Is 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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Episode Transcript

Speaker 1 (00:08):
Hey, Daniel, you used to live in Chicago, right, Yeah,
I did when I was working at the accelerator at Fermulab.
Does that mean you're like Chicago style pizza? Oh my god,
that is not pizza. That's like a castle roll, that's
like a mara neara swimming pool. I mean it's delicious,
of course, but it's not actually pizza is our tough
words for a Chicago style pizza. Does that mean you

(00:29):
prefer it in pizza like New York style pizza? Oh? Yeah, absolutely,
like the thinner the better, really like health it. I
don't know if it was 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 to the toppings too? Maybe that's why

(00:49):
people in New York or so thin. They have no death,
they're so shallow. Hi am or handmade cartoonist and the

(01:12):
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 penis 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

(01:35):
also a nice big slab of Chicago style whatever you
call it is also delicious whatever. And you don't even
want to call it a pizza. I don't know. It's
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 and a calzone is just a

(01:57):
close pizza. That's a pizza taca. But welcome to our podcast.
Daniel and Joorhead apparently talk about pizza and explain the
universe in production of I Heart Radio, a podcast which
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 conform, the

(02:17):
weird things that they 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

(02:39):
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 you have a Nobel
price there on top. Please just shaved Nobel prize on top.
That sounds pretty good. Yeah, you know, like gold shavings,
something that's edible. Right, you can also do that with
a Nobel price. You know, just adds a little bit
of intellectual richness to the smartest pizza ever. Yeah. We

(03:02):
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

(03:24):
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,

(03:45):
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're wondering about the dimensions
of the universe. I was. I mean that this is
not six year old Daniel, 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 too Spider Man's web? After all? So yeah, I

(04:06):
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

(04:27):
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

(04:48):
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

(05:10):
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

(05:31):
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 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

(05:53):
minds and understand like the true nature of the universe.
And we've done this lots of times as humans, discovering
the univers 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 X,
Y Z, whatever it is we're thinking now. Yeah, I
wonder if fish go fishing for ideas Also, I wonder

(06:16):
if they play Go Fish or if they have another
game called Go Human or something. And when are the
New York style pizza. Now that's a mind blowing multidimensional
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 on shovies, and
then that brings it all around to the fish idea.
But getting back to our dimensional question, it is weird

(06:37):
to think about the world 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 is having eleven or twenties six dimensions. Some
of these theories that unify gravity and wanted mechanics, things

(07:01):
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

(07:22):
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 in three or what if there
are things out there that are a less than three
dimensionals in their being. That's a super fun idea. And
there's this whole class of theories that suggests that maybe
the entire three D universe is actually just a hologram

(07:46):
of a two dimensional universe, meaning that we are actually
two dimensional beings. We're gonna 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 you know,
we don't go very deep here, No, we have to
pick one topic to go deep on, but we're always

(08:08):
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 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

(08:28):
it mean to have a dimensionality and audio? I guess
we're in stereos that's two D maybe. But anyway, so
today we're gonna 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

(08:49):
that on a podcast recently, you could disappear from inside
of 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,

(09:18):
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. Yeah. I
think he's starting 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 you

(09:39):
to have some fractional dimensions. So this is a kind
of a crazy question. Question is can an object the
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

(10:01):
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 it? Objects have two dimensions be essentially only
X and y and have no height right to be

(10:22):
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 um multidimensional or a
dual dimensional quarry. So, as usual Daniel went out there

(10:44):
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 here your speculation on the podcast, please
write to me two questions at Daniel and Jorge dot com.
It's what people had to say. I don't really think
that an object can be two dimensionals in a three

(11:05):
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 extent in the extent y
axis but they don't go into the Z direction, that

(11:26):
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 as songs have volume and
or there for three dimensional. But I think there are
um situations where, for instance, if you have one layer
of graphine it is so thin that it is treated

(11:48):
as if it's two dimensional. Then I am not sure
about this, but I think um with the modesty in
a conjecture, because with the conform of fuel theory, you
treat a three dimensional object, for instance a black hole
by looking only at its UM like surface or surface

(12:12):
area UM by translating it from the strength theories of
the cf G, you almost treated as if it's two dimensional.
I think, um, that might be an example. Alright, some
skepticism here, and none of these two said, yes, something
can be too D. We got rejected exactly, and you

(12:32):
had a third answer also, but no one didn't make
the cut. Is that a two D three D joke
joke 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
it to the object. One of them said that because
adams have volume, and the other one said because we
live in a three D space. So let's get into

(12:54):
these strange conundrums. So Daniel, first of all, what would
you say, is it to D object? How would you define?
As usual? The definition is going to be critical is
to exactly what we mean by 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

(13:16):
define your location in space, and so you can think
of an object having like one dimension is aligned two dimensions,
would be a square and any height on that square
would make it a cube. I would make it three dimensions.
So a two D object would be something that had
no measurement in the third dimension, that it's location in
the third dimension had only one edge, not two edges,

(13:40):
doesn't have like a start and an end. It's start
and end are exactly the same location. So it's you know,
it would be essentially infinitely flat sheet of paper for example.
You 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

(14:00):
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 fin that. We're looking for

(14:22):
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 would only exist on that
too D space, you know, basically flat land. Yeah, and

(14:43):
my cartoonists and so, you know, making things two days.
It's 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
stuck in a whole bunch of them together, they would
still be flat, they would still have zero height. Yeah,
because any number of times zero is zero. So you

(15:05):
can eat an infinite number of slices of two D
pizza and you've eaten zero volume of pizza. You won't
even grow in one dimension like your belt size dimension
no is 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? Thin?

(15:25):
Have we invented the perfect two D diet? Two D
Quantum Diet by Daniel? Download the app mat 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 at all to have
an object that is like that, that is infinitely thin?
Are there loss of physics that would prevent it? Or

(15:46):
is it theoretically possible? So I still have three answers
to that, you know, 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. There are point particles. We
don't know if the electron has any substructure in it,

(16:08):
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, and
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

(16:31):
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 quirk right,
and I lined it up with like a hundred other
quarts 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

(16:55):
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 you know particles are point objects,

(17:15):
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.

(17:36):
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 on that line.
Like let's say you empty out the universe. The universe

(17:56):
is empty and you only have two quarks. That's technically
to the object, 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

(18:16):
yes answer? What's your maybe answer? So The yes answer
was start from zer D particles, you can The no
answer was zer y 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 minimal thinness. Right,

(18:37):
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,

(18:58):
if something is thinner than the quantum minimum distance, then
you you kind of have to say it's flat, perfectly flat, right,
because you can't resolve that it's any thinner. You couldn't
have a thinner object except for in your mind as
a geometer imagining perfect to D objects. But in our
universe things you could build, you couldn't have a thinner object.

(19:20):
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 have tried
to avoid being shallow. All right, well, let's get it

(19:42):
into whether or not there are theoretically to the objects
out there and whether or not they exist in the
real world. At first, let's take a quick break. Alright,

(20:04):
we're talking about to the objects, Daniel, And now this
is a podcast. Does that mean that listeners have to
put on like two d your phone, 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, dude, two dudes, just
two dads or dudes. So technically it is a to
D podcast, that's right. And sometimes we agree with each

(20:25):
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 to mention. 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 that the physics does
allow for theoretical to the objects, yea theoretical to D

(20:47):
objects are not a problem. But we talked before about
this idea of the universe as a hologram. Is there
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,

(21:08):
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

(21:30):
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.

(21:50):
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

(22:11):
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

(22:32):
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.

(22:53):
I mean, it's it's kind of like you just stacking
pixels on top of each other, kind of right. It's
kind of like in a three D movie that you
when you go to the theater, it's like it's 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 Maldasena is called a D S c F T
because it shows us how one set of theories a

(23:15):
d S which means anti disit or 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,

(23:36):
And so the days and 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,

(23:58):
So that's a fun idea, and it helps think about
how to solve black holes and construct string theories, and
goes to fund 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
two D. Yeah, we're all inside a comic book, right,
It's like everything in the universe is a two D

(24:20):
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 two D surface of the paper. You
imagine a whole rich world in your mind. You know,
a well drawn comic creates into 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

(24:41):
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 called 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 count as exercise? When Superman flies? Does he

(25:01):
burning calories? Does his fit bit counter? 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 but 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. Where so he's basically
a plan basically a super solar cell. Yeah, solar battery.

(25:26):
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 all some ways in which
the theory says that you can't 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 they could possibly be in a quantum universe. Idea

(25:47):
there is that the universe we don't think is infinitely dividable.
We don't think you can take a mile and cut
in half and then cut it half again, and cutn't
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

(26:07):
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. The problem is that
we think that distance, if it exists, is probably really
really small, like ten to the minus thirty five, and

(26:28):
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

(26:49):
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 small
holler than the smallest resolution of the universe, and the
other one is making things smaller than the electron wave length.
So which one are Are they the same or which

(27:10):
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 unifer an electron,
is much much larger, and something that's really kind of
achievable because an electron has an extent in space which

(27:34):
is much more significant. So you know, can you build
something which makes it so that electrons can only move
in two dimensions? That could 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, and 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

(27:56):
that where the electrons only move in two dimensions, then
you might cansider 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. Are you talking about making something
that's just one layer of atoms? So the basic idea

(28:17):
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 cork and you line it up
and you make a sheet of corks. 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.

(28:40):
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 layer up

(29:01):
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. Really, are you saying my
ideas have no no? It turns out that you make them.

(29:23):
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

(29:44):
time you write on a surface of paper or you
sharpen your pencil, you are generating these sheets of graphine
just things. So like carbon kind of likes to do that, right,
like it, 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 like

(30:06):
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 C 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 named Judy Rohani.

(30:28):
She's very friendly. She's from Hungary and she just came
to u C I about a year and a half ago,
and she arrived during the pandemic, which means she's never
really gone to experience the campus life here. Wow. And
so she works on these two de 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,

(30:50):
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 the 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 Roney had to say, So, you know what,

(31:11):
like for theories, anything is possible, right because I just
take a TI to come on and then say like, well,
I just considered something that has two spatial demensions dimensions
instead of three, and that will give me some kind
of confinement. So you know, my mobile particles for examples,
like electrons, they can only move in two dimensions, but

(31:31):
not in the third dimension. And then then it 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 fifteen years ago, I was just like, yeah,
today is very theoretical. There is no such thing as

(31:52):
a two de material, right because why would it not
like fold up like that, you know, why wouldn't 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

(32:13):
is say like one automn thick or maybe maybe still
it's 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 bail them off from their three dimensional
let's say modern material or different types of materials. They

(32:35):
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 dissimilarities to see the
action three D models or materials. All right, I like it,
As she said, for a theorist, anything is possible. I

(32:57):
think I 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

(33:18):
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. If that

(33:40):
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 biscotty. You know, you have to pay
like a few bucks more starbucks, get put tomato, sauce

(34:01):
and cheese on, and poor he 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

(34:21):
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

(34:42):
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. All right, Daniel, we're

(35:03):
talking about real life to the objects. Now we talked
about in theory. It could be that we're all in
the to the world, or maybe you can make electrons
behave like they're in two dimensionals. But in the real
world that we live in, at least that the one
that seems like it's three dimensions, can you have to
the objects? So you sort of can, I mean it's
a little bit cheating. They're not technically two dimensions because

(35:26):
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

(35:48):
three dimensions. 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 gonna be talking about,
we see the mathematical relationships you expect from a two

(36:10):
dimensional world, not a three dimensional world. I see. So
there are 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? Interesting like if you do live in a cartoon?
Are you really real? If you cosplay enough a cartoon,

(36:32):
are you really in that cartoon? No judging, no judging.
So to 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

(36:52):
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

(37:15):
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

(37:37):
things on balls on the table, right like it 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 bounced 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 there really are confined you have like
a layer of glass over your ping pong table, then

(37:58):
they really are trapped in there, and the only way
they can move is in two dimensions. And 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 are stuck to the service of the liquid helium.
And like how you say it's some weird chemistry thing
and 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 be all right. So

(38:20):
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 graph being graphing 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

(38:41):
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 some
out how you build the thing, and there's a really

(39:02):
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 where they
discovered it by using scotch tape on a pencil lead shavings. Yeah,
in two thousand and ten. They won the Nobel Prize
for an experiment they published in two thousand four. And

(39:24):
these are two folks in the UK that, as you say,
you 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
pride these pieces of scotch tape open, and they would
do it again and again and again until they got

(39:44):
mono layers of graphite, which they called graphine. 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 by ten meters.
What they were able to do in their first paper
were pieces of graphing that were ten microns in size.

(40:06):
That's still pretty big. I mean it's like, you know,
maybe a couple of hundred adams in each side. Absolutely,
so it's pretty impressive. And they had some bigger pieces
that you could see by I they 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 used duct tape, then then you're

(40:28):
really doing real physics. I would guess that every Experimental
physics Nobel Prize since duct tape was invented has had
duct tapes somewhere in their experience. That Mr Duck should
get his own prize in engineering somewhere. But it also
means that we've probably all been generating sheets of graphing
every time we've used pencils, because this stuff really is
so riddle. You get these little sheets of graphing, these

(40:50):
two dimensional materials falling off of your pencils. Yeah, and
graphing is interesting because it's not just like flat, almost
two dimensional, but it has some pretty using 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 two hundred times

(41:13):
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
will be stronger than if you made it out of steel.
You 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

(41:34):
hammock that's so thin it would be invisible, and the
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

(41:55):
electrically conductive, most thermally conductive material basically we've ever discovered it.
Now is the idea then to make like computer chips
out of it, Like instead of using silicon and you know,
doping in and printing it, you could maybe draw it
using graphing. That was the original idea because we know
that chips need to get smaller and smaller for computers

(42:15):
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

(42:35):
are working on applications of graphing 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 the house. Yeah, and you get
really weird properties, like you can make sheets of graphing,
but there are also other kinds of materials you can

(42:56):
now make model layers of and you take one sheet
of graphing as sheet of something else, and you can
make these weird structures they're called hetero structures 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. You can
make materials that are totally different from anything we've been

(43:17):
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 can let
your kids draw in it with a pencil and it'd
be totally acceptable. Right, You're like, I have nothing, I
have nothing for that. All right, that's a cartoonist dream house,
it sounds like to me. All right. So then you
can also make these two D materials using quasi particles,

(43:41):
which I know we talked about before, but maybe we
didn't talk about the two dimensionality of them. Yeah, quasi particles. Remember,
our things 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 and a quantum field. You can also have
excited blobs of energy and other stuff that stays sort

(44:04):
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

(44:26):
is plasma or what's in your fluorescent light tumbe 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, a positive sheet in a
negative sheet, and those sheets can have excited states. Sometimes
like ripples go through those sheets and they act like particles.

(44:46):
So that's a quasi particle that's called an en eon. 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

(45:09):
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 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 it do D

(45:31):
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

(45:53):
of physics in these two d universes, and so you
can see that happening in these examples. And it's especially
weird for an eons 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

(46:15):
out in the same quantum state. Well, anyons can be
somewhere between fermions and bosons. They're not like fermions exactly,
They're not like boson's 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 and different, whole new ball game,

(46:36):
whole new comic book. It's a whole new ball game
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 to 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 entovies on them, and so that

(46:58):
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 already in experiment even as you
see I I and a lot of researching different two

(47:19):
dimensional materials. Graphin is not the only one. There are
materials so cood, wonderbos materials, and these are layer materials
that you can imagine as very similar to the graphite
of which you can peel off the grappin, so you
have very weakly connected layers and that you can just
build the layers of these materials. And what people can

(47:41):
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 making a sandwich or something of them. They're
doing ex ments are using orso graphine and hexagonal born

(48:03):
n trade and other condropost materials. And I think the
transition method that could janites I can pronounce that the
perfectly yes, that you can use to build these different
kind of so called hetero structures when you just leave
your you know, these different two dimensional materials on top
of each other and then create new types of materials

(48:25):
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 graphine, which is insanely
good conductor, but if I leave you and maybe the
becompany insulator and so on. So you know, all of
discussions and I think it's very nice because it's kind
of playground and you can build so many things with

(48:49):
this and not just you know, I kind of try
to engineer and make functional materials that you can then
use in applications for you know, the semi conductor business,
which is huge, right, so you can just make you know,
faster for more efficient chips and stuff like that, but
also completely new technologies. And I think a lot of

(49:09):
research has already put in the in the past I
think ten fifteen years. So you can take bread slices
and slices and then rebuild it in different slices to
make whatever you like, to make all sorts of new stuff. Yeah,
synthetic materials. Yeah. Like think you take a slice of
bread which is not a bread anymore. It is completely different,
and then you put some ham on it, and it's

(49:30):
not a sandwich. Is just something entirely different. You know,
it's likely So it's insane. All right. That was a
deep dive into some to the 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

(49:51):
somehow bound together? What would be the properties of that
kind of thing? How could you make it? Could you
like take graphine and somehow like slice it off using
two the 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 a half D first, you know what I mean?
Like that's crazy. Hey, Well, my wife says I'm too dimensional,

(50:14):
so I gotta mechanic go on a 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. You just you have to look
at it from the side. You can't look at it
hit on. All right, Well, we hope you enjoyed that.

(50:34):
Thanks for joining us, see you next time. Thanks for listening,
and remember that Daniel and Jorge explained. The Universe is
a production of I Heart Radio or more podcast from
my heart Radio. Visit the I Heart Radio Apple Apple Podcasts,

(50:55):
or wherever you listen to your favorite shows.