People might disagree about what kind of art they like. In fact, pretty much everybody does. But we all know what it means when we say that something is beautiful. It means that we appreciate it, that it moves us, that it strikes us, that we see an elegance in it. But what does it mean if you say a theory of physics or a little bit of math is beautiful? How can math be gorgeous? How can physics be elegant?
What does that really mean? Well, string theory is the theory of physics that's most often described as a bit of twenty first century gorgeous physics that fell into our laps. What does that really mean? What is so beautiful about string theory? And just because something is beautiful, does that tell us whether it's more likely to describe our universe to actually be right? That's the question we're going to be asking today on the podcast What's so beautiful about
string theory? Welcome to Daniel and Kelly's Extraordinary Universe.
Hello, I'm Kelly Wiener Smith, and I know nothing about string theory. In fact, sometimes my eyes crossed and I just blankly stare at the wall. When the conversation comes up, But today I'm gonna understand it.
Hi. I'm Daniel Whitson. I'm a particle physicist, which might make it sound like I should know string theory, but actually it means I just smashed particles together without understanding the nature of the universe.
Oh all right, Well, so I've got a question for you. I listened to your beautiful opening about what does it mean to have a gorgeous equation? So my question for you is, what is the most beautiful equation?
The most beautiful equation? Oh my gosh. To me, the most beautiful equation is actually not in physics. It's in math. Oiler's identity. It says E to the IPI plus one equals zero, And I just think it's incredible because it combines like a bunch of different stuff. You have E, pie zero, one and I all together, and it's so compact, and it's just so much encoded into it. It's like so dense with useful information. It tells you about how you can think about signs and cosigns in terms of
complex numbers. To me, it's just fascinating to have so much information packed so tightly and so beautifully into a single equation.
Awesome, A fine choice.
But I also have to say that in grad school, the moment I discovered I was not going to be a theoretical physicist was when I was sitting next to my office mate and I realized that he did his homework just like I did, but he did it two or three times in different fonts because he got really excited about like writing these equations. He's like, Oh, I'm all writing in italics, or I can write these symbols another way. And I realize, like, wow, this kid really
jams out about like writing down the equations. It's something about being a theoretical physicist that I just didn't have. I was like happy to be done with it once.
Yeah, I gotta be honest, that doesn't strike me as super efficient. I'm going to do the same thing three times, but I'm glad that he's super into it.
Yeah, but there's something about the equations and the formalisms and the expressions and even the fonts. The way you're writing these mathematical symbols, then you've got to be excited about if you're going to work in the nitty gritty of figuring these things out. Because being a theoretical physicist is a lot about writing equations on paper, So if you don't like that, then probably shouldn't be one.
Yeah, fair enough.
Well, today we're talking about a theory that is regularly described as beautiful, and I'll tell you by the end of the episode, I'm moderately convinced that string theory is beautiful, maybe even more than moderately convinced. But I think we should see what our audience thinks about out what's so beautiful about string theory? Is this something that people know already?
That's right. I reached out to our listeners to ask them what do they think is beautiful about string theory. If you'd like to contribute your voice for future episodes, please write to us two questions at Danielankelly dot org. We will sign you up. Also send us questions about anything. I got a recent question about somebody's dating life which I totally couldn't answer, but I enjoyed reading anyway, so feel free to write to us.
You should have sent that to me.
I was on Dan Savage's podcast, and I feel like that makes me a relationship expert, so you can just send those to me.
I've got it covered.
Okay, there, you go, folks, We are self proclaimed experts in anything, So think about it for a minute. What do you think is beautiful about string theory? Here's what some listeners had to say. I don't think the universe would be so elegant to be a dangled, naughty strandfield.
Mess unifies general relativeivity and quantum mechanics. Physicists love elegance and symmetry. It may also provide a new baseline of what's the tiniest thing, And then we.
Get to ask the question is that it? Or is there something beyond that? The amount of money that Brian Green was able to make by taking advantage of popularizing it, we're able to mathematically explain why gravity is so weak compared to the other forces.
So nusks, Dodd, what is string theory? The dad says, why you ask such difficult questions? Ask me something easier. So the sun says, okay, why does mum get so angry?
Ah?
Well, string theory is a theoretical framework.
It's a kind of symmetrical beauty.
The beauty to me is that we keep searching for the boundaries that would have to be the g string.
Nothing's beautiful best string theory except that confusion is beautiful. People want to try to bring everything thing all together into one unified theory that explains everything. I think that's what makes it beautiful.
And they look like worms string theory in all the theories that try to bridge this gap really show the spirit of scientists and researchers and physicists everywhere to keep on trucking.
The totality of its failure in the same way that a lot of other unfalsifiable and self sealing things are in life that we.
Love that the maths of it all is quite elegant.
What I like about the idea of it is that rather than trying to think of the universe in discrete particles, kind of just thinking about it in like pulses of energy.
I cool it confusing.
Well, Daniel, it looks like we're teaching the controversy today because our.
Answers range from I don't think there's anything.
Beautiful about it to you know, it's pleasing esthetically, And there was a good range of answers, what do you think is it beautiful?
I think it's fascinating to apply this subjective standard to something which is supposed to be objective. Right, we're talking about like the answer to the question of how the universe runs itself, the machinery of the cosmos. Why do we care about whether it's beautiful? Why should beauty be a guide? Like if we have two theories, should we pick the one that's more beautiful and follow that because
we think it's more likely. I think it's this sort of like bias we have that we think nature should be beautiful because we mostly look around and we're like, oh, yeah, the world is pretty. I wonder if aliens evolving on an ugly planet, one that they find like if kind of yucky, would tend to be biased towards yucky theories of physics because their life is pretty yucky. Or maybe everybody of alves to think that their planet is beautiful
and everybody tends towards beauty. I don't know. To me, it's a deep sort of philosophical question of what is beauty anyway, and why do we appreciate it in our world and why do we look for it in our physics?
All right, So first an observation in my experience, it seems to me that when people say, oh, this equation is beautiful, what it usually means is it makes their life easier. It explains a lot of things. And maybe this is human laziness is the wrong answer, because most of the people working on these equations or anything but lazy. But like, oh, it's nice. It explains a lot of things.
I don't have to worry about that stuff. So you did seem earlier to think that Euler's equation was beautiful, but now you seem to be a little bit more critical of people saying talking about equations that describe the universe as beautiful.
Do you feel like there's some difference there.
No, I can see beauty and I can appreciate it. It's like when you see a piece of machinery and there's only a few moving parts, but it can do something really complex, or you look at a piece of code and you're like, wow, that is so simple and yet powerful. You can appreciate the beauty of that. I just don't know why the universe has to work that way, Like
the universe could be a total mess. We could discover the way it works, be like, actually, I have some notes this could have been done better, you know, like more documentation please. So I can definitely appreciate beauty when I see it, and I think I can even capture what he's beautiful about something. I just don't know why we expect the universe to be beautiful. I mean, I hope that it is, but we'll see.
I mean, I think the universe is beautiful, like the sunsets are beautiful, the biodiversity is beautiful. But it certainly seems to me that anytime we try to explain what's happening, there's nothing beautiful in this.
But maybe that's just the.
Biologist working on ecological models, where we're like, this is a mess, and cells are a mess, and everything's a mess, but we're all just muddling forward.
And let's not even get into chemistry because that's a disaster.
Now, we weren't going to get in a chemistry Daniel, that's not what we do.
That's right, exactly. But neither of us are also string theorists. And so I reached out to somebody I know online, Thomas Van Reed, who is a string theorist and writes about this stuff. And I've seen him on social media venting gently about how string theory is not well understood and mis explained and misunderstood by the general public. So I invited him to come on the podcast and tell us all about it.
Let's jump right in.
So then is my great pleasure to welcome to the podcast Professor Thomas van Reid. He's a theoretical physicist at the Institute for Theoretical Physics at ku LEEUFN. Some of his recent work include papers called the Stability of axion, saxyon wormholes, and the quantum theory of gravitation, Effective field theories, and strings yesterday and today. So I thought he'd be a good person to talk to about string theory and its alleged elegance. Thomas, thank you very much for joining us.
It's my pleasure to be here.
So my first question for you is, what is this big problem that everybody's trying to solve. We hear a lot in popular science about how we have general relativity and we have quantum mechanics and these two theories don't work well together, and we need some theory of quantum gravity. Why do we need a theory of quantum gravity? What is this big issue? Why can't we just have gr and quantum mechanics and be happy with those.
So in everyday life, gravity is a classical force and there's no problem in understanding gravity. Sometimes it's a bit complicated, especially you know when you're looking at say, black hole mergers, you need full blown relativity. But it's still a classical theory. You can put it on a computer, you can do advanced calculations and you can understand what's going on.
And what do you mean when you say a classical theory? What does classical mean? It sounds like a technical word you're using.
Classical can mean two things. In physics, it's very confusing. So classical can mean that you do newtont mechanics and you don't do relativity. Relativity is a correction to Newton mechanics, and the correction takes into account that the speed of light is finite. So physics theories are always corrected by
some numbers. And you can think of the difference between relativity and Newton mechanics to be that one theory is corrected by the other by numbers which go like one added by the speed of light, which is a very tiny number. So that's the first sense of classical. I actually meant the second sense of classical, and that's where you say I take say it doesn't matter whether it's a Newtonian or a relativistic theory, but I add quantum mechanics.
They're in quantum mechanics. We also have a small number called Plank's constant, right, So very informally speaking, you could say that quantum mechanics correct classical mechanics by terms in equations that are powers of this small number.
So classical is a fuzzy word that basically means old fashioned, the same way like you might call classical music Mozart, but the kind of music I like to listen to is called classic rock on the radio, even though it's not that old. And so you're talking about two different senses in which physics has evolved from Newton to Einstein, and then from Einstein to like Schrodinger and Heisenberg and stuff.
And so in this sense, when you say a classical theory physics, you mean without quantum mechanics.
And you know, some of that must is pretty old. By that man, we are getting a little bit old, I'm sorry.
And for the record, notes are totally rocks.
Ok Okay, no, I'm not disagreeing there. So the biologist who's trying to keep up with the physicists here, all right, So it sounded to me like you were saying, quantum mechanics and general relativity can be reconciled if you just.
Divide by the right terms.
I was under the impression that they describe completely different phenomena and kind of don't work together at all.
It's too quick to say that they can easily be combined, but it's also too quick to say that they cannot be combined. So, first of all, indeed, are there regimes of interest where the two theories should be combined. Because usually gravity we think of very large things. Gravity is so weak that in order to see it you need
to have large objects, massive objects. You know, the Earth is pretty big, and I can still lift my glass of water from my table, meaning that, you know, the electromagnetic forces in my body are stronger than the gravity of the full Earth. So gravity is weak and things need to be big to be able to see it.
There's another option, if things are dense enough, you know, imagine taking the Earth and compressing it into the size of my water cup, Okay, and then even compressing it more so, then of course I will get into a regime where you say, well, you know, it becomes very small, and then the theory of econom mechanics becomes important. Yet also gravity becomes strong. And you can ask do we know of such regimes? And we do. I would say it's the most important regime for all of physics. It's
the early universe. So if we go back in time and we look with our telescopes, so looking with the telescope means that you look back into the you look into the past, you see that the universe was denser.
And if we just follow our classical equations, it actually tells us that the density will go to infinity, which is of course not true, but it isn't in the cation that in the very early universe, you know, everything was very tiny, so quantum mechanics was absolutely important and gravity was huge, so we need a theory of quantum gravity. One other example that we have already measured are black holes. Some black holes have always been a sort of a
theoretical invention, but they're not anymore. We have seen them. They're out there, okay. And what you sometimes wrongly hear when people you know, talk about signs in a for the for the bigger public, they would tell you that black holes, for sure are objects were Quantum gravity is important because gravity is strong near a black hole. That's
actually not entirely correct. If you look at a big black hole, for instance, a black hole in the in the middle of our galaxy, the gravitational parts that the horizon of that black hole is big, but it's not ridiculously big, okay, And the bigger a black hole, the weaker gravity is at the horizon of a black holes.
It's kind of entry intuitive a bit is that because you're further from the.
Center exactly, and it's also because the density of the black hole goes down as the black hole grows like the black hole. I think, if I'm not mistaken, you can always fact check this. But I think the black hole in the center of our galaxy as a density compared to water. So it's wrong to say that for sure quantum mechanics will be important near the horizon of a black hole. But what we are pretty convinced of is that if you would jump in a black hole,
we don't know what's there. But it cannot be classical physics anymore because at some point the classical equations tell you rubbish. They tell you things which are impossible, so we know the classical theory has to break down. So the assumption is that just as in the early universe, in the very center of a black hole, there's also quantum mechanics and gravity at play at the same time.
So I want to get back to what you said about things breaking down, but in a minute. First, I want to focus on this question of quantum mechanics and gravity at play at the same time. So you told us earlier that general relativity, or we can call it gravity, describes usually big things, and quantum mechanics usually describe small things. And now you're saying that at the beginning of the universe and inside black holes, we think both of those
are relevant. And that's why we need a unified theory, because we need some way to describe that and to disagree to conflict. Why is there a conflict and their predictions. Couldn't it just be that they make the same prediction for what happens in that scenario. Couldn't it just be beautiful, a fortunate harmony among the theories.
How what's the quickest way to explain? So let me give you an example that I hope more people know, maybe even from high school or first year of university. Say, okay, think of an electric field. So you have a charge particle, and a charge particle is surrounded by an electric field that it sources itself. So when you look at it classically, and when you think of a particle classically, it means
that a particle is a point. And maybe if people remember this still, there was this formula that it said that the strength of this electric field went like a negative power of the distance from the particle. Say, you know, take it's one over our squared. That's actually that the force. Then you find that this force becomes infinitely big as you approach the particle. Okay, it's the same for the energy. The total energy carried by that particle would be infinite.
And we know that can that cannot be correct. And then we have learned later on one hundred years ago, when people understood the quantum theory of charged particles, there was nothing going infinite. Things were just super well behaved, numbers were finite. Nothing weird was happening. And gravity is that sounds completely analogous, right. Even the formula for the force of gravity is almost the same as a formula
for the Kulan force. Both can give you infinities. And for the cool on force, we learned that that infinity is gone when you treat it quantum mechanically.
Both general relativity and quantum mechanics at some point start giving you infinities that make no sense when you push them to their extremes.
So quantum mechanics doesn't give you infinities, but the classical theory does, so relativity does. Yeah. So then the question is, if you treat relativity in a quantum mechanical way, would you get sensible numbers? And do you Well, that's a good question, so yeah, to be able to answer it, I should I should tell you this is the theory that of quantum gravity. And to say that something is the theory of quantum gravity, I mean you can write down a theory which is extremely hard, but imagine you
succeed and people succeeded. You don't know whether it's the only option, right, so you need to Normally you test the theory. And the problem is that to go out and test it requires you to look for these, you know, places where gravity is so strong, and I guess none of us wants to jump in a black hole. You could, but you know, you could test it, but unfortunately you would not be able to tell anymore to anybody else because you cannot escape from the black hole. Right, So
nature is playing a very mean trick on us. It seems that humanity, in order to test the theory of quantum bravity, it is forced to do something that kills you. You know, this actually goes under the name of censorship, cosmic censorship. It's actually something quite serious in the physics community. Gravity works such that you could actually just see quantum bravity. Unfortunately, there's always what we call a cosmic horizon preventing you to see it. Either it's the horizon of a black hole,
or you have to go back in time. But if you take your telescope, it's actually impossible to directly look at the Big Bang. So that's kind of mean. Otherwise you could just observe it.
Yeah, it's frustrating.
Religious, I would say God is playing you know, is an evil person, so to speak.
Yeah, I also believe in cause free speech. I think the universe should be free to tell us how it works. And I'm bummed about all this censorship. Okay, I have a lot more questions, but first let's take a quick break and let our brains rest a moment. Okay, we're back and we are talking to Thomas Van Riet, a self proclaimed string theorist, about how strength theory works and why it's so pretty. So let's go back to this question of infinities. You said just a moment ago that
it's hard, and we hear this a lot. Quantum gravity is hard. It's the hardest problem. And you're telling us that we have general relativity, which works beautifully outside of event horizons, and after some critical density in the universe. We have quantum mechanics, which works beautifully and very effectively for very small things and very high energies. Why is it hard to bring these two things together? What is the challenge? I mean, We've made a quantum version of electromagnetism,
We've made a quantum version of the nuclear forces. Like, why is it so hard to take gravity and make it quantum?
It is hard for two reasons. Maybe they're more, but there are two that are very sort of prominent. So one of them technically goes under the name that the theory of gravity is non renormalizable. We can come back to that it has to do with infinities of sorts. But actually we have some experience with non renormalizable theories in the past and resolve them. But still it usually means bad.
It's tough.
That's already what it tells you. The second thing is that gravity, at the same time is a theory or a classical theory of space and time, a theory of the background. Okay, so in quantum mechanics, the way the loss of quantum mechanics are formulated is that you assume that this background is fixed. What does it mean in practice is that you have two For instance, in let me try to give a good example that doesn't sound
too abstract. In quantum mechanics, you use the notion of two points in space time, whether they're what we call costly connected, whether they can talk to each other, whether you know you can send a lightweight from one point to the other.
You're talking about light counes.
Exactly, but somewhere maybe less technical. Imagine that right now there are people I don't know, ten kilometers away from us. If we want to communicate with them, we cannot do it right now. We can do it in a you know, a little bit of time, the little time it takes to send the light way. But so the two points that are us here right now, and then people a
little bit away, we are what you call disconnected. But imagine now that you have a theory of space and time where space and time are globally that's what relativity tells you. Then maybe that that whole notion changes, right as a quantum mechanics is telling you that things fluck to it. Things are very wobbly at a small scale.
They're so lobbly that maybe you know in your equations what you thought are disconnected points, maybe they're not disconnected anymore because you're wobbling your background that is telling you that it's connected or not, And that's what makes it kind of annoying.
Daniel, is this going back to our map analogy that we keep bringing up on the show or is this something different?
This is the same, Yeah, that's exactly right. In GR, we have the concept of distances which are not fixed, right, which can change. Whereas you're saying, in quantum mechanics, this is essentially the background. So quantum mechanics is assuming that there's a stage on which everything is happening, and GR is like the theory of that stage, and it's changing underneath it. But what I don't understand is why that makes it hard, Like can't we do quantum mechanics on
curved space? You know, you can think about your fields and my quantum mechanical view of space time is like, yeah, you have this backdrop and you put fields on top of it, and then you do the physics of the fields and stuff is propagating. Is it hard to do that quantum mechanical field theory in a curved space time? Having people been able to do that? What's so hard about that?
Very good? So indeed, relativity can curve space time, and then you need to formulate quantum mechanics on curved space. That is not easy, but that people have done for sure. One example why that is not so easy is that quantum mechanics tells you there has to be a global time direction. Things move forward or backward in time. On a curved space time, what you thought was time can actually at some point become space or vice versa. And a famous example is a black hole. Imagine you approach
a black hole, you jump through the horizon. What do you know is that you have to move forward to the singularity. But you see that means that that spatial that action became time because what is time for us? Time is the only dimension in which we cannot stop moving forward. I can decide now to sit on my chair, but I cannot decide to move backward in time or be still in time. I always have to move forward.
So the fact that once you pass the black hole horizon, you're moving forward in time, forward towards similarity me is that that forward direction became time, and time became actually a spatial direction. So for quantum mechanics, for shredding equation, that's pretty annoying, but we learned how to deal with it, and dealing with it gives you this amazing phenomenon, like
talking evaporation of black hoves. But what I said about quantum gravity is still something different because in quantum gravity, it's that curve background that is it self fluctuating under the confluctuations. Right, So there's no problem doing quantum mechanics on a curve background. It's just a bit more complicated
because of the problem I told you. But now the background itself should become dynamically in equalum theory, so that your standard sharting equation is not well formulated to deal with the fact that the background itself is the thing that is part of the theory.
I see. So you can do quantum mechanics on flat space, that's easy. You can do quantum mechanics when space gets curved. That's a little bit more technical, but people with big
brains to figure that out. But having the space itself respond to the quantum mechanics, to have it all be dynamical and link together and be harmonious, to have this back and forth where energy is telling space how to bend and space is telling matter how to move, that is too technical for people to have figured out, or that's the challenge.
That's a challenge ship absolutely.
And this I think also connects to the other comments you made about renormalizable theories, which I think is worth digging into for a minute because it connects to the example you talked about a moment ago about an electron having apparently infinite charge or apparently infinite energy. Right. If you take an electrons charge and you look at it
from a distance, it appears to have charge of negative one. Right, But as you say, an electron is surrounded by its feel and that field you can think of as a cloud of potential particles. And so if you actually think about what the charge of the electron is that we measure. It's the charge of the electrons surrounded by the cloud, right, And as you penetrate deeper into the cloud, you measure
a more and more negative charge. And then that charge if you get all the way through the cloud to the electron, the charge apparently becomes negative infinity, which is crazy and bonkers and unphysical. And so you were talking earlier about renormalizable theories and how we've managed to patch this up with quantum mechanics. Can you say a few words about what it means to renormalize the theory? How do you get rid of an infinity in the theory?
How do you solve that kind of problem where you're like, hold on a second, electrons can't have negative infinity charge? How do you solve that? What is renormalizablainy I just.
Clarify real quick so that the biologist and me wants to confirm. So when you guys say you're getting infinities, that's just a fancy way of saying we're wrong.
Like it's just this is not working, right, Okay, got it all right?
Yes?
Absolutely absolutely. To be honest, I think to explain to normalizability that the story of the infiniti This is what usually is told. Is I think leading people astray. It's not the right way of explaining it. May I try to explain it differently, but please go ahead of It's okay. Yeah, maybe it's good to go back to. You know what Newton got famous for, you know his theory, and what
is his theory saying? Maybe people remember that. You know, there's an equation that he got famous for, which is called ethical en times a, which is essentially telling you that a force on a particle equals the mass of the particle times the acceleration that the particle is undergoing because of the force. So you can ask yourself, is this really a lot? A lot of physics? Means that you suddenly there are three things you know and you actually found a connection between them. I would say, isn't
this a definition? The Newton just defined the workforce by saying it's en times a. It looks like that. But there's another famous example that you know in high school you learned Olmslow and usually you call it you say that resistance is voltage divided by current. See, that's not a lot. That's the definition of resistance. There's no information in that equation, but a definition on was successful because he said this R is a constant. That's that's the law.
R is a concept, and then it becomes something with predictive power. Namely, I measure the voltage over a resistant over a resistance, and then I know the current that goes through it. But that's only because my real equation is art equal the concept. So what's the equation of newtant? Newton's idea was only successful because he essentially wanted to
tell us this F is universal. Imagine the way an apple falls under this F whether how it falls in Cambridge or in China, it will be the same formula. So that means that once you have the formula for the F and you say it's true all over the universe, it becomes very strong the prediction. So Newton and his program was having a lot of predictive power by you know, moving around in the universe. He found something true all over the universe. Okay, so this is the same with normalizability.
So instead of moving around from the left to the right, up, down, whatever future past, renormalizability has to do with zooming in and zooming out. If I have an equation and I want you to have predictive power. It has to tell me what also happens when I zoom in or I zoom out. Okay, zoom, let us think of zooming in. That's what really the problem lies. It means that I
go to very small length skills. I want a theory which gives me a single equation with all the constants known and measured, so I can tell you what happens at small distance skills when I zoom in. A non renormalizable theory, it doesn't give you infinities. People should stop saying that they give you completely finite numbers after some mathematical trickery. But what it does is that the more you zoom in each time, the equation gains another constant that we know the value, and we have to go
out in nature nature and measure it. Right. So imagine you want to somebody asking me, okay, Thomas, what happens in a gravitational field at you know, a micrometer. I say, oh my god, I have to you know already maybe correct Neutant's law for quantum gravity. And I say, yeah, there's an extra constant in the equation. It's not you know, the force is not one over our square. There's maybe one over our cube, but it's not one. It will be some number multiplying the equation. Okay, I go out
in nature and measure it. Good. I have the number, and as somebody wants to go ten times smaller or twenty times smaller, suddenly a term which goes like one R to the power for becomes important. You need to know the coefficient of the term. I again have to do a measure. So you see I don't have predictive power.
That's the definition of a non revisable theory. It means that you know, the smaller you get, the more constant theory has to be more precise, but it cannot predict what the constants are, whereas renormalizable theory it says, hey, I don't need any new constant guys. I mean, I can tell you with the computation on what you know,
how the theory behaves at the smallest length skills. So unfortunately, the way historically this came about, and that's where the word nenormalizable comes from, is that you know, we were getting infinities and then we found we always say a mathematical treat but in fact it's a physics treat to get rid of them. But you see, that's that's not
the essential part. The essential part is whether the theory is predictive, whether there's only a few constants that you can get out, go out and measure, or whether you need an infinite amount of consonts if I want to get infinitely small. And so if we take Einstein's theory classical theory of gravity, we apply our usual techniques of quantum theory, we find that it's non renormalizable, not meaning that it gives you infinities. This is actually, I think
a bad explanation. It gives you too many consonants that we don't know what they are, and we will have to measure.
I see. So a renormalizable theory, you can say I don't really know what's going on inside the electron. Maybe there's other particles, maybe not, But I can measure the charge and I can move on, and I can say it's all wrapped up in this number. They'll charge it the electron. And as long as I can make a finite number of measurements, like I don't have to measure an infant number of properties in the electron, then I
have a theory. I can use because that can make a finite number of measurements in a finite amount of time. So a non renormalizable theory, you're saying, is one where you can't ever capture all those details in a single number or two numbers, or even a finite number of numbers. You'd need to measure an infinite number of parameters to have a theory that you can actually use to make calculations. But you said a minute ago that we have other
non renormalizable theories. I think, for example, quantum chromodynamics, it's non renormalizable, and we've made that work. I mean, I know it's a headache, but we've made it work. What is it about gravity that's so special that we can't use our non renormalizable fancy clever tricks to get quantum gravity to work?
Right, So you're saying humanity has dealt normalizable theories, made them to work, and I can tell you what the problem is. So I guess don't forget that before we already said that gravity had two problems for it to be hard to quantize. Non rymalizability was one of them. So there's still the other one. So that's part of my answer, But it's still I believe it's very different. Like the other part of my answer will be the following.
Usually what happens in physics. Actually, every instance we have seen so far where the theory was non renormalizable, we actually cured it by realizing that we didn't have all what we usually call degrees of freedom. Okay, so what does that mean? So I assume it I go to small distances, and I always assume that. You know, if I have the theory of the electron, there's only the electron. Say well, maybe they're very massive particles out there which
require a lot of energy to be created. In physics, having a lot of energy is the same as going to very small distances. So all non renormalizable theories we have encountered were always made renormalizable by realizing that we didn't take into account fluctuation fields particles that were just very massive so that we didn't measure them yet.
That's real quick.
Saying you needed more degrees of freedom means there was something else that wasn't included in the equation that needed to be.
The exactly absolutely absolutely, And then you see, oh this is nice, my theory becomes mathematically normalizable. But then actually we went out in nichere we found technologies to increase our energy in our experiment, and then we saw those particles that we predicted mathematically because we wanted the theory to prenormalizable. Okay, I think that's extremely beautiful. Like you you do something on mathematical clouds, it predicts new particles
for it to work out, and there you measure them. Okay. And here's the funny thing with gravity. What string theories will typically tell you. What I think more and more people are leaning towards it, is that if you want to make gravity normalizable, it looks like you the infinite amount of particles with ever increasing energy. And that sounds super bad when you say that first, because you're like, oh my god, infinite amount of particles to solve your problem.
It's like measuring an infinite number of concepts. You're not better off. Okay, So of course now I'm going to sell string theory here. No, what is so beautiful is that it's infinite tower of particles groups together in the motion of a string. It just meant that what we thought were particles, no, it was just a single object. There's no tower. It's just a string that can vibrate in different ways. So there's a lot of structure in that infant amount of particles that you need to invoke
together innormalizable theory. Yeah, otherwise it looks very bad, like every time you take in a new particle you find that renormalizability still requires a new one, and you think, oh my god, you guys are just you know, in an never ending street of problems. No, we see that every single particle we have to add as exactly properties
that we could have predicted from the previous one. So there's a beautiful structure, and what looks like an infinite tower of particles just becomes a single stringing object with almost no constant associated to it.
So there, you just said the word beautiful. What is beautiful about that? Is it? Because wow, this is a hard problem, and now have a solution. Is it like my headache is gone? Or is there something objectively beautiful about this particular solution?
Can I go back to a real quick question and then can we move to beauty because I don't want to miss my chance to understand this because I'm actually really following everything.
I'm excited.
Okay, So instead of needing to measure an infinite number of constants? Can we measure that string? Do we know how to measure the string? Does that make our situation any better?
I'm going to be honest in practice. No, but this week we could have predicted you in advance. Okay, So this has nothing to do with string theory. I just told you that the regime ware gravity and quantum mechanics are relevant. Is either we have to jump through a black hole, which is not nice as an experience, or we somehow have to be able to move back in time to the Big Bang, or people are able to
build you know, galaxy sized accelerated. That is a true statement independent of what the theory of quantum gravity is. It just you know, you predict what is the energy density needed to see those effects. Of course, one can be lucky and some effects of the highest energy densities or the smallest lendsciales can trickle you know how they say trickle down? Is it correct English? I don't know, but can leave an imprint on larger distances and smaller energies.
Is if it's something that we're looking into, we are hoping, you know, I'm praying, but we don't know for sure, So I hope that explains a bit, yeah, and not to the beauty. It's I like the questions that I'm trying to find an analogy. Okay, so imagine I don't know whether this reminds you of the word beauty, but imagine you have a super complicated puzzive in front of you.
I don't know, one billion pieces and you just don't know how to put them together, and suddenly you find two connecting and because you see two pieces that connect, you suddenly see the third piece lying there, and the more you put them together, suddenly it's just one structure
that is like extremely simple. Okay. It's like imagine if a blackboard full of equations and you cannot solve them, and suddenly you realize that your equation was too complicate, that terms are dropping against each other, and you keep on canceling terms, and suddenly you have an equation left which is just one centimeter insights. You're like, oh my god, this is you know, this is amazing. That's the kind of beauty we're talking about that we think that renormalizing
gravity is a nightmare. It gives you ugly theories. And then the first thing we try, which you know, just on mathematical grounds, and we get something that is in terms of the length of equations, is even smaller than any equation that we have had in the past. And that is what I think why so many people like it. And then the confusing part is that it's not because the size of the equation is small that it's easy
to solve. It just means that it's very elegant, okay, in the sense that, for instance, there maybe elegance is better than beauty. The elegant thing of string theory is that they're no constants in the.
Theory, no numbers at all.
No numbers at all exactly. Any other theory non physics has to have a lot of numbers that you go out and measure. String theory doesn't have a number. Actually it only is one. It's the size of the string as variables.
But no constants.
Is that I'm having trouble imagining an equation with no numbers that's exactly correct.
So it's like ex equals why not ex equals two point seven four times?
Why right? Where I didn't know the two point seven I had to go out and measure it, all.
Right, So I'm excited because this is the most that I've understood string theory in my.
Life so far, but I could still use the brake.
So let's go ahead, get some more coffee, a little bit more brain fuel, and we will be right back to talk more about string theory. All right, we are back with Thomas Van Reed. Let's jump back into string theory. So string theory we've discussed that it can help when you're in those really tiny little situations where you'd usually have to get a lot.
More calculate, a lot more constant.
Does it also work if you zoom out or is it just a theory for when you're super zoomed in?
This is an excellent question. So that's where it gets hard. Surprisingly Okay, So when you zoom out in physics, it means okay, large distance also means low energy. And what is the hardest part of working with high energy theories like string theory, is to understand if I take the theory and I run into low energies like the energy densities that we like, have you know in your office, okay, then it's not you, and so it becomes very difficult to understand. So how would the world look like on
this low density or large distances? I mean, string theory predicts a completely unique world. At small distances you see little, you know, vibrating strings behaving in a certain way. But then if you do mine it, it's not obvious what's going to happen. Okay, this is why we always say we have trouble or we are not sure whether we can reproduce the large the universe as we typically know. But this is not a problem of string theory. This is effect of all high energy theories. And maybe I
can give an analogy. Okay, so imagine that you have a rocky landscape, hills, mountains, whatever, very very complicated, many valleys, and you have a football. But the football has a lot of energy, you know, so then it's like up there up the tops of the mountains, right because it just says lots of alosity. It's moving through those valleys and it's just all the way up. But then you
know the restriction and the velocity is going down. Well, if I have many values, I don't know where the ball is going to roll down and where the value is that it's going to end. That's the problem we have. Well, I don't think it's a problem with theory, it's just it's typical. Actually, even the standard model has this property that this difficulty.
That's a great explanation. Thank you. Can you circle back and help us understand more specifically how string theory solves these problems of quantum gravity. You talked about how howing string replaces the infinite number of parameters you might have to measure how does it solve the problem of quantum mechanics and general relativity working together on this dynamic space time.
So first, I think it's very important to have a disclaimer. We don't have the full theory, right, so whether it solves all problems that we know quantum gravity we do not know. I have to be honest on this. I would say that from a mathematical point of view, the way it solves this is by not quantizing gravity. That's very strange to say what it is. That's why string
theory did so quantizing. When we use the word quantizing, it means that we take our classical theory it has a certain amount of variables like electromagnetism has the electric field and has the electron field, and always said that's quantizing. Let's make it quantum mechanical. So you could say, well, relativity is what we call the metric field. That's a field that describes how space and time curve. Okay, and that's what people usually do. They say, Oh, we learned
in history of quantized series. We take that classical what we call field and we turn it into a quantom mechanical field.
But how do you do that? How do you quantize the theory? You don't just like tap your magic wand down and say and now you're quantum mechanical.
Oh my god, this is tough. So mathematically you would say it turned a field into an operator, but that probably means a little two people listening, here's an attempt. I'm not sure it's even good. Quantum mechanics tells you that things there are only probabilities, right, what you thought as a particle. We sometly say it so a way, it's not a very good word. What we have in said is a probability distribution of where the party consulute.
So objects are turned into probability distributions. That's quantizing a theory. And then there's a certain equation for the probability distribution. But more mathematically, it means that you take a field and you make it into an operator.
No, that's a great way to think about it. A classical theory says that everything is specified and there is infinite information even if you don't have it, whereas a quantum theory leaves some uncertainty and says, well, this isn't determined. Maybe the electron is here, maybe the electron is there. Maybe the field is this value, maybe it has that value. And for those of you playing along at home, an operator here is making a measurement. It's like applying something
to it and getting a result out. And so that's a crucial element of quant mechanics. Okay, so now we're going to try to quantize space time and you say, we can think of the metric as a field. The metric is like how much curvature there is at every point in space. So if we think of like the curvature and space as a field, why is it hard to quantize that. Why can't we think of that as like, well, maybe the curvature is this value, maybe the curvature is
that value. Why can't we just think of that probabilistically.
That was the problem of the problems we talked about before. Then you run into the problem of non renormalizability. If you do it that way, or you're run into the problem that you know, it's a background itself that has to become a probability. So the formalism of Qunlem mechanics gets very confusing at that point. And as I said, we already knew that a theory that is non renormalizable means that you're not having the right degrees of freedom,
you're missing information. So the way string theory went about is people that discovered it. We're not trying to quantize gravity. Let's let's be clear on this. Okay. They wanted to solve another puzzle, and for some reason, which is a long story by itself, they were interested into string like objects and how they move and how strings move quantum mechanically. So they do their computation and they suddenly see that the string can fluctuate in what we mathematically call a
spin to field. If you don't know what a spin to field is, it's just a fancy way of saying it describes what I call the metric field. They just says, but that's strange. There's no space and time, and yet they found the structure, which is what they knew from relativity. And then they started to look into it deeper, and they wanted to understand the equations that that metric field obeyed, and they were completely surprised that, you know, they didn't
ask for it. They found Insten's equations. So this is also what I call absolute beauty.
Okay.
Other approaches to quantographty they said, let me take insent equations for true, just have them. I said, also just dropped them down. I said, I didn't know why these are my equations. Okay, he didn't derive them. And so the other approaches to quanto gravity say, let me take those equations that you know, quantitize them. String theories did something else. They were looking at strings vibrating for a completely different reason.
They not only recover Einstein's equations, the classical ones they predict, they literally predict them, but they immediately have them quanta mechanically, and it meant that they needed they have all these possible vibrations of the string. It's just one vibration that gives you this metric field, but the string can vibrate in so many other ways. And then suddenly it gave them other things. They knew, for instance, all the forces in nature. They come in two kinds. Okay, there's gravity.
This is a separate guy. It's is described by this metric field. And the other forces are with a manematical term are gauge forces, young meals forces. Electromagnetism is an
example of it, okay. And the two other are the nuclear forces, and they are all described by one equation which is called the Young Mules equation, and a special kind of young music equations that maybe people listening who had a little bit of a scientific, you know, education remember are what we call the maximal equations, which are
the equations of electric and magnetic fields. But this is part of a general mathematical equation which is called the young music question, which also mathematicians study for completely different reasons. But guess what they were looking at the other modes of vibration of the street, and without asking for it, the young music quations appeared, and at that point people
were like, my god, this is insane. Okay, So this is where all the hype came from, all right, from string theory, like the excitement of people all came from this. Not only do we you know, we get the classical theories we didn't ask for that we've gotten. So you get all advance, so to speak.
So I'm getting a sense from you that the elegance of string theory comes from the sort of discovery that it answers questions simply, and sometimes it answers questions we weren't trying to answer. In that sense, it feels more like you're accidentally revealing a big chunk of truth rather than you're like laboriously putting together an over complicated answer that's just an invention in your mind. Is that the feeling here that we've like uncovered a vein of reality.
Absolutely, And I think that's for all of science. Like I can imagine in biology, when you understood like gene structure and I suddenly realize how things work. It becomes so simple, Like I think the same evolution happened in biology. You have all this phenomena. At some point we learned about to sell and the smaller organisms, and all of these phenomena suddenly can be explained in a more microscopic way. So the theory becomes simpler. It became maybe I'm simplifying.
I mean, I'm not the expert here, but I would say biology at some point became the theory of the cell, which is so much smaller and so much in a way simpler.
So is it then about the theory itself or is it about the insights the theory gives you about how the universe works, or just the place where we are where we're like wollw We're frustrated by these problems for decades, and now finally the headache has gone away. I mean, can you look at the theory itself and say, this theory is beautiful? Is there a chance that we could have revealed the theory which feels truthful? But then you're like, actually, I don't like it. It's kind of ugly.
Right. I guess different versions of beauty were felt at different stages, right, So the people first making these discoveries of seeing einscience equations and so on, when you read their biographies, they really are like they talk about it extremely emotional, like they could be crying because they saw that part of beauty. But my generation came later, so we kind of you say, you got used to it,
you don't feel that beauty on it. The thing that strikes me is that when you first learn about Newton's second law, I don't think none of us feels what Newton felt at the time, and I think we are underestimating the emotions because one other things that I didn't tell you what Newton's second ploy is. It tells you about what we call the deterministic view of nature. Newton realized that this equation was telling you that, you know, I'm sitting on my chair and later on I will
walk away. But according to Newton's equation, I don't have the choice. I have no freedom. There's no freedom of you know, there's no free will.
Do the philosophers know you all have solved that problem.
No, it's the classical theory, right, So, but physics is deterministic, so the according to physics. I think we should emphasize this. There is no free will in physics. Anybody that tells you that there is is wrong physics. As I don't say we have solved it. But there is no free will in physics, absolutely not. Free will is completely in contradiction with physics. Not the illusion of free will, but free will. But it's no way, there's no room in physics for free will, not in the usual notion of
the word free will. Any I want to say that the beauty that we feel or now the students you know, which are younger than me. There are different versions of beauty.
It's more where you start applying the theory. I can give you one example of a thing that I found beautiful is like you have equations with singularities, like these infinities we talked about, and string theory can do calculations and you see there's no infinity, And then you learn how string theory tells you that there's no infinity, and it does it in a very creative and funny way. There's often a picture like you can even see it literally,
it's not an equation, it's not formal us. You can just see it, and that's kind of beautiful.
Too bad the listeners can't see your face because you have the biggest grin on that You've had the whole interview explaining how beautiful it is.
Like you're clearly getting a total kick out of this. It's it's awesome.
I think it is really hard to put yourself in the minds of earlier generations to appreciate how big some of those steps forward were. Like, it seems pretty basic what Aristotle accomplished. You like, things fall down. I could have said that, but you know, to systematize the world at all. What was a big step forward. I think you're right that it's underappreciated. So what is it that
we're underappreciating now in terms of strength theory. I mean, there's a lot of popular writing about strength theory, a lot of popular conceptions about it. But from somebody on the inside, what do you feel like is most often misunderstood or misrepresented about the nature of strength theory.
I have to be careful, careful not to become too sort of drawn into the sociological discussion, but I feel I cannot not say it so string theory, say, thirty twenty years ago, when it's people discussed it in science outreach, it was only the one, okay, And now it's the opposite, And I think that the opposite went so far that it's completely misrepresenting the field.
When you say the opposite, you mean like people being critical of string theory because it hasn't yet predicted some experiment and been proven.
Writers is exactly, this is an example exactly. So they will tell you this, and then of course you have to tell them, because they don't tell you this, that this is true for any theory of quantogravity and We knew this in advance. We knew this before we started working on string theory with absolute certainty that if you have access to the smallest Lend skills, you can falcify a theory one from the other. Okay, string theory from
the other examples. What is completely not obvious is that some of these high energy small distance effects have an imprint at larger distances. At a moment, we don't know, and we're actually looking into it. And this program has a name. I think it's super exciting. It's called the Swamp program, and it's where we try to look into that question. But at the moment we do not know.
But as any other supposed alternative to string hearing is not even there at that stage where they can even ask this question, does my theory predict something at a bigger length scale, because normally you don't expect it to be the case? Right, So can I get away of not sending a student into a black hole to learn about pornography? We don't know.
I mean, master students are expendable. You could send like four or five of them.
Unfortunately they can't explains what they're what they're seeing, right, so they couldn't explain it. That's that's a Otherwise I would, you know, be interested in maybe jumping into a black hole just to see because if you jump into a big black hole, actually it doesn't need to be a painful experience. You can pass the horizon without you know, feeling it too much, and then you could actually see a singularity.
You know.
Interstellary is a little bit about this, right, you jump into a black hole. There's a movie about it. But yeah, so I think is my frustration that there is a back correction to the original hype. But the back correction especially you know now on social media, but also i'd say conventional science outreach. To give an example, I saw my children that at an age where they get interested
in science and they start googling things. So I see their first hit on Google when they ask a question which is about fundamental physics, and the first hit that they have is criticism on stream. There it became so mainstream that this is the first thing you see, and that's not healthy anymore.
Okay, So just to make sure I understand, you're saying it's fair to criticize string theory and say you haven't made a prediction, which can be verified, But all the theories of quantum gravity also had that issue that we can't go inside a black hole, And many theories of quantum gravity haven't even come together and coalesced and enough detail to make any predictions, not to mention ones that can be tested. So then let me wrap up by asking you a last question, which is about the truth
of strength theory. I mean, you're excited about string theory because you think it's simple and it feels like a compelling potential answer to the question of like what really
happening in the universe. So do you think, for example, in some hypothetical scenario where aliens arrive on Earth and they're very advanced scientifically, and we can figure out how to communicate with them, et cetera, et cetera, what do you think are the chances that alien physicists are doing string theory that they have also stumbled upon this explanation.
Daniel always has to get aliens into the show at least once, and so here we go.
We all owe aliens. Actually, Okay, I don't know whether my answer is of any meaning, but I would say they will discover string theory. I actually don't even doubt it. I'm one hundred percent convinced. And as to the question before, people tell you that a theory without predictions is not science, and I think we have to really step away from this. So in science are two things. They're observables and they're computables, especially in theoretical sciences, and what a theory has to
get right are the computables. For instance, if I have a theory that can explain phenomena at large distances, but I look at small distances and the theory tells me that I can go back in time and kill my mother before I was born. I know that theory is nonsense, but I cannot make an experimental verification. But the theory
is just nonsense. It's not logical. And the thing that people that the audience and you know, the greater public needs to understand, quantum gravity is so extremely constraining in terms of just logical consistency that you almost uniquely arrive at an answer. And that's where this is true science. Okay, despite not having access at a moment to an experiment to test it, you almost uniquely are pushed into a
direction to solve this problem of non remortalizing. Now I'm selling it too much, But I hope you're understanding what I'm trying to say.
I've read a couple of books on strength theory and never understood them, but I've totally understood our conversation today.
So I'm this has been awesome.
Happy to hear that it's awesome.
And if aliens arrive and they don't do strength theory, maybe they can listen to this episode to get a primer on how strength theory works. Exactly, exactly, wonderful. Well, thank you very much for coming on the show and talking to us about the hard problem of quantum gravity and how string theory might be the solution. Thanks very much.
It us a lot of fun. Thank you so much.
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