Daniel and Kelly’s Extraordinary Universe - Is it possible to have a two-dimensional object?

Episode Date: June 24, 2021

Daniel and Jorge slice the Universe infinitely thin and talk about the theory and practice of 2D materials Learn more about your ad-choices at https://www.iheartpodcastnetwork.comSee omnystudio.com/listener for privacy information.

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Hey, Daniel, you used to live in Chicago, right? Yeah, I did when I was working at the accelerator at Fermilap. Does that mean you like Chicago-style pizza? Oh, my God, that is not pizza. That's like a casserole. It's like a marinera swimming pool. I mean, it's delicious, of course, but it's not actually pizza. Ooh, those are tough words for a Chicago-style pizza.

Does that mean you prefer thin pizza, like New York-style pizza? Oh, yeah, absolutely. Like, the thinner, the better. Really? Like, how thin? I don't know, if it would possible, I guess I'd eat a two-dimensional slice of pizza. Well, that's convenient. Then you can eat all the pizza you like, and in the end, you have eaten nothing.

What about the toppings? Do you like 2D toppings, too? Maybe that's why people in New York are so thin. They have no death. They have no death. They're so shallow. Hi, I'm Horhammey cartoonist and the creator of PhD comics. Hi, I'm Daniel. I'm a particle physicist and I really do have strong opinions about pizza.

Really? Yes, strong opinions about particles, about physics and about pizza and dessert and big goods. You have a lot of strong opinions, Daniel. I am particular about pizza and yes, big goods. The things I enjoy, I know what I like. And I do love thin, New York or Italian-style pizza, but also a nice pizza. big slab of Chicago style, whatever you call it, is also delicious. Whatever. Oh, man, you don't even want to call it a pizza. I don't know.

This is just a totally different kind of food. I mean, the only thing they have in common are carbs, cheese, and tomato sauce. Yeah, that's a pizza. Does that mean that, you know, pasta with tomato sauce and parmesan on top is also a pizza? Yeah, and a calzone is just a closed pizza. That's a pizza taco. But welcome to our podcast, Daniel and Jorge, apparently talk about pizza. and explain the universe,

a production of iHeartRadio. A podcast would we record just before lunch, if you can't tell. And we usually talk about all the crazy things out there in the universe. The amazing ways that matter can form, the weird things that it can do from really, really big stuff like entire galaxies and clusters of galaxies, down to really strange little objects, what those tiny little dancing particles can make

when they set their minds to it. That's right, because let's face it, we're all hungry, hungry for knowledge in this world. You all want to know what everything is made out of, how it all works, and how it's all put together, and how it all makes sense, if it does. That's right. I would like to order two slices of truth for lunch, please. Can you get a Nobel Prize there on top, please? Just shaved Nobel Prize on top.

That sounds pretty good. Yeah, you know, like gold shavings, that's edible, right? You can also do that with a Nobel Prize, you know, just adds a little bit of intellectual richness to it. The smartest pizza ever. Yeah, we like to talk about all the amazing things in the universe. all of the crazy stars and galaxies and black holes and neutron stars out there and also all of the little tiny particles that make us up who we are and that pizza that you had for lunch.

And we also like to think about the way the world is and why isn't it another way? Something I like to think about a lot when I was younger and even still today are the number of dimensions of space. You know, the way that we can move in 3D and what it would be like to be a four-dimensional being or to be a two-dimensional being in a three-dimensional world, these kind of mental exercises were fun for me

and made me wonder like, why do we live in a three-dimensional world? What would it be like to live in a universe with a different number of dimensions? Wow, that's what you wondered about as a kid? I was wondering, like, how does Superman fly? And how strong is Spider-Man's web? You know, you were wondering about the dimensions of the universe.

I was. I mean, this is not six-year-old Daniel. This is probably 14-year-old Daniel. But, yeah, I was thinking about that stuff. What if Superman was two dimensions? How many dimensions are there to Spider-Man's web after all? So, yeah, I think these questions are super fun, and they go to the heart of a really basic question,

which is why is our universe the way that it is? So that's why it's fun to explore these different kinds of objects and different kinds of geometries. And I remember thinking, what if there are other parts of the universe in which there are four or five dimensions of space? What if we are, like, trapped in a three-dimensional subset of the universe? Yeah.

Oh, man, I think 14-year-old. Jorge was definitely not wondering about physics. He's probably wondering about things we can't mention in this podcast. But yeah, this idea of dimensions is pretty mind-blowing. I mean, it's not something we think about every day, right? We're also used to living in this world with three dimensions, you know, up, down, left, right, front, and back. And it's kind of hard to wrap your head around or even imagine more dimensions or even less dimensions. Yeah, it really is hard to because we are so used to this.

But this is something we're doing in physics all the time is wondering if the way we think about the world is just based in our experience and maybe therefore not universal, not representative, right? We don't want to imagine the whole universe is just the way that we have experienced it. We want to break out of those intellectual chains. We want to be surprised and we want to discover that the universe is totally different. And that's why science is such an amazing tool because it lets us put aside our biases and chip away at the truth. Yeah, we want to free our minds. We do. We want to blow all of our minds. Yeah. Is it kind of like fish?

You know, they live in the water, their whole lives. They probably think the whole universe is made out of water and, you know, there's nothing but water. Yeah, precisely, because they've never experienced anything else. And so how could they possibly extrapolate? And it's only when they see weird things like, hmm, the water seems to have an edge. I wonder what's beyond it. When they start asking those questions about other parts of the universe, do they expand their minds and understand like the true nature of the universe? And we've done this lots of times as humans, discovering that the universe is pretty different from the one that our ancestors thought it was, which means there are probably crazy discoveries ahead where in 200 years people will look back and think, I can't believe they used to think, X, Y, Z, whatever it is we're thinking now.

Yeah, I wonder if fish, go fishing for ideas also. I wonder if they play Go Fish or if they have another game called Go Human or something. I wonder if they eat New York style pizza. Now, that's a mind-blowing, multi-dimensional question right there. Well, you can't eat Chicago pizza without a knife and fork, and they don't have hands, so I think that's answered. You can put anchovies, and then that brings it all around to the fish idea. But getting back to our dimensional question, it is weird to think about the world, the universe having more than three dimensions. And so this is something that physicists actually consider.

And some of them even think there are not just four or five dimensions. There's a whole bunch of dimensions out there. That's right. Even physicists that don't like anchovies think about the world as having 11 or 20. 26 dimensions. Some of these theories that unify gravity and quantum mechanics, things like string theory, which might be a candidate for a theory of everything, these work best if there are more dimensions of space and time for the forces and these strings to sort of wiggle in. The mathematics prefers 11 or 26 dimensions, which is pretty hard to get your mind around. Like, where are those

dimensions? How do you move in those dimensions? Why do we only experience three if there are 11 or 26. Yeah. And equally as my blown is to think is sort of in the other direction, right? To think about what if the world had less dimensions than three or what if there are things out there that are less than three dimensions in their being? That's a super fun idea. And there's this whole class of theories that suggest that maybe the entire 3D universe is actually just a hologram of a two dimensional universe, meaning that we are actually two dimensional beings. We're going to do a whole podcast episode about the holographic universe later on. But that's a really powerful idea actually in string theory that lets people do calculations that otherwise would be impossible. I feel like this

podcast is kind of two-dimensional, Daniel, because we don't go very deep here. No, we have to pick one topic to go deep on, but we're always touching on other things. And I'm always like, oh, remember that time we talked about this or that's an idea for another episode or this is fascinating, but the digression would take another 45 minutes. So let's save it for a whole other episode. I see what you're saying. Every other podcast is one-dimensional. We are two-dimensional. We're like the world's first 2-D podcast. I don't know.

Maybe we're zero-dimensional. I can't even tell. What does it need to have a dimensionality in audio? I guess we're in stereo, so that's 2D maybe. But anyway, so today we're going to explore this question on the other side is wondering what could there be and are there things that are less than three dimensions. Yeah, because it's fun to think about what it would be like to be in a four-dimensional world. If you were a 3D person in a four-dimensional world, we talked about that on a podcast recently. You could disappear from inside a prison and appear on the outside of it by moving in the direction of that fourth dimension.

So it's also fun to think about like, well, do we have objects in our world which are two-dimensional, which don't see this third dimension where we could do these crazy tricks on them. Yeah. So today on the podcast, we'll be asking the question. Can an object be two-dimensional? Now, Daniel, is that two, like the number two? or like, are you asking if something can have too many dimensions? Yeah, my wife says that to me all the time. Man, you are two-dimensional.

Stop being so dimensional. I think she's trying to tell you, you need to go in a diet, maybe. She's like, you have too many dimensions. You need to stop eating so much at New York style pizza. Yeah, I suppose. I suppose I need to have some fractional dimensions. So this is kind of a crazy question. Question is, can an object be two-dimensional?

Like, the object itself only exist in two-dimensions? or, you know, maybe it exists in a subset of our dimensions or does it mean that it's just like super thin? Yeah, I think the answer is yes to all of those. We exist in three dimensions. And so every object you look at exists in three dimensions. Every piece of food you've eaten, everything you've tripped over, everything you've looked at exists in three dimensions

because it's in this 3D space. And it's hard to imagine an object having four dimensions in our 3D space, but why can't an object have two dimensions, be essentially only X and Y and have no height, right? To be a super thin slice, is that possible to have a lower dimensional object in our universe? Yeah, so this is a kind of a mind-blowing question. And so as usual, we were wondering how many people out there

had thought about this question and whether or not they have an answer to this range and multi-dimensional or a dual-dimensional query. So as usual, Daniel went out there into the wilds of the internet to ask people, can an object, two-dimensional. Thanks again to our willing volunteers and if you would like to answer some questions about tricky topics and hear your speculation on the podcast, please write to me to questions at Danielanhorpe.com. Here's what people had to say. I don't really think that an object can be

two-dimensional in a three-dimensional space that we live in, but if I think about it, what is a volume of an object? It is the space between the particles and not the particles themselves. So if the particles somehow could form a perfectly flat sheet so that they only extend in the x and y axis but they don't go into the z direction that theoretically maybe we could call an object like this to be a two-dimensional object i suppose an object technically can't be two-dimensional because atoms have volume and are therefore three-dimensional but i think there are situations where for instance if you you have one layer of graphene, it is so thin that it is treated as if it's two-dimensional. Then I am not sure about this, but I think with the Maldesanic injection, because with the conformal field theory,

you treat a three-dimensional object, for instance, a black hole by looking only at its, like, surface or surface area. By translating it from the string theory to the CFT, you almost treat it as if it's two-dimensional. I think that might be an example. All right. Some skepticism here. None of these two said yes. Something can be 2D.

We got rejected, exactly. And you had a third answer also, but that one didn't make the cut. Is that a 2D 3D joke? I'm trying to make a joke out of this flat topic. I'm impressed by the depth of your sense. humor. All right. So none of the answers seem to think you can have a 2D object. One of them said that because atoms have volume and the other one said because we live in a 3D space. So let's get into these strange conundrums. So Daniel, first of all, what would you say is a 2D object? How would you define it?

As usual, the definition is going to be critical as to exactly what we mean by a 2D object. But let's start like really theoretically in an idealized sense. I think the world is having three dimensions in the sense that there's three extensions, right, three coordinates you need to define your location in space. And so you can think of an object having like one dimension is a line, two dimensions would be a square and any height on that square would make it a cube, right? It would make it three dimensions. So a 2D object would be something that had no measurement in the third dimension, that its

location in the third dimension had only one edge, not two edges, doesn't have like a start and an end, its start and end are exactly the same location. So it's, you know, it would be essentially infinitely flat sheet of paper, for example. I see. So it's an object. It has to be like a physical thing in our world that really only exists. Like it only takes up space in one direction. Like you said, it's invisible if you look at it kind of on the side.

Yeah. Because it can't exist in the third dimension. That means that if you measured its height, the top of it and the bottom of it would be exactly the same number right there's no height to it at all because anything more than zero would mean there's an extent in that third dimension and that it's just pretty thin not exactly thin that we're looking for something which really has zero height in that third dimension but it needs to exist in our space so we can interact with it you can see it from the side for example that's the question can an object like that exist an object on which you were a person and you were walking around you wouldn't even notice that there was a third dimension because you'd only exist on that 2D space, you know, basically flatland. Yeah, I'm my cartoonist and so, you know, making things 2D is kind of my jam. But I think it's also pretty cool to think about like what happens if you have multiple of these infinitely flat objects.

Like if you stack a whole bunch of them together, they would still be flat. They would still have zero height. Yeah, because any number times zero is zero. So you can eat an infinite number of slices of 2D pizza and you've eaten zero volume. of pizza. You won't even grow in one dimension, like your belt size dimension? No, it's zero volume, right? So that means essentially you can't have a 2D slice of pizza. Can you taste it though? Maybe you can taste it like if it hits your tongue, you know? Is that possible? It's we invented the perfect 2D diet. The new 2D quantum diet by Daniel and Jorge. Download

the app now. We will sputter a layer of pizza, 2D pizza onto your tongue. Yeah, because you can't pick it up, right? Well, I guess the question is, is it possible at all? to have an object that is like that, that is infinitely thin? Are there loss of physics that would prevent it, or is it theoretically possible? So I still have three answers to that, you know, a yes, a no, and then a maybe. So starting with a yes, you know that everything in our world is built out of particles. And particles in our model, how many dimensions do they have? Well, we think of them as points.

They are point particles. We don't know if the electron has any substructure in it. So we treat it as if it doesn't. We consider it to be a dot, essentially an infinitely small dot. That means it's zero dimensional. So in our theory, an electron takes up no volume. So if you can have a zero D particle, you can make a 1D object by having two of them. And then the line between them is a 1D object.

And four of them, or actually just three of them, make a plane. That in principle is a two-dimensional object. So that's sort of the yes answer on the theoretical idea. Like if I took one atom or like one quark, right, and I lined it up with like a hundred other quarks in the same line, that would technically be an object by our regular definition, but it would have only one dimension technically. Exactly. If you believe that particles are zero dimensional and, you know, I don't really know if that really flies because particles are an excitation in a quantum field and they're localized. So probably not exactly zero dimensional. But if you start from a zero-dimensional particle, then yes, a line of them is a one-dimensional object.

I guess the problem is that the particles are point objects, but they have kind of a 3D presence, right? Yes, they do have a 3-D presence because how would you build that 1D line of quarks? The way that you connect things is through their forces, right? The reason that an atom is an atom is because of the forces that bind the electron to the proton. And those forces, as you say, have a 3D presence. And if you have a pile of hydrogen, for example, the reason it's not just all in one spot is that those atoms repel each other. And so there are forces between them that give an object volume. And that volume is then three-dimensional because the forces are three-dimensional.

Right. But I guess even those forces could fall in that line. Like, let's say you empty out the universe. The universe is empty. And you only have two quarks. That's technically a 2D object, right? That's a 2D object, but it fails the other test. Like, could you stack another one on top of it exactly and get zero high?

height. If you bring another one next to it, it would not want to be exactly on top of it. And so really, it's a 3D object. It's just sort of like a very thin tube. All right. That was your yes answer. What's your maybe answer? Yes, the yes answer was start from 0D particles you can. The no answer was zeroity particles really have 3D forces. So no. The maybe answer is remember that our world is quantum mechanical. And so in some sense, you don't have to have infinite thinness to be at minimal thinness. Our universe has a minimal length.

So now imagine an object which is normal in one dimension and in the second dimension, but in the third dimension it has the minimal length, like the just one space pixel essentially wide. That you might consider to be a two-dimensional object. Oh, I see.

By like the definition of space in the universe, if something is thinner than the quantum minimum distance, then you kind of have to say it's flat, perfectly flat, right? Because you can't resolve that it's any thinner. Yeah, you couldn't have a thinner object, except for in your mind as a geometer, imagining perfect 2D objects, but in our universe, things you could build, you couldn't have a thinner object. So you should crown that

to be either the thinnest three-dimensional object possible or a 2D object. And we'll talk about it a little bit later, but there are some objects like that in our universe that follow the math for 2D objects. Interesting. It gets complicated. We'll have to go deep. We'll have to try to avoid being shallow. All right. Well, let's get it into whether or not there are theoretically to the objects out there and whether or not they exist in the real world. But first, let's take a quick break. a holiday rush, parents hauling luggage, kids gripping their new Christmas toys. Then, at 6.33 p.m., everything changed.

There's been a bombing at the TWA terminal. Apparently, the explosion actually impelled metal glass. The injured were being loaded into ambulances. Just a chaotic, chaotic scene. In its wake, a new kind of enemy emerged, and it was here to stay. terrorism law and order criminal justice system is back in season two we're turning our focus to a threat that hides in plain sight that's harder to predict and even harder to stop listen to the new season of law and order criminal justice system on the iHeart radio app apple podcasts or wherever you get your podcasts my boyfriend's professor is way too friendly and now

I'm seriously suspicious. Well, wait a minute, Sam. Maybe her boyfriend's just looking for extra credit. Well, Dakota, it's back to school week on the OK Storytime podcast, so we'll find out soon. This person writes, my boyfriend has been hanging out with his young professor a lot. He doesn't think it's a problem, but I don't trust her. Now, he's insisting we get to know each other, but I just want her gone. Now, hold up.

Isn't that against school policy? That sounds totally inappropriate. Well, according to this person, this is her boyfriend's former professor and they're the same age. And it's even more likely that they're cheating. He insists there's nothing between them. I mean, do you believe him? Well, he's certainly trying to get this person to believe him because he now wants them both to meet.

So, do we find out if this person's boyfriend really cheated with his professor or not? To hear the explosive finale, listen to the OK Storytime podcast on the Iheart radio app, Apple Podcasts, or wherever you get your podcast. Hey, sis, what if I could promise you you never had to listen to a condescending finance, bro, tell you how to manage your money again. Welcome to Brown Ambition. This is the hard part when you pay down those credit cards. If you haven't gotten to the bottom of why you were racking up credit or turning to credit cards,

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and you'll meet the team behind the scenes at Othrum, the Houston Lab that takes on the most hopeless cases, to finally solve the unsolvable. Listen to America's Crime Lab on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. All right, we're talking about 2D objects, Daniel. And now this is a podcast. Does that mean that listeners have to put on like 2D earphones?

Like a red and a blue one? Would that help? Well, they're hearing the answers in 2D, right? One from me and one from you, I guess. Yeah, dudes, two dudes. We're just two dads or dudes. So technically it is a 2D podcast. That's right.

And sometimes we agree with each other and sometimes we don't. Sometimes I'm negative, sometimes we cancel out. It's all a math problem. Hopefully there's constructive interference. in the explanation dimension. All right, you just went too deep there. I guess one question you can ask is whether or not you can theoretically have 2D objects. And as I understand it, physics does allow for theoretical 2D objects.

Yeah, theoretical 2D objects are not a problem. We talked before about this idea of the universe as a hologram. This is a really powerful idea. And it shows that all the information in a three-dimensional space can actually be encoded on the surface of that space. You know, take like a sphere and imagine all the stuff inside of it, all the physics that's going on inside that sphere might actually just be encoded on the surface of that sphere. And that's a really powerful idea because it helps people do some calculations. Like there's two totally different kinds of theories that have different dimensions and this links them together. It's really important results per string theory.

But also it's really cool for thinking about black holes, like what's inside a black hole and is it possible that all the information. inside a black hole is actually just embedded on the surface of the event horizon. Yeah, we had a whole podcast about whether or not the universe is a hologram imprinted on the surface of a black hole. And you know, as a cartoonist, I'm a big believer in

that you can capture whole worlds in a sheet of paper. You know, it's my whole philosophy of life. But I guess the question is, you know, it's cool that you can maybe project the whole 3D world into a 2D surface, like for example, of a black hole. But don't you lose information? Like, in a cartoon,

I don't know what's standing behind my cartoon characters. Like, wouldn't that information get lost? Yeah, so there's three spatial dimensions in the universe and then two spatial dimensions on the surface, but there are quantum fields on that two-dimensional surface, and those fields can encode all sorts of information. Like a field can have multiple dimensions. It can be a vector field, for example. At every point in space, a field can have more than one number.

You can have an entire vector, which is three numbers or five numbers or ten numbers. So you could have lots of information sort of packed into every unit of space. So even though the space has fewer dimensions, the fields in that space could have more information sort of per unit of space. So you end up with the same amount of information. You mean you're cheat. It comes down to the definitions. I mean, it's kind of like you're just stacking pixels on top of each other, kind of, right?

It's kind of like in a 3D movie that you, when you go to the theater, it's like the same screen, but it's giving you, twice the amount of information in the same image. Yeah, and it's just another way to mathematically express things. And this concept invented by Juan Maldicenna is called ADS-CFT because it shows us how one set of theories, ADS, which means antidecitor space, which is what gravity works in, is really equivalent to these conformal field theories, which operate in two-dimensional space. And so you're right, it's a trick, but it's also, it's a cool trick because it shows us that

two totally different fields are actually have been doing the same thing, the whole. whole time that 3D movies are really just movies right and so the idea is that maybe our entire universe that we think is 3D is actually only 2D like maybe we're all living on the surface of a black hole or something yeah maybe our universe actually is only two dimensions and we have this experience of a third dimension because of the richness of the quantum fields gives the illusion of a third dimension that's the hologram right so that's a fun idea and it helps us think about how to solve black holes and construct string theories and goes to fun philosophical arguments about like, well, what does it really mean to have three dimensions or two plus one

illusory dimensions? But, you know, if that's the case, that would mean that fundamentally the whole universe really is 2D. Yeah, we're all inside a comic book, right? It's like everything in the universe is a 2D object in that case, right? Yeah, and the comic book is really an excellent example because what do you do when you look at the comic book is you don't just examine the 2D surface of the paper, you imagine a whole rich world in your mind. You know, a well-drawn comic creates in the mind of the reader this whole

three-dimensional model. And that's exactly what we're talking about here is having enough information on a 2D surface to project out into a fully realized 3D world. Well, I call dibs and being Superman in this comic book. All right. I call dibs on all those super thin slices of pizza in your comic book.

Have at it. I'd rather fly than... Although if you're flying a comic book, you're really not going anywhere. Does that count as exercise when Superman flies? Does he burning calories? Does his Fitbit count it? Well, I think he can't fly if he doesn't get enough sun. So technically, I guess he is expending energy.

Is that right? He can't fly if it doesn't get enough sun? Does he photosynthesize? Yeah. Don't you know anything about Superman, Daniel? About the physics of Superman? Apparently, I don't. He gets his power from the yellow sun.

He's not aware. So he's basically a plant. He's basically a super solar cell. Yeah. Solar battery. All right. Well, so that's one. kind of two-dimensional object is this idea that the whole world is universe is two-dimensional,

but there are also ways in which the theory says that you can have kind of two-dimensional things in our 3D world, right? Yeah, and earlier we were talking about building things which are the thinnest they could possibly be in a quantum universe. The idea there is that the universe we don't think is infinitely dividable. We don't think you can take a mile and cut it in half and then cut it half again and cut it have again and keep doing that forever. We think that probably there's a smallest unit of distance below which it doesn't make any sense to talk about distance because there's no measure that's

smaller than that. It's like pixels on the screen. And so the idea is if the universe is quantized, if there's a minimum distance, then like a sheet of something which is the thinnest possible sheet might effectively be a 2D material. Now the problem is that we think that distance if it exists is probably really, really small, like 10 to the minus 35 meters. And we're certainly not capable of making anything or observing anything that thin today. But quantum mechanics has other implications. You know, quantum mechanics limits how particles can move. Another idea, which has been around for several decades, is to make something that's so thin that it's thinner than the wavelength of the electrons. So that the electrons in that object are essentially trapped to only

move in two dimensions because the thing they're stuck in doesn't allow them to get excited or move in that third dimension. I see. I feel like there's two ideas here. One is making things smaller than the smallest resolution of the universe and the other one is making things smaller than the electron wavelength. So which one are they the same or are they the same? Or are they talking about here?

They're not the same. One is very fundamental like to the nature of space and time and just sort of to get you thinking about how the universe really is quantized, how there's like. like units of thinness. And the thinnest unit for space is really, really, really thin. But the thinnest unit for an electron is much, much larger and something that's really kind of achievable because an electron has an extent in space, which is much more significant. So, you know, can you build something which makes it so that electrons can only move in two dimensions? That can be much, much bigger than the fundamental unit of space. I mean, imagine,

for example, taking two sheets of glass and putting ping pong balls between them. then the ping pong balls can move between the sheets of glass, but they can't move up and down at all. If you could build a material like that where the electrons only move in two dimensions, then you might consider that to be a two-dimensional material. I guess the hard question is, what is the object? Like, are the electrons the object or the thin sheet is the object?

Because the sheet itself isn't made out of multiple layers of atoms, or are you talking about making something that's just one layer of atoms? So the basic idea is to make something which is a single layer of atoms. It's a lot like what we were talking about earlier. We take a single quark and you line it up and you make a sheet of quarks. If you could get these things which bind together

and to make a single layer of atoms, like a material that's just one atomic layer thick, then the electrons in that material would move as if they were in a two-dimensional world. I see. So then you're saying like kind of like that collection of electrons is then sort of a 2D object because it can't really, you know,

move in any other dimension except the one on the surface. Yeah, because there's no room for them to move. Like ping pong balls trapped between two sheets of glass. Electrons are bound to the atoms. And if there's no like layer up or layer down for them to go, then they're sort of trapped on that sheet. So that's pretty cool. Is it hard to make something like that?

Like to make a sheet that's only one atom thick? It turns out it's surprisingly easy. And you probably make them all the time when you draw cartoons. Oh, really? Are you saying my ideas have no death? No, it turns out that you make them every time you sharpen a pencil, you make a two-dimensional material. Because carbon is a really amazing object, and it can form all sorts of really crazy stuff. And it is possible to make sheets of carbon that are just one atom thick.

And one way to do it is to break off pieces of basically graphite, which is pencil lead. And graphite is so brittle that basically every time you write on a surface of paper or you sharp, In your pencil, you are generating these sheets of graphene. Interesting. So like carbon kind of likes to do that, right? Like it kind of likes to arrange itself in little sheets and not like cubes or clusters. It likes to do all sorts of things. And so you have to get it to do this.

But graphite exactly is very brittle. And so it's not that hard to peel off layers of it to make these two dimensional sheets of carbon. And so I thought this was super interesting. And I went to ask a friend of mine who's actually a professor here at U.S. Irvine, is this possible what it really means and what she thinks about two-dimensional materials. Nice. Who did you talk to? So I talked to a young assistant professor named Judith Rouhani. She's very friendly. She's from Hungary and she just came to UCI about a year and a half ago. And she arrived during the

pandemic, which means she's never really gotten to experience the campus life here. Wow. And so she works on these 2D materials, right? She makes these flat sheets of carbon and then she puts electrons in them. And then the electrons sort of move around in the this one-dimensional world. Yeah, she's actually a theorist, so she mostly writes papers about them and thinks about them rather than actually building these things. But yeah, she's a pretty deep understanding of how they work. Oh, all right. So you asked her to talk to us about some of these materials? Yeah, I asked her if she thought two-dimensional materials were possible and what it meant for an object to be two-dimensional. All right, here is what Professor Rouhani had to say. So,

you know, like for theorists, anything is possible, right? Because I just take a two-dictional one hand and I say, well, I just consider something that has two spatial dimensions instead of three, and that will give me some kind of confinement. So, you know, my mobile particles, for example, see, like electrons, they can only move in two dimensions, but not in the third dimension. And then there comes, like, real life, you know, like, I have a real chunk of material that definitely has extensions in all three dimensions, right? So that's very different. It's like, I guess if you ask this question, like 15 years ago, I would just say, like, yeah, 2D is very theoretical. There is no such thing as a 2D material, right?

Because why would it not, like, fold up, like, you know, why would it stay, like, straight as a sheet of paper or something? Or, like, how could it exist? Like, what would stabilize anything like that? And now it turns out that there are actually two-dimensional materials. And then what those are kind of, like, if you imagine that you have a material that is, say, like, one atom thick or, maybe thin is a better way to say, or maybe just a few atoms thin, like maybe two or three atoms in. And that's actually possible to create these materials or actually kind of

peel them off from their three-dimensional, let's say, modern material or like different types of materials. They really exist and people are doing different kinds of experiments. And so it's not just, you know, theoretical dream anymore. It's actually an existing thing, which is very exciting because they do have a lot of these similarities to 3D electron, what are 3D models or materials. All right. I like how she said for a theorist, anything is possible. I think that really tells you something about this field. This is an idea which came about like in the 40s and 50s, people were wondering, is this really possible? They were thinking about it and theorizing about it. And only recently, only like 20 years ago, did this actually become realizable. So this is something,

It's sort of like the black holes for condensed matter physics. They're wondering, mathematically, we figured this out, but could anybody actually make this thing in real life? So I think we're sort of living in the science fiction future for a lot of these condensed matter physicists. That's pretty cool. And she says that, you know, if you do confine electrons into one of these thin materials, they do sort of actually kind of move like in a two-the-world. Yeah, and it makes the thing really, really different. And that's what's really interesting. If you take a whole loaf of bread and you cut in half, you have half a loaf of bread, right?

Right. But at some point, if you take really, really thin slices, it stops being bread and it starts turning into something else. Right. It turns into toast. That's totally different than bread. Or biscotti. It turns into biscotti. You know, you have to pay like a few bucks more at Starbucks to get. Yeah, put tomato sauce and cheese on it and Jorge will call it a pizza. But I think it's really cool that you take something and you make a thin enough slice that it basically turns into something else. Like imagine taking a loaf of bread and making it such a thin slice that you get a. slice of ham, you know, or it turns into cheese or something. That's basically what's happening here. You take graphite, which is, you know, this, like, thing inside pencil lead, and you take such a thin slice off of it that it comes off with completely different properties, totally

different sort of mechanical strength and electrical properties and all that stuff. Wow. That sounds like delicious magic right there. All right. So those are theoretical to the objects. And so now let's get into real 2D objects. Are any of these actually real? in our world, and maybe they're all around this.

So let's get into that. But first, let's take another quick break. December 29th, 1975, LaGuardia Airport. The holiday rush, parents hauling luggage, kids gripping their new Christmas toys. Then, at 6.33 p.m., everything changed. There's been a bombing at the TWA terminal. Apparently, the explosion actually impelled metal glass. The injured were being loaded into ambulances, just a chaotic, chaotic scene.

In its wake, a new kind of enemy emerged, and it was here to stay. Terrorism. Law and order, criminal justice system is back. In season two, we're turning our focus to a threat that hides in plain sight. that's harder to predict and even harder to stop. Listen to the new season of Law and Order Criminal Justice System on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. My boyfriend's professor is way too friendly, and now I'm seriously suspicious.

Well, wait a minute, Sam, maybe her boyfriend's just looking for extra credit. Well, Dakota, it's back to school week on the OK Storytime podcast, so we'll find out soon. This person writes, my boyfriend has been hanging out with. with his young professor a lot. He doesn't think it's a problem, but I don't trust her. Now he's insisting we get to know each other, but I just want her gone. Now hold up, isn't that against school policy?

That sounds totally inappropriate. Well, according to this person, this is her boyfriend's former professor and they're the same age. And it's even more likely that they're cheating. He insists there's nothing between them. I mean, do you believe him? Well, he's certainly trying to get this person

to believe him because he now wants them both to meet. So do we find out if this person's boyfriend really cheated with his professor or not? To hear the explosive finale, listen to the OK Storytime podcast on the Iheart radio app, Apple Podcasts, or wherever you get your podcast. Hey, sis, what if I could promise you you never had to listen to a condescending finance, bro? Tell you how to manage your money again. Welcome to Brown Ambition. This is the hard part when you pay down those credit cards.

If you haven't gotten to the bottom of why you were racking up credit or turning to credit cards, you may just recreate the same problem a year from now. When you do feel like you are bleeding from these high interest rates, I would start shopping for a debt. consolidation loan, starting with your local credit union, shopping around online, looking for some online lenders because they tend to have fewer fees and be more affordable. Listen, I am not here to judge. It is so expensive in these streets. I 100% can see how in just a few months you can have this much credit card debt when it weighs on you. It's really easy to just like stick your head in the sand. It's nice and dark in the sand. Even if it's scary, it's not going to go away just because you're avoiding it. And in fact, it may get even worse. For more judgment-free

Money Advice. Listen to Brown Ambition on the IHeart Radio app, Apple Podcasts, or wherever you get your podcast. I had this overwhelming sensation that I had to call it right then. And I just hit call. I said, you know, hey, I'm Jacob Schick. I'm the CEO of One Tribe Foundation. And I just want to call on and let her know there's a lot of people battling some of the very same things you're battling. And there is help out there. The Good Stuff podcast season two takes a deep look into One Tribe Foundation, a nonprofit fighting suicide in the veteran community. September is National Suicide Prevention Month, so join host Jacob and Ashley Schick as they bring you to the front lines of One Tribe's mission. I was married to a combat army veteran, and he actually took his own mark to suicide.

One Tribe saved my life twice. There's a lot of love that flows through this place, and it's sincere. Now it's a personal mission. Don't have to go to any more funerals, you know. I got blown up on a React mission. I ended up having amputation below the knee of my right leg and a traumatic brain injury because I landed on my head. Welcome to Season 2 of the Good Stuff. Listen to the Good Stuff podcast on the IHeart Radio app, Apple Podcasts, or wherever you get your podcast.

All right, Daniel, we're talking about real life 2D objects. Now, we talked about in theory, it could be that we're all in a 2D world, or maybe you can make electrons behave like they're in two-dimensional. But in the real world that we live in, at least the one that seems like it's three dimensions, can you have 2D objects? So you sort of can. I mean, it's a little bit cheating. They're not technically two dimensions because the materials themselves do have a height. But the mathematics on these materials is the same as if they were two dimensions. Like if the world was two dimensional, mathematics and physics especially would be different.

For example, we know that if you shine a light, then the strength of that light decreases like one over the distance. squared. That's one of the distance squared because our universe is in three dimensions. It's the same amount of light spread over the surface of a sphere and the surface of a sphere goes like the radius squared. So there's things like that where mathematical relationships tell you about the dimensionality of the world you're living in. And when we study the behavior on some of these physical materials we're going to be talking about, we see the mathematical relationships you expect from a two-dimensional world, not a three-dimensional world. I see. So they're like, 3D objects that behave or, you know, follow the rules of a two-dimensional universe.

Yes, exactly. And so in the sense, if you're following the math of a two-dimensional world, are you really a 2D object? Interesting. Like if you do live in a cartoon, are you really real or not? If you cosplay enough a cartoon, are you really in that cartoon? Hey, no judging. No judging. So step us through.

What are some of these real-life 2-D objects or 3-D objects that behave like 2D objects? So one of them is looking at the surface. of liquid helium. Liquid helium, of course, is helium that's super duper duper cold so that it turns into a liquid. And if you drop electrons onto liquid helium, then they like to stick to the surface. Like liquid helium is this really weird surface tension. The electrons like to stick to the surface, but they're free to slide along it because liquid helium is super fluid. So electrons can slide along it really easily, but they're stuck on the surface. And of course, the surface of an object is two dimensional. And so these electrons are confined to the surface, but they can slide around. So it's really

a lot like those ping pong balls stuck between two glass planes. And so this is something people can actually build. And they call this a two-dimensional electron gas. Not a gas because it's like something you can breathe, but these are just sort of like idealized particles bouncing around and moving. And it follows the laws of thermodynamics in two dimensions. It's almost like just having ping pong balls in a table, right? Like they're just sitting on the surface. of the ping pong table, and they sort of roll around, but they can't just jump off. Right, but if they bounce into each other, then they would sometimes leave the surface. You can get that sort of excitation in the third dimension.

But if they're trapped, if they really are confined, you have like a layer of glass over your ping pong table, then they really are trapped in there. And the only way they can move is in two dimensions. I see. So the electrons are sort of stuck to the surface of the liquid helium? Yeah, it's some weird chemistry thing where they're stuck to the surface of the liquid helium. I like how you say it's some weird chemistry thing when you don't have a good answer. That means I don't understand it. I'm not a chemist. All the chemistry is some weird chemistry thing to me.

All right. So that's one kind of 2D pseudo object. What are some other kinds? The most interesting and I think the most exciting is this thing called graphene. Graphene is a 2D sheet of carbon atoms that assemble themselves into an object. You know, that carbon can make lots of different things. It can make diamond. You can make graphite, which is basically coal, but it can also make all sorts of other things. And I love carbon and all of its forms because it really makes a point, which I think is really deeply true about the universe, which is that the nature of an object is not about what it's made out of, but about how those things are put together.

So you can put the same carbon atoms together to make a diamond or a lump of coal. And that really tells you that it's really just about how you build the thing. And there's a really weird and unique way that you can build it to make this single atomic layer of carbon atoms. And they call that graphene. Yeah, that was the Nobel Prize maybe like 10 or 15 years ago, right? Where they discovered it by using

scotch tape on a pencil lead shavings. Yeah, in 2010, they won the Nobel Prize for an experiment. They published in 2004. And these are two folks in the UK that, as you say, use scotch tape. They took like pieces of graphite and they realized

that if you get scotch tape on the graphite and you pull it away, you get thinner pieces of graphite. Sometimes very very, very thin. And then they would pry these pieces of scotch tape open and they would do it again and again and again until they got mono layers of graphite, which they called graphene. Right. It's like you create like a sheet of single carbon atoms.

Yeah, a sheet of single carbon atoms. Now in your mind you might be imagining like that they're rolling out some huge roll of this stuff that's like 10 meters by 10 meters. What they were able to do in their first paper were pieces of graphene that were 10 microns in size. That's still pretty big. I mean, it's like, you know, maybe a couple hundred atoms in each side. Absolutely.

So it's pretty impressive. And they had some bigger pieces that you could see by eye that weren't actually down to one atomic layer. There were like several atomic layers. This is not a very precise method, you know, scotch tape on pencil shavings, essentially. I mean, it's not like duct tape. If you use duct tape, then you're really doing real physics. I would guess that every experimental physics Nobel Prize, since duct tape was invented, has had duct tape somewhere in their experiment. you go that Mr. Duck should get his own prize in engineering somewhere.

But it also means that we've probably all been generating sheets of graphene every time we've used pencils because this stuff really is so brittle. You get these little sheets of graphene, these two-dimensional materials falling off of your pencils. Yeah, and graphene is interesting because it's not just like flat, almost two-dimensional, but it has some pretty amazing properties, right? It's really an incredibly different kind of stuff than graphite. You know, graphite this stuff in your pencil, not very strong, right? You wouldn't want to build like a sheet of armor out of this stuff.

But graphene is 200 times stronger than steel by weight. And it's like a sheet of it is a thousand times lighter than a sheet of paper. What does that mean stronger? Like if you pull in it or try to poke through it, it'll be stronger than if you made it out of steel. Mm-hmm. It can support the weight. So you could hang something from it, for example, or build things out of it. It's stronger than steel.

You could, for example, make a hammock that's so thin, it'd be invisible, and a cat could sit on the hammock and be, like, floating in air. Cool. And it also has interesting electrical properties, right? It's really an incredible material because it has the most electrical and thermal conductivity of any material we know about at room temperature. So it's like the strongest, lightest, most electrically conductive, most thermally conductive material, basically we've ever discovered. Now, is the idea then to make, like, computer chips out of it? Like instead of using silicon and, you know, doping it and printing it, you could maybe draw it using graphene. That was the original idea because we know that chips need to get smaller and smaller

for computers to get faster and faster. But we're sort of approaching the limit of what semiconductors can do. And it's really hard to imagine making things that are smaller out of metal. So these guys achieved creating a material which is electrically conductive and so can be used to form these chips. and is super duper narrow. So that's exactly what people are working on applications of graphene to do electronics and computer chips, but also construction, you know, making things out of this new kind of

material. Right. Like you can maybe stack these sheets and make super strong body armor basically or anything, right? A house. Yeah. And you get really weird properties. Like you can make sheets of graphene, but there are also other kinds of materials you can now make monolayers of.

And you take one sheet of graphene and a sheet of something else. And you can make these weird structures. They call heterostructures that now have other really strange properties. And so because these are weird 2D materials, you can stack them together to make 3D sort of like designer materials. You can make materials that are totally different from anything we've been able to make before. So it's opened up this whole new field of like engineering new kinds of materials. So you could build a house and then you could let your kids draw on it with a pencil and it'd be totally acceptable. You're like, I have nothing.

I have nothing for that, Jorge. That's a cartoonist dream house, it sounds like to me. All right, so then you could also make these 2D materials using quasi particles, which I know we talked about before, but maybe we didn't talk about the two-dimensionality of them. Yeah, quasi-particles, remember, are things that are not particles in the way that we think about them, but mathematically they follow the same rules as particles.

And so the way I think about it is like, well, a particle is a little excited blob of energy in a quantum field. you could also have excited blobs of energy and other stuff that stays sort of localized and moves around and so sort of follows the same math that we use to consider particles. And the kind of thing you can deposit energy into is like a sheet of plasma. You know, plasma is this fourth state of matter where you heat up stuff hot enough that the electrons go free and you have this basically gas of charged particles like what's in the sun is plasma or what's in your fluorescent light tube is plasma plasma because it's charged it has lots of really strong electromagnetic forces and so sometimes

it forms these sheets you know it's like separates into sheets like a positive sheet and a negative sheet and those sheets can have excited states sometimes like ripples go through those sheets and they act like particles so that's a quasi particle that's called an anion yeah and i know what's kind of exciting about these materials is their application in things like quantum computers right and encryption and making things that are sort of foolproof against quantum decoherence. There are certainly applications in quantum computers for some quasi-particles. I think for me, the exciting thing about them is that they follow rules of a different universe. They follow the rules of a two-dimensional universe, like the mathematical rules.

The things we're talking about very early in the top of the program, like, why is our universe 3D and not 4D and what would it be like? We can sort of see what a 2D universe really would be like. And we have the math to describe it, but now we actually get to see the physics of it. And you might wonder, like, well, what would a 2D universe be like? How could that be different? You know, in a two-dimensional universe, there's a different relationship, for example, right, between energy and velocity.

Like in our universe, energy is one-half mv squared, right? There's a v squared there. But in a two-dimensional universe, it's not v squared. It's a linear relationship between energy and velocity. So that's the kind of mathematical difference. You get like different kind of physics in these, 2D universes. And so you can see that happening in these examples. And especially weird for anions is that they follow different spin statistics. Like we have particles in our universe

that are either fermions or bosons. And fermions don't like to exist in the same quantum state, whereas bosons are happy to hang out in the same quantum state. Well, anions can be somewhere between fermions and bosons. They're not like fermions exactly. They're not like bosons exactly. They're like, has sort of like fractional in-between states. Cool. You'd have to start a whole new field called cartoon physics, basically, right? Like, it's a whole new, different, whole new ballgame. A whole new comic book.

It's a whole new ballgame and a whole new way to, like, explore the universe and see weird stuff and to get surprised. Well, it sounds pretty cool. It sounds like 2D objects are not just possible and theoretical, but they're also right here in our universe. You can make them, you can create them, you can sandwich them, you can make pizzas out of them. put anchovies on them. And so that opens things up to a lot of interesting new math and maybe a whole bunch of new materials. And so to have the last word,

we'll bring back Professor Rouhani to tell us a little bit about the future of these new and exciting materials. Oh, I think there is a lot of research already in experiment. Even at UCI, I need a lot of research in different two-dimensional materials. Graphene is not the only one. There are materials, so-called wonder-vose materials. And these are layered materials that you can imagine as very similar to the graphite,

of which you can peel off the graphene. So you have very weakly connected layers and then you can just peel the layers off of these materials. And what people can do with them is kind of engineer the band structure and therefore together with that engineer physical properties of material and create new type of material with completely new physical properties just by putting these layers on top of each other. like making a sandwich or something of them. They are doing experiments using oilso-grapine and hexagonaboronoboron nitride

and other, like, wonderful materials. And I think the transition metal, like calcogenites, I can pronounce, that you can use to build these different kind of so-called heterostructures when you just layer these different two-dimensional materials on top of each other and then create new types of materials. and, you know, examine how do I change the physical properties? Can I make a superconductor or can I make out of, you know, like I have graphene, which is insanely good conductor, but if I layer it, then maybe it will become an insulator

and so on. So, you know, all of these questions. And I think it's very nice because it's kind of a playground and you can build so many things with this and not just, you know, like kind of try to engineer and make functional materials that you can then use in applications for, you know, the semiconductor business, which is huge, right? So you can just make, you know, faster or more efficient chips and stuff like that. But also completely new technologies. And I think a lot of research is already put in the past, I think, 10, 15 years. So you can take bread, slice it into slices and then rebuild it

in different slices to make whatever you like, to make all sorts of new stuff. Yeah. You can use synthetic materials. Yeah, you take a slice of bread, which is not a bread anymore. It tastes completely different. And then you put some ham on it. And it's not a sandwich. It's just something entirely different. You know, it's like it's insane.

All right. That was a deep dive into some 2D ideas. Sounds like the future is bright for these 2D objects. Yeah. And people are just now thinking about even crazier ideas. Like mathematically, can you have a 1D object? Can you construct an object that's just a string of atoms? that are somehow bound together.

What would be the properties of that kind of thing? How could you make it? Could you like take graphene and somehow like slice it off using 2D scotch tape to make 1D strings? Is that the next Nobel Prize? Oh man. I feel like you should take it easy and just maybe go one and a half D first. You know what I mean? Like that's crazy.

Hey, well, my wife says I'm two dimensional. So I got to cut down. You're kind of going to D diet. Exactly. But until then, we can have fun thinking about these things, wondering what the math is like. in a one-dimensional universe, and maybe one day somebody will build a 1D object, and we can actually see how electrons move along it in one dimension. Right. You just have to look at it from the side. You can't look at it head on.

All right. Well, we hope you enjoyed that. Thanks for joining us. See you next time. from iHeartRadio, visit the iHeartRadio app, Apple Podcasts, or wherever you listen to your favorite shows. Boys. Then everything changed. There's been a bombing at the TWA terminal. Just a chaotic, chaotic scene. In its wake, a new kind of enemy emerged. Terrorism. Listen to the new season of Law and Order Criminal Justice System on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. My boyfriend's professor is way too friendly, and now I'm seriously suspicious.

Wait a minute, Sam. Maybe her boyfriend should be. just looking for extra credit. Well, Dakota, luckily, it's back to school week on the OK Storytime podcast, so we'll find out soon. This person writes, my boyfriend's been hanging out with his young professor a lot. He doesn't think it's a problem, but I don't trust her. Now, he's insisting we get to know each other, but I just want her gone. Hold up. Isn't that against school policy?

That seems inappropriate. Maybe find out how it ends by listening to the OK Storytime podcast on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. every case that is a cold case that has DNA right now in a backlog will be identified in our lifetime on the new podcast america's crime lab every case has a story to tell and the DNA holds the truth he never thought he was going to get caught and i just looked at my computer screen i was just like gotcha this technology's already solving so many cases listen to america's crime lab on the iheart radio app apple podcasts or wherever you get your podcasts This is an IHeart podcast.