What are paraparticles?

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24:24All 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? They are all just particles 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 Pauli exclusion principle named after Wolfgang Pauli says that no two fermions can ever be in the same quantum state.

25:08So 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, quantum 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 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 two pieces of matter can take up the same space as long as they have something to differentiate them.

25:46So 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 up. down because of this poly exclusion principle. It says you can never have two electrons in the same state.

26:19And 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 it has more energy, has more options for where the electron is around the atom, this P state. Now we're getting deep into chemistry, so I'm beyond my expertise.

26:52Right 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. Now, is this an observation of what's happening? Or do we understand why it has to be that way? It's still a little bit mysterious.

27:29Like, 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, fermions, no problem. You can now share a state. All of matter would collapse. Bad news. Exactly. It would 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 hand wavy explanations for why it is. We don't have a really full formal proof. We can't go from like, here are the fields.

28:01Here'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. I'm going to try to walk you through a hand-wavy version of that proof in a minute. But we couldn't have, like, started from scratch and really shown how this happens. And Feynman 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, quote, we do not have a complete understanding of the fundamental principle involved.

28:37Feynman 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 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.

29:06I get it. 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 Feynman 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. It may be correct, but it's a pretty strong statement of philosophy for a guy who was famously against philosophy.

29:38Yeah. And how do you think he would feel about the current state of things today? Although I'm going to 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, he might feel totally different about things. Yeah, Feynman 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 or a concept, in this case, Nothra's theorem, in one of his popular books, like for a popular audience.

30:15And 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 in lots of different directions. He's also famously kind of a jerk. And so he's sort of a problematic figure in that sense. I think if finally we're alive today, he probably would feel grumpy that people had come up with stuff without him.

30:51Great. I don't know. Hard to say. Well, he's in our past. He's in the rearview 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. And we've observed that bosons can. 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.

31:27You 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 pressure. That's why 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. They resist that. They can't do it. And so this has a real impact on 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 works. All right. So fermions are our introverts and the bosons are our extroverts.

32:03That's right. 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. 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? All right. So to understand how paraparticles might fit into this picture, because it sounds like there are only two options. Either you have half integer spin, you know, one half, three halves, five halves, or you have integer spin, zero, one, two, three, whatever. What's another option? How could you possibly have a third category, right?

32:38And 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 Pauli exclusion principle to explain why fermions behave one way and bosons the other way. Daniel's got pep. All right, let's do this. All right, so imagine two particles, particle one and particle two. In typical physicist fashion, those are very boring names for them, but okay. Okay, let's make them exciting names.

33:16What would be exciting names for these particles? I'm feeling if we name them like Frank and Rita, it's going to be hard to keep track. Maybe one and two was a good idea. Okay, wow. Backed off your criticism pretty quickly there, didn't you? Yeah, all right, you got me. All right, so particle boring one and particle boring two. All right. Now, each of them can do one thing right now. They have two different options. is 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 1A, 2B.

33:54That means particle one is in state A and particle two is in state B, right? You could also have 1B and 2A, right? Am I understanding? Yes, absolutely. Cool. Exactly. And so let's do that. Let's take our particles 1A 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 1A to B to 1B to 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 1A to B just to 1B to A.

34:33you go to minus 1b2a. 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. Okay, so we said that you can have 1a2b as one state. And you can have 1b2a as another state. Yes. But I thought that you were saying that actually you can't have 1b2a. It has to be negative 1B2A. You can have 1B2A. Oh, okay. But if you start with 1A2B and then you swap them, you don't end up at 1B2A. What you end up with is negative 1B2A. Okay. That's like saying, you know, take your driver's license and flip it around, right?

35:20You don't necessarily get it in exactly the same orientation depending on how you spin it, right? Some things like a sphere, doesn't matter how you spin it, you end up with exactly the same sphere. It's 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're spin one half, when you swap them, you get a negative sign in the quantum state.

35:53Okay, so that only happens with fermions, not with bosons. 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 1A, 2A, right? Both particles in the same state. You can't do that. Okay. Oh no, you can with bosons. 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 1A, 2A. We're like, we put two fermions in the same place, in the same state. Okay. Well, now let's swap them.

36:27Well, what happens? quantum field theory says we get negative 1A, 2A, 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 1A, 2A, you have to get 1A, 2A. But quantum field theory says, no, you have to get negative 1A, 2A. 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.

37:02Boom, 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'd 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. Okay. So the Pauli exclusion principle is a result of what happens with quantum field theory. 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?

37:34A negative sign in a quantum state is not observable because every observable you make is only sensitive to the quantum state squared. Remember, quantum states 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.

38:07Their rules when you swap them are different. If you swap 1A to B, and now you're talking about bosons, you don't get the negative sign. You just get 1B to A. Everybody's happy. So if you started with 1A2A and you swap them, quantum field theory says you get 1A2A. Common sense says you get 1A2A. 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. Okay, so just to make sure that I'm understanding.

38:42So like negative one and one, they cancel each other out when you add them together. Or when you square them, you get the same answer. 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 way. Exactly. And the important thing here is fermions have a different kind of spin and that changes what happens when you swap them. It introduces this negative sign. And if you're curious about why that is exactly, this is the bit that's famously impossible to explain with intuition.

39:22We have math for it. It's called the spin statistics theorem. And even Richard Meinman couldn't come up with an intuitive explanation for it. So I hope you're going to excuse me for not having one either. But if you take us at 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 you are excited about that, then stick with us because we're going to get to it after the break.

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42:45Okay, so we teased you before the commercial break that we're going to explain to you how paraparticles behave. Your wait is over. Daniel, tell us about paraparticles and how they behave. 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 spin 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.

43:25So it seems like there's no crack there. It seems like there's no room for another direction. And in the 1970s, somebody went through 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.

44:00you 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 broadened 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 caveats 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 sometimes. That's why it is so critical to read and to read the original papers.

44:34And for those of you wondering what that sound is in the background, that's a big rainstorm in Virginia right now. I love rain. Was that a dig on Virginia? Why do you assume that's a dig? That's definitely not a dig. Because I know you. This week, I'm in Aspen for the Aspen Center for Physics, and it rains every afternoon. And I love it. The smell of it in the mountains. It's just wonderful. The thing I do love about mountain rain is that it ends also quickly. Yeah. Well, our rainstorms don't last very long. And the reason you can hear it is because I converted the tack room in the barn, the horse barn that we have on our property, into my office.

45:13And so there's a metal roof above me. And so the metal roof really sort of 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. 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 1970s no-go theorem, the one that 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?

45:59So like a minus sign is a great example because you square it, you get 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, 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.

46:35So like you and I might see this electron differently because we're different observers and we might make different observations. So there's a little bit of like relativity there. So if you 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.

47:12Not yet, at least. 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've just sort of like mathematically shown that as far as we know, the rules of the universe don't disallow this. 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.

47:52This is like, you know, like biologists can't be like, well, what if the viruses were wearing hats? Maybe we should look for what's a good combination of hat and viruses. You're right. This is like taking the quantum particles and saying, hey, we've only been thinking about them wearing cowboy hats. What if they wear other kinds of hats? What if choice of hats is another 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.

48:27In the same way that Dirac looked at the solutions to the Schrodinger equation and he was like, oh, this is interesting. This allows you to have electrons, but it 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 it 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 in this case. What we've shown is that the mathematics of our description of the universe do allow for a third category of particles, paraparticles, but we don't know if they do ever exist in the universe.

49:08And if they do, we don't think they would be fundamental particles the way that 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 anyons or plasmons or phonons. These are things that follow the math of particles, but are 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 an electron gas and some weird metamaterial that solid state physicists cook up in their dark little labs.

49:47And so it might be something that people can create in the lab 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? It's very deep. 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.

50:21And 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 1970s. Like, dude, we're making progress all the time. And here's a great example. So are people currently working on experiments to try to find these particles? Yeah, more create than find. People are trying to engineer weird, exotic materials that might have these behaviors. And this is the kind of stuff solid-state physicists love to do. 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 2D universe?

50:57Or 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. It would be an emergent phenomenon, a quasi-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.

51:35This is how we learn where the boundaries are by pushing them, right? Yeah. 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 planet from an advanced civilization. And you ask them if their thing exists on their home planet. 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? This is a great question and a fair one, since I just wrote a whole book on how aliens might think about the universe.

52:11Y 'all should check it out. It's coming out in November. It's called Do Aliens Speak Physics? And I'm really excited about it. Two thumbs way up. 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?

52:44Why are you 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 they would make. And they might've even found other ways. Like there might be four, 17, or 92 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 10. When you found para, para, para, para particles, then talk to us. Exactly. Yeah, and maybe they'll listen to this podcast and they'll be like, ooh, particles and parasites. Maybe these guys are on the right track.

53:16Oh my gosh. Yeah. And at least they'll think that we're interesting. Aliens, if you are listening, please don't zap us from outer space. Come talk to us. Tell us about your secrets and tell us about your parasites, but keep them to yourselves. All right. 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. See y 'all next time.

53:54Daniel and Kelly's Extraordinary Universe is produced by iHeartRadio. We would love to hear from you. We really would. We want to know what questions you have about this extraordinary universe. We want to know your thoughts on recent shows, suggestions for future shows. If you contact us, we will get back to you. We really mean it. We answer every message. Email us at questions at danielandkelly.org. Or you can find us on social media. We have accounts on X, Instagram, Blue Sky, and on all of those platforms, you can find us at D &K Universe. Don't be shy. Write to us. For most kids, math class moves at the wrong pace.

54:34Some are way ahead of the class. Others need more help along the way. Brilliant is the online math tutor that's visual and interactive. It's helped millions of students excel in math. On Brilliant, students can build stronger foundations or move ahead as fast as they want, from fractions to calculus. They'll get hands-on, get tutoring that's personalized to them, and see results in weeks. Sign up today at brilliant.org slash tutor and get 20 % off. That's brilliant.org slash tutor. This is Jacob Goldstein from What's Your Problem? Running a business is hard enough. Don't make it harder with a dozen apps that don't talk to each other.

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55:53Help support healthy hair, skin, nails, bones, and joints so you can stay vital, stay you. Visit VitalProteins.com to learn more and where to buy. These statements have not been evaluated by the Food and Drug Administration. This product is not intended to diagnose, treat, cure, or prevent any disease. Ice Cube's Big 3 season is heating up and it all comes down to this the Big 3 playoffs are coming to Dallas, Texas the four best teams in the Big 3 battle it out for a spot in the championship the action starts with the legendary Big 3 Celebrity Game three games of the most physical, competitive and non-stop 3-on-3 action the game played the way you love watch live Saturday on CBS at 12pm Eastern, 9am Pacific and catch replays Monday on BET presented by iHeart This is an iHeart Podcast.

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