Will We Ever Prove String Theory?

For decades, string theory has been hailed as the leading candidate for the theory of everything in our universe. Yet despite its mathematical elegance, the theory still lacks empirical evidence.

One of its most intriguing, yet vexing, implications is that if all matter and forces are composed of vibrations of tiny strands, then this allows for a vast landscape of possible universes with different physical properties, varieties of particles and complex space-times. How, then, can we possibly pinpoint our own universe within a field of almost infinite possibilities?

Since 2005, Cumrun Vafa of Harvard University has been working to weed out this crowded landscape by identifying which hypothetical universes lie in a ‘swampland’ with properties inconsistent with the world we observe. In this episode of The Joy of Why, Vafa talks to co-host Janna Levin about the current state of string theory, why there are no more than 11 dimensions, how his swampland concept got an unexpected lift from the BICEP array, and how close we may be to testable predictions.

Listen on Apple Podcasts, Spotify, TuneIn or your favorite podcasting app, or you can stream it from Quanta.

Transcript

[Music]

JANNA LEVIN: I’m Janna Levin

STEVE STROGATZ: And I’m Steve Strogatz.

LEVIN: And this is The Joy of Why, a podcast from Quanta Magazine exploring some of the biggest unanswered questions in math and science today.

Hey, Steve.

STROGATZ: Hi, Janna.

LEVIN: Different day, different studio.

STROGATZ: Yes, I’m going for the Orson Welles look here.

LEVIN: I know. I actually like it. It’s looking good.

I want to talk to you today about something that’s gotten quite controversial, and so I really want to ask your honest take on string theory. How do you really feel about string theory?

STROGATZ: I don’t really have an informed opinion.

LEVIN: That has never stopped anybody.

STROGATZ: What I’m told is it’s helping a lot in pure math that the techniques from string theory are being imported into fields like algebraic geometry. As for what it’s doing for physics, I get the feeling it’s the best game in town, but it’s hard to tell yet whether it’s going to really describe the physics of our universe.

LEVIN: Yeah, I think it’s been a fascinating legacy. So, the excitement initially was that string theory might do for quantum gravity what all of these famous theories, like the electroweak theory and the theories about the matter forces, did for matter, which is to say it unified them all into one sort of elegant equation.

And so, the hope was that there would be one string theory, right? And instead, what happened is there ended up being this vast landscape of possible string theories, like 10 to the 500 possible vacua, or starting points. And that became, at first a tremendous disappointment. And then people sort of ran with it and started talking about the multiverse and then that led to very strong, I think, reaction against string theory. But that hasn’t rocked your world, that sort of reaction against it?

STROGATZ: My personal world?

LEVIN: Yeah. Yeah.

STROGATZ: I don’t know what to make of it. I mean, I do hear people criticizing it very much as being untestable in principle. A lot of people invoke Karl Popper and his, whatever era that was, 1940s or 50s-era philosophy of science.

There’s a part of me that wants to believe that this could work because it seems so compelling to be able to get rid of the problems of renormalization that have afflicted a lot of attempts to quantize gravity. And that was the initial selling point, wasn’t it? That string theory could handle that in a way that other theories had trouble with?

LEVIN: I would say that the big success was that gravitons, which are the little quanta of gravity waves  — the way that photons are the quanta of electromagnetic waves  — were natural. A natural ringing of a string in the same way that the other particles were harmonics on a string. And so that was really the enthusiasm. Whether it was not fully quantized is really a different story.

Well, you know, I brought some of these concerns up to our guest who is a very influential string theorist, Cumrun Vafa. He’s a professor at Harvard and it was interesting because he didn’t dismiss the concerns. And one of the ideas he had was to invoke a concept he’s called the “swampland.” So, it looked like there were all of these string theories, and it was totally proliferating, and we couldn’t find our universe in this muck. And so, he had a program instead to kind of cull theories that he could prove failed.

STROGATZ: First of all, I love the term swampland, very suggestive. But what are some of the admissibility criteria? What sends you to the swamp?

LEVIN: Yeah, it’s interesting. It’s such a complicated program, but it could be that it won’t lead to the kind of universe we observe today, or the matter fields don’t drop out to match what we expect from the Standard Model of particle physics, which is so successful. General relativity, it can’t look like a different theory of gravity.

So we have these key anchors. We want any theory that goes beyond these to be able to replicate the successes in the right regime. And so, I think it’s just kind of a way of whacking through the brush and clearing away what you know is weed, right? From what you’re hoping to find, I guess, which would in this analogy be like, I don’t know, the roses.

STROGATZ: This sounds great.

LEVIN: So, that’s sort of my synopsis of this scenario. But maybe we should hear from Cumrun himself. Here’s theoretical physicist, Cumrun Vafa.

[Music]

LEVIN: Cumrun, welcome to The Joy of Why. We’re excited to have you on the show.

CUMRUN VAFA: Thanks. It’s a great pleasure to be on this show.

LEVIN: I can see some equations on the blackboard behind you. I want to open for our audience just to ask, how does a person get into theoretical physics? What’s drawn you to that subject?

VAFA: My interest in theoretical physics started when I was a kid. I vividly remember my awe and amazement at the fact that the moon does not fall down as something needing some explanation.

And it bothered me that most people were not bothered by this fact, that there’s this thing up there and it might hit them on their head or something, but it was kind of, “Yeah, it’s cool. It’s beautiful. What’s the issue here?”

Why don’t you ask this question? Why is it not falling down? I mean, isn’t that the obvious question? So, these kind of things were always hitting me in some form or another. But it took a while for me to zoom into theoretical physics as a profession.

LEVIN: It really is one of the huge insights of Newton that the moon doesn’t fall to the Earth. Why that’s the case, and connecting that to the kinds of physics we understand on the Earth. I don’t know if people appreciate what an enormous leap it was to imagine that the moon was dictated by the same forces that plucked an apple from a tree.

VAFA: Exactly. And when I later learned Newton’s understanding of how this works, and the fact that why does the Moon fall ends up being, no actually the moon is falling, and how is that compatible with the fact that the moon is not hitting the ground? That, to me, was quite an “Ah!” moment, also that’s the way physics understands how things work.

LEVIN: And then, of course, Einstein hundreds of years later talks a lot about falling. He thinks about free fall in an even deeper way than Newton to some extent.

VAFA: Yes, in some sense, the fact that being in an elevator and falling, you wouldn’t know if you’re in outer space or falling. And the fact that there’s no experiment that can detect the difference was quite an insight. He has said that this is one of the happiest scientific thoughts he had.

LEVIN: I love that quote … happiest thought of my life. And the thought is really about gravity being a form of weightlessness. I feel heavy on my chair right now. I feel heavy when I’m walking around on my feet, but really Einstein began to think of gravity as, oh no, it’s actually removing all that stuff and experiencing this free falling weightlessness. How does that relate to his theory?

VAFA: The fact that the objects move the way they do regardless of their mass, so to speak, and that point that the things does not care about the trajectory you take in space-time. The fact that geometry of space-time dictates this to all of the objects around it, that was a beautiful geometrization of gravitational force.

LEVIN: Hmm. So, you’re a student of theoretical physics at some stage learning Einstein’s geometric theory of gravity and free fall. What draws you now the extra step to something as abstract and complex as string theory?

VAFA: The interest in string theory is related to the interest in trying to understand the fundamental laws of nature. How things work at the deepest level. What is everything made of? How are the forces interacting with each other? What are the forces? What are the fundamental things? And, in particular, it had been tried for many decades, but unsuccessfully, to understand Einstein’s theory at the microscopic level.

And that somehow didn’t work in the context of mixing it with quantum mechanics, which is the law that governs the microscopic physics. So, when you try to bring in quantum descriptions, which is needed for small-scale descriptions, with Einstein’s theory, which is great for large distances, the two didn’t quite fit together and somehow gave contradictory results.

And trying to resolve these paradoxes was one of the major issues that was difficult for theoretical physics for many decades. And basically people didn’t work on it because they had no good idea. And then, suddenly out of the blue somebody suggested string theory sounds interesting, just let’s study it. And someone said, “Oh, it sounds like it has gravity in it. And oh yeah, it has quantum mechanics and gravity together in a consistent way.” So, it was accidentally discovered to be an answer to the question that people were looking for.

LEVIN: So, it’s a kind of a step towards a quantum gravity theory of everything — just a small thing like that.

VAFA: Exactly. Just a random discovery, I would say.  Whether we deserved it or not, I don’t know, but in some sense it just happened that what people were studying ended up being an answer to quantum gravity.

LEVIN: Hmm, exploration is often underrated, don’t you think, in the physical process as though there’s really a hypothesis set forth before you take a step. That’s really not how it’s always done.

VAFA: They always say just do the exploration, have a good question and you might get an answer to something else. And this happens quite often in the history of science. And I think string theory is a great example of that discovery.

LEVIN: Now, before string theory, we might’ve imagined that when we looked at more probing microscopic levels, we’d find little tiny point particles, and some of those point particles might even be gravitons, which are responsible for negotiating gravity between masses. What’s different in the string theory description? Those little points are replaced by little loops of string, is it that simple?

VAFA: Yes, to some extent it’s that simple. So, the loops that we call strings, of course, could be so small that they look like points, and therefore there’s not much of a difference when you look at it from far away. But when you zoom in and when you go to very high energies, this thing can stretch and then it gives you features like an extended object like strings.

We actually have learned in studying string theory that it’s not just a one-dimensional thing, like a string. Sometimes higher-dimensional objects like membranes enter the story as well. And so, we have learned this more than just about strings, but we still call the subject string theory.

But we have learned that inevitably demanding the fundamental particles, everything is just point-like particles, is insufficient to give you a consistent picture of how gravity works at the quantum or microscopic level.

LEVIN: I’ve sometimes heard people refer to M-theory and then I hear various things about [what] the M stands for. Is the M for membrane?

VAFA: Well, I don’t know what M stands for, but I think the main statement here is that we don’t really understand what the theory is to be honest in this form. We know how it works in examples — and so sometimes people say M might stand for mystery.

So we don’t exactly know what M stands for really, but we are still working on understanding what this theory really is about. It’s one of those exciting human adventures that I think is still continuing after many decades.

LEVIN: So, are people imagining that the entire spectrum of particles that we used to think were fundamental like an electron or a quark or a graviton, are just different harmonics played on the same kind of fundamental string?

VAFA: That could very well be. In other words, the idea that strings in different excitations and different harmonics and different configurations lead to different particles is certainly one of the amazingly beautiful predictions of string theory. It unifies all the object into one thing, though it could be like a membrane as well.

So, we don’t have an exact description like that. But we think, generally speaking, the fact that particles can unify and be manifested by one object in some form is certainly a natural possibility there.

LEVIN: So that really does instinctively sound like a unification, right? Which is the huge ambition. Can I unify all of the matter forces and gravity all into one? What do you think are the strongest arguments that we have that string theory will continue to be rewarding as a unified theory of everything? Because as you said, it’s not complete yet.

VAFA: Yes. It’s not complete. So, one thing you just mentioned is the aesthetics. Of course, the unifying of particles and forces and gravity and everything together in one package is already quite amazing. So that already is enough motivation to continue studying it.

However, there’s a lot more. And we have learned that even if you are not interested in quantum gravity, per se. Suppose you’re just saying, you know, I’m interested in just particles and the forces between them. You encounter questions in that context which have to do with very strong interactions between these particles, and we end up not knowing the answer to those questions in general.

However, it turns out that what we have learned from string theory sheds light even on those questions. So, questions that have nothing to do per se with gravity have been answered using string theoretic ideas. And so therefore, we feel that the truth of the string theory is far beyond just the gravity, even though that’s the main claim to fame of quantum gravity and string theory together.

But I think the fact that there are more motivations to study string theory is already quite remarkable. And it’s reinforcing the idea that there’s got to be true in some form or another. It cannot be just randomly there and we just stumbled upon it.

LEVIN: There are also some pretty severe criticisms or critiques of string theory. And I know that people get very emotional about this. I’ve sort of heard it described as an attempt at a theory of everything, but is it turning to the direction that we now kind of have a theory with no predictions because there’s so many possibilities?

VAFA: Actually, that’s a very good question. There’s a misunderstanding that string theory gives a huge number of possibilities, infinitely many possibilities. And that’s the point I’m trying to clarify here.

What we are basically pointing out is that string theory gives you a finite number of possibilities. And cutting the possibility from an infinite set to a finite set is a remarkable reduction.

LEVIN: Yes. You eliminated an infinite number of things.

VAFA: When people criticize it in the way, say, “Oh, it doesn’t make a prediction about anything.” They’re putting a very high bar what string theory should be. Namely, when we talk, for example, about quantum chromodynamics, which is the theory describing how the quarks work and what are the forces between them inside the nuclei, and so on. There are infinitely many possible theories for that too. We just choose one of them, and nobody explains to you why that particular one is the one we use. So, if you want to choose that level of precision, then you have [to] say, “We don’t understand quantum chromodynamics.” No, that’s not what we say. We say, “Well, you just pick that one and just study it. And that’s the way the universe is working. Don’t ask more questions, so to speak.” So in that context, people don’t say that we don’t have a good theory of strong interactions. They’d say we do.

Now, string theory is trying to give you a broad perspective of what all universes could look like, not just our universe. And so that’s a grand, you know, ambitious kind of thing. It’s much more than just one theory described to one particular universe. Now, you might say, I don’t care about these other possibilities. I just want the answer to my universe. And then that’s where it becomes harder. And that’s where people become critical.

But if you look at it from the broad perspective of what it’s trying to do, which is trying to tell you what is the overarching truth of all possibilities, that’s surprising. And in that context, it tells you, for example, if you want to have the theories of strong interactions, there are only a finite number of possible ways. Whereas without gravity, without string theory, you would’ve thought there are infinitely many possibilities.

So, it cuts it down to a finite set. For example, the number of colors, we say there’s three of them, it could have been 4, 5, 6, say up to arbitrary integer. String theory says, nope, there’s an upper bound. It cannot go beyond certain numbers.

That is a surprise. So, it cuts the number down, not make it large.

LEVIN: Just for the audience, colors in this sense is an abstract property. It’s a cute name given to different kinds of quarks.

VAFA: That’s right.  So, we say that each quark comes with three colors. And that’s just three degrees of freedom, we just call them colors.

LEVIN: Now, to discuss this kind of landscape of possibilities as it’s often referred to, what are the differences in these universes from one point in the landscape of possibilities to another point in the landscape? What’s different about the universe than this one?

VAFA: So, in each conceivable universe that we can think of, in which case we have a quantum theory of gravity interacting with particles and forces, it appears in a particular dimension. You have to have a particular space-time dimension, which is what we call the macroscopic space-time, the big space, so to speak.

There are some curled up directions, what we call the compactification-scale manifolds. So, these are tiny things that we don’t care about in terms of large-distance observations that we do currently. So, you have to decide how many big dimensions do we want? For example, in our universe, there are three spatial dimensions, which are macroscopic and one time. So that’s the three plus one dimensional one. That’s one particular choice you’re making. But different universes that we begin in strength theory can have different dimensionalities—again, bounded. It doesn’t go too far up. It doesn’t go beyond 11.

And also, in each case that you choose dimensions, you could ask, okay, is it going to be like a flat space? Is it going to be some curvature in it? And this feature is sometimes related to the property, if you talk about the space-time curvature, in the context of the cosmological constant, which is positive in our universe.

In addition, you could say, how many particles do I have? What kind of forces do I have. So, all these different kind of choices that are consistent in string theory give rise to different dimensions, different number of particles and different kind of structure for the curvature of space-time.

LEVIN: This landscape of possibilities was disheartening to people for all the reasons you’ve just said, that suddenly where’s our single theory of the universe? And now you’ve given me an infinite number? But then you have this Swampland Initiative. Can you tell us how this helps restrict us to try to find a better description that might be just our universe?

VAFA: Yes. So let me just give the analogy. I said there are only three colors in our universe in the strong forces, but it could have had more degrees of freedom, what we call more colors. Could have had 4, 5, 6, et cetera.

So if you take the four-dimensional theory and ask, suppose I want to have the simplest four-dimensional theory I have with matter. It turns out the simplest four-dimensional theory with matter, which can be described with quantum gravity, is what we call in technical terms N equal to four supergravity theories.

Now, N equal to four supergravity refers to the statement that the theory has extra symmetries — what’s called supersymmetry. So, if you take this simple class and ask in this class do you have an upper bound in the number of colors? Then you can show that you have to have less than 24 colors. So suddenly you cut the number to a small set.

Now, if you did not know about string theory, you would’ve said, take any number of colors. That’s perfectly fine. Those options that could have been true, we could call potentially consistent theory, but most of them now we are claiming do not exist; more than 24 don’t exist. Those belong to the swampland. The ones that can be constructed in a string theory belong to the landscape.

So the first 23 or so are belonging to the landscape. The rest are the swampland. So therefore, what swampland brings to the table is suddenly makes a prediction now. You cannot have too large number of colors, for example.

LEVIN: So, you’re relegating to the swampland all of these inconsistent theories. You’re hedging in the landscape which is now going to be surrounded by the swampland of impossible universes. And so really the initiative is to restrict yourself more and more and more. So, what kind of criteria are you using to decide what’s viable and stays in the landscape of possibilities, and what has to be relegated to the swampland?

VAFA: We try to find a criteria which distinguish whether you are in the swampland or in the landscape. If I give you a putative theory and we ask you whether this is good or bad, whether it’s in [the] landscape or swampland, how do you judge it? What are the criteria?

It would’ve been natural to say, you know what? I would just put A, B, C, D as criteria, whatever they are to say if they are good, and then I will know once and for all I found the theory. However, we think the number of theories which are good are very, very small.

So, if you think about an ocean and suppose there are some little islands on it. And then I tell you, how could I find the islands? It’s much harder to say pinpoint one of the islands unless you really, really know where it is. And it’s much easier to say, you know what, if you draw this line on the ocean, there’s nothing on the left side of it. I can guarantee that you can’t find anything.

These criteria of where you cannot find a good theory or what is in the swampland is much easier than to say what is good. So in other words, the reason we have the swampland program is not that we are looking for bad things, but it’s much harder to find the good things. The good things are much more difficult because they’re very rare.

LEVIN: These islands of possibilities, just to clarify, they don’t have to be our universe, right? They just have to be a consistent universe. One that is mathematically sensible and consistent, even if maybe galaxies don’t form in that island universe, is that right?

VAFA: Exactly. So then if you wanted to quantify all the islands, it’s going to be very difficult, however, you know, we are lucky in the following way. You could say, well, we know one island namely, our island, our universe exists. And you can make observations on our universe. So, you can say that in this universe, these properties hold. And then you say, “Oh, if I knew that there’s this property on the island, then I can rule out some other property.”

In other words, we are using observations of our universe combined with the criteria we know has to be generally true, and suddenly we make predictions. And so that’s how we have actually made predictions for our universe based on the swampland principles.

[Music]

STROGATZ: It’s a little tricky. As I was thinking that instead of saying what the landscape is, the swampland is everything around the landscape. It’s all the negative space. Like, as a mathematician, the thought that occurs to me is maybe there are inequalities. Maybe if a certain parameter is too small then I know nothing like that could possibly be in there. And inequality constraints would give you whole big open sets in the space of possible universes. So, you could lop off enormous regions maybe. Is that the vision?

LEVIN: Yeah, I think that’s part of the vision. I’m sure you’ll remember that Alan Turing used this when he was cracking the Enigma code during the war. One of his big insights was to begin to prune away all of the encryptions that couldn’t possibly be right, because they had a very short list of identifiers that they anticipated from a correct cipher.

And so it allowed them to use a blunt tool, right, to kind of scoop away a whole range of possibilities. Leaving as Vafa is describing an island of possibilities, which is much, much smaller, and thereby narrowing the field that you have to scour for models that actually begin to look like our universe.

For instance, let me give you an example of what might be an attribute of the landscape. It might be that it’s a higher-dimensional space so it’s not just three dimensions of space and one time, but it has extra spatial dimensions and they’re wrapped up in this very complex origami. And most of those spaces we know very, very, very little about. It’s really hard to investigate them and to understand them and to understand what their predictions are, and if they could yield, for instance, the spectrum of particles that we observe around us. because it influences things like this.

So, they’re just trying to use a blunter instrument to eliminate from this huge range of possible geometries, for instance, a smaller number that might yield a universe that is compatible with the one we observe.

STROGATZ: And did you get the impression from talking to him that there’s some notches in his belt? Like have they eliminated anything so far?

LEVIN: Well, I do think they feel that they’ve had really surprising success, and maybe it was a surprise even to other people. But, more importantly, Vafa really feels this is experimentally testable, at least in principle. And while they haven’t been able to do that yet, that’s really the direction he wants to go in to combat not just the attitude, but maybe the failing on the theoretical side to take experiment more seriously.

So, more on this after the break.

[Music]

LEVIN: Welcome back to The Joy of Why. We’ve been speaking with Harvard theoretical physicist Cumrun Vafa about the string landscape and the swampland.

Now, string theory is often critiqued as not being concretely connected to experiment, and you’re really saying otherwise  —  that there is a way to actually dig into cosmological or particle physics experiments and use one lure to kind of hitch a whole bunch of other criteria to.

VAFA: Exactly, and that’s the exciting thing going on in string theory now. I can in fact tell you where the swampland program picked up speed.

So we proposed this general program in around 2005, and, by and large, it was just a very few number of papers coming on this subject until when BICEP [Array] came up with the measurement of what they thought was a gravitational wave. And the data that they were giving was in contradiction with some of the swampland principles. And so, we were dismayed that how could it be possible? We thought we understood this.

And then later BICEP was proven wrong. So then suddenly there’s a huge amount of activity came to this direction precisely because we now realize we can have concrete predictions that is relevant for observations and our universe.

LEVIN: So, you’re actually using observations of the light left over from the Big Bang of polarizations, of gravitational waves, also dark energy observations?

VAFA: Everything that we can see we can use and think about how this fits or doesn’t fit, or what aspects can be predictive when you combine it with the swampland principles.

LEVIN: Now, famously, string theory is also incredibly mathematical. Do you believe that we really have the right mathematical tools to keep progressing?

VAFA: I think we have more conceptual questions that we need to understand better. I don’t think math has become a hindrance, even though what you’re saying is absolutely true. That is, the subject is very mathematical and it has led to new areas of mathematics being researched. so in fact we can generate our own math tools. That’s not going to stop us. More, I think is the issue, even though we have deep interaction with mathematics, we actually have to go beyond that in the sense that we need to find what is string theory or what’s it trying to do and so forth. Those are harder questions.

And if you ask the same question “What is string theory?” Ten years ago, 20 years ago, the answer changes. And even now, if you ask what is string theory today from string theorists, you get different answers. They have different perspectives of what it is about.

LEVIN: Do you feel confident that we will reach a realistic, kind of, more complete description string theory in our lifetime?

VAFA: Well, we certainly are getting more and more complete. I don’t know if there’s an end to human understanding of nature. And I think the same might apply to string theory. I wouldn’t be as bold as saying, yes, we’re going to get to the end of the story even in anybody’s lifetime. Knowing that we are making progress, that’s for sure is happening now. That I can say. That’s what science is after all. We should be looking for progress and more clarification. So, we are certainly evolving in our understanding of what string theory is and how it may connect to our universe. And we have enough clues right now to be confident that we are on the right track.

Let me just say it by simpler example. We live in three spatial dimensions and one temporal dimension — that already should be surprising. If I give you a number integer D, which is the dimension of space and time from one to infinity, what are the chances that’s less than 10?

LEVIN: Right.

VAFA: I mean, that’s almost chance zero. It is zero chance, if it was a random number. It’s not. And the point here is that, for example, in the swampland program, we say the dimension cannot be more than 11.

That already is an example of why the thing is limited. So that’s very strong predictions. People don’t think about this natural thing because everybody takes for granted. Yes, we have three large dimensions and one time. So what? Well, that’s a big deal. Why not much, much more.

LEVIN: I think that goes back to when Einstein first starts to realize that space and time are actual mutable properties of the universe. You have to start to ask, why three and why one time? And I think he did ask that and just didn’t know.

VAFA: Yes. In fact, during his time, Kaluza and Klein came up with one more dimension and Einstein embraced that as an interesting extension of his theory. So these ideas about what are the limits of the dimension of space-time and how does it work is part of the bread and butter of string theory.

I think already we have enough clues in our universe that we feel confident that we’re going in the direction of realizing concrete predictions of string theory in our universe.

LEVIN: So, I’m fascinated to know what goes wrong when the number of dimensions goes above 11?

VAFA: So, one of the properties and symmetries that I mentioned was supersymmetry. And we know that whenever you don’t have this symmetry, you get instabilities. Instabilities means that you cannot have a stationary situation, like our universe looks like.

Now, we know that our universe does not enjoy the symmetry that I just told you about when you go look at large distances. But we think that even in our universe, if you go short distances, you might recover such a symmetry.

So, in other words, the symmetry, which allows us to have a long-lasting universe has a limit in terms of the number of dimensions you can go. And it turns out you can prove mathematically that it cannot go more than 11.

LEVIN: So how fascinating that the large number of dimensions, which we think of as the universe on the biggest scales is determined because of microphysics.

VAFA: That’s actually the most beautiful connection between the string theory and, more broadly, quantum gravity and quantum field theory. Quantum field theory, you build up things from small scale. You say what’s going on at the shortest scale, and then you can describe the larger scale. And that has been the mindset of physicists.

It ended up that if you study quantum gravity, it doesn’t work that way. Namely what happens at large distances is related to what’s happening at short distances and they are not independent. In other words, the large distance physics can dictate backwards what’s going on at shorter scales, which is not like what usually happens in quantum field theories.

LEVIN: And there’s another sense in which we can think about the connection of the small and the large dimensions that I’m hoping you can explain to us a little bit. And that is the possibility that 95% of what makes up the universe, which is in the form of dark energy, predominantly in some dark matter, could also be connected to these higher-dimensional theories, these string theories with these extra tiny wrapped-up dimensions. How do you make that incredible connection?

VAFA: This is one of the beautiful questions and connections with the ideas that are emerging in string theory. So, as you mentioned, 95% of the energy budget of the universe is not made of things we know of. It’s not made of electrons or protons and this and that, that we know of. It’s made of something else. In fact, of the order of 70% or so of it is what we call the dark energy. And in addition, there’s about 25% or so of the energy budget, which is what we call the dark matter. They’re weakly interacting with our particles, the electrons and the photons and all that cannot interact very effectively with them. So, they’re there. And the only reason we know they are there is because they interact with gravity, and gravitational effects we can detect.

So, what does this have to do with string theory and quantum gravity efforts to try to understand this? It turns out we have gotten super lucky. What we have learned using swampland ideas is that whenever you have a small parameter in a physical theory, it comes with consequences.

When you have an electric charge or you have masses or things, if things are extremely fine-tuned to a small value, then there’s some other predictions we can make. That’s one of the new things we have learned in string theory.

In particular, we have learned that whenever you are extreme fine-tuning, one of two things must necessarily happen. Either there are some extra dimensions which are beginning to be big, or there are some very tiny light strings which are becoming so ever-so light. This is a consequence of having some extreme parameters in your theory.

Now you might say, “Wow, where did that come from?” This very strong statement comes from a property we call string dualities. So string theory, when people study that, they try to take these extreme parameters to extreme regimes, and each time you take the parameters in your physical theory to extreme regimes, you found a new description takes over.

And so, when a new description takes over, you begin to find that this new description involves light particles. And these light particles tend to end up being related to two possibilities: either a light tower of strings; or long wavelengths of gravitons in some extra dimensions. These are the only two possibilities. So, these dualities, we don’t have a deep explanation of them, but we know it’s true in string theory.

Okay, so we take that as one of the swampland principles. Namely, if you have fine-tuned small parameter in your theory, look for either large dimension, or light strings.

LEVIN: Now, by a large dimension, you still mean kind of small.

VAFA: Larger than, I mean, our universe could be effectively infinite. So, we’re talking about the other curled-up dimensions, the curled-up dimensions that could go up to 11 altogether space-time. So the possibilities of having the seven extra spatial dimensions, one of them, or two of them, or three of them becoming big.

LEVIN: And big would be what? Like a micron big, a millimeter? Is that big?

VAFA: I mean, micron is huge, millimeter is huge, even atomic size in that sense is huge. The reason is that the fundamental scale in gravity is 10 to the minus 33 centimeters. And that is about 25 orders of magnitude smaller than atomic scale. It’s tiny, tiny, tiny. So, anything much bigger than that is called big for us now. So when I say big, I mean big compared to that tiny scale.

LEVIN: Right.

VAFA: Now, we are given this situation in our universe where one of the parameters in our universe is extremely small, and that is the dark energy. The dark energy is one of those amazing parameters in the theory, which has an extremely exciting, interesting history dating back to Einstein.

Originally, when he wrote his theory, he put this term — which he called the cosmological constant, which we now also call dark energy  — to non-zero value in order to get a static universe. And later he abandoned that after we found out that actually the universe is expanding, so he put the dark energy to zero, and it stayed zero in the minds of theoretical physicists for many, many decades after Einstein did that. Until shocking observations in late 1990s told us that it’s not zero. And the reason people were shocked was that if it was not zero, it was so, so, so small — 0.00000 … you have 120 zeros — and then you put the one at the end. It’s that small.

Okay, so that’s the tiny dark energy. Now, as I just was telling you about, whenever there’s a tiny number or fine-tuned parameter in your theory, you should be asking what’s happening to these extra dimensions? Are they getting large or is there light string somewhere?

So already we are saying that having a dark energy, which is so extreme, must necessitate having new particles, where are they? On the other hand, we say there’s dark matter. So now we are saying that two facts, the fact that dark energy extreme and there’s some extra light particles around could naturally play the role of dark matter. So that’s the idea that already automatically comes from the swampland principles.

Now you can say, “Can we make it more quantitative?” It turns out that the dark energy predicts actually a length scale. And it turns out that length scale is about a micron. Micron is 1000th of a millimeter. And it suggests that exactly one of the extra dimensions is of roughly that size.

Now, you could ask then, what about the dark matter? Well, the dark matter would be the graviton waves, which were created in this extra dimension, what we call the dark dimension. So we have three spatial dimensions that we know, which are huge. One more dimension, which is this micron scale. And then the rest of them we think are much, much smaller.

So, therefore this one-micron dimension space will potentially carry in it some long gravity waves which would play the role of dark matter. So, in this context, we have a unification of dark energy and dark matter, just from this simple principle that when you have extreme values in your physical theory, there are light particles.

LEVIN: So, you’re essentially saying that by observing the as-yet unknown dark energy and dark matter, this could be an observation — already — of dark dimensions. Now there’s other ideas competing, so it’s not a smoking gun, but we could actually be observing string theory.

VAFA: Exactly. But there’s actually more. Because this tower of particles I was telling you about, which comes from these light particles has to be weakly interacting, which is the smoking gun of dark matter. It’s weakly interacting not only with us, but even with themselves.

So that is a property, it’s a prediction, I would say. So, we are making a prediction that whenever you have this dark energy being so extreme, you better look for light particles, which are very weakly interacting, just like our universe has it. So, this is a prediction for our universe.

And in fact, it makes another prediction: You cannot directly detect them because their interaction strength is gravitational. So, these direct dark matter detections will not succeed based on this study. So, we are making very specific prediction.

But actually you can make it even a stronger prediction. If you have two objects, two masses at the distance are, Newton taught us that there’s a gravitational force between them, which attracts them. And this force falls off with the inverse square of the distance between them. That is a property of three-dimensional space and one time. If you increase the number of dimension, each time you add one dimension, the power of the distance in the force law increases by one.

So instead of distance squared in three spatial dimension, if you have one extra dimension, it becomes distance cubed. And if you have more, it becomes distance fourth and so on. So, if we have one larger dimension, it should have been distance cubed. So, we are making a prediction that if you bring these objects together and put them at a distance roughly of a micron or so, you should find the stronger gravitational force between them.

This experiment to detect this is actually being undertaken now to bring it down from 30 micron perhaps to 10 micron and below to try to see if the force law changes as we are making a prediction. So that’s a very concrete prediction that we are making based on this link.

LEVIN: Hmm. A lot of what we’re describing is of course a description of the universe writ large. And here we are on this little globe, all of us together, working in international communities to figure this out. And I’m wondering how that played a role in your own experience?

VAFA: That’s one of the aspects of science I cherish a lot. The fact that it doesn’t recognize any artificial borders. It’s universal. It’s a borderless and timeless adventure that human mind is engaged in and it’s something that gives you a way to connect with people across the world. It transcends cultures and it transcends artificial political lines that are drawn.

And in fact, I think, cultural aspects actually are helpful in formulating specific viewpoints about scientific questions, which is interesting because you have to come up with some kind of thinking, like for example, aesthetics of what is good, unification is nice or not. Symmetry is nice or not. And it’s good to have different cultural perspectives. So, bringing that to the table is in the best interest of advancement of science.

And so in this sense, I actually was born in Iran, and I think that many of the culture aspects that I bring with me on the table for the scientific discussion is maybe not as much shared because unfortunately there are not as many scientists from my country, as there could be. That’s my bringing what I bring to the table, but then there are all these other cultures and so put all these together. I think it’s great you have all these different perspectives, and we should cherish it.

LEVIN: It’s so beautiful. I love that description. I know that you’ve also been very interested in some of the philosophical lessons about what we can extract from physical laws that are bigger lessons than even physics. How does that influence your thinking as well now?

VAFA: Yes. I think that part of the reason many of us scientists study nature is deeper than just figuring out the equations, describing how things move or how things work. It’s just to understand the bigger picture of the meaning of existence, the meaning of things, which bears on philosophical questions.

So I think science and philosophy are not disconnected. You cannot ignore it. Perhaps, maybe too often, I hear our colleagues look down on philosophy and maybe, I think in some sense every scientist is perhaps an amateur philosopher, and we have our own viewpoint that’s not rooted in science, but we say, “Oh, this is aesthetically beautiful.” I mean, where is that coming from? That is not a scientific statement, but it drives us quite a lot. That’s motivation of a lot of our work is based on things that we consider pretty or beautiful or something which is not sometimes easy to quantify.

To me, a lot of things that we are learning in science point towards this quality of magic. But unlike the usual magics that once you explain it, it becomes boring, explaining these magics does not get rid of its charm. And that’s the amazing part of science, this magic always continues to exist. And that’s some unbelievable quality of the truth in our nature, and it’s philosophical, I would say. So I cherish the connection between philosophy and science.

LEVIN: Well, it’s been a pleasure to talk to you. We’ve been speaking with Cumrun Vafa here on The Joy of Why. Thanks so much for being with us.

VAFA: Thanks, Janna. It was a pleasure to talk with you.

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STROGATZ: Wow. If there’s a lot to chew on there. Let’s see I would love to hear some of your thoughts about magic, about philosophy and also about the diversity of cultures can be a strength in science.

LEVIN: Mmm-hmm. Yeah. I thought this was intriguing, the tension between magic and the reveal.

STROGATZ: Yeah.

LEVIN: I mean, how do you feel about that? We approach these problems because they’re mysterious, because we love the problem, right? We love the pursuit of something that seems magical, but he says the reveal doesn’t ruin it.

STROGATZ: Yeah, I love that. That’s an original idea. I hadn’t heard that before. Because it is true that, of course, that’s the whole point that magicians don’t tell you how they do their trick and they’re mad at other magicians who do, because it does tend to ruin the trick. And there’s, no analogous thing in science, right?

If you learn, for instance, how Kepler’s laws work, because you now know Newtonian calculus and theory of gravity, and that sort of explains it. That’s the reveal. And yet it’s not ruined because then Einstein gives you another reveal, and that’s not ruining it either, because maybe string theory has its own reveal.

LEVIN: Well, I thought it was very interesting that he was suggesting that the kind of approach that we have in physics, that things are beautiful, that is actually a very strong kind of scalpel we use to eliminate theories that we think are probably not viable because they’re just like, they’re really ugly and that nobody believes them.

STROGATZ: That one I feel is much dicier. We could probably get in an argument about that. That seems to me a relatively recent concept, like the insistence that nature has to be beautiful and that symmetry and beauty can be scientific criteria for deciding for or against certain theories that has worked for a few hundred years.

LEVIN: Few hundred?

STROGATZ: I mean, Feynman has remarks like this, that he claims he doesn’t care if it’s beautiful or not. He just wants to know the truth and I don’t know that beauty and truth, I mean, who says the world has to be beautiful?

LEVIN: Yeah. I mean, it could have been a failed program, right? So, I would say to that, oh, absolutely. It seemed reasonable to look for symmetries, which is part of the idea of beauty. It’s actually in a very concrete, explicit way, symmetry. and it could have failed. Absolutely.

STROGATZ: But it feels to me like it’s about 300 years of that. But wonder if we’re hitting the limits of that.

LEVIN: I would say Galileo was into this too, for sure. It’s hard to know.

STROGATZ: I’d love to hear more about it. We need to have him back.

LEVIN: Hmm. Well, Steve, always fun to talk to you. We’ll catch up again soon.

STROGATZ: I’m looking forward to it.

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STROGATZ: If you’re enjoying The Joy of Why and you’re not already subscribed, hit the subscribe or follow button where you’re listening. You can also leave a review for the show. It helps people find this podcast. Find articles, newsletters, videos, and more at quantamagazine.org.

LEVIN: The Joy of Why is a podcast from Quanta Magazine, an editorially independent publication supported by the Simons Foundation. Funding decisions by the Simons Foundation have no influence on the selection of topics, guests, or other editorial decisions in this podcast or in Quanta Magazine.

The Joy of Why is produced by PRX productions. The production team is Caitlin Faulds, Livia Brock, Genevieve Sponsler and Merritt Jacob. The executive producer of PRX Productions is Jocelyn Gonzalez. Edwin Ochoa is our project manager.

From Quanta Magazine. Simon Frantz and Samir Patel provide editorial guidance with support from Matt Carlstrom, Samuel Velasco, Simone Barr and Michael Kanyongolo. Samir Patel is Quanta’s editor in chief.

Our theme music is from APM Music. The episode art is by Peter Greenwood, and our logo is by Jaki King and Kristina Armitage. Special thanks to the Columbia Journalism School and the Cornell Broadcast Studios. I’m your host, Janna Levin. If you have any questions or comments for us, please email us at [email protected] Thanks for listening.

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