Consider a Spherical Cow with Lara Anderson

Summary

StarTalk Radio Episode Summary: "Consider a Spherical Cow with Lara Anderson"

Podcast Information:

• Title: StarTalk Radio
• Host: Neil deGrasse Tyson
• Guest: Brian Greene
• Release Date: June 17, 2025
• Episode Focus: String Theory and Its Implications

---

1. Introduction to String Theory

Timestamp: [02:13]

In this episode, Neil deGrasse Tyson welcomes Lara Anderson and renowned string theorist Brian Greene to delve into the complexities of string theory. Lara Anderson humorously questions the abundance of string theorists, highlighting the prominence of Brian Greene in the field.

Lara Anderson: "Is there room for more than one string theorist at the OK Corral?"
([02:20])

Brian Greene responds with a light-hearted remark, setting the stage for an in-depth discussion.

---

2. Understanding String Theory

Timestamp: [04:43]

Brian Greene explains the foundational goal of string theory: to reconcile Einstein's theory of general relativity with quantum mechanics, aiming to develop a consistent quantum theory of gravity.

Brian Greene: "String theory is an attempt to reconcile Einstein's theory of general relativity, a theory of gravity, with the formalism of quantum mechanics and quantum field theory."
([04:56])

He emphasizes that while string theory may not perfectly describe quantum gravity in our universe, it provides a theoretical playground for exploring quantum gravitational phenomena.

---

3. Challenges in String Theory

a. The Incompatibility of General Relativity and Quantum Mechanics

Timestamp: [05:19]

Lara Anderson probes the inherent incongruencies between general relativity and quantum mechanics, questioning why string theory prioritizes absorbing gravity into quantum physics rather than the reverse.

Lara Anderson: "You are trying to absorb Einstein's general theory of relativity into a quantum description. Why aren't you trying to take the quantum and absorb it into a general relativity description?"
([05:42])

Brian responds by highlighting the breakdown of both theories when attempting to merge them, leading to "disastrous infinities."

Brian Greene: "If you try and describe phenomena that might need both tools, ... the theories break down when you try and combine them and you don't end up getting useful answers."
([07:33])

b. The String Landscape and Extra Dimensions

Timestamp: [25:08]

The conversation shifts to the concept of the string landscape, where Brian Greene mentions the existence of approximately 10^500 possible configurations of extra dimensions required by string theory.

Brian Greene: "So this string landscape. A number of like 10 to the 500, which is unimaginably large, is thrown."
([31:56])

Lara Anderson analogizes this to having an instrument with billions of possible "songs," emphasizing the challenge of pinpointing the exact configuration that represents our universe.

Lara Anderson: "We have this instrument, and on the instrument, there's a certain amount of notes that are just resident in the instrument. And now we have to figure out one song, because all those notes can make however many billions of songs."
([26:44])

---

4. Advances and Insights from String Theory

a. The Holographic Principle

Timestamp: [34:33]

Brian Greene introduces the holographic principle, explaining how it connects gravitational theories to gauge theories on the boundary of space. This principle suggests that gravity and particle physics are deeply interrelated.

Brian Greene: "Gravitational theories can be related to gauge theories that live on the boundary of that space."
([34:33])

Lara Anderson seeks clarification through the example of a black hole's event horizon, to which Brian affirms the principle's validity in an idealized sense.

b. Mathematical Contributions and Duality

Timestamp: [51:30]

The discussion delves into duality in string theory, where different geometries or compact extra dimensions can lead to identical physical phenomena. Brian explains that this reduces the number of unique configurations that need to be explored.

Brian Greene: "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."
([51:30])

He further elaborates on mirror symmetry and its significance in reducing the complexity of the string landscape.

---

5. Overcoming Computational Barriers with AI

Timestamp: [42:14]

Addressing the computational challenges of solving Einstein's equations in higher dimensions, Brian Greene discusses the integration of machine learning algorithms to expedite numerical simulations.

Brian Greene: "We've started using machine learning algorithms to numerically solve some of these differential equations. ... we've found that using these techniques, we can speed up a lot of computations in a really substantive way."
([44:56])

This advancement has enabled researchers to compute quark masses in string theory for the first time, marking a significant milestone in the field.

---

6. Future Directions and Potential Discoveries

Timestamp: [50:48]

Brian Greene speculates on the possibility of new physics emerging from string theory, such as additional fundamental forces or explanations for dark energy and dark matter. He remains cautiously optimistic about the theory's potential to address unresolved questions in physics.

Brian Greene: "There are a lot of things that we know we don't understand very well, including dark energy and dark matter. That's definitely new physics."
([50:48])

---

7. The Interplay Between Physics and Mathematics

Timestamp: [57:12]

Lara Anderson and Brian Greene celebrate the symbiotic relationship between physics and mathematics, noting how advancements in one often spur progress in the other. Brian cites the minimal model program in geometry as an example of mathematical concepts inspired by string theory.

Brian Greene: "This type of structure, this dialogue between maths and physics, I personally think, is really fruitful."
([63:27])

He highlights how string theory has led to the discovery of new mathematical structures and theories, enriching both disciplines.

---

8. Conclusion

Timestamp: [67:11]

As the episode wraps up, Lara Anderson reflects on the profound interconnectedness of scientific and mathematical advancements, emphasizing the foundational role they play in our understanding of the universe.

Lara Anderson: "These are two fields that so often people in school say, I'm not good at math and I'm not good at physics, and I'm not, meanwhile, is the foundation of our understanding of our place and existence in this universe."
([65:25])

Neil deGrasse Tyson humorously admits to feeling overwhelmed yet enlightened by the intricate discussions on string theory.

Neil deGrasse Tyson: "I am just as dumb as I ever have been, but I feel smart."
([67:11])

The episode concludes with a reaffirmation of the collaborative spirit between physicists and mathematicians, underscoring the continuous quest to unravel the mysteries of the cosmos.

---

Key Takeaways:

• String Theory's Ambition: Aims to unify general relativity and quantum mechanics into a single coherent framework.
• Challenges: The vast string landscape with its numerous configurations and the difficulty of experimental verification.
• Advancements: Introduction of the holographic principle and the use of AI in solving complex equations.
• Interdisciplinary Impact: Significant contributions to mathematics, particularly in geometry and duality.
• Future Prospects: Potential for new physics discoveries addressing dark matter, dark energy, and beyond.

Notable Quotes:

• Brian Greene at [04:56]: "String theory is an attempt to reconcile Einstein's theory of general relativity, a theory of gravity, with the formalism of quantum mechanics and quantum field theory."
• Lara Anderson at [26:44]: "We have this instrument, and on the instrument, there's a certain amount of notes that are just resident in the instrument. And now we have to figure out one song, because all those notes can make however many billions of songs."
• Brian Greene at [34:33]: "Gravitational theories can be related to gauge theories that live on the boundary of that space."
• Neil deGrasse Tyson at [67:11]: "I am just as dumb as I ever have been, but I feel smart."

---

This episode offers a comprehensive exploration of string theory, its profound implications, and the intricate dance between theoretical physics and advanced mathematics. Whether you're a seasoned physicist or a curious enthusiast, "Consider a Spherical Cow with Lara Anderson" provides valuable insights into one of the most ambitious frameworks in modern science.

Transcript

[Neil DeGrasse Tyson]

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[Lara Anderson]

So Brian Green's not the only string theorist in town.

[Neil DeGrasse Tyson]

I was not aware of this. Lead to Brian.

[Lara Anderson]

Is there room for more than one string theorist at the OK Corral?

[Neil DeGrasse Tyson]

Yeah.

[Lara Anderson]

All updates on string theory and how it connects to mathematics. Multiple branches of it coming right up. Welcome to StarTalk, your place in the universe where science and pop culture collide. StarTalk begins right now. This is StarTalk. Neil DeGrasse Tyson, your personal astrophysicist Got Chuck nice with me. How you doing, Chuck?

[Neil DeGrasse Tyson]

Hey, I'm doing great, man. Thanks.

[Lara Anderson]

All right. A comedian, actor.

[Neil DeGrasse Tyson]

Yeah.

[Lara Anderson]

We've seen a few TV commercials here and there.

[Neil DeGrasse Tyson]

Yeah. You know, listen, sometimes I have nothing to do.

[Lara Anderson]

Well, today we got a really cool topic that's always on everybody's mind. Well, everybody who cares about the universe.

[Neil DeGrasse Tyson]

You know, even people who don't. But I'll get. I'll get into that later. Yeah. What we're talking about, I've heard some really weird stuff from people that, you.

[Lara Anderson]

Know, they want to get into it.

[Neil DeGrasse Tyson]

Yeah.

[Lara Anderson]

Okay.

[Neil DeGrasse Tyson]

Yeah.

[Lara Anderson]

All right. All right. We're talking today about string theory.

[Neil DeGrasse Tyson]

Yeah.

[Lara Anderson]

And now we have our man about town street theorist Brian Greene, right up the street. But I said, you know, all the universe is not Brian Greene.

[Neil DeGrasse Tyson]

You know, he would beg to differ.

[Lara Anderson]

So I said, so we reached out to the cosmos. Yes. All right. And we found Lara Anderson. Lara, welcome to StarTalk.

[Brian Greene]

Thank you very much. It's a pleasure to be here.

[Lara Anderson]

Yeah. So you are associate professor of physics at Virginia Tech. One of our producers is from Virginia Tech. So you're right at home here among us.

[Neil DeGrasse Tyson]

Yeah. You're family now.

[Lara Anderson]

Yeah. You're family.

[Brian Greene]

Good to be among friends.

[Lara Anderson]

Also, like Brian Greene, you have a double affiliation also with the mathematics department.

[Brian Greene]

I do. I'm an affiliate professor of mathematics, which means I can supervise math grad students as well.

[Neil DeGrasse Tyson]

So you just taking jobs from everybody? This professor's out on the street because of Laura Anderson.

[Brian Greene]

Entirely possible.

[Lara Anderson]

I can try to picture that, how they're like, I'll do your math homework for money.

[Neil DeGrasse Tyson]

Exactly. Will math for food.

[Brian Greene]

I think, unfortunately, that is a job.

[Lara Anderson]

It's called tutors. Really? Really.

[Neil DeGrasse Tyson]

Exactly.

[Lara Anderson]

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?

[Neil DeGrasse Tyson]

Yes.

[Brian Greene]

String theory is an attempt to reconcile Einstein's theory of general relativity, a theory of gravity, with the formalism of quantum mechanics and quantum field theory. So it is a consistent quantum theory of gravity. 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 ask questions about quantum gravity.

[Lara Anderson]

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, into a quantum description. Why aren't you trying to take the quantum and absorb it into a general relativity description.

[Neil DeGrasse Tyson]

Because inherent in what both of you said, there must be an incongruency that would cause you to have to do that.

[Lara Anderson]

Exactly. So why don't you start with that, Laura, what is the incongruency here that you're trying to resolve?

[Brian Greene]

Two of the greatest intellectual accomplishments of the 20th century, in my opinion, are Einstein's theory of gravity and the description of fundamental interactions in nature as described by particle physics. So things like a description of, you know, quarks, 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 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.

[Lara Anderson]

There'll be 13 decimal places, right? 13 significant figures, yeah.

[Neil DeGrasse Tyson]

I'm going to say that's pretty accurate.

[Brian Greene]

It's pretty great. Yeah. And like things like modern GPS wouldn't work without general 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, that would be a regime where you need both of 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, Things that just don't predict anything.

[Lara Anderson]

Wow.

[Neil DeGrasse Tyson]

Disastrous infinity, man.

[Lara Anderson]

You can't get more dissed than that.

[Neil DeGrasse Tyson]

Sounds like the worst marriage ever.

[Brian Greene]

Yeah, it's not great.

[Lara Anderson]

Disastrous infinities. So what gives you the confidence that it is the quantum physics understanding that will absorb gravity and not gravity absorbing quantum physics?

[Brian Greene]

It's a great question. So I think that it should be a two way street. So in order to describe either phenomena, you need something that can be described in both frameworks. Einstein's theory is sort of intrinsically classical, 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 level, if you sort of zoom in, should evolve into something quantum mechanical. But exact form of that is up for exploration.

[Lara Anderson]

Okay, okay, so that works. Now you mentioned fundamental particles, and you go back to ancient Greece. The atom was a fundamental particle that.

[Neil DeGrasse Tyson]

Was the smallest thing that you could.

[Lara Anderson]

Be, that you could be. Right. And then we break the atom. Oh, there's other particles. And so 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?

[Brian Greene]

Yeah, that's a great question. I don't think, 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 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.

[Lara Anderson]

Okay.

[Neil DeGrasse Tyson]

Oh, really? Right, Exactly. That's the little vibrating.

[Lara Anderson]

String is the fundamental.

[Neil DeGrasse Tyson]

String is the fundamental.

[Lara Anderson]

So take us there. Okay, yeah, take us out. Now, how do strings come into this?

[Brian Greene]

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 very rough idea is that just like a violin, string can vibrate in different ways and produce different notes. These little fundamental strings can vibrate into different configurations. And it turns out they can change their properties. 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. And that seems like a very sort of cute idea for how to describe a lot of physics in a very simple framework.

[Lara Anderson]

But if that's the case, in principle, you ought to be able to pluck the string that is otherwise an electron and get a quark out of it. Have you done this?

[Brian Greene]

No. And the problem with this, I'm going to tell you one thing that's really cool about this framework and then also two things that are not cool. One of them is very much to do with what you said. So why can't you just test or Observe are these strings. There's. 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, which unfortunately we do not have access to those type of energy scales yet.

[Lara Anderson]

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. And you'll probe regimes that previous accelerators could not.

[Brian Greene]

That's right.

[Lara Anderson]

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.

[Brian Greene]

Right. Which doesn't seem very viable.

[Lara Anderson]

No, it's not. So what's your. What's plan B?

[Brian Greene]

Before I answer that, 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 configuration of space and time. But if you ask the same question for these little one dimensional 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 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.

[Lara Anderson]

That sounds good. Wow.

[Brian Greene]

Okay, so you actually get gravity for free in this formulation of quantum mechanical strings. So 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 must satisfy.

[Lara Anderson]

So that's a good feeling then, because it means something is talking to something else in the formulation that was not crowbarred in to begin with.

[Brian Greene]

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, 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 the particle physics by one little extended object. You get gravity for free, only seems to work if the universe that this happens in has more than three spatial dimensions and one time like dimension that we seem to see in our universe.

[Neil DeGrasse Tyson]

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.

[Brian Greene]

Well, it's, I mean, it seems like a really big intellectual leap, right? 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 deal breaker? 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 question is, you know, could such extra dimensions exist? And if so, how would we try and probe whether that's the case? 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 is what's called compact, 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.

[Neil DeGrasse Tyson]

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 ayahuasca 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 that maybe that was a presupposed, pre planted, post hypnotic suggestion. Because I have actually read about string theory, because if it's not.

[Lara Anderson]

Or Laura, what drugs have you been taking?

[Neil DeGrasse Tyson]

My follow up question is, what did you do?

[Lara Anderson]

That's right.

[Brian Greene]

I hear the question.

[Vicki Brooke Allen]

Yeah.

[Lara Anderson]

Is it possible to have a compactified time dimension as well? Or is all the models Only stuck with one time dimension. Oh, wow.

[Neil DeGrasse Tyson]

I've never even considered that.

[Lara Anderson]

Yeah, imagine two dimensions of time. Wow. Holy crap.

[Neil DeGrasse Tyson]

Go ahead. Yes.

[Brian Greene]

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 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 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 to try and build through to this.

[Neil DeGrasse Tyson]

You would have to discard causality altogether in order to do that. Or would it just be it violates.

[Brian Greene]

I think in general the claim would be it would violate causality in such theories. So there may be some creative ways to get around that, but generically I think that's true.

[Lara Anderson]

By the way, we have Stephen Hawking on one of our earlier episodes. You find it in our archives. We went to University of Cambridge 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 that save us from this?

[Brian Greene]

I mean, there are a number of conjectures, say in the theory of gravity that say that causality is an important structure. So that in general one would not expect that consistent theories of gravity or indeed quantum mechanics should allow.

[Lara Anderson]

You just can't get it to work. Okay, okay, that's fine.

[Neil DeGrasse Tyson]

Yeah.

[Lara Anderson]

I mean, listen, that removes many movies in the repertoire where you gotta go back and change the past.

[Neil DeGrasse Tyson]

Exactly.

[Lara Anderson]

Like Terminator, all the Terminator is done.

[Neil DeGrasse Tyson]

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 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 because it ain't never going to happen.

[Brian Greene]

Well, I would say, you know, never say never. In insights you got to be careful. But 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.

[Neil DeGrasse Tyson]

And that's why I'm not a scientist.

[Lara Anderson]

And just considered to say never say never. You said no, you said never.

[Neil DeGrasse Tyson]

You just said never.

[Lara Anderson]

You can't say never, say never without saying never.

[Vicki Brooke Allen]

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[Brian Greene]

Hello, I'm Vicki Brooke Allen and I support Star Talk on patreon. This is StarTalk with Neil DeGrasse Tyson.

[Lara Anderson]

Before we sort of pivot to this whole thing of phenomenology, because 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, 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 hypothesis because you need to be able to test it. Without the test, go home. So let me hear your response to that.

[Brian Greene]

Absolutely. I think that's a really fair question 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, 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 structure and predictions and what you're learning from this theory. So to push back on the how are we going to test it? Let me observe first that in particle theory in general, the timescales between predicting structure in particle theory and then being able to see it in experiment over the last half century have gone increased in size considerably. So one example of this is the prediction of the Higgs boson made by Peter Higgs, which took about 50 years from the prediction that this particle should exist to its observation at the lhc.

[Lara Anderson]

That means the theorists are just way ahead of the experimentalist. You got some deadbeat experimentalists.

[Brian Greene]

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 be deciding what timescales are relevant for that question. For string theory, I would say the problem is a lot worse than it was for something like the prediction of the Higgs boson because the energy scales are so massive to directly observe strings. So for me personally, 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.

[Lara Anderson]

So you want to be alive when.

[Brian Greene]

Be alive when we decide this. And also, you know, if 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 sort of most direct way to those types of answers is that in string theory, many types of structure and results in physics are really intercorrelated. So it turns out that in something like the particle physics description of all the particles we know about so far, the standard model of particle physics, so.

[Lara Anderson]

That'S the organization of all the particles that we know in one chart. And you say this interacts with that, and this connects here. And it's a beautiful thing, actually, when you step back and it's a triumph. I mean, that happened. I'm older than both y' all. That happened in my lifetime. I mean, basically the 1970s, we started assembly a little earlier, too, but the full picture was coming together as we found these other particles to flesh it out.

[Neil DeGrasse Tyson]

So it's a periodic table of particles.

[Lara Anderson]

Okay, all right. An organization. Organization principle. Very good. Okay, so pick it up there. Sorry.

[Brian Greene]

Quick anecdote from when I was a kid. I got interested in physics, reading books like by people like Brian Greene. When I was in my early teens and I had a little. 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 super nerdy young person.

[Lara Anderson]

Girl geek in the house.

[Neil DeGrasse Tyson]

Love it.

[Lara Anderson]

Girl geek alert.

[Brian Greene]

Yeah, totally, totally. But I totally agree. It's the zoo of 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, 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.

[Lara Anderson]

Well, you said free numbers. You mean not predicted.

[Brian Greene]

Correct? Not predicted by the structure of the theory. Now, in contrast to that in string theory, if you found a solution in 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 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 much more rapidly than we're going to build an accelerator to see a string.

[Lara Anderson]

I love that.

[Neil DeGrasse Tyson]

Oh, that's.

[Lara Anderson]

Yeah, yeah. So what you're saying is whether or not you can test the dimensionality or the other sort of physicality of string theory. If your theorists can go in the back room and come out and say, I pluck this string this way, it's gonna give me an electron and it's gonna give me this mass.

[Neil DeGrasse Tyson]

Right.

[Lara Anderson]

And it's the only mass that's gonna come out of this.

[Neil DeGrasse Tyson]

Right. Cause that's the right number.

[Lara Anderson]

It's the right number and the right vibration and it's gonna look like an electron. That, that, that's a Nobel prize right there.

[Neil DeGrasse Tyson]

Yeah, it's like the way they do like modeling or weather modeling. 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.

[Brian Greene]

That's right. Again. So the idea is. I just articulated it. This has been around for, like, 40 years. 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 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? Initially, the hope was that maybe that was very restrictive. Maybe there was just a couple. The question of how many could you have? So if you said, what if we just had, say, two extra dimensions that obeys 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.

[Neil DeGrasse Tyson]

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 resident in the instrument. And now we have to figure out one song, because all those notes can make however many billions of songs. We gotta find the one song that all those notes can play.

[Lara Anderson]

But it also sounds like nature's just messing with us.

[Brian Greene]

Yeah, it sounds. So this is one of 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 in something like quantum field theory, which we already talked about for the standard model, this zoo of all the you know, quarks and leptons 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 parts of that theory that do, 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 true?

[Lara Anderson]

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, because otherwise it's just a just so story. Right, right. The universe is just that, and we explain it with just that. And it doesn't take you any further down the street. Is that a fair way to characterize it?

[Brian Greene]

Yeah. And another thing that people are asking 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 to describe our universe. So in physics, we talk about, you know, pretending that cows are spheres in order to make the math easier.

[Lara Anderson]

Consider a spherical cow. We do that all the time.

[Neil DeGrasse Tyson]

Okay.

[Lara Anderson]

Yeah. It's just easier that one.

[Brian Greene]

Our society of physics students has a spherical tau T shirt here for at Virginia Tech.

[Lara Anderson]

Yeah, yeah. It's a thing that's.

[Neil DeGrasse Tyson]

That's pretty wild.

[Lara Anderson]

It's a thing if you want to maximize the milk production of a cow.

[Neil DeGrasse Tyson]

Right.

[Lara Anderson]

Start with a spherical cow.

[Neil DeGrasse Tyson]

Start with a spherical cow. Yeah, right on.

[Lara Anderson]

Yeah.

[Neil DeGrasse Tyson]

I don't want that milk.

[Lara Anderson]

I don't want.

[Neil DeGrasse Tyson]

I don't want milk from a spherical cow. I'm sorry. Yeah, yeah. I'm going goat's milk from now on. Yeah.

[Brian Greene]

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 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 string theory, how could those two theories be related? And there's groups of string theorists who are trying to argue and provide mathematical theorems. For example, someone named Kirman Bafa at Harvard is created something called the coordism 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 should look like.

[Neil DeGrasse Tyson]

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?

[Brian Greene]

That's a different question, but an interesting one.

[Lara Anderson]

The answer is no.

[Neil DeGrasse Tyson]

The answer is no.

[Lara Anderson]

Okay, maybe we'll say that for later.

[Neil DeGrasse Tyson]

Yeah, we'll say that for later. Yeah.

[Lara Anderson]

Your specific specialty within string theory is particle phenomenology. And could you just introduce us to that?

[Brian Greene]

Absolutely. So that's the question of whether string theory can produce solutions that look like the particle physics that we see, the standard model, for example, and the interactions of the other fundamental forces that are in gravity. And so one of the things that I've worked on at various times over my career is trying to ask for the types of solutions that we see in string theory. What characterizes those that would give us things like we see in nature. So, again, coming back to this concept of the string landscape, 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.

[Lara Anderson]

Around 10 to the 500.

[Brian Greene]

10 to the 500.

[Neil DeGrasse Tyson]

That's not a number.

[Brian Greene]

That's not a number. It's crazy.

[Neil DeGrasse Tyson]

It's not even a number.

[Brian Greene]

But in that counting of solutions and string theory, 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 it's 10 to the 500. Yeah. None of those can possibly give rise to the type of physics we see. So the type 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.

[Lara Anderson]

Okay, so, so have you gotten there yet? What's, what's, you know, what's the hold up here?

[Brian Greene]

We're getting better. I mean, in all honest, you know, we have not delivered on that yet, but we are, I feel like, still making legitimate progress.

[Neil DeGrasse Tyson]

Okay, so how about this? Because 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 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?

[Lara Anderson]

Well, let me. I'm going to say that more tightly.

[Neil DeGrasse Tyson]

Say, you ready?

[Lara Anderson]

No, I love that. Go ahead. I loved it, but I want to say it another way.

[Neil DeGrasse Tyson]

All right, go ahead.

[Lara Anderson]

Okay. In your failures, how have you succeeded?

[Brian Greene]

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 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 mind. One is the discovery of the holographic principle, which says that phenomena like gravity are very deeply related to things called gauge theories, which again, describe the interactions of particles and charges, that these things can be related in different dimensions of spaces. So the statement is that gravitational theories can be related to gauge theories that live on the boundary of that space. Things like the holographic principle are an extremely deep 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 profound, I would say, observation that has arisen in string theory.

[Lara Anderson]

So the simplest example that I've heard of the holographic principle is the surface of the event horizon of a black hole.

[Neil DeGrasse Tyson]

Okay.

[Lara Anderson]

And correct me if I'm wrong here. So you fall through. The surface has a memory of everything that passed through.

[Neil DeGrasse Tyson]

Interesting.

[Lara Anderson]

And so you can think of the information content of the surface as the full understanding of anything that's inside.

[Neil DeGrasse Tyson]

That's inside because there's no loss of information because it's all retained on the surface.

[Lara Anderson]

And so that inside the black hole, 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 capture that correctly?

[Neil DeGrasse Tyson]

Wow.

[Lara Anderson]

Okay. Given that I've yet to heard a physicist rebut that. So is the general agreement that that's probably real?

[Brian Greene]

I mean, in an idealized sense, yes. How much that pertains what you learn from that in our universe, I think is still up for grabs. And this is, again, something people are thinking about very actively. Other analogies that I would give for useful stuff that's come out of string theory is relationships, again, between things like particle physics and cosmology. So the study of dark energy, dark matter, descriptions of inflation, those things being related to how particle physics realizes those, and also structure in mathematics. So there are a lot of new fields of mathematics that were sparked due to that dialogue between mathematicians and physicists that arose through string theory in these shapes of extra dimensions.

[Lara Anderson]

So that's good. So you're exciting mathematicians, right?

[Brian Greene]

Yes.

[Lara Anderson]

And then they reached out and wanted some of you in their department, right?

[Brian Greene]

Sometimes, yeah. And I think, you know, it's a very much a mutual relationship, which is.

[Neil DeGrasse Tyson]

Why you're taking a job away from another professor.

[Brian Greene]

So as one example of this, there's something called the minimal model program in geometry, which tries to classify basically all these higher dimensional 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 come up with sort of a zoo of every possible geometry?

[Lara Anderson]

This is your other specialty, algebraic geometry.

[Brian Greene]

That's right.

[Lara Anderson]

Was that a spin off of the rest of these interests, is that.

[Brian Greene]

No, it's very much tied to it. So the question of trying to produce particle physics from string theory, 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 quarks. So it's sort of intrinsically interdisciplinary in that sense.

[Neil DeGrasse Tyson]

Wow.

[Lara Anderson]

So I want to hear more about this geometry that's.

[Neil DeGrasse Tyson]

I mean, that's crazy.

[Lara Anderson]

So here's something that is so simple and low dimensional, so don't laugh at me, but I want you to take this to your level. I was talking with a topologist, algebraic or one of these math folk. And we were talking about knots, 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 square. Whatever your knot is.

[Neil DeGrasse Tyson]

Whatever knot.

[Lara Anderson]

Okay, Whatever's your knot. And then I. 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 unravel. So that just messed with me. And 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. All right? But I, in three dimensions, just pick it up and it's gone.

[Neil DeGrasse Tyson]

Right?

[Lara Anderson]

So I was just. I 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?

[Neil DeGrasse Tyson]

What kind of drugs are you hiding?

[Lara Anderson]

Where did you stop?

[Neil DeGrasse Tyson]

Come on, Laura, don't hold out on me. I shared my ayahuasca. Give us the real dope.

[Lara Anderson]

You never told us that ayahuasca high dimensionality person talked to you.

[Neil DeGrasse Tyson]

Well, you know what? I. I have. You guys are the first to know because it was so freaky. It freaked me out and I never talked about it. But then when she said.

[Lara Anderson]

String theorists of the future exactly said, you are our savior.

[Neil DeGrasse Tyson]

I was the Neo of string theory.

[Lara Anderson]

Yeah. What is the Matrix? Neo. So please tell us.

[Brian Greene]

So I really like the. The knot analogy. Let me give another one that's 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 or 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 this question of, you know, what can you not. And not what can you use to describe how space and time might curve? All of that changes with different dimensions.

[Lara Anderson]

Yeah. And so you have to get your brain up or up in there.

[Neil DeGrasse Tyson]

I'm telling you right now, I'm, you know, I need a nap just from this convers.

[Lara Anderson]

But the cop out 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 impactful are the compacted dimensions? 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?

[Brian Greene]

It does. It does care if it's compact. 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 be consistent gravity in those extra dimensions.

[Lara Anderson]

Suppose we lived in eight dimensions and he came up with general relativity in eight dimensions. Who were you to say his three plus one dimensional thing that higher dimensions have to obey that? He did that. In this measly three plus one dimensional world, you had to put commandments on higher dimensions. They are superior to us in every way and you know it.

[Neil DeGrasse Tyson]

Yes, I hate to say it, but higher dimensions look down on us. I'm sorry, I had.

[Lara Anderson]

That's a T shirt right there.

[Neil DeGrasse Tyson]

That is a good T shirt, man.

[Brian Greene]

So I actually torture my undergraduate students in my class on Einstein's theory, because Einstein's theory can be actually formulated in any number of dimensions very easily. So there's actually Nothing special about 4. So frequently for my students, I'll say, you know, imagine that this was in six dimensions or ten dimensions, or, you.

[Lara Anderson]

Know, she said it can be formulated easily, but she didn't say what she meant by easily.

[Brian Greene]

Very relative statement there. But one thing that isn't easy, and this is actually 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, and they are especially not good when they go into high numbers of variables and high numbers of dimensions.

[Lara Anderson]

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 point of. I mean, yeah, exactly, it's hard for you, but give it to an AI.

[Neil DeGrasse Tyson]

Yeah.

[Brian Greene]

So one of 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 for how. That means, you know, exact solutions. You could write down on a piece of paper for Einstein's theory, for the six dimensions that we would need for these string compactifications, they're called.

[Lara Anderson]

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 increment a model and see the results each time just to see where it goes.

[Neil DeGrasse Tyson]

Right.

[Lara Anderson]

And so that's ugly. We hate those. But we kind of recognize that that's like in chaos theory, you have to sort of calculate it out, right? You can't just write down the solution. So if you're saying you can't in principle, or it's just too laborious, just.

[Brian Greene]

Not knowing how to do it yet. So in general, solving Einstein's equations in any number of dimensions, you know, for any system, is hard because they're nonlinear. So what that means is that the gravitational theory is actually back reacting or talking to itself. So the fact that you have gravitons, 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 in general relativity, that doesn't work. You can't add two solutions and get another solution. You have to start over every time.

[Lara Anderson]

So 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 that up. But what you're doing is you're calculating with these differential equations, these equations that you can calculate at every time step, and it's following you on the time step. But you can't just solve out the whole whole shebang. So gotcha. So, all right, so tell me again why you can't use AI so we can actually.

[Brian Greene]

And that's a fun topic. So I was involved for a number of years with numeric simulations like you're describing, where you use a computer to try and solve the equations that you can't otherwise. And historically, in order to do those computations, we had to put them on supercomputer. Clusters and wait for months to get results. But now, actually with the advent of AI, this is something that my collaborators and I have worked on.

[Lara Anderson]

And now you just do it on your iPhone.

[Brian Greene]

Now we can actually do it on a laptop. 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, I've worked on that and lots of other people in the field have. And we found that using these techniques, we can speed up a lot of computations in a really substantive way. 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. 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 quarks look like in that universe? Now we can actually come up with those numbers using machine learning algorithms.

[Lara Anderson]

Chuck will go back on his ayahuasca trip and get the person from that dimension to verify the correct mass.

[Neil DeGrasse Tyson]

Yeah, yeah, exactly.

[Lara Anderson]

And Chuck will be the oracle of physics.

[Neil DeGrasse Tyson]

And I'm. I'm up for it. I'm telling you right now, I'm ready to handle it. I'm ready to go do more ayahuasca. So I'm ready.

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[Lara Anderson]

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 out of your work or some yet to be born genius that you'll look at and say, oh my gosh, I'm gonna give a fast astro case here. Okay. At turn of the century, the orbit 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. Tugging at it. Yeah. We even named the planet. I mean, that's how.

[Neil DeGrasse Tyson]

Oh, really?

[Lara Anderson]

Yeah. We called it Vulcan.

[Neil DeGrasse Tyson]

Oh, nice.

[Lara Anderson]

Yeah, yeah. Go 1910. Just look up planet Vulcan. Like, there it is. It's pretty wild. Okay. And so. And we were happy. Well, how come no one saw it? Oh, cause it's too close to the sun. It's in the glare. So we had, it was all there.

[Neil DeGrasse Tyson]

It was all worked out.

[Lara Anderson]

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 physics transformed the physics we were already working with and gave us better answers to move on with.

[Neil DeGrasse Tyson]

So what I learned from that is Einstein killed Vulcan. Tyson killed Pluto.

[Lara Anderson]

Stop. That's not the lesson I was trying to.

[Brian Greene]

It's a good lesson.

[Lara Anderson]

No, it's not. No.

[Brian Greene]

So new physics could take a lot of different forms. 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, so called fifth force, another version of something like electromagnetism or, you know, the strong weak nuclear force. That would be an example of new physics. Other things that we know we don't understand very well include things like dark energy and dark matter. Questions 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, you know, gravitational theory? What, what tells us how physics really behaves inside there? That's definitely new physics. And that would be the hope of the kind of thing you'd, you'd like to see.

[Neil DeGrasse Tyson]

Oh, wow.

[Lara Anderson]

So, okay, so you think there's new physics out there.

[Brian Greene]

Not again the claims on what constraint theory deliver. I'm still somewhat agnostic on that, but I think it's really interesting to try and push the theory to find out, say, 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 push it to try and make some of this structure visible?

[Lara Anderson]

So I love 100 years from now, look back on this conversation and say, look at those idiots. Back in 2025.

[Neil DeGrasse Tyson]

Yeah, this will be a kindergarten video 100 years.

[Brian Greene]

I hope so.

[Lara Anderson]

So I got something else here about a duality in string theory. What's going on there?

[Brian Greene]

Yeah, this is something that I and my collaborators are working on at the moment.

[Lara Anderson]

That's a cool word by the way. Duality.

[Neil DeGrasse Tyson]

I love duality.

[Brian Greene]

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 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. 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. 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. 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 which require less supersymmetry. So a less spherical cow than people had assumed in the past. Okay, yeah, we're growing some legs in the cow, for example. 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.

[Lara Anderson]

Wait, wait, catch us up on supersymmetry.

[Brian Greene]

So supersymmetry is something that comes along for the ride for some formulations of string theory, which says that all the quarks and leptons that we see in nature may have additional partners. So, for example, instead of, you know, a quark, you have a squark, another partner that would be much heavier than the existing particles that we've seen.

[Lara Anderson]

So when you're describing supersymmetry, it's a symmetry beyond the symmetries that are already known and loved in the Standard Model.

[Brian Greene]

That's right. So all these, these sort of three generations of quarks and leptons that we've seen already, 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 boson would have a fermionic partner and so on.

[Lara Anderson]

All right, 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 that could explain stuff that we don't now understand.

[Brian Greene]

That's an idea. And people initially thought this idea might explain some really important questions in particle physics. For example, to do with the mass of the Higgs boson. That would be what's called low scale supersymmetry. And particle experiments like the LHC searched very hard for this and didn't see it. So some people consider supersymmetry not a very useful idea because they thought, you know, it might appear in these regimes and it would not be useful. People are re investigating this question in string theory. You know, some of the solutions at string theory are supersymmetric, some are not. What we generally would agree on is that if you did have supersymmetry, it would have to be at a very high scale, so it would be much. These particles would be much heavier than you could see at 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 of the energy ratio and.

[Lara Anderson]

Not the other ones that would have helped birth it. So.

[Neil DeGrasse Tyson]

I'm gonna say that's rather convenient, though. I'm just gonna say.

[Brian Greene]

So the question is, like, why do you need that symmetry? Right. If you're kind of getting rid of it back when you really want to be talking about the physics. Yeah.

[Lara Anderson]

Conveniently discarding it.

[Brian Greene]

Yeah, that's a great, great question. 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 supersymmetry can you get rid of and then still preserve the features that are of interest to us? So the types of dualities I was describing, these are perhaps new because they involve less reliance on supersymmetry 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. But we don't need as much supersymmetry, if memory serves.

[Lara Anderson]

The graviton is not in the standard model. Is that correct?

[Brian Greene]

That's right.

[Lara Anderson]

So that means no one is thinking about a supersymmetric particle to the graviton, because that would be kind of interesting.

[Brian Greene]

Yeah, you. You certainly could. For any particle, you know, any gauge boson, you could have what's called a gauge, you know, so a. A supersymmetric particle gauge.

[Lara Anderson]

Eno. They're just making stuff. They're just pulling it out of the ass.

[Neil DeGrasse Tyson]

Yes. It sounds like you're naming, like, pharmaceutical products.

[Brian Greene]

This is before my era in physics, but I do feel that some of these names are very much a product of the 1970s.

[Lara Anderson]

I was in high school. That's how old amp 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? And we were just building this fabric of the universe out of that. That's kind of cool, actually, to be witness to it. It was fun.

[Neil DeGrasse Tyson]

That's fun.

[Lara Anderson]

Yeah. Not participant, but witness. Could you expend a moment just celebrating the idea of symmetry in physics?

[Brian Greene]

Yeah. This is a really, really great question. So symmetry in physics, this is something that is extremely deep and has been very, very predictive and powerful over years 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 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 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 arisen differently in nature. So there's some kind of highfalutin quote by Einstein that, you know, saying he wanted to probe God's thoughts, you know, in terms of his theories, which sounds extremely grandiose, both. But the tangible non theological 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 change that theory at all? Could there have been any other theory of gravity that could have worked?

[Lara Anderson]

What does it have to do with our understanding of what the word symmetry means?

[Brian Greene]

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, if you want to ask, how do the laws, how are the laws of physics impacted by the fact that if I do an experiment here and then I move that experiment five feet 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 or versus five feet 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 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 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 it stays the same, that actually tells me what equations are compatible with that in a really predictive way.

[Lara Anderson]

I've got another symmetry here, mirror symmetry. So what do you have for us there?

[Brian Greene]

So mirror symmetry was originally discovered 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 seemed 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 without intrinsically changing what it is. So the classic example is that you can change a donut into a coffee cup. So 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.

[Lara Anderson]

It or put another hole in it? And this is a coffee cup with a little finger hole with a handle. Yeah, yeah. It wouldn't work if it didn't have a handle.

[Neil DeGrasse Tyson]

Right, right.

[Brian Greene]

So it was just like a drinking glass. Doesn't work.

[Lara Anderson]

Yeah, not the coffee cup from Starbucks, because that doesn't have a handle.

[Neil DeGrasse Tyson]

Right.

[Lara Anderson]

Okay.

[Brian Greene]

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 doughnut, or if you could smush it around and turn it into the handle of a coffee cup. That's what's called a topological invariant. So the number of holes is one of these examples of topological numbers. So 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, it tells you that all of them are interchangeable in concrete ways.

[Neil DeGrasse Tyson]

Wow, man, that is insane.

[Lara Anderson]

First of all, why?

[Neil DeGrasse Tyson]

Why?

[Brian Greene]

It's a really great question.

[Neil DeGrasse Tyson]

That's so crazy. I love it, though.

[Lara Anderson]

But I got more here where we just. We're just cracking this egg, you know. What do I have here? Calabi Yao manifolds.

[Brian Greene]

So these are examples of configurations for the shapes of extra dimensions and string theory that satisfy Einstein's equations. So these are the half a billion possibilities that I was talking about.

[Lara Anderson]

Manifolds. Now, I didn't get the word manifold.

[Neil DeGrasse Tyson]

Yeah, y' all got that from Star Trek. Get out of here.

[Brian Greene]

Named after two very clever mathematicians. Yeah, These manifolds were conjectured to exist by a mathematician named Eugene Kolabi and proved by Yao, who won a field's medal for his proof that these things solved Einstein's equations.

[Lara Anderson]

Do you know about the Fields Medal?

[Neil DeGrasse Tyson]

No, I don't.

[Brian Greene]

So it's kind of like the Nobel Prize in mathematics. It's given to major, you know, substantive discoveries in mathematics. But the catch is you got to be under 40 to get it. So you have to be young and clever.

[Neil DeGrasse Tyson]

Oh, man. Of course, the mathematicians would use chronology as a determining fact. Yeah, discriminating.

[Lara Anderson]

It's ageist, I think it is.

[Neil DeGrasse Tyson]

Yeah, yeah, exactly.

[Lara Anderson]

Homological field mirror symmetry.

[Brian Greene]

So this is an example of something where there was a dialogue between string theory and mathematics that was really fruitful. So these observations about Claudia manifolds and their topology were first observed in string theory. And mathematicians went away and tried to sort of explain why that was happening and found a correspondence between a lot of deeper mathematical structures that actually led to another Fields Medal for a gentleman named Konsevich.

[Lara Anderson]

That's Maxim Kontsevich. Maxim Konsevich. That sounds Russian.

[Neil DeGrasse Tyson]

Yes, exactly.

[Brian Greene]

So this type of structure, this dialogue between maths and physics, I personally think, is really fruitful. We've learned a lot from mathematicians from building these kinds of things. And then the fun question that I'm asking recently is, could there be new variants of this that could lead to new physics, new predictions for particle physics, but also new mathematical structures. So some of the dualities we're looking at right now involve not just changing two manifolds or two configurations of geometry, but actually mixing things like electromagnetic fields in those backgrounds with geometry. So there's all sorts of weird and wonderful, you know, mixing of possible degrees of freedom in the theory that could still magically leave the physics alone.

[Lara Anderson]

There's surely plenty of physicists out there, are perfectly trained in all their physics, but don't have your math background. So In a way, they're kind of researching with blinders on. Given how much more you see in the mathematical regimes, is that a fair characterization here?

[Brian Greene]

The pushback? Somebody might say you're sort of torturing yourself by trying to solve really hard problems in math and physics at the same time. So there are lots of questions where you don't need this degree of math. But unfortunately, the path to the physical questions we want to answer leads through this crazy hairy geometry in high dimensions to be able to answer the physics we want in string theory. So we kind of don't have a choice.

[Lara Anderson]

This evokes Einstein, where I don't think he was totally up on non Euclidean.

[Brian Greene]

Geometry, differential geometry, all that different.

[Lara Anderson]

He wasn't totally up on that and needed some help. Right. Even though he had the physics going.

[Neil DeGrasse Tyson]

Oh, man, I would love to meet Einstein's tutor. What do you do? I tutor Einstein and geometry. That's all.

[Brian Greene]

Yeah.

[Lara Anderson]

This marriage of frontier physics and emergent math, I mean, this is. It's been going since the very beginning. And I might offer a cosmic perspective on that as we close it out.

[Neil DeGrasse Tyson]

Alrighty.

[Lara Anderson]

One of the features of research scientists in academia is you get really smart people working on problems where there's no obligation or expectation that there's a sellable product at the end of that exercise. What it means is that the mind can roam freely on the boundaries of what is known and unknown in the universe. And in physics, that has always occurred, has always occurred in tandem with advances in mathematics. You go back to ancient Greece, they're trying to measure the shape of the Earth. Is it round, is it not? The word geometry gets introduced, and if you look at what that means, it means Earth measurement geometry. And so you look at this juxtaposition of our advances in science and our advances in mathematics. And these are two fields that so often people in school say, I'm not good at math and I'm not good at physics, and I'm not, meanwhile, is the foundation of our understanding of our place and existence in this universe. So I look forward to further advances on the frontier of physics and how they marry with further advances in mathematics, no matter how obscure it might look to the passerby one day, in the end, you'll be living with it as we currently are, with all the trappings of modern engineering, technology and society at large. And that's a cosmic perspective. So, Lara, I mean, this has been a delightful conversation. We've learned a lot, or you've told us a lot. Maybe I learned maybe two thirds of it. What's your fraction on that?

[Neil DeGrasse Tyson]

I am just as dumb as I ever have been, but I feel smart.

[Lara Anderson]

There you go.

[Neil DeGrasse Tyson]

That's all that matters.

[Lara Anderson]

And so again, you're at Virginia Tech and you teach a course on general relativity, Einstein's relativity. Love it. So you are pure theorist, Right? So they don't invite you into the particle accelerators, Correct.

[Brian Greene]

I have been invited, but I'm kept on a very short leash and then let out again.

[Lara Anderson]

See, I was on a mountain once, observing in the mountains of Chile. I invited a theorist to come, and when he came, there was an earthquake.

[Neil DeGrasse Tyson]

Wow. So he's never invited back.

[Lara Anderson]

Yeah, this is. It was clear. Theorists are just get out of my. Get out of my lap. Do you know which end of the telescope to look through? No. It's a fun riff over time, but we know we need each other. Yes. Yes. So thanks again, Laura, for being on StarTalk. And Chuck, always good to have you, man.

[Neil DeGrasse Tyson]

Always a pleasure.

[Lara Anderson]

All right, this has been StarTalk String Theory Edition. Neil Degrasse Tyson. Keep looking.

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