What are quantum glasses?

Daniel and Jorge talk about finding order among the messiness of the Universe, and the strange frustration of quantum spin glasses.

 

See omnystudio.com/listener for privacy information.

Episode Transcript

Speaker 1 (00:09):
Daniel, where are you recording the podcast from these days?
Today I'm in my office at the university. Kind of disappointed.
Wanted you to be like at the control center of
the L C or right next to where the particles collide,
kind of like a sportscaster. Nothing so glamorous, but I
mean pain a picture for us. What is your office
look like? Is it like in a dark dungeon, or

(00:31):
is it at the top of the in the Penthouse,
at the Corner Office? You know, something in between. I've
got a nice window here with a view outside of
the southern California landscape, but it's not like the biggest
office on the floor. We've got some real big shots
around here. You're more of a meeting shot, small shot.
I'm a just right shot, your podcast shot now. Is

(00:52):
Everything in your office super organized, or are there like
huge stacks of papers everywhere? Well, I'm not the kind
of person who's at risk for because his desk collapses
under a huge tower of papers, but it's not exactly
like a well organized museum or anything. It looks lived in.
You know, I think lived in his code for missing.

(01:12):
I don't know. What do you call something that's like
halfway between being neat and missing. Well, I'm a physicist,
so I would call it a phase transition. It's like
a melting point. You're kind of like a slush, like
a slushy. I'm hoping that if they crank of the
A C maybe my office will organize itself into a
crystal and you'll freeze to death, also for serve for
future generations, but at least I'll look neat doing it

(01:34):
and you'll be pretty cool too. Hi, I'm poor. Hey,
I'm in a cartoonists and the CO author frequently asked
questions about the universe. Hi, I'm Daniel. I'm a professor

(01:57):
at U C Irvine and a particle is this who
worked at the large Hadron collider and I like to
think of myself as just messy enough, messy enough for what,
before not being neat, messy enough to have that lucky
stroke of insight, you know, when that pile of notes
you took three years ago at a seminar just sort
of falls into your view and provides that crucial piece

(02:18):
of information to unlock the puzzle you're working on. If
you're too neat and organized and everything's tucked away and
you never have that sort of serendipity. I see, and
I assume that because your scientists, you have this tested right,
you've a scientificity proven, like you've done the control of
studies where you're really neat and more missy. Yeah, I
have a bunch of other Daniels in the basement and
I make them be really neat and messy and I

(02:40):
keep track of their careers also, and I guess you're
the most successful one because you're not at the basement right,
so that proves your theory. I guess I'm the only
one with a podcast, which maybe means I'm a failure
as a scientist. I'm not sure the other ones are
actually doing physics. Is that what you're saying? They're still
newon research exactly, but anyways, welcome to our PODCAST, Daniel

(03:01):
and Jorge explain the universe, a production of my heart radio,
in which we try to find order in this messy universe,
this chaotic swirl of particles going to and fro weaving
themselves together into this incredible, beautiful reality that we want
to make sense of. While galaxies smash into each other
and particles annihilate each other, we step back and try

(03:23):
to organize all the things that are happening out there
in the universe into a crystalline set of ideas that
we can transmit along these audio waves into your brains.
It's right, because it is a pretty messy universe, full
of amazing and exciting things happening out there, particles crashing
into each other's black holes sucking up things. And yet
somehow we have, as humans, figured out that there is

(03:43):
a little bit of a order to all of this,
even if we aren't very ordered ourselves. And of course
we don't know if that order exists in the universe
or if it's just something we have imposed on it.
Does the universe actually makes sense? Are we just telling
ourselves these stories of UN in the philosophy of physics?
But so far it works for us. It lets US

(04:04):
build airplanes and transistors and all kinds of new materials
that ruin and save our lives. Are you saying the
universe is just messy enough? I'm saying it melts my
brain sometimes melts in your mouth. All that knowledge, I wonder,
what would you like if the universe melted in your
hand instead of your mouth? Well, first of all, can
you hold the universe in your hand? Only has a
thin candy coating, right, but you are in the universe

(04:27):
also putting your hand the inside the Eminem two. We
are all EMINEM's. That's the philosophy on this show. But
are you the chocolate or are you the candy? and
which color is your eminem? Knowledge is the chocolate and
this show is the candy coating. That helps it go
down smooth keeps it from melting in your mouth or
in your hand exactly as you crunch on through it,

(04:48):
or in your ears. That would be pretty messy. You
know what melt the chocolate in your ears. Are you
suggesting people do or do not put Eminem's in their ears?
That's sort of lost track here. I know children do
and we have kids listening. Are you saying you know
the results of that experiment, that if you put Eminem's
in your ears they do not melt? I can guess
what happens, but thing it's science is not about guessing.

(05:09):
It's about going out there and doing experiments and discovering
what actually happens when you make new arrangements that nobody
has ever thought of before. Sometimes it's adding weird metals
to other metals, sometimes it's putting eminem's in ears. That's right,
because we know the universe is made out of particles
and bits of energy out there. But as it turns out,
there are lots of different ways you can put together
those bits of matter and energy and which gives you

(05:31):
all kinds of different results, and there are people still
figuring this out. You know, I'm a particle physicists. Of
My natural inclination for understanding how the world works is
to take it apart, is to reduce it to its smallest,
most fundamental elements. But there are other people who work
in a completely different direction. Their basic question is, how
do we make some new kind of Goo? And can

(05:52):
we make good that can do things that Goo never
did before? They combine those fundamental pieces of the universe
in new ways to try to make him dance and
Jiggle and do things that no other kinds of Google
have done before. Yeah, because there are many different ways
that matter can arrange itself. They're called states of matter. Right,
there's liquid and gas and solids and plasma. Right that

(06:14):
those are the states of matter that we know of.
Those are the famous classical states of matter. But as
we explore the universe and push on these things we
discover the matter, can do all sorts of weird kinds
of things. We talked on the podcast recently about Cork
gluon plasma, or you called it Quasma, a great name,
by the way. Yes, I'm still waiting for my noble price. Well,

(06:35):
just keep eating Banasma as you wait. Yeah, yeah, that
might slip with the Noble Price Committee, but it's amazing
to me all the things that emerge in our universe.
You know, one deep answer to the question what is
the universe made out of is to reveal its fundamental bits.
But I think it's equally important to understand what those
bits do when they work together, because you can't explain

(06:56):
the entire universe from the fundamental pieces. Even if you
had a complete and unique string theory that described the
fundamental theory of everything, you couldn't use it to predict
hurricanes or traffic on the four oh five, because these
are properties that emerge at a different scale. When you
zoom out from the universe from this time, these little bits,
you notice these incredible properties, places where we find these

(07:18):
interesting and simple mathematical stories that we can tell about
the universe, whether or not they are fundamental. Yeah, so
there are these four basic states of matter that most
people are familiar with, solid gas, liquid plasma, and we're,
I guess they're popular and people know them because we
see them in our everyday lives. Right. They're sort of
what how matter usually sticks together. But, as you were saying,

(07:38):
there are many other ways that matter can stick together
if you go down into the weirder realm of quantum physics. Yeah,
if you stick things together in weird ways and Zap
them with lasers, you can find stuff that does things
that no other kind of stuff can do. You've probably
heard of Bose Einstein condensates, for example, weird collections of

(07:58):
particles that act all together as a single quantum state,
a macroscopic blob of stuff with quantum properties. That's another
example of how you can squeeze and tweak matter into
weird configurations to do new kinds of stuff and new
kinds of stuff. Is What we'll be talking about here today.
So to be on the PODCAST, we'll be asking the question.

(08:23):
What are quantum glasses? Now, Daniel, I'm guessing these are
not just things you wear to see quantum things better.
When we go to a quantum physics conference, everybody puts
these things on. It's not going to a three D movie, right.
It's for cure and quantum myopia. Is that what it's
there for? Or are they for drinking quantum wine or juice?

(08:44):
Quantum juice? So you can say I'm not sure if
I drink that glass of wine or if somebody else did,
shrouding your drink my glass of wine, I meaning glasses
of quantum. Have you drunk today? One and zero at
the same time. There's a probability distribution that I'm drunk
quantum glasses. So these are two words I'm familiar with,
but I've never seen them together in the same phrase.

(09:05):
These are really interesting kind of materials. Sometimes they're also
called spin glasses, as we'll learn about later, because they
involve quantum spin. So it's a really fun topic and
something a bunch of listeners have been emailing me about
because they saw articles about spin glasses and quantum glasses
and they wanted to understand. Hey, what are these things anyway?

(09:26):
Interesting and can you make a spin bottle out of glass?
Is that the same thing? I think you're thinking of
the game spin, the boss Spin right. Well, as usually,
we were wondering how many people out there had heard
of this phrase quantum glasses or had any idea of
what they are. So thank you very much to those
of you who are willing to answer these questions. It's
really helpful to give us a sense for what people

(09:47):
are thinking and what they already know. If you'd like
to participate for future episodes, please don't be shy. Right
to me two questions at Daniel and Jorge Dot Com
and I'll set you up. So think about it for
a second. What do you think quantum glass this are,
and what could you see with them? Here's what to
be glad to say. Quantum glasses, I guess, are not
spectacles to view through, but they should be a kind

(10:10):
of material. In material science, glasses are a class of
materials that are characterized by being that it disorganized. So
quantum glasses should be a quantum soup that is disorganized.
I have no idea. I don't think they're the tiny
little reading glasses that some people perched on the end

(10:32):
of their nose, nor are they the tiny little shot
glasses one might use for a very strong drink. Even
those are not quite quantum level, and one should use
distance glasses, if any, rather than reading glasses and not
drink alcohol while driving a Volkswagen Quantum. So I'm going
to take a wild guess that there's something that refocuses

(10:53):
beams of quantum particles, much like how eyeglasses and other
such lenses refocusames of light. I have absolutely no idea
what quantum glasses could be, so this is going to
be a completely uneducated guest in every way. My mind
originally went to glasses, like glasses who wear, but then
I also thought of glasses as like a container for

(11:15):
a liquid. So my guess is that it is some
type of container through which we can better observe quantum events,
events on a quantum scale. I think quantum glasses is
a system physicists use two negotiate quantum theory. Either that

(11:35):
or it's the glasses I used to use when I
was a heavy drinker. But take a guess. Quantum glasses
helps you see shrodingerl's cat, exactly what that cat is doing,
and it's no whereabouts. If I was to reduce, I

(11:55):
reckon it's some way of being able to utilize something
to view or to assess the way the quantum world
is behaving, similar to a spectacles on to say the world.
I wonder if it's got something to do with our
ability to say or interact with the quantum world. All Right,
a lot of interesting ideas. I love the tiny little

(12:16):
reading glasses. They're like little quantum particles you put in
your eyeballs. Is that what they're saying? No, I'm imagining
like literal tiny glasses perched at the very, very tip
of my nose, and they're there and they're not there
at the same time. But I'm most impressed with this
one guest that says glasses are disorganized. So maybe quantum

(12:38):
glasses are a disorganized quantum soup. That is so close
to correct I'm amazed. Yeah, yeah, I feel like maybe
they cheated or something that. I wonder if they read
an article about this. I don't know the rules are.
You're not allowed to Google. So, you know, maybe they
just intuited it. Maybe this person just is a physics genius. Wow,
maybe you should be hiring them, or maybe you already

(13:01):
hird them. I don't know. Did you ask your Grad Students? Sometimes?
I do sometimes, but these are all random Internet people,
although you know, some of our listeners are physics Grad
students and some of them aren't. So there's a pretty
wide spectrum of backgrounds. Yes, in the end we're all
random Internet people, Daniel, but anyways, lots of great ideas,
and so let's dig into it. What is a quantum glass? Daniel,

(13:21):
break it down for us. So, basically, our listener gave
us the answer. A quantum glass is a material where
the quantum states are disordered in a way that's similar
to way like a window glass is a disordered solid
rather than like an ordered crystal. You know. That means
that things on the inside are not like arranged, so
everything points in the same direction. It's sort of scrambled

(13:43):
a little bit. MM interesting because I guess bits of matter,
atoms and quantum particles, they have a specific direction, aren't
they just like little blobs? They do have specific directions
because they have quantum spins, right, and luxurns are not
just tiny particles with charred gen mass. They also have
other quantum properties, including this weird thing quantum spin, that

(14:05):
we don't fundamentally know what it is. We don't think
that these electrons are actually spinning because we think of
them as point particles. And even if you account for
the width of their wave function, if they were literally spinning,
then their surfaces would have to go faster than the
speed of light to explain all of this energy. It's
some other weird property. We have a whole podcast episode

(14:26):
about what is quantum spin. For today, all we need
to know is that it can have a direction. Electron
is gonna be like spin up or spin down, and
this is true for other particles. Protons and neutrons and
even for atoms, can have an overall spin. So that
gives them a directionality. They're not just points, right. They
have a property that somehow points in a certain specific

(14:47):
direction in space. And you said it's just sort of
like normal glass to like maybe let's start with that.
What is a normal glass? Yeah, so a normal glass
is something that feels solid. Like you go to Your
Window Pane Ene and you touch it, it it feels solid, right.
But most solids out there are not like glass. Most
solids are ordered. They're organized like a crystal, you know.

(15:08):
They're sort of like built out of a bunch of
tiny bricks that are all stacked together very nicely and
neatly into like a big cubic lattice. You can think
of them as like a bunch of atoms where the
atoms all line up in three directions. You know, if
you like sort of looked down it, you could line
up all the atoms sort of like in front of
you and then along the surface and this kind of thing.

(15:30):
So most stuff that's out there is fairly well organized,
but a glass is not a glass. It's just sort
of like a pile of stuff that's stuck together, but
it's not well organized. What do you mean? Mean? Like,
my wooden desk is neatly organized, but it looks pretty messy.
Your wooden desk is even more complicated because it has
all sorts of structure in the wood itself. But you know,

(15:51):
if you take it like a block of ice, it's
a single kind of stuff. It's cold and the atoms
inside of it are arranged in a lattice. There's like
the distance between two atoms is pretty much a single number,
and that's true for most things like metals, et CETERA.
But they're both solid, right, like a piece of glass
is solid, just like a piece of ice is solid too.
That's right. A piece of glass is solid because its

(16:11):
volume doesn't change and it's shape doesn't change. The build
just sit there, right. But if you zoomed in with
a microscope, an amorphous solid like glass would look very
different from a crystal solid, a crystal slid. You would
zoom in and it would look like it's built out
of these little pieces that are all arranged very nicely,
like somebody stacked a bunch of legos together, whereas an
amorphous solid would look like, you know, the inside of

(16:32):
your Lego bin before you built something would be like
a disorganized pile of stuff that's still somehow stuck together.
And you know, glass is an example of it. And
then we call these things glasses. But there are other examples,
like a lot of plastics are like this, gels are
like this. You know, sand is like this. If you
zoom in close enough, it's not like stacked up in
little bricks, it's just sort of like a big jumble.

(16:54):
But you're right, it is solid. It manages to stick
together well enough still have the properties of a solid, right,
although I've heard glasses actually a liquid, like a really
slow liquid, right, isn't it? That is something that is
said often, but I don't think it's actually true. I
think the people have been misled by old windows, for example,
that are thicker on the bottom than on the top.

(17:14):
That's mostly because of the glass making process at the time.
Glass itself, I don't think, actually flows on a time
scale that humans can measure, but on a long time
scale it sort of does. Right technically, it's true that
these things can flow on very, very long time scales,
but most of the things where you see it's like
thicker on the bottom than on the top is not
because the glasses flowed. It's a little bit unclear exactly

(17:37):
what the time scale is for glass to flow into
a puddle, for example. It might be a very, very
long time scale. Well, Um, I guess maybe a question
I have is what's the difference between something that is
a glass and something that is not a glass? Like
what makes some materials arrange themselves into crystal structure, lattices,
and what makes them just stick together morphously? The answer

(17:58):
is that it is complicated. For some materials it depends
on how they are cooled. So if you cool things really,
really fast, they don't have a chance for the crystal
to organize itself. Other materials just don't fall into a
crystal because of the way their interactions work. They can't
build a regular lattice it depends a lot on the
exact material and also on how you get it to

(18:19):
its state. So some things can be crystals or can
be glasses, and it just depends on how quickly they
are cooled down. Doesn't a lot of it also depend
on like the structure of the molecules in the material?
For example, you know, like maybe what I think, water
falls into crystals because the two H and the o
kind of form a kind of a weird shape and

(18:39):
there there are only so many different ways you can
kind of make those shapes stick together. Yeah, that's what
I mean by the interactions of the materials. They imagine.
For example, you have a weird shaped tile, a question
you can ask is like can I tile this across
the floor in a regular pattern? And that's basically what
you're trying to do when you build a crystal is
like fill up a space with a regular pattern with
a weird shape that you have. So, as you say,

(19:01):
for example, water has kind of a weird shape, but
it's capable of building crystal. But actually it can build
lots of different kinds of crystals based on the temperature
and pressure of its formation. There's like ice four and
ice six and ice. Nine. These are all different crystal
arrangements of the same basic thing, based on the temperature
and the pressure and the conditions in which it was formed.
So it's a really complicated question. Yeah, and I think

(19:22):
it also depends on like what makes the molecules stick
together right like an h do. It could be the
forces between the OHS, for example, what I'm just giving
out random example, or it could be, you know, the
forces between the H is and things like that, right exactly,
and some parts of it are stickier than others, right,
depending on the energy levels of their electrons. So it's

(19:43):
something that's not always easy to predict. Sometimes the best
way to figure it out is just to try. It's
just to go out and see what happens. So we
have people whose entire careers are just like mapping out
the phase diagram of various kinds of materials, understanding what
it does under certain configurations. Think maybe the takeaway is
that stuff sticks together in general and there are there

(20:04):
are many different ways for it to stick together and
sometimes they stick together in regular patterns, like in a grid,
and sometimes they just kind of bundle up like randomly, right,
and that's what a class is and classes is an
example of this category. You also have like plastics and
polymers and Thoms and gels. These all follow the same
kind of structure as glasses. They are amorphous rather than crystalline, right,

(20:26):
and those are the in the macro scale there are
morphous materials, kind of like the atom level, right. We're
not yet at the quantum level. Yeah, these are things
at the atom level exactly. So then you're saying a
quantum glass is a material in which stuff is stuck together,
but Um, it's a morphous in its quantum states. Yeah,
and I predict you're gonna be pretty unhappy with this

(20:47):
distinction about what's a quantum state or not, because in
the end all of these interactions are quantum, like when
two water molecules touch each other and form part of
a crystal. That is a quantum interaction between quantum particle.
But when we talk about quantum glasses, we mean that
we're adding a new dimension to it, that we're considering
another quantum property, in this case quantum spin, because we're

(21:09):
not interested in how the objects ordered themselves in space.
We're interested in the distribution of these spins. Are the
spins ordered or are the spins disordered. Well, I guess
maybe a distinction is that like, for example, for Water
and ice? I mean you're talking about atoms being in
a kind of a lattice, right, and atoms themselves don't
have spin, or you know, don't. Isn't it like the

(21:30):
electrons and the atoms and the corks and the atoms
that have spin, not the atom itself? The atoms themselves
do have an overall spin. It comes from adding up
the spin of all the bits, the nuclear spin, the
electron spin, and that's what's important for forming magnets, for example,
is the spin of the whole atom. It adds up.
So we do think about the spin of the atom itself,
not just the electrons inside of it. All right, well,

(21:51):
let's get more into it and explain what exactly is
a quantum glass and whether or not we've actually seen
them and can touch them and maybe use them to
read quantum books. So let's get into that, but first
let's take a quick break. All right, we're talking about

(22:16):
quantum glasses. Are these like x Ray glasses that let
me see through things? They'll let you see immediately to
the next big discovery in physics. I wish isn't I
just called working. What if I could just put on
quantum glasses and look at my calendar and be like
that's the day you're gonna make a big discovery, what

(22:39):
would you do? Would you work harder or less if
you need you're gonna make a big discovery next week. Well,
I know that napping is a crucial part of making
big discovery, so make sure to get that out of
the way first. Right, right, but would you have more
or less if you knew your feature? Well, future Daniel
would have already have seen his future using quantum glasses,
so that would be accounted for, sort of like Harry

(23:00):
Potter time travel. Right, right, I guess that you're saying
you don't have any free will. That's right, I'm completely
determined by my calendar. I just do whatever it says.
That's right. Your naps are determined by your future self.
It's not your fault. If I put make huge discovering
to the calendar, then I have no choice. I have
to make a huge discovery that day. Right. Yeah, that's
what I'm saying, but I'm saying like, how would it

(23:20):
affect your presence choices? I would type that into my calendar.
A lot of times. But anyways, we're talking about quantum
glasses and what they are, and we talked about how
a glass is a material in which all of the
bits in it are kind of disordered, amorphous, not in
any kind of grid or structure, and the same can
be said for quantum materials. That's right. And traditionally, when

(23:41):
we talk about glasses we talk about disorder in the
location of the atoms, so if you zoomed in with
a microscope you would see like a big pile of
stuff rather than a nice, crisp, organized lattice. And now
we're talking about something else. We're talking about quantum properties
of these objects. So you can have something which is
a nice organized lattice in space, like a grid of
atoms that are perfectly organized, but it can be a

(24:03):
quantum glass if their quantum properties are disorganized, if their spin,
for example, so their magnetic moment is not organized in
a very nice way. WHOA. So it's almost like something
you layer on top of other materials. This idea. It's like,
you know, we have this traditional distinction between glasses and crystals,
but that is sort of irrelevant here. Right what counts

(24:26):
is whether or not the quantum states are aligned in
a pattern or not. Exactly whether it's a quantum glass
depends on its quantum states, not the spatial locations. And
here mostly we're talking about things which are physical crystals.
You know, their atoms are nicely arranged in a grid,
but the quantum states of those atoms in the grid
are sort of scrambled. And you know traditionally if you

(24:48):
have stuff in a grid, the magnetic fields can be
nicely aligned. So the ferro magnets, for example, is something
where all the atoms have their spins in the same direction,
which is what controls their little magnetic moments and all
adds up to be a big magnet. So if you
have a fridge magnet for example, like a nice piece
of iron that's been magnetized, has all of its spins
in the same direction, they all add up together they

(25:10):
make like a permanent magnet. That's a ferro magnet. That's
not a quantum glass because the spins are all nicely
organized nicely right. That's what a magnet is. Right. Our
magnet is usually metal crystal where all of the atoms
in it have the same spin direction, which kind of like,
I guess, synchronizes them. And makes them add up to
a giant kind of spin or magnetic pole. Right. And

(25:33):
one reason that's possible is because the spins like to
align with each other. In a ferromagnetic material, that's the
relaxed state, that's the lowest energy states, when the spins
are pointing in the same direction. It likes to be
that way. There are other kinds of material, like anti ferromagnets,
where they prefer the spins to be the opposite directions,
where you want your neighbor to have the opposite spin

(25:55):
is you, and because of the way these molecules interact
in their funny shapes and all of their forces between them,
that happens to be the lowest energy state. That's the
opposite anti ferromagnet where you have a crystal, but it's
like spin up, down, up, down, up, down, up, down.
Both of these are examples of well organized magnetic lattices. Interesting.
And does that apply only to metals, like magnet metals?

(26:18):
Like can I take a block of ice and align
all of the magnetic spins in the atoms of water
in a block of ice to make it magnetic? You
can't do that with a block of ice. Now, a
block of ice is not ferromagnetic and it's also not paramagnetic.
paramagnetic ar materials that are sort of weakly magnetic and
if you put them in a magnetic field they will

(26:40):
eventually align, but then when you take the magnetic field
away they might lose it. But ice is neither of those.
Why not? Why can't I just, you know, somehow arrange
my water molecule so that all the spins are aligned?
It depends on how the bits of the atom are organized.
So it depends sort of like on the overall spin
of the atom. We were talking earlier about having spins

(27:00):
on the electrons and spins on the Nuclei. If those
sort of all add up to an overall small amount
of spin, then there's not really much to play with there.
But if they come together in a way that makes
like a large magnetic dipole for the individual atom, then
you have spins that can get aligned, and so that's
what sort of what's different between some materials which are
like ferromagnetic because they can be aligned, and other materials

(27:23):
that are not. M You're saying like in something like
a water atom or molecule, all of the electrons and
all the corks in it are not easily or readily aligned.
They like to kind of being random positions, which sort
of castles. There's spin out. Yeah, and some of these materials,
for example, the electrons want to be opposite spins so
that they cancel out, and other materials they're set up

(27:44):
in a way that electrons can all be in the
same spins. You have an overall spin to the atom
M and so that's the difference between a material that
can form a magnet and one that cannot. That's one
of the differences. This whole thing is very complicated. It's
difficult to make like broad generalizations, but that's sort of
like the cartoon picture. Why some things can be magnetic
and some things cannot. All right, so maybe tell me

(28:05):
more about these anti ferromagnetic materials. So the anti ferromagnetic
materials are the ones where they like to be opposite,
where every neighbor prefers to be the opposite of the other,
and it just depends on their interactions. Whether that's the
lowest energy states, so they like to be up against
each other or whether they like to be aligned with
each other. They like to be aligned with each other.
It's a ferromagnet. They like to be opposite with each other.

(28:26):
It's an anti ferromagnet imagine like a big sheet of
these atoms. If you want them to be all aligned,
there's an easy way to do that. You spin them
all up or spin them all down. Right, you want
them to be all anti line, there's still a pretty
easy way to do that. On a square lattice, like
every other one is up and every other one is down.
So up, down, up, down, up, down. And you can
imagine covering an entire plane or even a three d grid,

(28:50):
where every atom's neighbor has the opposite spin as it
does right. So if you're up, then you see down
everywhere around you in the Lattice, and if you're down,
you see up everywhere around to do in the lattice.
So there's a way there to make an overall relaxation
where everybody's in their lowest state and everybody's happy. I
guess I got a little confused because I think basically,

(29:10):
like all materials, is kind of a quantum glass, right,
like isis sort of a quantum glass because it's quantum
spins are in all kinds of directions. Right, like my
hand is a quantum glass in that sense of the
definition of it, I suppose. So ice and an example,
has sort of negligible quantum spins compared to the kind
of things we're talking about here. So it's not really
in the category of things that we're discussing. We're talking

(29:31):
about materials that do have quantum spins. Do they like
to be aligned or do they like to be anti aligned?
And can you make the material in such a way
that the whole thing is happy overall? The whole thing
is relaxed into its lowest energy state, either inferro magnets,
by lining up all the spins or anti ferro magnets
by flipping all of the spins right. But I think

(29:52):
you're talking now about like let's post a little challenge
for ourselves. Let's let's see if we can find material
that you can arrange in a crystal, in the lattice
in like a grid, but somehow also make all these
spins differently or randomly directed. Yeah, so a spin glass
is a kind of material where the spins can't all relax,
when you can't find a configuration where everybody's happy. We

(30:16):
talked a minute ago about anti ferromagnets, where things like
to be the opposite spin of their neighbor. And that
works in a square lattice right, where you have like
a neighbor to both sides and above you and behind
you and in front of you. What if, for example,
you have like a triangular lattice instead of a square lattice,
and so you have like two neighbors? Imagine just points
on a triangle. You Label one point up, the next

(30:37):
one down. What's the third point going to be? It
wants to be down because has one up neighbor and
it wants to be up because it has one down neighbor.
So it doesn't know where to go right. It can't
satisfy both of its neighbors at the same time. Well,
you're saying, I guess that these anti ferromagnetic I guess
atoms or molecules. They're sort of like contrarians, like if
their neighbor is up, they want to go down right

(30:59):
and if they have two neighbors that are up, then
they want to go down. I guess two questions. First
of all, why are they so continuing? Hey, some people
just can be grumpy and you shouldn't ask too many questions.
You know, it depends on the complicated interactions between the atoms.
Atoms are not simple objects. Have a spatial extent and
they're slashing around. They have all their internal forces. You're
closer to some bits of it than other bits of it,

(31:21):
and the spins of these objects interact right and some
of them like to be spin up and some of
them like to be spinned down. I guess the short
answer is that it's really complicated and sometimes it even
depends on distance. Like if you're close up, then they
like to have the same spin and as you get
further away, they like to have the opposite spin, and
then as you gave them further away, they like to
be the same spin again. It's really complicated and depends

(31:43):
on a lot of the details of that exactly. The
internal arrangements of each atom or molecule, I see. But
is it, I guess, kind of like a magnet, right,
like if I have two magnets and they're both, you know,
have the same North Pole pointed in the same direction,
like bring them together, like one of them will want
to flip over so that it's opposite the other one.
Is that kind of like the good analogy, or maybe

(32:03):
even the same thing? That's the same thing for the
Anti Ferro magnets right, except here we're talking about spins,
but it's very similar. You know, the minimum energy state
there is for one North Pole to be aligned with
the other magnets South Pole, and if you try to
push in the other direction, it's going to take some
energy to keep it there and if you let go
it will relax into the configuration where they have the
opposite directions, where the North Pole and one magnet is

(32:26):
aligned with the South Pole of other magnets. Okay, so
now I think what you're saying is, you know, we
have these materials, these atoms, that are contrarian. They like
to be opposite the spin of the its neighbors. So
now what happens? And if I put two up spins
next to it, it's gonna want to be down spin.
But what happens if I put an upspin and a
down spin next to it? It gets you a little confused, right,
or frustrated? Yeah, exactly, and that's what physicists call it.

(32:47):
They call it a frustration when you can't arrange the
spins in a way so the whole thing has minimum
energy right in a square lattice. Imagine four points on
a square could have like the top left to be up,
on the bottom right be up and the other two
points be down and everybody's happy because all the downs
have only up neighbors and all the ups have only
down neighbors. But in a triangular lattice you can't do that. Right.

(33:09):
The third point has one up neighbor and one down
neighbor and it can't decide which way to go. There's
two possible states there that have the same energy and
neither of them are like the minimum energy right. It's
like having a conversation between three people and one of
them is the contrarian. What happens that? When are the
other people agrees with them, but the only one does not?
What does the contrarian do? Exactly who to disagree with?

(33:32):
And so this is what a spin glass is, because
the spins end up sort of like disorganized. It's not
like a Pharo magnet where they're all pointing in the
same way, or an anti Faro Mac in a square
crystal where they're all pointing opposite directions. It's kind of
a disaster, right. So like tense, it's frustrated, it can't
quite relax, and so where the spins end up is
a little bit random. Interesting. So you're saying the part

(33:56):
of the definition of what a quantum glass is is
that kind of frust rate Shan built it into it.
Like if I build the lattice with contrarian atoms and
everyone's contrary to their neighbor, then it's and everyone's happy.
Then that's not a quantum glass. Right, exactly. That's just
a normal anti ferromagnetic crystal. But if you can somehow
frustrate the atoms, then you have a quantum glass, because

(34:17):
I guess everyone's frustrated and what constantly flipping back and forth?
Is that kind of what happens? Yeah, everyone's frustrated, it
can't find the minimum and it has new weird properties.
So when we talk about a phase transition, there has
to be like a change and how the material operates
in one of its properties. Right, we don't say that
cold water and hot water are different phases, even though

(34:38):
they are chemically different, because there's no like large change
in its macroscopic behavior. So for years or even decades,
there was an argument about whether spin glasses really are
their own phase of matter. And the people who say
that it is its own phase of matter. They argue
that it's unique because it has weird relaxation times. Like
if you take a ferromagnet or an anti ferromagnet and

(34:59):
you apply really strong magnetic field and you sort of
mess up the spins, it will relax pretty quickly when
you take away the magnetic field. But a spin glass,
if you do that, it will react really differently. It
will take like forever to relax and it will never
come back to its original position. So people argue that
that's enough of a different macro's copic property to be
its own kind of thing. What do you mean? It

(35:21):
takes a while, like the items keep switching back and
forth or what? There's like turmoil inside of the material. Yeah,
they have like decision paralysis. You know, it's like if
you go to the cookie aisle and there's like a
thousand cookies and your shopping list just says cookie. You're like, Oh,
do I get Oreos? Do I get chips of oil?
Look at those fudge ones. Oh No, I can't decide

(35:41):
what I want and they all seem equally good. You
could spend hours there wandering around switching, you know, taking
stuff in and out of your basket, not sure what
to actually buy, and so spin glasses are sort of
like this. If you perturb them, you give them magnetic energy,
you put them in the magnetic field and then you
take it away, they take a long time sort of
slashing back and forth spins, flipping and then flipping other spins.

(36:02):
They can't find a comfortable situation to relax in M
but I guess it isn't spin a quantum property, meaning
like each atom has a spin that's both up and down,
like they went in a particular direction? Wouldn't that sort
of collapse the wave function of that quantum state? Yeah,
really interesting question. It's true that spin is a quantum property,
which means both that it can either be up or down,

(36:24):
but not like in between. Right when you measure these
things either get up or down, but it means that
until you measure it, it's not necessarily determined. So what
that means is that the whole thing has like a
few different quantum states that are all possible. We're talking
about is what happens when you measure it right. So
you probe this thing. You ask like what's the spin
over here? What's the spin over here? What's the spin
over here? And you're right, that will collapse the wave

(36:46):
function so that everybody's going to make a decision, but
you come back another minute later and it's made a
different decision. You come back another minute later it's made
another decision. So you never really see it settle and
relax into a fixed state. Right. So when you're talking
about like this termoil, all the all the contrarians can
not being able to decide which way they're being contrring about.
It's more of like a quantum turmol right, like it's

(37:07):
not actually flipping back and forth and it's not like
you're at the cookie as'le trying to decide. It's like
you're sort of in this state where you're you're decided
and not decided. No, I think it really is decided
or not decided. I mean you can take pictures of
these things essentially using like skinning, tunneling, microscopy or otherways
to probe the magnetic field. So you can collapse these
wave functions and you can see them evolve over time.

(37:29):
So you can see these things really are flipping or
it's not like once you've collapsed the way function, then
it's happy and it's going to stay there. You can
collapse the way function, you can come back and collapse
it again and then again and again, you can see
that they're flipping their spins. So that's the interesting property
about spin glasses is that they have these really long
relaxation times. They're basically never in equilibrium. You know, another

(37:51):
way to think about it is like say you sit
down at a really long banquet table and there's silvil
ware to your left and to your right. Do you
take the one to your left or do you take
the one to your right? You know, if everybody takes
through to the left, everybody is happy. If everybody takes
their right, everybody's happy. People are arguing. You know, no,
that one's mine, that one's mine. Then you know you
can't really settle into a comfortable state. So spin glasses

(38:13):
are situations where, like, people can't agree about what the
rules are and so everybody's just taking whatever silverware. Well then,
you say, eventually it settles down. And so what is
it settled down into? Salad forks or main course for
that's the interesting thing about spin glasses is that it's
very hard to predict. You know, when we try to
understand the macroscopic properties of these things, we do so

(38:35):
by starting from the microscopic we say, okay, crystal is
made of these little bits, and then we expand our
understanding from that basis, stacking them together to make the
macroscopic properties. That's really hard to do with spin glasses
because they're so crazy and unpredictable. They're basically never in equilibrium.
So a lot of the mathematical tricks that we use
to understand crystals don't really work for spin glasses, which

(38:59):
lad to like invention of whole new categories of mathematics.
M interesting. All right. Well, let's get into those new
categories of maths and what these materials are good for
and what we can learn from them. But first let's
take another quick break. All right, we're talking about quantum glasses,

(39:29):
which is one of our listeners said, is where you
take shots of quantum whiskey or Tequila, one electron at
a time. Man, it's quantized. I'll take forever to get drunk. Danny.
That's the point, man, moderation in all things. Let See,
one atom at a time. Alright. So it sounds like

(39:50):
there are materials you can put together in a crystal
that are unhappy basically at their core, because all of
the atoms can't find a good arrangement of their want
them spin the everyone is sort of in this state
where they don't know whether to go up or down
in their spin, and so you create a material with
a lot of frustration in it exactly. And a lot
of these spin glasses are not just like one kind

(40:12):
of material and a lattice where they're all contrarians and
it's arranged in a way where they can't be happy.
A lot of the Times it's a few examples of
something that is magnetic inside a larger crystal. So you'll
have like a non magnetic material like gold or silver copper,
and you sprinkle into it a few percent of magnetic atoms,
iron or something else, and because of their interactions depend

(40:34):
on the distance, whether they like they have the same
spin or the opposite spin depends on how far apart
they are. You can end up with these disordered spins.
You're saying. That's how you make a quantum glass. You
embed magnetic atoms into a regular metal exactly, and then
you cool it down and you see, like how are
they frozen in interesting you like you bake in the
frustration of the magnetic atoms. You freeze it in. Yeah, exactly.

(40:58):
All right. Well, I guess a good question for me
is what are these materials good for or why are
we interested in them? So these things don't have like
an immediate practical application, if not, like with spin glasses,
you can make quantum computers or you can build a
better transistor or you can take tiny shots of hot
cocoa or something like that. There's no immediate application, but

(41:19):
it's an interesting and tricky problem and so people have
been thinking about it and, you know, sweating over it
and trying to figure out like can we describe these
things mathematically? Is there some way to figure this out?
To me, this is one of the deep questions of
physics itself, you know, because again, since we don't have
the fundamental theory of everything, all of the theories that
we develop are what we call effective theories. They're like

(41:42):
mathematical stories that we tell that describe the things that
we see, but they're not like written into the fundamental
firmament of the universe. You know, aliens, for example, might
not come up with these same effective theories. They're just
sort of useful descriptions, but it's incredible we can find them,
but sometimes they're harder to find than others. You know,
for Solids and for liquids we have found mathematical descriptions

(42:04):
that are useful. For Spin glasses, it's been much, much
harder because their interactions are more complicated and less regular,
but it's inspired people to come up with all sorts
of new mathematical tricks, one of which people think is
the reason why we discovered the Higgs Boson. I guess
maybe a step us through that a little bit more.
What does that mean? Like we have an effective theory

(42:25):
to describe like a regular magnet. Is that what you're saying?
We have like a mathematical way to study the model
how regular magnet works, but you're saying we don't have
one yet for these crazy, frustrated materials. We've been working
on we've been making progress. I mean by we I
mean all the other physicists. We're not goofing off making podcasts. We,
you know, as the general group of humans thinking about

(42:46):
these kinds of things, have been working on this for
a long time and I think it's always interesting when
it requires a new kind of math. And so there's
an Italian physicist Parisi who won the Nobel Prize for
this in twenty one, because he came up with a
new sort of math, thematical strategy for dealing with this complication.
You know, one of the real problems is that these
things can arrange themselves in lots of different ways and

(43:09):
when you poke them, you know, you give them a
little bit more magnetic energy. So you scramble all the
spins and you watch them relax. You wonder, like why
does it land in this configuration and not that one?
Can we predict this kind of thing? Can we come
up with some sort of mathematical way to grapple with
this and predict what's going to happen? You can't be
completely random. And I guess what do you mean by
a new kind of math, like a new kind of

(43:30):
like adding quantum to old math, or what does that mean?
The Way Mathematics bakes progress is that sometimes they need
to develop like a new kind of tool, you know,
like they find differential equations and here's strategies for solving
that kind of problem, or here's Algebra, you know, like
the people who figured out how to write equations down
and solve them to get understanding. We're able to solve
certain problems that other people couldn't. And, for example, descartes

(43:53):
made a lot of advances in geometry because he would
able to figure out how to use Algebra to tackle geometry.
Like if you could write down the equation of a circle,
then you could solve systems of equations and understand geometric patterns.
So here they've done something similar. They've invented to like
new mathematical tools, and these mathematical tools are really thinking
about the symmetry of the problem. Like you have this huge,

(44:16):
complex tree of options that a spin glass can do.
We can splip this way, you can flip that way,
you can flip the other way. So what Paris he
did was come up with a way to think about
this in sort of the larger context, like don't just
think about the one spin glass you have, think about
all the other spin glasses and you don't have like
replicas of that system and try to organize them into

(44:37):
like branches. So like, Oh, these guys are all similar
in this way, those guys are all similar in these
other way. Think about like the choices that were made
to get to this spin glass from the higher energy
spin glass, and he found these ways to like organize
these and use symmetries to like break down the problem
into smaller pieces, to organize this complexity, and that helped

(44:58):
to make sort of like approximate statements about which kinds
of spin glass final states were more likely than others,
like if you started here, you're likely to get to
neighboring final states where you weren't going to make a
big jump to something all the way on the other
side of the sort of symmetry organized set of states.
And you're talking about math that sort of analyzes one

(45:19):
of these grids right like you're looking at a grid
of these atoms, these frustrated atoms, together, and you're trying
to figure out, like, you know, are they all gonna
go up or down, or is they are they going
to alternate or are they gonna you know, how often
are you going to run into an up spin atom?
And you're wondering, if I poke this thing, how likely
is it to change to another configuration, or how likely

(45:40):
is it, after I've poked it, to come back to
this configuration? or how many spins are going to be
flipped after I poke it? Is it going to be
every single thing is flipped, or just a fraction of
you or flipped. So those the kind of questions people
are interested in, just like what are the behaviors of
these things? So press math gave us sort of like
a map for all those different configurations. He said like okay,

(46:00):
this configuration of the spin glass, you can put it
here on the map, and he was able to sort
of organize and create this idea of a distance between
one spin configuration and another. This distance is sort of
a mathematical way to calculate like how many spins are
similar or not, and he was able to organize it
in such a way that he showed that if you
poke this thing was more likely to end up in

(46:21):
a nearby configuration than a distant one, where the distance
here is something that he defined his strategy for organizing
these different configurations. So there is a pretty interesting kind
of material. I guess kind of to go back a
little bit to my earlier question is, you know, like
let's say I make a piece of quantum glass and
it has these interesting mathematical properties. What could I do

(46:42):
with it? Can I like make actual glasses out of
this glass? What would happen if I see through it?
Only if you can see through solid gold or silver
or copper. You know, there's not anything that I'm aware
that you can like do with it in your life
other than impress your physicist friends, which you know, has
its own inherent value. I mean it is sort of
a quantum object, isn't it? At the end of the day,

(47:03):
this glass is a quantum object. Could you do quantum
things with it? Or computation for a bit? Possibly? I'm
not aware of any applications for quantum computing. But I
think with the most interesting thing is just the math
that it makes us think about. It made these guys
think about symmetries and patterns in new ways and come
up with new mathematical tools. And whenever we develop new
mathematical tools we always find out that they're useful in

(47:26):
other places. So people have been thinking about these kinds
of symmetries and crystals for decades and decades in the
field we called condensed matter, the study of, you know,
dense objects like crystals, and because of that Mathematical Foundation
laying in condensed matter there's a lot of work on symmetries,
a lot of which informed Peter Higgs when he was
thinking about why particles get mass. He came up with

(47:48):
this idea of another field in the universe that imparts
the mass. But this field has to be really weird
and different from any other field he had seen before.
It would have to settle and relax into an on
minimum energy state. As we've talked about in the program
a lot of times. The Higgs field has some weird
energy bound into it. It can't relax to its lowest

(48:08):
energy state. It relaxed to this weird intermediate state, and
so thinking about the symmetry of that problem helped him
think about the symmetries and the broken symmetries of the
Higgs field and really inspired that Whole Direction of mathematics
and particle physics. And that kind of worked out right
for Peter Higgs and the press of humanity. But Peter

(48:29):
Higgs didn't know about these quantum glass is right. You're
just saying that they sort of use the same kind
of math and that's why it could be important. That's right.
Quantum glasses weren't well understood when he was talking about
this kind of stuff and he was thinking about it.
But the mathematics that underlie condensed matter and understanding these
symmetries led to both a deeper understanding of quantum glasses

(48:51):
and of symmetry breaking and the Higgs field. Well, it's
interesting that there is a connection, right. I mean there's
a connection between the such a fundamental particle in the
universe and maybe all particles and what happens at these
kind of microscopic levels. Right, maybe the idea that the
universe is there's a lot about symmetry in the universe.
There is a lot about symmetry in the universe and
also about these emergent phenomena. We've talked several times in

(49:13):
the podcast about things we call quasi particles. These are
weird materials that have states in them that looks sort
of like particles that act sort of like particles, you know,
like phonons, are waves that pass through a lattice in
the crystal and they're sort of similar to photons, but
instead of moving through the fundamental electromagnetic field of the universe,

(49:34):
they're moving through a crystal lattice. So we see these
same kind of properties emerging in condensed matter that we
often see also in the quantum fields of the universe,
and so there's a lot of connections between the mathematics
of solid objects and the mathematics of Space Time itself.
Does that inspire you to make your office more symmetric,

(49:55):
or do work in at causant state of frustration as well? No,
I'm always asking my department here. I'm like, can I
get a bunch of gold bricks? I'd like to build
a really strict, nice lattice to study their symmetry, but
so far having gotten a single delivery of a single
gold brick. And you just need to let him your
quantum glasses so he can see the future as well.
Or maybe he's just gonna Send Me Microscopic Quantum gold bricks,

(50:15):
whether either here nor there. Here's one atom of gold.
Good luck in this economy. I'd be very happy for
even one atom. All right, well, this is an interesting
new kind of material and with interesting properties that we're
learning more about, and it sounds like it's just another
example of the weird things we can find and in
this messy universe. You know, like maybe thirty years ago

(50:37):
we would never have imagined that we can make a
material that is magnetically frustrated. Yeah, and despite all the
mess that we find around us, we can still seek
order and find patterns and mathematical tricks to analyze it,
which turned out to not just help us understand the
stuff around us, but also reveal the mathematical patterns that
seem to be inherent in the universe itself. Well, we

(50:59):
hope you aoid dad. Thanks for joining us. Go have
a shot of some quantum drink. have an electron on me.
See you next time. Thanks for listening, and remember that
Daniel and Jorge explain the universe is a production of

(51:19):
I heart radio. For more podcast from my heart radio,
visit the I heart radio APP, apple podcasts or wherever
you listen to your favorite shows. Yeah,