Daniel and Jorge Explain the UniverseDaniel and Jorge explore the Pauli exclusion principle: why some particles avoid each other and how it affects the nature of our Universe.
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Hey, Jory, if you could only eat one flavor of ice cream for the rest of your life, be chocolate or vanilla?
Ooh do I have to choose? Can I do like a quantum superposition of the tooth flavors?
No, you are not a quantum hoohe, So you can only be in vanilla or chocolate. States.
It's a classic dilemma of classical physics.
Is it is? And so does your wave function collapse to vanilla or chocolate?
Obviously vanilla my favorite flavor.
Are you telling me for real you'd give up chocolate ice cream forever?
What if I break the loss of physics? Can I do something like a swirl?
Then you go to physics jail whether they don't have either flavor of ice cream?
They have swirls in physics jail, not even for my last meal.
All they have in physics jail is physics homework problems.
That seems a little inhumane, the ice cream part, not the homework part. I am hore Ham, a cartoonist and creator of PhD comics.
I'm Daniel. I'm a particle physicist and a professor at UC Irvine, and I choose the chocolate ice cream in one hundred out of one hundred multiverses.
Big fan of chocolate, Huh.
There's just no comparison. I mean, chocolate is delicious, but chocolate ice cream, it just elevates it beyond understanding.
Now, I think, I guess My question is when you say chocolate iking for the rest of your life, do you mean like you only get to eat chocolate ice cream for all your meals or is this like only for desserts.
Sometimes I think even I would get tired of chocolate ice cream if I ate nothing but that breakfast, lunch, and dinner, eventually it would get Although you know this milk chocolate ice cream is dark chocolate ice cream. There's chocolate and salt. There are lots of variations there.
But that's what I was going to ask, like what kind of chocolate. There's so many the flavors to choose from.
Yeah, and chocolate from all around the world. You know Madagascar chocolate, and then it's whale and chocolate. They're all subtly different.
And it was your stand on like chips like chunks of chocolate in your eyes.
Honestly, I think that ruins the texture. You know, a frozen blob. It's like chewing on a pebble, Like nobody wants to eat.
Rocks, right right right, So you're you're against some chocolate ice cream.
I'm saying chocolate chunks ruined the chocolate ice cream experience. Let's just have pure ice cream and not chunks.
But then now you got to define a size limit, like what size limit of chocolate particle? Are you willing to tolerate?
Chocolate? Ice cream is fundamental, man, It's not composite. It's so important to the universe. There's a chocolate ice cream field that permeates the whole universe.
Icee, I see, But I mean, I'm sure there's this sizet of chocolate particle that would you fly under your radar?
Yeah, you know, I think this calls for more experiments, for sure. And I actually did a little Twitter experiment myself. I was wondering if our supporters sided with the obviously correct me on the chocolate camp or the obviously incorrect you on the vanilla camp. So I went out into a little pole to ask people chocolate versus vanilla?
But did you say chocolate vanilla? What?
I didn't? I just said chocolate versus vanilla? Important science question.
Yeah, sounds like an ill designed experiment. I would expect more from a scientist.
Well, I didn't want to be over specific. I wanted to sample, you know, people's general vibe about these flavors.
The word chocolate and vanilla.
Yeah, exactly. It wasn't a question of like which one you prefer to spell, obviously, It's about the flavor and anyway, the Internet came down on my side, Chocolate fifty eight percent to vanilla forty two percent.
Wow, that's that's relatively close. I would say, don't you think I actually was surprised. I thought chocolate was going to blow vanilla out of the water a little bit more. Here you go, there you go.
Hey, you know I'll take a twenty point differential.
Well, we all know that whatever the internet thinks is the best choice for anything.
Well, I would say whatever our listeners thing is definitely you know, sampling the truth of the universe.
I see, did you have everyone sign a little like waiver to testify that their listeners? This is getting more unscientific by the moment, by the way.
They all follow us on Twitter. Why would somebody follow us on Twitter and not listen to the podcast? That just makes me.
Nose exactly if they're already listening to us in our podcast, why would they follow us.
On Twitter for important science questions like chocolate versus vanilla? The chance to weigh in on the ultimate debate in the universe.
Well, I guess if you'd like to go with the majority, you know, the mainstream, I guess that's your thing.
Right, Vanilla is definitely not the boring middle of the road choice.
For sure.
Vanilla is the rebel choice.
Yeah, it's the in the minority choice. But anyways, welcome to our podcast Daniel and Jore Explain the Universe, a production of iHeartRadio.
In which we appreciate all of the flavors of the universe, the quantum, the classical, the things that make sense, the things that don't make sense. We blend them all together into chunks so tiny and so smooth that you can appreciate them without having to chew on any intellectual pebbles.
That's right, because it is a delicious universe, full of amazing textures and flavors and temperatures of treats. And so there's a lot to talk about and a lot to try to explain to everyone.
And there's a wonderful and long history of trying to understand the universe, of looking at the stuff around us, seeing if it makes sense, breaking into smaller pieces and seeing those pieces make sense, digging in even deeper to smaller and smaller pieces, until eventually we get to stuff that seems to follow weird and different rules, rules that surprise and confuse us.
The universe is full of rules, interesting rules that are sometimes helpful, like Newton's laws or general relativity by Einstein. But sometimes there are rules that kind of doesn't quite make a lot of sense, at least to a human.
Because our tendency is to think about things in terms of the things we know. When we discover a new object, we think, Oh, maybe it's a little bit like a grain of sand, or maybe it's a little bit like a basketball. Can I apply the rules of waves to this thing? Can I apply what I know about bananas to this new discovery? So when we unearth quantum particles, our first guess is to think, oh, these are like tiny little dots that follow the rules of classical physics. Maybe they move through space, they have velocity and position, they're just super duper tiny. But what we've discovered is that they are not like anything we have ever seen before. They're not tiny little dots of sand, just like baseballs, but much much smaller. They're not even just like waves. There's something else, something weird, that follows a new set of rules that we have to discover and savor.
Yeah. I feel like whenever we start to talk about things that don't make sense, it probably means that we're going to the quantum realm and we're going to talk about quantum things.
Yeah, but this is our experience every time we extrapolate from our intuitive experience, from our understanding of the world around us, not just the tiny and the quantum, but also the very very big. Right, thinking about the universe as a whole, and maybe having an edge or having a beginning, all those things defy our understanding because they're not part of our experience, so we don't have like a natural vocabulary a way of thinking about them that's comfortable. Instead, we have to rely on mathematics to bridge us into a new language, a new way of thinking about the world.
Yeah, but I guess it's part of that is I wonder if it's just like the context in which we came up in as a species, like our size, that we just happened to evolve into, Like if we were much much tinier as a living thing, you know, maybe the quantum rules of the universe would make more sense than the classical rules of the universe.
I think that's probably true, And one day we might meet like microscopic aliens whose scientists of all finding quantum mechanics to be totally intuitive and classical physics to be very very weird. Of course, they wouldn't call it classical physics. They would call it like, you know, huge physics or something. They would think it's very strange that if you take ten to the twenty nine quantum particles, they somehow come together to act like one big particle.
That's an interesting question. I wonder, like, what's the smallest living sentient thing you can have? Like can you make a being out of straight up a few quarks, you know what I mean? Or the strings inside of quarks.
It's a really fun question. And Max Tegmark, who's a physicist in MIT, has this really fun paper about where consciousness comes from, and he thinks it's actually a state of matter. We're going to dig into it in a future podcast episode. But it might be that everything in the universe is aware and that even small combinations of objects can somehow do calculations and maybe even be conscious.
Dude, they have to smoke some special things in order to get into that topic.
Banan appeals, for sure.
Well, the quantum universe is full of interesting and weird rules, sometimes rules that don't seem to make sense, or that even seem kind of fair.
And as we explore the quantum universe, we discover these rules. A lot of the time these rules are just descriptive. They just describe what we see. They don't always fundamentally explain it. But sometimes we can actually find a reason for it. So that's sort of the strategy is like, look out in the universe, see what's going on, see what's not going on, so we can understand what the dos and don'ts of are the particle world, and then try to extract from that some fundamental reason why the universe is this way and not some other way.
So to the other podcast, we'll be tackling the question why can't two fermions be in the same quantum state. Now, first of all, Daniel, let me just say that I'm glad you're on board with the phrase the quantum realm. Have you sold out to the Marvel corporate machine yet?
Chiching, No, it's true. I have the new ant Man movie on the brain. Can't wait to see it.
Oh really, you're excited even though they're jumping into the quantum realm and finding all kinds of things inside of it.
Yeah. Absolutely, I like those movies. I mean they are scientifically mostly nonsense, but they also don't take themselves too seriously and they have fun with it, and I think they're really creative. The first couple had some really beautiful visuals of like what the quantum realm might look like, what it might be like to visit the quantum realm. So I think they're a lot of fun.
Oh wow, I feel like you are getting paid by Marvel Radio.
You're like, is this the Daniel? I know what I know science.
You like the random use of the word quantum.
No, I don't only like hard science fiction. I dislike hard science fiction that gets it wrong. You know, if you want to pretend to be serious about your science and then you get it wrong, then you get the merits from me. But if you're going to make fun of yourself along the way and just have a good time, then let's go for it.
Well, in this case, we're asking a kind of an interesting question here about the quantum nature of things, that why can't two fermions be in the same quantum state? Now, I imagine this is maybe not a question most people have thought about before.
This is something people run into in high school chemistry when they're like learning about electrons and electron orbitals. But it's a really deep and important concept in particle physics theory that relates to like how particles operate, what it means for particles to be identical, what it means to like swap particles from one state to another. Turns out to be a really deep and important concept in particle physics, and something a couple of listeners wanted to know more about. How does it actually work and why does it happen.
Maybe it'll be the plot of the next ant Men movie.
You can't have two ant Men in the same place at the same time.
Yeah, one. I think they have multiple ones in this latest movie. So maybe the plot line is toast, or.
Maybe it just means ant Man is a boson and not a fermion.
Or maybe he's an antiparticle.
I wasped right into that was usual.
We were wondering how many people out there had thought about this rule that applies to fermions or electrons, and so, as usual, Danny went out there to ask the internet, right.
That's right. Thank you very much to everybody who participates for this segment of the podcast, and if you would like to share your thoughts for our education and entertainment. Please don't be shy. Write to us two questions at Danielandjorge dot com.
So think about it for a second. Do you know why two fermions can't be in the same quantum state. Here's what people have to say.
I'm not sure of the terminology. I think there is an exclusion principle something that says that they can't occupy the same state or same space. I don't know if it's called the Paul exclusion principle. I'm not sure.
So I think the fermions are the for scaring ones. Why can't they be in the same quantum state? Or maybe they're all entangled with each other and so they all have to have like opposing states of some sort.
I am merely guessing that two fermions cannot have the same quantum state because they have different properties.
Well, maybe because they have the same charges, and then they need to find a more stable spot to be related to some other opposite charge particle.
I think it's about balance to fermines cannot be in the same quantic state for the same reason that a magnet cannot have the same pole in both sites.
I'm a bit fuzzy on what fermions are. But if they can't be in the same quantum state, I think it might be to do with the fact that it's kind of like magnets, where you need in order for them to be magnetic, you have to have one pole opposite to the other, something similar like that, where they one needs to spin off, one needs to spin down.
All right, A lot of fun answers here. Nobody mentioned Paul Rudd.
Nobody else out there is a shill for Marvel, like.
I am, hey, yeah, apparently you keep bringing it up.
You rather, Paul Rudd, I want in.
On this, By the way, if you have a hookup with Marvel, I'm totally in.
All right, sounds good. No, these answers are pretty good. They're sort of all over the place. I was a little surprised. I thought we'd hear more mentions of the poly exclusion principle. More people need to take or remember their high school chemistry.
You mean you were expecting more people to mention the poly exclusion principle.
Yeah, absolutely, I thought it was something people knew pretty well. I mean, I remember suffering through it in high school chemistry. I imagine a lot of other people have.
Well, let's step into it, Daniel. What is the paly exclusion principle and how does it apply to quantum states and fermions.
So the poly exclusion principle basically just says that you cannot have two fermions in the same quantum state. Right, It's basically a statement of the problem. Worse, it references these particles fermions, named after Enrico Fermi. But these are the particles that make up matter. So quarks and electrons are fermions, and this is why, for example, you can't have two electrons in the same state around a hydrogen atom. The poly exclusion principle forbids it.
Okay, So let me go back a little bit. So a fermion, it's what do you call the matter particles? Right?
Yeah, we have two different kinds of particles in the standard model. We have the particles that make up matter, so the electron, the quarks, for example, and out of that you can build protons and neutrons from which you can make the nucleus. Add electrons, you get atoms. Buying them all together you get molecules. We're basically built out of those things. There are also other particles These are the force particles. The particles like the photon that binds the electron to the nucleus and the wn the z bosons for the weak force, and the gluons for the strong force. These particles are the force particles. There's an interesting difference between these two kinds of particles. The first one the fermions. You can never have two of them in the same state. Two electrons can never be in the same state. But the other group, the force carrying particles, these bosons, there's no limit, Like you can have two photons in the same state, ten photons in the same state, a million photons all piled on top of each other. So fermions can never be in the same state. Those are the matter particles, and bosons can be in the same state. That's this weird division.
Okay, Now, let's maybe defline for people what is a quantum state, Like what does it mean to have a state and what can those states be?
So what can quantum particles do well? They can like be in some location. They can also have a certain amount of energy. They can have a certain kind of spin, like some of these particles can have spin up or spin down or other various weird kinds of spin. So basically, anything that describes the particle is part of its quantum state. A quantum state is just a description of the particle.
Like I mean, like, where is it and what's it doing? Yeah, exactly, that's what a state is.
M m. The way you might describe like a classical object by saying where is it, how fast is it going, what is it location in velocity, it describes the classical object. A quantum state is just a description of the quantum particle.
Like the state of a baseball might be like it's over here, it's moving in this direction, and it's also spinning in place, and maybe also like its temperature. Would that be kind of like what you need to describe a baseball?
Mm hmm. Imagine, for example, we live in the simulation and you are the programmer of the simulation. What details do you need to keep track of to run your simulation. That's the quantum state of a particle.
I see. Well, I'm not sure how many people out there know how to program, but I think maybe it's sort of like a list that identifies everything that we know about a particle. That's kind of what you're saying, right, And so for small particles, that list is not like an infinite list, right, Like it's a list of maybe like five things exactly.
It depends a little bit on where that particle is. An electron in free space doesn't have energy levels the way an electron around a hydrogen atom does.
Wait, what depends on the situation. So like, if I just have a particle out there in space by itself, what are its quantum state variables?
A particle just out there in space with like no potential, no forces on anything, a free particle, then the quantum states are just the location and the.
Energy and the energy what do you mean by energy.
Well, it's velocity, right, it's.
Kinetic energy m And it's spin as well.
Yes, absolutely, and it's spin. But remember out there in free space, the kinetic energy can have any value. Electrons are quantized into energy levels around a hydrogen atom because they're confined. The quantization only comes from the confinement. Electrons out in free space don't have like energy levels, whereas electrons around the hydrogen atom, for example, do, So there's an important distinction there about the quantum state of these particles or in free space, you would just say the energy around the hydrogenom you would say the energy.
Level, but when it's out in space you also count like the spin of it too, Right, are there any other quantum variables? I guess each kind of particle has different kind of variables attached to it.
Yeah, exactly. And electrons and have two different kinds of spin, spin up and spin down. Photons can have three different kinds of spin. The Higgs boson doesn't have any spin at all, So it depends a little bit on a kind of particle and also the situation that it's in.
Okay, So now the rule here is that no two particles can have the same quantum state. Now what does that mean for like particles out there in the open floating around space? Like that means that no two electrons can be in the same spot with the same velocity and the same spin.
So the rule is not that no two particles can be in the same state, but no two fermions. Number. Half of the particles we call them fermions, they can't be in the same state. The other half we call them bosons. They have no problem being in the same state. So electrons and quarks, they can't pile up on top of each other in the same state, whereas photons can. So your question is, like, what happens out there in empty space? Well, yeah, two electrons cannot be in the same state, meaning they can't be in the same location with the same spin and the same energy. That's just not possible.
Well that's interesting, Like that just seems to be like the rule the universe has, right, Like that's something that you think can't happen. But I guess as anyone actually tried to see if you can fit to electrons in the same spot.
Oh yeah, the universe tries to do it all the time. Remember, the universe likes to have things relax down to the lowest energy that's really what forces are. Forces are things that push things down to lower energy configurations. So think about what happens when you put electrons around an atom, right, the first one goes down to the lowest energy level, and then the second one can't go down to the lowest energy level because that's filled. Right, It's sort of like play and connect. For you put one piece in, the next one can't slot into that lowest level anymore. It has to go to energy level two.
I guess I'm trying to understand, Like this rule on the free space situation first, and then maybe we can get into the going around an atom situation after that, because like electrons, for example, don't have a volume to them, right, they don't have a solidness to them. So technically, like you could have an electron on top of another electron, but you're saying the universe somehow, for some reason, doesn't like that.
Yeah, Well, I think the free space example is a little artificial because you bring two electrons together, they will have a force between them. They will try to repel each other, so they're no longer free electrons, right, So that example is a little bit artificial. I think. You know, out in space, the universe does try to compress electrons down into tiny dots. We'll talk later about what happens. For example, in white dwarfs. White dwarfs don't collapse into black holes because the electrons resist being put on top of each other, and the forces are strong enough to overcome this electrostatic repulsion. But they're not strong enough to overcome this quantum resistance to electrons being on top of each other. But it's not exactly out in free space, because again, you know, electrons on top of each other there are pushing away against each other. There is potential energy there.
I guess. I mean, then, let's talk about two electrons out there in free space. And I know they repel each other by the electromagnetic force because they're both the same charge. But let's say you managed to overcome that. You're saying, like, there's something else pushing these two electrons from being on top of each other.
Yes, exactly. The universe will not allow you to do that, will not allow you to put two electrons right on top of each other because of this weird exclusion principle. And again, two photons and no problem even two W bosons, which do have a charge, right, so they would resist each other. Two W bosons no problem to electrons problem.
Interesting, Okay, so you can put two photons into each other, and you can't put two W bosons on top of each other, even though like the W boson, they have mass, right, So even things with substance can exist on top of each other. But somehow electrons that's a no go.
Yeah, exactly.
And is there a reason why.
There's definitely a reason why, and it's connected to the particle's spin. Electrons have spinned one half and photons and ws and zs have spin one, and so there's a fun and subtle reason for why that means they can't be on top of each other.
All right, Well, let's spin into that answer and figure out where exactly this rule comes from. Man, how does it impact the rest of the universe. But first, let's take a quick break.
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All right, we're talking about the intricate rules of the quantum universe, and one of those rules is that two fermions can't be in the same quantum state at the same time. Somehow, the universe has a problem with two fermions to matter particles somehow, I guess, I don't know, being in sync, being in the same place at the same time, and being totally identical.
Yeah exactly. It has an issue with fermions. Having essentially the identical setup is not allowed. It's like one per slot, you already filled your slot. You got to go to the next slot. You got to find another way to be.
I guess for the the idea of too electrons out in space, like, it's probably, first of all, very hard for two electrons to be in exactly the same space, but it seems like the universe just resists two electrons being really close to each other.
Even Yeah, if you have some volume out there and then a bunch of electrons, then the universe likes each electron to be like in its own little volume, you know, like V over N something like that, and so it resists electrons overlapping too much.
Oh, so the rule is more like it can be in the same state, but also like the universe doesn't even like for the states to be close to each other.
Yeah exactly, because remember, electrons have like a wavelength, and so as those wavelengths start to overlap, then the universe resists it. Technically, if you keep squeezing it, lets me get closer and closer and closer, but fundamentally it resists I'm being right on top of each other.
Okay, so the innert has this problem for emeons apparently, and the weight it kind of comes into effect that affects most people is as you were saying, when electrons start to orbit around the nuclei of atoms, right.
M hmm, exactly, and this has a huge effect on basically all of matter. Right. It's the reason that we have energy levels in atoms. It's the reason why we have the periodic table. It's the reason why atoms behave the way they do. The universe would be totally different if electrons could all like slot down to the lowest energy level. Now what I said earlier wasn't exactly correct. It was one little nuance, which is you can't have two electrons per energy level because they can have different spins. But the electrons have to be in different states. So you can have like one electron around hydrogenam no problem. For helium. You have two electrons, so they can both be in the lowest energy level, but they have to have different spins because they can't be in the same state. Then when you go to lithium, you have another electron. It can't fit in the lowest energy level. There's already two electrons in there, one spin up, one spin down. There's no other way to separate the electrons. There's no other label to distinguish it. So it has to go in the next energy level, goes in the second energy level, so that electron has more energy than the lowest level.
Well, I guess I just wonder how many people out there are familiar with this idea of energy levels in electrons orbiting the nuclei of atoms. Maybe can you connect for us this idea of like, okay, two electrons out in space can be in the same quantum state. They can to being on top of each other. But now you know, if they're orbiting around the nucleus of an atom, I feel like there's a bunch of space there. Why can't they kind of orbit at the same time. What does this mean about the energy levels?
Well, if you have an electron and it's around a nucleus, you've already confined it to a very small space, right, And so in order to have two electrons basically being on top of each other, from the point of view of the universe, those two electrons are on top of each other. If they're orbiting the same nucleus, they have to have some way to distinguish between themselves so they're not in the same state. As that means having differ from spin or having different energy. And around an atom, you can't just have any arbitrary energy out in a free space. An electron can have any energy at once. When an electron is captured by a nucleus, when it's in some quantum state that's settled into the potential around a nucleus, then it has certain energy levels it can be in that quantization. The fact you have an energy ladder rather than a full continuous spectrum comes from capturing the electron. It's the confinement that produces those energy levels. And so now instead of like being able to have two electrons with slightly different energy, now the electrons have like discrete options energy level one, energy level two, energy level seven. You can't have energy like one point two around the atom. It's not a solution to the Shirdinger equation, is it.
I wonder if it's a little bit like the Earth orbiting the Sun, like you know, if Earth is out there in space. It can go as fast as it wants in any direction at once. But if you're sort of requiring the Earth to go around the Sun and do it forever in a consistent way, there's only so many velocity it can have, and it's only so many energy levels it can have.
Well, but gravity isn't quantized to our knowledge that we think maybe eventually we will quantize gravity. So the Earth could exist at any radius around the Sun. It just has to have the right velocity. And so there is an infinite number of potential orbits for the Earth, whereas for a quantum object it really is different. It's determined by the shortening your equation, and there just are quantized solutions to that.
Okay, so now we've applied the rule to electrons orbiting in nuclei, and that tells you that two fermions can't orbit at the same level unless they have a different spin. Exactly why why is that? What does the spin do that lets them occupy the same orbit?
So the key thing is that they have to have different quantum states, and the spin is part of that quantum state. It's like one of the labels. So when you have electrons around an atom, you have four of these labels. You have N, which tells you the energy level, you have L which tells you like the sub level that you're in, M, which tells you which of those l's in. And then finally the spin And so the spin plays two rolls. One is like, it's another quality that the electron can have that lets it distinguish itself from something else. But also the electron having spin one half is the reason why electrons cannot do this. Photons have spin one which is why they can pile on top of each other, and electrons have spin one half, which is why they cannot pile on top of each other. It all comes down to these particles spin.
Well before we spin that way. I guess maybe it tells a little bit about what would happen if we didn't have this rule, Like if we didn't have the poly exclusion principle, what would happen to like electron orbitals and atoms and the things the molecules in our body.
So if we didn't have this, then electrons would all relax down to the lowest state. They would all be in the lowest energy level, because that's what the universe likes to do. It likes to spread energy out. It doesn't like to have little dense depositions of energy. So, for example, if you zap an electron and you give it extra energy, so it jumps up the ladder to like, you know, energy level ten, and you just wait a few moments, then it will radiate a way that energy and relax back down. So everything likes to sort of flow downhill to the lowest energy levels. And if you didn't have the poly exclusion principle, they would all just pile up at the lowest energy level, and that would make a big difference. For like, the size of these atoms. You know, the size of the atom is determined by the electron orbitals, and they get bigger and bigger and bigger as you get more and more electrons. Goals for example, has like you know, dozens of electrons, and so it's much larger than hydrogen. Hydrogen just has one electron, and so like, the very structure of matter depends on the volume of these atoms. If somebody like turned off the poly exclusion principle, we would all collapse to be much much.
Smaller, you mean, we would all go into the quantit realm, Like.
Man, no, we'd all be about the size of a chocolate chip, I think. But also it would change chemistry, right, The way that atoms bond together depends on these orbitals, the way that they interact, all their properties, like how they're metallic or how they glow, the energy they can absorb. All this stuff depends on the poly exclusion principle, And so the whole universe would be totally different if electrons could pile up at the lowest levels.
Okay, I think I see what you're saying. Like, if I just have the nucleus of an atom without any electrons, just sitting there, and I threw an electron into it, it would kind of snap into a certain orbit or kind of place or some sort of you know, cloud or function around that nucleus. Now, if I threw another electron, if it didn't have the polyexclusion principle, it would also fall into that lowest kind of orbit. But because you have the exclusion principle, the electron can't like get that close to the nucleus, and so it kind of forms another kind of orbit that is kind of maybe bigger, you mean, maybe bigger and more fragile too.
Yeah, exactly. Then that controls the volume of the atom, but also controls how these things operate, you know, how they build themselves into crystals, and then how electrons can flow through those crystals. Like why are metals conductors because they have a bunch of electrons in this conduction band they're forced to be up there, and they're higher energy level bands flowing around semiconductors for the same reason. So the reason we have all these complex structures and complex behavior, the periodic table and all that interesting chemistry comes from electron orbitals, which only are interesting because electrons populate them, and they only do that because of the pal the exclusion principle. Otherwise they would always just be in the lowest energy level.
Interesting. Now that we know what it is, let's maybe dig into the reason. Why Why does this have an issue with two fermions being on top of each other, Like it doesn't seem to have a problem with some of the other particles like the Higgs boson, or photons or w particles being ontop of each other. Why does it have this bias against electrons?
Don't be so negative about it, you know, maybe you could think about it like a special property you know, the electrons can like stand on top of each other to achieve things electrons could otherwise never do. Right, It's like an ability instead of a bias.
And I feel like the word exclusion is never good.
That's true, everyone.
Should be as inclusive as possible.
Well, the issue really does have to do with the quantum nature of these things. So fermions, electrons, and even protons which are built out of quarks. These things have a really weird property that we've never seen in classical physics, and it has to do with what happens when you swap two of them. So imagine just you have two particles, particle one in particle two, and maybe they're in different states. You call one state A, one state B. Doesn't really matter. Now, imagine what happens if you swap them. Right, you take particle one, which used to be in state A, and I say, now you're in state B. In particle two, which used to be in state BING, you say, now you're in state A, all right, And so you have two particles and you sort of swap their arrangements. The universe says, and quantum mechanics says that when you do that, the wave function that describes what happens and tells you what's allowed. That wave function gets a negative sign, and that doesn't happen for bosons. For bosons, the way function doesn't get a negative sign, and that has really really important consequences.
I think you're talking about like a mathematical operation, or are you talking about like if I physically take two particles and I swapped their states mathematically, the sign of the whole of the two particles somehow gets a negative.
Is that kind of what you think, Yeah, we're talking about the wave function, which is like the thing that determines what happens. Right. Remember, you take the wave function and you square it, and that tells you the probability of various things happening. If you're talking about like Schrotinger's cat, there's a wave function for it to be alive and a wave function for it to be dead. Those are two different possible outcomes, And the way that you discover the probability of one versus the other is you take the wave function for that outcome and you square it. That's the rule.
Now, a wave function is is like a mathematical concept or construct that describes what something is doing or going to do.
Yeah, it's the solution to the shortening equation.
That doesn't help me.
We don't really know what the wave function is. It's problematic philosophically, like it's a part of ourlations. We use it to make predictions. Nobody really knows, like is the wave function a real thing out there in the universe or is it just sort of like something in our heads. That's an intermediate step that we're using. But it definitely seems to be important, and it's part of the way we think about quantum physics.
Like maybe if you have a baseball and you're throwing a baseball, you might describe it using a vector, like a vector from here from the picture to the baseball that describes the ball. Wave function is kind of like that for quantum particles.
Right, yeah, exactly. And the wave function is weird because it can also be negative, and it can also be like complex, right, it can have imaginary numbers like one plus two I. Right. The wave function is really weird. It's not physical in that way. But the interesting thing is that that all goes away usually when you use the wave function to make a prediction, because you square it and the imaginary parts go away. And the negative signs go away. Nobody really cares about the wave function being negative usually, but in this one particular case it turns out to be weirdly really important because what happens if you you have two fermions which are identical, like two electrons, and they're in exactly the same state. Maybe they're both around a hydrogen atom, and they're in the same energy level and they have all the same spin. Right now, what happens, Well, take those two particles particle one, particle two. They're indistinguishable, right, They're in the same state, and you swap them, right, swap them from one to the other. Now, really that has no effect because you had two identical particles in the same state, you swap them, nothing should change. But the universe says if you do that, you get a negative sign for the wave function.
You mean, swap them, like pick them up and change their you know, like move them around, like swap their positions or swap them.
Hypothetically, like ask what would the wave function be if this particle was over here and that particle was over there. Don't actually do it, you just say, like, hypothetically, what would the wave function be if you have them in the opposite.
Configuration, but they're the same configuration.
Well, they're in the same state, but one of them has this label one. You know, one of them is particle one and one of them is particle two. Though they're in the same state, so you can't really distinguish them, right inticle, They have the same orbit, the same spin, everything is the same, and if you swap them as you're imagining, nothing changes because they're the same particle in the same state, so it should be the same. But the universe says, well, the wave function has to get a negative sign if you do this for fermions. So the only way to satisfy both of those requirements to say, well, it has to be the same if you swap them, and it has to get a negative sign if you swap them, is for the wave function to be zero. So if the wave function is zero, then when you swap it, zero is negative. Zero. It's the only number that is its own negative, and so from that you can conclude that this is impossible. The universe just doesn't do this. The wave function for two fermions being in the same state is always zero. That way it can satisfy both rules that swapping two identical particles, doesn't change anything, and that the wave function gets a negative sign.
And you were saying earlier that this is because of their spin, Like if because they have a certain spin when you try to do this swapping, then some weird things happen.
Exactly because this doesn't happen for particles of a different spin, like with folkons. Not an issue photons, the universe says, yeah, if you have two photons in the same state and you swap them, you don't get a negative sign. It only happens for fermions. And it's that negative sign that makes this impossible. It's a negative sign, which is why fermions can't be in the same state and bosons the universe doesn't have a problem with, and it just operates differently on bosons than it does on fermions. Then you might ask, well, like where does that negative sign come from? Why do fermions get a negative sign when you swap them. That's weird, right, Like why should you get a negative sign. You're just swapping two identical particles, it's basically the same setup. Why would you expect the wave function to be the opposite? And this is the weird thing that these quantum fermions can do that classical particles can't do. There's like no classical analog to this. There's no example in the natural world that you can think about with baseballs or coffee cups that is like this. It's most closely connected to rotating things. Like if you take your coffee cup and you spin it around three hundred and sixty degree, it's the same coffee cup. That makes sense, right, And the same thing is true for photons. If you take photons and you rotate them by three hundred and sixty degrees, you get the same photon. Electrons don't do that. Electrons, if you rotate them by three hundred and sixty degrees, you get the negative wavefunction then the original electron. So there's something weird and different about fermions that picks up this extra negative sign that's very different from anything we know about before.
And you said it has to do with the quantum spin, but I guess don't some of the fermions have no spin, or do all fermions All of these matter particles have spin, and do they have the same spin, And that's why they have this rule against them.
Exactly all fermions have the same spin. They all have spin one half, and that's sort of what it means to be a fermion. I mean, some people say, no, fermions are things that do this that don't overlap with each other. They follow the polyexclusion principle, and it's because they have spin one half. Other people say, no, fermions are all particles that have spin one half. But it's the spin one half that makes them do this, And it's too mathematical to explain, but if you like dig into the quantum field theory, this comes out of that mathematics of the quantum field theory. The particles that have fields that have spin one half, when you rotate them, you get this extra minus sign, or when you swap them, you get this extra minus sign. It's called the spin statistics theorem. And that's fundamentally where this comes from. So it's the one half spin nature of these particles that means that they can't pile up on top of each other, whereas particles with spin one or spin two could totally pile up on top of each other and be in the same quantum state no problem.
Or I'm getting the sense that maybe you gave them spin one half because they can't be in the same place at the same time. You know what I mean, Like like which game fur is the chicken or the egg? The spin or the exclusion principle.
Oh, that's a great question. Actually, this is how electron spin was discovered.
That's what I mean.
Yes, no, absolutely, this is why spin was invented to explain this, right, And the story is actually really fun. People were looking at electron orbitals back in the early days, like nineteen thirties and trying to understand why the electrons filled up the orbitals the way they did, and they had this idea of the exclusion principle, but they didn't understand like why you could have two electrons in the lowest level what's going on? And in the next level, why could you have eight instead of four? There was this weird factor of two that nobody could explain, and Paully wrote a letter to some other physicists about it, and he said that electrons have a two valuedness, not describable classically. He just meant like they have some physical property that has two options, like an up and a down, or a zero and a one, or you know, a switch that you could flip there's something else about the electrons that let them distinguish each other, so you can have two of them in the lowest energy level. That's how we discovered that electrons actually do have spin.
Or at least you called spin, because you quite have another name for it, right to explain this phenomenon.
Exactly, And it was two young Dutch physicists, gou Smidt and Uhlenbeck, who read this letter from Pauline and they were like, oh, wait, maybe electrons are spinning. So they did a bunch of calculations and they're like, ooh, electrons are spinning. This is really awesome, and they wrote this paper and they sent it off and then they showed it to another famous Dutch physicist, Lorenz, and Lorenz was like, y'all are totally wrong. Electrons can't spin. Their surfaces will be moving faster than the speed of light. So then they realized, oh my gosh, our paper was wrong, and they tried to retract it, but it was too late. It had already been published. And then it turns out that electrons do spin, but not in the way that they expected. They have this weird property quantum spin, which is not spin in the same way that like a baseball spins, it's some other weird kind of angular momentum. So the history of like the discovery of electron spin is pretty funny.
Man, particle physicists are pretty catty? Is that where short Anger's cat came from?
Exactly what? I love This story of two guys inventing spin for the wrong reasons, trying to retract it and then ended up being right, sort of accidentally interesting.
All right, Well, the universe us to have this rule, and it seems to be embedded in some of the mathematics that maybe makes the universe works. Let's talk about that thorny philosophical question and also some of the consequences of this poly exclusion principle on the rest of the universe. But first, let's take another quick break.
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All right, we're talking about the question of why can't two fermions be in the same quantum state? And what this means is that no to electrons or no, two quarks can be kind of on top of each other, not out there in free space and not orbiting around an atom, which is what gives us the wonderful chemistry that makes us who we are. And we talked a little bit about that. The reason that two fermions or two electrons or two quarks can't do this is because it messes up the math. Now, my question is, like, does that mean that the universe is mathematical? Like does the universe care about math? Like why does the universe care about math, Like if I were at the universe, I'd be like, I'm the universe. I don't care about math. Two plus two equals five. Why not?
We know, but it seems like the universe does follow mathematical laws, and the universe is self consistent, right, the universe doesn't have like two things going on at the same time or things that contradict each other. So it might just be that you can have lots of different universes out there, but only the ones that are self consistent that follow mathematical laws are the ones where you have, like people evolved with brains that to make sense of these things and study them. So we don't really understand it, but our universe does seem to follow mathematical laws, and when you find a mathematical principle, it seems to manifest itself in nature. Right. What we're talking about are the laws of how quantum feels operate, how they wiggle, how they transfer energy between them, the rules that they follow, and those rules seem to have like consequences way down the line that affect us and ice cream and stars.
I guess what's kind of weird is that I'm sure math has a bunch of other rules it likes to do, it doesn't like to do. Maybe not all of them are represented in a physical thing, right, Like not all of them have a physical manifestation of those principles. But this is a case where you know, you have something that doesn't work in the math, and it actually has like a physical, a tangible, you know, solid representation of that math.
Yeah, exactly. It's certainly true that there are more sort of mental universes in mathematics than exist in the physical universe. Like you could dream up all sorts of universes that don't exist out there. But once you think about just our universe, if you think about the mathematical laws that describe it, the universe basically does everything that the math allows. Like if it's possible for an electron to radiate a photon or you know, a Higgs boson or something, it will. So the universe does everything that's mathematically allowed. And so if something is mathematically forbidden, if something doesn't happen, it's probably because it's mathematically forbidden. That's like one way that we figure out what the rules are. We look and we say, hmm, how come you want and don't just turn into electrons sometimes what's going on there? And it turns out there's a mathematical rule that describes why that can't happen. It often reveals some like underlying physical principle, And so that's why it's so fun to find these rules, describe them mathematically, and then step back and think, why is the universe this way? Would it be possible to have a universe without this rule or is this rule necessary for the universe to like make sense at all?
Well, I guess what's weird too, is that, you know, like, I'd be fine if if the universe had this rule that said, oh no, you can't have the two electrons kind of on the same spot at the same time, and be like, okay, fine, that never happens. But it's almost like the universe resists even getting close to that possibility. Like if you take as we were talking about earlier, if you take two electrons and you try to squish them together and you can overcome the electromagnetic force that repels them, there's another force almost in the universe that kind of resists that squishing them together. Right, It's like the universe is like kind of freaking out a little bit like, ah, you're getting close to an illogical inconsistency. Keep those two things away.
Yeah, exactly. And some listeners have written in to ask about that. They're like, what's the mechanism of that? Which of the forces is the thing that keeps the electrons from being on top of each other? Because they imagine that like otherwise they would, And so in order to like change the direction of electron or something, you need to have some force that operates there. And if you try to read about it, it's a little bit confusing because there is a description of this, like Fermi pressure or this effective force that describes it. But if you think about forces in terms of like the fundamental forces, you know, the weak force, a strong force, the electromagnetic force, this is like an emergent force. This is something that comes out of observing these things and trying to describe the energy levels that they fall into and that they don't fall into. Really, there's no force that's doing this. It's just something the universe doesn't do. Like an electron just can't go there, you know, it's just like not an option for the electron.
So is there like some sort of force pushing these two things apart? That is working kind of on behalf of the Fermi exclusion principle. Is there that you think or is it more sort of like a quantum probability or improbability that keeps the two things apart.
It's not a fundamental force, but they're sort of like an effective force. I mean, think about like having a bunch of electrons and trying to squeeze them down into the same place. Well, what's really going on is that you can't have the electrons in the same state, and so the electrons resist that by having different energies, you know, the same way that like electrons around a nucleus will fill up the ladder of energies, so some of them have more energy than otherwise. Right, you're trying to squeeze a bunch of electrons down to a tiny little blob. They will resist it because some of them will have higher energy than otherwise, because they're forced into it, forced to stay in those higher energy states because of the ladder. And effectively that means that they are pushing back if they have more energy. They're like bouncing off the walls of your box with more momentum. They're pushing on that box, and so the fact that the electrons can't all go to the lowest state means to have more energy, which means effectively they're pushing back on you as you try to squeeze them down. So that's like an effective pressure, right. It's not like the electrons are pushing against each other or like there's a force between the electron and the walls of your box. But as you try to squeeze electrons down, you'll notice this effective pressure that wouldn't happen if you did the same thing with photons.
Oh, I see what you're saying. It's more like if you try to get an electron to collapse to the lowest possible, for example, orbit around in a nucleus, but there's already an electron there. It's not like the electron pushes back against you to try to collapse it. It's just that the electron doesn't give up. It's the energy that it has. Yeah, Like in order to squeeze it down to the lowest it needs to give up that energy. But because it can, it like the electron hold onto that energy. And that's basically the same as like pushing back against.
You exactly, And that's the mechanism for it to push back, and we actually see that happen out there in the universe. And for example, white dwarfs are these really really dense blobs of super hot metal. If they're left over. For at the end point of a star, a star has done all the burning that it can and it's blown up maybe and left behind its core. They're just sitting there, hot and glowing and eventually cooling down. These things are incredibly dense and the gravity is very very strong. So you might wonder, like, why doesn't the white dwarf collapse into a black hole? The thing that keeps a star from collapsing into a black hole is that it still has fusion happening. It's like radiating out energy, it's like blowing up. But a white dwarf isn't doing that anymore, so it's just like a blob of mass. Why isn't it collapsing into a black hole? And the answer is electron degeneracy. These electrons resist getting pushed on top of each other, and they prevent this thing from turning into a black hole. They're like one of the last barriers of defense against gravitational collapse.
Well it's pretty cool. Would you say white dwarfs are pretty awesome? Are they more awesome than chocolate dwarfs?
I think the fate of the universe is for all the white dwarfs to cool down and become black dwarfs, which means black dwarfs are cooler than white dwarfs, just like chocolate is cooler than vanilla.
Well, sure, if you leave, I screapout, nobody wants. Nobody's gonna want to eat that ice cream eventually.
But you know, if you add more mass to this white dwarf so the gravity gets stronger, you can actually overcome this electron degeneracy pressure. And what happens is not that the electrons give up and then like pile on top of each other. They're just not allowed to do that. What happens is the electrons combined with the protons to turn into neutrons, so they give up and become not electrons anymore, and then you can get things a little bit denser.
Mmm. You mean at some point like they just become pure energy and then they squeeze together.
Yeah, Well, the proton and the electron together can do like a reverse beta decay and become a neutron, and then you have a neutron star, which is just a big blob of neutrons, and those neutrons get squeezed together by gravity, and the neutrons are also fermions. One of the fascinating things about fermions is it's not just fundamental particles. You can put quirks together in various arrangements to make fermions. Like the proton is a fermion, the neutron is a fermion, and then the neutrons are resisting also because they are also fermions. The reason a neutron star doesn't collapse is because of the neutron degeneracy pressure. The same principle that kept the white dwarf alive is now keeping the neutron star from becoming a black hole. But then as you add more and more mass to that neutron star gets denser and denser, and eventually even the neutrons degeneracy pressure is overcome. But again not by the neutrons violating this rule of the universe. Instead, they just turn into something else. We've talked about the heart of neutron stars before. Nobody really knows what's going on, but it's not neutrons anymore. It's something else. Crazy that's happening. And to understand how you can keep adding mass and a black hole conform at the heart of it would require like a theory of quantum gravity that we just don't even have yet.
You mean, like, we have this exclusion principle, this rule about the universe that says you can't squish two framons together. But at some point, if you try harder, you can sort of bypass this rule because suddenly the things you're trying to squeeh together are no longer electrons or neutrons. They just kind of become pure energy or pure quantum potential, and then they become something else.
Yeah, exactly, And we see those examples in all sorts of situations, like even when it's not at the heart of a neutron star. Super Conductivity works this way. Electrons are fermions, right, they can't be in the same state. But if you get two electrons together and you sort of tie them up together into a single quantum object, they become a boson. There are two spin one half states combined to a spin one state, and it's called a Cooper pair, and it's a key to super conductivity because now these electrons can like flow and slide in the way that bosons can in lower energy states and make things move more quickly. So we can see fermions like exploiting this loophole by becoming bosons, by pairing up. So yeah, absolutely, you can avoid this rule of the universe by squeezing things down or tying things together.
I think what you're saying is that the universe has principles, but if you put enough pressure on it, it totally throws out those principles out the door.
Exactly. Even if I've agreed to eat chocolate ice cream for the rest of my life, I might sneak a sample of vanilla sometimes just for variety under enough pressure pressure at the heart of a neutron star.
Only then we eat vanilla ice cream.
No, I love vanilla. Did you know that vanilla beans are actually more expensive pound for pound than gold.
I didn't know that, but it doesn't surprise me because vanilla is the best. I'll eat vanilla anytime over a goal. All right, Well, it sounds like the universe has these strange rules about it, although under enough pressure or are there certain circumstances, it seems to throughout these or it finds loopholes around these principles, but that it's thanks to these principles that we have things like chemistry and we have chemiccry the way it is, and so without these rules, we wouldn't be here talking about these rules.
Yeah, exactly. It's the reason we even have a delicious dilemma between chocolate and vanilla, which.
I still think you can solve by just having a swirl.
That's the loophole, that's.
Right, Yeah, transform it into something else, rocky road. It's called rocky rost for it already. You spin it, spin it in a different way. All right. Well, we hope you enjoyed that. Thanks for joining us, See you next time.
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