantum mechanics, black holes is the arena in which those two things meet and give us a lot of trouble. And that's an important thing to try to understand.
They're interesting, of course, to observational astronomers and particularly to LIGO, in which the group at Cornell played a central role, the discovery of gravitational waves from colliding black holes. There's also been-- and this is all just in the last few years. There's also been a direct image taken of it.
Philosophers have become interested in how we're supposed to think about regions of spacetime which are completely inaccessible to experimental probes. There's a subject in mathematics, understanding stability of black holes, cosmic censorship, and so on. The history of it is really like nothing else. We'll touch on this briefly.
My undergraduates often come to me telling me that their computer science-- in their computer science classes, properties of black holes are discussed, because from an information-theoretic viewpoint, as we'll come to, they are very interesting objects. And of course, in string theory, they have played a central role, both in-- they have guided us into understanding the deeper structure of the theory.
And in this talk-- obviously, I'm not going to try to survey all of this-- I'm going to survey really my own path, which starts with the information paradox, which I will review. And more recently, I've been involved with some of the observational effort at the Event Horizon Telescope.
So I-- this is going to be, hopefully, an elementary talk. And let me start with, what is a black hole? So on the moon, if you want to get off the moon, where there's no atmosphere, and you boost off with a rocket, the escape velocity is 2 kilometers per second. And that means that if you're going faster than 2 kilometers per second, you can escape the gravitational pull of the moon and continue on indefinitely into outer space. If you blast off slower, and you don't turn your engine on again, you are doomed to fall back to the moon.
On the Earth, which has a stronger gravitational force, you need to be going faster. You need to be going at 11 kilometers per second in order to go out. And it was noticed already in the 19th century, in fact, long before Einstein, by Michell, that if you had a sufficiently massive object, light could-- since light travels at a finite velocity, nothing could come out of it, and it would be black-- of course, Einstein's theory. And that is a black hole. A black hole is a region of spacetime from which nothing can escape, not even light.
Now, the existence of such objects were predicted by Einstein's theory. And the fact that they were really robustly predicted to really put all the nails in the argument was due to Penrose, and that's what he won the Nobel Prize for last year. And so Schwarzschild-- it's thought that Einstein's equations are pretty complicated.
And it's said-- I've asked my historian friends. I don't know if this is true or not, but that Einstein thought nobody would ever be able to write down an analytic closed-form solution. But Schwarzschild, in fact, did exactly that only a few months later. And the solution that he found is now known as a black hole.
Now, usually in physics, once you solve the equation, you're done. And you can then compare to experiment. But that's kind of the end of the story, and then you look for a new equation, try to solve that. Not so with general relativity-- the solution was there in very explicit form more than 100 years ago. But nobody could understand what it meant.
And just to illustrate the point, and it took really 50 years to 60 years to understand what the classical theory of black hole. And to underscore that point, I have here a quote from Einstein which is essentially saying that Einstein-- that black holes don't exist and giving an argument for why they don't exist, that I would have flunked him in my general relativity course if he said that. Now, that is not to say that Einstein [LAUGHS] wasn't a very smart man. It's just to say that it was really hard to just look at this solution and understand what it meant. And the great minds were all stumped by it.
And now, of course, very strikingly, a few years ago, we saw gravity wave signals of black holes. We orbit around one at this very minute, a supermassive black hole at this minute, in the center of our galaxy. There are-- I don't know what the latest number is, but tens of thousands of them up in the sky. They're ubiquitous in the universe. And we did eventually come to understand what a classical black hole is, the structure of the theory of general relativity and what it would a black hole is. But it took a very, very long time.
And one way to describe it is that a black hole is the edge of the universe. Once you cross the horizon of the black hole, there's nothing there, and you're out of the universe. And the structure of the black hole is that they are-- you can think of them as really the simplest objects in the universe. And John Wheeler made the famous adage, described this by saying, black holes have no hair.
Now, this is markedly different from the stars that Bethe studied. Every star is different, even if it's the same size. They all have slightly different numbers of molecules, and each molecule and different chemical compositions. And they differ in innumerably-- well, not innumerable. You can enumerate. But they differ in many, many different ways-- the different molecules at five miles-- if you locate the molecule at a mile from the center of the sun-- one star and compare it to the one-- you know, they'll all be moving in different directions. There's all kinds of detailed information that you have in describing a star.
A black hole is really fundamentally different. According to the understanding at that time, black holes were characterized only by two things-- their mass, and also, it turns out, as Kerr showed-- this took 50 years, but Kerr showed 50 years later that black holes can also spin. So they just have a mass and a spin. They're a spinning empty hole.
So there was a kind of satisfaction that emerged in the '60s and the early '70s in our understanding of how black holes formed and what their properties were. And everything seemed to be going well. And then Stephen Hawking threw a monkey wrench into the whole business when he discovered that, in the real world-- in the real world, we have something called the uncertainty principle, from quantum mechanics.
And in the real world, which says that nothing-- nothing can be exempt from quantum mechanics. Everything has to be described by Schrodinger's equation, even a black hole. And everything is subject to an uncertainty principle. And loosely speaking, what that means is you can't quite say exactly where the horizon is. It wobbles around a little bit. And because it wobbles around a little bit, things can exploit quantum uncertainty to sneak out.
Now, there's a lot of mathematics. And this is the stuff that sneaks out. It's called Hawking radiation. And there's a lot of precise mathematics in this. And what Hawking showed in a formula that is inscribed on his headstone in Westminster Abbey now, that the stuff that comes out looks like thermal hot radiation. And the temperature is given by a very specific formula. It's Planck's constant divided by 8 pi times Newton's gravi-- so it's Planck's quantum constant-- divided by 8 pi times Newton's gravitational constant times the mass of the black hole.
Now, let me-- this is an incredibly interesting formula. First of all, it's a formula that-- you've got the temperature, which is a thermodynamic quantity. This is a thermodynamic law. What is a thermodynamic law? Well, in the 19th century, there were-- it was kind of the major-- if you wanted to get a job at a good place as a physicist or a chemist, the thing to do was to study the laws of thermodynamics.
You'd take up a pot of oil, and you'd heat it up, and you'd see how much the temperature rose. And that would tell you some temperature-energy relation for oil, and then you'd do the same thing with salt, and you'd do the same thing with vinegar, water, whatever. So all different-- so thermodynamic laws are, in the 19th century-- a lot of them were discovered in the 19th century-- they tell you how a temperature of something behaves as a function of its energy. That's a thermodynamic law.
Now, but this thermodynamic law, it involves thermodynamics. There's a temperature here. It also involves quantum mechanics. And it also involves general relativity. So it's an equation which sort of crosses between broad disciplines within physics and unites them together. OK.
So in one of what I regard as one of the most beautiful developments in the history of physics, in the 19th century, Boltzmann showed that thermodynamic laws are not fundamental laws, that they can be derived from something more fundamental. And the thing more fundamental that they can be derived from is the then very controversial, but of course, now it's well verified experimentally, is that matter is made up of-- all matter is made up of tiniest bits called molecules.
And once you hypothesize or eventually prove that matter is made up of little bits, you can apply statistical reasoning to the configurations of the bits and determine properties of-- basically determine the thermodynamic laws. So if you have a bunch of molecules that-- say, water vapor on one side of a gas, on one side of a box, there'll be a pressure that makes it want to expand into the rest of the box. And that pressure can simply be understood as, if you have a bunch of random molecules that are bouncing around, there's many more possibilities, many more configurations if they're spread out all over the box than if they're bunched up on one side.
And this reasoning made mathematically precise really describes all the thermodynamic laws. So all the thermodynamic laws, as a result of Boltzmann, we're relegated to a secondary status. They could be derived from statistical reasoning and a hypothesis of molecules.
Now, an important ingredient in this reasoning is counting the number of configurations that a system can have, a system with many components. And counting them, and that is like counting the configuration. The number of configurations is called-- or actually, the logarithm of it-- is called the entropy.
And entropy is also the same thing as gigabytes, right? So your smartphone has some number of configuration of the chips in it can be. And that tells you how much information it can store. And the information is stored by different arrangements of the chips. So it's a measure, the entropy is a measure, of the number of gigabytes or of the complexity of the system.
Now, I said that Boltzmann's reasoning enabled one to derive all thermodynamic laws. Unfortunately, there was still one odd man out. We could use Hawking's temperature-energy relation and some a few lines of elementary thermodynamic reasoning to infer how much the information storage capacity of a black hole must be. Anything that behaves in that way, whose temperature varies in the way given by Hawking's formula, as a function of energy, if you assumed that the temperature was-- had the same origin as all the other temperatures in nature, you can infer from that an entropy.
And that entropy is known as the Bekenstein-Hawking entropy. If you work it out, it's given by the area of the event horizon of a black hole divided by 4 times Newton's gravitational constant times Planck's quantum constant. So we should conclude that black holes are devices that have many-- they're objects that have many internal configurations.
And let me-- before we go on and discuss this, I want to say that this is a very big number for any real astrophysical black hole. And in fact, all the data and the Google data storage banks would fit inside a black hole which was a trillionth of a trillionth of a millimeter, a very, very small black hole. So we'd like to understand how this information is stored, where the gigabytes are. But I'll come back to that in a little bit.
And in fact, not only is this a very large number, but for various reasons, consistency arguments and various kinds of gedankenexperiments, many or most people believe that this is actually a fundamental universal bound on how much information you can store inside a region of a given size. And this implies that Moore's law, which says that the number of gigabytes that you can get on a chip of any fixed size doubles every five years-- and so if Moore's laws continues unabated-- it's a very long time, but if it continues unabated, in 300 years, we'll have saturated the black hole bound, and all our smartphones and desktops will have to have little black holes for storing the information. And we won't ever be able to make anything smaller than that.
OK, so if you were paying attention, you may have noticed that I made two statements which were exactly the opposite of one another. One statement that I just made is that black holes are the most complex objects in the universe, that they have more gigabytes within them-- the number of gigabytes in them is so big that it actually saturates a universal upper bound. It's just huge.
And then the other statement I made earlier is that there's nothing inside a black hole, that it can be thought of as an empty hole in space. And when something drops inside it, there's no trace of how that happened. Or there's no trace of what went in. It's gone forever from the universe. And they're hairless objects.
So this is-- there are several different statements of the black hole information paradox but this is the simplest one or one of the simplest ones. And the question is, how can something, at once, be both the simplest object in the universe and the most complex object in the universe? How can these-- how can we reconcile these two different ways of thinking about black holes? This is the information puzzle. And this was what was brought about by Hawking's famous work in 1974.
So from Schwarzschild's paper from 1916 to 1974, that was 50 years. Physicists struggled with understanding the classical structure of black holes, took that long to sort it out. That's pretty close to the time that it was sorted out. And since Hawking's paper in 1974, it's now nearly 50 years later, we've been struggling with understanding a quantum black hole. And like Einstein, I think our failure to so far fully understand it is not an indicator that we're all stupid, but more that it's just really a deep and difficult problem.
OK, and now, this problem-- the paradox becomes even more exacerbated when you think about what happens if you throw something into a black hole with information. If you throw your smartphone in there with text messages that haven't been recorded anywhere else, and then that black hole starts to evaporate and disappears, the information is completely lost. Now, losing information like that-- I've lost the thing on my-- let me-- I can just leave it. It doesn't matter. OK.
Losing information like that isn't just irritating. It's a complete disaster for physics. It means that you can't predict the future from the present, that there's some element of randomness. And the very foundation of physics is that the laws of physics govern the physical universe completely and that when we know all of them, we'll understand how everything evolves in time.
But if this were true, it would mean there were no-- that there aren't any exact laws of physics, that there's some element of randomness coming from god knows where. And that is really sort of the ultimate nightmare for physics. So a lot of people weren't ready to accept this. And so we've been struggling with this.
It's kind of amazing, I think, how much we've learned while struggling with it. And we've learned a lot. But we still haven't fully solved the problem. And so one of the important things that happened was that string theory, which I'm about to talk about, has turned out to be a very powerful tool to think about how such-- how it is possible for an object to be both maximally simple and maximally complex at once.
So let me just say a few words about string theory. So string theory, whether or not it is related to the real world, which is an important question but a subject for a different lecture, it is almost certainly a consistent, a mathematically consistent, theory which contains includes gravity and quantum mechanics and has black holes in it. And moreover, we understand the equations in a very precise way. And we have a lot of mathematical control over structures that arise within string theory.
And that mathematical control was developed over decades of many theorists exploring different corners of the theory and many important insights. And a lot of this was put together in the mid '90s. And a black hole was actually constructed in a complete way, using the ingredients in string theory-- strings and branes and other objects.
And it was found that-- and so the number of ways you could make a black hole within string theory was actually counted. So this is kind of like being able to open up a smartphone and count how many chips are in there. We were able to do that using string theory.
And the structure of how it worked turned out to be very interesting. There are some degrees of freedom that live on the horizon of the black hole and form a plate that you can think of it as a holographic plate that can be used to reconstruct the interior, much as the way, if you have a holographic plate and you shine a laser through it, it gives you an object of a higher dimension.
Now, an important ingredient of this is an emergent symmetry that appeared called conformal symmetry, which appears ubiquitously in many branches of physics. It occurs-- well, studying black holes here, in related contexts in astronomy. It occurs in studies of the CMB in the early universe. It occurs in the quantum hall effect. It occurs-- it's probably the most commonly emergent symmetry that arises in physical systems.
And that enabled us to get an alternate description of the black hole as a two-dimensional field theory. And there we could actually count the number of microstates. And it reproduced what Bekenstein and Hawking predicted using a macroscopic argument. This is a microscopic argument.
It's like the difference between what-- so this analysis is to black holes what Boltzmann analysis is to the thermodynamics of gases, liquids, and solids. And the maximally simple and the maximally complex descriptions were shown to be just alternate starting points for describing the same thing. And they can both be corrected systematically to describe the full object.
But we want to understand not just black holes that occur in string theory, but we want to understand the black holes that appear in the sky. And in the string theory description of black holes, at first, the first time the calculation was done, it was a very long and complicated calculation. But as often happens in science, tricks were discovered to make the calculation shorter and shorter until, finally, it was realized that the essence of the calculation really just cared about this emergent conformal symmetry, that that was the key to understanding where the black hole microstates came from.
And so one can ask whether you would ever have a conformal symmetry for black holes that appear in the sky. And the answer is, yes, indeed you can. And the conformal symmetry occurs when the black hole, a so-called extreme black hole, which is very rapidly rotating. And so let me now turn to those.
So Kerr showed not only that black holes-- Schwarzschild found a solution to the Einstein equation describing a static black hole. And many people realized or conjectured that there should be a more general solution in which a black hole is actually spinning, carries angular momentum, spinning like a top. And this solution, even though [LAUGHS] it was thought to exist back in the '20s, it took 50 years to write down the solution. And amazingly, the solution-- even though they're very complicated non-linear partial differential equations, amazingly, the solution could be written down in closed form.
And it's the spinning black-- every black hole that we see up in the sky is presumably spinning to some extent. There's no reason-- if you have one that's not spinning, and you breathe on it, it will start spinning a little. There's no reason for a black hole to not be spinning. So if these spinning black holes are what we-- the Kerr black holes are the ones that we see up in the sky.
Now, ordinary black-- Schwarzschild black holes are weird. But spinning black holes are even weirder. So if Andrew [INAUDIBLE], who's sitting in the fifth row there, were a spinning black hole, just to stay right here, he would be exerting a force on me, trying to drag me around with him. And just, then, to stay in the same place, I'd have to start walking slowly like this just to stay in the same place, like a treadmill.
The curvature of space would make a sort of-- would put me on to a spinning treadmill. So I'd have to walk in this direction just to stay in the same place. And the faster he spins, the faster I would have to walk to stay in the same place.
Now, if he were-- Kerr also showed that black holes can't spin as fast as they want. There's a speed limit on their spinning. And the speed limit, roughly speaking, can be stated as the fact that the horizon, the boundary of the black hole, can't be going around faster than the speed of light.
And so if you're-- for an extreme black hole, I would be-- the faster Andy would spin, the faster I would have to run to stay in the same place. And at some point, for an extreme black hole, I would have to be able to run faster than the speed of light to stay in the same place, which I can't. So extreme Kerr black holes, if you get to near one, you get dragged around inexorably. And so everything very near the horizon of an extreme black hole wants to go-- must, is dictated to, go around at the speed of light.
Now, that means everything is moving in the same direction rapidly. Now, it's hard to go at the speed of light. And when everything is forced to go at the speed of light, actually, there's very few ways that can happen. And so extreme simplifications occur in the structure of these extreme black holes. They are actually simpler than the Schwarzschild black hole, the ones that are spinning very rapidly.
And it was understood in a series of papers, including one-- in a series of papers that these have a conformal symmetry. And that conformal symmetry can explain-- can be used to explain the quantum degeneracy and the entropy of an extreme Kerr black hole. And a similar, though less rigorous, because we have less mathematical control over the real world than we do over string theory, to explain where-- to construct the hologram that surrounds a Kerr black hole and to explain where all the microstates in a Kerr black hole come from, which is a big part of solving the information problem for these rapidly spinning black holes.
Now, it turns out, oddly, that black holes in the physical universe like to spin rapidly, that there's more of them out there than you would think. And in fact, the black hole which has been studied the most-- it's one in our galaxy, GRS 1915+105-- by looking at the X-ray emissions, these people have argued that it splits within 2% of the speed of light. The horizon is spinning within the 2%.
Also, Cygnus x-1, the very first black hole candidate ever, is 2% below, or less, below light speed. And some of the supermassive black holes are also spinning very rapidly. And indeed, as they get older, they tend to spin faster. Now, black holes with big jets also have been noticed to often be spinning very rapidly.
So this is very interesting. We have this conformal symmetry that is related to understanding where black hole microstates come from. Now we're starting to-- back when this recent enterprise of trying to understand the quantum structure of black holes started, actual black hole observations seemed to be in the distant future. But wonderfully, in the last just five years, astronomical evidence for black holes has just started to pour out of the astronomical-- out of observatories. And moreover, just two years ago, we actually got, essentially, a photograph of one up in the sky.
And so the question, an interesting question, is, can we actually observe this conformal symmetry? So there's a symmetry that we're predicting. And we'd like to know how we can observe it.
OK, that's the-- so that's the famous picture from two years ago, where we had a dramatic-- this picture came after a two orders of magnitude increase. It's like we suddenly-- it's like you increase the number of pixels on your TV screen by a factor of 10,000. And we suddenly were able to do that looking up at the sky. And that brought in the biggest black hole up there, M87. It brought that into focus. So this was a spectacular advance.
And the question is, can you see anywhere in this image any kind of image of-- any kind of evidence for conformal symmetry? And of course, that would only be-- that symmetry will only be present if it's rapidly spinning. And the spin hasn't been measured yet, though it's promising that it's got a huge jet. Its jet is so big that it was-- so big and so luminous and long-- I think it was observed in 1918, really long time ago. The jet was observed.
So what are the predictions of conformal symmetry? Well just to give you an idea of what the power is, here is a picture of a prediction for the polarization of the image, which assumes only conformal symmetry. Now, this prediction was made before-- just before the image was released. And the image currently doesn't have enough resolution to see this and probably won't. It doesn't look very promising for this particular thing to be measured. But I'll talk about some other things. But I'm just using this as an example of the fact that this symmetry-- the existence of this symmetry has observational consequences.
Now, there is, however, a much more interesting instance of conformal symmetry that probably will be measured, seen in your-- if we're very lucky, we could see it in the next five or 10 years. But certainly this is something that should be measured in most of your lifetimes. And this is some work that really involved one of the things about modern progress in black holes. Now that's an observational science, there's a lot more discussion between theorists and experimentalists. And we're both learning a lot.
And so the thing that has a conformal symmetry is something called the photon ring. Now, in this picture, we haven't seen the photon ring yet. This is a ring of light, but it's not what we call the photon ring. The photon ring is a thin bright band that is almost, but not quite, visible. In fact, there's been some argument in the EHT collaboration about whether it could be pulled out of the already existing data. That's an indication of how close we are to seeing it.
But there's actually a whole series of thin, fine, bright rings here, which are-- well, the theory predicts and, in particular, the conformal symmetry predicts a very particular relationship between the successive rings. And it's quite likely that the next generation EHT, maybe even with a ground-based experiment, will be able to see this bright ring here. And I'm going to explain in a minute what the origin of these rings are and how they're related to conformal symmetry.
Yeah, here's the picture of what actually happens for a black hole and what we hope to see at the observatories. OK, so here's a black hole in the middle here. This is an image seen at the telescope. And this circle here is called the photon ring. So what actually happens here?
Suppose that-- sorry for picking on you, Andrew, but suppose Andy [INAUDIBLE] is sitting here outside the black hole, far away. We could just look and see the light that directly comes from him to us. But also, since there's a black hole here, there'll be light rays that go behind the black hole, get curved around by the curvature of space, and come back. And if you work it out, we'll see them upside down on the other side.
But that's not the end of it. You can have one that grazes the front of the black hole, a light ray that grazes the front of the black hole and comes out the same side but only a little thinner and taller. And if you keep going, there's an infinite succession of images. So a black hole is like a funhouse mirror where you can see infinite numbers of copies of yourself.
Now, if we were just to look at this-- so this is what we hope to see. So of course, we don't actually hope to see Andy's image reflected around the black hole. But there's a bunch of glowing stuff around the black hole. And all that glowing stuff around the black hole-- all the glowing stuff around the black hole both gives us direct images, which is what's been seen so far, but it will also have secondary and tertiary images from light rays that it emits and orbit some number of times around the black hole before getting to the telescope.
Now, it seems crazy. Each ring-- so these are the photon rings, and these are the photon subrings. Now, these images are related. There's a symmetry at play here. And that symmetry is a conformal symmetry and may well be related to the conformal symmetry-- this is some work in progress-- may well be related to-- it's certainly a symmetry which is there, but it actually may be related to the conformal symmetry that controls the black hole entropy.
So this conformal symmetry tells you the relation between this-- and it's a very non-trivial kind of relation. It depends on the spin of the black hole and relates the subsequent images in a very complicated way, which however, depends only on the structure of the black hole. So for example, if you want to study the funhouse mirrors, and you look at the person standing in front of them, you'll learn nothing about the structure of the mirror.
But if you look at the image-- and that's what we've done so far in this picture. If you look at the image, the image-- the relationship between the direct image and the reflected image has only information. The only new information is about the structure of the mirror. So the way to learn about the structure of the mirror is to compare the successive images. And so the way we're really going to learn about the structure of black holes from this observational-- observations is to look at the structure of the successive images.
Now, can you ever-- and now, here's the really-- so this is-- this kind of picture-- there's a fam-- so we've understood this photon ring structure better and better over the years. And really we only understood it well-- [LAUGHS] and this is quite typical in science-- we only understood it well when we had to explain what an observer was going to see. But the first paper describing some of its aspects was written by Bardeen in the early '70s. And there's a sentence in there-- it's a shame that this incredible structure has no hope of ever being observed by astronomers.
But now we're on the edge of it. And it-- now, there's one other important thing I need to tell you. It may seem like sort of a theorist's dream to see these finer and finer rings-- thinner and thinner and finer and finer rings, buried among the bright direct signal. How are you ever going to see them inside there? Well, that's the beautiful thing.
The picture of the black hole was a fake in the following way, which is very useful. They used a technique called VLBI which doesn't really give you the image. It gives you what's called the Fourier transform of the image. And the Fourier transform of the image-- in the Fourier transform of the image, these rings are separated. And they're separated by a lot.
And in order to see the successive rings you need longer-- so the Event Verizon Telescope, in order to get the fine resolution in the sky-- already that image is incredibly fine resolution-- they needed a giant telescope. So to see small things, you need a big telescope. That perhaps is intuitively obvious.
And they did a calculation 10 or 20 years ago that the size of the telescope they needed was the size of the Earth. How do you do that? Well, you take some number of telescopes-- that took seven telescopes around the Earth, and they synchronized them using atomic clocks and so on, and wired them together to work like one big telescope.
And that got them this image, which I showed you, which was almost, but not quite, fine-grained enough to see these rings-- close enough that people were arguing about whether the first one had actually been seen. So if you make a bigger telescope you're going to be able to see it, which means that we need to put some extension of it in orbit.
And probably the first ring can be seen by an orbiting extension in low-Earth orbit. And by the time to get to the second ring, you have a telescope on the moon. If we could get something on the James Webb, we could see even the third ring. And in fact, if you have a telescope that big, you only see the third ring. You can only see the very fine high Fourier components if you go to these very-long-baseline telescopes.
So the beautiful example of why we need it for theory lined up exactly with what astronomers are quite probably going to be able to see. So I think this is a very exciting thing in the future of physics. And I won't try to explain this, but I should say that LIGO will get at this same physics from a very different angle by measuring something called quasinormal modes, which are the ringdowns of coalescing black holes.
So in conclusion, the road to understand the fundamental laws of nature and to unravel these puzzles that are presented to us, there is no formula. We just keep running forward. We look-- we're lucky if we can see up to the next bend in the curve. We don't know how we're going to put it all together.
But in all this time that-- it's not Bethe's 70 years, as somebody [LAUGHS] has said. But I've been in this business for a while. And in all this time, there has never been a moment when exciting things weren't happening. And we still have a lot that we hope to understand. And thank you for listening.
Let me get a drink of water.
THOMAS HARTMAN: OK, we'll now take some questions. Paul.
AUDIENCE: [INAUDIBLE] show an intriguing picture, like leaders with the M87 with a bunch of spiral rings or [INAUDIBLE] or something. What exactly were those rings [INAUDIBLE] black hole itself is not emitting anything. Is it possible to observe that structure as well from [INAUDIBLE] telescope?
ANDREW STROMINGER: Yeah. So OK-- so the EHT not only gets intensity, but it gets polarization. And so these are the lines of the polarization. And of course, if there's something in between you-- if there's matter in between you and the black hole outside the horizon-- so this line here is the shadow-- sorry, it's not even the shadow of the black-- no, this line actually is the shadow of the black hole. Yeah, this is the shadow of the black hole. This is the line that is-- if it's illuminated from behind, you there's a circle within which you can't see any direct images or even secondary images of stars. That's the boundary, the edge of the black hole shadow.
But if you have stuff between-- outside the event horizon-- if I'm a black hole, and there's some stuff here emitting, it's outside the event horizon. So it could emit light that you would see. But it tends to be very faint. And so we estimated, really, order of magnitude estimates of what kind of luminosities you would expect from glowing matter near the horizon of a near-extreme black hole. And it doesn't seem to be-- it doesn't seem to be very large.
And as the polarimetry data has come in-- so we haven't found a special trick. With the photon ring, we had this trick with using the very-long-baselines that would enable us to see things that seem it might be impossible to see. But this looks like it's going to need three or four orders of magnitude improvement over what they've already have in order to observe.
AUDIENCE: [INAUDIBLE] now that I know what that is, what determines the position of that spiral?
ANDREW STROMINGER: OK, this is a totally cool thing. It just-- it's fun to explain this, and it's another example of how really crazy black holes are. So imagine all this coming from matter that's just very near the horizon of a black hole. This is M87. And this is not quite the middle. And let's call the north-- M87 has a jet-- has two jets.
And so if it's spinning, it's been noticed-- it's hard to measure the spin of a black hole. But it's been noticed but not really well understood. There seems to be a correlation between black holes which is partially understood. But there's a correlation between black holes which are spinning rapidly and have big jets. And M87 even has a huge jet.
So we think that we're looking at M87 about 17 degrees off axis. OK, so this point here would be the north pole of M87. This is the south pole of M87.
Now, why can you see the south pole? Well, why can you-- that's the back of M87. Well, why could you see that? Well, it's because you're going to have a photon at the south pole that gets curved around and comes up to your eye. And in fact, this-- and this is another instantiation of the photon ring physics. And these successive images are related by this same conformal symmetry.
Now, OK, the resolution isn't very good here, is it? But there's another North Pole down here somewhere, which is photons that didn't come straight from the north pole but wound around once and came up here. So if we did this picture in perfect resolution, it would have infinitely many north poles and infinitely many south poles. It would be really cool to see that. [LAUGHS] But I'm not I'm not very optimistic about seeing this. The photon ring is definitely-- seeing that is on the table. It's not funded in any way now, but people are definitely interested in it.
THOMAS HARTMAN: Yes.
AUDIENCE: So does the spinning of a black hole change over time? And does it change in a way that is related to its accretion of mass?
ANDREW STROMINGER: Yeah. So black holes do spin up. They-- as sort of the fixed point-- condensed matter physics people often talk about fixed points. And the fixed point of a black hole, I think-- I don't know how to make this precise. But in many situations, the fixed point is, for the black hole, to be spinning at the speed of light.
And in particular, you can show that a-- so a black hole that's surrounded by an accretion disk, usually the accretion disk, because of the dragging effect I was mentioning, will be spinning in the same way as the black hole. And the particles that drop onto it will tend to speed it up. As they feed it, they spin it up.
And maybe a really sort of cheap way to understand this is that, as a black hole spins up, it's Hawking temperature goes down. And when it reaches this extreme value, its temperature is going to 0. So it's not too far off to think of-- to equate a black hole spinning up with an object just wanting to cool down. Thermodynamically, that's what wants to happen.
THOMAS HARTMAN: Yes, over there.
AUDIENCE: So thank you so much for your lecture. And I was wondering if you had any suggestions for a student who didn't have much physics background but wanted to start studying physics. What books or resources would you recommend?
ANDREW STROMINGER: Sorry, I couldn't hear you very well through the mask. If you could just speak a little louder.
AUDIENCE: Yeah, of course. Thank you so much for coming to Cornell. And I was wondering what resources or books you would recommend to a student who didn't have much physics background but wanted to start studying physics.
ANDREW STROMINGER: Um, yeah. Wow, that's a hard one, because there's so many different-- there's so many different levels. The Feynman lectures have sure stood the test of time. [LAUGHS] I suppose they were the thing that got me interested. For more advanced stuff, like string theory or things where you're explaining the equations less, I like Brian Green's book, The Elegant Universe. Oh, yeah, and he was, of course, a Cornell professor when he wrote that. Is that right? I think that's right. Yeah, he was a Cornell professor when he wrote that. And yeah, those are two of my-- those are two favorite books.
THOMAS HARTMAN: Yep.
AUDIENCE: Does a black hole continue to be black from the inside? And is there visibility of light if someone were somehow able to enter one?
ANDREW STROMINGER: Yeah, am I supposed to be repeating the questions for the Zoom audience?
THOMAS HARTMAN: Oh, probably. Probably.
ANDREW STROMINGER: I should be? Yeah. So the question was, is a black hole black on the inside? And I'd say-- I mean, I think-- I think the answer is no, in the sense that, if you and I jumped into a black hole, and you were shining a flashlight at me, I'd still see the flashlight after we jumped into the black hole.
But of course, you can't look at the black hole once you're inside it. But there's-- I'd say it makes sense to talk about light inside a black hole, at least in classical general relativity. How you're supposed to think about the inside of a black hole in the full quantum theory is a huge, hot, recently explored subject that we don't have a clear answer to.
THOMAS HARTMAN: Maybe we have time for one more question. Yes.
AUDIENCE: So you talk about Hawking radiation and temperature [INAUDIBLE]. I guess is that something that's been built up from the [INAUDIBLE] we have observational evidence for it?
ANDREW STROMINGER: Yeah. So the question is, the Hawking radiation and the temperature of the black hole, is that something that's been built up from the theory, or do we have observational evidence for it? And that, exactly, actually, is an extremely interesting-- that's an extremely interesting question. We have not seen Hawking radiation from a black hole. Some people might argue that the cosmic microwave background is Hawking radiation emitted from the event horizon during the inflationary era-- OK, but not directly from a black hole.
And moreover, I talked about, to see the photon ring, the Event Horizon Telescope will have to improve by maybe an order of magnitude. But to see Hawking radiation from M87, the Event Horizon Telescope would probably have to improve its resolution by, I don't know, 100 orders of magnitude-- not going to happen. So it's harder-- it's harder to do than directly seeing strings in string theory. It's way, way outside anything that we could ever hope to directly verify experimentally.
And so the question which one would ask, and I'm going to ask it for you, [LAUGHS] is why don't people question it? So just as a sociological observation, I have never heard anybody say they don't believe that Hawking radiation exists. And why is that? So different people might give different answers to that question. But my answer to that question is that the calculation in the argument in his paper is so profoundly simple and assumes so little that there's just doesn't seem to be any [LAUGHS] other alternative.
Of course, one should and could question everything that hasn't been directly measured. But people don't seem to-- people don't seem to question it. And I think it's because it follows in such a simple way from basic things that we understand.
THOMAS HARTMAN: We'll end here for tonight. Let's thank Andy again for the beautiful lecture.
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As part of the Fall 2021 Hans Bethe Lecture Series at Cornell, Professor Andrew Strominger, Gwill E. York Professor of Physics at Harvard University presents "Probing the Edges of the Universe: Black Holes, Horizons and Strings".
Host: Tom Hartman
Abstract: The visible universe has edges, known as horizons, which surround black holes and other inaccessible spacetime regions. They are governed by a universal but still-mysterious set of laws discovered a half century ago by Stephen Hawking. These laws tell us that black holes are paradoxically both the simplest and most complex objects in the universe. A central goal of modern physics is to resolve this paradox; I will describe the compelling progress made towards this goal as well as future prospects for our understanding of black holes from string theory and from the recent Event Horizon Telescope image.