How small is an electron?

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Speaker 1: Hey, or hey, you're a visual artist, so I have a question for you about how you visualize things. Well, first of all, thank you for calling me an artist. Cartoonist don't usually get that kind of respect. But do you mean can I draw my answer? Yeah, maybe when we upgrade this podcast to a YouTube channel, But until then, here's my question. What is the biggest distance that you can visualize that you can sort of see in your mind? Well, I think anything bigger than the distance between my bed and the fridge feels like an infinity. I guess maybe like the biggest distance that I can wrap my head around would be maybe like the size of the solar system, you know, Like I think I have a intuitive sense of that, but maybe anything bigger it just kind of blows my mind. All right, So then turn it around. What is the small all this distance that you can visualize? Probably the width of a thinly sliced banana. Feels like maybe you should have had a snack before we did today's podcast. I am Rhammad, cartoonists and the creator of PhD comments. Hi, I'm Daniel. I'm a particle physicist and I don't eat bananas no matter how then you slice them really you're anti banana like you avoid them. I'm anti bananite, yes on the air. I didn't know that. Oh my god, how do we even get along all these years? I don't know if we I can continue doing this with you anymore. So if you if you get him in a salad, you picked them out or something. How far puts banana in a salad? What are you talking about? You were offending salads? How far this is anti bananas? Goes go? Daniel, Well, let's see, if I was dying of starvation next to banana tree, I would eat some bananas. I'll put it that way. I would. I see. Oh man, you don't know what you're missing. But for those of you who are not anti banana, welcome to this podcast. Daniel and Jorge Explain the Universe, a production of Our Heart Radio, and banana lovers and banana haters are all welcome on this podcast because we only the lovers, because we all share the love of the universe and the mystery is and the incredible cosmic questions like how can anybody stand to eat a banana? No? Like? How big is our universe? And does it all make sense? Should ever rebody Daniel that bananas are part of the universe. If you love the universe, technically you love bananas. But welcome to our podcast, in which we do try to explore everything around us, including bananas and other delicious or non delicious items, and explore lane how it all works to you. Yeah, we try to think about the bigness of the universe, the limits of space and planets and stars, but we also like to talk about the small things in life and in the universe, and and sometimes it really stretches your mind right to sort of sort of in one conversation think about how big the universe is and how also how small things are. Yeah, and we try to take you on a tour of the sort of current thinking of scientists. How do scientists think about this stuff? How do they fit the whole universe in their brains? Or what do they visualize when they think about the inside of a black hole? Or how do scientists think about the very very tiny What does a particle look like inside the mind of a party goal physicist? Yeah, because you know, we know that the universe is made out of tiny little particles, and we like to say tiny little particles. But I guess you don't often think about it, what tiny really means. Yeah, we do this a lot when we think about the quantum realm. We try to sort of use the ideas we have from our everyday experience and apply them to particles, apply them to these tiny little bits so that we can make sense of them, because you know, you can't see these things directly, so you have to sort of build a mental picture, and we try to talk about how they have mass and charge, and we even give them you know, labor and spin and other sorts of things that were familiar with from our world. But you have to wonder, like, how well does that really work? Is it really relevant or is the quantum realm just totally alien and we will never really get our minds around it. Yeah, I thought we had already decided that everything looks like Lego pieces down at the fundamental level. They don't look like little blocks with circles that say Lego on them. Well, it's easy to do a test. You know, if you step on them and they cause you great pain, then they definitely are the shape of Lego pieces. I think they make round legos too. Now finally to save parents, But you know, this is all we can do as humans is we can take the ideas we are familiar with and we can try to map them down to the quantum realm to think about this. Yeah, and sometimes that intuition kind of fails, right, or it breaks down when you get down to that quantum realm, that quantum level, right, our ideas of what something is, or how solid something is, or what shape it has, and it all sort of breaks down into kind of mathematical goop right down at the quantum. I think it has a little bit more substance than mathematical GOOPI gloop, but really it's a bit more No, it's a bit more poetic than mathematical sometimes because well, we try to draw connections, like we talk about quantum spin, and we fully admit that these particles are not actually spinning, but they're doing something that is very much like spin. It has a lot of similar characteristics, and so we draw this analogy. And I think this is one of the most beautiful things about physics, is trying to describe the unknown in terms of the known. You know, that's what languages, that's what art is, that's what that's what it means to explore the universe is to express it in a way that we can understand it, and so that's all we can do. Yeah, are you saying you don't understand google Goog? I'm saying googly groop suggests some lack of understanding or nonsense, whereas in its place there are some elegant intellectual structures to guide your mind. I see, you know, potato, potato again, theoretical structures, googly goog, it's all, it's all, you know, different names. But so to the other podcast, we thought we would take a trip down to that quantum level and kind of think about a particular, you know, object that I think we're all familiar with, and to sort of challenge our understanding of what it looks like and what shape it has and most importantly, what size it has down at the quantum realm. And this is something that I have struggled with as a particle physicist, just trying to visualize, just trying to conceptualize it. How do I put this in my mind? How do I think about this so I can get some intuition right? And so today we'll be tackling the question how big is an electron? Or how small is an electron? Oh? Man, is this another potato po typle thing. It's big and small depending on which country here. The representatives of the Electron Union prefer to be called big rather than small. Oh, I see, But what does the electron itself prefer? Does it see itself as a as a big or a little? Interview with an Electron speculative fiction novel by J H winner of the Nobel Price in literature and physics at the same time. But yeah, you know, electrons are everywhere. They're one of the three fundamental particles that make up everything that we are, that you are, That planets and stars and galaxies and dust are made out of um. And so it's an important particle. And it makes yourself phone work, which without which you would probably not be listening to this podcast. Yeah, and it sort of sits at the frontier of particle physics. Our goal is to explain everything in the universe in terms of the smallest bits and pieces, the tiniest, roundest lego pieces anywhere, And as far as we know, these are the smallest bits. And so we wonder, like, is it made of something smaller? How small is this thing? Anyway? Yeah, what's the size of an electron? I guess that's a question we haven't really talked about before. We just sort of talked about electron and what they can do and what they do, and we know they're small. But I guess the question here is how small it is? Or how big is it? Not? How big isn't it? Yeah, And like with many of these mappings to the quantum realm, I'm pretty sure you're going to be dissatisfied with the answer because did you misname something again? Is it not really called? Is it like an electron? Not really an electron? Well, I don't want to give away the end there, you'll have to stick around for another half hour. Well, this is a question that, as always, we were wondering how many people out there had thought about or wondered about and what they knew about the answer to this question. So, as usual, Daniel went out there into the wilderness of the streets of Irvine, California and ask people how big they thought an electron is. I like the way you make it sound dangerous, like I'm hacking my way through the jungle. I think talking to perfect strangers, it sounds terrified to me. Well, here's what people had to say. But before you hear these answers, think to yourself, what would you guess is the size of an electron? Very small? I know, like a couple of billion Adams can fit on a period in in a book, So an electron is Chillian quadrillion. I don't know. Sudden thinkers like small, like smaller than that. Best guys like like a hundred of a nanometer ten to the minus sixteen. Well, I guess it's when it's a way function falls off? Is one over eight or something like that? Is that how we want to call it? What's thirteen point six e v s and nanometers that it does red stuff? So a couple d nanometers? Let's doing that? Also, no idea, best es not that big tend to the negative on all eleven or twelve or something like that. Like all right, some pretty I feel like, pretty educated answers, Like some people were talking about electron volts even I like the guy who says smaller than a centimeter, like yeah, that's that's true, yes and also correct, Yes, it's definitely correct. Um. No, we shouldn't make fun of these people. They are giving us their time, their and their energy, and so it's fun just to just to know what people have in their minds. And I think one of the common answers is like, tend to the mind is a pretty big number. But yeah, know I thought they were pretty I guess you're at a at a university, so maybe a lot of these folks just think in physics or something. But um, you know, if you ask me, I don't know if I would guess with exact figures or units. Well it's interesting because if you ask me, I don't know what I would say. It's a tricky question. Even what is the meaning of the question, Like what does it mean for the electron to have a side? Is? So it's complicated. So someone interviewed on you on the street and ask you this question, you'd be like, let's sit down for a couple of hours, let me pull out my white board, thank you for asking that question. And you see the panic in their eyes. I've been waiting all my life for perfect strangers. They would feign a phone call and run away quickly. All right, Well, let's get into the trying to answer this question. And I guess the first thing is is that you're telling me is that this is even Um, it's kind of almost a philosophical question. It's like a tricky question in itself to ask what is the size of an electron? Yeah, And you have to be really careful about what you're doing. When you're asking a question that you're used to asking about macroscopic stuff and then applying that to microscopic stuff, you have to be really careful about what you mean and what exactly it is you're trying to learn. You know, like when we think about a ball moving through space, we can talk about its velocity. Cool, But when you want to talk about the velocity of an electron, it's more complicated because it doesn't have like the same kind of half and so it's philosophy changes, and sometimes you can know it, sometimes it's unknown, and so you know, there's an analogy you can make there, but you have to be careful about exactly what you're asking. And the same is true when you ask about the size of something super duper tiny, right, and and especially when you ask about the size of a single thing, right, Like what is it? What does it even mean to ask about the size of anything? Is it like how much space you occupy? Is it like the my longest dimension? Is it the distance between you know, one and one side of me to the other side of me. I think that's it. I think it's the distance between your edges. And so you have a size if you have edges that don't touch, right, if you have if there's a meaning to like there being a left of view and a right of view, and your size is the distance between them. You know, we have a meter stick, how big is it? Well, the left side is one meter from the right side. So that's sort of makes sense, right, And this this all sounds, you know, obvious, but it's going to be important when we get to the quantum realm to be thinking about it in the same same sort of set of ideas. Right, Yeah, I guess you've got to think about what makes it a thing and when is it stopped being a thing? And then then you calculate kind of the distance between the edges of what is and what is not a thing. Yeah, And so you answer the question like what a size mean, Well, it's the distance between the edges and that immediately, but you can see you to the other question, what is the edge, Like what is the edge of a meter stick or the edge of a banana? How do you define where that stops? And that's not so easy. Oh man, you just make me imagine it endless banana and I salivated a little bit. That's a whole universe to you, right there. Man, maybe the whole universe is just one banana. We are all just banana nos in a banana. We should start that in the restaurant. You know, Olive Garden has the endless bowl of salad, endless bread stick. We can we can start selling the endless banana. But anyways, so where is the edge of the banana? Right? You would think, oh, I'm looking at it, I can tell where it stops. And you either you poke it or you're just looking at it. It sort of gives you a sense for like where the edges. It doesn't have a fuzzy edge, like it stops the all the atoms that make up the banana are kind of stuck together, and at some point there aren't any more of the atoms that make up the banana. Yeah, although, if you're zooming close enough right, everything that's not an absolute zero is has a bit of a fuzzy edge, you know, it's like boiling off atoms. Like the reason you can smell banana is that there are volatile molecules on it that are always leaving and so zooming close enough, and there's there's a bit of a fuzzy edge there. But still you can like take a stick and you can poke the banana with your tiny stick and you can ask, like, when does the banana give me resistance? Or is the edge of it is sort of like, you know, where is it push back? Okay, so that that would be the edge of like an object microscopic option you're saying. It has to do with when it no longer interacts with you in the same way as the rest of the banana. Yeah, And there's an important idea there, I think, which is it's not where the stuff of the banana ends, it's where the bananas forces push back. Because you know, the banana itself is mostly made of these we'll talk about in a minute, but time much smaller particles, and the stuff of the banana, the thing that gives it its volume is the forces. Right, If there were no forces between these particles, they will collapse to a much smaller pile. Like you just made a pile of all the atoms inside the banana, it would be almost invisible. Most of that volume comes from them spacing each other. Out by the forces. So it's really the forces, the pushing back that gives the banana it's volume and therefore its size. I see, you wouldn't measure it as between the center of the rightmost atom of the banana to the center of the leftmost atom of the banana. You would be you would extend that a little bit to include like when that atom starts pushing back another adom that tries to poke through the banana. Precisely because if you bring your stick nearby, then the farthest, the most extreme atom and your stick is not going to touch the nucleus of that atom in your banana. They're going to push against each other before they touch. And so that's what I think of sort of the edge of the banana is that force field that sort of protects it from you know, external forces. Okay, so you're saying, as a physicist, you would define the size of something as as the edges of it, and the edges you would define is when they start pushing other things from going through it. Yeah, So really it's more about interactions than it is about matter itself and particle physics, we think a lot about particles and forces, matter and interactions. And I think the size of something really depends more on its interactions then on the stuff that's inside of it. And that makes sense because if you want to know the size of something, you want to know it for a reason usually right, like you want to see if the banana fits inside of a special you know, banana carrying case that you aren't designing. You need to know, you know, not when the set where the centers of the atoms are, but you want to know, you know, if you can fit the banana inside the case. That's exactly it. But it already raises some problems, like what if you had a blob of dark batter the shape of a banana, how big is it? Well, if you can't really interact with it, if you could like put your finger through it, then you know, does that mean that it's a banana shaped and blob of dark batter is smaller? It doesn't have a size maybe even boy. Yeah, so it gets it gets tricky pretty quickly. This thing, which which we thought was simple is actually turns out to be kind of subtle. Yeah, it's feel back the answer to this question and also get into how big an atom is, and then we'll get into how big an electron it is. But first let's take a quick break, all right, Daniel. So it seems like the question of how big something is is kind of fuzzy in itself, and so maybe a good way to kind of tackle it is to start with the next level down from a banana, which is like how big is a is one of the atoms in the in the banana. So remember that we decided that if we're going to talk about the size of the atom, we're not going to ask where is the stuff inside of it? We're gonna ask where does it push back when it's poked? And to figure that out, it's helpful to sort of imagine a whole pile of atoms packed together. Here you have you like imagine the banana is sort of like a crystal. You know, it's like closely packed atoms of the banana. And here it's determined again by the interaction between them, Like how closely packed are they depends on how much they resist being squeezed together. And in this case, for an atom, it's you know, for banana. For other stuff, it's a it's pretty small. It's like you know, fifty to a couple hundred trillions of a meter. Is what how you you would define how big anatom is. Yeah, that's like this the separation between the center of one atom and the center of another atom. Depending on the material, and different things can sort of pack more tightly together than other things. Like hydrogen, you can squeeze it down to like thirty trillions of an atom between protons. But if you're packing lead together, for example, it's almost two d trillions of a meter between sort of the centers of the nuclei. I say, it's it's like if you're trying to measure the size of a bunch of marbles. You would stick him in a container and see how many you can sort of cramp together, and that kind of tells you the size of each marble. Yeah, the distance between the centers of the marbles. There you pack them as closely as you can, and then you measure the distance between the centers of the marbles. Is that actually sort of because you know, when I think of an atom, I think of like, um, you know, like the popular culture drawing of an atom, which is like, you know, little balls in the center and then electrons flying around in orbit. You know, you know, and I know that you know, they're actually like electron clouds. But even the clouds have sort of a size, right, they're drawn as little balloons that stick out of this center. Is the size is the packing size that you're talking about, like how many you can crime in banana, the same as the size of those like electron clouds. Yeah, it's very closely connected. And for a reason, those electrons are the reason that the atoms don't pack more closely together, Like you bring two hydrogen atoms near each other. It's the electron clouds that determine how closely they get together because they form like a covalent bond and make an H two or something like that. And so it's those electrons that determine the interactions between the atoms and determine their spacing. And it's when those two things start overlapping, is when they can no longer really get closer together. So, yeah, the size of the electron cloud is very closely connected to the size of the atom. It really is what defines it. They're always interacting, right, no matter how far apart there are, Like if I had a hydrogen atom here and you had a hydrogen atom and Jupiter. Technically they're sort of repelling each other, right or and or attracting each other or not. They definitely do feel each other. You're write the the extent of the electromagnetic force is infinite, So there are electrons in Alpha Centaur that are pulling on you or pushing on you, or depending on whatever they're doing, technically touching you. Right, you're being touched by an alpha centaur right now. I just got chills down my spine a little bit to the left. Please, yes, thank you. Crash that is that I've had. Yeah, well it's a tricky concept. You're right. If we're going to define size by sort of how you were responding when you get poked, then you're right. You're being constantly poked by everything in the universe. Well, even the stuff like a build B zillion nine years away. Yeah, it is everything. Everything in the universe is feeling you. Although you know there's a time delay there, so the stuff in Alpha Centauri is only feeling. Stuff is feeling where we were a long time ago as a separate issue. So my size depends on time as well. Jeez. But you know, those those things are pretty negligible, and so you can think about like when these things really have an effect if you probe if you shot an electron at um hi'd gin atom, when would it deflect the electron? And if you shot you know, a meter to the right, it wouldn't change the path of the electron really at all. It would, but just it would be very little, It would be very little bit negligible. But then when you you know, hit it right on, then it's going to bounce right back. And and so you can use that to sort of get a sense for what is the meaningful sort of charge radius of a particle. And you're right, it's there's no crisp edge there. So there's a small complication there also because it turns out that the size of something depends on not just what you poke it with, but how hard you poke it. Like, if you poke an atom very gently, it'll seem bigger because you'll notice smaller deflections further away. If you poke it very hard, it will actually seem smaller because you'll overpower the electrons and the outside and only see the nucleus on the inside. There's no point at which it goes to zero though, you're right, right, yeah, So it's it's kind of fuzzy and maybe kind of arbitrary, but you're saying, it's like when when you would actually fee you the force of that electron, that's when maybe you would say, all right, it's sort of impinging on it, which means it's sort of bumping up against it. Mm hmm, And it's not totally arbitrary. Like when you squeeze atoms together, they settle in at a certain distance from each other, so that totally tells you what the equilibrium location is for for the distance between atoms, and that I think is a reasonable way to define the size. But you know, you're right, you have to think about, like what am my meaning by size in this context? In this other context? This basic thing we think about like should be obvious to talk about is it turns out to have a lot of wrinkles to it, all right, So that's kind of how you would define an atom is when it starts to push back another atom, and how much when you crow them inside of a box, you know, what's the natural spacing that they have between them? And it's you're saying sort of related to those electron clouds, which is how kind of how far away the electron goes from the nuclei right, Okay, so that's a that's an atom um. But I guess it gets strict when you talk about individual particles. So let's go down one more level to the proton inside of the nucleus. How big? How how big would you say a proton is? This is a wonderful question. And you know, if you're breaking open the atom, if you're shooting electrons at the atom, it's going to get repelled by the electrons on the outside of it. But if you give them enough energy, then they can sort of penetrate through there, and then you can start to probe the proton inside there, and you can ask, like, how big is this thing? And so we do that exactly. We shoot electrons at protons or hydrogen atoms or or it doesn't really matter if the electron is there anymore, because the probe we're shooting with has so much energy, and we see where does it bounce back and where does it sort of stop bouncing back, and that gives us a sense for how big the proton is, and so we actually have a number for that. But it's tricky because the proton is also made out of things inside of it, sort of like the atom itself. It is. Protons are made of smaller bits that are slashing around inside of it. Those are the corks. But remember that we're trying to define the size of an object, the proton this case, not by where the stuff is inside it, but where it pushes back. And the corks hang out together and push back against the other protons. So if we use our definition, it's the distance between the protons that's going to determine the size of the protons. And that's connected, of course to how the corks are arranged, how they're happy to be inside the proton. The proton is sort of like a cork atom. I See if they were comfortable being a mile apart, you know, like if you try to split it more than a mile or squish the more of them out, they would prefer to be a mile up apart from each other. Now, you would say the size of those two electron at courts is about a mile. So the size of the proton that's that's made up of those corks, yeah, it would be about a mile. But you know, we have nuclei and they have got protons and neutrons inside of them, and each one is like its own little particle. They get squeezed together, but they hang out. They keep their own little particle nature, and so it's just like packing marbles together. You can ask about like the distance between the center of one proton and another, or a proton and a neutron. That's what we think of as the size of the proton. How much can you pack in the quarts that are inside of the proton? Yeah, and that's a really crazy number. That's like one quadrillionth of a meter. It's a really small number. Uh. And that's smaller than a nanometer for sure. It's smaller than a centimeter as well. It's smaller than a mile apparently as well. Um, so that's pretty small. That's pretty small. Yeah, Like, how how big is that in relation to like the size of an atom. Well, an atom is you know, like ten to a hundred ish um trillionth of a meter, So this is one quadrillionth of a meter, So it's like one ten thousands or one hundred thousands the size of an atom. So it's very small compared to the atom. Bare to the electron radius, the proton is super tiny. Okay, wait wait, so um, we have an atom and how about the just the nucleus of the atom. How close together are those protons and neutrons in the nucleus packed together? Those are very tightly packed together. And and again remember that's because that's sort of how the size of the proton is determined. It's like how do those things cluster together? And so the size of like if you have the nucleus of an atom with you know, a hundred protons and neutrons in it, it's not that much bigger than one protonomy. It's like packing above those marbles together. So it's going to be ordered magnitude quadrilliants of a meter. Oh wow, so the new And that's why they say, like the anatom is mostly empty space because you know what you would say is the size of it. Actually the nucleus is like this tiny little bit of it inside. Yeah. And the way that they probe this is two different ways. One is they shoot an electron at proton. But sometimes also they just look at an atom. They just watch an atom sitting there. It's got a proton and an electron and the electron is whizzing all around. And sometimes this is super weird. Sometimes the electron goes inside the proton, like in a quantum mechanical way, or like it actually goes through what's the difference quantum mechanics is reality, dude, um, Like if you were to you know, I mean, like if you were to open the true Dinger's box and you would you would suddenly find it inside of the news. Yeah, the electron in one of its states has non zero probability density to be inside the proton. And when this happens, it's sort of like partially cancels some of the charge pull of this thing because you have the electron now inside the positive atom and then it escapes. But depending on the size of the proton it escaped, this happens more or less often, so you can measure like how often the electron is inside the proton, and that tells you how big the proton is, because the bigger the proton is, the more often this happens. So this is another way we sort of get a sense for how big is the proton. I see, using like probability, like you throw a bunch of darts at it, only sometimes you hit hit the proton. Then that sort of tells you the size. Yeah, exactly, And that's actually the most sensitive test. Basically using the hydrogen's own electron, like pass it through the proton and give you a sense for how big it is. It's crazy. Well, all right, so a proton is about you're seeing one ten thousands of the size of a typical atom. That's pretty small, because a pretty small. So alright, so let's get there. Let's get down now to the last level, which is how big is an electron? And I imagine that's going to be even smaller, but we'll get into that, but first let's take a quick break, all right, Daniel. So now we're down to one of the fundamental particles, the electron, and we're asking the question how big is it? Or how small isn't it? Or how big isn't it? Amount of negatives here, um and so, And I guess what we're talking going to talk about. It sort of applies to quarts as well, right, because we're now talking about single particles, not like clusters of particles. Yeah, and remember that our theory is very hierarchical. We start with matter, and then we go to molecules, from molecules to atoms, from atoms to protons and electrons, and then to quarks and electrons, and we're sort of have shells inside shells inside shells, and so this is sort of our current level of knowledge, and we can ask like, are these particles that we see, um, are they the smallest possible thing? Or is it possible there's something else inside them? So you're right there, quarks and electrons are sort of as far as we've gone, and so in some sense, asking how big are they is asking are they the end? Are they the tiniest, smallest possible thing? Or they possibly made of something smaller? Oh? I see, because if you can split them, that means there's something smaller inside. I guess that's pretty obvious. And that's for you. That sounds deep and it is deep, but it's also kind of obvious, like if you can break it into smaller pieces, then it's there were made of something else. As far as we know, quarks and electrons are not yet made of something smaller. But that doesn't tell you necessarily how big they are. Right, they could be the smallest possible thing and still have a finite size. Right they could be um, the legos of the universe. Lego. Yeah, it could be the smallest lego you can have, but um, that can be smaller, smaller, big, that could be smaller big, And that's fascinating when you learn a number about the universe. Like, let's say we somehow proved that quirks and electrons are not made of anything smaller. They have the smallest lego blocks, and we measured their size, Then we'd we'd know something really deep and basic about the universe, like it's made of legos this size, and you have to wonder, like, well, why that size and not something else? What does that tell you about the universe to know that fundamental fact? Yeah? Did you know there are legos that are smaller than the single unit lego? What? Like you you would think the smallest lego is just like one square with one circle on it, right by saying people have smashed the legos together and make some legos covered the constituent pieces and legos. No, yeah, they make uh this is kind of weird but uh probably not consequential. But um, they make smaller pieces. It makes pieces that fit inside of the whole that some of the single circle lego pieces have inside. Oh my god, you have just violated the standard model of legos. Noble price. Please you've got the prize from that one. Anyways, Um, so, yeah, so let's talk about how big an electron Isn't let's use that as our single particle example. And does it even make sense to talk about the size of a single particle, Daniel, It's hard to talk about the size of a single particle if you haven't measured the stuff inside of it. Because we've talked about the size of atoms and protons based on like how happy this stuff inside of it is to be next near each other, like how closely does it pack? So for a fundamental particle you have to go back to like the poking it and be like, well, if I poked an electron with a stick, where were pushed back? But that's sort of unsatisfying to me. Couldn't can't I just you know, pack a bunch of electrons in a in a glass jar and see, wouldn't that tell me sort of the size of it, Like how comfortable an electron is to another electron or to a proton. Wouldn't that sort of tell you this sort of the size, just like we did with the marbles and the atoms. Yeah, that sounds like a really fun experiment. I want to take like a gas of pure electrons and squeeze it down together and see what happens. The problem is that there's not like a clear answer, like the heart do you squeeze the closer they get together, it's not like an equilibrium like with protons or with atoms, because these are all just negatively charged particles. There's no chill state where they're like, hey, you're there, I'm here. All is good, and so instead you want to like take them and like poke them, like, well, if you poke them with an electron, then they bounce back for sure, But what if you poke them with neutrinos then they don't bounce back at all, Or what if you poke them with dark matter? Then they don't bounce back, And so you're back to this like fuzziness of like you know, if it depends on how it's pushing back, then it depends on what you're poking it with. And then size isn't something that's like inherent to the object. It's about the interaction, which means it depends also on the thing you're interacting it with, which is so frustrating. Oh, I see what you're saying. Like if I had a cloud of electrons, you could maybe talk about where the cloud is, and where the cloud isn't, where the electors are and where there aren't. But with one single electron, it's hard to say where it ends. It's hard to say where it ends, like is there a left side to the electron and the right side to the electron? Are those things even the same thing? Because it depends on what you you're trying to touch it with, right, Like, if you're trying to touch it with another electron, it would maybe repel at a certain distance, But if you try to poke it with a proton, then it would maybe attract at a different distance. Yeah, well not so much electron versus proton, because they both feel the electromagnetism. But what if you used a different force, if you use like the weak nuclear force, or if you used you know, gravity, or if you used electromagnetism, is them than the size that you would get from electron is different. And we're turning to a neutrino. An electron has those eyes. It doesn't like, I don't care, Like the neutrino doesn't care. A neutrino would pass through a cloud of electrons and have a much lower chance of interacting than another electron would, like it wouldn't even know it's there, yeah, or dark matter, right, pokeing a pile of electrons with a stick of dark matter, you're gonna get almost no interactions, or maybe no interactions. We don't even know about dark matter. And this is the problem. It makes sense to define size in terms of interactions, like where is something pushed back, But it also is troublesome because then it depends on what you're pushing on it with. So that's kind of a problem in defining the size of an electron because it depends on what you poke it with. So then we try something else. We say, well, let's think about it like quantum mechanically, Like we've talked about where the electron is, and it's defined by like it's quantum mechanical wave function, and you know you were talking about like those balloon shapes where the electron is. You know, it's the sort of the most you can localize an electron, Like what's the size of that quantum packet? You want to think about it like as a tiny quantum object. That's like another way to try to grapple with it because their probability curves right, Like you know where the cloud is fuzzy tells you that the probability that the electron is there is small, but where the cloud is kind of thick, it tells you that there's a high probability that the electron is there. But that doesn't really give you any insight because that size can be almost anything. It depends on the uncertainty principle. If you know almost nothing about the velocity of the momentum of the electron, then you can know exactly where it is, which means it has like zero that quantum mechanical packets zero with And on the flip side, if you know everything about its velocity, then it's packet is infinitely wide, like exists everywhere in the universe simultaneously have like a universe sized electron. So that's intellectually not that satisfying either. But what if you assume an electron is just standing still, like when you're to measure your kid how all they are and it's impossible because they keep moving. But what if you can get it to stand still? Oh wouldn't what would that happen? Would you be able to then get a pretty accurate size. If you're measuring the velocity of the particle, you're getting it to stand still has no velocity, and you say it has zero velocity, then it has infinite size because you can't know the product. Remember the product of the position and momentum uncertainty has to equal a certain number. And so if you're narrowing down the speed of the electron really really well, that means you don't know anything about where it is. It's an infinite plane. Wave size is only distance, whereas you know in particle physics, distance is kind of intertwined with time as well in velocity. But then on the flip side, if you say I don't care at all about how fast it is, I just want to know where it is, then you can localize it as much as you want. You can make it infinitely narrow. And so that also doesn't give you any sense of like the size of the electron. So strike to we can can use poking or are quantum mathematics. So does that mean that the electron has no size, that it's impossible to define the size of an electron. It kind of does currently. I mean in our theory, the way we actually use it is we assume the electron has no size at all, It has zero volume. That it's just like a point in space. The left is the right, the top is the bottom, the back is the front. There's no extent to it at all. It's sort of mathematically and and because of all the things we just talked about, I guess that that's true. Yeah, you can't measure the size of an electron. It doesn't make any sense to think about it. Yeah, in our theories, we just put zero because we assume that there's nothing there. We have no way to really see the size of the electron. But you know, we do continue to try. We do smash particles at the electron, hoping that we'll see a break open, hoping that we'll see other little particles come out of it. But I guess getting back to the size of the electron itself, um, I mean, it's not like it has no size because it's it's not a mile wide, Like, would you even say that the electron is all electrons are a mile mile wide? I don't know what to say for the size of the electron, you know, And that's why I predicted, I think correctly, that you'd be unsatisfied with Oh my god, it's not really you can't tell the future, can Yeah, well, I can in this case, like I think the way I think about it currently is as a point, But I also know that that makes no sense because like, how do you have something that has mass but has no volume because then has infinite density, which is nonsense, right is it? Electrons have mass, they have mass, and they have charge, Like where does that charge go? Where is it in the electron if it has no volume. We're just used to thinking about stuff as having sizes having volume, So to imagine that the basic building box of the universe themselves are of zero volume is really weird. But I guess maybe you know that that's the theory of it. But practically speaking, I mean, we can talk about what's what's practical to you and me is like electromagnetic forces, right, you know, And it doesn't make sense in terms of neutrinos are dark matter, but kind of what's practical electromagnetic forces? And so couldn't we sort of maybe give a practical size to the electron because of that, like like what's the closest to electrons in one atom? How close can they get to electrons in another atom? Wouldn't that give you a general size? Yeah, and we've done that we like pounded electrons near each other and try to get them as close together as possible, And so far we haven't found a limit, Like, there's no point at which the electrons will not get closer to each other. And so far we've gotten down about ten to the minus twenty meters. And you do that by shooting really high energy electrons at other electrons and try to get them really close together. So that's as far as we could tell. We can't tell the difference between the electrons have no volume, and they have some volume that's smaller than ten to the minus twenty. We can't tell the difference. So far. They look like their point like, but we have some sort of limited resolution there in our ability to probe. So what happens if I the whole universe was just like a proton and an electron, I guess the electron would orbit the proton. That's what hydrogen is. Yeah, The size the hydrogen comes from their interactions. Right, Most of the volume of all the stuff in the universe comes from the interactions, not from any actual volume of the particles that make them up. All right, Well, you're right, this is very unsatisfying. Anim Well, that's satisfying to me that at least I was right about that. But it's a it's a really fun puzzle because I think it's interesting to try to grapple with the quantum realm and try to understand what are the limits of our ability to map these concepts size and mass and charge and velocity down to these tiny particles that, in the end are the reality, are the truth about our universe. Yeah, And I think it's interesting how, you know, you sort of put it that it's all about the interactions, you know, And it's hard to think about an electron not having like a surface or you know, an st where it's no longer an electron, And it all sort of depends on what you're trying to look at it with, you know, Like if you're trying to look at it with neutrinos, then you wouldn't see anything at all. Yeah, But if you looked at it with the electrons, it would feel like a certain size maybe. Yeah. And this is connected to some of the other puzzles we talked about, like does the electron actually spin? We know that it's either a point, in which case it doesn't make sense for it to spin like a point literally cannot spin, or that it's super tiny. But if it's super tiny and it has a surface, then it's spinning so fast that that surface is moving faster than the speed of light. So at some point, like it doesn't even make sense for it to have a non zero size. At some point, nothing makes sense, Daniel, life is meaningless, And that's usually about forty five minutes into every episode. The incredible thing is that we can understand it at all, That we can take these ideas from our everyday experience of like eating bananas and throwing balls around, and then it can give us any side into the microscopic. You know that, because the microscopic is so weird, so alien, it's incredible it works at all that I even have a job. But yeah, but that's the thing it was. We don't understand it, but yet at the same time we're able to, you know, predict it and describe it with math. But that doesn't mean we understand it, right, That's what understanding is. As far as I know, I don't know any deeper level of understanding. When you pass it off to the philosophers and you can ask them, like, you know, what does it mean? Man? But in the end. What we're trying to do is physicists is just sort of describe accurately the world we see around us, build a model in our heads that makes sense, describe all this unknown in terms of the known. That's that's all the understanding we can hope for. Well, I guess what I mean is like at some point we thought the proton was a proton, and we had to math to describe it, and we thought we understood it. But then then it turned out we that we there was more to the proton than we thought, and we didn't actually understand the proton. It was made out of quirks, for example. So I feel like, you know, you have a mathematical di ccription of stuff, but you don't know if you're really understanding it to the fundamental level. And all of these mathematical descriptions they work up to a point. Like your idea thinking about a proton as a fundamental particle as a point particle that mostly works. It works unless you get up to really high energies, energies where you can see inside the proton, because the energies are greater than the bonds that are holding the proton together. And so as we keep pushing to higher and higher energies. We're looking deeper and deeper into the real truth the smallest scales of the universe. And that's what limits how small we can see is the energy with which we probe it. And that's why, like building a bigger super collider would let us maybe see whether the electron had bits inside of it. Yeah, keep funding physics is hey, I'm on message. If nothing else, keep sending those checks. Please, if you have to pick between donating to bananas or fundamental physics, you know where I stand on that. Bananas, right, because bananas are made out of fundamental partners. All right, Well, we hope you enjoyed that, And maybe the next time you take a bite out of a banana or your fruit of choice, maybe think about what it actually means to take a bite. I feel like we've thrown everything into question now, Daniel, Like, what does it even mean to take a bite into When my teeth end and when does the banana begin? I don't know, but every banana you've ever eaten is made out of zero volume particles. Chew on that and think about it until next week. Thanks for joining us, See you next time. Before you still have a question after listening to all these explanations, please drop us a line. We'd love to hear from you. You can find us at Facebook, Twitter, and Instagram at Daniel and Jorge That's one Word, or email us at Feedback at Daniel and Jorge dot com. Thanks for listening, and remember that Daniel and Jorge Explain the Universe is a production of I Heart Radio. For more podcast from My Heart Radio, visit the i heart Radio app, Apple Podcasts, or wherever you listen to your favorite shows. Yeah m