Lex Fridman PodcastSean Carroll: General Relativity, Quantum Mechanics, Black Holes & Aliens | Lex Fridman Podcast #428
EVERY SPOKEN WORD
150 min read · 30,143 words- 0:00 – 1:54
Introduction
- SCSean Carroll
The whole point of relativity is to say there's no such thing as right now, when you're far away. And that is doubly true for what's inside a black hole. And you might think, "Well, the galaxy's very big." It's really not. It's some tens of thousands of light years across and billions of years old. So, you don't need to move at a high fraction of the speed of light to fill the galaxy.
- LFLex Fridman
The number of worlds is-
- SCSean Carroll
Very big.
- LFLex Fridman
... very, very, very big. Where do those worlds fit?
- SCSean Carroll
So-
- LFLex Fridman
Where do they go?
- SCSean Carroll
... the short answer is, the worlds don't exist in space. Space exists separately in each world.
- LFLex Fridman
The following is a conversation with Sean Carroll. His third time on this podcast. He is a theoretical physicist at Johns Hopkins, host of the Mindscape podcast, that I personally love and highly recommend, and author of many books, including the most recent book series called The Biggest Ideas in the Universe. The first book of which is titled Space, Time, and Motion, and it's on the topic of general relativity, and the second, coming out on May 14th, so you should definitely pre-order it, is titled Quanta and Fields, and that one is on the topic of quantum mechanics. Sean is a legit, active theoretical physicist, and at the same time, is one of the greatest communicators of physics ever. I highly encourage you listen to his podcast, read his books, and pre-order the new book to support his work. This was, as always, a big honor and a pleasure for me. This is the Lex Friedman Podcast. To support it, please check out our sponsors in the description, and now, dear friends, here's Sean Carroll.
- 1:54 – 14:13
General relativity
- LFLex Fridman
In book one of the series, The Biggest Ideas in the Universe, called Space, Time, Motion, you take on classical mechanics, general relativity, uh, by taking on the main equation of general relativity and making it, uh, accessible, easy to understand. So, um, maybe at the high level, what is general relativity? What's a good way to s- start to try to explain it?
- SCSean Carroll
Probably the best way to start to try to explain it is special relativity, which came first, 1905. Uh, it was the culmination, right? Of many decades of people putting things together, but it was Einstein in 1905. In fact, it wasn't even Einstein. I should give more credit to Minkowski in 1907. So, Einstein in 1905 figured out that you could get rid of the ether, the idea of a rest frame for the universe, and all the equations of physics would make sense, with the speed of light being a maximum. But then, it was Minkowski who used to be Einstein's professor in 1907 who realized the most elegant way of thinking about this idea of Einstein's was to blend space and time together into space-time, to really imagine that there is no hard and fast division of the four-dimensional world in which we live into space and time separately. Einstein was at first dismissive of this. He thought it was just like, oh, the mathematicians are over-formalizing again. But then he later realized that if space-time is a thing, it can have properties, and in particular, it can have a geometry. It can be curved from place to place, and that was what let him solve the problem of gravity. He was always been... He had previously been trying to fit in what we knew about gravity from Newtonian, uh, mechanics, the inverse square law of gravity, to his new relativistic theory. It didn't work. So, the final leap was to say gravity is the curvature of space-time. And that statement is basically general relativity.
- LFLex Fridman
And, uh, the tension with Minkowski was, he was a mathematician.
- SCSean Carroll
Yes.
- LFLex Fridman
So, it's a tension between physics and, and mathematics. In fact, in, uh, your lecture about this equation, one of them, you, uh, say that Einstein is a better physicist than he gets credit for.
- SCSean Carroll
Yep. (laughs) I know, that's hard. That's a little bit of a joke there, right?
- LFLex Fridman
Yeah.
- SCSean Carroll
Because we all give Einstein a lot of credit, but then we also, partly based on fact, but partly to make ourselves feel better, tell ourselves a story about how later in life, Einstein couldn't keep up. Uh, there were younger people doing quantum mechanics and quantum field theory and particle physics, and he was just sort of, uh, unable to really philosophically get over his objections to that. And I think that that story about the latter part is completely wrong, like almost 180 degrees wrong. I think that Einstein understood quantum mechanics as well as anyone, at least up through the 1930s. I think that his philosophical objections to it are correct. (laughs) So, he should actually have been taken much more seriously about that. And what he did, what he achieved in trying to think these problems through is to really basically understand the idea of quantum entanglement, which is kind of important these days when it comes to understanding quantum mechanics. Now, it's true that in the '40s and '50s, uh, he placed his efforts in hopes for unifying electricity and magnetism with gravity. That didn't really work out very well. All of us, you know, try things that don't work out. I don't hold that against him. But in terms of IQ points, in terms of trying to be a clear thinking physicist, he was really, really great.
- LFLex Fridman
What does greatness look like for a physicist? So, how difficult is it to take the leap from special relativity to general relativity? How difficult is it to imagine that... To consider space-time together and to imagine that, uh, there's a curvature to this whole thing?
- SCSean Carroll
Yeah, that's a great question. Um, I think that if you want to make the case for Einstein's greatness, which is not hard to do, there's two things you point at. One is in 1905, his famous miracle year-... he writes three different papers on three wildly different subjects, all of which are, would make you famous just for writing that one paper. Um, special relativity is one of them. Brownian motion is another one, which is just, you know, the little vibrations of tiny little dust specs in the air. But who cares about that? What matters is it proves the existence of atoms. He explains Brownian motion by imagining there are molecules in the air and deriving their properties. Brilliant. And then he basically starts the world on the road to quantum mechanics with his paper on which, again, is given a boring label of the photoelectric effect. What it really was is he invented photons. He showed that light should be thought of as particles as well as waves, and he did all three of those very different things in one year. Okay. But the other thing that gets him genius status is, like you say, general relativity. So this takes ten years, from 1905 to 1915. He wasn't only doing general relativity. He was working on other things. He wrote... he invented a refrigerator. (laughs) He did various interesting things. And he wasn't even the only one working on the problem. There were other people who suggested relativistic theories of gravity. But he really applied himself to it and... An- and I think as your question suggests, the solution was not a matter of turning a crank. It was something fundamentally creative. You know, the... In his own telling of the story, his greatest moment, his happiest moment was when he realized that if... the way that we would modern... in, say it in modern terms, if you were in a rocket ship accelerating at 1G, at one, uh, acceleration due to gravity, if the rocket ship were very quiet, you wouldn't be able to know the difference between being in a rocket ship and being on the surface of the earth. Gravity is sort of not detectable or at least not distinguishable from acceleration. So number one, that's a pretty clever thing to think. But number two, if you or I had had that thought, we would have gone, "Ha, we're pretty clever." He reasons from there to say, "Okay, if gravity is not detectable, then it can't be like an ordinary force," right? The electromagnetic force is detectable. We can put charged particles around. Positively-charged particles and negatively-charged particles respond differently to an electric field or to a magnetic field. He realizes that what his thought experiment showed or at least suggested is that gravity isn't like that. Everything responds in the same way to gravity. How could that be the case? And then this other leap he makes is, "Oh, it's 'cause it's the curvature of space-time," right? It's a feature of space-time. It's not a force on top of it, and the feature that it is, is curvature. And then finally, he says, "Okay. Clearly, I'm gonna need the mathematical tools necessary to describe curvature. I don't know them, so I will learn them." And they didn't have MOOCs or AI, uh, helpers back in those days. He had to sit down and read the math papers and he taught himself differential geometry and invented general relativity.
- LFLex Fridman
What about the step of including time as just another dimension, so combining space and time? Is that a simple mathematical leap as Minkowski suggested?
- SCSean Carroll
It's certainly not simple actually. Um, it's, uh, it's a profound insight. That's why I said I think we should give Minkowski more credit than we do. You know, he's the one who really put the finishing touches on special relativity. Again, many people had talked about how things change when you move close to the speed of light, uh, what Maxwell's equations of electromagnetism predict and so forth, what their symmetries are, so people like Lorentz and Fitzgerald and Poincaré. There's a, a story that goes there. And in, in the usual telling, Einstein sort of puts the capstone on it. He's the one who says, "All this makes much more sense if there just is no ether. It is undetectable. We don't know how fast... Everything's relative, thus the name relativity." But he didn't take the actual final step, which was to realize that the underlying structure that he had invented is best thought of as unifying space and time together. I honestly don't know what was going through Minkowski's mind when he thought that, that... I'm not sure if he was, you know, so mathematically adept that it was just clear to him, uh, or he was really struggling it and he did trial and error for a while. I'm not sure.
- LFLex Fridman
I mean, do you, for him or for Einstein, visualize the four-dimensional space, try to play with the idea of time as just another dimension?
- SCSean Carroll
Oh, yeah. All the time. I mean, we of course make our lives easy by ignoring two of the dimensions of space. (laughs) So instead of four-dimensional space-time, we just draw pictures of one dimension of space, one dimension of time, the so-called space-time diagram. But, you know, I mean, maybe this is lurking underneath your question, but even the best physicists will draw, you know, a hor- a vertical axis and a horizontal axis and they'll go, "Space, time." But deep down, that's wrong (laughs) because you're sort of preferring one direction of space and one direction of time and it's really the whole two-dimensional thing-
- LFLex Fridman
Mm-hmm.
- SCSean Carroll
... that is space-time. The more legitimate thing to draw on that picture are rays of light, are light cones. From every point, there is a fixed direction at which the speed of light would represent and that is actually inherent in the structure. The division into space and time is something that's easy for us human beings.
- LFLex Fridman
What is the difference between space and time from the perspective of general relativity?
- SCSean Carroll
It's the difference between X and Y when you draw axes on a piece of paper. It's-
- LFLex Fridman
So really no difference.
- SCSean Carroll
There's almost no difference. There's one difference that is kind of important, which is the following. If you have a curve in space... I'm gonna draw it horizontally 'cause that's usually what we do in space-time diagrams. If you have a curve in space, you've heard the motto before that the shortest distance between two points is a straight line.... if you have a curve in time, which is by the way, literally all of our lives, right? We all evolve in time, so you can start with one event in space-time and another event in space-time. What Minkowski points out is that the time you measure along your trajectory in the universe is precisely analogous to the distance you travel on a curve through space. And by precisely, I mean it is also true that the actual distance you travel through depends on your path, right? You can go a straight line the shortest distance, an curvy line would be longer. The time you measure in space-time, the literal time that ticks off on your clock also depends on your path. But it depends on it the other way. So that the longest time between two points is a straight line, and if you zig back and forth in space-time, you take less and less time to go from point A to point B.
- LFLex Fridman
How do I make sense of that? The, uh, difference between the observed reality and the objective reality underneath it? Or is objective reality a silly notion, given general relativity?
- SCSean Carroll
I'm a huge believer in objective reality. I think that objective reality, objective reality-
- LFLex Fridman
You're a fan.
- SCSean Carroll
... is real.
- LFLex Fridman
Yeah.
- SCSean Carroll
Um, but I do think that people kind of are a little overly casual about the relationship between what we observe and objective reality in the following sense. Of course, in order to explain the world, our starting point and our ending point is our observations. Our experimental input, the phenomena we experience and see around us in the world. But in between, there's a theory. (laughs) There's a mathematical formalization of our ideas about what is going on. And if a theory fits the data and is very simple and makes sense in its own terms, then we say that the theory is right. And that means that we should attribute some reality to the entities that play an important role in that theory. At least provisionally until we come up with a better theory down the road.
- 14:13 – 19:03
Black holes
- LFLex Fridman
I think a nice way to test the difference between objective reality and the observed reality is what happens at the, uh, at the edge of the horizon of a black hole. So technically, as you get closer to that horizon, time stands still.
- SCSean Carroll
Yes and no.
- LFLex Fridman
Okay.
- SCSean Carroll
It depends on exactly how careful we're being. So here is a, a bunch of things I think are correct. If you imagine there is a black hole space-time, so like the whole solution to Einstein's equation and, and you treat you and me as what we call test particles. So we don't have any gravitational fields ourselves, we just move around in the gravitational field. And that's obviously an approximation, okay? But let's, let's imagine that. And you stand outside the black hole and I fall in. And as I'm falling in, I'm waving to you, you know, 'cause I'm going into the black hole. You will see me move more and more slowly, and also the light from me is redshifted, so I kind of look embarrassed 'cause (laughs) I'm falling into a black hole. And there is a limit. There is a last moment that light will be emitted from me, from your perspective, forever, okay? Now you don't literally see it, because I'm emitting photons more and more slowly, right? Because, from your point of view. So it's not like I'm equally bright. I basically fade from view in that picture, okay? So that's one approximation. The other approximation is, I do have a gravitational field of my own, and therefore as I approach the black hole, the black hole doesn't just sit there and let me pass through. It kind of moves out to eat me up.
- LFLex Fridman
Mm-hmm.
- SCSean Carroll
Because its net energy mass is going to be mine plus its. But roughly speaking, yes. I think, so I, I don't like to go to the dramatic extremes because that's where the approximations break down. But if you see something falling into a black hole, you see its clock ticking more and more slowly.
- LFLex Fridman
How do we know it fell in?
- SCSean Carroll
We don't.
- LFLex Fridman
All right.
- SCSean Carroll
I mean, how would we?
- LFLex Fridman
Yeah.
- SCSean Carroll
Because it's always possible that right at the last minute, it had a change of heart and starts accelerating away, right? If you don't see it pass in, you don't know. And let's point out that as smart as Einstein was, he never figured out black holes, and he could have.
- LFLex Fridman
Mm-hmm.
- SCSean Carroll
It's kind of embarrassing that it took decades for people thinking about general relativity to understand that there are such thing as black holes, because basically Einstein comes up with general relativity in 1915. Two years later, Schwarzschild, uh, Karl Schwarzschild derives the solution to Einstein's equation that represents a black hole, the Schwarzschild solution. No one recognized it for what it was until the '50s. David Finkelstein and other people. And that's just, you know, one of these examples of physicists not being as clever as they should have been.
- LFLex Fridman
Well, that's the singularity, that's the kind of the edge of the theory, the limit. So it's understandable that it's difficult to imagine the limit of things.
- SCSean Carroll
It is absolutely hard to imagine, and a black hole is very different in many ways from what we're used to. On the other hand, I mean, uh, I mean the real reason, of course, is that between 1915 and 1955, there's a bunch of other things that are really interesting going on in physics, the whole of particle physics and quantum field theory. So many of the greatest minds were focused on that. But still, if the universe hands you a solution to general relativity in terms of curved space-time and it's kind of mysterious, certain features of it, I would put some effort into trying to figure it out.
- LFLex Fridman
So how does a black hole work? Put yourself in the shoes of Einstein and take general relativity to its natural conclusion about these massive things.
- SCSean Carroll
It's best to think of a black hole as not an object so much as a region of space-time, okay? It's a region with the property, at least in classical general relativity, quantum mechanics makes everything harder. But let's imagine we're being classical for the moment. It's a region of space-time with the property that if you enter, you can't leave.Literally, the equivalent of escaping a black hole would be moving faster than the speed of light. They are both precisely, equally difficult. You would have to move faster than the speed of light to escape from the black hole. So once you're in, that's fine. You know, in principle, uh, you don't even notice when you cross the event horizon, as we call it. The event horizon is that point of no return, where once you're inside, you can't leave. But meanwhile, the space-time is sort of collapsing around you, uh, to ultimately a singularity in your future, which means that the gravitational forces are so strong they tear your body apart, um, and you will die in a finite amount of time. The time it takes if the- if the black hole is about the mass of the sun, to go from the event horizon to the singularity takes about one-millionth of a second.
- LFLex Fridman
(laughs)
- 19:03 – 23:10
Hawking radiation
- LFLex Fridman
And wha- what happens to you if you fall into the black hole? Like, if we think of an object as, uh, information, that information gets destroyed.
- SCSean Carroll
Well, (laughs) you've raised a crucially difficult point.
- LFLex Fridman
Hmm.
- SCSean Carroll
So, that's why I keep needing to distinguish between black holes according to Einstein's theory of general relativity, which is book one of Space, Time, and Geometry, which is perfectly classical. And then come the 1970s, we start asking about quantum mechanics and what happens in quantum mechanics. According to classical general relativity, the information that makes up you when you fall into the black hole is lost to the outside world. It's there. It's inside the black hole, but we can't get it anymore. In the 1970s, Stephen Hawking comes along and points out that black holes radiate. They give off photons and other particles into the universe around them. And as they radiate, they lose mass and eventually they evaporate. They disappear. So once that happens, I can no longer say the information about you or a book that I threw in the black hole or whatever is still there as hidden behind the black hole 'cause the black hole has gone away. So either that information is destroyed, like you said, or it is somehow transferred to the radiation that is coming out, to the Hawking radiation. The large majority of people who think about this believe that the information is somehow transferred to the radiation, and information is conserved. That is the- a feature both of general relativity by itself and of quantum mechanics by itself. So when you put them together, that should still be a feature. We don't know that for sure. There are people who have doubted it, including Stephen Hawking for a long time. But that's what most people think. And so what we're trying to do now in, uh, a topic which has generated many, many hundreds of papers called the black hole information loss puzzle, is figure out how to get the information from you or the book into the radiation that is escaping the black hole.
- LFLex Fridman
Is there any way to observe Hawking radiation to a degree where you can start getting insight? Or is this all just in the space of theory right now?
- SCSean Carroll
Right now, we are nowhere close to observing Hawking radiation. Here's the sad fact. The larger the black hole is, the lower its temperature is. So, a small black hole, like a microscopically small black hole, might be very visible if it's giving off light. But something like the black hole at the center of our galaxy, three million times the mass of the sun or something like that, Sagittarius A star, uh, that is so cold and low temperature that its radiation will never be observable. Um, black holes are hard to make. We don't have any nearby. The ones we have out there in the universe are very, very faint. So there's no immediate hope for detecting Hawking radiation.
- LFLex Fridman
Allegedly, we don't have any nearby.
- SCSean Carroll
As far as we know, we don't have any nearby.
- LFLex Fridman
Couldn't tiny ones be hard to detect, somewhere, at the edges of the solar system maybe?
- SCSean Carroll
Absolutely. So you don't want them to be too tiny or they're exploding, right? Or they're- they're very bright, and then they would be visible. But there's an absolutely a regime where black holes are large enough not to be visible because the larger ones are fainter, right? Not giving off radiation. But small enough to have not been detected through their gravitational effect. Yeah.
- LFLex Fridman
Psychologically, just emotionally, how do you feel about black holes? Do they scare you?
- SCSean Carroll
I love them. I love black holes. But the universe weirdly makes it hard to make a black hole.
- LFLex Fridman
Hmm.
- SCSean Carroll
Right? Because you really need to squeeze an enormous amount of matter and energy into a very, very small region of space. So we know how to make stellar black holes. A super massive star can collapse to make a black hole. We know we also have these super massive black holes at the center of galaxies. We're a little unclear where they came from. I mean, maybe stellar black holes that got together, uh, and combined. But that's, you know, one of the exciting things about new data from the James Webb Space Telescope is that quite large black holes seem to exist relatively early in the history of the universe. So it was already difficult to figure out where they came from. Now it's an even tougher puzzle.
- 23:10 – 32:06
Aliens
- SCSean Carroll
- LFLex Fridman
So these super massive black holes were formed somewhere early on in the universe. I mean, that's a feature, not a bug, right? That we don't have too many of them. Otherwise, we wouldn't have, uh, uh, the time or the space to form the- the little pockets of complexity that we call humans.
- SCSean Carroll
I think that's fair. Yeah. It's always interesting when something is difficult but happens anyway, right? I mean, the probability of making a black hole could have been zero, it could have been one. But it's this interesting number in between, which is kind of fun.
- LFLex Fridman
Are there more intelligent alien civilization than there are super massive black holes?
- SCSean Carroll
Yeah. I have no idea.
- LFLex Fridman
I think you would.
- SCSean Carroll
But I think your intuition is right, that it would have been easy for there to be lots of civilizations, and then we would have noticed them already. And we haven't. So absolutely the simplest explanation for why we haven't is that they're not there.
- LFLex Fridman
Yeah. I just think it's so easy to make them though. So there must be... I understand that's the simplest explanation.
- SCSean Carroll
(laughs)
- LFLex Fridman
But also-
- SCSean Carroll
How easy is it to make life or eukaryotic life-
- LFLex Fridman
It just-
- SCSean Carroll
... or multicellular life?
- LFLex Fridman
It seems like life finds a way. Intelligent alien civilizations, sure. Maybe there is...... somewhere along that chain, a really, really hard leap. But once you start life, once you get the origin of life, it seems like life just finds a way everywhere, in every condition. It just figures it out.
- SCSean Carroll
I mean, I get it. I get exactly what you're thinking. I think it's a perfectly reasonable attitude to have before you confront the data. I would not have expected Earth to be special in any way. I would have expected there to be plenty of very noticeable extraterrestrial civilizations out there. Um, but even if life finds a way, even if we buy everything you say, how long does it take for life to find a way? What if it typically takes 100 billion years? Then we'd be alone.
- LFLex Fridman
So it's a time thing. So to you really there's, most likely there's no alien civilizations out there. I just, I can't see it. I believe there's-
- SCSean Carroll
Yeah.
- LFLex Fridman
... a ton of them and there's another explanation why we can't see them.
- SCSean Carroll
I don't believe that very strongly. Look, I'm not gonna, uh, place a lot of bets here. I would not... I- I'm both pretty up in the air about whether or not life itself is all over the place. It's possible, you know, when we visit other worlds, other solar systems, there's very tiny microscopic life ubiquitous, but none of it has reached some complex form. It's also possible there's just, there isn't any. It's also possible that there are intelligent civilizations that have better things to do than knock on our doors. So, I think, you know, we should be very humble about these things we know so little about.
- LFLex Fridman
And it's also possible there's a great filter where there's something fundamental about, uh, once a civilization develops complex enough technology, that technology is more statistically likely to, to destroy everybody versus to continue being creative.
- SCSean Carroll
That is absolutely possible. I'm actually putting less credence on that one just because you need it to happen every single time, right?
- LFLex Fridman
Mm-hmm.
- SCSean Carroll
If even one... I mean, this goes back to von Neumann pointing... John von Neumann pointed out that you don't need to send the aliens around the galaxy. You can build self-reproducing probes and send them around the galaxy. And you might think, "Well, the galaxy's very big." It's really not. It's some tens of thousands of light years across and billions of years old. So, you don't need to move at a high fraction of the speed of light to fill the galaxy.
- LFLex Fridman
So if you were an ali- uh, intelligent alien civilization, the dictator of one, you would just send out a lot of probes, self-replicating probes?
- SCSean Carroll
100%. And-
- LFLex Fridman
Just spread out.
- SCSean Carroll
Yes. And what you should do, this is... So if you want the optimistic spin, here's the optimistic spin. People looking for intelligent life elsewhere often tune in with their radio telescopes, right? At least we did before Arecibo was sort of decommissioned. That's a, not a very promising way to find intelligent life elsewhere because why in the world would a super intelligent alien civilization waste all of its energy by beaming it in random directions into the sky? For one thing, it just passes you by, right? So if, if we're here on Earth, we've only been listening to radio waves for 100 or a couple hundred years, okay? So if an intelligent alien civilization exists for a billion years, they have to pinpoint exactly the right time to send us the signal. It is much, much more efficient to send probes and to park (laughs) , to go to the other solar systems, just sit there and wait for an intelligent civilization to arise in that solar system. This is kind of the 2001 monolith hypothesis, right?
- LFLex Fridman
Mm-hmm.
- SCSean Carroll
I would, I would be less surprised to find a sort of quiescent alien artifact in our solar system than I would to catch a radio signal from an intelligent civilization.
- LFLex Fridman
So you're a sucker for in-person conversations versus remote?
- 32:06 – 56:29
Holographic principle
- LFLex Fridman
So, if we return to black holes y- uh, and talk about the, uh, the holographic principle more broadly-
- SCSean Carroll
Mm.
- LFLex Fridman
... you have a recent paper on the topic. You've been thinking about the topic in terms of rigorous research perspective and just as a popular book writer.
- SCSean Carroll
Mm-hmm.
- LFLex Fridman
So, what is the holographic principle?
- SCSean Carroll
Well, it goes back to this question that we were talking about with the information and how it gets out. In quantum mechanics certainly, arguably even before quantum mechanics comes along in classical, statistical mechanics, there's a relationship between information and entropy. Entropy is my favorite thing to talk about, that I've written books about and will continue to write books about. So, Hawking tells us that black holes have entropy. And it's a finite amount of entropy, it's not an infinite amount. But the belief is, and now we're already getting quite speculative, the belief is that the entropy of a black hole is the largest amount of entropy that you can have in a region of space-time. It's sort of the most densely packed that entropy can be. And what that means is, there's sort of a maximum amount of information that you can fit into that region of space and you call it a black hole. And interestingly, you might expect, if I have a box and I'm gonna put information in it and I don't tell you how I'm gonna put the information in, but I ask, "How does the information I can put in scale with the size of the box?" (laughs) You might think, "Well, it goes as the volume of the box because the information takes up some volume and I can only fit in a certain amount." And that is what you might guess for the black hole, but it's not what the answer is. The answer is that the maximum information, as reflected in the black hole entropy, scales as the area of the black hole's event horizon, not the volume inside. So, people thought about that in both deep and superficial ways for a long time and they proposed what we now call the holographic principle, that the way that space-time and quantum gravity convey information or hold information is not different bits or qubits for quantum information at every point in space-time. It is something holographic, which means it's sort of embedded in or located in or can be thought of as pertaining to one dimension less of the three dimensions of space that we live in. So, in the case of the black hole, the event horizon is two-dimensional embedded in a three-dimensional universe and the holographic principle would say, "All of the information contained in the black hole can be thought of as living on the event horizon, rather than in the interior of the black hole." I need to say one more thing about that, which is that this was an idea... The idea I just told you was the original holographic principle put forward by people like Gerard 't Hooft and Leonard Susskind, a super famous, um, physicist. Leonard Susskind was on my podcast and gave a great, uh, talk. He's very, very good at explaining these things.
- LFLex Fridman
Mindscape podcast.
- SCSean Carroll
Mindscape podcast.
- LFLex Fridman
Everybody should listen.
- SCSean Carroll
That's right, yes. I'm not-
- LFLex Fridman
And you don't just have physicists on.
- SCSean Carroll
I, I don't.
- LFLex Fridman
I love Mindscape.
- SCSean Carroll
Oh, thank you very much.
- LFLex Fridman
Curiosity driven.
- SCSean Carroll
Yeah, ideas-
- LFLex Fridman
Exploration of ideas.
- SCSean Carroll
Big ideas from smart people, yeah. But anyway, what I was trying to get at was Susskind and also 't Hooft were a little vague. They were a little hand-wavy about holography and what it meant. Where holography, the idea that information is sort of encoded on a boundary, uh, really came into its own was with Juan Maldacena in the 1990s, uh, and the AdS/CFT correspondence, which we don't have to get into that into any detail, but it's a whole full-blown theory of... It's two different theories. One theory in N dimensions of space-time without gravity and another theory in N plus one dimensions of space-time with gravity. And the idea is that this N dimensional theory is, you know, casting a hologram into the N plus one dimensional universe to make it look like it has gravity. And that's holography with a vengeance, and that's the, that's an enormous source of interest for theoretical physicists these days.
- LFLex Fridman
How should we picture what impact that has, uh, the fact that you could store all the information you could think of as all the information that goes into a black hole can be stored at the event horizon?
- SCSean Carroll
Yeah, I mean, it's a good question. Um...... uh, one of the things that quantum field theory indirectly suggests is that there's not that much information in you and me compared to the volume of space time we take up. As far as quantum field theory is concerned, you and I are mostly empty space. (laughs) And so we are not information dense, right? The density of information in us or in a book or a CD or whatever, computer RAM, is indeed, uh, encoded by volume. Like there's different bits located at different points in space. But that density of information is super duper low. So we're just like the speed of light or just like the Big Bang, for the information in a black hole, we are far away in our everyday experience from the regime where these questions become relevant. So it's very far away from our intuition. We don't really know how to think about these things. We can do the math, but we don't feel it in our bones.
- LFLex Fridman
So you can just write off that weird stuff happens-
- SCSean Carroll
Well, we'd like to do better-
- LFLex Fridman
... uh, in a black hole?
- SCSean Carroll
... but we're trying. I mean, that's why we have a information loss puzzle because we haven't completely solved it. So here, just one thing to keep in mind. Once space time becomes flexible, which it does according to general relativity, and you have quantum mechanics, which has fluctuations and virtual particles and things like that, the very idea of a location in space time becomes a little bit fuzzy, right? 'Cause it's flexible, and quantum mechanic says you can't even pin it down. So information can propagate in ways that you might not have expected. And that's easy to say and it's true, but we haven't yet come up with the right way to talk about it that is perfectly rigorous.
- LFLex Fridman
It's crazy how dense with information a black hole is. And then plus, like quantum mechanics starts to come into play. So, you know, you almost want to romanticize the kind of interesting computation type things that are going on inside the black hole.
- SCSean Carroll
You do. You do. But I will, I'll point out one other thing. Um, it's information dense, but it's also very, very high entropy. So a black hole is kind of like a very, very, very specific random number, (laughs) right? It takes a lot of digits to specify it. But the digits don't tell you anything. They don't give you anything useful to work on. So it takes a lot of information, but it's not of a form that we can, uh, learn a lot from.
- LFLex Fridman
But hypothetically, I guess as you mentioned, the information might be preserved. The information that goes into a black hole, it doesn't get destroyed. So what, what does that mean when the entropy is really high?
- SCSean Carroll
Well, the black hole, I said that the black hole is the highest density of information, but it's not the highest amount of information because the black hole can evaporate. And when it evaporates, and people have done the equations for this, when it evaporates, the entropy that it turns into is actually higher than the entropy of the black hole was. Which is good, because entropy is supposed to go up. But it's much more dilute, right? It's spread across a huge volume of space time. So in principle, all that you made the black hole out of, the information that it took is still there we think in that information, but it's scattered to the four winds.
- LFLex Fridman
We just talked about the event horizon of a black hole. What's on the inside? What's at the center of it?
- SCSean Carroll
No one's been there. (laughs)
- 56:29 – 1:02:29
Dark energy
- SCSean Carroll
right after we discovered that the universe was accelerating. So in 1998, observations showed that not only is the universe expanding, but it's expanding faster and faster. So that's attributed to either Einstein's cosmological constant or some more complicated form of dark energy, some mysterious thing that fills the universe. And people were throwing around ideas about this dark energy stuff, what could it be and so forth. Most of the people throwing around these ideas were cosmologists, they work on cosmology, they think about the universe all at once. I, you know, since I like to talk to people in different areas, I was sort of more familiar than average with what a respectable working particle physicist would think about these things. And what I immediately thought was, you know, you guys are throwing around these theories, these theories are wildly unnatural, they're super finely tuned, like any particle physicist would just be embarrassed to be talking about this. But rather than just scoffing at them, I sat down and asked myself, "Okay, is there a respectable version? Is there a way to keep the particle physicists happy but also make the universe accelerate?" And I realized that there is some very specific set of models that is- that is relatively natural, and guess what? You can make a new experimental prediction on the basis of those, and so I did that, people w- were very happy about that.
- LFLex Fridman
What was the thing that would make physicists happy, that would make sense of this, uh, fragile thing that people call dark energy?
- SCSean Carroll
So the fact that dark energy pervades the whole universe and is slowly changing, that should immediately set off alarm bells, because particle physics is a story of length scales and time scales that are generally guess what? Small. (laughs) Right? Particles are small, they vibrate quickly, and you're telling me now, "I have a new field and its typical rate of change is once every billion years." Right? Like, that's just not natural. And indeed, you can formalize that and say, you know, look, even if you wrote down a particle that evolves slowly over billions of years, if you let it interact with other particles at all, that would make it inter- uh, move faster, its dynamics would be faster, its mass would be higher, et cetera, et cetera. So there's a whole story. Things need to be robust and they all talk to each other in quantum field theory. So how do you stop that from happening? And the answer is symmetry. You can impose a symmetry that protects your new field from talking to any other fields, okay? And this is good for two reasons. Number one, it can keep the dynamics slow. So if you just, you can't tell me why it's slow, you just made that up, but at least it can protect it from speeding up, because it's not talking to any other particles. And the other is, it makes it harder to detect. Um, naively, experiments looking for fifth forces or time changes of fundamental constants of nature like the charge of the electron, these experiments should have been able to detect these dark energy fields, and I was able to propose a way to stop that from happening.
- LFLex Fridman
The detection?
- SCSean Carroll
The detection, yeah. Be- because a- a symmetry could stop it from interacting with all these other fields and therefore it makes it harder to detect. And just by luck, I realized, because it was actually based on my first ever paper, there's one loophole. If you impose these symmetries, so you protect the dark energy field from interacting with any other fields, there's one interaction that is still allowed, that you can't rule out, and it is a very specific interaction between your dark energy field and photons, which are very common, and it has the following effect. As a photon travels through the dark energy, the photon has a polarization, up, down, left, right, whatever it happens to be, and as it travels through the dark energy, that photon will rotate its polarization. This is called birefringence. And you can kind of run the numbers and say, you know, you can't make a very precise prediction, so we're just making up this model, but if you want to roughly fit the data, you can predict how much polarization rotation there should be. Couple of degrees, okay? Not that much. So that's very hard to detect. People have been trying to do it. Right now, literally, we're on the edge of either being able to detect it or rule it out using the cosmic microwave background, and there is just, you know, truth in advertising, there is a claim on the market.... that it's been detected, that it's there. Uh, it's not very statistically significant. If I were to bet, I think it would probably go away. It's a very hard thing to observe. But maybe as you get better and better data, cleaner and cleaner analysis, it will persist and we will have directly detected the dark energy.
- LFLex Fridman
So if we just take this tangent of dark energy, (sighs) people will sometimes bring, bring up dark energy and dark matter as an example of why physicists have lost it, (laughs) lost their mind. We're just going to say that there is this field that permeates everything, it's unlike any other field, and it's invisible. Uh, and it, uh, helps us work out some of the math. Uh, how do you respond to that k- (laughs) those kinds of suggestions?
- SCSean Carroll
Well, two ways. One way is, those people would've had to say the same thing when we discovered the planet Neptune. (laughs)
- LFLex Fridman
Yeah.
- SCSean Carroll
'Cause it's exactly analogous, where we have a very good theory, in that case Newtonian gravity in the solar system. We made predictions. The predictions were slightly off for the motion of the outer planets. You found that you could explain that motion by positing something very simple, one more planet in a very, very particular place, and you went and looked for it, and there it was, right? It's, that was the first successful example of finding dark matter in the universe.
- LFLex Fridman
(laughs) The matter that we can't see.
- SCSean Carroll
Neptune was dark.
- LFLex Fridman
Yeah.
- 1:02:29 – 1:11:25
Dark matter
- LFLex Fridman
- SCSean Carroll
There's a difference between dark matter and dark energy, right? Dark matter, as far as we are hypothesizing it, um, is a particle of some sort. It's just a particle that interacts with us very weakly. So we know how much of it there is. We know more or less where it is. We know some of its properties. We don't know specifically what it is. But it, you know, it's, it's not anything fundamentally mysterious. It's a particle. Dark energy is a different story. So dark energy is indeed uniformly spread throughout space and has this very weird property that it doesn't seem to evolve, as far as we can tell. It's the same amount of energy in every cubic centimeter of space from moment to moment in time. That's why far and away the leading candidate for dark energy is Einstein's cosmological constant. The cosmological constant is strictly constant, 100% constant. The data say it had better be 98% constant or better, so 100% constant works, right? And it's also very robust. It's just there. It's not doing anything. It doesn't interact with any other particles. It makes perfect sense. Probably the dark energy is the cosmological constant. The dark matter, super important to emphasize here, you know, it was hypothesized at first in the '70s and '80s mostly to explain the rotation of galaxies. Today, the evidence for dark matter is both much better than it was in the 1980s and from different sources. It is mostly from observations of the cosmic background radiation or of large-scale structure. So we have multiple independent lines of evidence, also gravitational lensing and things like that, many, many pieces of evidence that say that dark matter is there. Um, a- and, and also that say that the effects of dark matter are different than if we modify gravity. S- so that was my first answer to your question is w- dark matter i- we have a lot of evidence for, but the other one is, of course, we would love it if it weren't dark matter. (laughs) Our vested interest is 100% aligned with it being something more cool and interesting than dark matter because dark matter's just a particle. That's the most boring thing in the world.
- LFLex Fridman
And it's, uh, non-uniformly distributed through space, dark matter?
- SCSean Carroll
Absolutely, yeah.
- LFLex Fridman
And so this-
- SCSean Carroll
You can even see maps of it that we've constructed from gravitational lensing.
- LFLex Fridman
So verifiable sort of clumps-
- SCSean Carroll
Yeah.
- LFLex Fridman
... of dark matter in the galaxy that explains stuff.
- SCSean Carroll
Bigger than the galaxy, sadly. Like, we think that in the galaxy, dark matter is lumpy, but it's, it's just m- it's weaker. Its effects are weaker. But over the scale of large-scale structure and clusters of galaxies and things like that, yes, we can show you where the dark matter is.
- LFLex Fridman
Could there be a super cool explanation for dark matter that would be interesting as opposed to just another particle that, that sits there in clumps?
- SCSean Carroll
The super cool explanation would be modifying gravity rather than inventing a new particle.
- LFLex Fridman
Oh.
- SCSean Carroll
Sadly, that doesn't really work. We've tried. I've tried. Uh, that's my third paper that was very successful. I tried to unify dark matter and dark energy together. That was my idea. Th- that was my aspiration, not even an idea. I tried to do it. It failed even before we wrote the paper.
- LFLex Fridman
(laughs)
- SCSean Carroll
I realized that my idea did not help. It helps... It could possibly explain away the dark energy, but it would not explain away the dark matter. And so I thought it was not that interesting actually, and then two different collaborators of mine said, "Has anyone thought of this idea?" Like, they had thought of exactly the same idea completely independently of me. I said, "Well, if three different people found the same idea, maybe it is interesting." (laughs) And so we wrote the paper. And yeah, it was very interesting. People are very interested in it.
- LFLex Fridman
Can you describe this, th- this paper a little bit? Like, it just... It's, it's fascinating how much of a thing there is, dark energy and dark matter-
- SCSean Carroll
Mm-hmm.
- LFLex Fridman
... and we don't quite understand it. So what, what was your dive into exploring how to unify the two?
- SCSean Carroll
So here is what we know about dark matter and dark energy. Um, they become important in regimes where gravity is very, very, very weak. That's kind of the opposite from what you would expect if you actually were modifying gravity. Like, there's a rule of thumb in quantum field theory, et cetera, that new effects show up when the effects are strong, right? We, uh, we understand weak fields. We don't understand strong fields. But okay, maybe this is different, right? So what do I mean by when gravity is weak? The dark energy shows up late in the history of the universe. Early in the history of the universe, the dark energy is irrelevant.... but remember, the density of dark energy stays constant. The density of matter and radiation go down. So at early times, the dark energy was completely irrelevant compared to matter and radiation. At late times, it becomes important. That's also when the universe is dilute and gravity is relatively weak. Now think about galaxies, okay? A galaxy is more dense in the middle, less dense on the outside, and there is a phenomenological fact about galaxies, that in the interior of galaxies, you don't need dark matter. That's not so surprising 'cause the density of stars and gas is very high there, and the dark matter is just subdominant. But then, there's generally a, uh, a radius inside of which you don't need dark matter to fit the data, outside of which you do need dark matter to fit the data. So that's again when gravity is weak, right? So I asked myself, um, of course we know in field theory new effects should show up when fields are strong, not weak, but let's throw that out of the window. Can I write down a theory where gravity alters when it is weak?
- LFLex Fridman
Hm.
- SCSean Carroll
And we've already said what gravity is. What is gravity? It's the curvature of space-time. So there are mathematical quantities that measure the curvature of space-time. And generally, you would say, like, I have an understanding, Einstein's equation, which I explained to the readers in the book, um, relates the curvature of space-time to matter and energy. The more matter and energy, the more curvature. So I'm saying, what if you add a new term in there that says the less matter and energy, the more curvature? No reason to do that-
- LFLex Fridman
Mm-hmm.
- SCSean Carroll
... except to fit the data, right? So I tried to unify the need for dark matter and the need for dark energy.
- LFLex Fridman
That would be really cool if that was the case, like-
- SCSean Carroll
Super cool, right? It'd be the best. It'd be great.
- LFLex Fridman
But it-
- SCSean Carroll
It didn't work.
- LFLex Fridman
(laughs) But it'd be really interesting if gravity did something funky when, uh, when, when there's not much of it, like the, almost like at the edges of it, it gets-
- SCSean Carroll
Yeah.
- 1:11:25 – 1:32:47
Quantum mechanics
- SCSean Carroll
- LFLex Fridman
You wrote the book Something Deeply Hidden: On the Mysteries of Quantum Mechanics and a new book coming out soon, part of that Biggest Ideas in the Universe series we mentioned called Quanta and Fields. So that's focusing on quantum mechanics. Big question first, biggest ideas in the universe.
- SCSean Carroll
(laughs)
- LFLex Fridman
Uh, what to you is most beautiful or perhaps most mysterious about quantum mechanics?
- SCSean Carroll
Quantum mechanics is a harder one. You know, I wrote a textbook on general relativity, and I started it by saying, "General relativity is the most beautiful physical theory ever invented." And I, I will stand by that. It is less fundamental than quantum mechanics. But quantum mechanics is a little more mysterious. So we, it's, it's a little bit kludgy right now. You know, if you think about how we teach quantum mechanics to our students, the Copenhagen interpretation, it's a god-awful mess. Like, no one's gonna accuse that of being very beautiful. I'm a fan of the many worlds interpretation of quantum mechanics, and that is very beautiful in the sense that fewer ingredients, just one equation, and it could cover everything in the world. Um, it depends what you mean by beauty, but I think that the answer to your question is, quantum mechanics can start with extraordinarily austere, tiny ingredients, and in principle, lead to the world. (laughs) Right? Uh, that boggles my mind. It's, uh, much more comprehensive. General relativity is about gravity, and that's great. Quantum mechanics is about everything and seems to be up to the task. And so I don't know, what, is that beauty or not? But it's certainly impressive.
- LFLex Fridman
So both for the theory, the predictive power of the theory, and the fact that the theory describes tiny things creating everything we see around us.
- SCSean Carroll
It's-... a monist theory. In classical mechanics, I have a particle here, a particle there. I describe them separately. I can tell you what this particle is doing, what that particle is doing. In quantum mechanics, we have entanglement, right, as Einstein pointed out to us in 1935. And what that means is, there is a single state for these two particles. There's not one state for this particle and one state for the other particle. And indeed, there's a single state for the whole universe called the wave function of the universe, if you want to call it that, and it obeys one equation. And it is our job then to sort of chop it up, to carve it up to figure out how to get tables and chairs and things like that out of it.
- LFLex Fridman
You mentioned the many-worlds interpretation, and it is in fact beautiful, but, uh, it's one of your more controversial things you stand behind.
- SCSean Carroll
Yeah.
- LFLex Fridman
You've probably gotten a bunch of flak for it. (laughs)
- SCSean Carroll
I'm a big boy. I can take it. (laughs)
- LFLex Fridman
Well, can you first explain it and then maybe speak to the flak you may have gotten?
- SCSean Carroll
Sure. You know, the classic experiment to explain quantum mechanics to people is called the Stern-Gerlach experiment. You're measuring the spin of a particle, okay? And in quantum mechanics, the spin is, you know, it's just a spin. It's the rate at which something is rotating around in a, in a very down to earth sense, the difference being is that it's quantized. So for something like a single electron or a single neutron, it's either spinning clockwise or counterclockwise. Those- those are the only two, let's put it this way, those are the only two measurement outcomes you will ever get. There's no, "It's spinning faster or slower." It's either spinning one direction or the other. That's it. Two choices, okay? According to the rules of quantum mechanics, I can set up an electron, let's say, in a state where it is neither purely clockwise or counterclockwise but a superposition of both, and that's not just because we don't know the answer. It's because it truly is both until we measure it, and then when we measure it, we see one or the other. So this is the fundamental mystery of quantum mechanics is that how we describe the system when we're not looking at it is different from what we see when we look at it. So what we teach our students in the Copenhagen way of thinking is that the act of measuring the spin of the electron causes a radical change in the physical state. It spontaneously collapses from being a superposition of clockwise and counterclockwise to being one or the other, and you can tell me the probability that that happens, but that's all you can tell me. And I can't be very specific about when it happens, what caused it to happen, why it's happening, none of that. That's all called the measurement problem of quantum mechanics. So many-worlds just says, "Look, I just told you a minute ago that there's only one wave function for the whole universe." (laughs) And that means that you can't take too seriously just describing the electron. You have to include everything else in the universe. In particular, you clearly have to interact with the electron in order to measure it. So whatever is interacting with the electron should be included in the wave function that you're describing. And look, maybe it's just you. Maybe your eyeballs are about to perceive it, but okay, I'm gonna include you in the wave function. And if you do that, let's be, you know, since you have a very sophisticated listenership, I'll be a little bit more careful than average. What does it mean to measure the spin of the electron? We don't need to go into details, but we want the following thing to be true. If the electron were in a state that was 100% spinning clockwise, then we want the measurement to tell us it was spinning clockwise. (laughs) We want your brain to go, "Yes, the electron was spinning clockwise," right? Likewise, if it was 100% counterclockwise, we want to- to see that, to measure that. The rules of quantum mechanics, the Schrodinger equation of quantum mechanics is 100% clear that if you want to measure it clockwise when it's clockwise and measure it counterclockwise when it's counterclockwise, then when it starts out in a superposition, what will happen is that you and the electron will entangle with each other. And by that, I mean that the state of the universe evolves into part saying, "The electron was spinning clockwise, and I saw it clockwise," and part of the state is it's in a superposition with the part that says, "The electron was spinning counterclockwise, and I saw it counterclockwise." Everyone agrees with this. Entirely uncontroversial. Straightforward consequence of the Schrodinger equation. And then Niels Bohr would say, "And then part of that wave function disappears." (laughs) And we're in the other part, and you can't predict which part it will be, only the probability. Hugh Everett, who was a graduate student in the 1950s who was thinking about this says, "I have a better idea. Part of the wave function does not magically disappear. It stays there." The reason why that idea, Everett's idea, that the whole wave function always sticks around and just obeys the Schrodinger equation was not thought of years before is because naively, you look at it, and you go, "Okay, this is predicting that I will be in a superposition, that I will be in a superposition of having seen the electron be clockwise and- and having seen it be counterclockwise." No experimenter has ever felt like they were in a superposition. You always see an outcome, okay? Everett's move, which was kind of genius, was to say, "The problem is not the Schrodinger equation. The problem is you have misidentified yourself in the Schrodinger equation. You have said, 'Oh, look, there's a person who saw counterclockwise. There's a person who's- saw clockwise. I should be that superposition of both.'" And Everett says, "No, no, no. You're not, because the part of the wave function in which the spin was clockwise, once that exists, it is completely unaffected."... by the part of the wave function that sends, says the spin was counterclockwise. They are apart from each other. They are un-interacting. They have no influence. What happens in one part has no influence in the other part. So Everett says the simple resolution is to identify yourself as either the one who saw spin clockwise or the one who saw spin counterclockwise. There are now two people once you've done that experiment. The Schrodinger equation doesn't have to be messed with. All you have to do is locate yourself correctly in the wave function. That's Many Worlds.
- LFLex Fridman
The number of worlds is-
- SCSean Carroll
Very big.
- LFLex Fridman
... very, very, very big. Where do those worlds fit?
- SCSean Carroll
So-
- LFLex Fridman
Where do they go?
- SCSean Carroll
... the short answer is, the worlds don't exist in space. Space exists separately in each world. So, I mean, there's a technical answer to your question, which is Hilbert space, the space of all possible quantum mechanical states. But physically, you know, we, we want to put these worlds somewhere. That's just a wrong intuition that we have. There is no such thing as the physical spatial location of the worlds, 'cause space is inside the worlds.
- LFLex Fridman
One of the properties of this interpretation is that you can't travel from one world to the other.
- SCSean Carroll
That's right.
- LFLex Fridman
Which kind of makes you feel that (laughs) they're existing separately.
- SCSean Carroll
They are existing separately and simultaneously.
- LFLex Fridman
A- and simultaneously.
- SCSean Carroll
Without locations in space.
- LFLex Fridman
Without locations in space. How is it possible to visualize them existing without a location in space?
- SCSean Carroll
The real answer to that, the honest answer is, the equations predict it.
- LFLex Fridman
Yeah. Yeah.
- SCSean Carroll
If you can't visualize it, so much worse for you, but the equations are crystal clear about what they're predicting.
- LFLex Fridman
Is there a way to get to the closer to understanding and visualizing the weirdness of the implications of this?
Episode duration: 2:35:23
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