Part 3! 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)
Imagine getting in a rocket ship and it'll be a big one. Trust me. Like a really awesome one. And it will have lots of foods and comfy beds and a pool table. Yeah.
Yeah. Pool table. I may have designed this rocket ship when I was 12. Anyway, you get in big rocket ship, blast off, you go in space, and you go in one direction. You just pick a point, say, the second star to the right, and you just go straight on till morning, and then you keep going and going and going.
You never turn left, right, up, down, just one direction. You see a bunch of stars, a bunch of galaxies. You travel through the universe, the cosmic web. It's pretty awesome, and you just travel for eons. Like, it just never stops.
But after a while, a long enough amount of time, you come upon a certain galaxy, and it's right directly ahead of you. You can't avoid it. So you enter the galaxy. You cross into the galaxy because you have no other choice because your special rocket ship that I made when I was 12, does not have directional control. So you enter the galaxy, and you find directly ahead of you a star.
Oh, wow. So you aim towards that star. And you find in orbiting that star directly ahead of you, a planet. And you get closer in that planet as blue and as continents and an atmosphere, the whole deal. Wow.
It looks like somewhere you could live. You land on that planet. You get out, and you realize you're on the Earth. You you if you want, you can go right back into the house where you left from assuming it's still there after all these eons of traveling through space. You know, maybe hundreds or thousands of years have passed, but you can tell that it this is the Earth.
The endpoint of your journey was the exact same place as the start of your journey even though you never changed directions. Congratulations. You've just discovered that the universe has a closed dimension. A closed dimension means that you can travel in one direction and end up in exactly the same spot. Another word for this and the word that you were gonna see a lot in string theory is that it is compact.
Compact. Okay. Compact, closed, doesn't matter. Like the Earth. The surface of the Earth is closed.
The surface of the Earth is compact. If I head out moving in one direction, I will end up exactly where I started. And, in fact, it's compact or closed in two dimensions because I can go north or south, and I can go east or west. That is two dimensions. No matter what, I'll end up exactly where I started.
Ergo, the Earth has two closed or two compact dimensions. But we're not really talking about the Earth here because we're talking about string theory. We are following the second thread, pun still very much intended, of the essential ingredients in string theory. In the first thread that we explored last time was strings themselves, strings as physical objects and how they vibrate different ways of vibrating, give rise to different properties of things that we call particles. So a string vibrates one way, you get an electron, vibrates another way, you get a top quark, vibrates another way, you get a photon, etcetera, etcetera.
But I mentioned at the end of the last episode that string theory requires a little bit more dimensions than we're used to. And these dimensions, as we'll explore more, have to be compact or closed. And and we can think of this as the analogy like the surface of the Earth. The surface of the Earth has two closed dimensions. But we're not talking about the Earth.
We're talking about the universe. We're talking about space time. We're talking about the fundamental aspects of reality. And when we look around our universe, we see three spatial dimensions and one dimension of time, and they're bound up together into this thing we call space time. We know that our universe is flat.
It's not curved like at the surface of the Earth. It's it's geometrically flat, but, we don't know actually if our universe is closed or not. You see, you can have flat space times that are still closed. The surface of a cylinder is still flat. I know that seems weird, but the definition of flatness is how parallel lines behave.
And if parallel lines stay parallel forever, then you've got flatness all the way around. Didn't mean to make that joke, but that's a pretty good one. And if you've got parallel lines that end up intersecting, then you have a closed geometry. And if you have parallel lines that end up spreading apart, you have an open geometry. As far as we can tell, based on an assortment of cosmological measurements that are not the topic of today's discussion, our universe is flat.
But flat things can still be closed because you can draw two parallel lines on a cylinder, and they will stay parallel. Same thing for a doughnut. You can draw parallel lines on the surface of a doughnut, and they will stay parallel. A doughnut is closed. It's compact in two dimensions, but it is still flat.
And also in a Mobius strip, if you take a piece of paper and you connect the ends, but before you connect, you flip one of the ends over so there's a little rotation in there, parallel lines still stay parallel. That's pretty cool. A Mobius strip is still flat. In fact, in three spatial dimensions, there are 17 different ways of making a closed universe. It can be closed in just one dimension.
It can be closed in one dimension with a flip. It can be closed in two dimensions. It can be closed with in two dimensions with a flip in one direction, but not the other, or not the first, but just the other, or both. It can be closed in all three dimensions, and you can add flips and rotations and all sorts of things, 17 different ways that we know of to have compact or closed dimensions in a perfectly flat universe. And it gets way worse if the universe was not flat.
If it was closed, like the surface of a sphere in three dimensions, there's, like, a bajillion ways to compact or close those dimensions. Like, just the topology goes nuts. As far as we can tell, our universe is not closed, or if it is, it's on scales way bigger than what we can observe, but that's not today. That's not for today. Today, we're talking about the structure of that space time and of that space time and what just really is reality.
Like, just how many dimensions do we live on? And, of course, like, we look around. We live in three dimensions. There's not an extra dimension that I can move in. It's just it, the left, right, up, down, forward, backward, and past, future.
That's it. Three of space, one of time. In our theories, our models of physics are all built in that four dimensional universe, And, specifically, we have general relativity. Our theory of gravity describes the geometry. It describes the bending and flexing of that four dimensional space time.
That's its job. That's what we call gravity is the geometry of space time itself. But what if there are more dimensions? You know, just play just play along. Just play along.
What if there are more dimensions? Well, it turns out that general relativity is agnostic when it comes to the number of dimensions. The math equations of general relativity don't actually care about how many dimensions of space or time. That's something you put in by hand. There's just general relativity being general relativity, and you have to tell general relativity, I want to work in three spatial dimensions and one temporal dimension.
What do you got for me in terms of gravity? We have to tell that from the outside. It's not baked into the equation themselves. The equations of general relativity say, yeah, give me, 47 spatial dimensions and 14 temporal dimensions, and I'll tell you what gravity looks like in that. And so whenever there's this kind of flexibility in an equation or theory, people like to play around.
It's just math, and math games are fun. Right? Right. Why not? We might learn something cool about the universe if we just play around.
So let's say we add an extra spatial dimension. I know it's not realistic. Obviously, like I said, we only live in three spatial dimensions, but come on. It's a math game. What's the harm?
Let's add a fifth dimension. So we have one dimension of time and four dimensions of space. Let's plug that in to general relativity and see what we get. And you get general relativity in five dimensions. Nothing special.
That's the whole point of general relativity being totally agnostic to the number of dimensions. But something interesting happens when you close that extra dimension, when you make it wrap in on itself, like taking a piece of paper and making it wrap in on itself. Something surprising happens. Theodor Kaluza did this in 1919, just a couple years after generality was published itself because, you know, nerds are bored and they see generality, and they're like, oh, I wonder what would happen if I had more dimensions to it. This work of Theodor Kaluza is often pointed to in the history of string theory.
Like like, oh, yeah. Yeah. Because string theory involves extra dimensions. Here's a theory of extra dimensions. It's a bit of a red herring, and I'll explain why.
The key idea is that string theory requires extra dimensions to work, and here's an idea preceding it by, like, forty years. You know, in the nineteen sixties, that's when string theory really got going. And here we are in the nineteen tens already exploring the concept of extra dimension. So it's more like string theory can point and say, hey. You know, we've tried this before, and we and we saw some interesting things.
And so it's not too crazy for us to try it again. Right? It's not that Kaluza's ideas directly led to string theory because string theorists if Kaluza hadn't existed, string theorists would've worked this out on their own anyway, but it was just something handy to point to. And the reason that string theory requires extra dimensions to work is that these strings need a lot of room to vibrate. If you constrict the strings to only exist in three spatial dimensions, and that means that they can vibrate in a certain way.
They can, you know, they can wiggle left or right or up or down or front and back. It turns out that's just not enough. It just makes the math fall apart, like the strings like aren't expressive enough in three dimensions. They need more room to to really explore their wiggles. They got too many wiggles to be contained in just three dimensions.
They can't do the things that you need strings to do in just three spatial dimensions. The original proto string theory of the nineteen sixties, which was people were trying to use to explain the strong nuclear force, needed 26 dimensions in order to operate to actually make this theory work. That seems a bit excessive. Modern string theory has 10 dimensions. Modern string theory evolved from this nineteen sixties strong force string theory, and it turns out in modern string theory, you only need 10 dimensions.
And then there's this other thing called m theory that is 11 dimensions. What is m theory? Good question. We have to wait a long time before we get to that. But no matter what, we need extra dimensions to make string theory work, so we need to figure out how well this works.
And it's perfectly valid to write down equations that only work or are only consistent in 26 dimensions. But as soon as you realize that your theory of physics only works in 26 dimensions or 10 or 11, you're confronted with a hard observational fact, which is that the universe has slightly fewer than 26 dimensions. So now what? Well, early string theorists pointed to the work of Kaluza, Theodore Kaluza, and later developments by Oskar Klein to give a, like, a way out to explain how this could work. So like I said, it's not like Kaluza's work led into string theory.
It's not really a precursor because Kaluza's and Klein's work didn't really go anywhere, but it set an example of how to think about the extra dimensions needed by string theory, and so it's worth a look. Also, Kaluza's theory had an interesting little nugget buried inside of it, which gets people all excited but really shouldn't. Don't worry. We'll get there. Anyway, no more teasing.
Kaluza added an extra dimension to our universe and worked it into general relativity and nothing much interesting happened. But then Kaluza added what he called a cylinder condition. It's what we would call a compactification or a closure. He he made one of the dimensions wrap in on itself. Then something very interesting happened.
Once you run through, once you add that extra condition and you create general relativity out of that with the same way Einstein created general relativity out of our four dimensional space time, when you create general relativity out of a five dimensional space time where one of the dimensions is wrapped up on itself, you get general relativity back in three dimensions plus time, and you get the equations for electromagnetism. You also get one extra equation for something called a scalar field that we're just not going to talk about right now, but it will come back later. Don't worry. And by right now, I mean, we're not gonna talk about in this episode. It'll be a couple months before we talk about a scalar field again.
So we can leave that to the side. The main point is that, wait, you get general relativity in normal space time, plus you get some extra bonus equations that are the equations of electromagnetism. So at first glance, it looks like you can unify physics by adding extra dimensions. Oh, I mean, isn't like just take a step back. Like, wait a minute.
If we add an extra dimension to the universe and this dimension wraps in on itself, not only do you get general relativity, you also get electromagnetism with the same set in the same understanding. People were very interested. Einstein himself was like, interesting at first. But once you try to actually use this framework and to do electromagnetism, like adding in, I don't know, electric charges to see how they behave, it all falls apart. The equations developed by Kaluza describe the electromagnetic field, but they don't actually tell you how that field actually interacts with electric charges, how it's generated by charges, how it makes them move around.
And when you try to sprinkle that stuff in, like, okay. I've got this really cool theory. Let me add some electric charges, see what goes on. It just it falls apart. Mathematically, it it collapses.
And now, a hundred years later, with hindsight, we see that it wasn't really the adding the extra dimension part that made it special. That's the red herring where it's like, oh, you think by adding dimensions to the universe, you can, in some sense, unify physics? That's wasn't it. It was the closing of the dimension. It was make it was this cylinder condition.
It was wrapping it in around itself. That's what made the electromagnetism pop out. It made it pop out because closing that dimension introduced what's called the symmetry. We're gonna talk a lot about symmetries, especially in the next episode, so don't worry too much about it. But you can you can get a sense that closing introduced some sort of symmetry, and electromagnetism itself has a symmetry inside of it.
It's a bunch of math jargon that we're not gonna worry about too much because we are gonna dig into it next time. It turns out that the symmetries baked into the equations of electromagnetism are the same kind of symmetries you get by a cylinder condition by closing a dimension in a universe. So, of course, this led to general relativity plus electromagnetism because the cylinder condition builds in the exact right kind of symmetry that is encoded in electromagnetism itself. Now this doesn't mean that electromagnet the existence of electromagnetism implies that our universe is closed in one dimension. It just means that the mathematical structures that you see in a cylinder and trying to describe a cylinder are the same kind of mathematical structures that you see in electromagnetism.
That's why it's a little bit of a red herring, but it's still pretty interesting. And I know I know I'm being super vague about this word symmetry. Don't worry. We're gonna dig in a lot in the next episode. It's not too important to our story, but I wanted to point this out because a lot of histories of string theory point to the work of Kaluza when they don't really need to.
It's important for sure, which is why I'm talking about it, but not in this way. Anyway, there's also this other minor problem that the universe obviously doesn't have a fifth dimension. But that didn't stop people from continuing to play with it because at the time, they didn't know about all these symmetries that we understand now. And so the obviousness of the connection wasn't, well, obvious to them. And so they were still surprised that electromagnetism could pop out of these equations just by adding an extra closed dimension.
And so they were working on it. They were playing with it. They were poking with it. And even though it didn't work, it was still, like, interesting mathematically, which kinda also sets a precedent for string theory in in its entirety. But, anyway, the work of Kaluza was purely classical, purely g r, classical electromagnetism.
It didn't include all the fancy pants quantum mechanic action that was also going around at the time, you know, in the twenties and thirties. So there's someone else, Oscar Kline, who tried to mesh Kaluza's work with adding this extra dimension with what we knew about quantum mechanics. And what we know about quantum mechanics is that when you close that dimension, when you wrap that dimension in on itself, it limits what can happen in that dimension exactly the same way as when we were talking about strings themselves last time and they close in on themselves. And because of quantum mechanics, because they're little loops, they can have only certain kinds of vibrations. They can have only certain kinds of wiggles because of the rules of quantum mechanics.
You can't just have any wiggle you want. You have to have quantized wiggles. And similarly, by closing this dimension and looking at the nature of the electromagnetic field in that closed dimension, Oskar Klein was able to find an explanation for why electric charge is quantized. And once you do that, you plug in all the known values of the actual electrical charges and the forces into that extra dimension. And it turns out that in order to make it work, in order for Kluge's idea to mesh well with quantum mechanics, that extra dimension has to have an incredibly small size.
It has to be about the Planck scale. This is another clue. Last time, I talked a lot about how the strings have to be small. They have to be down there at the Planck scale. Here's another thing pointing to the Planck scale as being important for strings because strings need closed dimensions.
They need extra dimensions, and they need these dimensions to be really, really small. They need them to be at the Planck Scale. And so here's just another thing pointing to the fact that strings are gonna be very small, and, also, the extra dimensions that they need to live in are also gonna be small. Because if the dimensions themselves are the Planck scale at, like, 10 to the minus 30 meters or whatever the number is, I don't know it off the top of my head. It's small, just smaller than the smallest possible thing.
If the strings are bigger than that, then they don't care about the extra dimensions, and so they don't get to do their stringy thing. The strings need extra dimensions in order to be as expressive as they can be in order to ex potentially explain physics, and the dimensions they live in have to be very, very small, Planck scale. Ergo, the strings themselves must also be small. But this smallness of dimensions, like, what in the world does it mean to have a small dimension? It's it's like it's so easy to say, but it's actually kinda hard to think about.
But what allows the universe to have tiny curled up dimensions, either one in the Kaluza's idea and Klein's idea or 26 in the early string theory idea, or 11 in m theory or whatever, is that the extra dimensions are tiny and curled up on themselves like a closed universe. In the big universe with our rocket ship, if one of the dimensions is closed, you travel in one direction, you end up where you started. The same is true for these tiny little curled up dimensions. As you move through our three-dimensional universe, you circumnavigate the tiny dimensions bajillions of times over. And I've already said it a couple times, so I might as well define it.
Bajillion is going to be the official Ask a Spaceman technical jargon word for a lot. Bajillion. You move we experience three spatial dimensions, and you move through these, But there's embedded inside of space. They're like every single geometric point, which means they literally fill up everywhere you look. Like, imagine, you know, just wave your hand in front of you.
And if you do this in public, people are gonna think you're stoned, but, no, you're thinking about science. As you're waving your hand in front of you, your hand is looping, making little loops around these tiny curled up dimensions countless times over, but this happens at such extremely tiny scales that you don't even notice. Everything looks smooth up here, but really as your hand is moving, it's making a little loop, loop, loop, loop, loop, loop, loop, loop, loop, loop, loop, loop, loop, loop to get to where it's going. It's like, you know, at the airport, when you when you're at security and you gotta put your bags in the scanner and there are all those rollers and you put the bin on the rollers and you move your bin down, that bin is just moving in one direction. Right?
It's just moving forward. But as it's moving forward, it's wrapping around those cylinders. Those cylinders are rolling. There that bin is circumnavigating each one of the rollers over and over and over and over and over again, many, many times over. That bin is circumnavigating that second dimension by making those rollers roll while still only moving in one direction in the macroscopic world.
This is a very critical concept for for string theory because string theory requires extra dimensions, and the only way to get extra dimensions in our universe is to make them very, very tiny and very, very curled up, so tiny and so curled up that we don't even notice. And we don't even notice in our particle colliders. We don't even notice in our big, fancy, expensive experiments. We only notice this at the Planck scale, the very tiniest scales that there are. This idea of Kaluza, of adding an extra dimension and generating electromagnetism, And then Klein of giving it a quantum interpretation and finding that this extra dimension has to be tiny and curled up.
It had didn't go anywhere by itself because you actually was you know, didn't actually make accurate predictions. And once you tried to add realistic things like electric charges, it all fell apart, but it did have two fruits. One of the fruits of Kaluza's and Klein's ideas was the concept of adding symmetries to unify physics. This had been a program going on since Newton, like I talked about been talking about for the past couple episodes. And here was more symmetries.
Here's one more thing like, oh, if you add symmetries with these dimensions, you can get some new combinations of physics. You can put different kinds of physics in the same roof. That's not a bad idea. It didn't work out for Kaluza and Klein in any interesting way, but this concept of adding symmetries, more symmetries, looking for more symmetries, and seeing how we combine things that will lead to somewhere that we're gonna talk about in the next episode. It also led to the invention of Patreon.
That's right. Patreon.com/pmsutter is how you keep this show going. I really appreciate it. I really do. And it it you look at those papers by Kaluza and Klein, and you can see the roots of Patreon right there.
I swear it. The other fruit, the actual other fruit, besides the concept of adding symmetries to unify physics in an advanced quantum mechanical way, the other fruit is that it gave the nineteen sixties string theorists something to point to when they found they needed extra dimensions. They're like, oh, shoot. In order to make our math work, we need extra dimensions. Our universe doesn't have extra dimensions.
What do we do now? Oh, wait. There was this Kaluza and Klein idea. That's right. There can be extra dimensions, but they can be all tiny and curled up on themselves.
String theory is saved. Like I mentioned a little bit ago, we haven't quite gotten to this part of the story in string string theory yet. We're still in the nineteen sixties here after three episodes in. But in the nineteen seventies, the 26 dimensional string theory was is going to be replaced with actually much more powerful broader theory that, quote, unquote, only needs 10 dimensions. But then later, that will be replaced in the nineties with an 11 dimensional theory.
But don't worry. We're getting it all there. No matter what, you need extra dimensions. And like I said, it's natural to assume that those dimensions are curled up really, really tiny. That was Klein's idea.
His contributions like, yeah. If you want these closed up dimensions, if you want quantum mechanics out of that, and we most certainly do, then these dimensions need to be down there at the Planck scale, which means the strings have to be down there too so that they can actually take advantage of the tiny dimensions, unlike us. Okay. Great. Sure.
Whatever. I guess. But remember I mean, that's it's like, okay. Fine. Like, if that's the way the universe is, that's the way the universe is.
Okay. But there's a little difficulty here. Remember how in three-dimensional flat space we could get 17 different ways of closing the dimensions, of compactifying dimensions, of wrapping dimensions, however you want, whatever word you want to use in just simple, boring, three-dimensional flat space. We had 17 different ways. And in curved space, it's even worse.
Well, if we're gonna look at, say, 10 dimensional string theory, One of those dimensions is time. Three of those dimensions are are normal spatial dimensions of our universe. That that gives you six extra spatial dimensions. How in the world do you wrap up six spatial dimensions in on themselves? Well, you know, it could be like circular.
Like, you could imagine a six dimensional cylinder, torus thing. Okay. Maybe you can't, like, strictly imagine it, but you can write it down. But there can be flips. There can be curls.
There can be seesaws. Like, wow. Like, just let your mind go of, like, how if I had to connect up six dimensions in on themselves and I could do it any which way I wanted and they can have any curvature they wanted, That's a lot. At first, string theorists just, like, didn't even touch this. They're just like, wow.
That's I I don't even know what to do. It was found out much, much, much, much later, decades later, that in order for string theory to work, the curled up dimensions obey a certain geometric structure because reasons. That was why I'm definitely not going into the guts of that one. For various reasons, the six curled up dimensions just can't do anything they want. They are somewhat constrained, and they're constrained in a way that's called the fancy jargon here is called Calabi yao manifolds.
Calabi and yao, two folks who figured this out. Manifolds just means like a geometry, a way of curling things up. Okay. That helps. So, the six curled up dimensions, they can't do anything they want.
They have to obey certain rules, and these certain rules are called manifolds. And you just can't go anywhere in a string theory discussion without tripping all over manifolds. It's Calabi this and Yao that, and it's just blah blah. Like, you run into it a lot because it's part and parcel of string theory. Just whenever you see manifold, just make a brain replacement with the phrase a particular way of curling up six dimensions.
But still, even with that constraint, like, okay. Thanks, Calavi. Thanks, Yao, for your contributions. I really appreciate it. There's still a lot of options for curling up the six dimensions.
Low estimate, 10 to the 500. High estimate, 10 to the 200,000. I'll say that again. The number of possible ways you can curl up six extra dimensions, even with the constraints that it has to be a Calabrio manifold, a particular arrangement. There's somewhere between 10 to the 510 to the 200,000 options.
And the more time goes on, the more we lean to the higher end, like 10 to the 10 to the 200,000. Which one is our universe? I mean, our universe can't do all of them. I mean, our universe can't do all of them. We only have one geometry and one topology for our universe up here in the three macroscopic directions.
And these microscopic dimensions, you know, which one? Which one is it? How are they curled up? Short answer is we don't know. The long answer is we really don't know.
The properties of the strings, how they act in the universe, what kind of mass they have, what kind of charge, what kind of spin, just how they behave is determined by their vibrations. Their vibrations, the different ways a string will vibrate is what makes the variety of particles that we see in the world. Vibrates one way, you get an electron. Vibrates another way, you get a top quark. But the vibrations are determined by the rules of quantum mechanics, which means they depend on the geometry, which means they depend on the particular way that the extra dimensions are curled up.
This is like Einstein's ultimate revenge. Einstein was all always like, it's just geometry, folks. Gravity is just geometry. And then we go and invent this whole quantum mechanics thing, and we get to string theory, and Oops. Surprise.
The geometry of the extra dimensions determines the physics of the strings. Last time, I used the example of a tuba, and you have vibrations in a string that are allowed. You know, only certain vibrations in a string are allowed, and you get notes like you like you get notes from a tuba. Well, if you have one particular manifold, one particular way of curling up the dimensions, one particular way of choosing one choice of a manifold that will affect how the strings vibrate, which will affect the kind of notes they have, which affects the kinds of particles that they create, that they are, that they behave like. So in one choice of Calabrio manifold, you get a tuba with its notes.
But if you make another choice of Calabrio manifold, you get a violin. And you make another choice of manifold, you get a clarinet. Our universe is only one instrument. The notes produced by the instrument are the different particles and forces of our universe, but it's only one instrument. Which instrument is ours?
Do we live in a tuba universe? Do we live in a violin universe? Do we live in a clarinet universe? We don't know. You think one approach to this?
Like, okay. Okay. Big problem. Yes. There's a lot of spaces.
Like like, just pick one. Pick a random shape. See how all the dimensions are curled up. See how run through the math to figure out how that affects the vibrations in the strings. Figure out how the vibrations in the strings lead to the physics that these different vibrations will have, these different modes, these different notes will have.
Like, oh, that note sounds like an electron. That note sounds like a photon. Or you try it out. You pick a Calabrio manifold. You run through the math, and you see a note, and you're like, oh, that note doesn't sound like anything we have in our universe.
Okay. Reject. Try another one. Make some notes on those strings. Oh, that note doesn't sound like oh, that makes a tachyon.
Can't do that. Don't have particles that travel faster than the speed of light. Sorry. Not that one. Okay.
Try another manifold. Another choice, another set of notes. Those notes don't sound like anything we see in our universe. Yeah. This is a there's a lot of shapes, 10 to 200,000.
So this is a boring, repetitive math problem, but, hey, that's why we invented computers. Right? They're great at boring, repetitive math problems. So we should be able to do a program where we just search through the manifolds looking for which one produces the notes of our universe. Tiny problem.
We don't know how a particular shape affects the vibrations in a string. I'll say it again. We don't know how our particular choice of Calabi Yau manifold affects the ways the strings express themselves. We don't know how a particular choice of geometry of the curled up dimensions affects the notes that the strings will play, the way they vibrate. And, hence, we don't know how a particular choice of how the curled up dimensions are curled up and arranged, how it produces the physics related to that choice of geometry.
We said another way, we have no way of determining which universe is ours. We can't go from a choice of Calabia manifold to a set of notes, to a set of particles and forces. We don't know. If I just gave you a Calabria manifold, you can't tell me if it's a tuba manifold or a violin manifold or a clarinet manifold. So I can't compare it to the sounds I see in the universe and say, no.
You really wanna look for a tuba universe. And if you don't hear a tuba, then it's out. You don't know how. It's like not knowing how to play the instrument. It's like a clavier manifold is just showing up like, here's an instrument, and you're just like, and you're just like, and, like, you don't know how to do it.
Why? Because we don't have a string theory. We don't have a final string theory. We only have approximations of what we hope to be a string theory. This is the whole thing of the perturbation theory.
We only have the approximations. We only have the perturbations. We all have the string theory itself. That was true in the nineteen seventies, and it's true today. We don't know if if string theory is the music of the universe, we don't know how to play the instrument.
There's one more thing that I wanna mention before I go today because we'll we'll come back to it. There's some very basic simple arguments to think that these extra dimensions are curled up at the Planck scale, you know, at this, like, 10 to the minus 30, super important. That's where quantum gravity is. Like, okay. That's fine.
But it doesn't have to. You know, that was Klein's work, but Klein's work was wrong. So, technically, I guess, we can do whatever we want. There is a modification to, quote, unquote, standard string theory called large extra dimensions, where large is is I'm talking like a nanometer or a femtometer, you know, 10 to the minus nine, ten to the minus 20 meters, which in particle physics is pretty dang large, and it's much, much, much larger than the Planck scale, like a billion times or a trillion or quadrillion times bigger than the Planck scale. Still submicroscopic, but just large compared to what it could be.
One of the problems of modern physics, one of the things we don't understand is why gravity is so weak, and it really is weak, folks. It's, like, billions upon billions of times weaker than the weak nuclear force, and it's just as late. That's weak. We don't know why. It's weird.
It's because it's unnaturally seems unnaturally weaker than everybody else. Large extra dimensions are an attempt to explain this. This is called the hierarchy problem, by the way, and we will dig into it more. In this view, gravity lives in all of the dimensions and just some of it leaks through into our three-dimensional world. Like you have moisture, water inside your whole body but some of it leaks out onto your surface, while the other forces of nature are just stuck on the skin itself, just in our three dimensions.
But gravity goes all the way into these large x dimensions and some of it leaks out. And so that's why it's weaker because it has it has to move in a lot more directions. So it just gets diluted by the time we see it in our three-dimensional world. Now you might ask why gravity does this and the other forces don't, but it's best not to ask questions like that. Thank you to everyone who asked me all sorts of questions about string theory, and we will come back next time for our third and final thread in the weaving together of string theory.
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Please keep the iTunes reviews coming. Please, hit me up with more questions, hashtag ask a spaceman. Go to askaspaceman@.com. Email me at askaspaceman@gmail.com. Love all the questions, but we are right in the middle of it, and we are gonna keep going with string theory.
I will see you next time for more complete knowledge of time and space.