SPENCER: Christian, welcome to the Clearer Thinking podcast.

CHRISTIAN: Hi. Thanks for having me on. I'm very happy to be here and discuss string theory.

SPENCER: Yeah, so string theory, it's pretty funny because I think a lot of people have heard about it, but they might have heard about it in some TV segment about how it's this great new thing that's going to revolutionize physics, or they might have heard about it on YouTube, where it's this trash science that's ruining everything and wasting taxpayer money. So it's almost like a bifurcation in perspectives.

CHRISTIAN: Yeah, I think right at the onset, it's important to separate two different definitions of string theory. One is what I will call the narrow definition, the old school textbook definition. If you look there on my bookshelf, there are two textbooks written by Joseph Polchinski. One way you could define string theory is by saying, "Open that textbook, and the contents of that textbook define what string theory is." That's sort of an old school perspective. But there's also a more modern broader definition, which is a collection of ideas that has grown out of the original string theory work. If you use that more modern umbrella definition, then many other aspects that do not directly involve strings, things that your viewers may have heard of, like holography, branes, black holes, and things like that, are also included. Moving forward through the discussion, I think I'll try to be very clear about whether I'm talking about this old school narrow definition or this broader definition because they're somewhat different.

SPENCER: And is the broader definition strictly bigger? Is it just including more stuff?

CHRISTIAN: Yeah, I think it includes more stuff. The analogy I like to use is if your viewers have either taken calculus or at least heard of calculus, they might have thought, "Okay, when calculus was first developed by Newton and Leibniz, maybe it wasn't completely understood." There was this famous criticism by Bishop George Berkeley that it was using the ghosts of departed quantities. There was a lot of criticism because it didn't quite make sense. But then after that, it developed into many other branches. It turned into an area of math called analysis. There's real analysis, complex analysis, partial differential equations, differential geometry, and all of these different things stemming from calculus. I would say that the modern definition of string theory is, in some sense, like that branching of calculus into those many different subdomains.

SPENCER: Now, at the most basic level, what is string theory if we just start with the simpler, smaller version of it?

CHRISTIAN: For the narrow definition, string theory is a theory that replaces point particles. In ordinary standard model particle physics, for instance, electrons are point-like, so they have no spatial extent. The most basic definition of string theory is a theory where those point-like particles are replaced by extended objects. They are strings instead of points; they are just little strings — they are extended. The most basic definition is a quantum and relativistic theory of strings rather than of particles. That definition generated a lot of excitement initially because people discovered that when you study one of these quantum mechanical relativistic strings — and I can define those terms more precisely if you like — an important consequence is that you find that the theory automatically contains something called a graviton. Gravity is a logical consequence of studying the theory of the string.

SPENCER: Was that intended, or was it being studied for some different reason, and then they just discovered that that was a consequence of the theory?

CHRISTIAN: It was actually by accident. It's kind of a funny history. So initially, string theory was proposed as a sort of theory of so-called hadrons. Hadrons are these particles made up of quarks, and people noticed this particular behavior, something called a Regge trajectory. String theory was proposed initially to explain this Regge behavior and to understand hadrons, which are, say, protons and neutrons. For instance, it was later discovered that that's wrong. The correct description of protons and neutrons is some other theory called quantum chromodynamics, which is now part of the Standard Model. String theory sort of had a period where it wasn't really clear what to do with it, but then people discovered, "Oh, wait, there's actually gravity in this theory as well." Then it had a resurgence as a theory of quantum gravity when people had this later realization.

SPENCER: So it was almost a fluke that this kind of discovery was made, that, "Okay, it produces a graviton." What's the significance of that? Is that a really big deal?

CHRISTIAN: To me, it is because one of the biggest open problems in theoretical physics, broadly, or at least if you consider it solved by string theory, was finding a theory of quantum gravity. It's often said that the theory of quantum mechanics that describes the very small and Einstein's theory of gravity, general relativity, which describes the universe and things on very large scales, are incompatible. In a sense, that's true. We do know how to combine quantum mechanics and gravity approximately at low energies. That's fine, and we can do that. That's in textbooks, but that's only an approximation. If you try to take that approximation and make it complete or exact at very high energies, it breaks down. That was a big open problem. The fact that string theory had a graviton in it, and it's a consistent theory that has quantum mechanics and gravity in it, is, to my mind, a very big deal.

SPENCER: So is this the right way to think about it — that if we're dealing with gravity and really big things, general relativity does an amazingly accurate job of describing it. If we're dealing with really, really tiny things where there's not much gravity, then quantum mechanics does a really amazing job. And then in sort of the middle region where things aren't too fast and there's not much gravity, Newtonian mechanics is a fine approximation. And really, we're talking about bridging those two extremes.

CHRISTIAN: Yes, that's exactly the right way to think about it. So it's similar to other cases, for instance, special relativity. So Einstein's theory of special relativity tells you that things behave very differently if you're moving very fast, close to the speed of light. And there's some approximation, Newtonian mechanics, as you said, which is valid when you're not moving very fast, but breaks down at some point. And in the same way, the approximate way of combining quantum mechanics with gravity, with general relativity, works okay at low energies, but it breaks down at very high energies. And that's important because there are certain situations like the very early universe. So shortly after the Big Bang, the universe was at very high energies as it was inflating or near, say, what's called the singularity of a black hole. The center of a black hole, at that point, the singularity is very small, but there's also very, very strong gravity. So that's a situation where you need both quantum mechanics and gravity in order to make sense of it. So combining them in a way that does not break down, which is what string theory does, is something important if you want to understand the physics of situations like those.

SPENCER: Someone might ask, "Well, does it really matter that much if we can combine the theories, if it only matters in the Big Bang and at the edge of a black hole?" Would the view be that, even if it's only at this extreme physics where it matters, getting those sort of deeper underlying true theories could lead us to all kinds of unexpected things that we never would have imagined?

CHRISTIAN: That would be my perspective. I mean, as a scientist, personally, my interests are purely, I almost want to say philosophical, because I don't believe that nature should play by two different sets of rules. I don't want quantum mechanics on one side and general relativity on the other. I think that there should be one unified framework which makes sense of everything. So that's my perspective. But you could also advocate for the perspective, which you just mentioned, that it's very hard to predict down the road what sort of applications things might have. You could have said the same thing about special relativity. So the statement we made a few moments ago that things moving very fast have different behavior. In particular, time dilates, so time slows down for things moving fast. You might have thought when Einstein proposed this in 1905, "Okay, who cares? I'm never going to be moving very fast or close to the speed of light." But it turns out that this time dilation effect, more specifically the gravitational version of it, gravitational time dilation is actually important for GPS. So GPS satellites, when you find your location on your iPhone, they sort of triangulate by passing messages or receiving messages from satellites. And if you did not take into account this effect of relativity, that time behaves differently for different observers, then you would get the wrong answer. GPS wouldn't work. So in that sense, even though maybe it was a hundred years later, after 1905 that we started to need that sort of technology, you could advocate for a similar viewpoint and say, maybe in some far future, things that we learn in string theory may also have useful applications.

SPENCER: Yeah, I think quantum computing is a great example where without quantum mechanics, it doesn't even seem like something that could be possible. It seems like ridiculous science fiction until you have quantum mechanics, and you're like, "Oh, wow, this has unlocked something we never thought could be done."

CHRISTIAN: Yes, that's right. Since, I think, Feynman and someone else, I think, sort of independently, around the same time, proposed using quantum mechanics to do computations, which probably, at that time, seemed like a crazy idea. But now, as some of your viewers may know, there are several quantum algorithms that are known to give dramatic speedups over classical algorithms. So for instance, if you want to search a list on a classical computer, if you want to search a list and see whether an item is in it, you at least need to look at every item in the list.

SPENCER: If it's not yet sorted, right? It's just an unstructured list.

CHRISTIAN: Yes, an unstructured list. So if you just want to look through a list, obviously the time it takes to solve the problem of checking whether an item is in a list scales linearly with the length of the list because you have to look at every item. But with a quantum computer, surprisingly, there's an algorithm that allows you to check whether an item is in a list, and it only scales the runtime of this algorithm as the square root of the length of the list, so you somehow don't have to look at every item. And that's an example of one of these cases where something which may have seemed rather niche or esoteric in physics ended up being useful and has a real-world application.

SPENCER: Yeah, and before quantum mechanics, it seems literally impossible. There's no conceivable way that could happen until we had this deeper theory of reality.

CHRISTIAN: Yes, I would advocate that curiosity-driven science, even if it does not immediately produce tangible results, is still worthwhile, both from an intellectual perspective and because who knows what could happen down the road?

SPENCER: Yeah. Many people are inspired by trying to seek deeper theories and think it's important in its own right, but some people want to see a payoff for it. Often, physics has had a huge payoff, but we often don't know what it's going to be in advance.

CHRISTIAN: Yeah, that's true. It also depends on what you mean by payoff. If it has to be a specific application to something with industrial uses, that's one notion of payoff. Another notion of payoff would be making predictions that can be experimentally verified. For instance, a famous example is the prediction of the viscosity of the quark-gluon plasma. This is a real measurable thing that was measured at the Relativistic Heavy Ion Collider at Brookhaven. This prediction actually came from something called holography, which is a piece of string theory. String theory tools were used to do a calculation that was then verified experimentally in a collider. In a sense, that's also payoff. It's a scientific payoff in the sense that it's a prediction that was verified. We don't yet have industrial applications for the quark-gluon plasma, but I wanted to separate these two notions of payoff. There are predictions that are verified, which are important, and then there are applications that you can actually use, which are somewhat separate, but there's an interesting interplay between them.

SPENCER: Yeah, we'll definitely get into the evidence for string theory, and what it's predicted, and that kind of thing in a little while. Before we do, another thing I think is potentially interesting here is that our philosophy or metaphysics about the universe can vary a lot based on our understanding of physics. When everyone believed Newtonian mechanics was true, it said things about the nature of reality. It said, "Oh, okay, the universe is deterministic. If you know the position and momentum of things, you can predict exactly what's going to happen." Then quantum mechanics totally threw a wrench in that and told us maybe the type of universe we're in is totally different, and our philosophy about the way the universe works is totally different. Even if the two models are making similar predictions in a lot of cases, let's say things are not moving too fast at reasonable sizes or whatever, they could have completely different viewpoints on how the universe functions.

CHRISTIAN: That's true. Yes, I guess there was a sort of clockwork universe type philosophy when Newtonian mechanics was the dominant paradigm, that everything just sort of evolves deterministically, as you said. So it could well be that a better understanding of quantum gravity, something like string theory, would also lead to some different philosophical views. For instance, an example that comes to mind is one of the ideas in string theory is this notion of emergent spacetime. The spacetime that we live in, the three space and one time dimension that we inhabit, we treat as sort of fundamental, like that's the underlying building block that underlies reality, and we just inhabit that stage. But one of the ideas being pursued in a subfield of string theory called holography is the notion that spacetime itself is not fundamental, but emerges from something else, from something called entanglement, quantum entanglement. That would be an example of, if it's true, that would be a sort of philosophical paradigm-shifting fact that would likewise completely alter the way that we think about the world.

SPENCER: It's sort of interesting how you could have a really close to correct theory that's very accurate, but it's philosophically totally wrong about the way the world works, and then you kind of get the right theory, and suddenly you're like, oh, actually, it doesn't work the way we thought at all.

CHRISTIAN: Yeah. To come back to relativity, I think that's another example where, before relativity, we viewed time as being absolute. There's one universal clock that ticks for everyone at the same time, and that's it. Time is just completely absolute. But then we learned that time is relative. Time passes differently for different observers, and that also has philosophical implications, because this sort of means that time isn't exactly what we thought it was. At least for me, I found that when I learned that as an undergraduate or even in high school, that's kind of a mind-blowing fact and changes your perspective.

SPENCER: Something I find very funny about physics is it's often actually weirder than the crazy, crackpot fake theories of physics. I know about crazy crackpot theories because my friend and I used to run a website called Ask a Mathematician/Ask a Physicist, where people would write about things. We received a lot of crackpot theories, and they're almost always less weird than the real theories, like, "Oh, there's time dilation, oh, there's non-determinism," etc.

CHRISTIAN: I think that's true. I've had my fair share of run-ins with crackpots and read some crackpot papers as well. But truth is stranger than fiction, I guess, is a good way to say it, because the true physics that we understand, and even the more speculative physics, like string theory, which we'll get to in a moment, is kind of mind-blowing. The sorts of things that emerge from it are surprising and tantalizing in a way that the crackpot theories, even though they're sometimes entertaining to read, just don't have the same sort of depth and beauty, I think, and the same level of surprise.

SPENCER: Yeah, wherever the laws of physics come from, whatever it is, it's not a human mind. So it's not constrained in the way we are. Could you explain a bit, and this would be hard to explain, why is it tough to combine quantum physics and relativity? What happens when we try to do that?

CHRISTIAN: Yeah, good. The technical statement is something called non-renormalizability. So what's the best way to explain this? I'll give an analogy. There's something known not in gravity, but in the standard model, the theory that describes particles like electrons, where the properties of particles actually change at different scales. The electron has some charge, and we learned in school that that charge is a fixed number. The value of the electron charge is this. It turns out that's not quite true. It depends on how closely you're looking at it, in some sense, at what length scale you're probing it. If you look closer and closer and zoom in, or equivalently, examine the electron at higher and higher energies, it turns out that that charge runs. We call it a running coupling, so to speak. That's part of a subject called renormalization. If you apply this same sort of renormalization strategy to this effective theory of quantum gravity that I described, where you sort of patch them together, and then you try to do this renormalization procedure and say, "Oh, okay, what happens when I zoom in, when I try to go to higher and higher energies," you get infinities. Things blow up, and the theory fails to make sense. Once you have these infinities, we say the theory is non-renormalizable, which means that, as we said before, it sort of makes sense as an effective theory at low energies. But once you go to high energies, you start getting infinities for answers, and there's nothing you can do about it.

SPENCER: I imagine people have tried all different ways to work around those infinities.

CHRISTIAN: Yes, there are various proposals. One of them, which we may discuss later as a sort of alternative path to string theory, is something called asymptotic safety. Asymptotic safety is a different approach to quantum gravity, which tries to find a way to start with conventional gravity combined with quantum mechanics, this sort of patchwork that works at low energies, and then find some tricks so that when you go to very high energies, or the ultraviolet, as we call it, you actually get a sensible, high-energy theory. That's a different research program, which I think is maybe complementary to string theory, but has not succeeded at this point. People have tried different approaches to your point, but as far as I know, none of them have succeeded in the sense that string theory has.

SPENCER: Can you tell us about string theory succeeding in this sense? What happens with string theory?

CHRISTIAN: Good. When I say succeed, I should be careful. I don't want to imply by "succeeding" that string theory is known to describe our world. That's still an open question. When I say it succeeds, I mean it succeeds in the sense of mathematical consistency. When you quantize this string, in particular, a string with supersymmetry, it gives you a theory with quantum mechanics and gravity, and it is finite at high energies. When you do this procedure, the nature of going to either very short length scales or, equivalently, very high energies, these infinities don't appear. The theory is finite and sensible. It's consistent; the words we use are UV complete. That means in the ultraviolet, at high energies, nothing goes wrong. In that sense, it succeeds in combining quantum mechanics with gravity all the way up to high energies.

SPENCER: So is it fair to say that, "Okay, we try to combine, we know we have to combine quantum mechanics and relativity to get a more complete theory because they contradict at high energies. When we try to do this, we get these infinities that screw everything up. They prevent us from doing calculations." Is string theory the only one that has succeeded at this?

CHRISTIAN: To the best of my knowledge, yes. There are other proposals. I mentioned asymptotic safety. Another alternative is loop quantum gravity. But in the math community, there are a few obstructions, so they have not yet demonstrated that loop quantum gravity is consistent with quantum mechanics. The technical statement is that anomaly cancellation has to occur. Loop quantum gravity has not yet demonstrated that it's consistent with quantum mechanics, and it has also not yet demonstrated that it reduces to Einstein's theory of gravity in some limit. So it's not yet quantum and it's not yet gravity. I guess among the words in loop quantum gravity, all that remains is the loop since it's not yet quantum and not yet gravity. To the best of my knowledge, string theory is the only one of the candidate proposals that is known to actually give a sensible theory of quantum gravity.

SPENCER: You can understand why physicists would have been very excited about it. They might still be very excited about it because it solved this real problem we have, and nothing else has been able to solve it. Is that fair?

CHRISTIAN: Yes, that would be my summary. There are many other things that came out of it in this umbrella definition, but in the narrow definition, that is the reason to be excited about string theory, that it gives you a consistent theory of quantum gravity.

SPENCER: And how popular is it now? Obviously there's all kinds of physicists doing lots of different work but if we talk about people doing fundamental physics, is it really popular? Are there many people doing other approaches?

CHRISTIAN: Within high energy theory specifically. Of course, there are people doing other things, like phenomenologists, for instance, who are a different type of theoretical physics. But within my specific subfield of high energy theoretical physics, if we use this umbrella definition of string theory, where you're not just doing the old school textbook stuff, but you're working on one of the spin-offs of string theory, to a first approximation, I think almost everyone, in my view, is within that broader umbrella. For instance, at the group at Northeastern that I work with, there are four faculty in the core high energy theory group. Within the umbrella definition, I would argue that all four of them are doing some sort of string theory, something within the broader definition. If you use the narrower definition, then maybe you say, "Okay, this doesn't really count. You're not really doing string theory. One can nitpick about what precisely counts as string theory." The operational definition I have in my head is, I say string theory is what string theorists do. If you go to, for instance, the conference website for the largest string theory conference every year, which is, perhaps unsurprisingly, called Strings. If you go to the Strings 2025 website and look at the list of talks, in my mind, I would say, "Okay, if this is a talk at a string theory conference, this should fit within the umbrella definition of string theory." If you use that definition, it's extremely popular. Almost everyone in the specific subfields of high energy theory is doing some variant of that.

SPENCER: Now, some criticism that string theory has gotten is that it's sort of sucked up energy from other approaches. People might say, "Well, yeah, okay, you can see why people like string theory. It solved this problem," but it's also been working on for a really long time. We need other approaches. We need new blood. Do you think that that's a fair criticism, that there isn't enough funding or enough manpower focused on other approaches?

CHRISTIAN: I think it's partly a fair criticism. What I would say is that people sort of vote with their feet, in the sense that people work on what they think is most promising. The reason why fewer people are working on things like asymptotic safety or loop quantum gravity, to a first approximation, is less because of some sort of funding allocation that all of the money is going to string theory. It's more that the researchers themselves decide that string theory is more promising and they're going to work on that or one of these offshoots of string theory. I do agree that quantum gravity is a hard problem, and it's good to have a sort of pluralistic approach, where we have different ways of going about it. But I would argue that within the umbrella definition of string theory, we sort of already have that, in the sense that many of these spin-offs that are not directly related to string theory are still approaching quantum gravity in a way that is string inspired, but which is sufficiently different from the old school definition of string theory that it gives us some diversity within the field.

SPENCER: So at least they're taking different approaches. What is in common? If you take the big umbrella of string theory, what does everyone kind of agree on or presume?

CHRISTIAN: Good. So I think everyone, to a first approximation, agrees that string theory is interesting. But maybe I'll give you one example of one of these spin-offs, and then try to answer your question about what they agree on based on this. So within string theory, there's something called holography, which I mentioned before. Holography is an equivalence between two seemingly different theories, a gravitational theory and a quantum field theory with no gravity. Holography works in something called anti-de Sitter space, which is a negatively curved space, which is not like the universe that we live in. So holography is part of string theory, but in some sense, it's a subset. One of the modern research programs is something called celestial holography. Celestial holography is now very popular, and they are asking the question, is there something like this holographic principle or this duality that applies in flat spacetime, which is closer to our world? Our world is approximately flat. Whether one considers celestial holography part of string theory is open to debate. But I think it would be fair to say that if you ask a celestial holographer what they agree with string theorists on, they would say, "I agree that string theory is interesting and consistent. It inspired this line of work because string theory gave us AdS holography, and now we're trying to do flat space holography." Those holographers might say, "Even if I'm not using string theory directly, it would be interesting if you could somehow embed the work that I'm doing within string theory in a more direct way, because that would increase my confidence that it's correct, as that would show that my work embeds in a theory that's known to be consistent." So those sorts of statements, I think people would agree on.

SPENCER: Now there's tons of dunking on string theory happening online, and sometimes these are getting hundreds of thousands of views, or even millions of views, which is just fascinating. I think that that's happening. I do really want to consider both sides of that and say, "To what extent are the criticisms fair? To what extent are they not fair?" The first one I want to talk about is actually funding, because sometimes it's discussed as though there's one game in town, and you can only get funding if you work on certain things. My sense is that academics largely control their own destiny in the sense that they can work on what they want. Typically, they can apply for whatever grants they want. They can write those grants in whatever way they want, but at the same time, they are constrained by what they can get approved, or where they can get funded, or what they can get in top academic journals, maybe most importantly. There can be a sort of faddishness, or the things that are cool to work on, or the things you can publish in top journals. Even if there's not a group of people at the top deciding what you work on, you can be blocked or limited based on what's going to get in the top journals. I'm curious to hear your thoughts on that.

CHRISTIAN: I think that's true. Yes. There is a sort of sociology and the faddishness, but I still think that, let's use an example since we're discussing funding. The Simons Foundation is one of the larger private science funding entities in the US. They fund certain collaborations.

SPENCER: Is it Jim Simons, the mathematician?

CHRISTIAN: Yes. Jim Simons, who unfortunately recently passed away and founded Renaissance, but that money goes to fund different types of research. If we look at examples of things that are being funded within the theoretical physics landscape, the examples that come to mind right now are: there's a Simons collaboration on what is called probabilistic paths to quantum field theory. This is a collaboration between pure mathematicians doing probability theory and quantum field theorists. Although some of the work in that collaboration connects to string theory, it's not directly string theoretic. It's more of a constructive quantum field theory program. Another Simons collaboration, which I'm actually a member of, is the collaboration on the physics of learning and neural computation. This is about trying to use physics to understand AI, and this connects to some of my work on neural networks and quantum field theory, and it also connects to string theory. There's a paper by my postdoctoral advisor and his PhD student that demonstrates that you can actually define string theory using a neural network. String theory appears in a tangential way within that collaboration, but it's not the primary focus. Using these two examples, these are collaborations that could have instead been entirely string theoretic. It could have been that there's the Simons collaboration on trying to do, say, string field theory, which is one of these more modern directions within string theory. If you look at what's being funded, I think there's not really a massive aggregation of money going into string theory specifically.

SPENCER: Suppose that you came up with a new idea for how to approach combining relativity and quantum theory, and it was totally out there in the sense that it wasn't connected to string theory, it wasn't connected to current theories, but it had a lot going for it, it was promising, at least from your estimation. Could you actually get funding to work on it through mainstream funding sources? Could you get it published in top journals? Or do you think it would be legitimately difficult?

CHRISTIAN: I think it depends on how promising it is. If I wrote something down and performed basic consistency checks, if I had a different way of combining quantum mechanics and general relativity, and I demonstrated, for instance, this anomaly cancellation that we mentioned before, which is essentially a consistency condition that shows that the theory doesn't break down, I think that would immediately be publishable in a top journal...

SPENCER: So is that related to what you were talking about before, with very high energies leading to infinities?

CHRISTIAN: It's somewhat related, but it's a different consistency condition, in some sense. So there are several consistency conditions that you need for a consistent quantum theory of quantum gravity to have. One of them is called unitarity, which is essentially conservation of probability. One of them is the lack of infinities, this finiteness, and the one that we were just discussing is this thing called anomaly cancellation, where there's some interplay between these. But the rough statement of anomaly cancellation is that we treat certain field configurations in different ways that a quantum field can exist as being equivalent. We identify them, so there's some equivalence relation, and that has to persist. If we treat them as equivalent, for consistency, they need to remain equivalent. An anomaly is what happens when you attempt to quantize the theory and these different field configurations that you thought were equivalent, and you demand them to be equivalent for consistency, end up being inequivalent. So it breaks. That's called an anomaly. So if, for instance, coming back to your previous question, if I had a new way of doing quantum gravity, and I even just demonstrated anomaly cancellation, forget the other ones, I do think that would immediately be publishable.

SPENCER: Indeed, in a good journal?

CHRISTIAN: Yes.

SPENCER: How high of a bar is that? Because if that's a nearly impossibly high bar, where it would take someone 20 years to develop a theory to get there, then that could be a really big barrier.

CHRISTIAN: Well, yeah, anomaly cancellation in the string theory case was proven by Green and Schwarz, and I'm not sure how long it took them, but I'm guessing less than a year. Okay, I apologize in advance for dunking on specific people, but since we were discussing crackpots, Eric Weinstein also has a proposed Theory of Everything, this geometric unity, and he was instructed very kindly that you could check anomaly cancellation in your proposed theory very easily. It would take a couple of days, according to the person who made this comment, and if you did that, people would take it more seriously. Despite that, this check has never been done. So I think anomaly cancellation, depending on the precise way the theory is formulated, should not necessarily be a super high bar. It's something you could do within days to months, depending on how complicated the theory is.

SPENCER: Have other theories of string theory passed that bar?

CHRISTIAN: I don't know of any other theory of quantum gravity that has anomaly cancellation. No, not to the best of my knowledge.

SPENCER: Got it. So, yeah, it's interesting. It sounds like, basically, there are certain hurdles. If you jump over them, you could get published. You might be able to get funding as well. Is that fair?

CHRISTIAN: I would think so. For instance, in that hypothetical situation, suppose I come up with a new theory and demonstrate anomaly cancellation. I am applying for various grants and fellowships now, but my rough estimation is that, based on the back of that initial work demonstrating anomaly cancellation, I suspect I would be competitive for something like a Royal Society Fellowship or a Marie Curie Fellowship, because that would already be of interest to the community.

SPENCER: Cool. So another big criticism levied at string theory is that it's been trying to do this for too long without enough success. And there are different versions of that criticism. One version of the criticism is that it hasn't made enough contact empirically with the world. So can you talk about that for a moment? What contact with experiment has string theory made, and how big a problem do you see that as being?

CHRISTIAN: Yeah. So here again, I'm going to have to distinguish between the umbrella and the narrow. If you're talking about the narrow definition, then the right way to interpret your question would be to say, "Has string theory constructed a specific what's called compactification?" There are different ways of compactifying these extra dimensions that we have in superstring theory, which lives in nine space and one time dimension. You have to get rid of six of them to come down to three space and one time dimension to match the world that we live in. You could ask the question, "How close is string theory to finding a compactification that matches the data of our world?" This criticism might be slightly fair in the sense that it has been a long time coming. People are working on this, and they're making progress, but I think they are getting closer and closer. I don't work on this personally, but my understanding is that the main ingredients of, say, the Standard Model of particle physics, emerge relatively naturally from the ingredients of string theory, and the more challenging task is getting all of the details just right, making sure that all of the couplings and all of these different knobs that you can tune actually match the ones that we see in our world. Progress is being made, but I think the criticism is partly valid. It's taking a long time, but it's a hard question. If you relax to the umbrella definition, then there are other things that string theory has done successfully, which have contributed to other areas of science, and one of them is, for instance, this calculation of the viscosity of the quark-gluon plasma that we mentioned before. Now there's a philosophical question of whether you attribute that to string theory and count it as a success of the theory, because it was really using holography, which is a part of string theory, to do a calculation of a real-world quantity, this viscosity. It got a pretty good answer, but that's not the same type of success as saying, "Oh, string theory literally describes our world. It's the true microscopic ontology of our world, and here is the correct way to see it." There are sort of two different things, and different levels of progress have been made in those two different buckets.

SPENCER: Yeah, I don't know how to talk about this terminology-wise, but it seems like there are almost three different things we're talking about. There's one, this, I almost want to call it a set of theories that string theory has, and we're trying to find out which of those actually describes our universe. But it's this kind of, maybe it could describe other universes that aren't even ours as well in this set. Then there's string theory as a set of tools, mathematical tools or ideas that could be applied to things that were totally outside of what was originally developed for. I know mathematicians that work on string theory, and they're not using it for studying the world at all. They're using it for doing math stuff. And then there's string theory as the final answer that would come out if we eventually found that one thing that fit our world, and we would say, "Ah, that's the string theory of our world," which we don't have yet.

CHRISTIAN: Yes, that's right. I think here it might be useful to come back to the calculus analogy because if you think of calculus, calculus is a toolkit, it's a mathematical structure. You can use calculus to do classical mechanics, Newtonian mechanics. You can write down F=MA, but if you had written down F=MA2 instead of F=MA, that would be the wrong theory. It does not describe our world, but that's not the fault of the toolkit. It's not calculus's fault that it has additional flexibility. It lets you write down other differential equations that happen not to describe our world, and it's useful for all sorts of other things that have nothing to do with Newtonian mechanics. So I think string theory, in my mind, is a similar sort of beast in the sense that we have not yet found the string theory version of F=MA, which describes our world. But despite this, it has been useful for all sorts of other things, including mathematics, as you said.

SPENCER: And should we think of that version of string theory as just sort of a mathematical toolkit that can be applied to different stuff?

CHRISTIAN: Yes, if you think of the broader framework as a math toolkit, then yes, I would view it as being more analogous to calculus that lets you do calculations. There's a funny story about this, if you'll permit me an anecdote. In 1991, a string theorist, Philip Candelas, gave a talk to some mathematicians at UC Berkeley. I was not there since I was minus one years old at that time. But he presented a certain math result, which is somewhat technical, but it's a counting problem. You're counting certain curves in these so-called Calabi–Yau manifolds. All you need to know is that the answers are some numbers, some integers that you count. He presented a calculation that was using string theory tools. It was using something called mirror symmetry. He said, "Hey, mathematicians, you are interested in this math problem. Here's the answer that I get using string theory tools." The mathematicians said, "Well, those numbers don't match what we got. We did this in a completely different way that did not use string theory, and we got a different answer." There was some tension, but then the mathematicians discovered that there was a bug in the code that they had used to compute these numbers, and when they fixed the bug, their answer exactly matched the string theory answer. That's an example where this has nothing to do with modeling our universe, but it demonstrates that string theory, like calculus, can be used for all sorts of other things, not just Newtonian mechanics or modeling the real world.

SPENCER: I think that's a good example. And I think this is one reason among multiple that this whole conversation gets very muddied. Because if we're thinking of string theory as this mathematical toolkit, the way we think of calculus as a mathematical toolkit, that sounds useful, both for pure math and maybe for applied stuff too, in some cases. But I think almost nobody is criticizing that. I think what people are criticizing is the quest to find the theory of everything that people refer to as string theory.

CHRISTIAN: That's right, yes, so it's good to clearly delineate, because it does seem like most of the public criticism around string theory is more about what we call string phenomenology, as I was mentioning before, trying to find the right F=MA. And okay, that's a hard problem. Some of the criticism, I think, is warranted in the sense that maybe decades ago, there was a lot of hype, and people believed that we were very, very close to solving that problem, to writing down the correct version of F=MA.

SPENCER: There were a lot of articles about, "Hey, they were going to, you know, this new theory of everything is just right at the doorstep," right?

CHRISTIAN: Yes, there were a lot of things like that. And people saying, "Oh, we're going to find supersymmetry at the Large Hadron Collider, like tomorrow or something." There was a lot of optimism. And I think some of the criticism is that, "Okay, you were very optimistic and maybe oversold string theory in the early days, and then you discovered the problem was harder than you thought, and now it's taking more time than expected to solve it." Some of that criticism, I think, is warranted, but it really depends on, I guess, what expectations you have of a subject in physics for it to be valid. Because the criticism of the hype, I think, is acceptable, but the criticism which says that string theory has made no intellectual progress or has no scientific content, people on YouTube say things along these lines, I think that's unwarranted, because there's all of the other stuff that it's done, both for mathematics, for quantum field theory, for various other subjects that it's contributed to. All of that has real and genuine intellectual content and is useful. This one part where we're trying to find the real world, "Okay, maybe you can criticize that, but smart people are working on it, and they're making progress."

SPENCER: Yeah, and obviously, in the process of doing, as you call it, string phenomenology, where you're trying to understand our actual Universe with string theory, many of these mathematical tools we call string theory were developed. So maybe you can give it credit for that. In a sense, in that quest, all this cool stuff came out of it. But I think it's still important to be able to have that conversation about the theory of physics itself and set aside the cool mathematical tools that have come out as a result.

CHRISTIAN: Yes, I think that's fair. Since you might say, "Well, okay, if you're making these arguments that string theory is interesting because it contributed to mathematics, then why is physics funding going to it instead of mathematics funding?" You could ask that question, and the answer is that some people doing what I would call string theory are funded through mathematics departments. But indeed, if we focus on the more narrow string phenomenology, criticism, then yes, I think I would concede a little more ground on the criticism of that direction, although I still think it's promising; it's still viable. So it's not the case that it's been ruled out. It's still possible that we will find the correct F=MA that describes our world.

SPENCER: Why does it have 10 dimensions? I feel this is something that's baffling to a lot of people, and please correct me if I'm wrong. But my understanding is that we've got the three dimensions of space. We all know we've got one dimension of time. Einstein wants to roll those together into space-time, this four-dimensional thing. Then something about the theory says we need six extra dimensions, but then, well, where are they? We have to kind of roll them up and make them really tiny, because otherwise it would be obvious that they aren't there. If they're rolled up and tiny, that's why we can't detect them, basically. Is that right?

CHRISTIAN: Yes, that's right. So the reason for the 10 dimensions comes back to this anomaly cancellation that we were discussing before. When you study the theory of the superstring, there's a consistency condition, the so-called anomaly cancellation, which was shown by Green and Schwartz. When you do this calculation and demand that the anomaly cancels so that the theory is consistent, it turns out that that condition is only satisfied if the number of spacetime dimensions is 10, and that's for the superstring. The superstring is the most popular starting point for doing this string phenomenology, to try to describe our world. But there are other string theories. I mean, there's so-called bosonic string theory, which is consistent in 26 dimensions. That theory has other issues. There's so-called topological string theories that are consistent in any even number of dimensions, like four, six, and eight, and so forth. This is kind of illustrating the umbrella. There are all sorts of different things within string theory, but the popular starting point for trying to describe our world is the one with 10 dimensions, and the 10 comes from this anomaly cancellation.

SPENCER: So it sounds like we can think of string theory as a set of theories, and they have different trade-offs. If you do the 10 dimensions, you get this nice property, and we like that. Some people are going to go that direction. Other people say, "Maybe there's another way we could do it with a slightly different variant, and that's going to require 26 dimensions," etc. Is that fair?

CHRISTIAN: I think that's fair. Yes. I think fewer people are doing the 26-dimensional version because that theory, this bosonic string theory, has an issue that it has what's called a tachyon. A tachyon signals some sort of instability in the theory, which means that the bosonic string as we typically study it seems inconsistent. It may be that so-called tachyon condensation happens, and this theory goes to some other vacuum, which we don't understand at the moment. So that theory has its own obstructions. It might be that secretly, there's some way of making the bosonic string consistent, but it also does not have fermions, and fermions are what make up the matter that we see, like electrons, for instance. So that theory has its own drawbacks. The superstring does have fermionic matter, which is why it's a more popular starting point, and that's why most people are starting with this 10-dimensional theory and then trying to find the right way of curling up the other six, as you said.

SPENCER: And my understanding is that in this sort of curling up of the dimensions, there may not be free parameters in the sense of single numbers you can set, but there's this huge set of theories, a really enormous set of theories that we're trying to find the right theory among, the one that fits our universe. Is that fair?

CHRISTIAN: That's right, yeah, there's a lot of knobs that you can tune. The space that we most often choose for curling up those six extra dimensions is something called a Calabi–Yau manifold, named after Calabi–Yau, of course. You need a six-dimensional Calabi–Yau, as we said, to come down from 10 to four. It turns out that there's a huge number of Calabi–Yau manifolds. In addition to choosing this manifold, there are other choices that you have to make in doing this compactification from 10 to four. The main technical obstruction is figuring out which of these many choices leads to the world that we live in. It's kind of like there are a lot of differential equations that you could write down, coming back to the calculus analogy. It's finding which one is F=MA. But there's very interesting recent progress on this. Thomas Harvey, who's one of my colleagues at IFI, is now applying machine learning techniques. You can try to say, "Okay, suppose that I do a particular compactification. I pick some way of curling up the dimensions, some way of making all of these other choices. Given those choices, he can then compute the masses of quarks, which are real physical things." Quarks make up protons and neutrons. You can use machine learning to try to figure out, if the masses of the quarks turn out to be something like this, can I move around and tune the knobs differently to get closer to the true values of quarks that we observe? There are very interesting modern techniques being applied to this problem. But to your point, indeed, the main technical obstruction is this huge search space.

SPENCER: Is it fair to say that each point in that giant search space is a hypothetical universe with its own physical laws?

CHRISTIAN: Yes, that's exactly right. Each one of those would have a different collection of particles that interact in different ways. In principle, it would have a different cosmology. The universe might be expanding the way ours is, or it might not. The challenge is that each of those is a possible universe that describes an enormous landscape. This is the string landscape, as it's referred to. There's a landscape of possible universes, and the problem is finding where in that landscape our universe is.

SPENCER: Is this where the kind of swampland idea comes in as well?

CHRISTIAN: Yes, that's a very interesting, sort of recent direction in string theory. How to explain it? The swampland is kind of asking the opposite question. It's saying, "Rather than starting from a theory of everything that makes sense at very high energies, what constraints can we impose purely at low energies? Which would come from the assumption that my low energy theory descends from a complete theory at high energies." It's trying to rule out possible parts of the landscape and partition it into the good parts, the actual landscape, and then the swampland, which are the parts that are inconsistent. That's very interesting because, rather than doing a search through an entire space in a positive sense, where you're trying to look for the right answer, it's somehow going the opposite way. It's trying to find what the rules are that rule out particular candidates. It's going in the dual or negative sense to try to cut down the search space.

SPENCER: Do we know of a physical observation that, at least in theory, could be made, even if it would be ridiculously hard to make, that would rule out the entire set of all string theories? "Oh, if we measured that thing and saw it had this value, all the string theories are dead."

CHRISTIAN: It's very hard, because there are very few model-agnostic predictions of string theory. Again, there are so many universes. It's very hard.

SPENCER: But it's not all possible universes. Let's talk about Fourier analysis and math. You find that any repeating signal can be decomposed and rewritten as a bunch of sines and cosines. You could imagine someone saying, "Oh, I have this new theory. Look, I can write it as sines and cosines." Then someone might respond, "Yeah, but you could do that with anything. You have a really powerful set of math, but you haven't actually added anything, because any signal could be decomposed that way with some exceptions, maybe you can't," but I guess what I'm getting at is the set of string theories encompasses every possible universe. Are there actually ones that don't fit this model that could really rule out the whole thing at once?

CHRISTIAN: Yeah, good. For instance, if you could somehow demonstrate that there are not 10 spacetime dimensions, in some way, I'm not sure how you would do this via a measurement, then that particular avenue of string phenomenology, where you start with the 10-dimensional superstring and compactify, would be ruled out. If you could do a measurement that does that, then although string theory would survive as a collection of useful ideas, that particular research direction would be dead. But it's very difficult to propose an experiment that would conclusively rule out, say, 10 dimensions, because at any energy scale, it could be that the extra dimensions are just much smaller than you thought. You attempted to do some calculation, and you couldn't go to high enough energies. It's very difficult to rule out string theory with direct experimental observations. In that sense, you might argue that it's in some sense unfalsifiable, but I would say that within specific model-building choices, there are predictions and bounds. For particular types of compactifications, you can set bounds and say, "Okay, within this family, we would see these particular observables." You could go do measurements and try to rule out that class of compactifications, or you could attempt to falsify string theory on the grounds of mathematical consistency. If it turns out that the anomaly cancellation paper that kicked off the interest in string theory secretly had a mathematical error in it somewhere, and there was something wrong, and the anomalies don't cancel and string theory doesn't make sense, then I think everyone would agree, "Okay, we're going to go work on something else."

SPENCER: So let's suppose that it doesn't have any mathematical problems. It's not an inconsistent theory, but suppose it just turns out that our universe doesn't match string theory. It's just that we were really unlucky that it happened to have all this promising seeming stuff. How would we know that? Unless we actually figure out that other theory, would we just keep studying string theory forever in that world?

CHRISTIAN: Yeah, I think, well, if it turned out that we were unlucky, and nowhere in the string landscape is our universe.

SPENCER: That's what I'm saying, yeah. Let's suppose that it's true.

CHRISTIAN: If that's true, yes, then I think, well, in that scenario, I guess the first statement I would make is that I would probably still continue working on it just out of mathematical interest. But then I think the community would — if this were somehow known — then we would have to sort of start from scratch. We would have to start looking for a different theory of quantum gravity and come up with something different, which alludes to the point that we made before that some people are trying these alternate approaches, but I don't have a sharp way of diagnosing whether that would be true, or I don't have a good answer to the question of how do we know whether we live in this unlucky non-string theoretic universe.

SPENCER: And I guess my sort of deeper question there is, let's suppose that were true, what would we do? Because obviously we would never know it. It seems we could just endlessly work on this. As long as there's no mathematical inconsistency, could you ever actually get to a place where you're like, "Nope, this isn't our universe?"

CHRISTIAN: By experiment, you mean?

SPENCER: Well, through any method, I guess, other than the mathematical inconsistency, is there a way to be like, "Oh no, we've ruled it out. Our universe isn't in there."

CHRISTIAN: Good, I guess, if we were super powerful and we could kind of search the space of all possible compactifications. If you had billions of dollars in compute and could check the implications of each possible string compactification, and you found that in every single case that you could possibly check, of which there are believed to be finitely many, you check all of them and you find that none of them quite match our world, then we would say, "Okay, then we definitely live in a universe that is not described by string theory."

SPENCER: Got it. And so we would need some sort of super advanced technology, presumably, to be able to definitively rule it out.

CHRISTIAN: Yes, I think that's right. Since it's such an enormous search space, at the moment, doing some sort of exhaustive cataloging of all of the different possibilities is intractable, but it's conceivable that in the future, a super powerful, advanced civilization might be able to go through all of the possible string compactifications and check each of them, and then you could rule it out.

SPENCER: And this is a related critique, but it's a little hard to express. It was what I was trying to get at before, which is, is it possible that the true universe is in that set? But it's more like string theory is just so powerful it could describe any universe, so it doesn't end up doing any work. In some sense, it's like, "Oh yeah, you have just a completely general theory that could describe just about anything. And any such theory will contain our universe." But you haven't really gotten anywhere. Any sufficiently powerful theory that contains nearly every universe will have our universe. Does that make sense as a critique?

CHRISTIAN: I think I understand, but I would view that as a feature and not a bug, in the same sense that you wouldn't critique calculus for allowing you to write down all possible differential equations that describe all possible dynamical systems. It's a very powerful framework. So it is unfortunate that it's so powerful, in some sense, because it makes it hard to find the universe that we live in. But I view this as more of an embarrassment of riches, that the framework is so powerful that it allows you to describe so many possible universes, and it sort of makes sense as a critique, but I'm not so bothered by it, I guess would be my answer.

SPENCER: Let me put it a different way. Suppose someone was able to prove that our universe can be represented as a Turing machine or something like that. And then they say, "Look, I've solved physics. Our universe is a Turing machine. Now we just need to find which Turing machine it is." You kind of feel like, "Okay, it's really cool that they can show it's a Turing machine." But you kind of feel like they haven't done the work yet. They've just put in this ridiculously large class of theories, and yet, in theory, it would be in there, but they haven't. The theory hasn't really done the work to tell us what our universe actually is. Does that make sense?

CHRISTIAN: Yes, I think that makes sense. So I think the advantage of the string theory case over that case is the number of consistency conditions that it's been subjected to. If you say, "Okay, the universe is a Turing machine, great. There are many Turing machines, and I have to search through them." But I think in that case, if you had done the same level of consistency checking as has been done in string theory, where you say, "Suppose the universe is a Turing machine, all of these other things have to be true. There are all of these very tight constraints that come from consistency and things like that." If all of those checks had also been performed in the Turing machine case, then I think it might be equally interesting as string theory. But the large search space has a lot of internal structure, and there are many points at which it could have failed. There are many steps in the process of constructing this landscape of theories at which it could have turned out to have been wrong, and all of those checks so far have passed. I view this in a sort of Bayesian way, where each time there was a chance that this entire construction could have been wrong, and it turned out not to be wrong. This is repeated many times. I'm kind of updating my Bayesian prior each time that this thing is likely to describe the world, and getting closer and closer to a positive answer.

SPENCER: Yeah, that makes sense. I think we have to adjust it a little bit, though, based on human creativity. If you made one really hyper-specific theory, and it has no parameters, and then it gets subjected to all these tests, and it passes one and passes another, that's incredible. You're like, "Every time it passes one, if you didn't have any reason to know that it would pass it, it's an incredible verification of the theory." But let's say you have a million parameters you can tune, and you're like, "Oh, it didn't pass this test. Okay, we've got to twist it this way. Okay, now it passes." Then you're kind of like, "Well, it's less impressive." I'm not saying it's not impressive. It's still very impressive, but you've got to say, "Ah, my Bayesian update has to be a lot lower." Because we're throwing human creativity about how we change the theory to make it pass? Or is that not true, what I'm saying?

CHRISTIAN: Yeah, I think we should separate two things here, since the huge number of knobs that you can tune come from this choice of compactification. So the 60 spaces come from 10 to 4, but the theory itself, so string theory, the superstring theory itself, has one parameter. There's a single parameter defining the entire theory, which is roughly the length of the string. For the superstring, the dimension is fixed. If you say, "Okay, you can consider the different string theories, the 26-dimensional one, the 10-dimensional one, or M theory, or whatever." But if we focus on the superstring for the moment, that theory has only one parameter in it, which I find quite beautiful. It's, in some sense, essentially unique. The huge search base is coming not from the definition of the theory itself, but from the fact that we need to come down from 10 to 4.

SPENCER: I see. So in passing those tests, there wasn't actually that much wiggle room or that much play with how much they could adjust the theory. It genuinely passed tests that we didn't expect where we didn't know if it would pass.

CHRISTIAN: That's right, yes. So there are many points at which you could have said, "Okay, I have this theory with one parameter. I can't tune it in order to make it pass these checks; I just have to let it be a completely free parameter." And despite that lack of freedom, you could check all of these things: the anomaly, cancellation, the finiteness, all of these other things. And String Theory passes all of those tests without any fine tuning. The only step at which you have to do fine tuning is when you say, "Okay, now I have this great theory that lives in 10 dimensions and seems to have all of these cool properties. Now I need to come down from 10 to four." That's where the fine tuning problem comes in.

SPENCER: Got it. Suppose that you know, magically, you were about to learn the truth about whether our universe is modeled by these string theories. What probability would you assign to it turning out to be true?

CHRISTIAN: Oh, so you're asking me to guess. How confident am I that string theory describes our world? Basically, you want a percentage number. Yeah, that's a good question. I think I'm probably around 70 to 80%.

SPENCER: Okay, pretty high.

CHRISTIAN: Yeah. Different people will have different answers even within our community about this. But I think I'm cautiously optimistic.

SPENCER: Let's talk about the critique around testability. Because I think this is one of the things that really bothers people that, as far as I understand, string theory has not made a testable prediction that has then been verified. Is that accurate?

CHRISTIAN: That is correct, if you mean in the narrow sense.

SPENCER: The narrow sense, exactly, of string phenomenology trying to describe our universe. Has it made predictions that have been falsified?

CHRISTIAN: No, to the best of my knowledge, there are no predictions. You could take a very hard-nosed stance and say, "Okay, string theory predicts 10 dimensions and we don't see them," and say, "Okay, I don't believe your compactifications. I take as ground truth that we live in four dimensions." In that case, you would say, "String theory made a prediction that was falsified." But if we're being somewhat more charitable and say we're allowed to do this compactification process, then to the best of my knowledge, string theory has not made a prediction that is falsified. No.

SPENCER: So what is going on when you get things like physicists saying, "Oh, it's the Large Hadron Collider. I think you're going to find this thing or that thing that seems to be coming from string theory," and then we don't find those things? How do we make sense of that?

CHRISTIAN: Yeah, that was part of the criticism around the hype surrounding string theory. String theory has supersymmetry in it. That means that in order to make contact with our world, there needs to be some mechanism by which that supersymmetry is broken at low energies. At very high energies, the supersymmetry is restored. As you come down, at some point, the supersymmetry is broken. Since we don't seem to notice supersymmetry in our world, at the Large Hadron Collider, people thought, "Well, okay, since we're going to higher and higher energies, maybe we'll start to see some of these superpartners." The supersymmetric particles are paired with the particles that we already know and love. It turns out that at the energy scales probed at the LHC, we did not see supersymmetry. This is not a falsification of string theory because it could have just turned out that we were unlucky, and the energy scale that you need to go to in order to see supersymmetry just happens to be higher. That's part of this string theory-inspired set of predictions for what we might see at the LHC or at a future collider.

SPENCER: So there were some more specific models that said, "Well, maybe we'll see it there," but we don't know for sure because it could be higher energy. That's where those predictions came from.

CHRISTIAN: Yes, that's right. If I wanted to play devil's advocate and criticize string theory, I would say, "Well, you're sort of evading the question because every time you predict supersymmetric particles and they're not observed, you sort of back off and just say, 'Oh, they're at slightly higher energies,' and that's why you're not falsifying my theory." That's the critique that some people would make, and I would just say that, unfortunately, it is a feature of the theory that we don't know the energy scale at which supersymmetry is broken or restored, and that's just an uncomfortable fact that we have to.

SPENCER: Got it. Now, some people will say, "Well, is it really science if you're not making predictions about the world and then checking them? Hasn't something fundamental about the nature of science broken down? Is there a definition of science that doesn't involve checking things in the world and making sure they match the theory?"

CHRISTIAN: Yeah, I think the ultimate goal is still to make predictions and test them against reality. So I would say it's still science. But unfortunately, one gets diminishing returns, and part of the criticism of string theory, I think, is motivated by the fact that we were very fortunate. In the 20th century, there was an enormous amount of progress. We figured out quantum mechanics, we figured out general relativity. We started to find all of these new particles. And there was a sort of golden age where all of this progress was made very quickly.

SPENCER: It was like 1970 or something and we just had this ridiculous number of breakthroughs.

CHRISTIAN: Yes, there were just a bunch of breakthroughs, like Nobel Prizes for new particles, all this stuff in a very short time span. Unfortunately, not that that work was easy; that was very difficult work, but the low-hanging fruit has been picked. Now, to do quantum gravity, it just turns out that this problem is much, much harder. I would argue that we are still doing science because we ultimately do want to make predictions and test them, but we've gotten to the point where, in this curve of diminishing returns, the amount of work that we need to put in to get more predictions is just higher, and it's just going to take a longer time to get to the point where we can actually make contact with reality.

SPENCER: It seems to me, and please correct me if you disagree, the strongest case for string theory is that it did these miraculous mathematical things that we wouldn't necessarily expect it to do, and that no other theory has been able to do. A good theory has to do this, and it's done a bunch of them, which is really hard and impressive. In a Bayesian sense, the fact that it's been able to do that a number of times raises the question: if it's not describing our world, why does it keep working for these things? On the other hand, I also see it as a valid critique that it's not actually making contact with experimental predictions, which makes me very nervous. If it's not our universe, how are we going to ever know that? Are we just going to spend another a hundred years going down this pathway? It seems we may not realize it if it's not our universe. What do you think about that way of presenting it?

CHRISTIAN: I think that's fair. There is a danger when you're working on a very hard problem for a long time that you may invest all of this energy and it turns out that it was not going to work. That is a valid critique. From my perspective, the amount of contact that string theory has already managed to make with our world inspires enough confidence in me. Another example is the study of black holes. We mentioned before that black holes are a regime where you need to understand both quantum mechanics and general relativity. Black holes are known to have an entropy, the so-called Bekenstein-Hawking entropy, which is somewhat surprising. For those that don't know, entropy is a way of measuring if you have a coarse-grained system, like if you only have access to the temperature in the room rather than having the fine-grained information of where every single particle of air is and how fast they're moving. That's the microscopic description. If I only have access to the temperature, which is some average energy of the particles, then you can associate some entropy, measuring how many different microstate configurations would have been compatible with that coarse-grained data. It turns out that black holes also have entropy. One of the big successes of string theory was that it was able, in a particular setup due to Strominger and Vafa, to compute the black hole entropy and explain what those microscopic configurations are that give rise to this coarse-grained entropy. If string theory is able to correctly predict the entropy of black holes, which is not something we can directly measure, I can't go up to a black hole and just measure its entropy in a direct sense, but it can reproduce this fact, which we know is true about black holes. That sort of statement makes me more confident in this Bayesian sense that it's likely to describe our world. I realize I'm evading the question a little bit since none of these are direct experimental observations, and I concede we don't have any of those, but there's this mountain of indirect evidence, which I find compelling.

SPENCER: That's really interesting. Is that the mathematical machinery that we got from doing string theory that's being put to use, or is that actually the physical theory about the universe that's being used to get that match with the entropy number?

CHRISTIAN: Yes. That's using a particular string theory solution. In this landscape, there are many options. In this calculation, they pick a particular one. Here's a good solution of string theory that happens to have a black hole in it, and they're able to, in that particular situation, count how many different ways the black hole could be arranged such that the coarse-grained data is the same. They do the calculation, and it matches what Hawking tells us the entropy of a black hole actually is. You might push back and say, "Well, that particular solution they used is not the one that corresponds to our world."

SPENCER: And that's such a funny idea because it's not even our universe, but somehow gives the right answer, right?

CHRISTIAN: Yes. So in some sense, I guess it's telling us that black hole entropies are somehow more universal than might have been thought. So that black holes, even in universes which are not the same as ours, still have similar statistical properties or similar entropies. So maybe there's some sort of universality statement, since the same thing happens to apply in our world.

SPENCER: And I assume they didn't just cook up that to be the universe that gave the right answer. It's like they picked it because it had this black hole, not because it gave the correct number.

CHRISTIAN: That's right. Yes. And since then, there's been a lot of work doing this in other setups besides that one, and also finding corrections. So this black hole entropy has some leading term and then some subleading corrections. And you can compute these subleading corrections in string theory, and they also match. So all of these things seem to suggest that, "Okay, even though these calculations are not done in our world, they have black holes. And apparently the black holes behave the same way in those alternate universes as they appear to behave in our world."

SPENCER: Yeah, that's fascinating. I never heard that example, but that's quite interesting evidence related to string theory. Even if we don't know which universe it is, it's capturing something about universes like ours that are relevant.

CHRISTIAN: Yeah. So I think you may or may not consider this evidence, depending on your philosophical inclinations, but I guess it illustrates the broader point that even though we don't know where in string theory our universe is, one thing you might try to do is say, "Okay, what features are common across consistent universes and can therefore be ported somehow to understand something about our world?" I guess this black hole example is one instance of this.

SPENCER: Why do people on YouTube hate string theory so much?

CHRISTIAN: Yeah, that's an excellent question. I think there's different types of criticism on YouTube. I think some of it is bad faith actors who would like to manufacture controversy where there isn't as much as they might think.

SPENCER: When you say bad faith. Do you mean that they don't actually hate it, they're just pretending they get it? Or do you mean that they do hate it, but they're also trying to use it for some ends you think are bad?

CHRISTIAN: I think probably the latter. So examples I'm thinking of are people like Sabine Hossenfelder and Eric Weinstein, who maybe genuinely hate string theory. Maybe they don't, but I think the criticisms that they're making are unjustified and much too sweeping. The reason for that, I think, is probably audience capture; just the algorithm maybe rewards people who manufacture controversy and rage bait viewers and things like that. So that could be part of the reason for the criticism. Part of the reason might be more measured, and on YouTube, for instance, Angela Collier has a much more reasonable video critiquing string theory, and I actually respect her, and I think that's a better criticism. That goes to this overhyped nature that we were discussing before, that it always seemed like the discovery of, say, supersymmetry was right around the corner, and it turned out not to be there. So some of the hatred on YouTube is for the more valid reasons that we've discussed before, and some of the criticism on YouTube, I think, is merely to get people riled up basically.

SPENCER: My understanding is that Sabine Hossenfelder, who's now really popular on YouTube, is generally very skeptical of fundamental physics and thinks the whole thing has gone the wrong way. She has a whole book about how physics got caught up in doing math. Would you think that there is a kernel of valid criticism there, or do you think she just doesn't have a good point?

CHRISTIAN: I read her book, and I find it difficult to extract a kernel of good criticism there, since it seems that she is uniformly critical of essentially all approaches to unification and quantum gravity. I recently gave a sort of mini talk with slides dissecting some of her statements and explaining why I disagree with them on scientific grounds on the Professor Dave Explains channel. So I think her attitude is essentially to equate all approaches to fundamental physics and say, "This is nonsense. That's nonsense. All of this is nonsense. Everything that these guys are doing is insane," which I think is completely unjustified. I think the overwhelming majority of scientists are acting in good faith. They're genuinely trying to solve hard problems, and they're using the tools that they think are most appropriate for the task. It just turns out that with the toolkit that we have right now, string theory seems to be the best option to use to solve these hard problems.

SPENCER: My strongest version of her argument, if I try to make her argument, is that it can be appealing to focus on elements of a theory that are not necessarily grounded in reality. For example, as a mathematician, I know that mathematicians love beauty, whatever that is. They can be drawn to beauty in math, and it can become a funny thing where they respect certain results and not other results based on this notion of beauty or harmony. It's a little hard to know what they're talking about. "Should we really be doing math based on that?" The reality is, I think that does influence math to some extent. It's not the main thing, but it is to some extent. I think she's arguing that some of the heuristics people use when they're looking for physical theories might have this kind of nature to them, where you're looking for something that seems beautiful, or you make assumptions about the way nature ought to be because that's the way humans want it to be. Do you think there's something there?

CHRISTIAN: I acknowledge the criticism, but I would say that historically, it does seem like looking for elegance has been productive in physics. For instance, Einstein's theory of general relativity could have ended up being very ugly, but it essentially turns out that once you incorporate differential geometry and say, "Okay, space-time is now a curved manifold, that's how you do the setup of Einstein Gravity." That's a very elegant unification, in the same way that special relativity unifies the three space dimensions with one time dimension and says, "Okay, let's package that all together into one four-dimensional space-time." It's an appealing picture, and it ended up being correct. I would concede that some of the criticism is fair because not every theory that seems initially beautiful ends up being correct. A common counterexample people give is, I think it was Kelvin. Kelvin proposed at some point that maybe the periodic table is explained by knot theory. If I remember correctly, maybe hydrogen was the unknot and helium was the trefoil. All of these different knots were supposed to correspond to different elements in the periodic table. That seemed kind of elegant, but it was very quickly realized that that's simply not true because it fails various checks. I will concede that sometimes something which seems initially beautiful may be false, but there are many examples where beauty has been a good guiding heuristic. The fact that string theory is both beautiful and has passed all of the checks that we discussed before sort of softens this criticism that maybe we're being deceived by a mirage of beauty or something and the theory is actually wrong.

SPENCER: So you're not saying that physicists don't use elegance or beauty as a criterion. You're just saying that actually, it's a justified criterion to some extent, not to use it to the exclusion of everything else, but as part of the approach.

CHRISTIAN: Yes, I think that's right. The beauty heuristic is one part of it. If it just turned out that the true theory of quantum gravity was extremely ugly, maybe it's not elegant. It's just a horrible thing to write down. That's fine; we would still accept that, but I would be slightly surprised if that were true because it seems like in the past, things that are elegant have ended up being right. Quantum field theory, in some senses, is another example where you say, "Is light a particle or a wave? Quantum mechanics kind of tells us that it's sort of both, which seems confusing." But then when you understand that light is really just a field, a photon field that permeates space-time, and there can be little ripples in that field which explain the way that light behaves, to me, that's a very elegant solution. It nicely packages the way that we thought about light before, and it ended up being correct. In short, beauty is one heuristic, but it's not the only one.

SPENCER: It's interesting. I sort of half agree. I feel there are different versions of beauty, and some of them are actually better guides, and some are less good guides. For example, if you don't understand something very well, it can be easy to think of it as multiple things when it's really one thing. If it turns out it's multiple things, and it's actually one thing when you think it's multiple things, it's going to seem much more beautiful once you get the right answer. That's a kind of elegance that could be a good heuristic. "Could we be looking at one thing that we think is multiple things?" To me, that makes sense, but I also think there's just this aesthetic thing that humans have; we just like certain things, and I don't see any particular reason why the human mind's aesthetic would particularly match the true laws of physics, per se.

CHRISTIAN: I think that's fair. Yes, there's sort of anthropic bias. You might say that our brains are built in a particular way. Unfortunately, humans are the ones doing physics, so we're stuck with the biases that we have. Until we get super powerful AI that can do physics for us and might have a different sense of beauty, this is the one that we're sort of stuck with. I think just the a posteriori examples that we mentioned before, where it has been useful in the past, is enough for me, at least personally, to continue to use it as a heuristic.

SPENCER: It would be interesting if it turned out the true laws of physics have just 40 million terms in them, just a ridiculous mess. What we've been doing is finding these incredibly beautiful, simple theories that are just somehow an approximation of this monstrosity.

CHRISTIAN: Yeah, that could well be true. I guess the universe has no reason to be kind to us, but the Einstein field equations in general relativity can be written in a single line. The definition of the Standard Model of particle physics, although it has a lot of stuff in it, if you package it correctly, can also be written in a pretty neat form. So far, the universe has been rather generous to us in giving us relatively beautiful and succinct physical laws. You're right.

SPENCER: It's almost eerie. I find it almost eerie how simple the laws we found are.

CHRISTIAN: Yes, there was no reason for it to be the case necessarily. So maybe it breaks down at some point. There is a possibility that we got lucky with the first few levels of physics, and they were all very beautiful. But once you go all the way to the top and the theory of everything, it stops being beautiful. That's logically possible, but I'm going to hope that's not the case and keep working on it regardless.

SPENCER: Another point, and we've touched on this briefly, but it's often made by YouTubers, is that physics has dramatically slowed down. I think it's important here to separate different branches of physics because usually what they're talking about is sort of fundamental physics, like the search for the deep fundamental laws. I think everyone agrees it has slowed down, but they may disagree about the reason for that. There are also other areas of physics that maybe haven't slowed down. So, could you comment on that?

CHRISTIAN: I suppose that's true. Yes, you might make the comment, "Well, okay, the standard model has not been updated in decades or something." We found the Higgs, but besides that, that was predicted some time ago. Other areas of physics, I think, for instance, condensed matter — I'm not an expert in condensed matter physics — it seems like those other areas are not having the same sort of slowdown. Maybe it's just because there's more low-hanging fruit to be picked in those areas, like condensed matter or biophysics, for instance, astrophysics and cosmology. I know very little about these fields, but my impression is that they are not having the same degree of slowdown as we are in fundamental theory.

SPENCER: They also might think it's possible some of them get more benefit from the newest technology coming out as well.

CHRISTIAN: That could also be true, yes, since in those areas, to my understanding, they don't have the barrier we have now, which is essentially we are in a data-starved environment. The reason why we can't test string theory is we can't go to high enough energies at this point, or we can't go up to a black hole and really poke it and see how a black hole behaves. So I think that's the reason for the slowdown in fundamental physics. But despite the data-starved environment, there's still been a lot of theoretical progress. These are not predictions, but some of the things that we've been discussing, this quark-gluon plasma stuff, the black hole microstate counting, there is progress, for instance, one of Witten's famous papers demonstrated that this so-called Chern-Simons theory, which appears somewhere in string theory, is related to knot theory. So you can compute these Jones polynomials, which are features of knots, by doing a quantum field theory calculation. I find this remarkable. So if you count that as progress, then theoretical physics has not really stalled. We've been thinking a lot and learning a lot of cool things about, I guess, the grammar of quantum gravity, so to speak. But I would say that although we're learning more and more about the grammar of quantum gravity, the final sentence where this is the answer, this is the quantum gravity theory that describes our universe, we have not landed on yet.

SPENCER: Yeah. And I imagine you would say, "Okay, there was this incredible progress in the early 1900s that a lot of low-hanging fruit was picked. We're just in a harder domain now. That's exactly what you should expect to happen when you've made a lot of breakthroughs." It gets harder to make new ones," whereas other people say, "Oh no, that shows the whole field went off the rails in the 1980s or something." Is that fair? That kind of bifurcation of viewpoints?

CHRISTIAN: Yes, I think that would be my rebuttal, because the fact that the standard model has not been updated in a while would probably be used as part of this criticism to say, "Oh, physics has stalled." But I would say, "Well, okay, yeah, we're in a harder environment, and now when you don't have access to data, we can't actually go to higher energies, or go back to the early universe and see exactly what was happening before inflation or anything like that." What else do you do? You either throw up your hands and stop and go work on something else, or you use the only tools that you have available in the absence of data, which are things like consistency conditions and theoretical checks, and that's what we've been doing in my field, at least. So I don't know if that counts as stalling, because those consistency checks and theoretical results, I think, are still interesting, but they have not yet led to testable predictions, which I guess a critic would label as a slowdown.

SPENCER: This mystery isn't as deep as the grand theory of everything, but why is content that is on string theory so popular?

CHRISTIAN: Yeah, it's an interesting question. I think maybe some of it is anti-intellectualism. It's not really clear to me. I find string theory very cool, so it's difficult for me to put my mind in the place of someone who enjoys anti-string theory.

SPENCER: You could imagine a world where it's just this niche thing that's interesting to learn about, but nobody really engages with it from the public.

CHRISTIAN: I guess that's true. You don't see people dunking on niche areas in math, like the Langlands program or something. So, yeah, I think the popularity of anti-string theory content maybe comes from, I guess, the kind of easy slogans that one can throw out, like, "Oh, you know, 10 dimensions sounds ridiculous, so it's easy to make fun of that." Or, "Oh, you have this enormous landscape. It's unfalsifiable." Things like that. They're kind of easy things to make fun of, I guess. And I think I've tried to argue that although these are challenges that need to be overcome, they're not serious issues. But I guess to maybe a lay audience, when you say some of these crazy sounding things, like 10 dimensions, it sounds very funny, and it makes it easy to laugh at string theory. And that might be some of the reason for the popularity of this dunking content. I guess.

SPENCER: Do you think it also ties into a broader, kind of anti-establishment worldview, and that somehow it's resonating because of that?

CHRISTIAN: That could also be part of it. So that seems, at least to be Eric Weinstein's point of view, is that there's somehow a cabal of string theorists, and they're, I don't know, maybe the king is Edward Witten, and Edward Witten is kind of secretly controlling the entire field and telling everyone what to do. And there's, you know this, I don't know, yeah, string theory establishment. So anti-establishment rhetoric, I guess, is part of string theory dunking. But what I would say is that there is no secret, smoky backroom deal happening where all of the string theorists are getting together and deciding what they're going to do. It's again, these people voting with their feet, and again, coming back to the diversity of different things that people do within the string theory umbrella. I don't think that this establishment criticism is really fair, because a lot of people in the umbrella are doing things related to, say, quantum information or related to condensed matter, and connections between condensed matter and string theory. So I don't think it's really as much of an establishment as the critics might say.

SPENCER: There's a sort of broader establishment that we might be talking about here as well, though. It seems to me that trust in science broadly and in particular, trust in certain areas of academia have really fallen. I don't have numbers on that, but that is at least the vibe, and I wonder if it also is resonating. For that reason, it's like, "Oh, look at this. Look at academics. They don't know what they're talking about. They're doing, you know, these claimed experts are actually full of shit. They're using taxpayer money for ridiculous things."

CHRISTIAN: Yes, yeah, I think that's also part of it, unfortunately, especially in the US, that's becoming more and more popular now, in part because of the administration. So maybe string theory is sort of catching strays, so to speak, that it's getting hit by this broader anti-intellectual trend, or distrust of academia overall. But yeah, I would go double down on my previous statement that I do think scientists are acting in good faith. You could argue about how taxpayer money should be allocated, and I think that's a fair discussion, but the funding agencies like NSF and DOE, they do a serious job of trying to evaluate the proposals that are put in front of them, and what is good science and what is bad science. So I think the system is working in the way that it should. So the good ideas are being pursued, and I think that this wasting of taxpayer money rhetoric is a bit misinformed.

SPENCER: I have a funny perspective on all this, because my field that I spent the last decade plus working on is psychology, and I come to it with a bit of an unusual perspective, because I'm a mathematician by background. But really, psychology is where I focus, and psychology legitimately has really serious problems. I think psychologists will tell you that. This is not a critique from outside the house; it is a critique from inside the house. You had the replication crisis, where maybe 40% or even 50% of papers were not replicating. You redo the exact same study, and you don't get the same result. My perspective is academia can go off the rails. I think that psychology did go off the rails for quite a while. I think it's getting back on the rails. I think there's real progress being seen, but it's certainly not beyond the realm of possibility that you have an entire academic discipline that does nonsense for a while.

CHRISTIAN: Yeah, I think that can certainly happen. I perhaps selfishly would argue that it has not happened in my field. I guess we don't have quite the same issues as psychology, because it's easier to replicate a mathematical proof; you just check the steps yourself instead of actually doing an experiment. To a first approximation, I do think that the papers that are put out in my field represent genuine results. The refereeing process has its flaws, but it works to a first approximation. I think that we're still firmly on the rails. But of course, this is coming from inside the house, so I'm biased.

SPENCER: It's funny when I talk to people who've never been in academia, for some reason, they seem to think that the review process is this friendly thing. My experience with papers is that reviewers don't want to publish your paper; they're ready to tear it to shreds. If they see flaws with it, they're very happy to not publish it. Essentially, I would say it's an adversarial process. Would you agree with that?

CHRISTIAN: Yes, and I think it's supposed to be. It's similar to a PhD defense. When you defend, you're supposed to be grilled, and this is part of the scientific process. Whenever I give talks, I receive questions that to someone outside of academia might seem adversarial or mean, but I enjoy this, and it's part of the process. Nasty referee reports that complain about things or push back in seminars are all things that improve our understanding of our work and make us think more deeply about it, to ensure that it's correct and that we're doing good science. I think that's all part of the guardrails, I guess, that are keeping us moving in the right direction.

SPENCER: Yeah, I think that people publishing papers in these journals really do get extreme critiques, and the people looking for flaws in the work, I think when it goes off the rails, sometimes it's because something that is actually bad becomes accepted for some reason. This is part of what happened in psychology. There were certain bad methodologies that for some reason, there was a norm that allowed them to happen and didn't view them as bad. Suddenly, reviewers weren't rejecting papers with an N equals 20, and they weren't rejecting papers that had, what we today would call PIAAC, but I think that was because there wasn't such an understanding of these things. There wasn't a norm around these things. Eventually, part of what I think made psychology better and improved it is that the norms caught up to, "Oh, wait, these are not acceptable practices."

CHRISTIAN: Yes, good. I think something like that. It may turn out in 20 years or something like that. I don't know of any specific examples of bad practices that are necessarily happening in my field now. One analog might be that some people write more speculative papers where they generate conjectures. For instance, a criticism of this swampland program that we were discussing before, which is sometimes leveled, is that these guys generate many swampland conjectures, which they believe must be true in any theory that comes from a consistent theory of quantum gravity, but then they simply generate those conjectures and don't try to prove them. That's one criticism you might make, where you say, "Okay, this is an example of a bad practice that is becoming normalized." More recently, I think people have been making serious efforts to say, "Okay, now we have to actually roll up our sleeves and try to test some of these conjectures and see if they're actually correct, rather than just generating an infinite set of swampland conjectures and then calling it a day." Bad practices can slip in, and in 20 years, we might look back and say, "Okay, maybe this particular thing within string theory was a bad practice at the time, but I think by and large, there's no sort of large crisis within the field I work in at least."

SPENCER: You've been very generous with allowing me to throw criticisms at you, and I think you've responded in a way that shows you are very accepting that your field is not perfect. To wrap up, I just want to ask you, what are you really excited about in terms of research in your area? What do you see as bright spots and things that could make progress in the future?

CHRISTIAN: Yeah, good. I mentioned the AI stuff a little bit before, but I'm actually very excited about connections between AI and physics and using AI tools to solve physics problems. Since AI is becoming more and more powerful, it might help us address some of these thorny issues that even in purely theoretical work like string theory, we've been struggling with for some time. For instance, I'll give you one example of progress in this direction. I mentioned several times that you have to curl up these six dimensions to go from 10 down to four. There's a question when you choose one of these so-called Calabi–Yau manifolds to come down from 10 to four. What sort of geometry do you want to give it? The technical term is a metric, or Riemannian metric on this space. For a long time, people did not know how to write down any closed form expression for this metric that describes the geometry. It was just not known. Then fairly recently, people discovered that using neural network tools, you can actually learn the geometry of a Calabi–Yau, so you can design an appropriate loss function and then train it, and the neural network gives you a numerical representation of the actual geometry of that six-dimensional space that you come down on. That's something I think is exciting. As AI gets more and more powerful, we might be able to use it to address more and more of these problems in string theory, and eventually, if we're lucky, maybe make contact with reality and finally have a good response to the fair critiques that you've been raising.

SPENCER: Christian, thanks so much for coming on the Clearer Thinking Podcast.

CHRISTIAN: Yeah, I had a great time. Thanks for having me.