Part 2! 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)
What really happens in the microscopic world? And by really, I mean really. So you're gonna shoot two electrons at each other. Why? It doesn't matter.
You're just gonna do it. What happens? What we wanna know is how can we predict what an electron shooter collider experiment will see. Wanna shoot two electrons, and I wanna be able to predict what's gonna come out the other end. Is that such a bad question?
No. It's a great question. When it comes to macroscopic objects like baseballs, I can follow with my eyes. If I have a baseball shooter collider experiment and they shoot baseballs at each other, I can just watch them. Little bit more challenging with electrons.
I can't really follow the electrons as they do their thing. So I need to use math to figure out the details. I need some physics. I need a theory of physics that will tell me how two electrons will interact. The standard approach and the approach that we talked a lot about last time in quantum mechanics, quantum field theory, quantum electrodynamics, quantum this, quantum that, if it's got quantum in the name, the approach is to follow the electrons in the math, tracing out each step carefully.
Okay. These are the trajectories of the electrons. These are when they get close. We're gonna build a model of how they interact when they're right next to each other, and then the math will tell us what happens next. Seems pretty dang straightforward.
Right? You have your math machine that the sole purpose of the machine is to describe how electrons interact. You start your clock at zero, and you let the math do its thing until you're done. And I'm not leading you astray. This is exactly what physicists do.
You have a electron interaction machine, and you just put in the inputs. Okay. I've got two electrons with these energies and these trajectories. Go. Magic machine of science, tell me what the answer is, and then outcomes is like the electrons scatter other goes that way.
That's it. That's how it works. The key ingredient in this, let's say, the meat grinder for your meat is are you ready for this? This is a really fun word. It's called the Lagrangian.
Oh, let's say that one out loud together. Ready? Lagrangian. It sounds so sophisticated. It's named after Joseph Louis Lagrange, who had absolutely nothing whatsoever to do with quantum mechanics, but he was an all around smart guy, and he was able to develop a machine for classical physics for things like gravity and stuff bouncing off of each other.
And we've adopted that language into quantum mechanics, and so it's used all over the place. I don't think he knew he was gonna be this famous or his name would be attached to so many things in quantum mechanics. But, hey, that's life. Good for you, Lagrange. Anyways, a Lagrangian is your meat grinder.
Your Lagrangian is your machine for telling you how things interact. In exceedingly simple terms, what you do, if you wanna model, if you say, okay. How are two electrons gonna bounce off of each other? If you wanna model that interaction, you write down all the sources of energy in a very clever way, all the sources of energy, like like the kinetic energies, the potentials, all that in a very clever way. That's that's the construction.
Congratulations. You've built this Lagrangian. And after lots and lots of nasty math, you can now predict how the system will evolve with time. That's your machine. That's your machine for electron interactions.
It's nice, and it works, except when it doesn't. And we are on episode two of our journey in evaluating if string theory is worth it. But last time, we talked about the motivation for string theory, and that motivation comes from some unresolved problems in physics. And it turns out that physics has a long and storied history of having unresolved problems. It it kind of all the time.
You can wind the clock back a hundred years, two hundred years, three hundred years, and there's always unresolved problems. Most of the problems with enough time and enough sweat, you know, eventually become resolved, which is great, and we actually make progress and learn things about the way the universe works. But physics in the nineteen sixties was facing almost an identity crisis. We were building giant atom smashers. You know, we had a few earlier in the twentieth century, but now we like, we have the technology where they could get really, really, really big.
And we were smashing atoms all over the place. We were slamming them into walls. We were slamming them into each other. And we were doing it in circles. We were doing it in straight lines.
It was all really fun. And we were creating loads and loads and loads of particles. You know, we take a proton and smash it against something and out come all sorts of weird stuff. We learned that, like, protons and neutrons weren't fundamental for a long time. We thought they were they were tiny little things just like electrons.
When we smashed them and they broke into pieces and all the pieces were laying around, we're like, well, I guess it's made of all their stuff. We had protons. We had neutrons. We had pions. We had mesons.
We had cions. We had resonances. It was just it was a mess. We had no clue what was going on. There are just too many things.
This was confusing. We were trying to build models, machinery for predicting and calculating fundamental interactions, but there were too many players. Like, instead of two baseballs or two electrons, there's, like, 50 baseballs and also basketballs and also footballs and also sometimes the players fight with each other, and sometimes they hit each other or bounce off of each other, and then, you know, it's just on and on and on and on. Like, there's just too many things. The Lagrangian, which is the machinery we use to explain and understand and predict microscopic behavior, couldn't make sense of it.
There there was getting too big. It was getting too wheely. Like, we couldn't keep track of everything, and we couldn't make predictions, which is a really lame state to be in if you're a physicist because you like to make predictions. That's the whole point. Faced with this in the nineteen sixties of just what's going on with protons and neutrons and pions and mesons and kaons, we start getting creative with our ideas.
One of the creative ideas was actually born way back in the nineteen forties, '20 years earlier, thanks to none other than Werner Heisenberg. Now I have yet to do a full episode on all things awesome and great in quantum mechanics, but there's one thing you need to understand about Heisenberg. Heisenberg didn't mess around. Nobody puts Werner in a corner. He didn't have much time for these interpretations or philosophies or cats and boxes or blah blah blah.
He was a physicist physicist just shut up and calculate. And when all the people started asking deep existential questions about how our interactions actually took place at the quantum level and what is reality, Heisenberg responds with two simple words. S matrix. Does the letter s count as a word? I don't know, but it stands for scattering, scattering matrix.
He's like, look, guys. All you care about is prediction. Right? That's what we want at the end of the day. That's why we're building Lagrangians.
That's why we're doing quantum mechanics is so that when we run experiments, we can predict what those experiments will see. This is the whole point. So he's like, why don't we just get right to that? Why don't we get right to the prediction step? We know the input state.
Like, we know how we're gonna set up our experiment. We know the inputs. We know it's going to be, say, a couple of electrons. We're gonna put them here, and we have their energies and all that, and just, you know, calculate the output state, calculate what happens on the other side. It's like, okay.
If you if you really all you care in a baseball game is who wins, then just skip all the part about actually playing. Like, just set them up and then just, like, check back later and build a mathematical structure that allows you to just check back later and just find out who wins. You don't care about, like, the plans and, oh, I stole first one blah blah blah blah. You don't care. You just care about who wins.
You wanna make your prediction. You care about results. Heisenberg was a results driven scientist, hence the scattering matrix or the s matrix. It's a strategy that skips the Lagrangian. It skips the details of the interaction.
It skips the meat grinder. It skips the machine. It gets straight to the point. What happens when two electrons collide? Who cares?
What we care about is what we will measure when it's all done. It's a cool idea. Old Heisey gave it a shot. The math was horrendously complex because you're trying to encode all the interactions without actually going through the machinery of the interaction. You're just just trying to skip it and get straight to the end.
In the nineteen forties, a few people try it. Nobody liked it. They forgot about it, and the idea died. But then the nineteen sixties started happening. Everything was groovy.
Everything was hip. I don't know what these words mean, but it was different in the nineteen sixties. And there was a new generation of physicists, and they had new problems. And one of the problems was trying to understand the inner workings of what we now call the strong force. They were just opening up this strong nuclear force in the fifties and sixties.
Once they started running these massive particle colliders, and they were producing heaps of particles all over the place, and they recognized that there is a new force of nature involved in the production of all these weird particles, like the protons and the kaons and the mesons, and they had no clue what was going on. And they couldn't apply their tried and trusty techniques to the problem. They couldn't use, say, quantum field theory to solve the problem of what's happening in these colliders. So they started rummaging around in their parents' attic, you know, looking if one of the great ones had left behind a little nugget of wisdom, a little pearl, a tool, something that they could use. And some folks found a dusty old copy of Heisenberg's s matrix idea.
And since the quantum field theory path wasn't looking so hot in the nineteen sixties, they thought I'd give it a shot. I was like, we got honestly, we're kinda out of ideas. We're a little bit desperate. Insert a montage here of years and years and lots of people working really hard on the math, and there's, like, collider experiments and circuitry and chalkboards and clipboards and conference presentation. So, you know, montage moment here.
And out comes a theory based on this s matrix concept that Heisenberg developed in the forties that has hints of perhaps sort of in a certain way if you squint your eyes explaining the strong nuclear force. Like, it was on the path to approaching like, yeah, we we can develop a consistent way of describing the strong nuclear force if we use these s matrix ideas. One of the features of this theory is that it's starred a certain mathematical function that repeats itself, A mathematical function that repeats itself, that loops back in on itself. That was one it would appear over and over as very, very useful in this s matrix idea for trying to get results. You know where this is going, but they didn't at the time.
But one of the things about s matrix theory remember, like, the Lagrangian technique, the quantum field theory technique, the technique we like to use and had been so successful up until the nineteen sixties was that you have your machine that tells you how electrons or any particle interact. You set up the inputs. You let the clock run forward. They do their thing. The math and machinery evolves all those interactions through time, and you end up with your output.
The s matrix theory skips all that. It doesn't care about time and space. It's just inputs and outputs. Like, you just put your input in, turn the crank, and output, you know, outcomes the results, the predictions of the theory. It it doesn't sit in time and space.
It doesn't evolve a system through time. This made people nervous because we like to think of interactions happening through space and time, And so they worked a bunch of theorists worked in the nineteen sixties to give this s matrix idea in interpretation that we could follow along in both time and space. I know this violated Heisenberg's original intent. He's like, what's the point? But he was dead by now, so he couldn't object.
We're gonna take his idea, which is showing some promise and explaining the strong nuclear force, and we're going to cast it in terms of things evolving through time and space like we're used to. And the mathematical structure in s matrix featured these mathematical functions that tended to repeat themselves, And what did they find when they took s matrix theory and put it on top of the space time and let it evolve? They found strings. They found little itty bitty loops of strings. These strings appeared to be fundamental.
They weren't a field like we're used to in quantum field theory. They weren't a particle. They weren't a warping of space time. They were just strings. Are the strings made of something even smaller?
Maybe, maybe not, but it doesn't matter for our purposes or their purposes. But but what are these weird little strings? Like, you just find it's it's so strange. Like, you have mathematical functions that repeat themselves in the s matrix theory, and then you mush around, squeeze around, and stretch, the mathematics so that you can make sense of it in terms of things evolving in space and time and out pop these little strings. In the early nineteen sixties version of this earliest, almost proto string theory, The strings are just the things that carry the strong nuclear force, and they do it in a very strange way.
Like, if you just ask, like, hey. We just discovered a new force in nature. It's kinda strong. We're calling it the strong nuclear force. Seems like a cool name.
How does it do its thing? How does it make proton a proton? How does it make nuclear interactions work? Well, in this view, the strong nuclear force is just is carried by these little wibbly wobbly bits of strings that that flip and flitter back and forth. How big are the strings?
Well, it's a fundamental object, or or we'll at least pretend or treat it as a fundamental object until we learn something better, and we've never learned something better. So we're gonna go with that. It has an enormous amount of tension. These strings, they're they're just like creatures of pure energy, and so they, like, they just wanna pull themselves in as tightly as possible. They don't like to extend themselves.
They don't like to get nice and big because nice and big means they have a lot of potential energy, and nobody likes to have a lot of potential energy. So they squeeze and squeeze and squeeze and squeeze. They can press to be as small as possible, but they don't vanish, and they don't vanish because of quantum mechanics. Remember, the whole point of quantum mechanics is that energy comes in chunks. Energy comes in steps.
And a lot of times, we find in quantum mechanics that you can't have zero energy. You're just not allowed. Like, an electron around an atomic nucleus can't have zero energy. The zero energy of that system is the electron crashing into the nucleus. This obviously doesn't happen because atoms are kind of stable.
Instead, the lowest energy possible arrangement of an atom is to have an electron in an orbital around the nucleus. Why? Because quantum mechanics. That's why. And so strings try to be as small as possible, but they don't have zero energy because quantum mechanics, and so they scrunch down to be really, really small and tight.
And that smallness is somewhere around the Planck scale. The Planck scale you know, I've I've done episodes on, like, you know, the Planck number or what that means. Very, very basically, the length scale is, like, 10 to the 30 times smaller than u. It's very, very small, smaller than atoms, smaller than subatomic part. It's just tiny.
This is the scale where quantum gravity becomes important. This is the scale where space time gets really, really weird, and we don't understand it. These are the energy scales where we believe the forces of nature are unified. And this is the scale, the Planck scale, this little length scale. This is where the strings end up.
So if you just made a a string, a quantum string, it would naturally shrink itself down to get this small and no smaller. Maybe there's something smaller than that, but we're just so far beyond what we can possibly even hope to understand even mathematically. We're just gonna assume that these strings are fundamental. We're just gonna assume that that's it unless unless we hear otherwise. And in order to do all these things that strings do, they need to be this small because if they're bigger, they wouldn't be able to explain, say, the behavior of the strong nuclear force.
So we've got strings. They're small. They're super small. They're smaller than anything we've ever seen, and they'll vibrate. Why?
Again, because quantum mechanics. One of the weird things about quantum mechanics is that nothing ever sits still. Nothing ever is fixed. Everything's always always jiggling. Always like like like, just too many cups of coffee.
Like this. We're doing great, guys. Like, that's just how everything is. Everything's always jittering around. In strings, these little little loops of stringiness, they're not really made of anything because they are the things that everything else is made of.
Strings are just strings. The same way that fields are just fields. Space time is just space time. We're gonna use the same logic for that. Strings are just strings, and they'll vibrate.
They'll be wiggles, and they'll they'll be different wiggles. And what's amazing, what what people found out in the nineteen sixties, is that these strings, they're very tiny. They'll wiggle in different ways, and the vibrations on the string affect how they behave. Like, if they're vibrating one way, they'll behave in a certain way. And if they're vibrating another way, they'll they'll behave in a different way.
And how a fundamental thing behaves is exactly what we call a particle, because we define particles by what they do, how they are. We define an electron by its mass, by its charge, by its spin, by what it does, how it behaves, how it acts. And and we can tell apart an electron from, say, a photon because they have different masses, different charges, different spins, different rate. Like, they they're just different. They act different.
But strings reverse that. They just vibrate. That's all they do. There's just the string, and there's just vibrations, but they can vibrate in different ways. These different vibrations, like, if they vibrate one way, that manifests as a certain set of properties.
Okay. If it if it vibrates this way, then it's gonna act this way, act as if it has a certain amount of mass, a certain amount of electric charge, a certain spin, and then it vibrates a different way. If you take the exact same string and you make it vibrate a different way, then it starts acting a different way, acts like it has a different mass and a different spin and a different charge. But a string, if you just if I just held up a string, you can make it wiggle in an, you know, all sorts of different ways. You can make it wiggle in an infinite number of ways, but also because of quantum mechanics.
Like, quantum mechanics is essential to understanding how strings behave. Quantum mechanics also says that you can also only have certain vibrational modes. You can only have certain ones allowed on your string. So quantum mechanics is baked into the concept of stringiness. One way because this makes sure that strings just don't vanish, that they just have a minimum amount of energy, which means they shrink down to have a certain size, but no smaller.
Quantum mechanics also tells us that strings will just naturally vibrate because that's what anything microscopic does, and quantum mechanics will limit what kinds of vibrational modes are allowed on a string. For example, let's say you have a tuba. It's your favorite instrument. A tuba can't make every sound possible. You can only have certain notes, only certain sounds, only like resonances inside the tuba.
Only certain combinations of vibrations or waves can make the sounds of a tuba. Quantum mechanics turns a string into a tuba. It's gonna be your choice, folks, over this series of what is the worst analogy. Feel free to vote on that. What?
You can quote me on this on social media if you want or to a friend. Quantum mechanics turns strings into tubas. Wow. Okay. Moving on.
But how a tuba sounds affects how it will be used in the band. Quantum mechanics makes sure that strings have a certain set of notes. Each note corresponds to a different particle. I play one note on a tuba. I have one set of vibrations.
It acts one way. That is one kind of particle. I play a different note on a tuba. It has a different set of vibrations. It acts a different way.
I have a different particle. So on and so on. You can see an example of this as a very, very rough example because it's very, very hard, at least for me, to conceptualize how a vibration in a string can give rise to a certain spin or electric charge. Mass is a little bit easier because string, you've got your string. It's vibrating.
Let's say it vibrates more. That represents more energy. Like, there's there's more energy in the wiggles of the string. It's had more coffee as more energy, and energy is mass equals m c squared. So it's very this is just me.
Like, it's easy for me to conceptualize how different vibrations on a string will give the string different masses. How vibrations give rise to different spins or electric charges, that's harder for me to conceptualize, but it is baked into the mathematics of string theory. And quantum mechanics also may ensures that we only have a certain set of notes. You can't just have any mass of a string. You can't have anything you want.
No. You can have this one. You can have that one. You have this one. Over here, you can have that one, and this is how you get your different particles.
I'm skipping ahead a little bit in the nineteen sixties. They didn't know this. In the nineteen sixties, they were just using strings to try to understand the strong nuclear force, but that's this is where we're going. In particular, strings were a theory of bosons. Here's another fun jargon word, bosons, and I'm going to dig in more deeply, in a couple episodes.
But for now, bosons are the carriers of the forces of nature as opposed to the fermions, which are the building blocks of nature. I did a whole episode on the particle zoo, and we are gonna return to this later when we get into supersymmetry. That'll be fun. There's a lot of words. We're gonna churn through it, and we're all gonna smile and pretend we're enjoying it.
The nineteen sixties version of string theory was just concerned with bosons, just concerned with the carriers of the forces of nature. It was just and especially with the strong force, and the strings discovered in the sixties in the mathematics just, quote, unquote, gave rise. You know, that's the best way I can say is that it gave rise to the properties of the strong force. It's like, you know, they played around with s matrix theory, that they adapted it to have this space and time interpretation to see how things were actually evolving, and they ended up building an instrument. And this instrument had vaguely tubalike sounds.
And one of the notes that this tuba could make sounded like the strong force. It didn't know or care about anything else. There were no other instruments in the band. It couldn't play other notes. They were able to make this tuba play one note.
Yes. I just tried to imitate the tuba. They just played one note, but that note in the string theory kinda sorta smelled like the strong nuclear force. Quantum field theory was having a really hard time explaining the strong nuclear force. There it was just too complicated.
There are too many particles involved. There are too many interactions, and it was just going crazy. The difficulties that plagued quantum field theory to explain the strong nuclear force were handled in a different way by the strings. I remember when I was taking this note, I almost wrote easier. I almost said the difficulties that play the quantum field theory to explain the strong nuclear force were handled in an easier way by the strings, but it's not quite.
That's not entirely true. The strings were just different. Quantum field theory was having some difficulties, but string theory wasn't always it's not like string theory was just like, ta da. Here's an explanation of the strong nuclear force. No.
There are some hints. There are some things that that kind of looked like the strong nuclear force, but it wasn't easy. It wasn't great. But since at the time, quantum field theory was totally stuck in a morass, which was really annoying because quantum field theory just had so many great successes in explaining electromagnetics. And now it was like, oh, by the way, there's a new force, and, like, our fancy new theory couldn't explain the new force.
People were eager to try new things like this, you know, this, like, string interpretation of the strong nuclear force. Perhaps that's the best way to say it. One of the problems with applying quantum field theory to the strong nuclear force is that there were too many interactions. Remember last time we talked about how two electrons bouncing off of each other? In there, there's an infinite number of ways for two electrons to bounce off of each other.
And so you have to work out all the different ways, and you have to come up with very clever machinations to get around that so you can actually make a prediction. And this would this procedure was going nuts with the strong nuclear force because there are just too many things involved. There are just too many characters, too many players. It wasn't just two electrons. It was just too many things.
And so quantum field theory was falling apart. But string theory was able to make some progress because strings have an extent, because they're they're actually large. Because string theories actually take up some space, they they almost smooth over the interactions. Like, it's just a bunch of interactions that you're worried about. Like, oh, what happens if if the photon splits off into a positron and an electron and then those split off?
And it's like you get, like, really, really stressed out. Because the strings take up space. It's like like sticking your thumb on a bit of dirt and just smudging it out. You're just like, no. No.
Don't need to worry about it. Smooth it's just it's just cool, man. Don't worry about it. The spatial extent of the strings helps get rid of some of those problems. You got too many interactions, and the interactions are happening at really, really small scales, like, say, around the playing scale.
Like, that's where you're getting all this little fizz and jitter and extra corrections, and it's making life miserable right there, well, the string is just like, oh, you don't have to worry about that. Say, go on. Keep doing your calculation. But you know what? Don't worry about all those extra details.
I got you covered. The strings, just do that. They just make life a little bit easier in that regard. Just like, don't worry about the details, man. Just focus on the big picture.
Strings yeah. That's exactly what the strings do. There's just focus on the big picture. So strings present a different different picture of how, say strong Force operates or later as we would discover and we'll we'll go over how anything interacts. You start with instead of having two particles or two fields doing complicated things, you have two strings, two wiggling vibrating strings, and they get close to each other, and then they kiss, and then they touch, and then they merge, and then they're one big string for a while, and then they separate.
And there's like, you know what? I I just wanna be friends. And then they break apart, and then they go on their merry way. That's a much different picture of how subatomic interactions occur. For one thing, it's there's no bouncing.
There's no exchanges of anything like photons or whatever the strong nuclear force is. There's just strings merging and unmerging, falling in love and breaking up over and over and over again. And then all the little calculations that you had to do, all the tiny little interactions that were causing so many headaches, Strings, just forget about that. It's just don't just focus on the strings merging, and you'll get the job done. That sounds nice.
Sounds lovely, actually. Actually. Like, wow. I don't have to do all those calculations? I don't have to worry about the small stuff?
String theory is just going to be the story of two strings merging together and then unmerging, and that's all I need to do to understand fundamental subatomic interactions? Wow. Not so fast. The actual guts of the procedure, the actual machinery, the like, how string theory operates involves something called here's another fun jargon word, and this is gonna crop up over and over and over again, so we better memorize this one. It's called perturbation theory perturbation theory.
You know what? Just take a breath. Put this episode on pause. Dry for a bit. Jog.
If you're jogging, just be quiet for a while. Go grab a sandwich. I'll grab a sandwich. I'll be right here when you're ready to come back. Welcome back.
We need to talk about perturbation theory. Let's say I wanna buy a couch from you. You've got a couch for sale, and I wanna buy it. Is it leather? Is it a sectional?
It doesn't matter. It's a couch. And you're selling it, and I wanna buy it for the purposes of this analogy. How will I pay for it? Well, it's a good thing you contributed to Patreon.
Go to patreon.com/pmsudder. As little as $1 a month It keeps this show going, and it lets me buy a couch from you. So it's it's win win all around, honestly. So I swing by your place to, check out the couch because I wanna make sure it fits in my living room. Like, I wanna know how big your couch is.
And for some reason, you can't just tell me, so I have to do this myself. First crack, I'm just gonna eyeball it. I'll look at it. I'm like, it's about eight feet. Right?
And if you're on the metric system, you don't know how long it is. Don't worry about it. It doesn't matter. Okay. It's it's the length of a couch.
Like, it's about an eight foot couch, but I wanna be a little bit more precise. So I take that old calculation. I knew it was around eight feet, but then I, like, you know, go to the edge and, like, I I spread out my hands. And I'm like, oh, oh, yeah. I'm using a slightly more accurate method.
I the couch is eight and a half feet long. But I really like you know, it's gonna be very tight squeeze, like, through the doors and stuff, so I wanna be a little bit more precise. So I get out a ruler, and I know it's around eight and a half feet, but I get a little bit more precise method. I'm like, oh, oh, oh, actually, there's a little bit overestimated. It's actually 8.4 feet.
But you know what? I just I just really, really wanna know. Little bit more precision. This this just isn't good enough, so I'm gonna take a fourth crack. I'm gonna get a laser.
Yes. I'm really serious about this. Now I use a laser, and I get 8.3875 feet. Good enough. Now I know.
Now I know I can buy the couch. We just used a perturbation method. We started with a rough guess, and then we made refinements on top of that guess using more precise tools. But each tool was a little bit harder to use. Like, it's easy to eyeball something.
It's a lot harder to use a laser. Perturbation theory is at the heart of basically all physics, especially subatomic physics. Seriously. All physicists just spend all day long sitting in front of computers being perturbed. Why?
Because math is hard, and we want to make it easy. We just wanna make predictions for experiments like Werner Heisenberg taught us and go home. Perturbation theory allows us to start with the simplest possible scenario and then build up more and more position until it's good enough, like it matches the accuracy of our experiment. And then, okay, done. We don't need to calculate anymore until the experimenters build a bigger version of their machine.
But for now, we're it's good enough. This concept of perturbation theory only works if each level of difficulty, each added calculation makes only a small change on the final answer. So you can start with your rough guess and then build more refinement, and you're not really moving very far away from your first guess. That's the only way to know that when you've stopped, when you say, okay. I've reached enough.
I I had the laser, but I'm not gonna go to a more advanced method to measure the length of the couch. That's how you know that you've actually reached your desired level of precision. Because if you added more and more complicated calculations and the answer was bouncing all over the place, then you'd have you'd have no clue if you were done or if you'd ever be done. In case you're wondering, this whole discussion from the last episode and this episode about all the possible ways that two electrons could collide, starting with, okay, they just exchange one photon and then, oh, they exchange one photon. But in the middle of the process, that photon splits to become an electron and positron before reemerging, reemerging back to be a photon and, you know, etcetera, etcetera.
That was perturbation theory. That was perturbation theory. Perturbation theory is how we understand and do the machinery of calculating, say, how two electrons bounce off of each other. Perturbation theory fails when gravity is taken to account because there's too many complex things going on that don't just make a small change, they make a big change. Every time you change space time between those two electrons, your answer goes all over the place, and so perturbation theory just collapses.
You can't rely on it. String theory smooths over a lot of the issues with perturbation theory because it just says, like, oh, there are just some things you don't need to worry about. Like, you don't need to go down to that deep of a level with all these super submicroscopic interactions. Like, you just don't need to care about it because you just need to care about two strings merging and then splitting apart. But string theory does have a perturbation theory too.
String theory smooths over some problems that we have in quantum field theory, but it has its own problems too. It still needs perturbation theory. Why? Because no matter what, you're gonna live in a quantum world. No matter what, there's gonna be more than one way for two particles, whatever they are, whether they're fields or strings or whatever to interact, and you just can't get around that.
But what you end up doing is have a different way of constructing that. It could be that two strings get close to each other. They kiss. They merge together, become one string, and then they split apart. Okay?
That's one path. You can also have two strings merged together, become one string, split apart, then merge together again, then split apart, then merge together again, and then split it off for the final goodbye. Like, getting back with an x once or twice or 53 times. There is more than one way for two strings to collide and be together for a while before parting ways. An infinite number of ways for strings to interact.
So at first blush, string theory has the exact same problem that quantum field theory does. Quantum field theory, there's an infinite number of ways for two electrons to interact. We're able to solve that problem through perturbation theory because we can say, oh, all the extra ones, once we reach a certain level, once we've included enough interactions, we simply don't need to care about the rest, and we can bundle those up together. We can use some fancy math tricks, and we can actually make a prediction. Also, this is perturbation theory.
String theory also has a perturbation theory, which it starts with just the simplest way for two strings to merge and interact and builds up to more complicated ways. Is string theory like quantum field theory where perturbation theory works, where we know that we're getting closer and closer to the accurate answer, the correct answer, the more levels we add so we know that when we stop, that's as far as we need to go? Or is it like quantum gravity where perturbation theory, we don't know if it's right, where every time we add a new interaction, the answer goes in a completely new direction, and it's hopeless? Which is it? Is the perturbation theory used in strings, like, good or bad?
Is it useful or useless? And you're ready for the answer? In the nineteen sixties, we didn't know. And today, we don't know. The thing is we don't have an actual string theory.
We only have the perturbation theory version of it. We don't have the actual tool like we do in quantum field theory. We have something that we hope looks like the tool but is easier to work with, but we don't know if it even resembles the original tool at all. We have quantum field theory. We have quantum electrodynamics.
We have these field theories. They're too hard to work with in a lot of cases, but we can use perturbation theory to actually make progress and make predictions, which is what rescues us. String theory, we just have the approximation. We just have the perturbation theory. We don't have the actual string theory to compare to.
For an example, let's say you have a complicated machine press with lots of buttons. It's very, very powerful, but it's really, really hard to use because you lost the manual. Perturbation theory is like a hammer. It's much simpler to use. It can't be used in all applications.
But since we have the complicated machine press to compare it to, we know when we're using the hammer that it's the right application. Like, when we need to make things flatter, the machine presses do complicated. There's too many buttons, but, hey. I can take a hammer to it, and I can get close enough. In string theory, we have a screwdriver and just a screwdriver.
And, sure, if you're trying to build a house, a screwdriver will come in handy, but it can't be used for all the jobs, and we don't know which jobs are best. We just have the approximation. We just have the screwdriver. Is there real string theory a power drill? Like, are we close with our screwdriver to, like, up generally approximating what the actual string theory is capable of doing, like a hammer can kind of approximate what a machine press does?
Or is it a circular saw? Is the real string theory a circular saw? In which case, we're sitting here holding the screwdriver saying, wow. We're way off base. We are using the wrong tool.
We don't know. The methods developed in the nineteen sixties based on s matrix and given this stringy interpretation were only approximate methods. There is no actual theory, just ideas that loosely collected to form what we hoped would be a theory, and that situation hasn't really changed in sixty years. And I'm just gonna leave the implications of that hanging there for now, but don't worry. We'll come back to it.
We have no form of string theory. We have no actual string theory. We have approximations to what we hope is string theory. But in the nineteen sixties, we still have this approximation method. We still had a screwdriver, so we went around seeing if if this would be useful.
Only at the time in the nineteen sixties, it was only used to explain the strong nuclear force. These approximation methods were used, like, the mathematics that we actually had, the tools that we actually had, the perturbation theory that we actually had were used to make predictions for the behavior of the strong force, and it got it wrong. And what's worse, the theory predicted the existence of something called tachyons. Tachyons are particles that travel faster than light. That was kind of a red flag.
That's like, wait a minute. We know the tachyons don't exist. We know that there's particles that don't travel faster than the speed of light. And you're saying that this toolkit, which makes wrong predictions for the behavior of the strong nuclear force, also predicts the existence of particles that travel faster than speed of light in blatant and arrogant and offensive contradiction to special relativity, which has been tested six ways to Sunday. It wasn't looking good.
By the late nineteen sixties, early '19 seventies, quantum field theory was able to tackle the strong nuclear force. We had to invent a few things. We had to invent quarks and gluons in order for quantum field theory to understand the strong nuclear force. But once we realize that, like, oh, I see a proton is actually made of three quarks, and they exchange there's a new force carrier called the gluon, and there's eight of them, blah blah blah blah blah. We can apply the machinery of perturbation theory, quantum field theory, all of our toolkits where when we're able to make predictions and understand the world of the strong nuclear force.
And, really, the this early version of string theory, this kind of proto string theory, should've just died right there. We didn't have a full theory. We only had the approximation methods, so we didn't know if we were right. It was making predictions that violated experiment, and it predicted the existence of particles that simply were impossible to exist. It shoulda died.
And to a large extent, it did. A lot of people put away string theory. When the nineteen seventies had some surprises in store, And I'm gonna get to them, but not yet because there's one little nugget of the early string theory that is weird. And the weird part of the early string theory that I wanna talk about next is that it can only work in a universe with 26 dimensions. That is weird.
Thanks to all the fantastic people that asked me questions through all these years about string theory, including John c on email, Zachary h on email, at edit room on Twitter, Matthew y on email, Christopher l on Facebook, Krzna w on YouTube, Sayan p on YouTube, Neha s on Facebook, Zachary h on email, Joyce s on email, Mauricio m on email, xrennickshrah on Twitter, Panos t on YouTube, Dhruv r on YouTube, Maria a on email, Tur b on email, Oi Snowy on YouTube, Evan t on Patreon, Dan m on Patreon, unknown on the website. John t on Facebook at TW Blanchard on Twitter, Ari on email, Christopher m on email, at Unplugged Wire on Twitter, Giacomo s on Facebook, and Gully Foyle on YouTube. And, of course, thanks to all my top Patreon contributors this month, Matthew k, Justin g, z, Justin g, both Justins, Kevin o, Duncan m, Corey d, Barbara k, Newdude, Chrissy, Robert m, Nate h, Andrew f, Chris l, John, Cameron l, Nalia, Aaron, and Aaron s. It's your contributions and everyone else's that Keep this string train rolling. And you can go to patreon.com/pmsutter to learn how you can contribute.
Thanks to everyone for listening. We are gonna keep going in this journey of strings so that we can finally judge it. But it's gonna take a while, but we're gonna enjoy the journey for what it is. And I will see you next time for more complete knowledge of time and space.