Transcription
You are part of the Harvard Black Hole Initiative, which has theoretical physicists, experimentalists, and even philosophers. So, let me ask the big question: What is a black hole? From a theoretical, from an experimental, uh, maybe even from a philosophical perspective?
So, a black hole is defined theoretically as a region of space-time from which light can never escape. Therefore, it's black. Now, that's just the starting point. Many weird things, uh, follow from that basic definition, but that is, that is the basic definition.
What is light they can't escape from a black hole? Well, light is, uh, you know, the stuff that comes out of the Sun, that stuff that goes into your eyes. Um, light is one of the, the stuff that disappears when the lights go off. This is stuff that appears when the lights come on. Um, of course, I could give you a, a medical definition, but, um, or physical mathematical definition, but I think it's something that we, uh, will understand very intuitively.
What is light? Black holes, on the other hand, we don't understand intuitively. They're very weird. And one of the questions about black holes, which I think you were alluding to, is, you know, why doesn't light get out? Or how is it that there can be a region of space-time from which light can't escape? It definitely happens. We've seen those regions. We have spectacular pictures, especially in the last several years, of those regions. Um, they're there. In fact, they're up in the sky, thousands or millions of them. We don't yet know how many. Um, but the proper explanation of why light doesn't escape from, uh, a black hole is still a matter of some debate.
Um, and one explanation, which perhaps Einstein might have given, is that light carries energy. You know, it carries energy because, you know, we have, uh, photocells, and we can take the light from the Sun and collect it, turn it into electricity. So, there's energy in light, and anything that carries energy is subject to a gravitational pull. Gravity will pull at anything with energy. Now, it turns out that the gravital, gravitational pull exerted by an object, uh, is proportional to its mass. And so, if you get enough mass in a small enough region, um, you, you can prevent light from escaping.
And let me flesh that out a little more. Um, if you're on the Earth and you're on a rocket ship leaving this, the surface of the Earth, and if we ignore the friction from the air, um, if your rocket accelerates up to 11 kilometers per second, that's escape velocity, and it can, if there were no friction, it could just continue forever to the next galaxy. On the Moon, which has less mass, it's only seven kilometers per second. So, but going in the other direction, if you have enough mass in one place, the escape velocity can become the speed of light.
If you shine light straight up away from the Earth, it doesn't have too much trouble. It's going way above the escape velocity. And, but if you have enough mass there, even light can't escape the escape velocity. And according to Einstein's theory of relativity, there is an absolute speed limit in the universe: the speed of light. And nothing makes any sense, nothing could be self-consistent if there are objects that could exceed light speed. And so, uh, in these very, very massive regions of space-time, even light cannot escape.
And the interesting thing is, Einstein himself didn't think that these, uh, objects we call black holes could exist. But let me actually linger on this. Yeah, that's incredibly interesting. There's a lot of interesting things here. First of the speed limit. How wild is it to you, if you put yourself in the mind, in the time of Einstein, before him, to come up with a speed limit that there is a speed limit, and that speed limit is the speed of light? How difficult of an idea is that? Is it, you know, you said from a mathematical physics perspective, everything just kind of falls into place, but he wasn't perhaps maybe initially had the luxury to think mathematically. He had to come up with it intuitively. Yes. So, like, what, how common intuitive is this notion to you? Well, is it still crazy? No, no. So, it's a very funny thing in physics. The best discoveries seem completely obvious in retrospect. Yeah. Even my own discoveries, which of course are far lesser than Einstein's, but many of my papers, many of my collaborators get all confused. We'll try to understand something. We said, we've got to solve this problem. We'll get all confused. Finally, we'll solve it. We'll get it all together. And, um, then we'll all of a sudden, everything will fall into place. We'll explain it. And then we'll look back at our discussions for the preceding months and literally be unable to reconstruct how confused we were. Yeah. And how we could ever have thought of it any other way. So, not only can I not fathom how confused Einstein was before he, when, you know, when he started thinking about the issues, I can't even reconstruct my own confusion from from two weeks ago. I, you know, so the really beautiful ideas that physics have this very hard to get yourself back into the mindset. Of course, Einstein was confused about many, many things. Um, it doesn't matter if you're a physicist. It's not how many things you got wrong. It's not the ratio of how many you got wrong to how many you got right. It's the number that you got right. So, Einstein didn't believe black holes existed, even though he predicted them. And I went and I read that paper, which he wrote. You know, Einstein wrote down his field equations and in 1915, and Schwarzschild solved them and discovered the black hole solution, uh, three or four months later, in very early 1916. And, um, 25 years later, Einstein wrote a paper. So, with 25 years to think about what this solution means, yeah, wrote a paper in which he said that black holes didn't exist. And I, I'm like, whoa. You know, if one of my students in my general relativity course wrote this, you know, I wouldn't pass them. I get to see mine. Oh, you wouldn't pass them. Okay. All right. Get to see by this. Okay. Same thing with gravitational waves. He didn't believe. Oh, he didn't believe in gravitational waves either. He went back and forth, but he wrote a paper and I think '34 saying that gravitational waves didn't exist because it, people were very confused about what a coordinate transformation is. And in fact, this confusion about what a coordinate transformation is has persisted, and we actually think we were on the edge of solving it 100 years later.
Well, 100 years later, what is a coordinate transformation as it was 100 years ago to today? Let's imagine I want to draw a map with pictures of all the states and the mountains, and then I want to draw the weather forecast, what the temperatures are going to be all over the country. And I do that using one set of weather stations, and I number the weather stations. And you have some other set of weather stations and you do the same thing. So, the coordinates are the locations of the weather stations. Yeah. They're how we describe where the things are. At the end of the day, we should draw the same map. That is coordinate invariance. And if we're telling somebody, uh, we're going to tell somebody at a real physical operation, we want you to stay as dry as possible on your drive from here to California, um, we should give them exactly the same route, no matter which weather stations we use or how we, you know, it's a very trivial. It's the labeling of points is an artifact and not in the real physics. Sure.
So, it turns out that that's almost true, but, but not quite. There's some subtleties to it. The statement that you should always have the same, give this the same kind of trajectory, same kind of, uh, instructions, no matter the weather station. Yeah. Yeah. There's some very delicate subtleties to that, which began to be noticed in the, in the '50s. It's mostly true, but when you have a space-time with edges, it gets very tricky how you label the edges. And space-time in terms of space, in terms of time, in terms of everything, just based on either one, okay, space or time, that gets very tricky. And Einstein, uh, didn't, didn't have it right. And in fact, he had an earlier version of general relativity in 1914, which he was very excited about, um, which was wrong. Gave it, wasn't fully coordinate invariant. It was only partially coordinate invariant. It was wrong. It gave the wrong answer for bending light to the Sun by a factor of two. There was an expedition sent out to measure it during World War I. They were captured before they could measure it. And that came, that came Einstein four more years to clean to clean his act up, by which time he had gotten it right. So, it's a very, it's a very tricky business. But once it's all laid out, it saves, uh, it's, it's, it's clear then.
What do you think Einstein didn't, uh, believe his own equations and didn't think that black holes are real? Well, why was that such a difficult idea for him? Well, something very interesting happens in Schwarzschild's solution of the Einstein equation. I think his reasoning was ultimately wrong, but let me explain to you, uh, what it was. Um, at the center of the black hole, behind the horizon, in a region that nobody can see and live to tell about it, as the center of the black hole, there's a singularity. And if you pass the horizon, you go into the singularity, you get crushed, and that's the end of everything. Now, the word singularity means that, um, it just means that Einstein's equations break down. They become infinite. You write them down, you put them on the computer. When the computer hits that singularity, it crashes. Everything becomes infinite. There's two. So, the questions are just no good there. Now, that's actually not a bad thing. It's a really good thing. And let me explain why. Um, so, it's an odd thing that Maxwell's theory and Newton's theory never exhibit this phenomena. You write them down, you can solve them exactly. They're really, Newton's theory of gravity, they're really very simple theories. You can solve them. Well, you can't solve the three-body problem, but, um, you can certainly solve a lot of things about them. Uh, nevertheless, there was never any reason, even though Maxwell and Newton perhaps fell for this trap, there were never any reason to think that these equations were exact. Um, and every, there's no equation, well, there's some equations that we've written down that we still think are exact. Some people still think are exact. My view is that there's no exact equation. Everything is an approximation. Everything is an approximation.
Are you trying to get as close as possible? Yeah. So, you think, are you saying objective truth doesn't exist in this world? The internet is going to be very much. We could discuss that, but that's a different. Okay. That's a different thing. Um, we wouldn't say Newton's theory was wrong. It had very, very small corrections. Incredibly small corrections. It's actually a puzzle why they're so small. So, if you watch the procession of Mercury's perihelia, this was the first indication of something going wrong. It corrected Newton's theory. Mercury has an elliptical orbit. The long part of it moves around as other planets come by and perturb it and so on. And so, this was measured by Le Verrier in 1859, and he compared theory and experiment, and he found out that the perihelion process moves around the Sun once every 233 centuries instead of every 231 centuries. Okay. Now, this is the wonderful thing about science. Why was this guy, I read you to give any idea how much work this is, you know, but of course, he made one of the greatest discoveries of the history of science without, you know, even knowing what it, what good it was going to be.
So, that's how small that was the first sign that there was something wrong with Newton. Yeah. Nah. So, the corrections to Newton's law are very, very small, but they're definitely there. The corrections to electromagnetism, they're mostly the ones that we see are mostly coming from quantum effects. And so, so the corrections there for, uh, Maxwell's equations is when you get super tiny. And then the corrections for the, um, for Newton's, uh, laws of gravity is when you get super big. That, that, that's when you require corrections. That's true. But I would phrase it as saying when it's super accurate. You know, if you look at the Bohr atom, Maxwell's electromagnetism is not a very good approximation to the force between the proton and the electron. The quantum mechanics. If you, if you, if you didn't have quantum mechanics, the electron would would spiral into the proton and the atom would collapse. It's quantum, you know, so that's a huge correction there. Sure. So, every theory gets corrected as we learn more. You're just no reason to suppose that it should be otherwise.
How is this really to the singularity? Why does it go there? So, when you hit the singularity, you know that you need some improvement to Einstein's theory of gravity. And that improvement, we understand what kind of things that improvement should involve. It should involve quantum mechanics. Quantum effects become important there. It's a small thing. And, um, we don't understand exactly what the theory is, but we know there's no reason to think, you know, Einstein's theory was invented to describe weakly curved things, the solar system and so on. It, it's incredibly robust that we now see that it works very well, uh, near the horizons of around black holes and so on. So, so it's a good thing that the theory drives itself. That it predicts its own demise. Newton's gravity had its demise. There were regimes in which it wasn't valid. Maxwell's electromagnetism had its demise. There was, uh, regimes in which quantum effects greatly modified the equations. But general relativity, all on its own, found a system which originally was fine, would perversely wander off into a configuration in which Einstein's equations no longer applied.
So, to you, the edges of the theory are wonderful. The failures, the edges are wonderful because that keeps us in business. So, that one of the things you said, I think in your Ted Talk, that, uh, the fact that quantum mechanics and, uh, and relativity don't describe everything and then they clash is wonderful, right? I forget the adjective you used, but it was something like this. So, why is that, uh, why is that interesting to you? There's no question in my mind, of course, many people would disagree with me, that now is the most wonderful time to be a physicist. So, so people, people look back at, at, it's a classical thing to say among physicists, "I wish it were 1920." Right? Quantum mechanics had been just understood. There was the periodic table. There was, but in fact, that was such a rich thing that, well, so that, what a lot of exciting stuff happened around 1920. It took, it took the whole, it took a whole century to sort out the new insights that we got, especially adding some experimental stuff into the bit, into the bunch, actually making observations and adding all the experimental things. Computers also help with visualizations and all that kind of stuff. Yeah. Yeah. Yeah. It was a whole sort of wonderful century. I mean, the seed of general relativity was the incompatibility of Maxwell's theory of the electromagnetic field with Newton's laws of gravity. They were incompatible because if you look at Maxwell's theory, there's a contradiction if anything goes faster than the speed of light. But Newton's theory of gravity, the, uh, gravitational field, the gravitational force is instantaneously transmitted across the entire universe. So, you could, you know, if you had a, a friend on, you know, in another galaxy with a very sensitive measuring device that could measure the gravitational field, that could just take this cup of coffee and move it up and down in Morse code, and they could get the message instantaneously over another galaxy. That leads to all kinds of contradictions. It's not, it's not self-consistent. It was exactly in resolving those contradictions that Einstein came up with the general theory of of relativity. And it's fascinating how this contradiction, which seems like maybe it's kind of a technical thing, led to a whole new vision of the of the universe.
Now, let's not get fooled, because lots of contradictions are technical things. We haven't set up the, we run into other kinds of contradictions that are technical, and they, they don't seem to, we just, we understood something wrong. We made a mistake. We set up equations in the wrong way. We didn't translate the formalisms, as opposed to revealing some deep mystery that's yet to be uncovered. Yeah. Yeah. And so, we never, we're never very sure which are which are the really important ones. But to you, the difference between quantum mechanics and general relativity seems, the the tension, the contradiction there, seems to hint at some deeper, deeper thing that's going to be discovered in the century. Yes, because that one has been understood since the '50s. Pauli was the, uh, first person to notice it, and Hawking in the early '70s gave it a really much more visceral form. Um, and people have been hurling themselves at it, trying to reduce it to some technicality, but nobody has succeeded. And the efforts to understand it have led to, uh, all kinds of interesting relations between quantum systems and and applications to other fields and and so on.