Part 7! How did String Theory get started? What has made the idea so popular over the decades? Can we ever truly have a theory of quantum gravity? What is supersymmetry, the landscape, and the AdS/CFT Correspondence? What do holograms have to do with this? How many dimensions do we live in? Why does String Theory have such a hard time making predictions? How are we supposed to judge a theory that isn’t done yet? It’s a non-stop String Theory bonanza as I discuss these questions and more in today’s Ask a Spaceman!
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EPISODE TRANSCRIPTION (AUTO-GENERATED)
You might think, given the way I ended the previous episode in our string theory series, which we are now entering our fourth month. And I swear this is gonna be our last month. I shouldn't do that. I hope this is gonna be our last month of our string theory exploration. And you might think that given the way I ended the previous episode that this one will be the last episode where we finally evaluate string theory.
We put it on trial. We decide if we should keep paying for it, but it's not because there's a major topic I need to talk about first. In some ways, this topic is considered a detour from the main goal of string theory, which is trying to explain quantum gravity and develop a theory of everything. And in other ways, this topic is considered one of the most fruitful avenues for modern string theory research. Some people call it a waste of time.
Some people call it the third superstring revolution. But whatever it is, it has a horrible name. I mean, string theory has great branding. It's all about strings. It's a theory.
It sounds sexy and new and fresh. What I'm going to talk about today is by far the most active branch of string theory research, and it goes by the name of the ADS CFT correspondence. We're just going to have to accept the fact that I'll be saying that phrase a lot, so we might as well get used to it. The ADS CFT correspondence. It sounds like some obscure accounting phrase.
No offense to any accountants in the audience. It sounds boring, and it deserves to be said boringly. This correspondence isn't really strings to theory itself, but more like more like a wholly owned subsidiary of string theory. But it's a huge part of the modern as in post Brian Greene's elegant universe string theory program, and so it must be a part of our final judgment, and, hence, we need to talk about it a lot. So let's talk.
And let's talk about black holes. Yes. Black holes. Who knew that a discussion on string theory and fundamental physics would somehow involve black holes? Well, we knew because the centers of black holes are singularities.
They are points of ultimate infinite density. If that's not a region of quantum gravity, then I don't know what is. Whatever happens, string theory needs to talk about black holes. But surprisingly, the direction we're going to take isn't about the singularity. It's about the horizon.
It's about the edge of the black hole, the boundary. I've done in that previous episodes about something called the black hole information paradox, and don't worry. I'm going to give it a very brief rundown right now. Step one, information goes into a black hole. Imagine throwing a book or your least favorite person.
Step two, observe that black holes are black, at least in general relativity. They are described by their mass, their charge, and spin regardless of who or what you threw in there. It could be your most favorite person or your least favorite person. The black hole doesn't look any different. This is not necessarily a problem if black holes live forever.
The information that you threw into the black hole is presumably just locked up inside. Okay. We can't access it, but it's still there. So step three, be Stephen Hawking. Realize that black holes don't live forever and emit radiation that just looks like a bunch of noise.
Note that this isn't proven in any way. This is still just a hypothetical idea. That's because the way Stephen Hawking derived this was by looking at the nature of quantum fields in the gravitational environment of a black hole. We kind of sort of know how to do that. Sometimes?
Maybe. We don't know. We think it might be right. There's no reason to suspect that Hawking radiation doesn't really exist, but I just want you to keep in mind, it's not proven. It's just a hypothetical idea.
But we're gonna go with it for our story to proceed. On to step four. We have a problem. Information goes into a black hole. Information doesn't come out.
Black hole disappears. Where did all the information go? Keep in mind that this has a very tedious and exhaustive mathematical description, but that's the basic summary of the black hole information paradox. So step five, ponder deeply. In the pondering, we realize something interesting about black holes.
When they eat, their volume goes up and their surface areas go up. Duh. They they get bigger when stuff goes in. But you would normally think that their volume goes up proportionally to what they eat, but instead it's their surface areas. One bit of information that goes into the black hole doesn't lead to one unit of volume increase to the black hole, like a small little cube added to the black hole, but instead one unit of surface area, a little square on its surface.
When information falls into a black hole, it increases in size proportional to the surface area, not the volume. Now I want everyone to put their hands on their chin and say, with me. Ready? Here we go. Usual caveat.
This is all hypothetical, unproven ideas, but let's keep the cameras rolling anyway. Black holes are very much three d objects. Right? They're spheres. But it looks like there's a connection between what they eat and their surfaces, not their volumes, their surfaces, which are only two dimensions.
The surface contains or encodes the information that falls into a black hole. And when a two d thing holds all the information needed to build a three d thing, we call that a hologram. And since you know we're gonna pull in string theory in all its extra dimensions soon, we can generalize this. When a low dimensional thing, whatever that thing is, holds all the information needed to build a higher dimensional thing, whatever that thing is, that's called a hologram. And these sorts of ideas are called the holographic principle, which are inspired by thinking about black holes because what isn't, but expanded to other concepts.
And you know string theory involves gravity, and so you know, you read all sorts of popular accounts of we really live in a hologram. Gravity is a hologram, etcetera, etcetera. I don't know whose voices this is. It doesn't matter. But even the scientists themselves who are working on holographic principles or holographic descriptions of gravity will say this kind of stuff.
I'm not gonna make a lot of definitive judgments in this series, but I'm just gonna come come out and say say that this is nonsense, which I dug into a lot in the black hole information paradox episode. Even if and I'm gonna outline this. Don't worry. Even if all of what I'm about to talk about works out, it doesn't mean we live in a two dimensional space. It doesn't mean we live in a hologram.
Even if there is a quote unquote holographic theory of gravity, it means that all it means that some gravity problems are best solved on a two d surface around our universe, not in our universe itself, which makes it a cool math trick. And, hey, cool math tricks are awesome. We love them. They help us solve real world problems. We use them all the time in physics.
But that's it. A cool math trick. So, anyway, let's talk about some cool math tricks. The holographic principle itself is very vague in general, which is, wouldn't it be totally awesome if we were a hologram? Or more little bit more rigorously, what if we could solve some problems on the surface of a volume instead through the volume itself?
Might that make our lives a little bit easier? Okay. Okay. And these holographic principle ideas were bouncing around in the nineties. And in the late nineteen nineties, it found a surprising application to string theory called the ADS CFT correspondence.
This correspondence isn't the holographic principle, but it's an an application of the idea. The ADS CFT correspondence is itself unproven. It's really more of a conjecture, but the community expects to have it fully proven in a few years. Although they said the same thing about string theory back in the Reagan administration. So, you know, take it with a grain of salt.
But what is the the AdSCFT correspondence, and why do we care? Well, let's dig into the alphabet soup that the theoretical physicists have thrown at us. First, the ADS. And before I get too deep, I want you to believe me that I'm trying to make this episode as straightforward as possible, but it's just this topic is really, really, really dense, where every other word is a weird jargon word invented by a random mathematician for the sole purpose of communicating to another random mathematician. But here we are in our seventh episode on string theory, and we are brave, we are tough, we will persevere, we will overcome, and we will make it to the finish line.
ADS stands for anti de Sitter. Not helpful. De Sitter is short for Willem de Sitter, a Dutch mathematician who played around a lot with GR, especially looking at various kinds of space times filled with various kinds of substances, like what if it's what if the universe is made of a lot of matter or a lot of energy or curvatures one way or the other, just playing around. He figured out that one kind of space time in particular that had no matter in it at all and a positive cosmological constant, this space time that he just happened to figure out out looks suspiciously a lot like the universe we live in today because what we call the cosmological constant is dark energy. This kind of space time but he didn't know that at the time.
That's for sure. He was just playing around with the math, and it turns out one of the things he played with is useful to describe our universe. This is called a de Sitter space time because he figured it out and credit goes where credit is due. Anti means opposite, and so the opposite of de Sitter is not desutter. It's anti de Sitter.
It's a universe with no matter in it and a negative cosmological constant. Doesn't look like anything resembling our own universe. It's just a mathematical construct. It's just hanging out. It's just one of the things he played.
Like, well, maybe this is what the universe looks like and just put it out there. Doesn't apply to our universe, but it was hanging out in the cupboard, you know, in the back, past the dried chickpeas. It was there. There was this cosmological model called de Sitter space. It's been pretty useless, so we might as well try to do something with it.
Okay. That's the ADS. That's the ante desider. It's just a space time. It's a particular structure of space time.
The other side of the ADS CFT correspondence is the CFT, which stands for conformal field theory. Again, not really helping. Okay. Physicists love to take a theory and poke and prod at it, making changes to the math to see if it ends up making changes to the final results. This is how we found all those juicy symmetries and dualities and unifications that we've explored for the past ages.
By the way, I don't know if I told you this, but I have not stopped growing my beard since we began this series a few months ago. I I trim it regularly, but I also haven't stopped growing it. One thing physicists really love to do is to take the underlying coordinates of a system and stretch them out like a big rubber sheet and see if anything changes. Or if there's some interaction that has a particular strength, they like to change the strength of the interaction and see, you know, if if any of the physics changes. You know, if if two electrons meet each other and bounce off of each other and then that electromagnetic interaction has a certain strength, well, what happens if we make it stronger or weaker?
Do do the electrons not care, or do they bounce off less efficiently, more efficiently? Do they go haywire? Just there we're just curious. It helps us it helps us just examine the nature of the system. If we make these kinds of changes and nothing changes in the end result, this is called scale invariant, as in the results don't change when a certain scale is changed.
Like, if you change how strongly electrons interact and it doesn't affect any interactions of electrons, then the interaction between electrons is called scale invariant. It's like if you put different kinds of gas with different octane levels in your car and then your fuel efficiency stays exactly the same, then we would say your car's engine is scale invariant. Or if I were to stretch things out, if I were to make a soccer field twice as long but the game stays the same, then the game would be scale invariant. But we're not talking about scale invariance. We're talking about conformal invariance, which is a certain special case of scale invariance.
And in the physics lingo, that's all fashionable nowadays, almost always whenever someone says conformal or conformal invariance, they almost always mean scale invariance when it comes to some energy of interaction, some strength of interaction. It's just it's just the way the jargon has taken us in the past twenty years. And field theories are the mathematics that we use to describe everything from gravity to the weak nuclear force to the electromagnetic force. Like, it's all fields. Fields, fields, fields.
Field theory is our theory of fields, which means it's our theory of physics. And so a conformal field theory is a theory of some physics, some model of some interaction that doesn't change when you monkey around with the energy scale. For example, if I run a particle collider at 1% power and see some cool physics, and then I run it at 10% power and I see the exact same physics, same same output, and then 20% and see the same and skip right up to full power, and I see the exact same physics every single time, then it a a theory of fields that are conformally invariant, a theory of fields that are scale invariant, a theory of fields that don't change the output when you change how strong the interactions are. That's nice. By the way, almost all of the universe is not described by a conformal field theory.
The physics of our universe is not scale invariant. That's probably why it seems a little bit weird, and I had to really dig in because it just goes against our intuition. It's like, yeah. If you make electricity stronger, all electrical interactions are gonna be different. It is not scale invariant.
You can write down quantum field theories that are conformal field theories, and they'd be wrong. That's the whole problem. Interactions between fundamental particles are different at different energies. Forces change their nature. They can even merge together.
Some interactions simply don't even turn on. Some particles don't even appear until certain energies. It's a mess. It's not scale invariant at all. Apparently, when quantum field theory was first gaining steam in, like, the thirties and forties, lots of people hoped it would be a conformal field theory because it makes life way easier and would be generally slick.
But Wolfgang Pauli, who knew how to throw quantum shade like nobody's business, whenever he would encounter a presenter or a paper discussing a conformal field theory as a proposal, he would just tell them to, and I quote, shut up. So now we have the pieces of the AdSCFT correspondence. On one side, we have a structure of space time that does not look like our universe at all. And on the other side, we have the description of physics that does not look like our universe at all either. Wow.
Why do we care? We care because it turns out that these two things might be deeply related, and it maybe might tell us something interesting about the universe. Stay with me here, folks, because I can I know this is sounding a little bit sketchy, but we're almost there? We're almost there. It turns out that if you have a string theory operating in an anti de Sitter ADS spacetime I know, I know, I know, I know, I know, string theory needs a bunch of higher dimensions to really work, but let's just play pretend.
If you have a string theory operating in that kind of universe, then you can map it to the boundary of that space time. And on the boundary, the string theory math gets replaced with the math of a conformal field theory. This is an application of the holographic principle because you're connecting what's going on in a volume to what's going on at this surface. And what's really curious is that the string theory inside the volume in that ADS space time has gravity because it's string theory, and string theory automatically has gravity. But the CFT, the conformal field theory on the boundary, doesn't.
It just looks like any other old quantum theory, and it's interesting because you can work in both directions. Say you're trying to, I don't know, find a unified theory of quantum gravity by a string theory. Some people have tried it. That model, that physics, contains a bunch of unsolvable math problems, and you're kind of stuck and we've been stuck on that for a few decades. Well, then the AdSCFT correspondence allows you to map that problem onto the boundary.
Imagine taking all the guts of the universe and just splatting it onto the surface of that universe, onto that shell around it. And then once you've made that mapping, you can try to solve a conformal field theory, a quantum theory that doesn't include gravity on that surface, and then map your way back to understanding what's going on inside the volume. A conformal field theory on the boundary is still a nasty problem, but we've been solving quantum field problems for decades, and we're kind of good at it. So this is that shortcut trick that I mentioned, that we don't really live in a hologram. But if you're trying to understand quantum gravity and you can't make any headway using string theory inside the universe, then you can map everything onto the surface, potentially, map everything onto the surface, solve your problem on the surface using a conformal field theory that has no mention of gravity at all, get a result, and then remap it into the volume, and you've made some prediction in the limiting case where the space time inside the volume does not look like the universe.
And you can work the other way. String theory doesn't have a final form yet. We don't have the string theory, but it does have a pretty large and extensive toolkit of, you know, assorted mathematical odds and ends. It's pretty handy in some cases. So if you happen to have a thorny conformal field theory problem, you can map that into the volume and take a crack at it with our knowledge of string theory.
You know, good luck with that, but it's worth a shot. You might make some headway. That's pretty handy. Right? Or at least it might be if we find the right applications.
It's it's it's like inventing a new tool, like, ADSCFT or excuse me. The ADSCFT correspondence is a new kind of tool, and we're just looking around and see if has any utility, if it has any function in the real world. It's a neat idea, and it tells us something deep potentially about the holographic principle and maybe about gravity, but it was just begging for an application. The challenge with the first approach, trying to solve string theory problems with conformal field theories, is that the conformal field theories you need to make this connection work are very difficult, so difficult it doesn't look like you can find solutions for them. In the jargon, they're strongly coupled, which means that our usual toolkit of using perturbation theory to solve quantum problems just breaks down, and it's not clear you can even make any progress.
And even then, you've only made progress in string theory. So even if you can solve the the equations like, the whole point is to take say, wow. String theory is impossible. I can't make any progress. I'm gonna transform it into a field theory and maybe make progress there, but it turns out those field theories are very painful, and we can't make any progress.
But even if you could and then you mapped it back to your string theory, that string theory has to live in order for this correspondence to work. The string theory has to live in an anti de Sitter space time, which is not our universe. So even if you solve something, even if you discovered something, congratulations, You've unlocked the ultimate mysteries of time and space for somebody else. And the challenge with going in the opposite direction of, say, you've got a thorny, conformal field theory problem and you wanna use the toolkit of string theory to solve it is that, well, almost nothing in our universe can be described by conformal field theory, so, its usefulness as a tool is somewhat suspect. Still, there are some possible hints of applications.
Some calculations have been attempted to explain quark gluon plasmas. These are very high energy state of matter where the strong force is just let loose and crazy, and there's all sorts of quarks and gluons, and they just do whatever they feel like without having to bind up into protons and neutrons. We've made some progress. Some regions of quark gluon plasma, some ways of trying to understand them can be described in very limited cases as a conformal field theory, and so this AdSCFT correspondence has been applied to that in some ways. It's almost like bringing string theory back to its roots.
Like, we started sixty years ago with string theory trying being born out of an attempt to understand the strong nuclear force, and here we are again finally getting on to that after a few generations. There are some problems in condensed matter physics, like, superconductors and whatnot that this correspondence might be helpful in. It solves some problems in Patreon because every dollar contributed in string theory becomes 10 on the boundary of patreon.com/pmsudder, where you can also go in addition to this correspondence. You can go and keep this show going. I really appreciate it.
And to bring this all the way back home, this correspondence can serve as a potential solution to the black hole information paradox using the AdSCFT correspondence. It may be that the information of a black hole is encoded on its surface, and it sneaks its way into the Hawking radiation, which means that if you're watching a black hole evaporate, you could eventually reconstruct everything that went into it. This, of course, assumes that we understand Hawking radiation. This assumes that we understand black hole information. This assumes that the holographic principle holds for for black holes.
And for this correspondence, it assumes that this correspondent works. It assumes that the calculations we're doing are in any way faithful and representative of the universe we live in, etcetera, etcetera, etcetera. Maybe there's a resolution of the paradox there. That's nice. But where does that leave us in string theory?
Like I said earlier, most people working on string theory these days are actually working on the AdSCFT correspondence. And for most applications, it isn't trying to solve string theory. So it's not necessarily string theory, but it's an application of the tools and methods developed for string theory. What that most application of this correspondence is in trying to solve some of the nasty, thorny, conformal field theory problems that crop up every once in a while. But it also hasn't been proven, and its utility is suspect because both sides look so unlike our actual living, breathing universe.
Right? We do not live in an anti de Sitter universe. So whatever you learn about there isn't gonna really apply. And most the vast majority of physical systems are not scale invariant, so you're not gonna learn a lot there for most systems. Attempts have been made to try to stretch beyond conformal field theories and to work with a de Sitter space time or a flat space time, something that looks you know, something resembling parts or of our universe or the whole entire universe, but we haven't made a lot of progress.
And it's been about twenty years now since this correspondence was first proposed. But lots of people are interested in it and think it's a pretty promising way to potentially solve a bunch of little niggling hard to calculate problems, so it can't be all that bad. Right? Right? And that's where we are today.
I think we've arrived. I think we've explored every nook and cranny of string theory that we reasonably can. So I think for our next episode, this is it. After this journey of months, I think it's time to put string theory on trial. Thank you so much to all of my Patreon contributors this month and all of the months.
Patreon.com/pmsutter is how you seriously keep the show going as little as a dollar a month. This is my income. This is my job. This is my livelihood, and you guys are a major part of it, and I can't thank you enough. But I would especially like to thank my top Patreon contributors this month, Matthew k, Justin z, Justin g, Kevin o, Duncan m, Corey d, Barbara k, NooterDude, Chris c, Robert m, Nate h, Andrewv, Chris l, John Cameron l, Nalia, and Aaron s.
Also, there's a bunch of people that ask questions about string theory over the years. John c on email, Zachary h on email, at edit room on Twitter, Matthew y on email, Christopher l on Facebook, Chrisna w on YouTube, Psi NP on YouTube, Niha s on Facebook, Zachary h on email, Joyce Joyce s on email, Mauricio m on email, at Schrennick Schra on Twitter, Panos t on YouTube, Dhruv r on YouTube, Maria a on email, Terbi on email, Oi Snoy on YouTube, Evan t on Patreon, Dan m on Patreon. Some beautiful person on the website, John t on Facebook, at t w Blanchard on Twitter, Ori on email, Christopher m on email, at Unplugged Wire on Twitter, Giacomo s on Facebook, and Gully Foyle on YouTube. So many questions, so little time. Keep them coming.
Keep the reviews on iTunes coming. Keep telling friends and family and enemies and people who love and or hate string theory. Or if they have complicated relationships with it like I do, send them this way. Thank you so much for listening, and I will see you next week. No.
Next week. I will see you next time for more. And this is it in this series, complete knowledge of time and space.