What's the amplituhedron?

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Speaker 1: Ay, Daniel, do you sometimes think that physics is too complicated? Yeah? Sometimes I think it's amazing that we can understand anything at all that's going on out there in the universe. Don't you think there might be a simpler answer to everything out there? That does strike me sometimes if I'm like doing a calculation and I get a whole page of mathematical symbols, that I wonder, like, did I miss a mind is sign somewhere or a factor too? Yeah? Right, Like maybe there's a better way of looking at things that might be simpler. Yeah, Like maybe we should just do physics with cartoons instead of math exactly. Basically my messages you should hire more cartoonists. Well, you know, we do try to do that a little bit with Finnman diagrams. They're basically cartoons. Oh, there you go. Feinneman was a cartoonist, although his punch lines MA not so funny, and so maybe cartoons are actually the problem. Yeah, that's the simple answer, isn't it land the cartoonists. It's all because of big cartoon Hi. I'm jorgem and cartoonists and the co author of Frequently Asked Questions about the Universe. Hi I'm Daniel. I'm a particle physicist and a professor at u C Irvine, and I'm always amazed that we can understand anything about the universe. I'm always amazed that I understand anything at all. Welcome to our podcast, Daniel and Jorge Explain the Universe, a production of I Heart Radio, in which we think about the biggest questions in the universe, the hardest questions, the easiest questions, the most confusing questions, and we try to explain all of them to you. So it's some questions you don't want the answer to. But I look out at the universe and I wonder, why is it possible to use our kind of little brains to come up with these little stories that can actually tell us something about what's going on out there in the universe. We fight these intellectual battles with the chaos of the universe, and sometimes we come out with a nice little story. Well, you're assuming we know the answer to things. Maybe we don't. Maybe what we think about the universe is actually wrong, or actually much simpler than what we think. Well, it's definitely true that everything we think about the universe is probably wrong, but we hope that the degree of wrongness is decreasing with time, that we're like asymptotically approaching some kind of truth, you know, the way that like Newton's theory of gravity wasn't wrong, it just wasn't as close to the truth as Einstein's right. But wouldn't you need science, you know, if you're getting less wrong, in which case that science could also be wrong. Yeah. Actually there's a whole field of philosophy and how to quantify scientific wrongness, and a lot of people argue but exactly how to do those calculations. So yeah, there's the science of new in science. It sounds like relying on philosophy to tell you if science is right, and I don't know that's the best idea. I think. In the end, everything relies on philosophy. It's the foundation of everything. Maybe not breakfast, but it's a foundation of all intellectual pursuits. Doesn't sound very scientific though, Yeah, philosophy is definitely not scientific. You know. Sometimes you talk about ideas that you can't test, but they're still important for understanding the way we think about things. I guess technically all PhDs are philosophers, right, that's what the pH PhD means right, that's right. Yeah, you have a philosophy degree in mechanical engineering, don't you. Yeah, I think I think about mechanical engineering all the time, philosophy of mechanical engineering. I'm thinking of giving myself a PhD in cartooning from a cartoon university. Yeah, why don't you just found your own university? Absolutely? You know. I once went to the crackpot session at the American Physical Society annual meeting. This is the meeting where they have to give you a presentation if you're a member. If you pay a hundred bucks, you can give a talk at the American Physical Society. And there's always one session where they put all the people who are like Einstein was wrong and everything is worldpools man. And one of my favorite talks at that meeting was given by a guy who came from a university he named after himself, where he was the honor or a chair named after himself, and he had given himself the prize named after himself. Isn't that what all universities are anyways? I mean, Stanford just made one and named it after himself. But is that really a session? It's called the crackpot session. Or is that just what you're calling those people? That's what I call it, But I think officially on the schedule, it's like miscellanea. On the schedule, it's Daniel's colleagues. It's definitely one of the funnest sessions to go to. It's a lot of creative ideas there. Yeah, well some of the ideas might sound crack, but but but sometimes you know, looking at things in a different way can be the right way to kind of push science forward. Right, absolutely, that's right. We need creativity and a basic element of doing science is thinking about new ways to do things, new ways to think about the universe, new ways to tackle problems. Yeah, sometimes the biggest discoveries in science come when people think about new ways or new descriptions of what they already know or they think they know. Yeah, And there are lots of times in the history of science when people are struggling with something. Things seem confused, using, or complicated or getting really elaborate, and then somebody has a new idea and all of a sudden it seems simple again, like when people were trying to understand the motion of the planets and putting the Earth at the center of the solar system required all these complicated shenanigans, you know, loops within loops within loops. But if you just put the Sun at the center of the solar system, boom, you had a much simpler mathematical explanation for what you were seeing. So there are these moments when just another way of looking at things, a different way of doing calculations, a different starting point, can really simplify what was once very difficult. I thought you were going to say, it's simpler if you just give up or change careers or become a philosopher, then you're just run into new kinds of problems. Man, you can't run away from your problems. New kind of financial problems usually be switched to philosophy. But it is interesting how in science sometimes you do sort of need that kind of change in perspective and then it all sort of makes sense. I imagine the quantum revolution was kind of like that too. Absolutely that required a complete evolution in our very understanding of the nature of the universe at its most microscopic. But as soon as Plunk and Einstein thought about light as made out of these little quantized packets instead of just like classical waves, then all of a sudden, the photoelectric effect made a lot of sense, and black body radiation suddenly didn't have a catastrophe in it. So all sorts of problems that were plaguing people for a long time just sort of went away as soon as you took a new approach at things. And you can sometimes get the sense of this yourself. If you're ever doing a calculation and things are just like going horribly wrong, then maybe you've made a little mistake, or maybe you sort of like tried it the wrong way. You know, you're using the wrong mathematical tool, or you're thinking about in an overly complicated way. There's just sometimes a simpler solution at hand. Yeah, and so I guess scientists are always looking for better ways of looking at things. I guess you're always trying to simplify your life, right, Nobody wants to complicated life. Yeah, that's right. We have a certain set of mathematical tools that we can use to do calculations, to try to figure stuff out, to answer questions that we have, and sometimes they work beautifully and it's just like a few lines on a page and boom you get an answer, and then you can test it with the experiment and you can learn something about the universe. Sometimes they get bogged down and you end up with like pages upon pages of calculations or thousands upon thousands of lines of computer programs just to get a sample answer. And that makes you wonder, like are we going in the right direction, or maybe we need a new kind of tool you know, should you be trying to describe the motion of a baseball by thinking about all the tiny little particles inside of it? Or is there a simpler equation that describes the trajectory of an object under free fall? Right? Right? The old like goes up, must come down wall, and it's an incredible thing in our universe, right that, Sometimes a new approach can make things much easier. You know, you can solve almost any problem in lots of different ways. Students of physics know this. If you're tackling a homework problem, you can start it in some way that gives you pages of equations, and other ways you can find the answer in just three lines. So we have lots of different mathematical toolkits, and some of them are appropriate are some problems, but not so appropriate for others. Right, And that's kind of where particle physics is these days, right, I mean sometimes you need supercomputers, right to sort of predict what's going to happen at some particle collisions. Yeah, we use these little cartoons, these finming diagrams to describe what we can happens when particles collide. But in complicated situations sometimes you need thousands or millions of these diagrams that lead to huge calculations that are really hard to do. We can't do them by hand anymore. We have to use supercomputers. And that makes people wonder like, maybe this isn't the way the universe is doing this calculation. Maybe instead of adding up all these time a little bits, we need to step back and get a more global view. Maybe there's a simpler approach. Yeah, maybe there's a simpler way to do Daniel's job. And so to the on the program, we'll be asking the question, what is an AMPLU two hedrawn? Well, that's a hard word to say. How many syllables is that? Like? Ten? It's like the most complicated word for an idea that's supposed to simplify things, all right, I want to just call it a d I don't know if somebody need to call you up and ask you for advice about how to name this thing. Obviously, Yeah, I do have a PhD and naming things in physics by now. It's given to me by Daniel Whites in university. That's right, philosophy of naming things two pH pH PhD. But this is a really fun new idea in physical It's sort of a glimmer of an idea. It's like a potential new way forward that might make things that once we're very, very complicated, nearly impossible, suddenly just snap into focus. And it involves a lot of geometry and possibly quantum field theory. So we're gonna have a lot of fun here on this audio podcast. Exactly what's better for talking about geometry than an audio format. It's like talking about architecture or describing geometry. It's the same concept. Are you saying there aren't architecture podcasts. I'm sure there are. I'm sure they'll go as well as today. But it is a long word, and it's also an interesting word, maybe one that a lot of people haven't heard before. So as usually, we were wondering how many out there had heard of this concept. So thank you very much to everybody who volunteers to answer these questions without a chance to prepare at all. It's very valuable for us to hear what you guys are thinking about, and also very helpful for other listeners to know whether or not this is something other people have heard about. So thanks very much for participating, and if you would like to hear your voice on the podcast, please don't be shy right to us. Two questions at Daniel and Jorge dot com. So Dannon went out there into the wilds of the internet to ask people what do you think and amply to hedron is or is pronounced? Here's what people have to say. It sounds like a shape, I guess, but a made up one. So now it's the shape the sound waves make when my husband plays guitar out of a two vamp. What is I've never even seen this word before and full of pedro uh uh amplute, hedron, amplitude something. Is it some kind of weird amplitude particle? That's that's mine. That's my guess. I can even pronounce that, but um, you know again the word head drawn. I'm guessing it has something to do with the shape that has multiple sides. An amplitude hedron is a quasi three dimensional shape where all of the faces, instead of being two dimensional surfaces, all right, forces with varying amplitudes. If I look at the two base words amplitude heedron, I know a heedron is a geometric shape with a number of facets or faces um. Amplitude looks like the word amplitude, meaning strength or degree um. Putting their two words together, However, I simply have no idea. It sounds like a geometric shape, and I would say it has to do with the amplitude of something I couldn't tell. Unfortunately, I don't know what it is, but it sounds cool, and I would really know, I really really want to know what it is. I think a head drown is a kind of particle, so it must have maybe something to do with the amplitude of a particle. That's my best guest. And note, of course that I didn't pronounce it for these people, right, I sent them an email, so they had to deduce for themselves how to say this word. Oh man, it was like a double quiz. Can you guess what it is and how it's pronounce or even spelled? Yeah, and a lot of people saw he drawn and thought about had drawn, because of course we're talking about had drawns all the time on this podcast, so that's a reasonable misunderstanding, right right. It sounds like you named the hadron a little bit confusing there. Do you think we should have had a large he drawn collider? I think that's how a lot of people pronounce it. Anyways, you might as well. Today we are smashing polygons and triangles, smashing geometry. But it is sounds like a lot of people have heard of the word before, although they are a lot of people sort have caught on that it has maybe something to do with amplitude. Yeah, there's some intuition here that the basic ideas involved our amplitudes and geometry, and in fact that's the core idea. It's a way to try to use geometry to help calculate particle amplitudes like how wide they are or what sized pants they were? Is that what you mean? Well, particle amplitudes are what tell us what's likely to happen when you smash two particles together. To say, for example, you throw an electron at a positron, and you wonder like what's going to happen Each possible outcome has an amplitude. One possible outcome is that they bounce off each other and go back the other direction. Another possible outcome is that they annihilate and turn into a photon, which then turns into something else. There's a whole list of possible outcomes from quantum mechanics and quantum mechanics. A scigns each of these things an amplitude. That's actually what you get out of the shorting or equation, and the larger the amplitude, the more likely it is for that outcome to happen. So it's sort of like a way of calculating the probabilities for an outcome of a particle collision. As a shorthand is the amplitude, because that's what comes from the wave function, right, Because that is the best possible name you could give to the probability of an outcome, is the amplitude, which normally means the width of something right right, Well, in this case, it's talking about the height of the wave function. So if you solve the Shorteninger equation for some situation, you get the wave function, and the amplitude of that wave function is what we're talking about here. To get the probability, you take the amplitude square, you take it to magnitude, because the amplitude can be a complex number, though the probability is one step beyond the amplitude, and the amplitude does in fact talk about sort of the height of the wave function. Well, this might get a little bit abstract and complicated, so maybe let's start with the basics and start with the question we're asking, which is what is an amplitue hedrawn? So how would you describe what this thing is? So an amplitude heedraw and isn't like an abstract geometric object. Imagine some high dimensional space, you know, not just two dimensions or three dimensions, but like ten or eleven dimensions. Let's not let's no, that doesn't help me much. Let's start with just three dimensions. Like what would an amplitudehedron look like or is or would be in just like three dimensional space? So an amplitude hedron in three dimensional space is just a polygon, right, Just it's like a bunch of points with lines in between them. So it's a shape like a triangle or a pyramid. Triangle could be one, a tetrahedron could be one. You know, it depends on what kind of thing you're trying to calculate, you know, a decahedron, All these kind of things could be amplitude heedrons. The point is it's a geometric object. So it's like a shape like just the a connection of dots in space, kind of like if you did a connected dots and three dimensional space, you would get some kind of weird polygon, you know, geometric shape exactly. So put a cloud of dots in space and now connect them with lines and then put planes between those lines. You have like a shape, like a three D shape, right, like a surface, you know, imagined like a mesh of points that make a surface. And so you have this object. It's just like a three D object in space. And it turns out that there's a connection between the geometry of this object, meaning like how you calculate its volume and things we want to know about particles. So if the points you created represent the particles that you're interested in, then the volume of this object that that's created helps you calculate what's going to happen to those particles when they collide. So that's the amplitu hege on. It's like a geometric object that helps you calculate what's going to happen to particles when they smash together. Right, But the points in the geometric shape are not the actual particles, right, They just represent points in some space that you're doing your math in for the particles, Like, they're not the actual particles floating in space. They're not the actual particles floating in space. You know, they're like possibilities. They are things that you're connecting together in some space that you're doing your meth in, right exactly. And often we create abstract spaces to do calculations, Like a lot of normal vanilla quantum mechanics is in complex space, meaning you have real numbers and imaginary numbers, and you have to keep track of both of them. Does it actually exist in reality? Like the complex numbers are imaginary, right, they're not real, but we keep them around to do these calculations. So we do this all the time in physics. We create an abstract space, something which isn't real, but where mathematical objects live, so we can do calculations in that space that give us answers about what happens in our universe. Right, Like a particle in space might have a place and a velocity, but maybe you're doing your math in some other properties of that particle or some other kind of space that describes the particle. Yeah, like the wave function, right, where is the wave function for the particle. It's in some abstract space because it's gonna have weird values like two plus five I. It doesn't exist in the universe. You can't look at it and say this is where the wave function is. It's right here, doesn't have a location, exists in some sort of abstract space. Okay, So an amplitude heedron is like a geometric shape in some kind of space that you're doing your meth in that somehow represents particles. And I think you're saying the d the idea is that maybe this shape in this space of math that you're doing could somehow make calculating things about particles easier. Yeah. The thing that we want to calculate is what happens when we run our collider, when we smash particles together. What happens We want to be able to calculate that because we're gonna do those experiments and we need to be able to predict what's going to happen and compare our predictions to the experiment, and so these amplitude heedrons make those calculations much much simpler. Those calculations which turn out to be really complicated and burden some in a lot of basic situations, can become really simple if you use the amplitude heedron. Well, maybe step us through this. Why is it complicated? I mean, you're just smashing like two protons. Why is that hard to figure out what's gonna happen. It's hard to figure out what's going to happen because lots of different things can happen. Say you're smashing two particles together. Let's not use photons from the moment, because they're actually even more complicated because they're not actually fundamental particles, their bags of particles. So let's say you're smashing together to fundamental particles like an electron and a positron. So what can happen? While they can turn into a photon, and that photon can turn into another pair of particles. But along the way that photon can do other things. It can create other virtual particles which then spawn other photons, or before the collision happens, you know, one of the electrons could radiate an extra photon. There's all sorts of different things that can happen, and we can calculate that. We calculate each of those things by drawing a little fine min diagram that describes what's going to happen in that situation. But to figure out what is the overall chances for something that happen, you have to add up all the different possibilities. You have to account for all the different ways that each thing can happen. So if you want to know, for example, all right, what's the probability that if I smash my electron and positron together, I'm going to get a photon of this energy? Get to figure out all the different ways that can happen and add them all up, and technically there's an infinite number of ways that that can happen. Do you end up adding up lots of little pieces to try to get this answer, So it becomes really complicated if you want precise answers about even pretty basic interactions, right, because I think maybe one thing people don't understand or know about particle physics is that it's not like you just smash particles and then you see what comes out. I mean, you do see what comes out. But sometimes you don't really know what actually happened even though you have the bits of the remaining bits that that came out. Why could have happened between the actual smashing and the debris that you get afterwards. There can be a lot of possibilities there, Right, Yeah, we don't see the actual collision. We can't trace all of the details. So if all you see is what came out, like you put an electron opositron in and out came a muan and an antimuan, you don't know exactly what happened in the intermediate step. There's lots of different ways to go from your initial step electron apositron to your final outcome. And in order to calculate the chances of seeing that, in order to figure out how often you expect to see that outcome, you need to account for all the different ways that it can happen, and so you have to add up all those possibilities, and that can become really complicated. Right, Like, maybe can you step us through an example like the Higgs boson? Right, Like, you don't actually see or catch a Higgs boson when you smash particles together, but you can sort of figure out that it was likely that there was a Higgs boson somewhere in the middle. Using all of the possible ways or knowing all the possible things that could have happened, Yeah, we can talk about the Higgs boson. For example, we discovered the Higgs just about ten years ago, actually on this day, by seeing how it turned into two photons. So we don't see the Higgs boson itself, We see two photons that come out from the detector. We take those two photons and we add them together and we see that they probably came from a particle at about a mass of a hundred and twenty five GV. But there's lots of ways for that Higgs boson to be created. You can have that Higgs boson created because two quarks from the protons fused together. You can have that Higgs boson be created because a couple of gluons fused together. And before the blue ones fused together. They can do all sorts of really complicated things like turn into top corks or turn into other corks. So if you want to write down the ways that this can happen, you start to get a pretty long list of ways that can explain just this pretty simple thing of producing the Higgs boson and seeing it turn into two photons. Right, it's like you gotta know all of the possible things that could happen so you can duce would actually happen. Yeah, and even more important, you have to understand the other things that can come out that word from a Higgs boson, Like it's possible to produce two photons without involving a Higgs boson. There's lots of ways to do that. In fact that that's much more common. So if you're gonna say I've discovered the Higgs boson, you need to understand all those collisions that produced Higgs boson looking like things that weren't actually Higgs boson. So we need to understand, like the background, how often do we expect to see these kinds of things if there wasn't a Higgs boson. Those calculations are even more important if we're going to claim discovery of a new particle. We need to understand how often we'd see this kind of signature without the Higgs, and those calculations and require lots and lots of these Fineman diagrams to add up, because the Fineman diagrams can only describe like the most basic interaction. One particle comes in, another one comes in, and they do something. But most things that happen in nature require lots of these things. It's like putting together legos to build something complicated, right, Anything that's interesting or complicated requires lots of these pieces to come together, right, Because in a way, you're sort of like you're just kind of guessing that the Higgs boson was there, right, But to make it a good guest, to make sure that it's the best guest possible, you kind of have to rule out or take into account everything else it could possibly happen. And that's the complicated part to caltily. Right. Yeah, you could call it a guest, or you could say, you know, it's a statistical statement. We never know anything for sure, as we were saying philosophically earlier, but we can make a statistical statement about the probability of having seen this kind of data if there wasn't a Higgs boson, and we claim discovery of the Higgs, when that probability is very very small, and we're very confident that if the Higgs wasn't there, it's very unlikely that we would have seen this peak in our data, and so you're right, we need to calculate that very precisely. And to do that, we need to understand exactly what we expect to see without the Higgs boson. So seeing all those collisions that would produce things that look sort of similar to the Higgs, we need to understand that really, really well. And to do those calculations is hard, and it gets harder and harder as our energy goes up and as the number of particles involved in the collision goes up, and so it becomes really important. Okay, cool, So let's dig into what makes it such a hard calculation and how this amplitude hedron could maybe simplified. But first, let's take a quick break. All right, we're talking about an amplate two heedron, which I'm guessing, or at least I'm making a statistical statement that, Um, it's a complicated word. It's a complicated word for sort of a beautiful and simplistic geometric idea. Wish they would have chosen a beautiful and simplistic geometric word for it. Yeah, let's try it, Dannie, what would you have called it? That is not my area of skills. How about just an ahedron that sort of sounds like an antihedron, like you collid to heedron and ahedron together and boom. About just a geometric shape, a symmetron or something that but that probably exists already. There you go, Yeah, it's good transformers. But I guess the basic idea is that making predictions in particle collisions is really hard and you need a lot of masks. Nowadays you need supercomputers, and people argue for years over whether you're accurate to the right decimal place, and so it's kind of complicated. And maybe step us through Daniel, then why is it so complicated to calculate everything that can happen in a particle collision? It's complicated just because there are so many different ways that you have to account for, you know. I think a good analogy is thinking about, like how our comedies figured out how to calculate the volume of a really complicated shape, right. I think the story is he wanted to be able to figure out what the volume was of the king's crown so we could figure out what the mass and the density was to see if it was real gold. But it's hard to do calculations with weird shapes. You know, it has like curved and triangles, and how could you do this? Well, one thing you could do is like laboriously measure every tiny little shape of the crown and think about it as a little triangles and squares and add them all up. It would take you a long long time, but in principle, you could add up the volume of the crown. The other way to do it is just like sink it in a bathtub of water and see how much the water goes up. And that gives you the same answer because the water like feels in all the cracks and so like, that's an example of how you can use the universe. Use this trick in the universe to make what seemed to be like a hard calculation much simpler. And so in particle physics, it's sort of the same story. Figure out like what happens when two gluons smashed together. You have to think about all the different ways that they can smash together, in all the different ways that they can produce results, And so it's adding up lots and lots and lots of little bits. Each little bit is not hard. It's like calculating the volume of a cube is not hard. Each individual one is not hard. But when you have billions of them and you have to multiply them against each other to get trillions of diagrams, then it becomes really difficult to do these calculations right. And I think part of what makes these calculations difficult is that they're kind of recursive, or they're kind of like almost like a fractal, Like two particles can smash and they turn into one thing, but then that thing could also turn into something else in the meantime, But then the two things that that thing turned into could also turn into something else, and then it can actually loop back and turn into the original particles, and so you get these kind of infinite loops of things that could happen during that closion. Yeah, the loops are especially tricky because they don't involve anything that you see and imagine, for example, two particles coming in and two particles coming out. You might imagine the simplest possible thing, which is just like put too fine and diagrams together and you get that kind of interaction. But you can also add a loop where like in between some new particles created and it only exists briefly and then it's reabsorbed, right, So it creates this like loop in the Fineman diagram, which otherwise just looks like a tree structure. And those loops require integrals because you have to sum overall that if impossible momentum that loop could have. And then as you say, you could have interactions involved two of those loops, or three of those loops, or five and twenty seven of those loops. So it gets to be really laborious to get an exact answer. In fact, to get an exact answer, you have to include an infinite number of diagrams. So we never actually do that, right. I wonder if it's kind of like playing chess, you know, like to know if a good move is the right move, you would have to kind of calculate all of the possible things that could happen after you make your move, right, And so you get into these branching kind of scenarios where there's like an infinite number of possibilities and you only really know if this one is the right move if it gives you a winning strategy in all of them. Yeah, and there's lots of different ways to get to a win, right, and so in a similar way, you need to think about all the possible intermediate things that could happen from here to where you want to go, Like is it possible from my opponent to derailist strategy? So you have to think about lots of different possibilities. Absolutely, So if you could come up with a way to very simply calculate the probability of winning or losing when you make a move, that would be tremendously helpful in chess. Right, it would make chess a very simple game. That's why chess is hard, because it's difficult to calculate these possible outcomes for every given move, Right, Like, maybe there's a move where you can just stand up and punch your opponent and win, and then that's a much simpler way to solve the whole scenario. Right, is that still chess? Though I'm not. That's m M a chess. There's this moment in particle physics a couple of decades ago when folks were working on one of these calculations involved like billions of terms, billions of terms to the billions. Wait is it infinite actually? And so billions billion is actually just an approximation or is is billion, like all of it. The full calculation would be an infinite number, but to get a reasonably accurate calculation, they needed to use about a billion terms. Yeah yeah, and each term is like a possibility of what can happen during a collision, right exactly. To calculate these probabilities, you have to take these things and square them, which means you get all these cross terms. So the number of terms just getting really really large. But these guys were working really hard and they took these billion terms. They're really good with symbols, right there is how this special skill like know how to manipulate symbols on the page. And they were able through like just sweat and blood and fought to reduce this thing down to a nine page formula, which means like it took nine pages just to write down the expression, right, the algorithm expression for the answer to this thing. They reduced her from a billion terms down to a nine page formula, which is already really impressive. Well that depends that did they use both sides and what size font did they use? Like, if he's a big enough font, anything can be a nonpage formula. You know, this is standard ltech on an eight and a half by eleven, or maybe it was a four. It's one of those European But the really cool thing about it was not that they got it down to a nine page formula, which is totally unwieldy, but that then they took an intuitive guess. They're like, you know what, I think that this probably could be reduced to a simple single expression, like a very small short expression but just a few variables in they that gives you the same answer. They made this guess based on their experience because they're like familiar with these kinds of calculations and they've seen things before, and they said, maybe this is similar to other results we've gotten. Is it possible it just works like this? So they guessed the answer, and then they checked it with a computer. Right, They said, well, does this give the same result in every single case? And the computer said that it was right. So that means that there is an answer, right, There is a simple mathematical expression that gives you the answer you want that doesn't require a billion terms, It doesn't require a nine page formula. It is just a simple thing you can write down in like one second. Well, that's crazy. They just guess what it could be yeah, you know, based on a lot of experience and intuition. They guessed based on other similar things that they had looked at. You know, they've done a lot of these calculations in the past. So there is guessing in physics, there is guessing, absolutely, but then they checked it right. And so to me, that's a lot like this Eureka moment of our comedees right figuring out that there is a simpler way to do this calculation, that you don't have to add up all the little pieces one by one, that there is an expression, it's out there, the math is waiting for us, that there is a simpler way to do these things. That was sort of like a real moment of inspiration for a lot of people in particle physics, because it suggested that if we could somehow figure out a mechanical, like a methodological way to get to that short answer quickly, then we wouldn't have to go through this thousands and billions of terms and nine page calculation and then guessing right. It's not like a robust way to do science, right. It's kind of like the baseball analogy you brought up earlier, like to calculate what happens when you throw a baseball. You could maybe like track each and every single particle in the baseball and how it's interacting with each other and all the air molecules. Or you can just use like a parabola, right, and which also tells you the same and sort of where the baseball is gonna land exactly, because a lot of those little details end up averaging out. You know, maybe you need a billion terms. So maybe those billion terms actually half of them pushed this way and the other half pull the other way, and so they basically just cancel out to something simple. And so the path of a bag bolt isn't governed by what an electron is doing on the bottom half of it. It's this big overall average effect that's actually quite simple. You can describe it with a simple differential equation of F equals m A. So that's what we're looking for in particle physics. We feel like maybe we're just dealing with the microscopic little details when what we really want is the big picture. Right when what you really wanted just to get up and punch the other player, all right, I think you imagine physics conferences are a lot more exciting than they really are. I think if you go around calling people crack pots, you might you might get punched in the face. My favorite part about the crack pot session is sitting there, everybody else in the session totally dismisses the other people. They're like, oh, this is crack pottery. I can believe this guy is even in this session. I can't believe it. None of them take each other seriously, Like, everyone in the crap pot session doesn't know it's called the crap pots. That's what you're saying. That's exactly what I'm saying, even you sitting in the audience. Somehow, that's why I was there because I wanted to see it. Well, so then this is where that concept of an amplitud heedron comes in. Right, It's a possible way to simplify this huge calculation that you right now have to do to figure out what's going to happen at a particle collision. Yeah, it's a new recipe. It says, don't start from the Fynman diagrams at all. Instead, put your points together, draw this geometric object, and the volume of that object, this new weird shape that you've made, is the thing that you want is the amplitude of these particles interacting. So if you can figure out a way to calculate the geometry of this object in a simple way that you can go straight to your answer without adding up all the little bits. There's this theorist at Cambridge I really like, David Skinner, and he said that using Fynman diagrams the old way of doing things is sort of like taking a ming vase and smashing it on the floor and then trying to like, you know, add up what it looked like from those little shards, and so instead just like, hey, enjoy the vase, it's beautiful. Well, maybe step us through a little bit of how this amplitude headron comes up and what the connection is to particle physics, like how do you get an ampletohedron of say, an electron smashing into another electron. So the thing is to avoid thinking about it in terms of space and time the way Fynman diagrams do Flyman diagrams think about these particles. If you know how they look at their these line drawings, they think about particles moving through space, right, so like this one comes close to this one, and then when they get really close they turn into something else, very similar to the way we think of our classical objects, right, like two balls flying through the air and then they bounce off each other. It's sort of relying on our intuition. It helps us keep track of like how things work and how things bounce off each other. Right, sort of like a baseball. We know in our heads that it's made up of little particles, and all the particles are flying together at the same time. But you're saying, don't think about all the particles. Maybe think about the baseball as something else. Yeah, And so instead of thinking about in terms of these Finneman diagrams, Roger Penrose came up with a new kind of diagram that thinks about sort of the relationships between the particles and all the possible relationships they can have. And this is something called a twister diagram E W I, S, T O R. And it helps you think about how the particles can be related to each other. And it doesn't think about the particles in our kind of three D space, you know, like X, Y and Z, the kind of space that we live in. It thinks about them in some sort of like abstract space, like we're talking about before space that doesn't represent our universe and where you are. It's just sort of like a mathematical kind of calculation. How do you get to that space? Like how do you transform a particle which has an x y z and I'm guessing a probability in a way function, how do you get into that new abstract space. So in that abstract space, a particle has a different kind of representation and our kind of space, a particle is like a dot in three dimensional space, but in this twister space. First of all, that space is complex, which means like things in that space can have imaginary values, are not limited to physical numbers, you know, like one, two, three, four, or even like three, one four, one, five, nine, But you can represent them in this kind of space. And this is a kind of mathematical thing physicists do all the time, like invent a whole new space and then and figure out how to represent particles in that space. And if you can invent the space and you can invent the representation, like how you write down particles in that space, then you can play all sorts of new games in that space. And sometimes those new games are useful, sometimes they're just mathematical silliness. And sometimes they're actually very related to what's happening in the real world, and so that's what's going on here. Penrose invented this new space. I wonder if it's a little bit like radar coordinates, Like you can think of as a point as having an x y in two dimensional space, or you can think of it as having it like a direction and a speed or for example m Those are still physical though, right, that's still embedded in the same physical space. But there must be some sort of transformation between the two, right that it does take the physical into these this abstract space, or not at all. There is a transformation in the sense that you're still representing things like particles. But this new space doesn't respect space and time in the same way. Space and time the way we think about them don't exist in this abstract space. And that actually turns out to be something of a breakthrough for this because it helps us think about like where space and time come from. It might be that thinking about the universe in terms of space and time is sort of the mistake we made why we can't, for example, get to a theory of quantum gravity, because it makes us think about how things bounce against each other in a certain way. Thinking about it in terms of this more abstract space allows us to get rid of concepts like space and time and then to do these calculations. But yeah, there definitely is a connection between particles in our space, the things that we think about, and particles in this sort of abstract space. It's sort of similar to the idea we talked about once the universe as a hologram, like maybe this three dimensional space that we think about, this information in this three dimensional space is actually encoded in another kind of space, like a two dimensional space with different kinds of wiggles on it, and so it's possible, for example, to describe a three dimensional space in terms of information on a two D surface. So it's sort of like that. It's like map the whole universe to a new way to organize information, and then the ideas that maybe in this new space, this super accomplished calculation is a lot simpler. So let's get into what these twisters are and what it could all mean for the future of particle physics. But first, let's take another quick break. Are we're talking about ample two heedrons, which I think it's taken us as long just to figure out how to pronounce it. I'm trying to avoid saying it if at all possible. Let's let's have a whole podcast where we avoid talking about the subject. Isn't that what we do every episode? Usually we avoid the subject. Here, I'm actually avoiding the word itself. Oh boy, it's it's like Baltimore, the thing that must not be named. Okay, so you're saying this. This ampl two heedron might simplify a lot how you do particle collisions, because it's sort of maybe cuts through the fog of all the possibilities, Like it's somehow looked at things in a much more simple or or maybe um broader way. And it's based on these things called twisters, which I guess is just kind of like a mathematical thing. Yeah, it's a new mathematical construct invented by Roger Penrose, and he described them as sort of like square roots of space time, which is sort of like, you know, I understand those words, but what does it mean when can put them together? It's sort of like think about again imaginary numbers, Like imaginary numbers are like the square root of minus one, So is an imaginary number real? Like is I out there somewhere in the universe. It's not, but we can still do math with that. We can play with it. It helps us do calculations, and it is the square root of minus one. So now think about these twisters is like not spacetime itself. You can't think about them as space time. But if you put them together in sort of a way, then spacetime comes out of it the way like minus one can come out of two imaginary numbers. And so these twisters are like, you know, basic components that you could put together to make space time. But it's sort of a more natural, underlying way to think about the univer Earth. And so these twisters exist in this abstract space or the astract space. Is these twisters, twister and diagrams help us do calculations in this abstract space. So you create these points in that space, you can make these shapes in that space. You can calculate the volume of those shapes in that space, and the volume of those shapes helps us predict what happens like in our universe, in our space time. WHOA what do you mean? Like you you find the volume of the space and it tells you, hey, um a Higgs boson came out, yeah, or it tells you here's the probability of a Higgs boson to come out. It's really cool because calculating volumes is typically pretty easy. Like if you have three dimensional cube, the volume is easy to calculate if you know the sides right, and there's a little bit of magic there. Right, you're adding up like an infinite number of infinitesimals to get the volume of this thing. But it's a very simple calculation. It's length times with time's height. It's very simple. There's a little bit of like calculational magic that happens there. And so in this twister space, calculating the volume of these weird amplitude hedrawn EAPs is also pretty straightforward. Nima Arkani Hammed, one of the guys who invented this thing, showed how to write them down in this compact notation where you calculate the volume, and then there's this connection. Here's the beautiful part between this volume and all the possible things that can happen to these particles in the same way that like the volume of a cube adds of all the infinitesimal bits inside the cube. Now, the volume of this amplitude, he john represents all the possible things that the particles represented by the points can do with each other. And it works without having to know all of the things that can happen, you know, without having to catalog all of the possibilities. Yeah, you just sweep them all into the volume, right, because you don't really care how many loops of gluons were created when this happened, or how many photons happened. Like, we can't see those things. We don't really care what happens. We care but the input and the output. And so this lets you go from the input to the output much quicker without having to make all those little calculations along the way. In another mathematical analogy, like think about calculus. You need to integrate some function, right, x squared plus two. How could you do it? Well? One way you could do is like draw the function and add up all the little slices to get the area under the curve. But calculus gives you a formula. It says, oh, here's a way to manipulate that expression to give you a simple expression for the answer. Right, we know how to integrate x squared plus two, And it's like you know, excute or three plus two x right, there's an expression that just gives you the answer. You don't have to do all the calculations. And so in the same way, the amplitude heatron is like that shortcut to the answer. Right. Although I'm not sure a lot of people agree that calculus makes things simpler in their lives. I guess it sounds really cool and it sounds really amazing, this amplituo headron. It sounds like it would solve a lot of problems and make things simpler. Is it real is does it actually work or is it still kind of a tentative maybe possibility of how things could be done, or has it been proven right? So it does work in some scenarios and makes some calculations very very simple. It hasn't been proven to be totally correct in every single case. People are still playing with it. It's like a very new mathematical tool. But it has a lot of promise, you know, and in the calculations people have done, it's come out correct. There aren't a whole lot of folks in the universe who know how to use this thing, Like I can't sit down and do a calculation with this thing. It's you know, beyond my level of calculational abilities is probably like a dozen or two dozen people in the world who are like actually know how to use this new mathematical tool. Wait, what do you mean only a few people know how to how it works or how to use it. Don't they print out a recipe or something for how to use it? I mean there are recipes, but it involves like kind of esoteric mathematics that are just not very familiar to most people, even particle physicists, like particle theorists here in my department. I don't think they could sit down calculate amplitude he dron volumes. I'm sure if they spend some time they can figure out how to do it. But it's not like a very widespread technique so far. All right, So then it's proven to work in some cases, but maybe not all or or is it just it hasn't been applied to other cases yet? You know one case it hasn't been applied to yet, for example, is quantum gravity. You know, it's been applied to quantum field theory. When we have these calculations and alving these little particles smashing together, these are the kind of calculations we already know how to do. This would be sort of a shortcut. People are excited because it might also apply to quantum gravity. It might help us do things like figure out what the gravitational attraction is between two quantum particles, which currently we just don't know how to do. We don't have a theory of quantum gravity that works. So one thing that hasn't been done yet is developed the amplitude he drawn to figure out if it can be applied to do calculations for quantum gravity. Also, there are some promising hints there, things that make people think maybe it is a new way forward. Well, that'd be interesting if it can solve quantum gravity. But I thought the main problem was it quantum and relativity that didn't really play well together. Like one assumes spacespendable, the other one assumes it's not, and so they really just don't play it well together. Is this a possible way to bridge the two things. Yeah, because a lot of those problems revolve around starting with space. Right, you have space which general relativity defour worms, and you have space which particles move through. And there are a lot of assumptions that go along with starting from space. One assumption is locality. We assume that things can, for example, only perturb other things that are near them. You know, so for example, you can't do something here which instantaneously affects something in andromeda. You can have sort of like short range connections between things by exchanging particles. But if your calculations don't start from assuming that space is a thing, they just start from this like abstract twister space, then you have a new kind of freedom and how you like build your theory, and maybe space sort of emerges from it, but you don't have to follow all the same rules that you thought you had to follow before. Maybe we can get rid of this requirement of locality. Maybe it's not actually an absolute thing in the universe, but eventually you have to be able to transform it back from the afflex space to the real space time that we live in. Wouldn't that be a problem then probably not. If you're concerned, is like, well, locality is a thing. We're pretty sure or that the universe is local. You know, we've seen that these things work in this sort of way. There feels like there is space in our universe. We're not talking about breaking that open and saying space isn't the thing at all. We're just talking about breaking those rules sometimes, you know, in the same way that like Newtonian theory worked and then it was replaced by Einstein's gravity, which disagreed with it only sometimes right, sometimes it to totally agree. And so if you can now have a new description of, for example, what happens inside black holes or what happened at the very beginning of the universe, that doesn't make all the same assumptions that we're trying to force quantum gravity into. You're a little bit more freedom to do something crazy. And you know, we don't know what's inside black holes. We don't know what happened at the early universe, So there's room there for crazy stuff to have happened which wouldn't be allowed by our current ideas of quantum gravity. And then maybe like quantum gravity or unified theory of quantum gravity in the real world, maybe emerges from all of this math in the abstract space. Is that kind of what might happen. Yeah, in the end, you have to be able to shuggle all of these calculations back over to our world to predict experiments, to say does this actually work? You know, math is fun, but in the end we're hoping that it describes the universe. There's another like deep philosophical question no one knows the answer to, like why does math work at all? Why does it seem to describe our universe? We don't know, But as physicists were excited when a piece of mathematics helps us calculate something about the universe, not just do some fancy geometry in an abstract space. So it has to in the end predict something we can test to prove that it really is a description of the universe. That's useful, and you know, speaking philosophically, if it does work, if it turns out this is a very useful piece of mathematics, then a lot of people take that to be something real. You know. I think about the other geometrical revolution in physics, which was general relativity. General relativity says, no, gravity is not a force. It's actually just a consequence of this complex geometry of space time, which was invisible to us until now. But we don't just think about that it's like an abstract calculation. We think about that is real. We think about space is actually really being curved. So in the same way, if this turns out to be right. If it turns out that calculations in this abstract twister space are the things that actually determine what happens in our space, that this abstract twister space is like somehow more fundamental. There'll be people who will say that's the real universe, man, that the universe really is in this abstract space without our kind of physical space and time, and that what we're experiencing is sort of like a hologram. It's just sort of like a construct that emerges from that. Like maybe we're all living inside of the amplitude heedron kind of and are what we see every day is is not real or it's just some kind of projection of the amplitudehedro. Yeah, and those two things are not the same, Right. It can be very real but also just to be a projection of the amplitude hedron. It can be real without being fundamental, Like I'm real, you're real. Doesn't mean that we're like basic elements of the universe. We arise from the complex to ing and frowing of all the little particles that make us up. Doesn't make us less real, just means that we're not inherent possible for there to be a universe without me and without you and without a podcast. It might be it's possible to have a universe without space and time, but with this abstract twister space, and then we'll all be forced to say the word amplicto heatron all the time. That'll be real fun. It would be the only word in the universe. But as you said, it does seem to work for certain cases, and that means that it has a promising future, like maybe it will sort of let you predict particle collisions from now on. Yeah, it's just fun to have a new mathematical tools something which is really good at this kind of calculation that's really important and the kind of calculation that we're bad at right now. And so it's just sort of like another tool in our arsenal. You know how, sometimes when you're solving a problem, you'd like to solve it using equations on a piece of paper, because the rules of algebra guide you there. And sometimes it's easier to use geometry to like envision how two lines cross or how a plane intersects a circle. So it's good to have lots of different mathematical tools in your toolkit because sometimes one of them makes a problem easy when other ones would make it hard. Right, right, I just have to learn how to draw cartoons in with twisters, I guess, or twisty pens in abstract twelve dimensional space amplitude cartoons. There you go. Yeah, and so in this twister space, locality is not fundamental, and also unitarity, this requirement that quantum information not be destroyed in the universe, and that might help us explain things like what happens to information that flows into a black hole, you know, which we talked about on the podcast a few times. So nima Ar Kannie Hahmed, one of the smart guys who came up with this, He says that locality and unitarity are both suspect. He doesn't believe that they really are fundamental elements of our universe. He thinks they're like almost approximate quantities that we've come to rely on, but aren't real and deep and true. They're just sort of real maybe in the amplitudehedral projection that we live in, but in the real three universe maybe they don't matter. That's what you're saying. Yeah, exactly, there's sus as my kids would say, And this is exciting because it's a pattern in physics. We tear the ail away and reveal the reality is different from the way that we expected. And those are the kind of discoveries that I live for. Cool. If only you knew how to use it exactly, maybe you should be spending some one time trying to learn it rather than talking about person in the world who knows how to calculate with these things. There you go, a small rarefied. It's supposed to being one of the three people who have podcasts, right exactly, one of the few rare people who have a podcast and who can pronounce amplitude heedron three times. Quite man, Yeah, that's an even harder thing. I think they can give you a PhD for that from the amplitudhedro and University. All right, well, it sounds like it's another stay tuned whether this new way of looking at things can actually revolutionize our view of reality and what actually happens when two particles collide. And sometimes progress is made by people smashing things together and discovering new phenomena in the universe, and sometimes it's made just by people thinking mathematically about patterns and shapes and relationships and coming up with new mathematical tricks to solve those problems. Yeah, a lot of people are probably thinking, man, I should have paid more attention in geology class. I could change the universe. Well, we hope you enjoyed that. Thanks for joining us, see you next time. Thanks for listening, and remember that Daniel and Jorge Explain the Universe is a production of I Heart Radio. For more podcast from my Heart Radio, visit the I heart Radio app, Apple Podcasts, or wherever you listen to your favorite shows. H