Transcription
If we return to black holes, uh, and talk about the the holographic principle more broadly, you have a recent paper on the topic. You've been thinking about the topic in terms of a rigorous research perspective and just as a popular book writer. So, what is the holographic principle?
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 going to put information in it, and I don't tell you how I'm going to put the information in, but I ask, how does the information I can put in scale with the size of the box? 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 Q-bits 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 and Leonard Susskind. Super famous, um, physicist. Leonard Susskind was on my podcast. Didn't give a great, uh, talk. He's very, very good at explaining these things.
Mcap podcast. That's right. Yes. You don't just have physicists on. I, I don't. I love Mcap. Oh, thank you very much. Curiosity-driven, yeah. Ideas, exploration of ideas from SM people. Yeah. But anyway, what I was trying to get at was Susskind and also at T. 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+1 dimensions of space-time with gravity. And the idea is that this N-dimensional theory is, you know, casting a hologram into the N+1 dimensional universe to make it look like it has gravity. And that's holography with a vengeance. And that's, that's an enormous source of interest for theoretical physicists these days.
How should we picture what impact that has, uh, the fact that you can 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? Yeah, I mean, it's a good question. Um, 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. 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 are 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.
So you can just write off that weird stuff happens in a black hole, like to do better, but we're trying. I mean, that's why we have an 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? Because it's flexible, and quantum mechanics 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. But 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.
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. 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. 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?
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.
We just talked about the event horizon of a black hole. What's on the inside? What's at the center of it? No one's been there. So this is a theoretical prediction. But, you know, I, I'll say one super crucial feature of the black holes that we know and love, that you know, the kind that Schwarzschild first invented. There's a singularity, but it's not at the middle of the black hole. Remember, space and time are parts of two different, two, uh, parts of one unified space-time. The location of the singularity in the black hole is not the middle of space, but our future. It is a moment of time. It is like a big crunch. You know, the Big Bang was an expansion from a singularity in the past. A big crunch probably doesn't exist, but if it did, it would be a collapse to a singularity in the future. That's what the interiors of black holes are like. You can be fine in the interior, but things are becoming more and more crowded. Space-time is becoming more and more warped, and eventually you hit a limit, and that's the singularity in your future.
I wonder what time is like on the inside of a black hole. Time always ticks by at one second per second. That's all it can ever do. Time can tick by differently for different people. And so you have things like the twin paradox, where two people, initially, are the same age. One goes off near the speed of light and comes back. Now they're not. You can even work out that the one who goes out, out and comes back will be younger because they did not take the shortest distance path. But locally, as far as you and your wristwatch are concerned, time is not funny. Time, the, your, your neurological signals in your brain and your heartbeat and your wristwatch, whatever is happening to them is happening to all of them at the same time. So time always seems to be ticking along at the same rate.
Well, if you fall into a black hole, and then I'm an observer just watching it, and then you come out once it evaporates a million years later, I guess you'd be exactly the same age. Have you aged at all? You would be converted into photons. You would not be you anymore, right? So it's, it's not at all possible that information is preserved exactly as it went in. It depends on what you mean by preserved. Um, it's there in the microscopic configuration of the universe. It's exactly as if I took a regular book made of paper and I burned it. The laws of physics say that all the information in the book is still there in the heat and light and ashes. You're never going to get it. It's a matter of practice, but in principle, it's still there.
But what about the age of things from the observer perspective? From outside the black hole? From outside the black hole, it doesn't matter because they're inside the black hole. No. So, but is there, okay, there's no way to escape the black hole except to let it evaporate. To let it evaporate. But also, you know, by the way, just in relativity, special relativity, forget about general relativity. It's enormously tempting to say, okay, here's what's happening to me right now. I want to know what's happening far away right now. 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. So you're tempted to say, well, how fast is their clock ticking or how old are they now? Not allowed to say that according to relativity, because space and time are treated the same. And so it doesn't even make sense.
That's what, what happens to time in the holographic principle? As far as we know, nothing dramatic happens. Um, we're not anywhere close to being confident that we know what's going on here yet. So there are good unanswered questions about whether time is fundamental, whether time is emergent, whether it has something to do with quantum entanglement, whether time really exists at all. Uh, different theories, different proponents of different things. Um, but there's nothing specifically about holography that would make us change our opinions about time, whatever they happen to be. But holography is fundamentally about, it's, it's a question of space. It really is. Yeah.
Okay, so time is just a, like an, time just goes along for the ride as far as we know. Yeah. So all the questions about time is just almost like separate questions, whether it's emergent and all that kind of thing. Yeah. I mean, that might be a reflection of our ignorance right now. But yes, if we figure out a lot, you know, millions of years from now, about black holes, how surprised would you be if they travel back in time and told you everything you want to know about black holes? How much do you think there is still to know? And how mind-blowing would it be?
It does depend on what they would say, you know. I think that there are colleagues of mine who think that we're pretty close to figuring out how information gets out of black holes, how to gravity things like that. I'm more skeptical that we are pretty close. I think that there's room for a bunch of surprises to come. So in that sense, I suspect I would be surprised. The biggest and most interesting surprise to me would be if quantum mechanics itself were somehow superseded by something better. As far as I know, there's no empirical evidence-based reason to think that quantum mechanics is not 100% correct. But might not be, that's always possible. So, and there are again, respectable friends of mine who speculate about it. So that's something I would, that's the first thing I would want to know.
Oh, so like the black hole would be the most clear illustration? Yeah. That's, that would show if there's something. It would, it would show up there. I mean, maybe the point is that black holes are mysterious for various reasons. So yeah, if our best theory of the universe is wrong, that might help explain why.
But do you think it's possible we'll find something interesting like black holes sometimes create new universes, or black holes are a kind of portal through space-time to another place, or something like this? Like, and then our whole conception of what is the fabric of space-time changes completely, because black holes, it's like a Swiss cheese type of situation. Yeah.
You know, um, that would be less surprising to me because I've already written papers about that. We don't have, again, strong reason to think that the interior of a black hole leads to another universe, but it is possible. And it's also very possible that that's true for some black holes and not others. Um, this is stuff we don't know. It's easy to ask questions we don't know the answer to. The problem is the questions that are easy to ask that we don't know the answer to are super hard to answer because these objects are very difficult to test and to explore. For us, the regimes are just very far away. So either literally far away in space, but also in energy or mass or time, or whatever.
You've, uh, published a paper on the holographic principle, or that involves the holographic principle. What can you explain the details of that? Yeah, you know, I'm always interested in, since my first published paper, taking these wild speculative ideas and trying to test them against data. And the problem is, when you're dealing with wild speculative ideas, they're usually not well-defined enough to make a prediction. Right? Like it's kind of a, I know what's going to happen in some cases, I don't know what's going to happen in other cases.
So we did the following thing. As I've already mentioned, um, the holographic principle, which is meant to reflect the information contained in black holes, seems to be telling us that information, there's less information, less stuff that can go on than you might naively expect. So let's upgrade "naively expect" to predict using quantum field theory. Quantum field theory is our best theory of fundamental physics right now. Unlike this holographic black hole stuff, quantum field theory is entirely local. In every point of space, something can go on, and then you add up all the different points in space. Okay, not holographic at all. So there's a mismatch between the expectation for what is happening even in empty space in quantum field theory versus what the holographic principle would predict. How do you reconcile these two things?
So there's one way of doing it, uh, that had been suggested previously, which is to say that in the quantum field theory way of talking, it implies there's a whole bunch more states, a whole bunch more ways the system could be than there really are. And the, and just, I'll, I'll do a little bit of math just because there might be some people in the audience who like the math. If I draw two axes on a two-dimensional geometry, like the surface of the table, right? You know that the whole point of it being two-dimensional is I can draw two vectors that are perpendicular to each other. I can't draw three vectors that are all perpendicular to each other, right? They need to overlap a little bit. That's true for any number of dimensions. But I can ask, okay, how much do they have to overlap? If I try to put more vectors into a vector space than the dimensionality of the vector space, can I make them almost perpendicular to each other? And the mathematical answer is, as the number of dimensions gets very, very large, you can fit a huge extra number of vectors in that are almost perpendicular to each other.
So in this case, what we're suggesting is the number of things that can happen in a region of space is correctly described by holography. It is somewhat overcounted by quantum field theory, but that's because the quantum field theory states are not exactly perpendicular to each other. I should have mentioned that in quantum mechanics, states are given by vectors in some huge dimensional vector space, very, very, very, very large dimensional vector space. So maybe the quantum field theory states are not quite perpendicular to each other. If that is true, that's a speculation already. But if that's true, how would you know? What is the experimental deviation?
And it would have been completely respectable if we had gone through and made some guesses and found that there is no noticeable experimental difference, because again, these things are in regimes very, very far away. We stuck our necks out. We made some very, very specific guesses as to how this weird overlap of states would show up in the equations of motion for particles like neutrinos. And then we made predictions on how the neutrinos would behave on the basis of those wild guesses. And then we compared them with data. And what we found is, we're pretty close, but haven't yet reached the detectability of the effect that we are predicting.
In other words, well, basically, one way of saying what we predict is if a new neutrino, and there's reasons why it's neutrinos, we can go into if you want, but it's not that interesting. If a neutrino comes to us from across the universe from some galaxy very, very far away, there is a probability as it's traveling that it will dissolve into other neutrinos because they're not really perpendicular to each other as vectors as they would ordinarily be in quantum field theory. And that means that if you look at neutrinos coming from far enough away with high enough energies, they should disappear. Like if you see, if you see a whole bunch of nearby neutrinos, but then further away, you should see fewer.
And there is an experiment called IceCube, which is this amazing testament to the ingenuity of human beings, where they go to Antarctica and they drill holes and they put photo detectors on a string, a mile deep in these holes. And they basically use all of the ice in a cube, you know, I don't know whether it's a mile or not, but it's like a kilometer or something like that, some big region. That much ice is their detector. And they're looking for flashes when a cosmic ray or neutrino or whatever hits an ice molecule, water molecule in the ice, flashes in the ice. They're looking for flashes in.
But isn't there some crazy, I mean, what do the detectors of that look like? It, it's a bunch of strings, many, many, many strings with 360-degree photo detectors. Yeah. And you will. That's really cool. It's extremely cool. And they've, um, done amazing work and they find neutrinos. They're looking for neutrinos. Yeah. So the whole point is, most cosmic rays are protons, because why? Because protons exist and they're massive enough that you can accelerate them to very high energies. So high-energy cosmic rays tend to be protons. They also tend to hit the Earth's atmosphere and decay into other particles. So neutrinos, on the other hand, punch right through, at least usually, right? To a great extent. So not just Antarctica, but the whole Earth. Occasionally a neutrino will interact with a particle here on Earth. And his neutrino is going through your body all the time from the Sun, from the universe, etc. And so if you're patient enough and you have a big enough part of the Antarctic ice sheet to look at, it's the nice thing about ice is it's transparent. So you've built yourself, nature has built you a neutrino detector.
So IceCube does. Why, why ice? So is it, is it just because the low noise and you get to watch this thing and it's, it's much more dense than air, but it's transparent. So yeah, much more dense, so higher probability. And then it's transparency. And then it's also in the middle of nowhere, so you can. That's all you need. There's not that much ice, right? Yeah. So more ice in Antarctica than anywhere else, right?
So anyway, you can go and you can get a plot from the IceCube experiment, how many neutrinos there are that they've detected with very high energies. And we predict in our weird little holographic guessing game that there should be a cut-off. You should see neutrinos as you get to higher and higher energies, and then they should disappear. If you look at the data, their data gives out exactly where our cut-off is. That doesn't mean that our cut-off is right. It means they lose the ability to do the experiment exactly where we predict the cut-off should be. Oh boy.
Okay, um, but why is there a limit? Oh, just because there are fewer, fewer high-energy neutrinos. So there's a spectrum and it goes down. But that, what we're plotting here is number of neutrino versus energy. It's fading away. And they just get very, very few. And you need the high-energy neutrinos for the, your effect is a little bit bigger for higher energies. Yeah. And that, that effect has to do with this almost perpendicular thing. And let me just mention the name of Oliver Friedrich, who was a postdoc who led this. He deserves the credit for doing this. I was a, a co-author and a collaborator. I did some work, but he really gets the lion's share. Thank you, Oliver. Thank you for pushing this wild science forward.