🔬Doing Vibe Physics — Alex Lupsasca, OpenAI

Introduction to AI

0:00Okay, so I think we're at this special time now where, at least in some directions, AI has become superhuman, at least on certain tasks. And that's what led to these recent papers that resolved a problem that was puzzling physicists, experts in the field for over a year, and they weren't able to resolve it, and AI was able to do it very quickly. So I think that's a certain milestone that we've passed. I'm glad that you guys are bringing attention to this, because I think maybe for the average person on the street who doesn't care about theoretical physics, this is not very noticeable.

0:35But I think it's a very profound change, and we've really passed some kind of threshold.

Welcome to AA

0:40Welcome to the AA for Science podcast, part of Lean Space Network. I'm Brandon. I develop RNA therapeutics using AI at Atomic AI. I'm joined by my co-host, RJ Haneke, CTO and founder of Mirror Omics. Yeah, it's a pleasure to introduce Alex Lubczoszka, professor at Vanderbilt University and fellow at OpenAI. He has, for a young researcher, he has quite a storied background. Amongst other things, he's the winner of the 2024 New Verizon's Breakthrough Prize.

1:13It's the, call it the Oscars for Science. I asked ChatGPT, is this the most prestigious award someone of his career could win? And it recommended a second one called the IUPAP Award, which turns out he had also won. Anyway, right now he's having fun at OpenAI, doing some really cool research of pushing the foundation of theoretical physics using GPT models.

Research Background

1:38A pleasure to be here. The one message I wanted to convey is that I think we're on this trajectory, which I personally find very surprising and kind of surreal, but also amazing. Where I would say a little over a year ago, AI was very useful for email, but not the kind of work that I do that I consider important theoretical physics calculations. I thought, oh, that's special, much harder than email, and AI is not going to be able to do that. And then there were a series of developments that came in rapid succession that completely changed my mind.

2:10And I can walk you through some of these examples specifically.

ChatGPT-03

2:15In particular, ChatGPT-03 was the first really strong reasoning model that could do actual math that was useful for my research and could save me a lot of time. That's when I started to really pay attention and use it a lot more. And I thought, wow, this is a great tool. I got to get ahead of this and learn how to integrate it into my workflow. Then when GPT-5 came out, it was able to reproduce one of my best papers that took me a very long time to come up with in like 30 minutes. And that's when I really became AI Pill.

2:45I thought, oh, my God, this changes everything. It's the most important discovery in my lifetime. It's going to affect everything about how we do research. And frankly, a lot of my colleagues, I would go around telling them, this is currently getting your attention. And yeah, I was getting lots of different reactions, but I think people weren't quite getting it. But I talked to OpenAI. They were also really excited. And I thought, I don't know that much about AI, but I have to get in on this. And to understand that this is happening and not be a part of it is a huge mistake.

Joining OpenAI

3:18So I have to go to OpenAI. So I was on sabbatical. It was very easy to come here and join the company. And then it just kept ramping up even beyond that. And to the point where now I think most of my senior colleagues in physics are aware of where things are ahead of and they're all getting on board. So yeah, I think that's an awesome story. Sorry, I was just saying, I find it really funny that story because it reminds me of a lot of different people who had the same realization with codex.

Codex

3:53Starting sometime last fall, especially, it just took off. And a bunch of people are like, even like Andrej Karpathy went from, oh man, this is, you know, 20% of my work. It's kind of a nice, you know, assistant to, oh crap, what just happened? Well, yeah, in August, actually, I remember when GPT-5 came out. At that point, I was really following AI pretty closely. And I think on Twitter, the reception was lukewarm. A lot of people were like, well, we expected a lot more and it's not better at writing email. And I remember thinking, well, okay, GPT-3 could write email.

4:26How much better can it get at writing email? That's not the point. But at the science frontier, the capabilities were really taking off. Yeah, there was a lot of attention, I think, paid even to O3. GPT-5 was a huge jump. And I think 5.4 is also a huge jump. I don't know how noticeable it is on the outside, although I did hear some, I saw some chatter online. People are running these independent benchmarks, which do show this. So I think people are realizing.

4:56And also, anyway, in practice, researchers are now all over AI using it. And yeah, I'm getting inbounds all the time because I'm the resident scientist doing physics at OpenAI. And so everybody is sending me papers, chats, like, oh my God, this happened. I got one just this week. Somebody said, Codex just wrote up a simulation of the SYK model. This is like a very technical thing in quantum mechanics and gravity. And like, yeah, a lot of research groups have been trying to run this simulation and it couldn't do it. And Codex did it in 10 minutes.

5:27Just because setting it up was so hard. Well, I think partly it's because of the Venn diagram, where you look at the people who have the physics knowledge and the people who have the top coding skills and maybe the overlap is not that large, although I think it's been growing. But I think in this example, there are a lot of really good people in physics with coding skills who've been trying to simulate these things. So in Codex, it's just really good now. Okay. Yeah. Nice.

Gluon Paper

5:54Okay. So I think we're at this special time now where, at least in some directions, AI has become superhuman, at least on certain tasks. And that's what led to these recent papers, which maybe we should talk about, that resolved a problem that was puzzling physicists for experts in the field for over a year. And they weren't able to resolve it. And AI was able to do it very quickly. So I think that's a certain milestone that we've passed.

6:26And I'm glad that you guys are bringing attention to this, because I think maybe for the average person on the street who doesn't care about theoretical physics, this is not very noticeable. But I think it's a very profound change. And we've really passed some kind of threshold. Specifically focus on the glue-on paper and the physics part. And we can get to the AI part later. Okay.

Physics Principles

6:46So in physics, there are two basic principles of nature that we think every law should respect or every theory should respect. On the one hand, there's the principle of relativity, which at some very high level declares there's an absolute law that cannot be broken, which is that you cannot transmit information faster than the speed of light. But then there's another principle, which is the uncertainty principle, that underlies quantum mechanics, which says that everything's a little fuzzy.

7:20You know, position, velocity, there's a little fuzziness to that. And so you can see immediately at this level of description already, there's a tension between these two principles. Because one is an absolute law declaring you cannot go fast and speed of light. And the other one is saying it's a little bit fuzzy. And this is just to give a sense of how when you try to write down these principles in mathematics, the equations don't really play nicely with each other. And so it's been a real struggle to come up with physical theories that can reconcile simultaneously both principles

7:54to describe the physical world around this. And I would say that the great achievement of 20th century physics, which is really one of the greatest triumphs in human thought as far as I'm concerned, is the elaboration of this framework called quantum field theory, which is a general framework that can describe the physical forces of nature in a way that accommodates both of these principles. And in quantum field theory, which is our best theory to date,

8:25obviously it gets a little bit technical. But again, try to keep it pretty high level. What you're trying to compute or describe are the probabilities for certain events to occur. Because you're in this quantum mechanical setting, you can't say with certainty what's going to happen when you have a certain experiment. But you want to predict probability distributions. And in quantum mechanics, probably distributions are obtained by squaring certain complex quantities. And by complex, I don't mean complicated.

8:55I mean, they're not real numbers. They're real plus imaginary numbers, which we call quantum amplitudes. So the goal of a theory is to predict quantum amplitudes, which are these objects, complex objects that square the quantum probabilities. And that's the most you can say about the outcome of an experiment. And these quantum amplitudes, in particular, there's a variety of them called scattering amplitudes, which describe the following scenario. Suppose you have a bunch of particles that you throw at one another.

9:25This is what happens in particle colliders like the LHC at CERN in Geneva. So you take a bunch of particles, you smash them together. Stuff happens. They interact via the physical laws of nature. Here, various processes occur, and then other particles come out as a result at the end of the interaction. And so scattering amplitude is the object that describes the probability for a particular type of interaction. We have some particles coming in with some energies and momenta,

9:57and some other particles coming out with other energies and momenta. And so these scattering amplitudes, they're functions of all the data describing the particles coming in and the particles coming out. So in general, you can have arbitrarily many particles involved in an interaction. And this is one of the hallmarks of quantum field theory, that particles can be destroyed. So you don't have the same number of particles at the end necessarily as you had in the beginning. Particles can be created. Lots of things can happen. And in general, you want to describe all the possibilities.

10:30And so you want to have an amplitude for an arbitrary number n of particles. So that's called an n-point amplitude because there's n particles coming in and out. And it turns out in quantum field theory that if you have a particular force and you're able to compute the n-point amplitudes, these functions of the n parameters of the functions that square to the probabilities, then you know everything about the theory, more or less.

11:02There's always an asterisk, but it's basically the entire content of the theory. So if you have a theory that tells you any number of particles come in and go out, then I can declare anything about that system. Exactly. Then you know everything. And importantly, these amplitudes, they're not just numbers, they're functions. Because the probabilities that they compute depend on how much energy do the particles have, what are their momenta. And also a particle has something called, a lot of particles like the photon,

11:35which is the particle of light, has a polarization. So when you look at the surface of a lake and you have polarized sunglasses and you turn your head, you can see more or less sunlight reflected off of the lake. And that's because a photon, which you can think of as a little particle of light, as it propagates, it carries a little arrow perpendicular to the direction of propagation, which is called the polarization. And this polarization has a direction and sunglasses can selectively let in light with one polarization and not the other.

12:09And this polarization actually, as light travels, it can rotate, it can wind, it can do its own thing. And in general, if it winds in a right-handed way, so as the particle travels, if the polarization winds to the right, we call that a positive helicity or a right-handed polarization. And if it winds in the other direction, we call that a left-handed helicity or negative helicity. So in general, these amplitudes, which are the fundamental object in quantum field theory,

12:39that we want to contain all the information there is to know about physical forces, these amplitudes depend on not just the energies and momenta, but also the polarizations. Now I've told you about how there's two basic principles of nature, relativity and quantum mechanics. They come together in this framework, quantum field theory. And I keep talking about forces. So there's four fundamental forces of nature. There's electromagnetism, which is responsible for basically the properties of atomic elements

13:11and the periodic table and therefore chemistry and biology and everything that you see, touch, feel pretty much is all due to electromagnetism, textures, colors. And this force is mediated by the photon, which is the particle of light. That one is the most familiar to us. Then there's gravity, which is another force that we feel very much because it keeps us to the ground. And then there's two nuclear forces, the weak and the strong nuclear force, which we don't really notice directly in our daily lives. But the weak nuclear force is responsible for radioactive decay and other such processes.

13:45And the strong force, which is the strongest of them all, is what binds the nucleus together. So you learn in high school that light charges repel. Well, but if so, then why do protons stick together inside the nucleus of the atom? They should repeal one another. And indeed, that's the case. But if you bring in really close, then the strong force kicks in and overwhelms the relatively weaker electromagnetic force. So the strong force is mediated by the exchange of the particles of the strong force,

14:16which are called gluons, because they're what glues together the nucleus of the atom. So gluons are the particles of the strong force. And gravity is mediated by gravitons. I think the gluon paper, I think, was sort of maybe the starting point for this, maybe not. But the gluon paper had a really specific result, right? Yeah, absolutely. So maybe let me just flash the paper itself. So we put this on the archive a little over a month ago now.

14:47And here's the paper. Let me explain in a few sentences, now that I've given a lot of background, what the title means. Yeah. So the title says, single minus gluon tree amplitudes are non-zero. This might sound forbidding, but I think we can unpack this for the audience. Um, so gluons are the particles that carry the strong force and gluon amplitudes are functions that describe the quantum probabilities for gluons to interact via the strong force.

15:20Now, the word tree here is a little bit of a technicality. It means we're only considering processes where no gluons are created or destroyed. If gluons are created or destroyed, then you get loops, which we can explain later. But this is just a technicality. So we're considering special interactions where the same gluons that come in also come out. So for anyone who's ever fit a polynomial, you can think of tree as being like a linear term and then loops can be higher order terms. Correct.

15:50Exactly. Way more complicated than that. But conceptually, it's like kind of the lowest order in a series. And so single minus, now I have to explain that. So remember, I told you earlier how particles have polarizations. So when you try to study gluon amplitudes, this is like a whole industry of physics. You know, it's a very complicated field. People have written thousands of papers over the decades. So you always want to try to understand the simplest examples first.

16:21That's why you start with the tree amplitudes for the leading effects. And then you worry about the loop corrections. So you might think that the simplest example to start with is one in which all the particles have the same helicity. So say they're all right-handed, or that is to say, they're all plus helicity particles. It's been known for a long time that actually, in that case, the amplitude is just zero, which means the interaction is forbidden and cannot happen. That's one way. It's just a symmetry just explicitly forbids this.

16:54So you don't even have to calculate anything, you just know. Yeah. Just dimensional analysis. It's a very general argument. Yeah. You don't need to do very much work. And so, yeah, it's true that it's the simplest example, but it's so simple that nothing happens. Yeah. So, okay, the answer is trivial. You might ask, what about the next level up? What about if... Oh, no, I want to understand this. You have, like, a bunch of gluons. They're coming into an interaction. Yeah. They're all in the same helicity. Yeah. And then you're just saying, that just can't happen.

17:26Yeah. Okay. Like, because, like, I take my gluon gun and shoot, and he takes his gluon gun and shoot, and they go there, and then that just can't happen. They'll just go right to each other. Oh, so they just won't interact. They won't interact. Ah, okay. Yeah. Okay, yeah, yeah, yeah, yeah. That's a good clarification. Yeah. And now you might ask, what if one of them has the opposite helicity, but all the others have plus helicity, but one of them has a minus helicity? So that's what we would call a single minus amplitude.

17:57And if you look at the lecture notes and textbooks that have been written on this, the same argument that rules out the all plus amplitudes also appears to rule out the single minus amplitude. They're too simple. They can't really interact. There's nothing to see here. Move on. So then you might ask, okay, well, what about the next thing where there's two particles that are minus helicity and all the others? If so, if there's any of them, there's n minus two others that have positive helicity.

18:29And so these would be double minus amplitudes. And people in the 80s studied and computed these amplitudes. They're not zero. And in particular, there were two physicists, Park and Taylor, who found this beautiful result. They did a lot of really hard work and computed these amplitudes, very technical, difficult calculation. But at the end, you get all these terms and you have to sum them all up and almost all of

18:59them cancel. And at the end, you're left with this very simple formula that fits in half a line, which is now known as the Park-Taylor formula for these amplitudes. And these amplitudes are now called MHV amplitudes, which stands for maximally helicity violating, because they have the largest, or so we thought, possible asymmetry between the plus and the minus helicity particles, the most asymmetry.

19:30Now, let's get to this paper, which came out last month. So this is a paper written with Alfredo Guevara, who's a postdoc at the Institute for Advanced Study, David Skinner, a professor at Cambridge University, Andrew Strominger, a professor at Harvard, used to be my advisor, and also Kevin Wheel, who'd studied as a particle physicist in a previous life. So how did this happen? Well, maybe we'll get into how I ended up at OpenAI a little bit later. But I ended up at OpenAI, started to improve the model's abilities to do physics.

20:03The models got really, really good at physics. And I thought, OK, it's so good now we should try to solve some actual research problems at the frontier. And I called up Andy, who used to be my advisor, and I said, hey, Andy, do you want to come here to the SF, visit OpenAI, and we can try to solve one of your problems in physics? And I thought, you know, it's probably not going to work, but if it doesn't work, at least we'll figure out why it doesn't work. And, you know, I can do this with a different physicist every month, and eventually something

20:34will work. And in the meantime, we'll learn how to improve the models. So it's all fun and useful. And so Andy was the first one that I invited to do this. And he said, well, I have this perfect problem that I've been thinking about with Alfredo and David for the past year. I'll explain now the problem. But the amazing thing is that we decided to start working on it using AI a little bit before Andy was scheduled to come, like the week before. And in fact, using ChatGPT, we solved the problem before he even got off the plane.

21:07Which was a huge surprise to him. Yeah, I think. And to me, to be honest, I had not expected that. And it's a really cool story. So Andy, David, and Alfredo understood a year ago that this statement that the single minus amplitudes, the statement that they're zero, is not exactly correct. Because the usual argument in the lecture notes and textbooks has a loophole. And the loophole is that it assumes that the particles are coming from generic directions.

21:41But in a certain regime where the particles are exactly aligned with one another, we say they're collinear. Then the usual argument has a loophole. And it's possible for the amplitudes to not be zero. But then if they're not zero, what are they? So suddenly these really simple amplitudes previously thought to be zero, if they're not zero, we should compute them and they should do something really nice and simple and special. Now, I'm burying a lot of, I'm sweeping a lot of details under the rug here.

22:12This has to work in some different signature space time. It connects to lots of other things they've been worrying about. We're not going to worry about this. I mean, I was actually hoping at the end, maybe we could talk about what it means to be two dimensions in space and two dimensions in time. But yeah, I mean, I think like part of this is doable. The loophole is one about, you know, the alignment of the particles, but it's also a loophole about the space-time of physics that the universe we're living in. And this is not so... This is really mind-bending stuff. So, they understood that they're not zero and they started to compute them.

22:49And Alfredo is really, I think, the unsung hero of this story because he did a lot of really hard work to compute these things by hand. And I'll just show you an example. So we, in the paper, there's a lot of formalism. Um, so here is the beginning of the definition of the general answer. One. Yeah, it's very hard to unpack, but it starts here. Then you have to define these vertices, objects, V, and they're complicated. They involve sine and theta functions of spinners.

23:22And then you have this recursive formula. But okay, it's a whole mess. And concretely, if you try to unpack this definition, remember these amplitudes are a function of the number of particles involved. So there's a three-point amplitude where there's only three gluons in the interaction. And, you know, the answer is pretty simple. This is some function that we've defined here. Not that complicated. Then this is the four-point amplitude where now there's four particles. And you can see that we go from one term to a sum of two terms here.

23:52But then once you get to five particles, you start to get a lot more terms. There's eight of them being summed here. And by the time you get to six terms, it explodes in your face. For those people not watching this on YouTube and listening, this equation takes up a quarter of the page, is 32 terms, each of which is a product of four terms, each of which is itself encapsulating a rather complicated formula. Yeah. So this is super nasty. And that's as far as Alfredo got or anyone else.

24:24So Alfredo, is this just an expansion of some sort of, how hard is it to do this expansion? Very hard. And there's a nice graphical way to understand this in terms of Feynman diagrams. I hadn't planned to explain this, but there's a visual, this is kind of a visual subject. So the math is very complicated. And already back in the 40s, Richard Feynman, who's one of the pioneers of quantum field theory,

24:55came up with this very visual way to organize our understanding of the subject. So you can doodle these little cartoons that represent possible interactions. And the rules of quantum mechanics actually say that in these amplitudes where you scatter a bunch of particles, you get to fix what comes in and what comes out, because that's the question you're asking. What's the probability for a certain interaction? But then everything that happens in between, you don't get to choose that because the physical laws determine what happens. And actually in quantum mechanics, you're supposed to consider all the possibilities.

25:29All the ways in which the incoming particles can interact and transform into the outgoing particles. And you're supposed to average or sum over all the possibilities to get the final amplitude for the process as a sum over the amplitudes for each individual possibility for how you could get there. So just to be clear, there's incoming particles, they interact, and then there's all these different, they each have their own amplitudes. And then it's sort of like, I select for this one, one possibility, and this one, one possibility.

26:03And then I get like one possible interaction. And then there's an infinite number of those for each. And then I sum those infinite possibilities. So, and I get that. Yeah, so in principle, there are infinitely many pictures to sum over. But that's why we organize them by how complex they are. And it turns out that every time you get an interaction, every time there's a vertex where lines meet, that point interaction comes with a power of the coupling constant, which controls the strength of the interaction. And it turns out that every additional interaction makes the amplitude more suppressed.

26:38So it contributes less to the final answer. And so you want to first consider the diagrams with the fewest possible number of interactions because they will give you most of the total final amplitude. And then if you're trying to get a more and more refined answer, you then consider the more and more complicated cartoons with more and more interactions. And in fact, this is one of the ways in which the diagrams can get complicated is that they can have loops. So for instance, here you have a particle that decays into two particles, creating this

27:10loop because then they meet up again and disappear. So in this interaction, you have intermediate particles being created and destroyed. But whenever that happens, you get two extra vertices in your graph. So these diagrams are suppressed because it's less likely to happen that you get these extra felicitous interactions. And so you have to, you don't need to worry about this as much. It's like a small correction. And of course, in principle, you can keep going, but you're never, you're never done. It's just in very special circumstances. The higher order powers in a polynomial or something, or a Taylor series.

27:42And so to go back to the story back in the 80s with the MHV amplitudes, which I think now is a bit of a misnomer, I would call them double minus amplitudes because that's where we're going to get to in a second, right? There was this heroic calculation where a lot of Feynman diagrams were summed and they were considering more and more interactions with more and more particles. And every time there were more and more terms, but they all canceled to the end, always give a simple answer. And in fact, that's what this PT term, PT stands for Park Taylor.

28:13These formulas are, you know, they fit in a line. So it's not that complicated, but it's very surprising that such a messy calculation at the end would clean up into such a simple result. And so what Alfredo, Andy and David did was to understand that these single minus amplitudes in the special case where some of the particles are aligned, they don't have to be zero. And then you can do this very complicated Feynman diagram expansion to get the answer, which is not zero. But the problem is if you do it this way, well, you can represent the answer in some horrendous,

28:47horrendously messy, complicated way. But if you unpack it, it's extremely complicated. It's complex in the following sense. When you consider the endpoint amplitude, so the probability of n particles interacting, the number of terms in your answer, which correspond to the number of diagrams roughly that you have to add up, it grows factorially in n, the number of particles. And factorial growth is really bad. It's super exponential. It grows faster than an exponential. So it blows up in your face. This is what you're seeing here.

29:18And that's because roughly you have to draw all the possible cartoons and the possible combinations is a combinatorial problem. And that's where the factorial behavior comes from. But we know from the 80s that in the actually more complicated double minus case, Park and Taylor found this miraculous simplification. And so Andy, Alfredo and David spent the last year chasing the analog of the Park-Taylor formula, the very simple answer that was obtained in the 80s for the double minus amplitudes.

29:48But now for these single minus amplitudes, which they understood are not zero, but then what are they? And they were getting this really complicated answer. And okay, you never know in physics ahead of time if something will simplify. You have to believe in it to find the simplification. But because the double minus one simplified, it felt like these should simplify too. And we think they're important for lots of things and that these are somehow really important objects that are very fundamental. And so they should have a nice description. And so they spent a year looking for that. There's a funny, the next line, if you scroll down, is something like, we need a simpler formula.

30:22Right. So when we wrote the paper, we need a more concise formula. It's needed. Yeah, a more concise formula is needed. And this is where AI comes in. Because when I asked Andy, hey, do you have a problem in your pocket that we should use AI to target? He said, well, I have just the perfect thing for you. We've been puzzled about this. It's really important. It's really interesting. It connects to all these things. And we don't know the answer. Yeah, I mean, like, when I was a grad student, if I had approached something like this, I

30:54would have probably plugged it into a computer algebra system, chugged along, tried a few limiting cases, see if there's any, like, magical, you know, simplifications which happen. This type of thing is, you know, something that oftentimes you see this and you're like, we need a different approach. Exactly. Then, before Eddie even got here, we started to play with ChatGPT and Alfredo, Andy, and I were trying different things. Lots of different chats happening, going back and forth. David as well.

31:25And the first thing that happened is that we fed the five-point amplitude into ChatGPT. And we're like, can you simplify this? And it was like, you know, there's a special region. So, there's an extra assumption that you can make in which this answer simplifies to this one. So, this assumption is equivalent to, you have one particle coming in and it decays into n minus one. That's one way to think about it, roughly. But we're in two time dimensions, so.

31:57Yeah, it's complicated. But basically, you can look at what we call phase space. It's the entire space of possibilities for all the energies of incoming particles in the momenta. And there's a special region in that phase space where one particle has one different sign of its frequency compared to the other. And in that region, there's a big simplification that happens that ChatGPT found. And I should say, this was the public model, but the pro version of that thing is really hard. So, was that a known fact that it just was able to relate to the problem?

32:28Or was that something that it put together? As far as I know, it put that together. It said, you know, this five-point function, which is a sum of eight terms, each one of which is a product of three terms. They're all pretty complicated. It said, hey, like, actually, this simplifies to this product of only three terms. And we stared at this and thought, wow, that's really nice. We didn't know this. It's actually, in hindsight, once you know, you can re-derive this. But it takes a while to understand where this comes from. So, I think that was a leap of insight that the AI had.

33:01And I think what it did, I mean, at some point said, I wrote a Python code and I ran through all 5,000 possibilities. And I did use this. So, it's the equivalent of running his computer algebra system, but it just decided to do it on its own and came up with a huge simplification. So, great. Awesome. This was after making the assumption? This is after the one-particle decay assumption. Yeah. So, it figured out, there was a lot of exchange. This is very experimental. We're talking about it a lot. It figured out there's some region in which things simplify in that region.

33:35It said, okay, this thing simplifies. And RGBT came up with that simplification as well of the album? Yeah. Yeah. And then we were like, okay, well, let's give it the six-point function, which Alfredo heroically computed and by we didn't have the seven-point function. I mean, I don't think anybody could use the identity to expand it. It would be disgusting. And then chat GPT does its little thing. And then it's like, yep, simplifies to this. And we thought, whoa, okay. Yeah. That is really nice. Because now, instead of 32 terms, it reduces to just four terms.

34:08And it's not a sum of 32 terms. It's a product of only four terms. And then we asked chat GPT, okay, well, can you guess the general formula for all N? And that step, by the way, I mean, you could imagine using some programming language or symbolic manipulation software to do these reductionals in certain examples. But to tackle the general case, I don't know how to use a computer to do that. But chat GPT said, yeah, this is the answer in the general case. Boom. How long does that take? You know, it's like using pro with things for 20 minutes at a time.

34:41You go back. But it wasn't like six days or something. No, no, no. It's just like over the course of several interactions. And the amazing thing is that the formula that it proposed, instead of having this factorial growth, which is super exponential, where the number of terms, as you consider an increasing number N of particles, the number of terms blows up. Here, it's actually linear. So if you double the number of particles, you only double the number of terms. It's the nicest possible behavior you could imagine. This is the equivalent, I think, of the Park-Taylor formula for the double minus amplitudes that

35:15was known back in the 80s, but now for the single minus amplitudes. And this was gassed by GPT, I think it was 5.2 at the time, GPT 5.2 Pro. But it couldn't quite derive it. So I said, hmm, looks like this, but I don't know how to prove that. Yeah, I think the model was not quite strong enough. Okay, prove it. But part of my work at OpenAI has been to develop stronger physics capabilities in the models. And a lot of people have been adding lots of, you know, it's not just my singular contributions,

35:48there's a lot of great research happening and all comes together, you know, it takes a village. But we had this internal model that could think for a very long time and was extra strong in physics. So we gave it the whole problem from scratch without actually giving it this. We just formulated the problem in a very sharp way and asked the model to solve, to find the answer for the amplitude in the general case in this region, because now we'd identified that this was the special place to look.

36:19And it took 12 hours, which is a long time, but it came back with the same formula, which we had not given it. So it rediscovered the correct formula, but this time it also found the proof that the formula is correct, it derived it. And in fact, the remainder of the paper after we state the equation is devoted to the proof that is basically what came out of the AI. So we say the rest of this work is devoted to proving that the conjecture is correct. There's three steps. First, you show this. Second, you show blah. And third, you show blah.

36:50And then this is basically what the AI came up with. So now I can finally summarize the paper. The title is Single Minus Gluon Tree Amplitudes or Non-Zero. So these special interactions between gluons, where only one of them has a different helicity from the others, which were previously thought to never occur. However, actually, these interactions can happen. So the amplitudes are non-zero. That's the main claim of the paper. I think it's quite surprising. I think it's like a really nice paper. And the final result, I guess there's two results.

37:23One is understanding that it's not zero. That came from the humans like a year ago, but they were trying really, really hard to find this simple answer for what the amplitude is. And they were kind of stumped for a year. They were able to get this indirect representation that's extremely complicated in terms of the Feynman diagrams. But they were looking for the simple formula that is the analog of this Park Taylor work from the 80s for the more complicated amplitudes. And that was done with the AI. And so I think that's a really interesting result. Yeah, it's amazing.

37:53It totally changes the way you should think about where we are in physics and how AI is going to change that. You know, it's not just hype. I mean, this is like a real thing to happen. It's a result that top researchers in this field were thinking about for a year. And then the AI solved it. So I find it interesting. There's several things about the story, which I think people didn't understand on Twitter. If maybe scroll down to like equation 38 to what's it? 35 to 38. Yeah. Like, so I would say most even intro grad students would look at 35 to 38 and say, 39 is actually a very natural extension of this.

38:24Like, that is, I don't think, you know, that surprising. I think it's interesting. I didn't know until just now that you can, that when you proved 39, that was a fresh session. That was without the limiting cases, you started from scratch. How did you do it that way? Um, because I guess it's an extra way to be confident in the answer. If the, if a different model independently comes up with it from scratch, then you're

38:55not just feeding, spoon feeding the answer that you think is correct. That's an extra confirmation. Um, but yeah, I think we thought a lot about how to put this out into the world and there's no perfect way to do this. I, you know, clearly we could have done a better job of communicating it. One thing that was important to us is to not make this paper about AI, because I think this is a really interesting physics result. You know, people will keep reading this paper. I hope for a long time, we didn't put AI in the abstract because this is a physics result

39:28that stands on its own. There's one paragraph really about AI where we just say the final formula was first conjectured by GPT 5.2 pro and then proved by an internal open AI model because, you know, that's what happened. It's true. But we didn't really want to get into it because I think that's not the point of the paper. I mean, it's really interesting how it happened, but the result stands on its own. And I think if you read a paper today that was written 20 years ago that used the computer to do some critical step in the argument, and it had this whole discussion of how, well,

40:01I loaded MS-DOS 3.1 and it had five floppy disks and I had to swap my floppy disks. You wouldn't care. That's not why you're reading the physics paper today. So we didn't really want to go into that in the paper and we talked a little bit about it in the blog post that we released with the OpenAI, which is this one. And then I guess on Twitter, there were a lot of questions and I wrote some tweets that I think clarified it. And there was somebody who is a physicist who wrote a great blog post, like actually understanding

40:32the story. And The Economist also put out a great article about it, which they really understood what happened. And I thought it was a great, great coverage. Science Magazine also read about it. Harvard, the Institute for Event Study, put out a press release. So I think it got a lot of attention, but it's kind of a subtle thing to explain. It took us an hour to go through what happened and what was done. So, you know, it's hard to explain. I think it would have been kind of a distraction from the physics point of the paper to go into that. Okay, let's talk about the physics then. Give us a sense because, you know, my theoretical physics on the frontier comes from PBS Space

41:06Time, right? Like I'm, you know, it's a great channel and fantastic channel and gives you a great high level picture, but hard to know how this sits in the pantheon of papers that represent the cutting edge of theoretical physics. You're asking me how good is the paper? Not exactly that. I want to just understand, like, it seems like you're comparing it to this previous result that is pretty significant and, like, you know, like highly cited and very important. How does this compare to that?

41:38Okay, you're putting me in a bit of a tough spot. I will say, I think the result is surprising. That's why the title is what it is, you know? Single minus amplities are non-zero. And if you're somebody who works in this field, that should catch your attention. Ultimately, it's very hard to know in science when you release something into the world, how it's going to be received and how impactful it will be. I think the true value of a paper can only be assessed into the future based on how much

42:08future work it leads to and what developments it opens up. So maybe a better way of asking is, so my understanding is that that previous paper kind of opened up a whole line of thinking about... Yeah, I think this is a great segue to the second paper that came out just three weeks later. Perfect. So it got its own blog post. This was March 4th, so I guess two weeks ago now. So we were talking earlier about how there's four forces, strong force mediated by gluons,

42:39and then gravity that's mediated by gravitons, except gluons we can produce at the LHC and we can measure their effects fairly directly. Gravitons, we think, are also around us, being produced all the time, even as I move my hands. But we've never done an experiment that directly measures gravitons. But they're supposed to be the quantum of gravity. So they're really interesting from a theoretical standpoint. And so going back to RJ's question earlier, what are the gravitons?

43:09So these different answers we could give, ultimately, the correct answer depends on what the theory of quantum gravity, which we don't know yet. If you just naively try to take all of your tricks from field theory that we know from the standard model, apply it to gravity, things just break down. The theory is not self-consistent. There's some definition. Various problems. Yeah. Just like if you took, in this room, there's light flowing around, there's some indivisible

43:41bit of light that you, at some point, can break up into smaller bits. That's the quantum of light. We call that the photon. And the gravitational force is mediated by the exchange of gravitational force or gravitational waves. If you try to take a gravitational wave and break it up into smaller and smaller pieces, at some point, you get a quantum that you can't break up anymore, and that would be the graviton. That's how we understand them. So there's the idea being that you can't, you get to a certain point and you can't have

44:15less gravity than that. You either have some or none. Right. That's one way to think. Yeah. And so we wrote this paper, which is called Single Minus Graviton Tree Amplitudes Are Non-Zero. So it's the same title, almost, except with Graviton instead of Gluon. And that's on purpose, because we wanted to extend the result. And it's the same story in the sense that it was thought that all symbol minus amplitudes are zero. But actually, it's not true also for gravity.

44:48But gravity is a lot more complicated. So now if you want to compute the graviton amplitudes, it's potentially a lot harder. Do gravitons have phase the same way that Gluons do? Is that it? So they actually have spin 2 rather than spin 1 is getting into the weeds. So the amount of the numbers you have to use to describe them are a little bit different. They're doubled in some sense. Okay. So their polarization is more complicated. I see. But this isn't really getting into the weeds. But the special region in which the final answer simplifies has two labels because it's

45:23a spin 2 particle. Whereas in the Gluon case, there was only one label because it was a spin 1 particle. So this is like... So it's not the same math. Gluons and gravitons do have some spiritual similarities compared to other types of particles. In the sense of... They're particles of force. Yeah, yeah. But they're like sort of doubled. Yeah. They're sort of doubled. Yeah. Yeah. I mean, okay. I guess the people watching this podcast probably like to geek out all this. So the modern definition of a particle in quantum field theory, which is our best verified

45:54framework for nature, is that particles are irreducible representations of the Poincaré-Gru. We just lost 90% of our audience. Yeah. Okay. Maybe we cut this. So there's mathematical representations. And they've all been classified. All the possibilities are known by Wigner, actually, a brain physicist. And it turns out that the representations or possible particles are completely labeled by the mass and the spin and the charge of the particles. So these are the three quantum numbers.

46:26And particles of long-range forces, like gravity and electromagnetism, have zero mass. And they have to have integer spin. And spin 1 is three of the four forces, and spin 2 is gravity. And then that's it. But let's set that aside. The really cool thing about this paper is that, well, first of all, it came out three weeks after the first one, which is really fast. And I think this is a great example of AI accelerating science. And in fact, we could have put this paper out three days after the first one, because that's

47:00how fast we got the answer out of ChadGPT. But it took us three weeks because we wanted to check very carefully if that is correct. But most of the time was spent verifying the answer, not dreading, which is insane. Actually, if you take a step back, if you told me a year ago, yeah, like you're going to have this AI that just does really hard calculations for you. And then most of the human effort goes to verifying the answer. I've thought that, you know, you're crazy. So it's very surreal.

47:31And then we also had to write it up as a nice paper, which, you know, put in the citations and references that takes some time. And also had a baby in the meantime. So it was some lost time there. But we did this really fast. So I think it's an example of accelerated science. Another really cool thing is that for this paper, we didn't have to use an internal open AI model that had to think for hours. This was all done using the publicly available GPT Pro. In fact, we shared one of the main prompts that we used. It's if you go to the blog post, extending single minus amplitudes to gravitons, and you

48:05scroll down to the text, there's a link to one of the chats that we used. So you can see we use ChadGPT 5.2 Pro. And the amazing thing about this is that we gave it the glue on paper as a seed. And we said, we can understand the paper. Make sure you understand the manipulations and the appendices, because that's where most of the hard work goes. And it comes back and it says, yep, I understood the paper. Let me focus on the appendices. Here's what happened. And basically, the punchline is that GPT Pro, with the glue on paper as an anchor, was

48:39able to do the graviton calculation, which is really different mathematically, completely on its own from, well, I guess not from scratch, but from the glue on paper. But it's just a different thing. And it was strong enough to do it completely. So you took the conceptual leap from the previous paper and just said, okay, what math do I need to make that same conceptual leap? And it's different math. That's an important thing to emphasize. So in particular, there's a crucial application of something called the directed matrix tree theorem. And Alfredo and David, we've been thinking about these things for a very long time.

49:13We're like, oh, that's really cool. That's surprising. We hadn't thought of that or seen that before. That was like known math, but it was because maybe it has such broad understanding of math and physics that it's able to say, oh, this is a good thing to apply in this case. Yeah, exactly. And so here it understood the paper, the glue on one. And then we said, okay, well, the task is to generalize this paper to the gravity case. Here are two key changes, but otherwise, manipulations should be similar.

49:45So we tweaked some things at the get-go. And then we said, good luck, you're a brilliant theoretical physicist. So it's like, you know, we give it two paragraphs. So we give it the glue on paper, a couple paragraphs, and said, good luck. Thought for 20 minutes. And boom, it starts to think. So it starts at the beginning. It works through the implications. It's all like really interesting stuff. And then it says, here's what I would do next to turn this into the gravity paper. If you want, I can do blah. And so we said, yeah, go ahead. So another thought for 31 minutes.

50:16Thought for 31 minutes. Yeah. So this exchange is 110 pages, but I think it's hilarious. I would describe this as vibe physics, because you can see, so now it goes away. There's a lot of hard work, goes on lots of equations. It's starting to do the, okay, so now you have to use this different math. You have to use these tree calculations, LSE reduction formulas. Okay, there's a lot of stuff happening, stumble for trees, concrete checks. It's starting to, yeah, well, this is one of the things I love is that it's able to do the same things that a human would do,

50:48which is check some basic cases, a study check, and to get intuition. And so it comes back every 30 minutes and says, well, here's what remains to finish the full gravity paper. And there's a list. If you want, I can write the gravity analog. Yes, do that. This is the first step. Okay, it goes back and thinks for 34 minutes, half collinear support, and starts to be set. Okay, these formulas are actually made in the paper in some form. This is all correct. There's a bunch of stuff. At the end, it says, if you want, the next most useful thing I can do is do this.

51:21And we're like, yeah, verify this by performing the explicit check. And it goes on. Just to cut to the end, finally, we say, okay, write up the paper. And you can see the paper that it writes. And it's very close to the final thing that we actually put on the archive. So did it make suggestions that were not what you would have suggested as the next steps? It's very smart. It knows kind of where to go.

51:51It's useful to steer it. But if you compared what it came up with, with the actual paper that we put in, the intro, the abstract and introduction were written by Andy, who's an amazing writer. And I think he gave this wider perspective on the problem and how it fits into physics and how it connects to other things that, you know, the AI didn't do it. Just the intro at road was more generic. But okay, AI could write really well. We didn't really try to make it. Yeah. And the other thing is we added this section, this section too, which was not part of that initial exchange.

52:29It's about how these graviton amplitudes transform under certain symmetries of physics. And that's something that we're really, really interested in because we eventually want to understand quantum gravity, as I mentioned earlier. And typically the first step to uncovering a new theory is to understand what are its symmetries. That's something that gives you some kind of ground to stand on. Andy in particular has been pushing this program of celestial holography, which is like a whole thing we could get into, but it's an exploration of the symmetries of quantum gravity.

53:02And he really wanted to understand this. And there's a separate chat. We didn't share that one where we led the AI to explaining how these answers fit into the symmetries that we know the theory should have. And that's something that went in there. But actually, I think from section three onwards, it's pretty much very close to what the AI wrote. So I would say this is really remarkable. It's a real solid result in quantum gravity that was done pretty much completely by an AI with humans steering it and asking kind of the right questions.

53:39But all the math was derived by ChatGPT Pro, the public model you can access. And most of the time spent by us to humans was like checking everything and writing it up. And that's really wild. I mean, we're really... So, I mean, as a physicist, you find yourself where a lot of coders have found themselves where there's a kind of a fundamental, maybe epistemological question here that if now as a physicist, like I could have done that, right?

54:11Like maybe, like I needed a little more background, but like a lot of it was like, yeah, go ahead, right? Like take this paper, give us some prompt. You guys obviously prompted it very well, but there wasn't like maybe an undergraduate in physics could have come up with a lot of that. And so the question is, how does the undergraduate in physics now learn when they don't have to do the hard calculation themselves? Similar to that, how does the undergraduate coder... Actually, you're opening up many different strands of conversation, Charles.

54:44Super interesting. So let's try to unpack that a little bit. Um, so the most direct thing you asked is, how does the next generation learn? Yeah. That's a really good question. I think about this a lot. And now that a lot of senior physicists in the field are coming to grips with these new capabilities, one of the questions that comes up very quickly is, how do we train the next generation? Because the way we were trained is by going through these, you know, those, these difficult rites of passage where you have to do these really arduous calculations.

55:17And this is how you build confidence in your own abilities and check, test your knowledge. And it's not just about what you're capable of doing. It's about knowing that you're capable of doing it and proving it to yourself and building that self-confidence is important. And we don't have a good answer. This is something that academia is going to have to grapple with. So one thing that is especially difficult is that as a professor, I have graduate students. And the, the gap between where classes take you, even graduate courses, they only go so far.

55:49They go very far, but only so far. And the gap between where that ends and research begins is actually huge. And it's, it's growing wider. Usually as a professor, what you do is when you take on new students, you keep in your pocket a few easy problems in the sense that, you know, they're going to work. And some questions that, you know, in principle, you could work out, not that difficult, but you give them to a student so that they go through the exercise of learning everything around the question, developing the technology.

56:22And then you know enough about the problem that you're sure there's an answer that you can get there and you can advise the student in the process of discovering it. And I think the issue is that many such problems now, I would say these models can probably crush. Yeah. These are problems that we usually take. Again, you know, timescale for a theoretical physics paper is six months to a year. That's pretty typical. So if you tell a student, go away and think for six months about this one question and you have to work really hard and learn a lot of stuff around it and do lots of calculations, even the most determined students, would they not, within the course of six months, ever ask Tatuisi for help?

57:03Yeah, that's a little bit weird. Right. Now, it's also an opportunity because I remember that time in my graduate school career, in my second year of grad school. I took all my graduate courses my first year and then my second year was my first project and it was actually the hardest time for me in graduate school to traverse the desert for more classes to take you to the research frontier. It's very hard. And there's a lot of time spent banging your head against the wall, like all the time you're confused, you don't understand things just because you need to absorb so much knowledge.

57:35And AI can totally help you with that. Yeah. It's the best teacher. It knows everything. It can unpack any complicated fact to any desired level of detail. Actually, my experience as a trained professional physicist working on my own research using GPT now is that I would say there's two key ways in which my research has completely changed. One is that I spend much less time being confused. So, I'll do a calculation, get an answer, and I think, huh, how does this fit in with this other fact that I know?

58:09Like, how do I reconcile these things in my mind? I'm confused. Yeah, I do that all the time. Yeah. In research, usually you take a step, then you're like, you hit a roadblock, an obstacle, you're confused, then you have to think for a few days. Maybe you go for a walk or, you know, work on another project, come back, get a new idea, but you spend a lot of time confused. That's nature research. With GPT, I'm like, hey, I just did this. I found this, how does this match with this other thing? And then it's like, oh, well, you forgot this thing, or, oh, you didn't quite think about it correctly, or does the standard fact, you know. And so, the amount of time you spend confused just dramatically shrinks and you move so much faster.

58:44That's one of the accelerating effects. The other accelerating effect is that, you know, I only have so much free time and energy, especially when you become a professor, you have to teach, you have students, you have grants, you have a lot of things you have to do. So, your free time to think about research without distractions shrinks. And also, you know, you only have so much energy to do hard calculations. And so, what you would usually do is, if you have a problem, you know, you're at point A and you want to get to point C, you think about the route. Oh, I have to go through point B first and actually maybe do multiple points.

59:16And you try to plot in your mind the course that you're going to take before you actually go start to do the hard work. You try to think really hard about where you're going and to chart a course. With AI, actually, you can launch 10 instances of chat and have each one try a different route and send it as a scout that moves very fast into the unknown, pushing outwards. And you can just very quickly get some feedback to see, okay, these approaches are not promising. These are much more promising. And then if you follow them, there's a huge difference between being the first to push into the unknown versus following someone ahead of you.

59:50And even if ChatGPT doesn't always get everything right, just kind of having a scout that signposts some key steps along the way that you can use to anchor your own movement is extremely helpful. So, there are two concrete ways that AI has changed the way I work. And I think if you're entering research, having an assistant that can help you find your way to where you're trying to go can be very good. So, I think it's inevitably going to change how we work, how we operate, and how we train students.

1:00:23And, you know, part of what's exciting about my job is trying to figure how all of this works. But it's not just a job for OpenAI. It's actually a job for every researcher and professor more generally to think about this. I think the future is very bright because we have some challenges to overcome. But on balance, this is such an amazing tool. I think it's going to give human physicists AI superpowers because of what I just described. You can do so much more. And I think actually the kind of skill that is really useful to get great results out of AI is very similar to the kind of skill that you develop as an academic collaborating with other humans.

1:01:06This is like a collaborator. And if you're a professor who's been advising students and postdocs, you know, a lot of what being a professor involves is knowing for each student postdoc that you're working with exactly what question to give them. So matching the problem to the person and knowing how to give them the question in what way with how much deep, what level of detail, not too much, not too little. And that's actually kind of what you have to think about when you interact with ChatGPT.

1:01:36So I think that it's a transferable skill. And people who are good at this are about to get AI student powers. What you just described there reminds me of several conversations we've had on the podcast thus far, which keep coming up to this concept of taste. One of the things that especially you say theoretical physics, high energy physics has maybe had a problem with. I'm not sure if you want to describe it that way. But it can be very trendy that like there are certain things which become in fashion because maybe right now we're in a world where we don't have the data to define new directions to really guide or constrain where we're going.

1:02:15I'm curious, like how does essentially something which is superhuman in that it has basically all known physics and is interact with a field where at its core, what oftentimes can be popular or people start working on is more based upon general aesthetics or what, you know, the community collectively thinks is cool at the time. Because I can imagine it could vibe so many different worlds, you know, like for example, just using client space, using this sort of two time two spatial dimensions for this was already sort of an assumption that I think is actually kind of important in some ways and does provide feedback to our world.

1:03:00But in the concept of, you know, you could have asked ChatGVT to solve this problem in all sorts of number of ways. And, you know, maybe it could come up with all sorts of things which don't really align with maybe the useful taste. As a community, how do you actually deal with that? Like a proliferation of really interesting results, but it's actually not clear what is where the field should go. I mean, you're getting at the heart of what does it mean to do progress in theoretical physics and research?

1:03:32This is a hard question and there is a simple answer. If there were, it would be research. Let me say a couple of things. The first one is when you go to graduate school in physics, it's usually because you're really interested in the big questions. Why are there three dimensions of space? What happened at the Big Bang?