Is The Universe Made of Tiny Vibrating Strings? With Lara Anderson

0:00 Could such extra dimensions exist? And if so, how would we try and probe whether that's the case? If you imagine looking at an extended object like a wire, it just looks one-dimensional. It just looks like it has a length. But if you were able to get really close to that wire, you'd see that it also has something like a thickness. And so that extra direction is what's called compact. Is it possible to have a compactified time dimension as well? Oh wow. Yeah. Imagine two dimensions of time. Wow. The problem with two time dimensional theories and compact time dimensions in general is that it's very hard to maintain causality. Higher dimensions look down on us. That's [Music]

0:46 Star Talk. Neil deGrasse Tyson, your personal astrophysicist. Got Chuck Nice with me. How you doing, Chuck? Hey, I'm doing great, man. Thanks. All right. a comedian, actor. Yeah. Seen a few TV commercials here and there. Yeah. You know, I'm uh Listen, sometimes I have nothing to do. Okay. Well, today we got a really cool topic that's always on everybody's mind. Well, everybody who cares about the universe, you know, even people who don't, but I'll get I'll get into that later. Yeah. You know what we're talking about? I've heard some really weird stuff from people that you know, they want to get into it that Yeah. All right. All right. We're talking today about string theory. Yeah. And now we have our man about town string theorist Brian Green right up the street, right? But I said, you know, all the universe is not Brian Green. You

1:32 know, he would beg to differ. So I said, so we reached out to the cosmos. All right. And we found Laura Anderson. Laura, welcome to Star Talk. Thank you very much. It's a pleasure to be here. Yeah. So you are associate professor of physics at Virginia Tech. One of our producers is from Virginia Tech. So you you're right at home here among us. Yeah, we you're family now. Yeah, you're family. Good to be among friends. Also like Brian Green, you have a double affiliation also with the mathematics department. I do. I'm an affiliate professor of mathematics, which means I can supervise math grad students as well. So you just you're just taking jobs from everybody. His professor's out on the street because of Laura Anderson.

2:27 I I can try to picture that how they they're like I'll s I'll do your math homework for for for money. Exactly. Will math for food. I think unfortunately that is a job. It's called tutors. Really? Really? Exactly. uh and your research includes I have here the geometry and particle phenomenology in string theory. So we just want let's just get to the bottom of this. What is string theory? Yes. String theory is an attempt to reconcile Einstein's theory of general relativity the theory of gravity with the formalism of quantum mechanics and quantum field theory. So it is a consistent quantum theory of gravity. um may not be the way that quantum gravity works in our universe, but at the very least, it's a theoretical playground where we get to

3:13 ask questions about quantum gravity. Now, you've made an assumption in there, and I agree with this assumption, but I want to hear you defend it. You you are trying to absorb Einstein's general theory of relativity, our modern understanding of gravity, right, into a quantum description. Why aren't you trying to take the quantum and absorb it into a general relativity description? Because inherent in what both of you said there must be an inongruency that would cause you to have to do that. Exactly. So why don't you start with that law? What what is the inongruency here that you're trying to resolve? Two of the greatest intellectual accomplishments of the 20th century in my opinion are Einstein's theory of gravity and the description of

3:59 fundamental interactions in nature um as described by particle physics. So things like uh a description of you know quirks fundamental particles how they interact with each other that gives us a description of things like electromagnetism and the strong and weak nuclear forces. these sort of basic building blocks of matter, these fundamental Legos that we can hook together, they're described very well by by quantum field theory. The issue, the the sort of discrepancy between these two is that each separately are able to make predictions that are incredibly accurate in our modern world. So, we can make predictions to like 13 significant figures using either of these theoretical frameworks. That' be 13 decimal places, right? 13 significant figures. Yeah, I'm going to say that's pretty accurate. It's pretty great. Yeah. and like things like modern GPS wouldn't work without general

4:45 relativity. So we have a lot of ways of testing these theories. They seem really robust and that they're telling us really important things about how the world behaves. Unfortunately, if you try and combine the two, so you try and describe phenomena that might need both tools. So for example, things where the interaction of particles and very short distance scales are in play, but also where there's really strong gravitation. So for example, inside a black hole, um that would be a regime where you need both of these these theories, these frameworks to agree and give you concrete predictions. And unfortunately, the theories break down when you try and combine them. And you don't end up getting useful answers. You get very manifestly wrong answers. They're called disastrous infinities. Um things that just don't predict anything.

5:30 Disastrous infinities. Man, you can't get more diss than that. Sounds like the worst marriage ever. Yeah, it's not great. Disastrous infinities. So, so what gives you the confidence that it is the quantum physics understanding that will absorb gravity and not gravity absorbing quantum physics? It's a great question. So, I I think that it should be a two-way street. So, um in order to describe either phenomena, you need something that can be described in both frameworks. Einstein's theory is sort of intrinsically classical um meaning that this picture of the curvature of space and time. It's not designed for sort of the quantum mechanical uncertainties that we know and observe in particle physics. So in that sense we know that Einstein's theory probably at a granular

6:15 level if you sort of zoom in should evolve into something quantum mechanical. Um but exact form of that is up for for exploration. Okay. Okay. So that works. Now you mentioned fundamental particles and you go back to ancient Greece the atom was a fundamental particle that was the smallest thing that you could be that you could be right and then we break the atom oh there's other particles and so you you you listed like electron that's fundamental and you mentioned quarks what gives you the confidence that we can't keep dividing cutting further further yeah that's a great question I don't think I I think most theoretical physicists would not say that we are 100% confident that we stop there. This is the the zoo of particles that we've observed so far that seem to match the

7:00 phenomena, the forces and interactions and effects that we see in nature very well. But absolutely there could be smaller things in play and indeed string theory posits that there are. Okay. Oh, really? Right. Exactly. That's this little vibrating. So the string is the fundamental string is the fundamental. So take us there. Take us out. Now how does strings come into this? So, the idea behind string theory, the, you know, the the two-minute version of what string theory tries to do is it says, imagine that instead of describing particles as little point particles that move through space, imagine that instead if you were able to zoom in far enough that you could have an object that has an extended length associated to it. And the the very rough idea is that just like a violin string can vibrate in different ways and produce different

7:46 notes, these little fundamental strings can vibrate into different configurations. And it turns out they can change their properties. Um the mathematics of how you describe these things moving can change their properties based on how they vibrate. So they can vibrate one way and be an electron. They can vibrate another way and be a quark. Um, and that seems like a very sort of cute idea for how to describe a lot of physics in a very simple framework. I But if that's if that's the case, in principle, you ought to be able to to pluck the string that is otherwise an electron and get a quark out of it. Have you done this? No. And the problem with this, so I'm gonna tell you one thing that's really cool about this framework and then also two things that are not cool. One of them is is very much to do with what you said. So

8:33 um why can't you just test or observe you know are these strings there? The theory predicts that these fundamental length scales of strings are so small that we would need a particle accelerator about the size of the solar system in order to smash atoms together and directly see those strings. Um which unfortunately we do not have access to those type of energy scales yet. Just to affirm what is implicit in your statement. The larger the particle accelerator, the faster you can speed the particles so that when they collide, there's much more energy in that collision. You'll probe regimes that previous accelerators could not. That's right. Okay. And so you just scale up what we got going now and you need something the size of the solar system to get to these energies, right? Which

9:18 doesn't seem very viable. No, it's not. So what's your what's plan B? Yeah, before I answer that, let me let me just throw one thing out there about string theory that I think is important to say. So, if you ask about quantum mechanical point particles and you say what kind of spaces could they move through, it turns out that quantum field theory or quantum mechanics can be formulated in any type of space. So, they can move through basically any background that you choose, any any, you know, configuration of space and time. But if you ask the same question for these uh little onedimensional strings, if you say where can a quantum mechanical string move, it turns out that the only spaces that they're allowed to move in and do their their thing of vibrating in different ways and being different particles, the only space they can do that in are spaces that obey Einstein's equations of general relativity. That sounds good.

10:05 Wow. Yeah. So you actually get gravity for free in this formulation of quantum mechanical strings. So we we sometimes say that quantum gravity is consistent and also compulsory in string theory because it's being you know you're forced on you by the equations that the strings may satisfy. So that's a good feeling then because it means something is talking to something else in the form in the formulation right that that that was not crowbarred in to begin with. That's right. So it's sort of being handed to you and that fact is I think something that early in the development of string theory got a lot of people excited. Unfortunately, like many good things, uh things come with a catch. And the catch in string theory is that this beautiful formulation I just described of, you know, you can describe all of particle physics by one little extended object. You get gravity for free only

10:51 seems to work if the universe that this happens in has more than three spatial dimensions and one timelike dimension that we seem to see in our universe. So, you need extra dimensions because right now we live in four dimensions, which is three spatial plus time. you need more dimensions in order to make this thing work, but we don't have access to more dimensions. So, we can't really say for sure. Well, it's I mean, it seems like a really big intellectual leap, right? We're we're pretty happy with our three dimensions of space and one dimension of time. So, the first pass is like could this at all is this just a dealbreaker, right? Is there any way that this could be consistent with what we've already observed about the universe? And as you were just alluding to, right, the

11:36 question is, you know, could such extra dimensions exist? And if so, how would we try and probe whether that's the case? Um the the requirement that we can see right off the bat about these extra dimensions is if they were to exist, they can't be the same size as the rest of the dimensions that we see in our universe. So if we look around, we can see that, you know, we have very large spatial extent for, you know, front, back, side to side, up and down, and of course time. But if there were these other directions, they would have to be really, really small compared to the rest of our universe. And the analog for that is if you imagine looking at an extended object like a wire from really far away, it just looks one-dimensional. It just looks like it has a length. But if you were able to get really close to that wire, you'd see that it also has something like a thickness, a radial direction. And so that extra direction

12:22 is what's called compact. Um meaning that it's very small compared to say the length of the wire. So, one thing that we do know is that if this had any chance of working, these extra dimensions would have to be compact and very small compared to the rest of our universe. Okay, you're freaking me out right now because and this I mean I'm just going to say it. So, I was down in Costa Rica doing Iawaska for a week. And in that time I had an experience where I met these beings who told me about dimensions that existed inside of our dimension. So they were alongside of yet inside of the dimension that we live in. And I can only think

13:10 that maybe that was a pre-supposed pre-planted post-hypnotic suggestion because I have actually read about string theory because if it's not or or what drugs have you been taking to to get your and my my follow-up question is what did you do? That's right. I I hear the question. Yeah. Is it possible to have a compactified time dimension as well or is we only is all of the models only stuck with one time dimension? Oh wow. I never even considered that. Yeah. Imagine two dimensions of time. Wow. Holy crap. Go ahead. Yes. So the problem with two time dimensional theories and compact time dimensions in general is that it's very hard to maintain causality in such

13:55 theories. So if you have a time direction that can loop back on itself, it's possible to have the whole go back in time and shoot your grandpa situation hitting you pretty hard. So to maintain consistent theories with multiple time directions or or compact time directions, it's not I'm not going to say it's impossible, but most people don't consider that a very viable way forward. You would have to discard causality altogether in order to do that. I think in general the claim would be it would violate causality in such theories. Um, so there may be some creative ways to get around that, but generically I think that's true. By the way, we have a Stephen Hawking on one of our earlier episodes. You can find it in our in our archives. We went to University of Cambridge and and chilled with him for a bit. Tell me, he proposed a time travel conjecture something like that. Tell us what that was and does

14:41 that save us from this? Is that I mean there are a number of of conjectures say in the the theory of gravity that say that um causality is an important structure. So that um in general one would not expect that consistent theories of gravity or indeed quantum mechanics should allow such you just can't get it to work. Okay. Okay. That that's fine. I mean yeah I mean listen that me that that removes many movies in the repertoire where you got to go back and change the past. Exactly. Like Terminator the Terminator is done. Forget about it. We look back on the past but we look forward to many futures. So the idea of being able to look back and say at this particular point all those many futures still exist if I could get back to that point then I could change it to one of these other

15:27 tracks you know which I mean it's a great fantasy and it makes sense to have that fantasy but what you're saying is it's a stupid fantasy cuz it ain't never going to happen. Well, I would say, you know, never say never in insights. You got to be careful, but um certainly it's not something that I think most people have a good idea how to make work in a consistent way at the moment. And that's why I'm not a scientist. And just consider to say never say never. You said never. You said never. You just said never. You can't say never say never unless you're saying never. Hey Star Talk fans, I don't know if you know this, but the audio version of the podcast actually posts a week in advance of the video version. And you can get that in Spotify and Apple podcast and most other podcast outlets that are out

16:14 there. Multiple ways to ingest all that is cosmic on Star Talk. Before we sort of pivot to this whole thing of phenomenology cuz I want to know it's a big word with a lot of syllables. I've heard it invoked before especially in particle physics. But before we step there, I just want to understand how will you ever test string theory? And we know in advance that you have naysayers out there uh physicists among them who are saying you're diverting time, resources, graduate students, faculty positions to something that doesn't even classify as a legitimate scientific theory or or hypothesis because you need to be able to test it. Without the test, go home. So let me hear your response to that. Absolutely. I think that's a

17:01 really fair question. um you know for any theoretical framework where you're trying to describe things if there's a big intellectual leap right and for example extra dimensions is a pretty big leap um you have to justify that with a payoff right you have to say what is the benefit that I'm going to give you in terms of you know structure and predictions and and you know what you're learning from this theory so to push back on the you know how are we going to test it um let me observe first that in uh particle theory in general the time scales between predicting structure in particle theory and then being able to see it an experiment over the last half century have gone you know increased in size considerably. So one example of this is the prediction of the Higs Bzon made by Peter Higs which took about 50 years from the prediction that this particle should exist to its observation at the LHC. That means the theorists are

17:48 just way ahead of the experimentalist. You got some deadbeat experimentalists there. I I would not say that at all. I would say that that dialogue of theory and experiment is really important. But I'm just pointing out that direct experiment of you know direct verification by experiment of lots of things is hard. That doesn't mean that one shouldn't do it. It just means that you know you have to to be deciding what time scales are relevant for that question. Um for string theory I would say the problem is a lot worse than it was for something like the prediction of the Higs boson because the energy scales are so massive to directly uh observe strings. So for me personally, I I'm interested in trying to decide whether string theory is useful a lot faster than that in the point of view of my career and I remain very agnostic as to whether that's the case. So you want to be alive when when I want to be alive when we decide this and also you know if

18:33 somebody could could demonstrate to me right now that string theory was for sure not useful for our universe I'd choose to work on something else. So what do I think is the the sort of most direct way to those types of answers is that in string theory many types of structure and and results in physics are really intercorrelated. So it turns out that in something like um the the particle physics description of all the particles we know about so far the standard model of particle physics. So that's a the organization of all the particles that we know on one in one chart and you say this this interacts with that and this connects here and it's a it's a beautiful thing actually when you step back it's a tri I mean that happened in I'm older than both y'all that happened in my lifetime in the basically the 1970s we started

19:20 assembling a little earlier too but the full picture was coming together as we found these other particles to flesh it out so it's a periodic table of particles okay all right an organiz organizing principle. Very good. Okay. So, pick it up there. Sorry. Quick anecdote from when I was a kid. I got interested in physics reading books like by people like Brian Green when I was, you know, in my early teens. And I had a little um I'd written down the standard model like on a piece of paper. I made my little zoo of particles and I like carried around on a piece of paper for a bit as a a super, you know, nerdy young young person. Girl geek in the house. Love it. Girl geek alert. Yeah, totally. Totally. But um but I totally agree. It's it's the zoo of what what we know is there. And the point I was going to make in relation to string theory is that in something like the standard model, there's a lot of free numbers. So

20:05 for example, nothing in that theory tells you what the mass of the electron is or how the quarks couple to each other. Those numbers are just observed in our universe. Well, you said free numbers, you mean not predicted, correct? Not predicted by the structure of the theory. Now, in contrast to that, in string theory, if you found a solution of string theory that produced particle physics like we see in our universe, none of those numbers are free. They're all determined by the configuration of these extra dimensions and the structure of the theory. So, it's a huge array of physics that you have to get right all at once. And here I've been talking about particle physics, but you also have to answer questions about cosmology and the large scale structure and history of the universe. So, how are you going to decide if string theory is wrong? I think that it's most likely that we

20:50 would be able to say that the structures that we see in nature, we can argue that we either can or can't get the right sort of regimes of numbers and effects that we already know are there um much more rapidly than we're going to build an accelerator to see a string. I love that. Oh, that's Yeah. Yeah. So, what you're saying is you you whether or not you can test the dimensionality or or the other sort of physicality of string theory. If you could, if your theorist can go in the back room and come out and say, I I pluck this string this way, it's going to give me an electron and it's going to give me this mass, right? And it's the only mass that's going to come out of this, right? Cuz that's the right number. That's the right number and the right vibration and it's going to look like an electron. That that that's a Nobel Prize right there. Yeah. It's it's like it's like the way they do like modeling or weather modeling. they

21:38 we have a prediction and then we run the model on what's already been done and if we get those numbers then we can have confidence in the predictive model itself. That's right. Again, so the idea is I just articulated it. This has been around for like 40 years. Um this was what when people were first formulating string theory, everybody was excited and they thought we were going to do exactly what you just said. You know, you're going to go around, you're going to look at the solutions of the string theory, you're going to say, "Boom, here's our universe. Here's all these numbers. We just predict everything. it's great. That hasn't happened and uh there's you know people are still trying to think about this. So what are some of the big obstacles? One of the issues is that it turns out that when you ask how many different configurations for these extra dimensions can there be? Um initially the hope was that maybe that was very restrictive. Maybe there was just a

22:24 couple. Um the the question of how many could you have? So if you said what if we just had um say two extra dimensions that uh obeyed the consistency equations from string theory. Turns out there's a unique answer from the differential equations that tell you what that shape could be. If you ask is there, you know, what happens if there are four extra dimensions, there's a unique answer. And then if you say, what happens if there were six extra dimensions, which happens to be the extra dimensions that we think needs to arise to give what we see in nature. Turns out there are half a billion configurations and counting that have been found so far. So, it sounds to me like what you guys are saying is we have this instrument and on the instrument there's a certain amount of notes that are just resonant in the

23:10 instrument and now we have to figure out one song because all those notes can make however many billions of songs. We got to find the one song that all those notes can play. But it also sounds like nature's just messing with us. It sounds so this is a one of the the things that people push back on string theory on is they say okay if all these possible solutions of string theory exist how is it ever going to be predicted and you know you could just have this big soup of things and some people have even made that argument. They call it the string landscape where they say you know you could just land anywhere. So so what if there's some place in the string landscape that looks like our universe there's all this other junk. What is the theory actually telling us then? And the argument I would I would say against that is that

23:56 in something like quantum field theory which we already talked about for the standard model this zoo of all the the you know quirks and lepttons that we know in nature there are an infinite number of quantum field theories that I could write down that aren't our universe but it doesn't matter because we do know how to write down one that does look like our universe. So string theory is sort of a natural extension of quantum field theory in some ways and it has a lot of flexibility that may have nothing to do with the physics that we observe in our universe. But the question is once you zoom in on the the parts of that theory that do you learn anything? So for example, do you find that if you see the particles that we already know that additional particles must be there or additional forces or can we correlate features in cosmology and the large scale structure of the universe like dark energy or dark matter with particle physics that we know to be

24:43 true? I don't want to lessen the significance of how you describe that. But if I understand it, you're saying on this, like you said, this landscape of half a billion possible songs that it could be and you want the one song that's yours, it's not useful if you find it unless upon finding it, you get other insights about the universe we're in. Uhhuh. Because otherwise, it's just a just so story. Right. Right. It's the universe is just that and we and we explain it with just that and it doesn't take you any further down the street. Is is that a fair way to characterize it? Yeah. And another thing that people are asking in within string theory is how many possible quantum theories of gravity could there be? So imagine that string theory isn't how our universe works. We know it's a quantum theory of gravity, but it might be too idealized

25:29 to describe our universe. So in physics, we talk about, you know, pretending that cows are spheres in order to make the math easier. Consider a spherical cow. Oh, gotcha. We do that all the time. Okay. Is it? Yeah. It's just easier that way. Our uh our society of physics students has a spherical cow t-shirt here for at Virginia Tech. Yeah. Yeah. It's a thing. That's that's pretty wild. It's a thing. If you want to maximize the milk production of a cow, right? Start with a spherical cow. Start with a spherical cow. Yeah. Right on. Yeah. I don't want that milk. I don't want I don't want milk from a spherical cow. I don't I'm sorry. Yeah. Yeah. I'm going goats milk from now on. Yeah. But yeah, the point I'm making is that maybe string theory isn't, you know, it's just too idealized to describe how quantum gravity works in our universe. But a lot of theorists are questioning, okay, if

26:15 that's the case, we know this is a quantum theory of gravity. So if you had another one, right, like the right one that isn't a string theory, how could those two theories be related? And there's groups of string theorists who are trying to argue and and provide mathematical theorems. Um, for example, someone named Kerman Bafa at Harvard has created something called the coortism conjecture. And what he's positing is that perhaps if you had more than one quantum theory of gravity, they must be connected in some way. Otherwise, you would develop inconsistencies in how you could describe quantum gravity quantum gravitational effects. So the the argument I'm making here is that even if string theory isn't the right one, whatever that might mean, maybe it's connected to the right one. So maybe we still learn structure about how string theory can inform what our universe

27:02 should look like. Is is this what not exactly what you just said but the comprehensive look at all of this is this what gives rise to the multiverse and infinite number of universes that's a a different question but an interesting one that the answer is no the answer is no okay we'll say that for we'll say that for later on your specific specialty within string theory is particle phenomenology and could could you just introduce us to that absolutely so that's the question of whether string theory can produce solutions that look like the particle physics that we see the the standard model for example um and the interactions of the other fundamental forces that aren't gravity and so one of the things that I've worked on um at various times over my career is trying

27:48 to ask for the types of solutions that we we see in string theory what um characterizes those that would give us things like we see in nature so um again coming back to this concept of the string landscape Um there's a famous number of like possible solutions that you can get for this this string landscape. A number of like 10 to the 500 which is unimaginably large is thrown around. 10 to the 500. 10 to the 500. That's not a number. That's not a number. It's crazy. That's not even a number. But in that counting of solutions in string theory, um so this is again, you know, something that people say, oh, you know, 10 to the 500, how are you going to learn anything? But all of those 10 to the 500 that people have counted historically, none of them included an electron. Okay? So if you know something about the universe you want to model, you don't care if there's

28:34 10 to the 500. Yeah. None of those can possibly give rise to the type of physics we see. So the type of of research that I do is trying to correlate what shapes for these extra dimensions, what properties of string theory will narrow the field down to things that are close to our universe. Okay. So So have you gotten there yet? What's what's you know what's the hold up here? We're getting better. I mean in all honesty um you know we we have not delivered on that yet but we are I feel like still making legitimate progress. Okay. So how about this? Because uh one of the great redeeming qualities of all scientific discovery or the search thereof is even if I don't get to the thing I am trying to find out along the way I find out all this other great

29:20 stuff that now gives us computers and digital cameras and GPS but I didn't get to what I wanted. So what what have you guys contributed that has been your happy accident? Well, let me say that more tightly. Say it. Tighter. You ready? No. No. I love that. Go ahead. I loved it, but I want to say it another way. All right. Go ahead. Okay. Um, in your failures, how have you succeeded? So I think the the answer to that is is really big and string theory as a field has really expanded to you know huge different numbers of sub fields and researchers who do really different things. So there are many different answers to that question I could like you know percolating in the back of my

30:06 mind. One is um the discovery of the holographic principle which says that uh phenomena like gravity are very deeply related to things called gauge theories which again describe the interactions of particles and charges. Um that these things can be related uh in different dimensions of spaces. So the statement is that uh gravitational theories can be related to gauge theories that live on the quote boundary of that space. um things like the holographic principle are an extremely deep uh bit of structure that says that you know gauge theories and particle physics and gravity are not as different as we thought they were. That's that's a really um profound I would say observation that has arisen in string theory. So the simplest example that I've heard of the holographic principle

30:52 is the surface of the event horizon of a black hole. Okay? And and correct me if I'm wrong here. So you fall through the surface has a memory of everything that passed through. Interesting. And so you can think of the information content of the surface as the full understanding of anything everything that's inside that's inside because there's no loss of information because it's all retained retained there. So that inside the black hole and and if we are inside a black hole of our universe because we have a horizon which you can analogize to an event horizon then we would be the holographic projections of that. So is this a fair did I c did I capture that correctly? Wow. Okay. Given that I've yet to heard a physicist rebut that. So

31:39 is it general agreement that that's probably real? I mean in an idealized sense yes. um how much that you know pertains uh you know what you learn from that in our universe I think is still up for grabs and this is again something people are are thinking about very actively um other analogies that I would give for you know useful stuff that's come out of string theory is um relationships again between things like particle physics and cosmology so you know the study of uh you know dark energy dark matter descriptions of inflation those things being related to you know how particle physics uh realizes those and also structure in mathematics Um so there are a lot of new fields of mathematics that were sparked due to that dialogue between u mathematicians and physicists that arose through string theory and these shapes of extra

32:24 dimensions. So that's good. So you're exciting mathematicians, right? Yes. And then they reached out and wanted some of you in their department, right? Sometimes. Yeah. And and I think you know it's a very much a mutual relationship which is why you're taking a job away from another professor professor. So as one example of this um there's something called the minimal model program in uh geometry which tries to classify basically all these um higherdimensional complex shapes like all of them you know can you write down compact geometries in any number of dimensions and characterize all their properties and and come up with sort of a zoo of every possible geometry. Well we get this is this is your other specialty algebraic geometry. That's right. Was that a spin-off of the rest of these interests? Is that No, it's very much tied to it. So the question of trying to produce particle physics from

33:12 uh string theory that's that's a particle physics question but the actual computation you have to do really rests on the properties of these compact extra dimensions. So you have to do a ton of geometry to extract the numbers that you want like the mass of the electron and the coupling of the quirks. So it's sort of intrinsically interdicciplinary in that sense. Wow. So I want to hear more about this geometry. That's I mean that's crazy. So here's something that is so simple and lowdimensional. So, don't laugh at me, but I was but I want you to take this to your level. Uh, I was talking with an a topologist algebra or some one of these math folk and we were talking about knots. Okay. Just knots. All right. And you take a string and tie a knot in it. And it's a knot. It's a square knot or any whatever your knot is. Whatever knot. Okay. Whatever is your knot. And

33:59 then we That's We're in three dimensions here. So, a one-dimensional string can make a knot. I said, "What's that in four spatial dimensions?" He said, "You can't tie a knot in four dimensions. You would just lift it up and it would just un unravel." And I and I So that just messed with me. And then I then I thought, let's take away a dimension. Let's go to two dimensions. Okay. Okay. Two dimensions. And if you have two dimensional people in a flat surface, if you take a rope and just loop it on itself, they cannot undo that. That is an unsolvable knot to them because they can't pass it back over itself to come around. Right. All right. But I in three dimensions just pick it up and it's gone. Right. So that was so I was just I

34:45 couldn't sleep that night and then I wondered myself what is going on in the mind of someone who's imagining all of this in even higher dimensions than that. What kind of drugs are you hiding? Did you stop? Come on Lara, don't hold out on me. I shared my Iawaska. Give us the real dope. You never told us that Iawaska highdimensionality person talk to you. Well, you know what? I I have You guys are the first to know to be honest because it was so freaky and freaked me out and I never talked about it. But then when she said string theorist of the future said you are our savior. I was the Neo of string theory. Neo. Yeah. What is the matrix Neo? So please tell us. So I really like the the not analogy. Let me give another one that's

35:32 sort of more directly related to the kind of stuff I do. So we talked about, you know, Einstein's theory of gravity. You could ask imagine that the entire universe was two-dimensional, right? Could you have curvature that could lead to like gravitational like theories in two dimensions? And it turns out there's only one number that you get to to specify. And it's basically, you know, if you imagine like the surface of a sphere, it's whether it's, you know, positively curved or negatively curved like a saddle. That's it. And so you can't have dynamical gravity in two dimensions. Likewise, you know, the form gravitation takes will change as you go up in dimension. So absolutely the this question of you know what can you not and unnot? What can you use to describe how space and time might curve all of that changes with different dimensions.

36:18 Yeah. And so you have to get your brain up in that. I'm telling you right now I'm you know I need a nap just from this conversation. So, so, but the the copout thing here is all the higher dimensions are all compacted, so I don't have to think about or worry about it. I'll never see them, right? How how impactful are the compacted dimensions if you if you're trying to manifest gravity in higher dimensions? Does gravity care if it's compacted or not? Does it just care about the dimensionality? It does. It does care if it's compact. It It cares about the compactness. It cares about the shape of those extra dimensions. And indeed, we believe in string theory that those extra dimensions have to still obey Einstein's equations. So they still have to to be consistent gravity in in

37:05 those extra dimensions. Suppose we lived in eight dimensions and he came up with general relativity in eight dimensions. Who who were you to say his 3 + one dimensional thing that higher dimensions have to obey that? He did that in this measly 3 + 1dimensional world. You can't put you can't put commandments on higher dimensions. They are superior to us in every way and you know it. Yes. I I I I hate to say it but higher dimensions look down on us. That's I'm sorry I had that's a t-shirt right there. That is That is a good t-shirt, man. So I actually torture my my undergraduate students in my class on Einstein's theory. Um because Einstein's theory can be actually formulated in any number of dimensions very easily. So there's actually nothing special about

37:52 four. Um so frequently for my students I'll say you know imagine that this was in six dimensions or 10 dimensions or you know she said it can be formulated easily but she didn't say what she meant by easily. Very relative statement there. But one thing that isn't easy and this is actually uh related to why it's hard again to you know really bring string theory to its full fruition is that when you do do Einstein's theory in higher dimensions the equations you have to solve are nastier. So, humans are not really good at nonlinear differential equations. Um, and they are especially not good when they go into high numbers of variables and high numbers of dimensions. So, isn't that something? Okay. So, why don't you just get a math fluid AI bot to do this? I mean, that's the whole that's the whole point of I

38:38 mean, yeah, exactly. Just it's hard for you, but give it to an AI. Yeah. So, one of the the things that we've had to try and do in string theory to extract some of these predictions is actually solve Einstein's equations for these extra compact dimensions. And we don't know any analytic solutions um for how that means, you know, exact solutions you could write down on a piece of paper um for Einstein's theory for the six dimensions that we would need um for these these string compactations. They're called in science. you can solve a problem analytically with an equation and say there's the answer and some you can't and you have to actually run the experiment or or increment a model and see the results each time just to see where it goes, right? And so that's ugly. We hate those, but we kind of

39:23 recognize that that's like in chaos theory, you have to sort of calculate it out, right? You can't just write down the the solution. So, uh, if you're saying you can't in principle or it's just too laborious, just not known how to do it yet. Um, so in general, solving Einstein's equations in any number of dimensions, you know, for any system is is hard because they're nonlinear. So, what that means is that the the gravitational theory is actually backreacting or talking to itself. So, the fact that you have gravitons, you know, the the quantum mechanical description of gravity in the space, that can create more gravity. So this is really wild in terms of the differential equations because normally you could say I find one solution to the theory and I find another and I can just add them together and still get a solution. But

40:08 in general relativity that doesn't work. You can't add two solutions and get another solution. You have to start over every time. So so when we when we model we do this in astrophysics all the time. There's stuff that's just too complicated. But I know at any instant what's supposed to happen and then I just load load that up. But you what you're doing is you're calculating with these differential equations. These are equations that you can calculate at every time step and it's following you on the time step. Right. All right. But you can't just solve out the whole the whole shebang. So got So all right. So you But so tell me again why you can't use AI. You So we can actually and that's that's a a fun topic. So um I was involved for a number of years with numeric simulations like you're describing where you use a computer to

40:54 try and solve the equations that you you can't otherwise. And historically in order to do those computations we had to put them on supercomputer clusters and like wait for months to get results. Um but now actually um with the advent of AI this is something that my collaborators and I have worked on and now you just do it on your iPhone right now we can actually do it on a laptop. Um, so we've started using machine learning algorithms to numerically solve some of these differential equations. So this is different than using like, you know, looking at photos on the internet and then having AI generate a new photo. We don't have these solutions. So there isn't a database that you can train an AI model on, but you can still use the framework of these neural networks to try and solve really complicated equations. And indeed, um, I've worked on that and and lots of other people in the field have. And we found that using

41:40 these techniques, we can speed up a lot of computations in a really substantive way. And this actually made it possible just recently for groups to compute quark masses in string theory for the first time. So to be clear, these are not the quark mass values that we actually observe in nature. Um that would be awesome, but we don't see that yet. But we can say if you just hand me some extra dimensions, whatever they may be, and then say what would the you know the quirks look like in that universe, now we can actually come up with those numbers using machine learning algorithms. Chuck will go back on his Iawaska trip and get the person from that dimension to verify the quark quark mass. Yeah. Yeah. Exactly. And Chuck will be the oracle of physics. And I'm I'm up for it. I'm telling you right now. I'm I'm ready. I'm ready to go do more Iaska. So I'm I'm ready.

42:27 So let me ask another thing. You talk about what discoveries can come out of this. Is it possible because this excites us all. We don't say it every day, but we feel it. Could any of this could any of this bring forth new physics? Because up till now, everything you've said has been within the framework of the quantum quantum field theory, general relativity. And imagine before Einstein was born, you would not even know that relativity was a thing you could use to solve your problems. So, is there some new physics waiting to emerge either either out of your work or some yettobe born genius that will you'll look at and say, "Oh my gosh, I'm going to give a fast astro case here."

43:14 Okay. Uh at turn of the century, uh the orbit of of Mercury around the sun wasn't quite following Newton's laws, you know. It was like, well, there's probably another planet there tugging on it. Yeah. We even named the planet. I mean, that's how Oh, really? Yeah. We called it Vulcan. Oh, nice. Yeah. Yeah. Go 1910. Just look up planet Vulcan. Like there it is. Okay. And so and we were happy. Well, how come no one saw it? Oh, cuz it's too close to the sun. It's in the glare. So we we had we had it was all there. It was all worked out. All worked out. And then Einstein comes up with general relativity. He wasn't trying to explain it, but he showed that at very strong gravity, Newton's laws fail. You plug into his equations and there's no disagreement with the thing. So Vulcan died overnight. But the new

44:00 physics transformed the physics we were already working with and gave us better answers than to move on with. So what I learned from that is Einstein killed Vulcan, Tyson killed Pluto. Stop. That's not the lesson I was trying. It's a good lesson. No, it's not. No. So new physics could take a lot of different forms. Um so you know one example might be perhaps there are more than the four fundamental forces that we've already observed in nature. So could there be you know a so-called fifth force uh another version of something like electromagnetism or um you know the strong weak nuclear force. Um that would be an example of new physics. Uh other things that we know we don't understand very well include things like dark energy and dark matter. um questions

44:47 like you know general relativity tells us that there are these disastrous infinities you know in the center of black holes there's singularities so what actually repairs those singularities in a quantum uh you know gravitational theory what what tells us how physics really behaves inside there um that's definitely new physics and that would be the hope of the kind of thing you you'd like to see oh wow to so so okay so you think there's new physics out there not again the claims on you know what can string theory deliver I'm I'm still somewhat agnostic on that. Um but I think it's really interesting to try and push the theory to find out say you know can you show that this just can't be used to model our universe which is a real possibility and it's going to break somewhere you can't get there or can you you push it to try and make some of this structure visible. So I just I'd love 100 years from now look

45:34 back on this conversation and say look at those idiots back in 2025. Yeah. This will be a kindergarten video 100 years from now. I hope so. So, I got something else here about a duality in string theory. What's going on there? Yeah, this is something that I and my collaborators are working on at the moment. That's a cool word, by the way, duality. I love duality. Duality. So, the idea behind duality is that you could have two different theories or two different geometries as they arise for these compact extra dimensions in string theory that secretly are different sides of the same coin. So an analogy that I give sometimes in talks is if you ever looked at some of these optical illusions photos on the internet where you know you have a picture that's either a vase if you look at it one way or two faces if you look at it the other way you can say you know is it a vase or

46:19 is it faces and the answer is it's both right it's both packaged the question in string theory is you have all these different you know half a billion configurations for extra dimensions do they all lead to different physics and the answer that we think is no um there are known equivalences of different so-called topological spaces. These are things that have, you know, a different geometric properties like their number of holes and their structure. Um, those different topological spaces can actually lead to the same physics that we would see. So that if there's redundancy in that that is really powerful because it means you don't have to search through half a billion possibilities. You can, you know, maybe sort of fold those possibilities in half and only look at some portion of them. Um, some of these dualities have been around for, you know, 20 years in string theory. and my collaborators and I think we have new examples uh which require uh

47:06 less um super symmetry. So a less spherical cow than people had assumed in the past. Okay. Yeah. We're growing some legs in the cow for example. Um and we think that this may improve our ability to calculate lots of things and also teach us some new properties mathematically about how these spaces can behave. Wait, catch us up on super symmetry. So super symmetry is something that comes along for the ride um for some formulations of string theory which says that all the quirks and lepttons that we see in nature may have additional partners um so for example instead of uh you know a quark you have a squirk a another partner um that would be much heavier than the existing particles that we've seen. So when you're describing super symmetry, it's a symmetry beyond the symmetries that are

47:54 already known and loved in the standard model. That's right. So all these these sort of three generations of of quirks and lepttons that we've seen already um there would be another whole set of those particles that would share many of their properties but be heavier in mass and sort of the opposites and that each theory, you know, each particle that was say a bzon would have a firmionic partner and so on. All right. So, so what you're saying is you're not content with just these three regimes we have in the standard model. Just hand us somewhere in the universe other regimes above that and see what properties they might have and that could explain stuff that we don't now understand. That's an idea. And people initially thought this idea might explain some really um important questions in particle physics. uh for example to do with the mass of the Higs

48:40 Bzon that would be what's called low-cale super symmetry and particle experiments like the LHC search very hard for this and didn't see it. So some people consider super symmetry not a very useful idea because they thought you know it might appear in these regimes and it would not be useful. Um people are reinvestigating this question in string theory. You know some of the solutions of string theory are super symmetric some are not. Um what we generally would agree on is that if you did have super symmetry it would have to be at a very high scale. So it would be much um these particles would be much heavier than you could see in an experiment like the LHC and that the symmetry would be spontaneously broken in universes like ours. So that by the time you got down to, you know, where we live now, you would only see the standard model particles at the energy and not the other ones that would have

49:25 helped birth it. So So um I'm going to say that's rather convenient though. I'm just going to say so the question is like why do you need that symmetry right if if you're kind of getting rid of it back when you know you really want to be talking about the physics yeah conveniently discarding it that's a great great question um in some string theories it still plays a role in terms of regulating the quantum mechanical behavior of the theory and making it well behaved so in that sense you know you're still using it theoretically for something even though you don't need it to describe the particle physics that we are observing in nature. But I think all string theorists would ask, it's a really interesting question to say how much of the super symmetry can you get rid of and then still preserve the features

50:12 that are of interest to us. So the types of dualities I was describing, these are are perhaps um new because they involve less reliance on super symmetry than we had in the past. And so we're still observing this sort of redundancy or these different descriptions of the same physics packaged different ways. Um, but we don't need as much super symmetry. If if memory serves, the graviton is not in the standard model. Is that correct? That's right. So that means no one is thinking about a super symmetric particle to the graviton because that would be kind of interesting. Yeah, you you certainly could for any particle um you know any gauge bzon, you could have a what's called a gino. So a a super symmetric particle. Gauge eno. They're just making pulling it out of the ass.

50:57 Yes. It's sounds like you're naming like pharmaceutical products. This is before my era in physics, but I do feel that some of these names are very much a product of the 1970s. I was in high school. That's how old I am in the 1970s. And I'm just, you know, there was like the particle of the month club. What new particle was being discovered in the new accelerators in California and elsewhere. Uh, and we were just building this fabric of the universe out of that. That's kind of cool actually. Fun to be witness to it. It was fun. That's fun. Yeah. Not participant, but witness. Could you expend a moment just celebrating the idea of symmetry in physics? Yeah, this is a really really great question. So, symmetry in physics um this is something that is extremely deep and has been very very predictive and powerful over the last hundred years

51:43 of physics. So this is a question that in my classes to undergraduates I try and convey that a lot of physics is based on looking at a phenomena that you see like an apple falling from a tree and saying you know how do I model the the path that that's going to fall right like how do I write an equation that describes that but once you start talking about symmetries and these are uh basically rules for how you might change a space or an equation in ways that can leave it alone. Once you start talking about symmetries, you actually have the power to ask, could the theory that I'm describing be any different? It allows you to ask questions about not just what you observe, but whether any theory that you write down could have uh arisen differently in nature. So there's some um kind of highulutin quote by

52:29 Einstein that you know saying he wanted to to probe God's thoughts um you know in terms of his theories which sounds extremely grandiose but the the tangible non theological um underpinning of that is that you can ask for a theory if I write down this theory like Einstein's theory of relativity could it have been different what is the freedom to uh change that theory at all could there have been any other theory of gravity that could have worked what does it what what does it have to do with the our understanding understanding of what the word symmetry means. Right? So the idea behind symmetries is that if I tell you about the rules for what I can do for a theory and leave it alone, that is equivalent to specifying the theory. So for example, um if you want to ask how do the laws how are the laws of physics

53:15 impacted by the fact that if I do an experiment here and then I move that experiment 5t to the left and do the same experiment, I should get the same answer. Right? What is that the implication of that for the laws of physics? It turns out that that phenomena that you know the laws of physics shouldn't care whether your laboratory is here versus 5t to the left. That's very much linked to something like the conservation of momentum in classical physics or the fact that you should do an experiment today and get the same answer tomorrow is related to the idea that energy is conserved in classical physics. So all of these um sort of can I shift something you know in some concrete way. There I talked about, you know, moving an experiment or doing the same experiment at different points in time. But, uh, in more general, you can say if I could characterize all the different ways that I can, you know, pick something up, turn it over, look at it, you know, shift its description, and if

54:02 it stays the same, that actually tells me what equations are compatible with that in a really predictive way. I've got another symmetry here, mirror symmetry. So, what do you have for us there? M so mirror symmetry was uh originally discovered um in the context of these string compactifications. So considering solutions of string theory that could lead to you know physics like we we see in our universe. The compact extra dimensions that people were trying to write down they discovered that all the solutions they could find seem to come in pairs and these pairs involved interchanging topological numbers. So a topological number is all the ways that you can change a geometry or sorry is characterized by all the ways you can change a geometry um without

54:47 intrinsically changing what it is. So the classic example is that you can change a donut into a coffee cup. So you you picture you know taking yourself a donut and if you imagine the material was all rubbery and you could stretch it and squish it any way you want but not cut it. How can you deform that shape or change it or put another hole in it? And and this is a coffee cup with a a little finger hole with a handle. Yeah. Yeah. With It wouldn't work if it didn't have a handle. Right. Right. So it was just like a drinking glass. Doesn't work. Yeah. Not the coffee cup from Starbucks because that doesn't have a handle. Right. Okay. Okay. The the idea there is that a geometry with a single hole. You can't change the number of holes. Whether that's the center of the doughut or if you could smoosh it around and turn it into the handle of a coffee cup. Um that's what's called a topological invariant. But the number of holes is one of these examples of of topological

55:34 numbers. So a a donut has one hole. You could imagine, you know, a donut that was built to have two holes and so on. You know, this this kind of thing describes or characterizes geometry. So in mirror symmetry, all these geometries come with topological numbers. But any combinations you could have, it turns out you could have in more than one configuration. And this again sort of divides the space of possible geometries in half in this case. Uh it tells you that all of them are are you know interchangeable in concrete ways. Wow. Man, that is insane. First of all, why? Why? It's a really great question. That's so crazy. I love it though. Well, but I got

56:19 more here. Well, we just we're just we're just cracking this egg. You know what? Do I have a kabi yao manifolds? So these are examples of configurations for the shapes of extra dimensions in the string theory that satisfy Einstein's equations. Um so these are the the half a billion possibilities that I was talking about. Manifold I didn't get the word manifold. Yeah, y'all got that from Star Trek. Get out of here. Named after two very clever mathematicians. Um yeah, these manifolds were conjectured to exist by a mathematician named Eugene Kabi and proved by uh Yao who won a Fields Medal for his proof that um these these things solve Einstein's equations. Do you know about the Fields Medal? No, I don't. So, it's kind of like the Nobel Prize in mathematics. Um it's given to major, you

57:04 know, substantive discoveries in mathematics. Um but the catch is you got to be under 40 to to get it. So, um you have to be young and clever. Oh, man. Of course, the mathematicians would use chronology as a determining fact. Yeah. Discriminating. It's agist. I think it is. Yeah. Exactly. Homological

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