What are paraparticles?

00:00:13
Speaker 1: How does the universe work? What are the rules that govern its most microscopic nature. For a few hundred years, we've been making progress on this question, mostly by taking things apart, and when we zoom into the universe at the smallest level, it seems so far like there are two different categories of particles, matter particles like quarks and electrons, and force particles like photons and gluons. For a long time, it seems like that has to be all there is. What else could there possibly be? But experiments aren't the only way to reveal the secrets of the universe. Another very fruitful path is to follow the math. When we ask what else the math allows, we sometimes get predictions for very weird phenomena like antimatter, or black holes or Higgs bosons, which turn out to be real in the universe. So can the math show us another kind of particle? A weird third way beyond matter and forces. Welcome to Daniel and Kelly's Extraordinary mathematical Universe.

00:01:27
Speaker 2: Hello, I'm Kelly Wiersmith. I study parasites and space, and I think there are four kinds of particles.

00:01:35
Speaker 3: Are parasites the fourth particle?

00:01:37
Speaker 2: I mean if physics were any good, the answer would be yes. See what I think is that y'all like symmetry, and I think that if you decide there's three kinds of particles, that will be an odd number and you'll have to decide there's another kind, so that it's even Hi.

00:01:53
Speaker 3: I'm Daniel.

00:01:53
Speaker 1: I'm a particle physicist, not a paraparticle physicist or a parasitical particle physicist or any.

00:02:00
Speaker 3: Those other varieties.

00:02:01
Speaker 1: But I do love understanding the nature of the universe and finding symmetry in.

00:02:05
Speaker 2: It all amazing. So are you one of those physicists who feels like there needs to be symmetry in these answers or does it just kind of depend on the topic?

00:02:14
Speaker 1: Wow, what a deep question to drop on me at the top of the episode. I think what we've learned so far is that there is symmetry in the universe. Like all the rules we've discovered about physics seem to follow symmetric patterns. There's like reflections and translations, and you can generalize this into abstract algebra called group theory. So the universe seems to be well described by symmetries in mathematics. Does that mean the universe is symmetric or that's just the way we like to think about it. I mean, that's a deep question in philosophy. We're not going to answer it today. But I appreciate symmetry.

00:02:46
Speaker 3: I love it. I love the mathematical beauty of what we've learned about the universe.

00:02:51
Speaker 2: Why should the universe be symmetrical instead of like just a mess? Like as an evolutionary biologist, like it all being held together with like duct tape and zip ties makes more sense to me then it being beautifully symmetrical. But why is it symmetrical?

00:03:04
Speaker 1: I think I have a natural preference for explanations that are simple, that are harmonious and parsimonious, right, Like we think that the universe should be in the end described by one simple idea, and so we're constantly looking for that, and symmetry helps us restrain that. It helps us reduce the number of options, you know, like instead of having to come up with ten numbers, what if there's a symmetry that tells you that those numbers are all related, so there really is just one number that turns into ten. But you might also ask the basic question like, well, why do we expect the universe to be simple and parsimonious, and I don't have an answer for that, you know, just so far that seemed to work, you know, looking for the simplest explanation so far has found us things that work in the universe. They predict experiments, they describe things we haven't seen yet. So many times in the history of science we followed the symmetry in mathematics to make discoveries like particles or like electromagnetism. You know, Maxwell looking at these equations and seeing a lack of symmetry and penciling in the piece he needs to make the equation symmetrical, discovering something real in the universe, or Peter Higgs finding a piece that clicks together with all the other pieces to answer why symmetry is broken, so it seems to work, is the only real answer I can give you.

00:04:24
Speaker 2: Interesting, you know, So I was I'm reading this book called The Remedy right now, and it is about how like Coch and Pasteur determined that microorganisms caused disease. And the author was arguing that actually this kind of flew in the face of we should look for the simplest answer, because the simplest answer at the time was that bad air causes all of these maladies, and so having one cause that explained all of this stuff seemed much simpler than you know, Tuberculosis is caused by this tiny organism, and smallpox is caused by that tiny organism that we can't even see. And so the fact that bad air was simple a sort of made people cling to it a little bit longer than this more complicated answer that tended to be right. And so I think in almost every case it makes a lot more sense to look for the simplest explanation first, but you should not let it close your eyes to the more complex answers that might actually be the reality of the situation.

00:05:15
Speaker 1: Yeah, you should choose the simplest answer that works, that actually describes the universe. Yes, not the simplest answer that doesn't describe the universe. But you're right, you don't know in advance what's going to work and what isn't, And so we often start from the simplest thing because why not right, And if that doesn't work, then we move on to something more complicated.

00:05:33
Speaker 3: And that's how we get chemistry and biology and.

00:05:36
Speaker 1: All sorts of other delicious, beautiful messes of science. Right, that have yet to pull themselves together into a single parsimonious explanation. And that's also one reason why I am a physicist, because physics, I feel like, is closer to getting to a single answer than chemistry is. For example, I was always frustrated in chemistry, like this rule for this thing, and this rule for that thing, and this other rule except for this other scenario. Maybe I just have a bad memory and it's hard to hold all those things in my head. But I just really like to look, here's one equation. Start from that you can get to anything. That just always appealed to me.

00:06:09
Speaker 2: That's so interesting. I think we live on very different sides of this gradient. So like for me, you know, you said biologists and chemists have yet to come up with a simple theory. I don't feel like that's what we're trying for at all.

00:06:20
Speaker 1: Like why maybe that's why you haven't found one.

00:06:24
Speaker 2: Why would you assume that there is one? Like life is beautifully complex, you know, the it depends is where all the fun lives. I think. You know, you're like, oh, that's frustrating, and I'm like, no, that's that's the exciting part. Like what it depends on what life is complicated and messy and that's what makes it beautiful.

00:06:41
Speaker 1: But isn't it beautiful when you find things that are true across all of life? Right Like DNA, for example, undergirds a lot of life on Earth, and that's really powerful to discover that and to understand it. Right, Yeah, it's not as fascinating as like this one kind of frog does this one kind of thing on random tuesdays in my opinion.

00:06:58
Speaker 2: Well, I will politely disagree with you. I think what the frogs are doing on tuesdays I am deeply interested in. But yes, you know, I think it's beautiful that you know, the blueprint for life is stored in the same material no matter what organism you're looking at. But we all do very different things with that material. You know, bacteria do horizontal gene transfer. They're swapping genes back and forth, and you know, we have to have sex to swap genetic material, and we've got recombination and I don't know anyway, that's where the it depends gets fun again.

00:07:31
Speaker 1: Well, we have made a lot of hay in physics, at least in looking for symmetries and then trying to understand when there are holes, is there something to fill that hole? Right the way we did with antiparticles and the way we did with all the quarks, and so often mathematical beauty really does lead us to new discoveries. And that's what we're talking about today on the podcast. Whether there is another bucket, another kind of thing out there in the universe that we can use to describe how everything works, maybe explains why those toads do that thing.

00:08:01
Speaker 3: On Tuesday, at.

00:08:03
Speaker 2: The end of all of our banters, I'm like, how are we going to get back on track? And you always get us there.

00:08:07
Speaker 1: Okay, it's sometimes a bigger step than I expect.

00:08:11
Speaker 4: But.

00:08:14
Speaker 2: You're good at jumping that chasm. So all right. So today we're talking about paraparticles and I had never heard of para particles before, and so let's see if our audience is on the same page as Kelly. So we asked, what are para particles? And here are the answers we got.

00:08:32
Speaker 4: I wonder if it's something to do with larger things showing particle light behavior in certain circumstances. I'm so glad there isn't. TONI exam at the end of the podcast.

00:08:43
Speaker 2: Piece of a particle, like a very small part of the particle, some sort of entity that exists alongside the traditional particles.

00:08:53
Speaker 3: Somewhere between a real particle and a ghost particle, like a virtual particle, and then it's enabling interactions with others.

00:09:02
Speaker 4: I think it's like a super superposition. And it's one of those weird things about quantum mechanics that if you look at it, it just disappears off.

00:09:11
Speaker 2: I might be particles that we believe exist but haven't I prayed for yet.

00:09:16
Speaker 3: Kind of like a particle but not quite.

00:09:19
Speaker 2: Something that acts like a particle when certain conditions are.

00:09:23
Speaker 3: Met at something that's almost a particle. Paraparticles rely on their neighboring particle for existence. I'm completely stunned by this one.

00:09:32
Speaker 2: The virtual particle pairs that spring to existence in a vacuum. Is a paraparticle something that lives off of or takes advantage of another particle?

00:09:43
Speaker 3: Is it a paralyzed particle?

00:09:45
Speaker 2: So lots of playing with what para means in other contexts. I like it got you all are very clever.

00:09:52
Speaker 1: But they missed the obvious. Nobody went for the connection to parasites.

00:09:56
Speaker 2: Guys, Guys, I work so oft hard so hard. Oh wait, no, no, no, that's not true. Somebody said, relying on their neighbors for existence, that's their parasitical particles. That's right way to go, that particular audience member. Thank you for paying attention all this time.

00:10:17
Speaker 1: I was just glad that nobody went for the sort of anti academic grifter line, the like academics are just parasites on society and they're sucking money and scams and don't really believe anything they're doing, all that bad faith nonsense you sometimes see in various corners of the internet.

00:10:32
Speaker 2: Oh wow, are you I feel like there's a bit of insecurity today.

00:10:40
Speaker 1: I just want to address the reality, you know, that kind of stuff is out there in the universe. Anyway, I was very happy to hear all these positive and constructive answers. Thanks everybody. If you'd like to contribute your ideas for future episodes, don't be shy right to us two questions at Daniel and Kelly dot org. You can hear your voice on the podcast.

00:10:57
Speaker 2: Amazing. All right, So let's dig in. So what are a particle? So you said in the introduction that there are maybe three kinds of particles. Can we start by reviewing the first two kinds, because I'm sure that you've mentioned in the past that particles come in matter and force flavors. But every once in a while, at the end of an episode, I'll discover my brain has reached capacity and maybe some stuff overflowed out the top, and so remind me what are meta particles? What are force particles? And then we'll get into this third kind.

00:11:26
Speaker 3: Yeah, sure, no problem. I'd be careful with the word flavor.

00:11:29
Speaker 1: Though flavor has a particular meaning in particle physics, it means something else, and it's not like you know, cookie dough and mint chocolate chip. It's like the difference between electrons and muons and towels or different flavors of leptons.

00:11:42
Speaker 2: Like that's an actual like physics jargon term is flavors.

00:11:46
Speaker 1: Oh absolutely, And there's amazing the whole subfield of particle physics called flavor physics. And then the people who work on the flavor of particles that have a lot of mass, that's called heavy flavor physics, which sounds like it should be a hip hop group, but it really is a bunch of nerds.

00:12:00
Speaker 2: Well, you know, nerds can have hip hop groups. You don't have to be so judgy.

00:12:05
Speaker 3: Yeah, heavy flavor flakes, let's hear it.

00:12:08
Speaker 2: I love it.

00:12:10
Speaker 3: All right.

00:12:10
Speaker 1: So today we're talking about one way to distinguish particles, and that's by their spin. So there are particles that make up matter, me and you, and everything that's out there and everything you've ever eaten are made out of quarks and lectons. So the upcork and the down cork make up protons and neutrons. You add electrons, which are kind of lefton, and you can make any atom. Right from that, you can make any molecule. And anything anybody has ever seen or thrown at their sister is made out of this kind of stuff, right, Okay, So this is what we call matter particles. And all these particles have something in common, which is their quantum spin has units of one half, which means they can have spin up one half or spin down one half. So all these particles, which we call fermions after Enrico Fermi, these are matter particles. They're particles with one half spin.

00:12:59
Speaker 2: Can you help me like visualize that, like, are they actually spinning?

00:13:03
Speaker 1: M You know the answer to that question, Kelly is nobody knows. Quantum spin is a super fascinating topic because on one hand, it's very different from a real spin, like normal spin, like you take a ball and you spin it. We can talk about the angular momentum, we can talk about the velocity on the surface. A classical object has spin and it has angular momentum, right, And we know that that angler momentum is important to the universe because it's preserved. Like if you spin a ball in space, it keeps spinning. And the reason that like our galaxy is spinning is because of conservation of angular momentum. The reason the solar system has the shape that it does, it's like sort of flat. The way the galaxy is a disc is because of angle momentum. Anglementum is a really big important thing in the universe. Things really do spin. Quantum particles don't spin in the same way because electrons are not tiny little balls. And like one hundred years ago, when they were thinking about this, they were like, well, what if they spin, how fast would they be spin? They try to calculate, like how fast the surface of an electron is spinning, and you get an answer that's like higher than the speed of light. So it's obviously nonsense. Whenever you do physics and you get an answer that doesn't make sense, like something has gone wrong along the way right.

00:14:14
Speaker 2: Or you've created a new field.

00:14:17
Speaker 1: In this case, the answer is that these are quantum particles. They're not classical, so you can think of them as existing physically the same way, where every part of them has a location every moment in time, so they don't physically spin. You shouldn't think about these quantum particles as like little balls that are spinning, and so you might ask, well, if it's not spinning, why do you call it spin. We call it spin because it has a lot of the same properties as classical objects spin. For example, it's conserved right, and it's conserved together with other kinds of angular momentum, meaning that what the universe cares about is the total angler momentum, including spin. So you can convert like normal angler momentum like the Earth is spinning, into quantum angle momentum spin, and back and forth. The universe requires you to conserve the sum of those two, which tells you they're like the same kind of thing the same way that like energy is often conserved, but it's the sum of kinetic and potential energies. Which tells you like, Okay, these are two kinds of the same thing, because what the universe cares about is the sum of them, not the individual ones. So we know that quantum spin is similar to real spin classical spin because the universe conserves the sum of those things, and quantum spin has other similar properties, like things that have quantum spin and electric charge have little magnetic fields because charges in motion give magnetic fields. So like an electron which is spinning, has a little magnetic field, and that's why it's like bent by magnetic fields, et cetera, et cetera. So we don't really know what it is, but we know that it acts a lot like spin, so we call it quantum spin, which I think is a pretty good name, even though it's not spinning.

00:15:57
Speaker 2: Okay, all right, So I usually to hear things like four times before they stick in my brain. I think we're at like two, so be prepared to repeat that. But so to try to help me, all right, So, fermions, these are the mass or the matter particles. Yes, and so I'm gonna think of fermions as like it's firm matter. It makes us be although you know now you're gonna misspell fermions from here on out because it's not spelled like firm. But anyway, all right, that's how I'm remembering it. And so now let's talk about force. And so I always thought force was like a field, and I didn't think of it as a particle anyway. So let's go on. So the bosons are force particles.

00:16:38
Speaker 1: Yes, And let me also liabrate on the comment you made about field versus particles. There are two ways of thinking about what stuff is and how it's pushed. One is the field picture, which is really natural to a lot of particle physicists. There's an electron field, and the electron is actually just a ripple in that field, and there's an electromagnetic field, and photons are ripples in that field. And in that view, the fields are the fundamental thing, and particles are just ripples in those things. They are like emerging phenomena from the fields, and the fields can interact. And we talk about that picture a lot on the podcast. There's another way to think about things and say, you know, fields are just like a construct in our minds. We never see them directly. We only see them acting on particles, and the particles are the things we can see. We see dots on the screen, we see electrons moving through wires, etc. So particles are the real things. And so from that point of view, we have electrons and they're little particles, and we have quarks and their little particles, and then the forces we can talk about other particles. So we have like the photon. What happens when two electrons repel each other, they exchange photons. So this is the particle picture of the universe. Everything is made out of little particles, and it can explain matter. It's a little bit more awkward, but it can also explain forces right in that picture, like electrons exchange photons. That's the way they attract or repel each other. And it's a little bit awkward because like how exactly they do electrons and positrons attract each other by exchanging photons.

00:18:03
Speaker 3: It's hard to imagine you.

00:18:04
Speaker 1: Could like attract Zach by throwing a ball at him, right, it feels like it would only push him away. But you know, this is the quantum world, and you can do weird things like you can throw a photon with negative momentum, so when Zach catches it, he's pulled towards you. It's like a tractor beam photon.

00:18:20
Speaker 2: And biology is too complicated, doesn't make sense. What are you guys thinking?

00:18:26
Speaker 1: Yeah, yeah, And this is one reason why I think the field picture is a little bit more natural.

00:18:31
Speaker 3: But anyway, we can.

00:18:31
Speaker 1: Talk about these forces as mediated by particles. And these particles have a property which is that they don't have half integer spin like one half or negative one half. They have integer spin. So a photon, for example, can have spin one, spin zero or spin negative one. And the W boson and the Z boson, and the Higgs boson and the gluons, all the particles that correspond to the forces and how matter particles exchange momentum, they all have the same property that their spin is integer values, you know, half it's like plus two minus one, this kind of stuff. So those are particles we call bosons. So the fermions and the matter particles, the bosons are the force particles in this picture.

00:19:11
Speaker 2: All right, So now we've got through the two kinds of particles, and let's bring a little bit of pep into this conversation after the break, So we'll talk about the Paul exclusion principle when we get back all right, So we've established that we have two kinds of particles. We've got the fermions, which are the matter particles, and the bosons, which are the force particles. Why does it matter that we divide them in this way? Why can't they all just be particles.

00:19:58
Speaker 1: They are all just partticles or fields equivalently, but they have very different behaviors, and that behavior is really important. Specifically, bosons can do something fermions will never ever ever do, which is, bosons can be in the same quantum state and fermions never will. So you made this joke about PEP. The poly exclusion principle, named after Wolfgunning Poll says that no two fermions can ever be in the same quantum state. So if you have two identical particles like two electrons, they can't have all the same quantum description, which would be like their location, their momentum, their spin, their energy, all this kind of stuff. They can't be identical. They have to be unique. Every fermion has to have a different quantum state.

00:20:44
Speaker 2: Does it make sense to think of that? So our fermions are our matter particles. Does it make sense to think of it as like two pieces of matter can't take up the same space. Or this is like a totally different thing than thinking about it that way.

00:20:58
Speaker 1: Two pieces of matter can't up the same space as long as they have something to differentiate them. So, for example, electrons have two possible spins right, spin up and spin down. So in the ground state of an atom, for example, you can have two electrons with exactly the same energy, the same momentum, the same location, the same energy, the same everything, but one is spin up and the other is spin down. That's why you have two electrons in the lowest state. That's where that two comes from. Because there are two options for spin. You can't have two electrons both spin up, and you can't have two electrons both spin down.

00:21:32
Speaker 3: Because of this poly.

00:21:33
Speaker 1: Exclusion principle, it says you can never have two electrons in the same state, and that's why you don't get all of the electrons in the ground state. If you already have two electrons in that ground state, it's full. It can't take anymore. There's no third spin right, So when another electron comes along, it has to have a higher energy, has to be in the next energy level because the lowest rungs are filled and it's one electron per unique state, right, So the lowest energy level has two of those. The next one, because has more energy, has more options for like where the electron it is around the atom this p state. Now we're getting deep into chemistry, some beyond my expertise right away. But that's why you can have more electrons in that second one, and then more in the third level and more in the fourth because there's more options for differentiating exactly which version of that energy level you're in. And this is why we have chemistry. This is why gold looks the way it does. This is why we have water, this is why atoms bind together. This is why our whole universe looks the way that it does, because fermions cannot be in the same state.

00:22:37
Speaker 2: Now, is this an observation of what's happening or do we understand why it has to be that way.

00:22:45
Speaker 1: It's still a little bit mysterious, Like, it's definitely an observation and we've never ever seen it violated. And if it was violated, like the whole universe would look different, Like if somebody turned this rule off and said, hey, fermeons, no problem. You can now share a state. All of matter would collapse.

00:23:00
Speaker 2: Bad news exactly, it would.

00:23:03
Speaker 1: Be bad news. So I don't recommend it. If you're sitting in the Universe control room and you have your finger on that knob, call me please before you do anything. We do have some handwavy explanations for why it is. We don't have a really full formal proof. We can't go from like, here are the fields, here's how Fermions will behave. What we can do is prove the negative, like we can show why Fermions can't do this thing, Like we can show that if Fermions did this thing, it would lead to some contradictions. So I'm trying to walk you through a handwavy version of that proof in a minute. But we couldn't have started from scratch and really shown how this happens. And Fineman famously said that we don't have a full proof, and also it's really challenging to give an intuitive explanation for this because quote, we do not have a complete understanding of the fundamental principle involved. Finan was big on this theory that like, if you can't explain it simply, you don't really understand it, which I think is really interesting as a hypothesis because it kind of lines up with what we were talking about earlier, and it touches on something we were talking about, I think on the discord of like how on this pod we're constantly trying to explain complicated stuff in an intuitive way. Without all the math. You can't just be like, here's a bunch of math. This math tells you what the answer is. We want to tell a story that connects with the ideas in your head, so you go, oh, that makes sense.

00:24:24
Speaker 3: I get it.

00:24:25
Speaker 1: Why it's this way and not the other way. And that's very different from the mathematical explanation or concepts that we often have in academia and we teach in college and in graduate school, and that most physicists have in their minds. This is like an intuitive grasp of something you have to develop in order to explain it and find me is saying that without that extra piece, this like parallel explanation, that's intuitive, you don't really understand it. And I think that's fascinating and maybe correct. But it's a pretty strong statement of philosophy for a guy who was famously against philosophy.

00:24:56
Speaker 2: Yeah, and how do you think he would feel about the current state of things today. Although I'm gonna go ahead and admit that I hate questions where they're like, what do you think Benjamin Franklin would think about blah blah blah. It's like, I'm not Benjamin Franklin, and if he was raised in our time, you might feel totally different about things.

00:25:12
Speaker 1: Yeah, Feineman is a complicated character because, on one hand, super genius dude, lots of important insights, also lots of great explanations, and he did something which I think is really impressive that I've never seen before, which is he came up with an explanation of or a concept in this case Nuther's theorem in one of his popular books, like for a popular Audience, and that explanation then got transformed into a full rigorous proof, which is now the go to rigorous proof you find in like formal physics books. Usually things go the other way, you like, start with a full rigorous proof and then you develop the intuitive explanation. But he actually came up with it for the general public and then it turned into a rigorous proof, So that's pretty cool. Like, the guy definitely had talents and lots of different directions. He's also famously kind of a jerk, and so it's sort of a problematic figure in that sense. I think if finally we're a lot today, he probably would feel grumpy that people had come up with stuff without him.

00:26:09
Speaker 3: Great, I don't know Hardy.

00:26:12
Speaker 2: Well, he's in our past. He's in the rear view mirror. Okay. So we have observed that fermions don't occupy the same state. We kind of understand why it would be nice to understand better.

00:26:22
Speaker 1: And we've observed that bosons can, right. We see this all the time. Like you put two photons in a box, they're very happy to sit right on top of each other to be in exactly the same state. And this lets you do things like make Bose Einstein condensates and macroscopic objects that have quantum properties because all the photons are in the same state, and you can't do that with electrons. You put too many electrons together, they get this degeneracy pressure. They don't want to be in the same lowest state, so some of them have to be in a higher energy state, and that's where you get like pressure. That's why like white dwarves don't collapse because the electrons inside them if they collapse would have to end up being in the same lower energy state, and they resist that they can't do it, and so like, this has real impact in the universe, and it affects how we do experiments and all sorts of stuff. And so this is definitely real and we have some understanding of how it.

00:27:13
Speaker 3: Works, all right.

00:27:14
Speaker 2: So fermions are our introverts and the bosons are our extroverts.

00:27:22
Speaker 1: Electrons just want to be in their own house, like watching their own TV show at night by themselves, and photons are always up for a party.

00:27:29
Speaker 2: Okay, So now we have a pretty good understanding of fermions and bosons and what they can and can't do. How do we get from here to paraparticles?

00:27:37
Speaker 3: All right?

00:27:37
Speaker 1: So to understand how paraparticles might fit into this picture, because it sounds like there are only two options. Either you have half into your spin, you know, one half, three halves, five halves, or you have into your spin zero one, two, three, whatever. What's another option? How could you possibly have a third category?

00:27:55
Speaker 3: Right?

00:27:55
Speaker 1: And that was the prevailing wisdom for a long long time until very recently. But to understand where the loophole is, we've got to dig one level deeper into understanding why fermions behave this way and why bosons behave the other way. So we're going to go through this sort of rough and imperfect proof of the poly exclusion principle to explain why fermions behave one way and bosons the other way.

00:28:18
Speaker 2: Daniel's got pep, All right, let's do that.

00:28:22
Speaker 1: All right, So imagine two particles, particle one and particle two.

00:28:26
Speaker 2: In typical physicist fashion. Those are very boring names for them, but.

00:28:29
Speaker 1: Okay, okay, let's make them exciting names.

00:28:34
Speaker 3: What would be exciting names for these particles? Now?

00:28:36
Speaker 2: Feeling if we name them like Frank and Rita, it's gonna be hard to keep track. Maybe one and two was a good idea.

00:28:43
Speaker 1: Okay, wow, that doctor criticism pretty quickly there. Alright, alright, alright, so particle boring one in particle boring.

00:28:50
Speaker 2: Two, all right.

00:28:51
Speaker 1: Now, each of them can do one thing, right now, They have two different options. They can be in state A or state B. Okay, so particle A can do two things. It can be in state A or it can be in state B. Particle two can also be in state A or state B. And then we can describe the full quantum state of the pair of the particles as saying like one A two B. That means particle one is in state A, in particle two is in state B.

00:29:16
Speaker 2: Right, you could also have one B and two A, right, and I.

00:29:19
Speaker 1: Understanding absolutely exactly, And so let's do that. Let's take our particles one A to B and let's swap them. These are identical particles, okay, there's nothing different about them. Every electron in the universe, for example, is the same. And so let's just swap them. So we go from one A to B to one B two A. Right now, the quantum field theory of fermions, the math of fermions, because they have spin one half. When you do this, you get a minus sign. So you can't go from one A to B just to one B two A. You go to minus one B two A. You get a negative sign in front of the quantum state. And this has to do with what happens when you're swapping them and you're making a face that tells me I need to pause so you can ask a question.

00:30:06
Speaker 2: Okay, So we said that you can have one A to B as one state, and you can have one B two A as another state. Yes, but I thought that you were saying that, actually, you can't have one B two A. It has to be negative one B two A.

00:30:22
Speaker 1: You can have one B two ah. Okay, but if you start with one A two B and then you swap them, you don't end up at one B two A, which you end up with is negative one B two A.

00:30:32
Speaker 2: Okay.

00:30:33
Speaker 1: That's like saying, you know, take your driver's license and or flip it around right, you don't necessarily get it in this exactly the same orientation depending on how you spin it.

00:30:42
Speaker 3: Right.

00:30:43
Speaker 1: Some things like a sphere, doesn't matter how you spin it, you end up with exactly the same sphere as perfect symmetry. Other things have like a handedness or an orientation right, like or take your left hand and turn it around. It doesn't look exactly like your right hand. Right, maybe it looks like a mirror image of your right hand. It's like negative of your right hand. So this is the part where we're being like a little bit fuzzy and sloppy. But fermions, because they spin one half when you swap them, you get a negative sign in the quantum state.

00:31:11
Speaker 2: Okay, So that only happens with fermions, not with bosons.

00:31:15
Speaker 1: Only with fermions, not with bosons. And that's what makes this impossible. That's where we have a contradiction, right, because say you have these two particles in the same state. Say you started with one A two A, right, both particles in the same state.

00:31:29
Speaker 2: Can't do that, Okay, Oh no, you can with bosons.

00:31:32
Speaker 1: You can with bosons. Well, let's say we have fermions and we try to do that. Let's try to do that and see what happens. Okay, so we have one A two A where like we put two fermions in the same place, in the same state. Okay, Well, now let's swap them. Well, what happens. Quantum field theory says we get negative one A two A. Okay, right, because when we swap fermions we get a negative sign. But these are supposed to be indistinguishable particles, so if you swap them, you shouldn't get any change because there's no real difference. You're swapping one A to two you have to get one A two A. But quantum field theory says, no, you have to get negative one A two A. So we have two different rules. One that says if you have particles in the same state and they're indistinguishable, and you swap them, nothing happens. And the other rule from field theory that says if they're fermions and you swap them, you get a negative sign. Boom, that's a contradiction. So that tells us you just can't do this. You can't have fermions in the same state because then if you swap them, you get a contradiction. Quantum field theory says you're supposed to get a negative sign. Common sense says you can't get a negative sign if you swap things that aren't different.

00:32:36
Speaker 2: Okay, So the Pauly exclusion principle is the result of what happens with quantum field theory.

00:32:42
Speaker 1: Yes, exactly. And you might think, well, what's this negative sign? What is going on there? Remember that this negative sign is part of the quantum state. It's not something we observe, right, a negative sign and a quantum state is not observable because every observable you make is only sensitive to the quantum states squared. Remember quantum state. It can also be like complex numbers. You can have like a wave function has like four plus two I in it, and you can't observe those things, but when you square it, the imaginary part goes away, so we can't observe this. It's like a hidden internal part of the quantum state. We can't observe. And yet the math is there and it's real, and it tells us that fermions cannot do this thing because it leads to an inherent contradiction. Now, spin one particles, bosons are different. Their rules when you swap them are different. If you swap one A two B, and now you're talking about bosons, you don't get the negative sign. You just get one B two A. Everybody's happy. So if you started with one A two A and you swap them, quantum field theory says you get one A two A. Common sense says you get one A two A, no contradiction. Everybody's cool. It's that negative sign, that unobservable negative sign in the quantum state that appears for fermions when you swap them. That causes them to never be allowed to be in the same quantum state if they're indistinguishable fermions.

00:33:58
Speaker 2: Okay, so just to make sure that I'm under so like negative one and one, they cancel each other out when you add them together.

00:34:04
Speaker 3: Or when you square them you get the same answer.

00:34:06
Speaker 2: Okay, And so I should be keeping that in my head. This isn't like we arbitrarily identified that some state is negative one, and you could have called the states A, B, and C. Like there is actually something about negative one and one that is different in an important mathematical.

00:34:24
Speaker 1: Way, exactly. And the important thing here is fermions have a different kind of spin, and that changes what happens when you swamp them and introduces this negative sign.

00:34:33
Speaker 3: Okay.

00:34:33
Speaker 1: And if you're curious about why that is exactly, this is the bit that's famously impossible to explain with intuition.

00:34:39
Speaker 3: We have math for it.

00:34:40
Speaker 1: It's called the spin statistics theorem. And even Richard Meineman couldn't come up with an intuitive explanation for it. So I hope you're gonna excuse me for not having one either. But if you take us out a word for that, the fermions, when you swap them, you get a negative sign that's not observable, but it does prevent them from ever being in the same quantum state. Then you can go from there to understand why the Fermi exclusion principle happens. And it's going to lead us to think about the third way that paraparticles might behave And if.

00:35:07
Speaker 2: You are excited about that, then stick with us, because we're gonna get to it after the break. Okay, so we teased you before the commercial break that we're going to explain to you how para particles behave. Your weight is over, Daniel tell us about paraparticles and how they behave.

00:35:43
Speaker 1: So for a long time, decades and decades, people thought that fermions and bosons were the only options, not only because hey, look, spin one half and integer spins seemed like the only choices because like spin one third or spin two thirds is impossible, but also in terms of the explanation we just gave, it feels like there are two options. Either you add a negative sign when you swap them, like fermions, which means you can't be in the same quantum state, or you don't like bosons, which means you can be in the same quantum state. So it seems like there's no crack there. It seems like there's no room for another direction. And in the nineteen seventies somebody went to a bunch of math to prove that there is no third option under certain conditions. So like if you live in a universe where space has three dimensions, then there is no other option. You have fermions and you have bosons, and that's its zip and period. So people sort of put this away for a long time. They were like, yeah, well that's done. Somebody proved it dot dot dot. Nobody should ever spend time thinking about it again. And that's like a famous place to make a big discovery, because I'm sure this happens in biology. Also, you have a paper which makes a big advance and then it gets sort of summarized in a shorthanded sort of way that ignores some of the assumptions that went into it, and the conclusions just sort of get broaden a little bit, and then people treat the lore as if it was real and complete, and people rarely go back and read the original paper to discover ooh, actually there are coveyats here. So there are loopholes, and people who do and discover those loopholes and then explore them can like crack open a whole new area of physics.

00:37:17
Speaker 3: Sometimes.

00:37:17
Speaker 2: That's why it is so critical to read and to read the original papers.

00:37:21
Speaker 1: And for those of you wondering what that sound is in the background. That's a big rainstorm in Virginia right now.

00:37:27
Speaker 2: I love rain. Was that a dig on Virginia?

00:37:30
Speaker 3: Why do you assume that's a dig? That's definitely not a dig.

00:37:33
Speaker 2: This is because I know you.

00:37:36
Speaker 1: This week I'm an Aspen for the Aspen Center for Physics, and it rains every afternoon and I love it. The smell of it in the mountains is just wonderful. The thing I do love about mountain rain is that it ends also quickly.

00:37:48
Speaker 2: Yeah, well, well those are rainstorms don't last very long. And I am the reason you can hear it is because I converted the tech room in the barn, the horse barn that we have on our property to my office, and so there's a metal roof above me, and so the metal roof really makes the sound of rain much louder, which I love when I'm sleeping up here at night. Every once in a while I have sleepovers up here with my daughter on Friday nights. But anyway, sorry about the background noise, everyone, no problem.

00:38:16
Speaker 1: And we now have enough background to understand paraparticles because very recently two physicists at Rice University, which we both know and love found some loopholes in this nineteen seventies no go theorem, the one the famously said it's impossible to have anything but a fermion and a boson. And the loophole is, what if you give these particles some other kind of properties, things that like a minus sign, are not observable directly and disappear when you square it right. So like a minus sign is a great example, because you square it, you have plus one. If you didn't have a minus sign, you can't tell plus one squared and minus one squared have the same answer. But they came up with another thing you can add to this particle, like another category, another part of the description, not a minus sign, but like a new dimension to this quantum field, a new attribute, a new label you can give it, and this kind of thing. Also when you square it, it goes away. So there's some technical details here, but the sort of way to understand it intuitively is that these internal states depend on the observer a little bit. So like you and I might see this electron differently because we're different observers and we might make different observations.

00:39:31
Speaker 3: So it's a little bit of like relativity there. So if you.

00:39:34
Speaker 1: Add this to some particle states in a weird mathematical way, you can create a new kind of behavior. So it sort of like fuzzes up a little bit, this notion of indistinguishable particles. Are the particles indistinguishable or not? So you might be wondering, well, we have electrons and we have photons. Are there things out there in the universe that follow this new weird quantum math. The answer is, we don't know, not yet. What they've done is show that there is another mathematical description of fields and particles that you can construct that has like a third kind of behavior. It's not a fermion and it's not a boson, but it is self consistent and mathematical. Nobody's built one, but they just sort of like mathematically shown that as far as we know, the rules of the universe don't disallow this.

00:40:25
Speaker 2: So I don't want to ever question the amazing research that comes out of Rice University. But it sounds like okay, So they're like, well, there's this one thing we can't see and can't measure, and so let's add another thing we can't see or we can't measure. It's just like fire, you know, like biologists can't be like, well, what if the viruses we're wearing hats, maybe we should look for what's a good combination of hat and viruses?

00:40:49
Speaker 3: Right.

00:40:50
Speaker 1: This is like taking the quantum particles and saying, hey, we've only been thinking about them wearing cowboy hats.

00:40:55
Speaker 3: What if they wear other kinds of hats?

00:40:56
Speaker 1: What if choice of hats is another like degree of freedom for describing these particles. And it turns out if you do that, it cracks this open a little bit and it lets you have another category. And so that's interesting mathematically. It's only interesting physically if it describes the universe. If the universe does this in the same way that like DrAk looked at the solutions to the Shortener equation and he was like, oh, this is interesting. This allows you to have electrons but also allows you to have positively charged particles. That doesn't mean the universe does it, right. It could have just been like a mathematical oddity like, oh, the math allows this, but does the universe choose it? And turns out yes, the universe does choose to make antiparticles, and the universe in many other cases chooses to explore all the avenues of symmetries. We don't know if it does.

00:41:44
Speaker 3: In this case.

00:41:45
Speaker 1: What we've shown is that the mathematics of our description of the universe do allow for our third category particles paraparticles, but we don't know if they do ever exist in the universe, and if they do, we don't think they would be fundamental particles the way like photons and electrons are, because there are no fundamental particles we know of that fall into this category. You'd have to make like quasi particles the way you make like anions or plasmons or phonons. These are things that follow the math of particles. But our waves not in a fundamental field like the electromagnetic field or the electron field, but a wave in something else, like a wave in air, or a wave in water, or a wave in electron gas in some weird meta material that solid state physicists cook up in their dark little labs. And so it might be something that people can create in the labs someday in the future and show, oh, look, we've created this new quasi particle that has a different kind of mathematical behavior than fermions or bosons. So that would be cool and something nobody had seen before. Doesn't mean we can make hoverboards or we can make wormholes or anything like that yet, But you never know with fundamental physics, like what's this going to lead to?

00:42:58
Speaker 3: It's very deep.

00:42:59
Speaker 1: It's very much at the foundation of quantum field theory and our understanding of like the mathematics of it. So it's exciting when anybody makes any progress in that area. And it's a great example to push back on the nonsense you might hear online that like physics hasn't made any progress since the nineteen seventies. Like, dude, we're making progress all the time. And here's a great example.

00:43:19
Speaker 2: So are people currently working on experiments to try to find these particles?

00:43:23
Speaker 3: Yeah, more create than find. People are trying to engineer weird.

00:43:28
Speaker 1: Exotic materials that might have these behaviors. And this is the kind of stuff solid state physicists love to do, you know. They're like, what if we made super thin layers of graphene and then super thin layers of this, and could we force the electrons to act as if they're in a two D universe? Or can we see superconductivity or whatever. So they're very clever at engineering materials to make quantum states behave in new ways, and that's the most promising way. We might see something that's a paraparticle, you would be an emergent phenomenon, a quad particle that comes out of the behavior of these weird exotic systems and not exotic and like impossible or wrong in any way, just like not something we find in nature usually. But that's the cool thing about being humans. We're like constantly pushing the boundaries and saying, hey, can the universe do this? What happens if we do that? And it teaches us things about the universe. This is how we learn where the boundaries are by pushing them, right, yeah.

00:44:26
Speaker 2: Yeah, So when we have a guest on our show, you usually end the interview by asking them if an alien were to visit our planets from an advanced civilization, and you ask them if their thing exists on their home planets. That's your way of testing how confident they are that the thing actually exists. So, Daniel, if aliens from an advanced civilization landed on Earth, do you think they would know about paraparticles and would think that paraparticles existed?

00:44:52
Speaker 1: This is a great question and a fair one, since I just wrote a whole book on how aliens might think about the universe. Y'all should check it out. It's coming out in November. It's called Do Aliens Speak Physics. I'm really excited about it.

00:45:03
Speaker 2: Two sums way up.

00:45:05
Speaker 1: My personal suspicion is that particle physicists are too up in their own heads and they think that the whole universe uses their mathematical description of how things work. And that's just like too self centered to put ourselves at the heart of the understanding of the universe. And likely there's a bunch of arbitrary assumptions we've made, and probably aliens have a completely different description of how the universe works, and they're like, what, why are we even using quantum fields? That makes no sense. Here's a much simpler way. But if they are using quantum fields, then I think this is an inevitable discovery.

00:45:41
Speaker 3: They would make.

00:45:41
Speaker 1: And they might have even found other ways, like there might be four, seventeen or ninety two different kinds of particles and they're like, what y'all have only found three? Come back to us. You can join the cosmic society when you're up to ten.

00:45:53
Speaker 2: When you found particles, Then if they talk to us exactly.

00:45:59
Speaker 1: Yeah, and maybe they'll listen this podcast and ooh, particles and parasites.

00:46:02
Speaker 3: Maybe these guys are on the right track.

00:46:03
Speaker 2: Oh my gosh. Yeah, at least they'll think that we're interesting.

00:46:07
Speaker 1: Aliens, if you are listening, please don't zap ups from outer space.

00:46:10
Speaker 2: Come talk to us, tell us about your secrets, and tell us about your parasites, but keep it to yourselves, all right.

00:46:18
Speaker 1: Thanks everyone for going on this journey with us into the heart of particle physics, how it works, what we know, what we don't know, and the hints that mathematics is giving us about what we might learn about the fundamental nature of space and time and matter and energy and aliens.

00:46:33
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