What’s the idea behind the holographic principle? What does it have to do with black holes and the early universe? Does this…mean something? I discuss these questions and more in today’s Ask a Spaceman!
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Hosted by Paul M. Sutter, astrophysicist at The Ohio State University, Chief Scientist at COSI Science Center, and the one and only Agent to the Stars (http://www.pmsutter.com).
EPISODE TRANSCRIPTION (AUTO-GENERATED)
You know what time it is. It's time for Ask a Spaceman. I'm your host, Paul Sutter. You've got questions and I've got answers. You know how this show works, but let's compress it one more time. You go online to Twitter or Facebook. Use the hashtag Ask a Spaceman. You can also follow me directly on Twitter and Facebook. My name is at Paul Matt Sutter. You can also visit the website, AskASpaceman.com. You can also email AskASpaceman at gmail.com. You can also go to YouTube.com slash Paul M. Sutter. And I'm out of breath. So many ways to ask questions. Get those questions to me. Keep in common. I love all the questions because that means I can keep doing this show, answering them. It is so much fun. You have no idea. We have a simple goal with this show, complete knowledge of time and space. And on the road to complete knowledge of time and space, we have today's questions. We have Liberty on Twitter asking, how about making a podcast on the hologram theory next time? Well, it won't be next time.
I don't know when you posted this. I'm pretty sure it was a long time ago. We also have Andrew B. on email asking, what is the holographic principle? Very, very cool set of questions. I want you to take a bite of something. I don't care if you have any food around you. If there's someone sitting next to you on the bus or the train or the car or whatever, just reach over and take a bite of whatever they're eating. When you take a bite of something, your mass grows. When your mass grows, your volume grows. When your volume grows, your surface area grows. All in proportion to each other. Imagine eating the smallest possible morsel of food. One atom. You are going to pop into your mouth a single atom and swallow it. Your volume will grow by the volume of that one atom. Your surface area will also grow, but not as quickly. You don't get the entire surface area of that atom added to the surface area of your body, only a small portion of that. But you're not a black hole, are you? I hope not.
If you were a black hole, if you were to eat something, your mass, your volume, your surface area would all grow, but there's a crucial difference. When a black hole eats something, its surface area grows faster than you might expect. Let's say a black hole consumes one bit of information. What does information mean? Why am I using that word? Well, all atoms, all particles, all whatever, carry with them certain facts. Their position, their velocity, their spin state, their mass, their charge, et cetera, et cetera, et cetera. You can actually load up a lot of information in one particle. So when you consume an atom, you're consuming a tremendous amount of information. If you consume a single particle, you're still consuming a lot of information. What's the smallest amount of information a black hole can consume? Well, how about one photon, one bit of light with wavelength equal to the width of the black hole? Let's define that to be a single bit of information. That's the smallest thing that a black hole can consume.
And something interesting happens. When a black hole eats one bit of information, its surface area grows by the plank length squared. Planck length? Lots of jargon here. You know what the Planck constant is, right? It's the quantum constant. It relates how much energy a photon of a given wavelength has. It kind of sets the scale for the quantum mechanical world. It is the constant, named after the scientist Max Planck, who figured it out, that led us all into the entire quantum mechanical world. That's a whole other show, so feel free to ask about Planck's constant and its meaning. You can combine Planck's constant, which is a particular number, with other constants like the speed of light, like Newton's gravitational constant, like the Boltzmann constant, like the permittivity of freezes. There's lots of constants floating around in the universe, all right? You can combine them to get other useful numbers, and these useful numbers might have length, or volume, or mass, and they give us some guideposts about where the quantum mechanical party starts getting interesting.
The Planck length is one such number. It's equal to 1.6 times 10 to the minus 35 meters, which is small, I guess. I don't really have any useful metaphors here for you. It's just an incredibly tiny number. The Planck length is very important for our understanding, especially of quantum gravity. When you get to small scales, say subatomic scales, that's when quantum mechanics takes over from classical mechanics. And if you get to really, really, really small scales, like around the Planck length, That's where our concepts of space-time start to break down. That's where quantum gravity starts to become important, and we don't really have a theory of quantum gravity. So things are a bit hazy at scales below the Planck length, below 10 to the minus 35 meters. that's very, very small compared to things like the proton or an atom. So we can do lots of quantum mechanics at these scales without having to worry about what's going on at smaller stuff, but that is the signpost. So if you square that, if you draw a little box, a little square, that's one Planck length on one side and another Planck length on another side, that's like a Planck area.
It's like a fundamental quantum unit of area. And isn't it interesting? then when a black hole eats one bit of information, its surface area grows by this very precise amount. Its volume doesn't grow by the plank length cubed like you would expect. When black holes consume information, their area grows in a very specific way. So the information going into a black hole is related directly to its surface, not its volume. Hmm. It suggests it suggests I'm using that strong word suggests that the action of a black hole happens on its surface, not in its interior. It's like instead of eating things and you consuming them and then going inside your body, it's like you just tape them to your stomach and call it a day. That's a very, very different picture of eating than we're used to. It's not about volume growing. The volume does grow, but not in the way you expect. It's more about the surface area growing. And this is the core of what we call the holographic principle. The holographic principle, or a hologram, is when you can represent all the physics, all the information, all the guts of a full three-dimensional object on just its two-dimensional surface.
Imagine. If by looking at someone's skin, you could learn everything you needed to know about their organs, their blood type, what they had for breakfast, what they're thinking right now. It would be really, really, really gross. And so I'm very thankful that is not the world we live in. But imagine if you could just look at the two-dimensional surface of someone's skin, you could capture all the three-dimensional information. Just how weird is that if all the information contained in a living, breathing, three-dimensional person is mapped onto the two-dimensional surface of their skin? Another example is holograms. Usually when you take a picture, which is two dimensions, of a particular scene, which is three dimensions, you lose some information. If I were to take a picture of you and then look at that picture later, I wouldn't know what the back of your head looks like. Because I didn't take a picture of that. I lost information from that mapping from three dimensions to two dimensions.
But holograms are designed to preserve that info. A two-dimensional image that lets you see all three dimensions. That is the definition of a hologram. In general, and mathematics likes to be general, anytime you can preserve information in a lower-dimensional context... For example, from going from three dimensions to two dimensions, which is hopefully obviously important for physics, that is a hologram. That is the holographic principle at work. This technique of preserving three-dimensional information in a two-dimensional context might apply to black holes. We haven't fully worked out all the consequences. It might also solve something else we know as the black hole information paradox, but that's another episode, so feel free to ask about that. So that's nice. Whatever. Black hole might be completely described by its surface. What does that have to do with anything that we might care about? Well, black holes are regions of intense gravity. Strong enough... that we have to care about quantum effects and that's why we don't fully understand black holes because they live at the intersection between quantum mechanics and gravity.
We don't have a quantum theory of gravity so we can't fully describe black holes yet. Lots of interesting stuff happening on the surface of black hole at that event horizon. And a lot of interesting stuff happening at the center, the region we call the singularity. The point of infinite density that isn't really infinite, but the only tool we have of understanding the center of a black hole is general relativity. General relativity says it's infinite, but we know that's wrong. Singularity doesn't really exist, must be replaced by something else once we figure all that junk out. Black holes contain singularities. Where else does a singularity occur? Bingo, the Big Bang. The earliest, earliest, earliest moments of the universe was hot and dense and exotic. At some point, the universe was so small, so hot, so dense that quantum gravity took over. And we don't fully understand that earliest moments because we, like I said, we don't have a quantum theory of gravity. It's hard to make progress in understanding the very early, less than a fraction of a second universe.
So what can we do? Can holograms save us? It's now time to introduce the most jumbled, nonsensical six letters that you're likely to encounter in your entire life. ADSCFT. ADSCFT. It's not a labor union. It's not a secret spy plane. It's not word scramble. It's, and I'll try to say this with all due respect, the only interesting thing to come out of strength. String Theory is another episode, so of course, ask. Generally, I'm not the biggest fan of String Theory, and I'd love to get into it in more detail, but... The main reason is it's beautiful, it's elegant, it's mathematical, it's blah, blah, blah, blah, blah. It also doesn't do anything. It's a blueprint for a hammer, not a hammer itself. Or it's a sketch of what might be a blueprint for a hammer, not the hammer itself. So I can't use it to go around explaining the universe. It doesn't have any utility. It can be the most elegant and beautiful mathematical structure known in the history of civilization. But if I can't use it to explain real observable phenomena in the universe, it's just that.
And I love mathematicians. No disparaging mathematicians here. But mathematicians masquerading as physicists is where I start to draw the line. But again, that's another episode. I don't want to get myself worked up too much about that. The mathematics of string theory is hard, and nobody can make any real progress in solving it. That's the key issue. We've been trying for decades, and we can't make progress in solving these problems that crop up in string theory, except maybe through ADS-CFT. ADS-CFT. Burn it into your brain. It's an application of the holographic principle, and it stands for, are you ready for this? ADS stands for anti-de Sitter. CFT stands for conformal field theory. This is gonna take a while to unpack. First, I'll do the CFT first, conformal field theory. Field theories are our language for quantum mechanics. Quantum field theories is how we describe the electromagnetic force, the weak nuclear force, the strong nuclear force, in a properly quantum mechanical way. I've done episodes describing field theories in the past.
I encourage you to look those up, pull them up, where I go into all the glorious and gory details of field theories. They're just a language for describing physics that we know and love. Conformal ones are... I don't know. They're special. They behave nicely. The mathematics are especially able amenable to easy calculations. Let's put it that way. Anti-de Sitter is a particular solution to general relativity. Named after one of the early researchers in general relativity, De Sitter. In this, he described one particular solution as this is the opposite of that solution, hence Anti-de Sitter. Anti-de Sitter, a particular solution to general relativity, it describes an empty universe. completely devoid of anything, with negative spatial curvature. Negative spatial curvature means that parallel lines eventually separate on very, very large scales. Empty universe, negative curvature, anti-de Sitter solution. It's a particular space time. In the late 1990s, it was discovered that there are some interesting connections between anti-de Sitter space times and conformal field theories.
Of all things, who would have guessed? There's a correspondence. There's a connection. Specifically. Anti-de Sitter spacetimes, like any spacetime, has a surface. It has a boundary. And if you're trying to solve a super hard problem inside that boundary, inside the volume of the space described by anti-de Sitter mathematics, I don't know, maybe you're trying to solve quantum gravity with string theory. Just tossing that one out there. It turns out you can map all of the information contained in the volume of an antedecider spacetime onto its surface. So you can make that holographic projection from three dimensions to two. You map everything out onto surface. You take everything contained in that universe, splat it out onto its boundary, and just look at the boundary itself. And the nature of the problem changes. That super hard problem that you're trying to solve inside The volume of that space-time, like quantum gravity with string theory, transforms. It changes character. It changes nature into a conformal field theory on the surface.
We don't have the tools. We don't have the expertise to solve string theory problems. But we do know how to solve conformal field theory problems. We do it all the time in quantum mechanics. It's our bread and butter. We've been doing it for decades. So by mapping, by making this holographic mapping from three dimensions to two in this very special space-time, we can transform the nature of our problems from unsolvable to kind of solvable. I know this topic is a jargon minefield. It's a one-way trip to jargon town, and you're going to go. So why don't we take a little break and contribute to Patreon. Patreon.com slash PMSutter is how you support this show. I can't emphasize it enough. It is your incredibly generous contributions that keep this show alive. Patreon.com slash PMSutter. As little as a dollar a month is all it takes to keep this show going. And I can't thank you enough for your extreme generosity. Now that you've gone to Patreon.com slash PMSutter, you've made your monthly contribution.
Now you can come back to the show. ADSCFT, Anti-Desider Conformal Field Theory, is a pretty big deal. It's also incredibly technical, as you might guess, because, like, everything in string theory is incredibly technical. It hasn't. I need to emphasize, it hasn't solved string theory. It hasn't solved quantum gravity. It's maybe, maybe an important clue that there might be routes to a solution using this technique someday, maybe. Perhaps. Kind of. Sort of. If we're lucky. Here's the upshot. Here's the super high-level summary. There are some problems that are so hard in three dimensions that we basically don't know how to solve them. We don't even know if solutions exist. We don't have the right tools. So instead, we'll map everything to a two-dimensional surface. The problem changes character. to a form where we do have the tools so we can solve the problem there on the boundary, on the two-dimensional surface, then translate the solution back into the three-dimensional world to make progress.
It might work with gravity. Solving quantum gravity in three dimensions is hard and possibly impossible. So instead, let's map the problem to two dimensions. In two dimensions, gravity disappears. The gravity that we're trying to solve completely disappears. It's replaced with a bunch of field theories. So solve the problem there where gravity doesn't even exist on the boundary. The mathematics have changed so much that gravity just drops out. It's replaced with a bunch of field theories where we know that we have the tools to solve. So solve it there, map the solution back to three dimensions, and voila! You have a route to understand quantum gravity without ever solving quantum gravity. It's a shortcut. It's a dirty secret to getting around this horrible, horrible problem. While this works and has been shown to work in a few limited cases, we don't yet have a working correspondence to our real-life universe. Our universe, for instance, is not described by an anti-de Sitter spacetime.
For one, it's not empty. It's full of matter. It's full of radiation. It's full of dark energy. For two, it doesn't have negative curvature. It has zero curvature. We live in a flat universe. So the anti-de Sitter space-time provides the special trick that allows us to flip back and forth to make that mapping possible with the holographic principle. That does not apply to our real universe. We do not live in an anti-de Sitter universe. We live in a different kind of universe. And our universe is evolving with time. Our boundary of our universe is constantly evolving. It's constantly expanding. So all the known correspondences between anti-de Sitter spacetimes and conformal field theories aren't as neat and tidy as you might think. And the field theory is on the opposite side of the coin. So you've made this great transition. You've eliminated gravity from your equations. Now you just have to solve a bunch of field theory problems on your boundary. But guess what? Sometimes those field theory problems are super hard.
Just because you can solve them in principle doesn't mean you can solve them in practice. If they're very strongly coupled, if they're very difficult to navigate, you've just swapped out one problem for another. You've just gone from the frying pan right into the fire. And maybe you haven't made any progress at all. So it's an improvement from string theory, which looks impossible, and we've been trying for decades and haven't really gone anywhere, to a problem that's merely insanely difficult, which I guess you gotta take it when you can get it. Man, if you can make any progress at all, you gotta celebrate, and this is considered progress. And I use the example of the black hole to show this holographic principle at work. That's why there's so much interest in black holes, because it might give us a clue of how this correspondence happens, of how we can utilize holographic principles to make progress on this very, very difficult problem of quantum gravity. But let's say, let's say we do it.
Fast forward 10 years, 20 years, 1,000 years, however long it will take. Let's say we're able to find a correspondence where we can map our full, complex, rich, interesting three-dimensional universe to its boundary. And I'm using air quotes here on the word boundary. Our universe doesn't have like a physical boundary, but we do have a limit to what we can see. It's called the horizon. So that will do the trick for our purposes here in the mathematics. We can map our realistic, our real three-dimensional universe to its two-dimensional horizon, its quote-unquote surface or boundary. Let's say the mathematics transform so much that gravity disappears on that boundary, that you can make some solution there, make progress in the field theories, map it back with your solution, and make predictions for how the universe ought to evolve and behave. You know, do problems in quantum gravity. Does that mean we live in a hologram? Does that mean our three-dimensional universe is a mirage? That really life and everything you know and love is taking place on a two-dimensional surface? And it just seems like the universe is three dimensions? I've seen some theorists actually say things along these lines.
And I don't think it's accurate. It's a mathematical trick. It's a way to map a very complex problem to a domain where the solution is easier to obtain. Then you obtain the solution, then you map back so you can make predictions. We use mappings all the time in physics. We do it in mathematics, mathematical physics. When we're trying to solve problems, we get a set of equations and say, man, that's really hard. We can apply some transformations to it to make the problem actually solvable. And then when it's solved in that domain, we translate it back to the original situation that we were trying to get at all along. We do it all the time, but we don't claim that the mappings are reality. We don't claim that this is, oh, this is really the way the universe works, is in this mapped space. No, we just acknowledge it as a mathematical trick and move on with our lives. So I personally have a lot of trouble swallowing the concept that just because you can make solving gravity easier using the holographic principle doesn't mean that everything is a hologram.
Just because you can make this mapping happen, and by the way, we can't make it happen. This technique has not solved any problems that are applicable to the real universe, but I'll give them the benefit of the doubt. Let's say we can someday make that happen, that we can understand quantum gravity using this holographic technique. It doesn't mean the technique represents the real physical universe. Just because you can find a solution through one route doesn't mean that route is reality. Of course, that leads down to a huge rabbit hole of what is real. Are electrons even real? Because electrons, we just have a set of observed phenomena and we have a model that best explains that observed phenomena. So doesn't electron exist? And I'm thinking that's another show. I'm thinking that's another show. But I'm feeling pretty strong about the holographic principle that we do not really, quote unquote, live in a hologram, that our universe isn't really two dimensional in our three dimensions is just an illusion.
It's a way, a potential, a potential. But it's the best shot we have right now of solving quantum gravity. It doesn't mean that's what reality really is. Thank you so much to Libra T and Andrew B for asking the questions that led to today's episode. Go to astrotouring.com, by the way, before you go, after you've done the Patreon thing, go to astrotouring.com and sign up for a trip with me and Fraser. It's going to be so much fun. I'm really looking forward to it. And also, spaceradioshow.com. Space Radio is live. It's going. We're recording shows every single week. You can call in and talk to me on the recording. Go to spaceradioshow.com. for instructions for all the episodes. Thank you to my top Patreon contributors this month, Justin G, Matthew K, Kevin O, Justin R, Chrissy, and Helga B. It is your contributions and everybody's contributions that keep this show going. That's patreon.com slash pmsutter. Keep those questions coming. Just get out there and do it, and I'll see you next time for more Complete Knowledge of Time and Space.