Daniel and Jorge Explain the UniverseIs it possible to have a two-dimensional object?
Daniel and Jorge slice the Universe infinitely thin and talk about the theory and practice of 2D materials
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Hey, Daniel, you used to live in Chicago, right.
Yeah, I did when I was working at the accelerator at Fermilab.
Does that mean you like Chicago style pizza?
Oh? My god, that is not pizza. That's like a castle role, it's like a marinera swimming pool. I mean it's delicious, of course, but it's not actually pizza.
Oh there's our 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 halted.
I don't know, it feels possible. I guess I need 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 two d toppings too? Maybe that's why people in New York are so thin. They have no death, they're so shallow. I am or hammade 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 pinions about particles. About physics and about pizza and dessert and big goods. You have a lot of strong opinions, Daniel.
I'm 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 big slab of Chicago style whatever you call it, is also.
Delicious whatever 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 pizza.
That's a pizza taco.
But welcome to our podcast Daniel and Forehead 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 a Nobel price 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 Noble price. You know. That's a little bit of intellectual rites.
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 parkles 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 three D? 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 are wondering about the dimensions of the universe.
I was.
I mean, this is not six year old Dame though, this is probably fourteen 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 fourteen 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 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, 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.
That 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, hmmm, 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? 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 two hundred years people will look back and think, I can't believe they used to think XYZ 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 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 could put on schovies, 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 eleven or twenty six dimensions. Some of these theories that unify gravity and quantum mechanics, things like string theory, which might be 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 eleven or twenty six 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 eleven or twenty six?
Yeah, and equally as mind blowing is to think it's 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 all less than three dimensionals in their being.
That's a super fun idea. And there this whole class of theories that suggests that maybe the entire three D 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 let's people do calculations that otherwise would be impossible.
I feel like this podcast is kind of two dimensional, Daniel, because you know, 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 that 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 forty five 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 two D podcast.
I don't know, maybe we're zero dimensional. I can't even tell. What does it mean to have a dimensionality in audio? I guess we're in stereo, so that's two D 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 three D 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 too 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 too dimensional? Now, Daniel, is that too 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 too dimensional. Stop being so dimensional.
I think she's starting to tell you you need to go in a diet. Maybe she's like, you have too many dimensions that 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 a kind of a crazy question. Question is can an object be two dimensional? Like the object itself only exists 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 three D space. And it's hard to imagine an object having four dimensions in our three D space. But why can't a 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 strange 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 be 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 me two questions at Daniel and Jorge dot com.
Here's what you 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 extent hy exist, 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 or there for three dimensional. But I think there are situations way. For instance, if you have one layer of graphine, it is certain that it is treated as if it's two dimensional. Then I'm not sure about this, but I think with the moldest conjecture, because with the conformal field theory, you treat a three dimensional object, for instance a black hole by looking only at it's like surface or surface area. By translating it from the string theory to the CFG, 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 two D.
We got rejected exactly.
And you had a third answer also, but the one didn't make the cut.
Is that a two D three D joke.
To take a joke out of the out of this flat topic.
That I'm impressed by the depth of your sense of humor.
All right, So none of the answers seem to think you can have a two D object. One of them said that because Adams a volume, and the other one said because we live in a three D space. So let's get into these strange conundrums. So Daniel, first of all, what would you you say is a two D object? How would you define it?
As usual, the definition is going to be critical as to exactly what we mean by a two D 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, would make it three dimensions. So a two D 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. It 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 then 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 don't only exist on that two D space, you know, basically flat land.
Yeah, I'm a cartoonist and so, you know, making things two D is 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're stuck in 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 infinitive number of slices of two D pizza and you've eaten zero volume of pizza.
Yeah, 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 two D 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 weir thin?
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Now we will sputter a layer of pizza two D pizza onto your tongue. Yeah, because you can't pick it up right.
Well, I guess the question is is it possible it 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 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 one D object by having two of them, and then the line between them is a one D object, and four of them are 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 one 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 and 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 you know the particles are point objects, but they have kind of a three D presence.
Yes, they do have a three D presence, because how would you build that one D 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 three D 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 they 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 two D object, right.
That's a two D object, But it fails the other test, like could you stack another one on top of it exactly and get zero 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 three D object. It's just sort of like a very thin tube.
All right. That was your yes answer. What's your maybe answer?
Yes, So the yes answer was start from zero D particles, you can The no answer was zero D particles really have three D 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 a minimal thinness, right. 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 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 two D 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 two D 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 two D 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.
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All right, we're talking about two d objects, Daniel, and now this is a podcast. Does that mean that listeners have to put on like two d earphones, like a red and a blue one. Would that help?
Well, they're hearing the answers in two d right, one from me and one from you.
I guess, yeah, dudes, two dudes, just two dads or dudes. So technically it is a two d podcast.
That's right. And sometimes we agree with each other and sometimes we don't.
Sometimes it is 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 to the objects. And as I understand, the physics does allow for theoretical to the objects.
Yeah, theoretical to the 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 for 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 cartoon is. 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 three D world into a two D 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.
Mm, you mean, you're cheat.
It comes down to the definitions.
I mean, it's kind of like just stacking pixels on top of each other kind of right. It's kind of like than a three D 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 one Maldicena is called ADSCFT because it shows us how one set of theories ADS which means anti dissitor 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 time, that three D movies are really just movies.
Right, And so the idea is that maybe our entire universe that we think is three D is actually only two D, 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 mean that fundamentally the whole universe really is two D.
Yeah, we're all inside a comic book, right, It's like everything in the universe is a two D 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 exis the two D 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 two D surface to project out into a fully realized three D world.
Well, I called 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 you're really not going anywhere.
Does that counts exercise? When Superman flies? Does he burning calories? This his fifth bit counted?
Well, I think he can fly if he doesn't get enough sun, So technically I guess he is expending energy.
Is that right? He can't fly but he 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 sunwar So he's basically a plant, basically a super solar cell. Yeah, solar battery all right, Well, so that's one kind of 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 three D world, right.
Yeah, And earlier we were talking about building things which are the thinnest that could possibly be in a quantum universe. Thedea, there is that the universe we don't think is infinitely dividable. We don't think we can take a mile and cut in half and then cut in half again, and cut and half 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 two D material. Now, the problem is that we think that distance, if it exists, is probably really really small, like ten to the minus thirty five met 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 those electron wave length. So which one are are you? Are they the same or which one are you 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 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. 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 the 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 two D 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 nof.
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 you 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 sharpen your pencil, you are generating these sheets of graphine.
Interesting, So like carbon kind of likes to do that, right, Like it kind of likes to arrange itself in those sheets and not like the 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 like 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 UC Irvine, is this is 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 and named Judith Rohanyi, 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 two D 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 this one dimensional world.
Yeah, she's actually a theorist, so she mostly like 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. 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 Rohani had to say.
So you know, like for theorists, anything is possible, right, because I just to come on and then say like, well, it's just consider something that has two spacial dimensions instead of three, and that would give me some kind of confinement. So you know my mobile of Porticus 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 or three dimensions, right, So that's very different. It's like, I guess if you ask this question like fifteen years ago, I also say like, yeah, two D is very terretical. There is no such thing as.
A two D material, right, because why would it not like fold up, you know, like like you know, why would it stay like straight as a sheet of paper or something, or how could it exist? Like what would stabilize.
Anything like that? And now it turns out that 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 autom thick or maybe maybe still it is a better way to say, or maybe just a few atoms in, like maybe two or three atoms in, and that's that's actually possible to create these materials. So actually kind of field off from their three dimensional so let's say modern material or different types of materials, they really exist and people are doing different kind of experiments and so it's not just in all theoretical dream anymore. It's actually an existing thing, which is very exciting because they do have a lot of these similarities to sred action sudium models or materials.
All right. I like, as 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 forties and fifties, people were wondering, is this really possible? They were thinking about it and theorizing about it, and only recently, only like twenty 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 D world.
Yeah, and it makes the thing really really different. And that's what's really interesting. It's that if you take a whole loaf of bread and you cut in half, you have half a loaf of bread, 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 bread or biscotti. It turns into biscatti. You know, you have to pay like a few bucks more Starbucks to get.
Yeah, put tomato, sauce and cheese on it and poor, hey, we'll 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 to the objects. Are any of these actually realizable in our world? And maybe they're all around this, So let's get into that. But first let's take another quick break.
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All right, Daniel, we're talking about real life to d objects.
Now.
We talked about it in theory. It could be that we're all in the too the world, or maybe you can make electrons behave like they're in two demands, but in the real world that we live in, at least that the one that seems like it's three dimensions. Can you have two of the 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 three D 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 two D object? Hmmm?
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 this step us through what are some of these real life to the objects or three the objects that behave like to the 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, and 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 pingpong 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 and 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.
And like how you say it's some weird chemistry thing. I mean, you don't have a good answer.
That means I don't understand it. I'm not a chemist. All of chemistry is some weird chemistry thing to be all right.
So that's one kind of two D pseudo object. What are some other kinds?
The most interesting, and I think the most exciting is this thing called graphene. Graphene is a two D 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, and that was the Nobel Prize maybe like ten or fifteen years ago, right, whereas they discover it by using scotch tape on pencil lead shavings.
Yeah, in twenty ten. They won the Nobel Prize for an experiment they published in two thousand and four. And these were 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 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 ten meters by ten meters. What they were able to do in their first paper were pieces of graphene that were ten microns in size.
That's still pretty big. I mean it's like, you know, maybe a couple one 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 then you're really doing real physics.
I would guess that every experimental Nobel prize since duct tape was invented has had duct tape somewhere in their experience.
That mister Ducks 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 riddle. You get these little sheets of graphine, these two dimensional materials falling off of your pencils.
Yeah, and graphine 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 is 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 two hundred times strong, longer than steal 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 can 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 normally 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 graphine.
That was the original idea because we know that chips need to get small learn 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 as a sheet of something else, and you can make these weird structures they called heterostructures that now have other really strange properties. And so because these are weird two D materials, you can stack them together to make three D sort of like designer materials, 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 can 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 for.
That, or right, that's a cartoonist dream house, it sounds like to me.
All right. So then you could also make these two D 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 and has lots of really strong electromagnetic forces, and so sometimes it forms these sheets, you know, it's like separates into sheets, like 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 enion.
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 full proof against quantum decoherence.
There are certainly applications in quantum computers for some quasi particles. I think that. 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 mathematical rules. The things we were talking about very early on the top of the program, like why is our universe three D and not four D and what would it be like? We can sort of see what a two D 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 two D 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. There'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 two D universes, and so you can see that happening in these examples. And especially weird for enions 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, 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 two the objects are not just as 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 atrophies 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 Rohani to tell us a little bit about the future of these new and exciting materials.
Oh.
I think there is a lot of research order in experiment even as you see I and a lot of research in different two dimensional materials. So graphin is not the only one. There are materials so called wonderbose materials, and these are layered materials that you can imagine as very similar to the graphite of which you can peel off the graffine, so you have very weakly connected layers and that you can just peel the layers 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, making a sandwich or something of them. They're doing experiments using osograffine and hexagona boronitride and other wonderbose materials. And I think the transition metal like co genites I can pronounce, yes, that you can use to be ad these different kind of so called heterostructures when you just layer you know, these different two dimensional materials on top of each other and then you know, 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 graffine, which is insanely good conductor, but if I layer it and maybe become an insulator and so on. So you know, all of the discussions 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 ten to fifteen years.
So you can take bread, slice it and the slices and then rebuild it in different slices to make whatever you like, to make all sorts of new stuff. Yeah, synthetic materials.
Yeah, I think 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 stand, which is just something entirely different.
You know.
It's so it's insane, all right.
That was a deep dive into some two D ideas. Sounds like the future is bright for these two D objects.
Yeah, and people are just now thinking about even crazier ideas, like mathematically, can you have a one D 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 two D scotch tape to make one D strings? Is that the next Nobel Prize? Oh?
Man, I feel like you should take it easy and just maybe go one and half the first, you know what I mean? Like that's crazy.
Hey, well my wife says I'm two dimensional, So I got a contention.
Can of going out the 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 one D 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.
Thanks for listening, and remember that. Daniel and Jorge Explain the Universe is a production of iHeart Radio. For more podcasts from iHeartRadio, visit the iHeartRadio app, Apple Podcasts, or wherever you listen to your favorite shows. When you pop a piece of cheese into your mouth, you're probably not thinking about the environmental impact. But the people in the dairy industry are. That's why they're working hard every day to find new ways to reduce waste, conserve natural resources, and drive down greenhouse gas emissions. House US dairy tackling greenhouse gases. Many farms use anaerobic digesters to turn the methane from manure into renewable energy that can power farms, towns, and electric cars. Visit you as dairy dot COM's Last Sustainability to learn more.
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