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Speaker 1: Hey, Joe, if you could only eat one flavor of

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Speaker 1: ice cream for the rest of your life, would it

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Speaker 1: be chocolate or vanilla? Who do I have to choose?

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Speaker 1: Can I do like a quantum superposition of the tooth flavors? No,

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Speaker 1: you are not a quantum Jorge, so you can only

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Speaker 1: be in vanilla or chocolate. States It's a classic dilemma

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Speaker 1: of classical physics, isn't it is? And so does your

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Speaker 1: wave function collapse to vanilla or chocolate? Obviously vanilla my

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Speaker 1: favorite flavor. Are you telling me for real you'd give

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Speaker 1: up chocolate ice cream forever? What if I break the

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Speaker 1: loss of physics? Can I do something like a swirl?

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Speaker 1: Then you go to physics jail whether they don't have

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Speaker 1: either flavor of ice cream? It haves swirls in physics jail,

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Speaker 1: not even for my last meal. All they have in

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Speaker 1: physics jail is physics homework problems. That seems a little inhumane,

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Speaker 1: the ice cream part, not the homework part. I am

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Speaker 1: more hammy cartoonist and the creator of PhD comics. Hi,

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Speaker 1: I'm Daniel. I'm a particle physicist and a professor at

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Speaker 1: UC Irvine, And I choose the chocolate ice cream in

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Speaker 1: one hundred out of one hundred multiverses. Big fan of chocolate, huh,

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Speaker 1: there's just no comparison. I mean, chocolate is delicious, but

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Speaker 1: chocolate ice cream, it just elevates it beyond understanding, No,

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Speaker 1: I think. I guess My question is when you say

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Speaker 1: chocolate I thing for the rest of your life. Do

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Speaker 1: you mean like you only get to eat chocolate ice

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Speaker 1: cream for all your meals? Or is this like only

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Speaker 1: for desserts subtimes? I think even I would get tired

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Speaker 1: of chocolate ice cream if I ate nothing but that breakfast,

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Speaker 1: ludge and dinner, eventually it would get old. Though. You

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Speaker 1: know this milk chocolate ice cream is dark chocolate ice cream.

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Speaker 1: There's chocolate and salt. There are lots of variations there.

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Speaker 1: But that's what I was going to ask, Like what

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Speaker 1: kind of chocolate? There's so many the flavors to choose from. Yeah,

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Speaker 1: and chocolate from all around the world. You know, Madagascar chocolate,

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Speaker 1: and then it's whale and chocolate. They're all subtly different. Now,

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Speaker 1: what's your stand on Like chips like chunks of chocolate

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Speaker 1: in your ice cream? Honestly, I think that ruins the texture.

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Speaker 1: You know, a frozen blob. It's like chewing on a pebble,

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Speaker 1: Like nobody wants to eat rocks, right, right, right, So

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Speaker 1: you're you're against some chocolate ice cream. I'm saying chocolate

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Speaker 1: chunks ruined the chocolate ice cream experience. Let's just have

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Speaker 1: pure ice cream and not chunks. But then now you've

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Speaker 1: got to define a size limit, like what sized limit

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Speaker 1: of chocolate particle are you willing to tolerate? Chocolate ice

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Speaker 1: cream is fundamental, man, It's not composite. It's so important

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Speaker 1: to the universe. There's a chocolate ice cream field that

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Speaker 1: permeates the whole universe. I see, I see, But I mean,

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Speaker 1: I'm sure there's this size of chocolate particle that will

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Speaker 1: fly under your radar. Yeah, you know. I think this

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Speaker 1: calls from more experiments for sure. And I actually did

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Speaker 1: a little Twitter experiment myself. I was wondering if our

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Speaker 1: support orders sided with the obviously correct me on the

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Speaker 1: chocolate camp or the obviously incorrect you on the vanilla camp.

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Speaker 1: So I went out into the little pole to ask

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Speaker 1: people chocolate versus vanilla? But did you say chocolate vanilla? What?

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Speaker 1: I didn't? I just said chocolate versus vanilla? Important science question.

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Speaker 1: Oh yeah, it sounds like an ill designed experiment, Danny,

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Speaker 1: I would expect more from a scientist. Well, I didn't

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Speaker 1: want to be over specific. I wanted a sample, you know,

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Speaker 1: people's general vibe about these flavors, the word chocolate and vanilla. Yeah, exactly.

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Speaker 1: It wasn't a question of like, which one you preferred

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Speaker 1: to spell? Obviously, it's about the flavor. And anyway, the

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Speaker 1: Internet came down on my side, chocolate fifty eight percent

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Speaker 1: to vanilla forty two percent. Wow, that's relatively closed, I

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Speaker 1: would say, don't you think I actually was surprised. I

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Speaker 1: thought chocolate was going to blow vanilla out of the

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Speaker 1: water a little bit more. Here you go, Hey, you

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Speaker 1: know I'll take a twenty point differential. Well, we all

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Speaker 1: know that whatever the Internet things is the best choice

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Speaker 1: for anything. Well, I would say whatever our listeners thing

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Speaker 1: is definitely you know, sampling the truth of the universe.

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Speaker 1: I see, did you have everyone to sign a little

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Speaker 1: like waiver to testify that they're listeners? This is getting

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Speaker 1: more unscientific by the moment. By the way, they all

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Speaker 1: follow us on Twitter. Why would somebody follow us on

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Speaker 1: Twitter and not listen to the podcast that just makes

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Speaker 1: no sense exactly. If they're already listening to us in

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Speaker 1: our podcast, why would they follow us on Twitter for

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Speaker 1: important science questions like chocolate versus Vanilla, the chance to

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Speaker 1: weigh in on the ultimate debate in the universe. Well,

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Speaker 1: I guess if you'd like to go with the majority,

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Speaker 1: you know, the mainstream, I guess that's your thing, right.

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Speaker 1: Vanilla is definitely not the boring, middle of the road choice,

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Speaker 1: for sure. Vanilla is the rebel choice. Yeah, it's the

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Speaker 1: indie minority choice. But anyways, welcome to our podcast Daniel

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Speaker 1: and Horry Explain the Universe, a production of iHeartRadio in

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Speaker 1: which we appreciate all of the flavors of the universe,

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Speaker 1: the quantum, the classical, the things that make sense, the

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Speaker 1: things that don't make sense. We blend them all together

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Speaker 1: into chunks so tiny and so smooth that you can

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Speaker 1: appreciate them without having to chew on a intellectual pebbles.

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Speaker 1: It's right because it is a delicious universe, full of

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Speaker 1: amazing textures and flavors and temperatures of treats. And so

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Speaker 1: there's a lot to talk about it in a lot

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Speaker 1: to try to explain to everyone, And there's a wonderful

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Speaker 1: and long history of trying to understand the universe, just

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Speaker 1: sort of looking at the stuff around us, seeing if

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Speaker 1: it makes sense, breaking into smaller pieces and seeing those

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Speaker 1: pieces make sense, digging in even deeper to smaller and

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Speaker 1: smaller pieces, until eventually we get the stuff that seems

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Speaker 1: to follow weird and different rules, rules that surprise and

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Speaker 1: confuse us. The universe is full of rules, interesting rules

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Speaker 1: that are sometimes helpful, like Newton's laws or general relativity

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Speaker 1: by Einstein. But sometimes there are rules that kind of

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Speaker 1: don't quite make a lot of sense, at least to

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Speaker 1: a human because our tendency is to think about things

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Speaker 1: in terms of the things we know. When we discover

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Speaker 1: a new object, we think, oh, maybe it's a little

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Speaker 1: bit like a grain of sand, or maybe it's a

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Speaker 1: little bit like a basketball. Can I apply the rules

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Speaker 1: of waves to this thing? Can I apply what I

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Speaker 1: know about bananas to this new discovery? So when we

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Speaker 1: unearthed quantum particles, our first guests is to think, oh,

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Speaker 1: these are like tiny little dots that follow the rules

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Speaker 1: of classical physics. Maybe they move through space, they have

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Speaker 1: velocity and position, they're just super duper tiny. But what

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Speaker 1: we've discovered is that they are not like anything we

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Speaker 1: have ever seen before. They're not tiny little dots of

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Speaker 1: sand just like baseballs, but much much smaller. They're not

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Speaker 1: even just like waves. There's something else, something weird, that

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Speaker 1: follows a new set of rules that we have to

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Speaker 1: discover and savor. Yeah. I feel like whenever we start

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Speaker 1: to talk about things that don't make sense, it probably

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Speaker 1: means that we're going to the quantum realm, that we're

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Speaker 1: going to talk about quantum things. Yeah, but this is

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Speaker 1: our experience every time we extrapolate from our intuitive experience,

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Speaker 1: from our understanding of the world around us, not just

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Speaker 1: the tiny and the quantum, but also the very very

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Speaker 1: big right thinking about the universe as a whole, and

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Speaker 1: maybe having an edge or having a beginning. All those

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Speaker 1: things defy our understanding because they're not part of our experience,

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Speaker 1: so we don't have like a natural vocabulary, a way

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Speaker 1: of thinking about them that's comfortable. Instead, we have to

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Speaker 1: rely on mathematics to bridge us into a new language,

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Speaker 1: a new way of thinking about the world. Yeah, but

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Speaker 1: I guess it's part of that is I wonder if

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Speaker 1: it's just like the context in which we came up

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Speaker 1: in as a species, like our size that we just

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Speaker 1: happen to evolve into. Like if we were much much

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Speaker 1: tinier as a living thing, you know, maybe the quantum

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Speaker 1: rules of the universe would make more sense than the

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Speaker 1: classical rules of the universe. I think that's probably true,

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Speaker 1: And one day we might meet like microscopic aliens whose

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Speaker 1: scientists of all finding quantum mechanics we totally intuitive and

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Speaker 1: classical physics to be very very weird. Of course, they

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Speaker 1: wouldn't call it classical physics. They would call it like,

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Speaker 1: you know, huge physics or something. They would think it's

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Speaker 1: very strange that if you take ten to the twenty

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Speaker 1: nine quantum particles, they somehow come together to act like

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Speaker 1: one big particle. That's an interesting question. I wonder, like,

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Speaker 1: what's the smallest living sentient thing you can have? Like

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Speaker 1: can you make a being out of straight up of

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Speaker 1: a few quarks, you know what I mean? Or the

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Speaker 1: strings inside of quarks. It's a really fun question. And

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Speaker 1: Max Tegmark, who's a physicist at MIT, has this really

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Speaker 1: fun paper about where consciousness comes from, and he thinks

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Speaker 1: it's actually a state of matter. We're going to dig

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Speaker 1: into it in a future podcast episode. But it might

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Speaker 1: be that everything in the universe is aware, and that

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Speaker 1: even small combinations of objects can somehow do calculations and

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Speaker 1: maybe even be conscious. Dude, they gonna have to smoke

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Speaker 1: some special things in order to get into that topic. Bananappeals,

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Speaker 1: for sure, Well, the quantum universe is full of interesting

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Speaker 1: and weird rules, sometimes rules that don't seem to make sense,

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Speaker 1: or that even seem kind of fair, And as we

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Speaker 1: explore the quantum universe we discover these rules. A lot

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Speaker 1: of the time, these rules are just descriptive. They just

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Speaker 1: describe what we see. They don't always fundamentally explain it.

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Speaker 1: But sometimes we can actually find a reason for it.

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Speaker 1: So that's sort of the strategy is like, look out

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Speaker 1: in the universe, see what's going on, see what's not

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Speaker 1: going on, so we can understand what the dues and

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Speaker 1: don't have other particle world and then try to extract

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Speaker 1: from that some fundamental reason why the universe is this

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Speaker 1: way and not some other way. So to the other podcast,

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Speaker 1: we'll be tackling the question why can't two fermions be

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Speaker 1: in the same quantum state. Now, first of all, Danny,

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Speaker 1: let me just say that I'm glad you're a bored

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Speaker 1: with the faith the quantum realm? Have you sold out

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Speaker 1: to the Marvel corporate machine yet to ching? No, it's true.

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Speaker 1: I have the new ant Man movie on the brain.

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Speaker 1: Can't wait to see it. Oh really, you're excited even

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Speaker 1: though they're jumping into the quantum realm and finding all

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Speaker 1: kinds of things inside of it. M Yeah, absolutely, I

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Speaker 1: like those movies. I mean, they are scientifically mostly nonsense,

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Speaker 1: but they also don't take themselves too seriously, and they

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Speaker 1: have fun with it, and I think they're really creative.

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Speaker 1: The first couple had some really beautiful visuals of like

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Speaker 1: what the quantum realm might look like or what it

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Speaker 1: might be like to visit the quantum realm, so I

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Speaker 1: think they're a lot of fun. Oh wow, I feel

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Speaker 1: like you are getting paid by Marvel, right, You're like,

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Speaker 1: is this the Daniel? I know what science you like?

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Speaker 1: The random use of the word quantum. No, I don't

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Speaker 1: only like hard science fiction. I dislike hard science fiction

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Speaker 1: that gets it wrong. You know, if you want to

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Speaker 1: pretend to be serious about your science and then you

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Speaker 1: get it wrong, then you get the merits from me.

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Speaker 1: But if you're going to make fun of yourself along

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Speaker 1: the way and just have a good time. Then let's

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Speaker 1: go for it. Well, in this case, we're asking a

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Speaker 1: kind of an interesting question here about the quantum nature

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Speaker 1: of things. So why can't two fermions be in the

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Speaker 1: same quantum state? No, I imagine this is maybe not

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Speaker 1: a question most people have thought about before. This is

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Speaker 1: something people run into in high school chemistry when they're

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Speaker 1: like learning about electrons and electron orbitals. But it's a

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Speaker 1: really deep and important concept in particle physics theory that

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Speaker 1: relates to how particles operate, what it means for particles

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Speaker 1: to be identical, what it means to like swap particles

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Speaker 1: from one state to another. Turns out to be a

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Speaker 1: really deep and important concept in particle physics, and something

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Speaker 1: a couple of listeners wanted to know more about. How

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Speaker 1: does it actually work and why does it happen? Maybe

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Speaker 1: it'll be the plot of the next ant Men movie.

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Speaker 1: You can't have two ant Men in the same place

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Speaker 1: at the same time. Yeah, I think they have multiple

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Speaker 1: ones in this latest movie, So maybe that's the plotline

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Speaker 1: is toasted, Or maybe it just means ant Man is

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Speaker 1: a Boson and not a Fermion, Or maybe he's an

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Speaker 1: ant t particle. I wasped right into that was usually

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Speaker 1: we were wondering how many people out there had thought

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Speaker 1: about this rule that applies to fermions or electrons, and so,

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Speaker 1: as usual, Danny went out there to ask the internet, right,

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Speaker 1: that's right. Thank you very much to everybody who participates

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Speaker 1: for this segment of the podcast, and if you would

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Speaker 1: like to share your thoughts for our education and entertainment,

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Speaker 1: please don't be shy write to us two questions at

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Speaker 1: Daniel and Jorge dot com. So think about it for

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Speaker 1: a second. Do you know why two fermions can't be

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Speaker 1: in the same quantum state? Here's would be glad to say.

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Speaker 1: I'm not sure of the terminology. I think there is

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Speaker 1: an exclusion principle something that says that they can't occupy

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Speaker 1: the same state or same space. I don't know if

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Speaker 1: it's called the poly exclusion principle. I'm not sure. So

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Speaker 1: I think the fermions are the force caring ones. Why

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Speaker 1: can't they be in the same quantum state? You know,

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Speaker 1: maybe they're all entangled with each other and so they

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Speaker 1: all have to have like opposing states of some sort.

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Speaker 1: I am merely guessing that two fermions cannot have the

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Speaker 1: same quantum state because they have different properties. Well maybe

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Speaker 1: because they have the same charges, and then they need

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Speaker 1: to find more stable spots to be related to some

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Speaker 1: other opposite charge particle. I think deferments cannot be in

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Speaker 1: the same quint of state for the same reason that

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Speaker 1: a magnet cannot have a same pool in booth sides.

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Speaker 1: I'm a bit fuzzy on what fermions are, but if

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Speaker 1: they can't be in the same quantum state, I think

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Speaker 1: it might be to do with the fact that's kind

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Speaker 1: of like magnets, where you need in order for them

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Speaker 1: to be magnetic, you have to have one pole opposite

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Speaker 1: to the other. Something similar like that, where the one

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Speaker 1: needs to spin up one needs to spin down. All right,

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Speaker 1: A lot of fun answers here. Nobody mentioned Paul Rudd.

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Speaker 1: Nobody else out there is a shill from Marble like

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Speaker 1: I am. Apparently you keep bringing it up. You rather,

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Speaker 1: Paul Rudd. I want in on this. By the way,

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Speaker 1: if you if you have a hook up with Marvel,

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Speaker 1: I'm totally in. All right, sounds good now. These answers

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Speaker 1: are pretty good. They're sort of all over the place.

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Speaker 1: I was a little surprised. I thought we'd hear more

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Speaker 1: mentions of the poll exclusion principle. More people need to

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Speaker 1: take or remember their high school chemistry. You mean you

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Speaker 1: were expecting more people to mention the poll exclusion principle. Yeah. Absolutely,

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Speaker 1: I thought it was something people knew pretty well. I

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Speaker 1: mean I remember suffering through it in high school chemistry.

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Speaker 1: I imagine a lot of other people have. Well, let's

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Speaker 1: step into it, Danny. What is the poly exclusion principle

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Speaker 1: and how does it apply to quantum states and fermions.

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Speaker 1: So the poly exclusion principle basically just says that you

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Speaker 1: cannot have two fermions in the same quantum state, right,

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Speaker 1: It's basically a statement of the problem. Of course, it

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Speaker 1: references these particles fermions, named after Enrico Fermi. But these

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Speaker 1: are the particles that make up matter. So quarks and

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Speaker 1: electrons are fermions, and this is why, for example, you

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Speaker 1: can't have two electrons in the same state around a

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Speaker 1: hydrogen atom. The poly exclusion principle forbids it. Okay, so

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Speaker 1: let me go back a little bit to a fermion.

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Speaker 1: It's what you call the matter particles, right, Yeah, we

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Speaker 1: have two different kinds of particles. In the standard model,

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Speaker 1: we have the particles that make up matter, so the electron,

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Speaker 1: the quarks, for example, and that of that you can

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Speaker 1: build protons and neutrons, from which you can make the nucleus.

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Speaker 1: At electrons you get atoms. Buy them all together, you

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Speaker 1: get molecules. We're basically built out of those things. There

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Speaker 1: are also other particles. These are the force particles. The

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Speaker 1: particles like the photon that bind the electron to the nucleus,

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Speaker 1: and the w and the z bosons for the weak force,

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Speaker 1: and the gluons for the strong force. These particles are

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Speaker 1: the force particles. There's an interesting difference between these two

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Speaker 1: kinds of particles. The first one the fermions. You can

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Speaker 1: never have two of them in the same state. Two

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Speaker 1: electrons can never be in the same state. But the

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Speaker 1: other group, the force carrying particles, these bosons. There's no limit,

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Speaker 1: Like you can have two photons in the same state,

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Speaker 1: ten photons in the same state, a million photons all

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Speaker 1: piled on top of each other. So fermions can never

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Speaker 1: be in the same state. Those are the matter particles,

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Speaker 1: and bosons can be in the same state. That's this

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Speaker 1: weird division Okay, now let's maybe define for people what

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Speaker 1: is a quantum state, Like what does it mean to

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Speaker 1: have a state, and what can those states be? So

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Speaker 1: what can quantum particles do well. They can be in

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Speaker 1: some location. They can also have a certain amount of energy,

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Speaker 1: They can have a certain kind of spin, like some

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Speaker 1: of these particles can have spin up or spin down

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Speaker 1: or other various weird kinds of spin. So basically, anything

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Speaker 1: that describes the particle is part of its quantum state.

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Speaker 1: A quantum state is just a description of the particle,

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Speaker 1: Like you mean, like where is it and what's it doing? Yeah, exactly,

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Speaker 1: that's what a state is. The way you might describe

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Speaker 1: like a classical object by saying where is it, how

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Speaker 1: fast is it going? What is it? Location and velocity?

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Speaker 1: That describes the classical object. A quantum state is just

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Speaker 1: a description of the quantum particle. Like the state of

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Speaker 1: a baseball might be like it's over here, it's moving

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Speaker 1: in this direction, and it's also spinning in place, and

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Speaker 1: maybe also like it's temperature. Would that be kind of

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Speaker 1: like what you need to describe a baseball. Imagine, for example,

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Speaker 1: we live in a simulation and you're the programmer of

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Speaker 1: the simulation. What details do you need to keep track

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Speaker 1: of to run your simulation? That's the quantum state of

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Speaker 1: a particle. I see. Well, I'm not sure how many

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Speaker 1: people out there know how to program, but I think

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Speaker 1: maybe it's sort of like a list that identifies everything

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Speaker 1: that we know about a particle. That's kind of what

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Speaker 1: you're saying, right, And so for small particles that list

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Speaker 1: it's not like an infinite list, right, Like it's a

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Speaker 1: list of maybe like five things exactly. It depends a

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Speaker 1: little bit on where that particle is. An electron in

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Speaker 1: free space doesn't have energy levels the way an electron

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Speaker 1: around a hydrogen atom does. Wait, what it depends on

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Speaker 1: the situation. So like, if I have just have a

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Speaker 1: particle out there in space by itself, what are its

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Speaker 1: quantum state variables? A particle just out there in space

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Speaker 1: with like no potential, no forces on anything, a free particle,

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Speaker 1: then the quantum states are just the location and the

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Speaker 1: energy and the energy. What do you mean by energy, Well,

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Speaker 1: it's velocity, right, it's kinetic energy, and it's spin as well. Yes, absolutely,

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Speaker 1: and it's spin. But remember out there in free space,

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Speaker 1: the kinetic energy can have any value. Electrons are quantized

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Speaker 1: into energy levels around a hydrogen atom because they're confined.

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Speaker 1: The quantization only comes from the confinement. Electrons at in

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Speaker 1: free space don't have like energy levels, whereas electrons around

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Speaker 1: a hydrogen atom, for example, do. So there's an important

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Speaker 1: distinction there about the quantum state of these particles. Are space,

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Speaker 1: you would just say the energy around the hydrogenontom, you

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Speaker 1: would say the energy level. But when it's out in

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Speaker 1: space you also count like the spin of it too, Right,

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Speaker 1: are there any other quantum variables? I guess each kind

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Speaker 1: of particle has different kind of variables attached to it. Yeah, exactly.

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Speaker 1: And electrons can have two different kinds of spin, spin

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Speaker 1: up and spin down. Photons can have three different kinds

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Speaker 1: of spin. The Higgs boson doesn't have any spin at all,

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Speaker 1: So it depends a little bit on a kind of

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Speaker 1: particle and also the situation that it's in. Okay, So

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Speaker 1: now the rule here is that no two particles can

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Speaker 1: have the same quantum state. Now what does that mean

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Speaker 1: for like particles out there in the open floating around

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Speaker 1: space like that means that no two electrons can be

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Speaker 1: in the same spot with the same velocity in the

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Speaker 1: same spin. So the rules not that no, two particles

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Speaker 1: can be in the same state, but no, two fermions number.

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Speaker 1: Half of the particles we call them fermions, they can't

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Speaker 1: be in the same state. The other half we call

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Speaker 1: them bosons. They have no problem being in the same state.

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Speaker 1: So electrons and quarks they can't pile up on top

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Speaker 1: of each other in the same state, whereas photons can.

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Speaker 1: Question is, like, what happens out there in empty space? Well, yeah,

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Speaker 1: two electrons cannot be in the same state, meaning it

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Speaker 1: can't be in the same location with the same spin

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Speaker 1: and the same energy. That's just not possible. Well that's interesting,

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Speaker 1: Like that just seems to be like a rule the

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Speaker 1: universe has, right, Like that's something that you think can't happen.

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Speaker 1: But I guess is anyone actually tried to see if

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Speaker 1: you can fit to electrons in the same spot. Oh yeah,

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Speaker 1: the universe tries to do it all the time. Remember,

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Speaker 1: the universe likes to have things relax down to the

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Speaker 1: lowest energy. That's really what forces are. Forces are things

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Speaker 1: that push things down to lower energy configurations. So think

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Speaker 1: about what happens when you put electrons around an atom, Right,

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Speaker 1: the first one goes down to the lost energy level,

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Speaker 1: and then the second one can't go down to the

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Speaker 1: lost energy level because that's filled. Right. It's sort of

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Speaker 1: like playing connect for you put one piece in, the

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Speaker 1: next one can't slot into that lowest level anymore. It

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Speaker 1: has to go to energy level two. I guess I'm

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Speaker 1: trying to understand like this rule on the free space

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Speaker 1: situation first, and then maybe we can get into the

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Speaker 1: going around an atom situation and after that because like electrons,

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Speaker 1: for example, don't have a volume to them, right, they

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Speaker 1: don't have a solidness to them. So technically, like you

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Speaker 1: could have an electron on top of another electron, but

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Speaker 1: you're saying the universe somehow, for some reason, doesn't like that. Yeah. Well,

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Speaker 1: I think the free space example is a little artificial

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Speaker 1: because you bring two electrons together, they will have a

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Speaker 1: force between them. They will try to repel each other,

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Speaker 1: so they're no longer free electrons, right, So that examples

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Speaker 1: a little bit artificial. I think you know, out in space,

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Speaker 1: the universe does try to compress electrons down into tiny dots.

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Speaker 1: We'll talk later about what happens. For example, in white dwarfs.

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Speaker 1: White dwarfs don't collapse into black holes because the electrons

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Speaker 1: resist being put on top of each other, and the

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Speaker 1: forces are strong enough to overcome this electrostatic repulsion, but

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Speaker 1: they're not strong enough to overcome this quantum resistance to

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Speaker 1: electrons being on top of each other. But it's not

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Speaker 1: exactly out in free space, because again, electrons on top

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Speaker 1: of each other there are pushing away against each other.

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Speaker 1: There is potential energy there. I guess I think that

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Speaker 1: let's talk about two electrons out there in free space,

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Speaker 1: and I know they repel each other by the electromagnetic

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Speaker 1: force because they're both the same charge. But let's say

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Speaker 1: you manage to overcome that. You're saying, like, there's something

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Speaker 1: else pushing these two electrons from being on top of

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Speaker 1: each other. Yes, exactly. The universe will not allow you

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Speaker 1: to do that, will not allow you to put two

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Speaker 1: electrons right on top of each other because of this

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Speaker 1: weird exclusion principle. And again, two photons and no problem,

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Speaker 1: even two W bosons, which do have a charge, right,

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Speaker 1: so they would resist each other to W boson's no

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Speaker 1: problem to electrons problem. Interesting. Okay, so you can put

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Speaker 1: two photons and two of each other, and you can't

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Speaker 1: put to W bosons on the top of each other,

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Speaker 1: even though like the w boson they have mass. Right,

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Speaker 1: so even things with substance skin exists on top of

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Speaker 1: each other. But somehow electrons that's a no go. Yeah, exactly,

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Speaker 1: And is there a reason why. There's definitely a reason why,

428
00:21:48,480 --> 00:21:52,560
Speaker 1: and it's connected to the particles spin. Electrons have spin

429
00:21:52,680 --> 00:21:55,160
Speaker 1: one half, and photons and ws and zs have spin

430
00:21:55,320 --> 00:21:58,480
Speaker 1: one and so there's a fun and subtle reason for why.

431
00:21:58,520 --> 00:22:00,240
Speaker 1: That means they can't be on top of each other.

432
00:22:00,320 --> 00:22:03,800
Speaker 1: All right, well, let's spin into that answer and figure

433
00:22:03,800 --> 00:22:06,760
Speaker 1: out where exactly this rule comes from and how does

434
00:22:06,800 --> 00:22:09,640
Speaker 1: it impact the rest of the universe. But first, let's

435
00:22:09,680 --> 00:22:25,040
Speaker 1: take a quick break. All right, we're talking about the

436
00:22:25,119 --> 00:22:28,600
Speaker 1: intricate rules of the quantum universe, and one of those

437
00:22:28,680 --> 00:22:31,720
Speaker 1: rules is that two fermions can't be in the same

438
00:22:31,800 --> 00:22:35,080
Speaker 1: quantum state at the same time. Somehow the universe has

439
00:22:35,119 --> 00:22:40,440
Speaker 1: a problem with two fermions to matter particles. Tohow, I guess,

440
00:22:40,520 --> 00:22:42,200
Speaker 1: I don't know, being in sync, being in the same

441
00:22:42,200 --> 00:22:45,560
Speaker 1: place at the same time, and being totally identical. Yeah, exactly.

442
00:22:45,560 --> 00:22:49,320
Speaker 1: It has an issue with fermions having essentially the identical

443
00:22:49,480 --> 00:22:53,440
Speaker 1: setup is not allowed. It's like one per slot. You

444
00:22:53,520 --> 00:22:55,159
Speaker 1: already filled your slot. You got to go to the

445
00:22:55,200 --> 00:22:57,040
Speaker 1: next slot. You've got to find another way to be

446
00:22:57,520 --> 00:23:01,320
Speaker 1: I guess for the idea of too electrons out in space, like,

447
00:23:01,600 --> 00:23:03,800
Speaker 1: it's probably, first of all, very hard for two electrons

448
00:23:03,800 --> 00:23:06,440
Speaker 1: to be in exactly the same space, but it seems

449
00:23:06,440 --> 00:23:10,200
Speaker 1: like the universe just resists two electrons being really close

450
00:23:10,280 --> 00:23:12,480
Speaker 1: to each other. Even Yeah, if you have some volume

451
00:23:12,640 --> 00:23:15,320
Speaker 1: out there and then a bunch of electrons, then the

452
00:23:15,400 --> 00:23:17,880
Speaker 1: universe likes each electron to be like in its own

453
00:23:17,960 --> 00:23:21,120
Speaker 1: little volume, you know, like v over end something like that,

454
00:23:21,160 --> 00:23:26,320
Speaker 1: and so it resists electrons overlapping too much. Oh, so

455
00:23:26,520 --> 00:23:28,840
Speaker 1: the rule is more like it can be in the

456
00:23:28,880 --> 00:23:31,480
Speaker 1: same state, but also like the universe doesn't even like

457
00:23:31,720 --> 00:23:34,480
Speaker 1: for the states to be close to each other. Yeah, exactly,

458
00:23:34,480 --> 00:23:37,320
Speaker 1: because remember, electrons have like a wavelength, and so as

459
00:23:37,320 --> 00:23:41,040
Speaker 1: those wavelengths start to overlap, then the universe resists it. Technically,

460
00:23:41,040 --> 00:23:43,159
Speaker 1: if you keep squeezing, it'll let them get closer and

461
00:23:43,200 --> 00:23:46,240
Speaker 1: closer and closer, but fundamentally it resists them being right

462
00:23:46,320 --> 00:23:48,280
Speaker 1: on top of each other. Okay, so the universe has

463
00:23:48,440 --> 00:23:51,960
Speaker 1: has this problem for emeons apparently, and the weight kind

464
00:23:51,960 --> 00:23:55,720
Speaker 1: of comes into effect that affects most people is as

465
00:23:55,720 --> 00:23:59,600
Speaker 1: you were saying, when electrons start to orbit around the

466
00:23:59,680 --> 00:24:03,520
Speaker 1: new of atoms, right exactly, And this has a huge

467
00:24:03,520 --> 00:24:06,320
Speaker 1: effect on basically all of matter. Right. It's the reason

468
00:24:06,320 --> 00:24:08,720
Speaker 1: that we have energy levels in atoms. It's a reason

469
00:24:08,720 --> 00:24:10,880
Speaker 1: why we have the periodic table. It's a reason why

470
00:24:10,920 --> 00:24:13,159
Speaker 1: atoms behave the way they do. The universe would be

471
00:24:13,200 --> 00:24:16,359
Speaker 1: totally different if electrons could all like slot down to

472
00:24:16,400 --> 00:24:19,240
Speaker 1: the lowest energy level. Now what I said earlier wasn't

473
00:24:19,320 --> 00:24:22,000
Speaker 1: exactly correct. It was one little nuance, which is you

474
00:24:22,040 --> 00:24:24,880
Speaker 1: can't have two electrons per energy level because they can

475
00:24:24,920 --> 00:24:27,480
Speaker 1: have different spins, but the er electrons have to be

476
00:24:27,480 --> 00:24:30,600
Speaker 1: in different states. So you can have like one electron

477
00:24:30,640 --> 00:24:33,960
Speaker 1: around a hydrogenom no problem. For helium. You have two electrons.

478
00:24:34,040 --> 00:24:36,359
Speaker 1: They can both be in the lowest energy level, but

479
00:24:36,400 --> 00:24:38,760
Speaker 1: they have to have different spins because they can't be

480
00:24:38,800 --> 00:24:41,119
Speaker 1: in the same state. Then when you go to lithium

481
00:24:41,200 --> 00:24:43,399
Speaker 1: you have another electron. They can't fit in that lowest

482
00:24:43,480 --> 00:24:46,000
Speaker 1: energy level. There's already two electrons in there, one spin up,

483
00:24:46,040 --> 00:24:49,520
Speaker 1: one spin down. There's no other way to separate the electrons.

484
00:24:49,520 --> 00:24:52,360
Speaker 1: There's no other label to distinguish it, so it has

485
00:24:52,400 --> 00:24:54,399
Speaker 1: to go in the next energy level, goes in the

486
00:24:54,440 --> 00:24:57,560
Speaker 1: second energy level, so that electron has more energy than

487
00:24:57,600 --> 00:24:59,800
Speaker 1: the lowest level. Well, I guess I just wonder how

488
00:24:59,800 --> 00:25:02,000
Speaker 1: many people out there are familiar with this idea of

489
00:25:02,240 --> 00:25:07,480
Speaker 1: energy levels in electrons orbiting the nuclei of atoms. Maybe

490
00:25:07,520 --> 00:25:10,280
Speaker 1: can you connect for us this idea of like, Okay,

491
00:25:10,280 --> 00:25:14,200
Speaker 1: two electrons in space can't be in the same quantum state.

492
00:25:14,200 --> 00:25:16,080
Speaker 1: They can to be one on top of each other.

493
00:25:16,400 --> 00:25:19,360
Speaker 1: But now you know, if they're orbiting around the nucleus

494
00:25:19,359 --> 00:25:21,480
Speaker 1: of an atom, I feel like there's a budge of

495
00:25:21,520 --> 00:25:24,920
Speaker 1: space there. Why can't they kind of orbit at the

496
00:25:24,960 --> 00:25:27,479
Speaker 1: same time. What does this mean about the energy levels? Well,

497
00:25:27,520 --> 00:25:29,600
Speaker 1: if you have an electron and it's around a nucleus,

498
00:25:29,600 --> 00:25:32,720
Speaker 1: you've already confined it to a very small space, right,

499
00:25:32,760 --> 00:25:35,280
Speaker 1: And so in order to have two electrons basically being

500
00:25:35,280 --> 00:25:36,760
Speaker 1: on top of each other from the point of view

501
00:25:36,760 --> 00:25:38,480
Speaker 1: of the universe, those two electrons are on top of

502
00:25:38,520 --> 00:25:41,000
Speaker 1: each other. If they're orbiting the same nucleus, they have

503
00:25:41,080 --> 00:25:43,560
Speaker 1: to have some way to distinguish between themselves so they're

504
00:25:43,600 --> 00:25:45,560
Speaker 1: not in the same state. As that means having different

505
00:25:45,560 --> 00:25:49,280
Speaker 1: spin or having different energy, and around an atom, you

506
00:25:49,320 --> 00:25:52,120
Speaker 1: can't just have any arbitrary energy out in free space.

507
00:25:52,160 --> 00:25:54,199
Speaker 1: An electron can have any energy at once. When an

508
00:25:54,200 --> 00:25:57,080
Speaker 1: electron is captured by a nucleus, when it's in some

509
00:25:57,200 --> 00:26:00,760
Speaker 1: quantum state that's settled into the potential around an then

510
00:26:00,800 --> 00:26:04,080
Speaker 1: it has certain energy levels it can be in that quantization.

511
00:26:04,160 --> 00:26:06,439
Speaker 1: The fact you have an energy ladder rather than a

512
00:26:06,480 --> 00:26:10,080
Speaker 1: full continuous spectrum comes from capturing the electron. It's the

513
00:26:10,160 --> 00:26:13,960
Speaker 1: confinement that produces those energy levels. And so now instead

514
00:26:14,000 --> 00:26:16,000
Speaker 1: of like being able to have two electrons with slightly

515
00:26:16,040 --> 00:26:20,280
Speaker 1: different energy, now the electrons have like discrete options energy

516
00:26:20,359 --> 00:26:23,280
Speaker 1: level one, energy level two, energy level seven. You can't

517
00:26:23,280 --> 00:26:25,960
Speaker 1: have energy like one point two around the atom. It's

518
00:26:26,000 --> 00:26:28,280
Speaker 1: not a solution to the Shortinger equation, is it. I

519
00:26:28,320 --> 00:26:30,800
Speaker 1: wonder if it's a little bit like the Earth orbiting

520
00:26:30,840 --> 00:26:33,160
Speaker 1: the Sun. Like you know, if Earth is out there

521
00:26:33,160 --> 00:26:35,000
Speaker 1: in space, it can go as fast as it once

522
00:26:35,040 --> 00:26:37,199
Speaker 1: in any direction at once. But if you're sort of

523
00:26:37,560 --> 00:26:41,520
Speaker 1: requiring the Earth to go around the Sun and do

524
00:26:41,560 --> 00:26:44,760
Speaker 1: it forever in a consistent way, there's only so many

525
00:26:44,840 --> 00:26:48,240
Speaker 1: velocities it can have. Any's only so many energy levels

526
00:26:48,240 --> 00:26:50,960
Speaker 1: it can have well, but gravity isn't quantized to our knowledge,

527
00:26:50,960 --> 00:26:53,679
Speaker 1: like we think maybe eventually we will quantize gravity. So

528
00:26:53,760 --> 00:26:56,640
Speaker 1: the Earth could exist at any radius around the Sun.

529
00:26:56,680 --> 00:26:59,000
Speaker 1: It just has to have the right velocity. And so

530
00:26:59,040 --> 00:27:01,960
Speaker 1: there is an infinite number of potential orbits for the Earth,

531
00:27:02,359 --> 00:27:05,600
Speaker 1: whereas for a quantum object it really is different. It's

532
00:27:05,640 --> 00:27:08,119
Speaker 1: determined by the shortening your equation, and they're just are

533
00:27:08,240 --> 00:27:12,359
Speaker 1: quantized solutions to that. Okay, so now we've applied the

534
00:27:12,480 --> 00:27:16,439
Speaker 1: rule to electrons orbiting in nuclei, and that tells you

535
00:27:16,480 --> 00:27:19,760
Speaker 1: that two fermions can orbit at the same level unless

536
00:27:19,800 --> 00:27:23,040
Speaker 1: they have a different spin. Exactly why is that? What

537
00:27:23,119 --> 00:27:26,720
Speaker 1: does the spend that lets them occupy the same orbit?

538
00:27:26,880 --> 00:27:28,840
Speaker 1: So the key thing is that they have to have

539
00:27:29,080 --> 00:27:32,000
Speaker 1: different quantum states, and the spin is part of that

540
00:27:32,080 --> 00:27:34,400
Speaker 1: quantum state. It's like one of the labels. So when

541
00:27:34,400 --> 00:27:36,879
Speaker 1: you have electrons around an atom, you have four of

542
00:27:36,920 --> 00:27:39,800
Speaker 1: these labels. You have N which tells you the energy

543
00:27:39,880 --> 00:27:42,000
Speaker 1: level you have, L, which tells you like the sub

544
00:27:42,160 --> 00:27:44,800
Speaker 1: level that you're in, and which tells you which of

545
00:27:44,800 --> 00:27:47,199
Speaker 1: those ls you're in, and then finally the spin. And

546
00:27:47,240 --> 00:27:49,320
Speaker 1: so the spin place two rolls one is like, it's

547
00:27:49,320 --> 00:27:51,800
Speaker 1: another quality that the electron can have that lets it

548
00:27:51,840 --> 00:27:55,680
Speaker 1: distinguish itself from something else. But also the electron having

549
00:27:55,760 --> 00:27:59,440
Speaker 1: spin one half is the reason why electrons cannot do this.

550
00:28:00,040 --> 00:28:02,639
Speaker 1: Photons have spin one which is why they can pile

551
00:28:02,680 --> 00:28:05,440
Speaker 1: on top of each other, and electrons have spin one half,

552
00:28:05,480 --> 00:28:08,160
Speaker 1: which is why they cannot pile on top of each other.

553
00:28:08,359 --> 00:28:14,080
Speaker 1: It all comes down to these particles spin well before

554
00:28:14,119 --> 00:28:16,719
Speaker 1: we spend that way. I guess maybe it tells a

555
00:28:16,760 --> 00:28:18,840
Speaker 1: little bit about what would happen if we didn't have

556
00:28:18,920 --> 00:28:22,600
Speaker 1: this rule, Like if we didn't have the poly exclusion principle,

557
00:28:22,880 --> 00:28:25,560
Speaker 1: what would happen to like electron orbitals and atoms and

558
00:28:26,280 --> 00:28:28,320
Speaker 1: the things the molecules in our body. So if we

559
00:28:28,359 --> 00:28:30,760
Speaker 1: didn't have this, then electrons would all relax down to

560
00:28:30,800 --> 00:28:33,520
Speaker 1: the lowest state. There would all be in the lowest

561
00:28:33,640 --> 00:28:35,520
Speaker 1: energy level, because that's what the universe likes to do.

562
00:28:35,560 --> 00:28:37,359
Speaker 1: It likes to spread energy out. It doesn't like to

563
00:28:37,400 --> 00:28:40,800
Speaker 1: have little dense depositions of energy. So for example, if

564
00:28:40,840 --> 00:28:43,240
Speaker 1: you zap an electron and you give it extra energy,

565
00:28:43,280 --> 00:28:45,160
Speaker 1: so it jumps up the ladder to like you know,

566
00:28:45,360 --> 00:28:47,880
Speaker 1: energy level ten, and you just wet a few moments,

567
00:28:47,920 --> 00:28:50,240
Speaker 1: then it will radiate a way that energy and relax

568
00:28:50,480 --> 00:28:53,440
Speaker 1: back down. So everything likes to sort of flow downhill

569
00:28:53,440 --> 00:28:56,080
Speaker 1: to the lowest energy levels. And if you didn't have

570
00:28:56,120 --> 00:28:59,160
Speaker 1: the poly exclusion principle, they would all just pile up

571
00:28:59,200 --> 00:29:01,560
Speaker 1: at the lowest energy level, and that would make a

572
00:29:01,600 --> 00:29:05,200
Speaker 1: big difference for like the size of these atoms. You know,

573
00:29:05,240 --> 00:29:08,760
Speaker 1: the size of the atom is determined by the electron orbitals,

574
00:29:08,800 --> 00:29:11,400
Speaker 1: and they get bigger and bigger and bigger as you

575
00:29:11,440 --> 00:29:14,160
Speaker 1: get more and more electrons. Gold, for example, has like,

576
00:29:14,200 --> 00:29:17,840
Speaker 1: you know, dozens of electrons, and so it's much larger

577
00:29:17,880 --> 00:29:21,440
Speaker 1: than hydrogen. Hygen just has one electron, and so, like,

578
00:29:21,480 --> 00:29:23,880
Speaker 1: the very structure of matter depends on the volume of

579
00:29:23,880 --> 00:29:27,560
Speaker 1: these atoms. If somebody like turned off the poly exclusion principle,

580
00:29:27,720 --> 00:29:30,560
Speaker 1: we would all collapse to be much much smaller. You mean,

581
00:29:30,640 --> 00:29:34,440
Speaker 1: we would all go into the quadic realm, and man, no,

582
00:29:34,520 --> 00:29:36,320
Speaker 1: we'd all be about the size of a chocolate chip,

583
00:29:36,360 --> 00:29:39,680
Speaker 1: I think. But also it would change chemistry, right, The

584
00:29:39,720 --> 00:29:42,880
Speaker 1: way that atoms bond together depends on these orbitals, the

585
00:29:42,920 --> 00:29:45,640
Speaker 1: way that they interact all their properties, like how they're

586
00:29:45,680 --> 00:29:48,800
Speaker 1: metallic or how they glow, the energy they can absorb

587
00:29:48,920 --> 00:29:51,440
Speaker 1: all of this stuff depends on the poly exclusion principle,

588
00:29:51,560 --> 00:29:54,160
Speaker 1: and so the whole universe would be totally different if

589
00:29:54,160 --> 00:29:57,640
Speaker 1: electrons could pile up at the lowest levels. Okay, I

590
00:29:57,680 --> 00:29:59,160
Speaker 1: think I see what you're saying. Like, if I just

591
00:29:59,240 --> 00:30:02,960
Speaker 1: have the nuclear of an atom without any electrons, just

592
00:30:03,040 --> 00:30:05,800
Speaker 1: sitting there, and I threw an electron into it, it

593
00:30:05,840 --> 00:30:09,080
Speaker 1: would kind of snap into a certain orbit or kind

594
00:30:09,120 --> 00:30:11,959
Speaker 1: of place or some sort of you know, cloud or

595
00:30:11,960 --> 00:30:15,480
Speaker 1: function around that nucleus. Now, if I threw another electron,

596
00:30:15,720 --> 00:30:18,160
Speaker 1: if he didn't have the poly exclusion principle, it would

597
00:30:18,240 --> 00:30:21,880
Speaker 1: also fall into that lowest kind of orbit. But because

598
00:30:21,920 --> 00:30:24,960
Speaker 1: you have the inclusion principle, the electron can't like get

599
00:30:25,000 --> 00:30:27,719
Speaker 1: that close to the nucleus, and so it kind of

600
00:30:27,720 --> 00:30:31,400
Speaker 1: forms another kind of orbit that is kind of maybe bigger,

601
00:30:31,520 --> 00:30:35,120
Speaker 1: you mean, maybe bigger and more fragile too, Yeah, exactly.

602
00:30:35,240 --> 00:30:37,520
Speaker 1: Then that controls the volume of the atom, but also

603
00:30:37,560 --> 00:30:40,360
Speaker 1: controls how these things operate, you know, how they build

604
00:30:40,400 --> 00:30:44,040
Speaker 1: themselves into crystals and then how electrons can flow through

605
00:30:44,080 --> 00:30:46,960
Speaker 1: those crystals. Like why are metals conductors Because they have

606
00:30:47,000 --> 00:30:50,080
Speaker 1: a bunch of electrons in this conduction band they're forced

607
00:30:50,120 --> 00:30:52,640
Speaker 1: to be up there in their higher energy level bands

608
00:30:52,640 --> 00:30:56,880
Speaker 1: flowing around semiconductors for the same reason. So the reason

609
00:30:56,960 --> 00:31:00,600
Speaker 1: we have all these complex structures and complex behavior, periodic

610
00:31:00,640 --> 00:31:04,880
Speaker 1: table and all that interesting chemistry comes from electron orbitals,

611
00:31:04,920 --> 00:31:08,680
Speaker 1: which only are interesting because electrons populate them, and they

612
00:31:08,720 --> 00:31:12,120
Speaker 1: only do that because of the Pauly exclusion principle. Otherwise

613
00:31:12,200 --> 00:31:15,400
Speaker 1: they would always just be in the lowest energy level. Interesting.

614
00:31:15,480 --> 00:31:17,120
Speaker 1: Now that we know what it is, let's maybe dig

615
00:31:17,160 --> 00:31:19,680
Speaker 1: into the reason. Why Why does it have an issue

616
00:31:19,720 --> 00:31:22,640
Speaker 1: with two fermions being on top of each other, Like

617
00:31:22,640 --> 00:31:24,240
Speaker 1: it doesn't seem to have a problem with some of

618
00:31:24,280 --> 00:31:27,200
Speaker 1: the other particles like the Higgs boson or photons or

619
00:31:27,320 --> 00:31:31,080
Speaker 1: w particles being at each other. Why does it have

620
00:31:31,200 --> 00:31:36,840
Speaker 1: this bias against electrons? Court, don't be so negative about it.

621
00:31:36,880 --> 00:31:38,360
Speaker 1: You know, maybe you could think about it like a

622
00:31:38,440 --> 00:31:41,320
Speaker 1: special property. You know, the electrons can like stand on

623
00:31:41,360 --> 00:31:44,320
Speaker 1: top of each other to achieve things electrons could otherwise

624
00:31:44,400 --> 00:31:47,640
Speaker 1: never do. Right, It's like an ability instead of a bias.

625
00:31:47,920 --> 00:31:51,920
Speaker 1: I feel like the word exclusion is never good. That's true,

626
00:31:52,080 --> 00:31:55,000
Speaker 1: everyone should be as inclusive as possible. Well, the issue

627
00:31:55,040 --> 00:31:57,680
Speaker 1: really does have to do with the quantum nature of

628
00:31:57,720 --> 00:32:01,120
Speaker 1: these things. So fermions, electrons, and even protons which are

629
00:32:01,120 --> 00:32:03,400
Speaker 1: built out of quarks. These things have a really weird

630
00:32:03,440 --> 00:32:07,200
Speaker 1: property that we've never seen in classical physics, and it

631
00:32:07,240 --> 00:32:09,720
Speaker 1: has to do with what happens when you swap two

632
00:32:09,720 --> 00:32:12,480
Speaker 1: of them. So imagine just you have two particles, particle

633
00:32:12,520 --> 00:32:15,800
Speaker 1: one and particle two, and maybe they're in different states.

634
00:32:16,040 --> 00:32:18,240
Speaker 1: You call one state A and one state B. Doesn't

635
00:32:18,280 --> 00:32:21,200
Speaker 1: really matter. Now, imagine what happens if you swap them. Right,

636
00:32:21,240 --> 00:32:23,360
Speaker 1: you take particle one, which used to be in state A,

637
00:32:23,840 --> 00:32:26,320
Speaker 1: and I say, now you're in state B. In particle two,

638
00:32:26,400 --> 00:32:27,880
Speaker 1: which used to be in state B, and say now

639
00:32:27,880 --> 00:32:30,840
Speaker 1: you're in state A. All right. And so you have

640
00:32:30,880 --> 00:32:33,280
Speaker 1: two particles and you sort of swap their arrangements. The

641
00:32:33,400 --> 00:32:36,719
Speaker 1: universe says, and quantum mechanics says that when you do that,

642
00:32:37,120 --> 00:32:40,000
Speaker 1: the wave function that describes what happens and tells you

643
00:32:40,000 --> 00:32:42,720
Speaker 1: what's allowed, that wave function gets a negative sign, and

644
00:32:42,840 --> 00:32:45,840
Speaker 1: that doesn't happen for bosons. For bosons, the wave function

645
00:32:45,880 --> 00:32:48,600
Speaker 1: doesn't get a negative sign, and that has really really

646
00:32:48,640 --> 00:32:52,560
Speaker 1: important consequences. I think you're talking about like a mathematical operation,

647
00:32:52,760 --> 00:32:55,680
Speaker 1: or are you talking about like if I physically take

648
00:32:55,680 --> 00:32:59,320
Speaker 1: two particles and I swapped their states mathematically the sign

649
00:32:59,400 --> 00:33:03,240
Speaker 1: of the whole how the two particles somehow gets a negative.

650
00:33:03,360 --> 00:33:04,920
Speaker 1: Is that kind of what you think? Yeah, we're talking

651
00:33:04,960 --> 00:33:07,480
Speaker 1: about the wave function, which is like the thing that

652
00:33:07,560 --> 00:33:10,680
Speaker 1: determines what happens. Right. Remember, you take the wave function

653
00:33:10,760 --> 00:33:13,040
Speaker 1: and you square it, and that tells you the probability

654
00:33:13,040 --> 00:33:15,880
Speaker 1: of various things happening. If you're talking about like Shortinger's cat,

655
00:33:16,120 --> 00:33:18,080
Speaker 1: there's a wave function for it to be alive and

656
00:33:18,080 --> 00:33:20,040
Speaker 1: a wave function for it to be dead. Those are

657
00:33:20,040 --> 00:33:23,480
Speaker 1: two different possible outcomes, And the way that you've discover

658
00:33:23,800 --> 00:33:25,840
Speaker 1: the probability of one versus the other is you take

659
00:33:25,880 --> 00:33:28,000
Speaker 1: the wave function for that outcome and you square it.

660
00:33:28,400 --> 00:33:31,040
Speaker 1: That's the rule. Now, a wave function is like a

661
00:33:31,160 --> 00:33:36,000
Speaker 1: mathematical concept or construct that describes what something is doing

662
00:33:36,080 --> 00:33:38,440
Speaker 1: or going to do. Yeah, it's the solution to the

663
00:33:38,440 --> 00:33:41,440
Speaker 1: Shortinger equation. That doesn't help me. We don't really know

664
00:33:41,520 --> 00:33:44,600
Speaker 1: what the way function is. It's problematic philosophically, like it's

665
00:33:44,600 --> 00:33:48,360
Speaker 1: a part of our calculations. We use it to make predictions.

666
00:33:48,480 --> 00:33:50,960
Speaker 1: Nobody really knows, like, is the wave function a real

667
00:33:51,000 --> 00:33:52,720
Speaker 1: thing out there in the universe or is it just

668
00:33:52,760 --> 00:33:55,480
Speaker 1: sort of like something in our heads. That's an intermediate

669
00:33:55,520 --> 00:33:58,080
Speaker 1: step that we are using, but it definitely seems to

670
00:33:58,120 --> 00:33:59,880
Speaker 1: be important, and it's part of the way we think

671
00:34:00,000 --> 00:34:02,600
Speaker 1: about quantum physics. Like maybe if you have a baseball

672
00:34:02,640 --> 00:34:05,080
Speaker 1: and you're throwing a baseball, you might describe it using

673
00:34:05,120 --> 00:34:08,920
Speaker 1: a vector, like a vector from here from the pitcher

674
00:34:09,040 --> 00:34:12,239
Speaker 1: to the baseball that describes the ball. Wave function is

675
00:34:12,320 --> 00:34:15,680
Speaker 1: kind of like that for quantum particles, right, yeah, exactly.

676
00:34:15,760 --> 00:34:17,960
Speaker 1: And the wave function is weird because it can also

677
00:34:18,200 --> 00:34:21,680
Speaker 1: be negative, and it can also be like complex, right,

678
00:34:21,680 --> 00:34:25,440
Speaker 1: it can have imaginary numbers like one plus two I. Right.

679
00:34:25,480 --> 00:34:27,920
Speaker 1: The wave function is really weird. It's not physical in

680
00:34:27,960 --> 00:34:30,279
Speaker 1: that way. But the interesting thing is that that all

681
00:34:30,320 --> 00:34:33,000
Speaker 1: goes away usually when you use the wave function to

682
00:34:33,000 --> 00:34:35,080
Speaker 1: make a prediction, because they square it and the imaginary

683
00:34:35,080 --> 00:34:37,440
Speaker 1: parts go away and the negative signs go away. Nobody

684
00:34:37,480 --> 00:34:40,680
Speaker 1: really cares about the wave function being negative usually, but

685
00:34:40,719 --> 00:34:42,759
Speaker 1: in this one particular case it turns out to be

686
00:34:42,840 --> 00:34:45,839
Speaker 1: weirdly really important because what happens if you have two

687
00:34:45,880 --> 00:34:48,400
Speaker 1: fermions which are identical like two electrons, and they're in

688
00:34:48,480 --> 00:34:51,680
Speaker 1: exactly the same state. Maybe they're both around a hydrogen

689
00:34:51,719 --> 00:34:53,440
Speaker 1: atom and they're in the same energy level and they

690
00:34:53,440 --> 00:34:56,399
Speaker 1: have all the same spin. Right, now, what happens, Well,

691
00:34:56,560 --> 00:35:00,719
Speaker 1: take those two particles, particle one particle two. They're interesting, right,

692
00:35:00,840 --> 00:35:03,719
Speaker 1: They're in the same state, and you swap them, right,

693
00:35:03,800 --> 00:35:06,120
Speaker 1: swap them from one to the other. Now, really that

694
00:35:06,200 --> 00:35:09,080
Speaker 1: has no effect because you had two identical particles in

695
00:35:09,120 --> 00:35:12,160
Speaker 1: the same state, you swap them, nothing should change. But

696
00:35:12,239 --> 00:35:14,680
Speaker 1: the universe says if you do that, you get a

697
00:35:14,719 --> 00:35:17,440
Speaker 1: negative sign for the wave function. You mean, swap them,

698
00:35:17,520 --> 00:35:20,160
Speaker 1: like pick them up and change their you know, like

699
00:35:20,239 --> 00:35:23,960
Speaker 1: move them around, like swap their positions, or swap them hypothetically,

700
00:35:24,120 --> 00:35:26,960
Speaker 1: like ask what would the wave function be if this

701
00:35:27,000 --> 00:35:29,080
Speaker 1: particle was over here and that particle was over there.

702
00:35:29,160 --> 00:35:32,160
Speaker 1: Don't actually do it, you just say, like, hypothetically, what

703
00:35:32,200 --> 00:35:33,920
Speaker 1: would the wave function be if you had them in

704
00:35:33,920 --> 00:35:37,080
Speaker 1: the opposite configuration? But they're the same configuration. Well, they're

705
00:35:37,120 --> 00:35:38,839
Speaker 1: in the same state, but one of them has this

706
00:35:38,920 --> 00:35:40,839
Speaker 1: label one. You know, one of them is particle one

707
00:35:40,880 --> 00:35:42,480
Speaker 1: and one of them is particle two. Though they're in

708
00:35:42,520 --> 00:35:44,759
Speaker 1: the same state, so you can't really distinguish them. Right,

709
00:35:44,800 --> 00:35:47,200
Speaker 1: they're identical. They have the same orbit, the same spin,

710
00:35:47,320 --> 00:35:49,520
Speaker 1: everything is the same, and if you swap them, as

711
00:35:49,640 --> 00:35:52,400
Speaker 1: you're imagining, nothing changes because they're the same particle in

712
00:35:52,440 --> 00:35:54,640
Speaker 1: the same state, so it should be the same. But

713
00:35:54,680 --> 00:35:57,160
Speaker 1: the universe says, well, the wave function has to get

714
00:35:57,160 --> 00:35:59,680
Speaker 1: a negative sign if you do this for fermions. So

715
00:35:59,719 --> 00:36:02,680
Speaker 1: the only way to satisfy both of those requirements to say, well,

716
00:36:02,719 --> 00:36:04,600
Speaker 1: it has to be the same if you swap them,

717
00:36:04,640 --> 00:36:06,600
Speaker 1: and it has to get a negative sign if you

718
00:36:06,640 --> 00:36:08,880
Speaker 1: swap them is for the way function to be zero.

719
00:36:09,360 --> 00:36:11,600
Speaker 1: So if the way function is zero, then when you

720
00:36:11,640 --> 00:36:14,360
Speaker 1: swap it, zero is negative zero. It's the only number

721
00:36:14,400 --> 00:36:17,160
Speaker 1: that is its own negative, and so from that you

722
00:36:17,200 --> 00:36:20,120
Speaker 1: can conclude that this is impossible. The universe just doesn't

723
00:36:20,120 --> 00:36:22,640
Speaker 1: do this. The wave function for two fermions being in

724
00:36:22,640 --> 00:36:25,440
Speaker 1: the same state is always zero. That way, it can

725
00:36:25,440 --> 00:36:29,000
Speaker 1: satisfy both rules that swapping two identical particles doesn't change

726
00:36:29,000 --> 00:36:32,080
Speaker 1: anything and that the wave function gets a negative sign.

727
00:36:32,239 --> 00:36:34,760
Speaker 1: And you're saying earlier that this is because of their spin,

728
00:36:35,440 --> 00:36:38,840
Speaker 1: Like if because they have a certain spin when you

729
00:36:38,920 --> 00:36:41,400
Speaker 1: try to do this swapping, then some weird things happen

730
00:36:41,560 --> 00:36:44,799
Speaker 1: exactly because this doesn't happen for particles of a different spin,

731
00:36:44,880 --> 00:36:48,239
Speaker 1: like with photons, not an issue. Photons, the universe says, yeah,

732
00:36:48,239 --> 00:36:50,080
Speaker 1: if you have two photons in the same state and

733
00:36:50,160 --> 00:36:52,920
Speaker 1: you swap them, you don't get a negative sign. It

734
00:36:53,000 --> 00:36:56,040
Speaker 1: only happens for fermions. And it's that negative sign that

735
00:36:56,120 --> 00:36:59,040
Speaker 1: makes this impossible. It's a negative sign, which is why

736
00:36:59,160 --> 00:37:02,200
Speaker 1: fermions can't be in the same state and bosons the

737
00:37:02,320 --> 00:37:05,480
Speaker 1: universe doesn't have a problem with and it just operates

738
00:37:05,480 --> 00:37:08,600
Speaker 1: differently on bosons than it does on fermions. Then you

739
00:37:08,680 --> 00:37:11,480
Speaker 1: might ask, well, like, where does that negative sign come from?

740
00:37:11,520 --> 00:37:14,080
Speaker 1: Why do fermions get a negative sign when you swap them.

741
00:37:14,120 --> 00:37:17,000
Speaker 1: That's weird, right, Like why should you get a negative sign?

742
00:37:17,040 --> 00:37:20,640
Speaker 1: You're just swapping two identical particles, it's basically the same setup.

743
00:37:20,840 --> 00:37:23,239
Speaker 1: Why would you expect the wave function to be the opposite?

744
00:37:23,640 --> 00:37:26,360
Speaker 1: And this is the weird thing that these quantum fermons

745
00:37:26,440 --> 00:37:29,839
Speaker 1: can do that classical particles can't do. There's like no

746
00:37:30,000 --> 00:37:34,320
Speaker 1: classical analog to this. There's no example in the natural

747
00:37:34,360 --> 00:37:36,960
Speaker 1: world that you can think about with baseballs or coffee

748
00:37:36,960 --> 00:37:40,200
Speaker 1: cups that is like this. It's most closely connected to

749
00:37:40,840 --> 00:37:43,239
Speaker 1: rotating things, like if you take your coffee cup and

750
00:37:43,280 --> 00:37:46,080
Speaker 1: you spin it around three hundred and sixty degrees, it's

751
00:37:46,120 --> 00:37:48,520
Speaker 1: the same coffee cup. That makes sense, right, And the

752
00:37:48,560 --> 00:37:50,960
Speaker 1: same thing is true for photons. If you take photons

753
00:37:51,000 --> 00:37:53,120
Speaker 1: and you rotate them by three hundred and sixty degrees,

754
00:37:53,120 --> 00:37:56,960
Speaker 1: you get the same photon. Electrons don't do that. Electrons,

755
00:37:57,000 --> 00:37:59,360
Speaker 1: if you rotate them by three hundred and sixty degrees,

756
00:37:59,440 --> 00:38:03,080
Speaker 1: you get the negative wavefunction than the original electron. So

757
00:38:03,120 --> 00:38:06,839
Speaker 1: there's something weird and different about fermions that picks up

758
00:38:06,840 --> 00:38:09,759
Speaker 1: this extra negative sign that's very different from anything we

759
00:38:09,840 --> 00:38:11,799
Speaker 1: know about before. And you said it has to do

760
00:38:11,840 --> 00:38:14,640
Speaker 1: with the quantum spin, but I guess don't some other

761
00:38:14,680 --> 00:38:18,319
Speaker 1: fermions have no spin? Or do all fermions all of

762
00:38:18,320 --> 00:38:20,759
Speaker 1: these matter particles have spin, and do they have the

763
00:38:20,800 --> 00:38:24,920
Speaker 1: same spin? And that's why they have this rule against them? Exactly,

764
00:38:24,920 --> 00:38:27,360
Speaker 1: all fermions have the same spin. They all have spin

765
00:38:27,440 --> 00:38:29,759
Speaker 1: one half. And that's sort of what it means to

766
00:38:29,800 --> 00:38:32,279
Speaker 1: be a fermion. I mean, some people say, no, fermions

767
00:38:32,320 --> 00:38:35,000
Speaker 1: are things that do this that don't overlap with each other.

768
00:38:35,040 --> 00:38:37,920
Speaker 1: They follow the poll exclusion principle, and it's because they

769
00:38:37,920 --> 00:38:41,000
Speaker 1: have spin one half. Other people say, no, fermions are

770
00:38:41,040 --> 00:38:43,640
Speaker 1: all particles that have spin one half. But it's the

771
00:38:43,680 --> 00:38:47,239
Speaker 1: spin one half that makes them do this. And it's

772
00:38:47,239 --> 00:38:49,520
Speaker 1: too mathematical to explain, but if you like dig into

773
00:38:49,520 --> 00:38:52,480
Speaker 1: the quantum field theory, this comes out of that mathematics

774
00:38:52,560 --> 00:38:55,239
Speaker 1: or the quantum field theory. The particles that have fields

775
00:38:55,280 --> 00:38:58,040
Speaker 1: that have spined one half, when you rotate them, you

776
00:38:58,080 --> 00:39:00,520
Speaker 1: get this extras sign, or when you swam them, you

777
00:39:00,600 --> 00:39:03,880
Speaker 1: get this extra minus sign. It's called the spin statistics theorem.

778
00:39:03,920 --> 00:39:07,000
Speaker 1: And that's fundamentally where this comes from. So it's the

779
00:39:07,120 --> 00:39:10,480
Speaker 1: one half spin nature of these particles that means that

780
00:39:10,520 --> 00:39:12,800
Speaker 1: they can't pile up on top of each other, whereas

781
00:39:12,800 --> 00:39:15,799
Speaker 1: particles with spin one or spin two could totally pile

782
00:39:15,840 --> 00:39:17,520
Speaker 1: up on top of each other and be in the

783
00:39:17,560 --> 00:39:20,680
Speaker 1: same quantum state no problem. Or I'm getting the sense

784
00:39:20,719 --> 00:39:23,880
Speaker 1: that maybe you gave him spin one half because they

785
00:39:23,920 --> 00:39:25,640
Speaker 1: can't be in the same place at the same time,

786
00:39:26,160 --> 00:39:29,920
Speaker 1: you know what I mean, Like, like, which game for

787
00:39:30,080 --> 00:39:32,279
Speaker 1: is the chicken or the egg? The spin or or

788
00:39:32,320 --> 00:39:35,520
Speaker 1: the exclusion principle? Oh, that's a great question. Actually, this

789
00:39:35,680 --> 00:39:39,799
Speaker 1: is how electron spin was discovered, That's what I mean. Yes, no, absolutely,

790
00:39:40,080 --> 00:39:43,919
Speaker 1: this is why spin was invented to explain this, right,

791
00:39:44,320 --> 00:39:47,040
Speaker 1: and the story is actually really fun. People were looking

792
00:39:47,080 --> 00:39:49,720
Speaker 1: at electron orbitals back in their early days, like nineteen

793
00:39:49,800 --> 00:39:52,960
Speaker 1: thirties and trying to understand why the electrons filled up

794
00:39:52,960 --> 00:39:55,000
Speaker 1: the orbitals the way they did, and they had this

795
00:39:55,080 --> 00:39:57,840
Speaker 1: idea of the exclusion principle, but they didn't understand, like,

796
00:39:57,920 --> 00:40:00,719
Speaker 1: why you could have two electrons in the lowest level,

797
00:40:00,760 --> 00:40:03,200
Speaker 1: what's going on? And in the next level, why could

798
00:40:03,200 --> 00:40:05,400
Speaker 1: you have eight instead of four? There was this weird

799
00:40:05,440 --> 00:40:09,319
Speaker 1: factor of two that nobody could explain, and Paully wrote

800
00:40:09,320 --> 00:40:11,360
Speaker 1: a letter to some other physicists about it, and he

801
00:40:11,400 --> 00:40:17,080
Speaker 1: said that electrons have a two valuedness, not describable classically.

802
00:40:17,400 --> 00:40:20,279
Speaker 1: He just meant like they have some physical property that

803
00:40:20,320 --> 00:40:22,480
Speaker 1: has two options, like an up and a down, or

804
00:40:22,520 --> 00:40:25,080
Speaker 1: a zero and a one, or you know, a switch

805
00:40:25,120 --> 00:40:28,120
Speaker 1: that you could flip. There's something else about the electrons

806
00:40:28,400 --> 00:40:30,520
Speaker 1: that let them distinguish each other, so you can have

807
00:40:30,560 --> 00:40:33,440
Speaker 1: two of them in the lowest energy level. That's how

808
00:40:33,440 --> 00:40:36,560
Speaker 1: we discovered that electrons actually do have spin, or at

809
00:40:36,640 --> 00:40:40,680
Speaker 1: least you called spin, because you quite have another name

810
00:40:40,680 --> 00:40:43,480
Speaker 1: for it. Right. To explain this phenomenon exactly. And there

811
00:40:43,520 --> 00:40:47,640
Speaker 1: was two young Dutch physicists, Gaussmidt and Uhlenbeck, who read

812
00:40:47,719 --> 00:40:49,919
Speaker 1: this letter from Pauli and they were like, oh, wait,

813
00:40:50,040 --> 00:40:52,719
Speaker 1: maybe electrons are spinning. So they did a bunch of

814
00:40:52,719 --> 00:40:55,160
Speaker 1: calculations and they're like, oh, electrons are spinning. This is

815
00:40:55,160 --> 00:40:57,640
Speaker 1: really awesome. And they wrote this paper and they sent

816
00:40:57,719 --> 00:40:59,400
Speaker 1: it off and then they showed it to another famous

817
00:40:59,480 --> 00:41:02,800
Speaker 1: Dutch physicist, Lorenz, and Lorenz was like, y'all are totally wrong.

818
00:41:02,880 --> 00:41:06,000
Speaker 1: Electrons can't spin. Their services would be moving faster than

819
00:41:06,000 --> 00:41:08,200
Speaker 1: the speed of light. So then they realized, oh my gosh,

820
00:41:08,200 --> 00:41:10,120
Speaker 1: our paper was wrong, and they try to retract it,

821
00:41:10,160 --> 00:41:11,960
Speaker 1: but it was too late. It had already been published.

822
00:41:13,400 --> 00:41:16,239
Speaker 1: And then it turns out that electrons do spin, but

823
00:41:16,320 --> 00:41:18,440
Speaker 1: not in the way that they expected. They have this

824
00:41:18,560 --> 00:41:22,239
Speaker 1: weird property quantum spin, which is not spin in the

825
00:41:22,280 --> 00:41:25,040
Speaker 1: same way that like a baseball spins. It's some other

826
00:41:25,120 --> 00:41:27,680
Speaker 1: weird kind of angular momentum. So the history of like

827
00:41:27,719 --> 00:41:31,000
Speaker 1: the discovery of electron spin is pretty funny. Oh Man,

828
00:41:31,239 --> 00:41:35,480
Speaker 1: particle physics are pretty catty. That we're short. Anger's cat

829
00:41:35,560 --> 00:41:38,359
Speaker 1: came from exactly what. I love this story of two

830
00:41:38,360 --> 00:41:41,360
Speaker 1: guys inventing spin for the wrong reasons trying to retract

831
00:41:41,400 --> 00:41:44,960
Speaker 1: it and then ended up being right, sort of accidentally interesting.

832
00:41:44,960 --> 00:41:47,120
Speaker 1: All right, Well, the universe us to have this rule,

833
00:41:47,480 --> 00:41:49,960
Speaker 1: and it seems to be embedded in some of the

834
00:41:50,200 --> 00:41:54,120
Speaker 1: mathematics that maybe makes the universe works. Let's talk about

835
00:41:54,200 --> 00:41:58,000
Speaker 1: that Thorney philosophical question and also some of the consequences

836
00:41:58,040 --> 00:42:01,480
Speaker 1: of this poly exclusion inciple on the rest of the universe.

837
00:42:01,840 --> 00:42:16,719
Speaker 1: But first, let's take another quick break. All right, we're

838
00:42:16,719 --> 00:42:19,640
Speaker 1: talking about the question of why can't two fermions be

839
00:42:19,680 --> 00:42:22,719
Speaker 1: in the same quantum state? And what this means is

840
00:42:22,760 --> 00:42:25,520
Speaker 1: that no two electrons or no two quarks can be

841
00:42:25,719 --> 00:42:28,080
Speaker 1: kind of on top of each other, not out there

842
00:42:28,080 --> 00:42:31,000
Speaker 1: in free space and not orbiting around an atom, which

843
00:42:31,040 --> 00:42:35,000
Speaker 1: is what gives us the wonderful chemistry that makes us

844
00:42:35,000 --> 00:42:37,440
Speaker 1: who we are. And we talked a little bit about that.

845
00:42:37,719 --> 00:42:40,920
Speaker 1: The reason that two fermions or two electrons or two

846
00:42:40,960 --> 00:42:44,120
Speaker 1: quarks can't do this is because it messes up the math.

847
00:42:44,520 --> 00:42:46,680
Speaker 1: Now my question is, like, does that mean that the

848
00:42:46,800 --> 00:42:50,600
Speaker 1: universe is mathematical? Like does the universe care about math?

849
00:42:50,719 --> 00:42:53,359
Speaker 1: Like why does the universe care about math? Like? If

850
00:42:53,400 --> 00:42:55,520
Speaker 1: I were the universe, I'd be like, I'm the universe.

851
00:42:55,560 --> 00:43:00,279
Speaker 1: I don't care about math. Peoples two equals five? Why not? Well,

852
00:43:00,320 --> 00:43:03,120
Speaker 1: I don't know, but it seems like the universe does

853
00:43:03,239 --> 00:43:07,040
Speaker 1: follow mathematical laws, and the universe is self consistent, right,

854
00:43:07,080 --> 00:43:09,440
Speaker 1: the universe doesn't have like two things going on at

855
00:43:09,440 --> 00:43:12,520
Speaker 1: the same time or things that contradict each other. So

856
00:43:12,560 --> 00:43:14,200
Speaker 1: it might just be that you can have lots of

857
00:43:14,239 --> 00:43:16,319
Speaker 1: different universes out there, but only the ones that are

858
00:43:16,360 --> 00:43:19,600
Speaker 1: self consistent that follow mathematical laws are the ones where

859
00:43:19,600 --> 00:43:22,560
Speaker 1: you have, like people evolved with brains that to make

860
00:43:22,600 --> 00:43:26,000
Speaker 1: sense of these things and study them. So we don't

861
00:43:26,040 --> 00:43:28,880
Speaker 1: really understand it, but our universe does seem to follow

862
00:43:29,040 --> 00:43:32,279
Speaker 1: mathematical laws, and when you find a mathematical principle, it

863
00:43:32,320 --> 00:43:35,799
Speaker 1: seems to manifest itself in nature. Right. What we're talking

864
00:43:35,800 --> 00:43:38,719
Speaker 1: about are the laws of how quantum feels operate, how

865
00:43:38,760 --> 00:43:42,080
Speaker 1: they wiggle, how they transfer energy between them, the rules

866
00:43:42,080 --> 00:43:44,840
Speaker 1: that they follow, and those rules seem to have like

867
00:43:44,960 --> 00:43:49,840
Speaker 1: consequences way down the line that affect us and ice

868
00:43:49,840 --> 00:43:53,120
Speaker 1: cream and stars. I guess what's kind of weird is

869
00:43:53,160 --> 00:43:56,680
Speaker 1: that I'm sure math has a bunch of other rules

870
00:43:56,719 --> 00:44:00,200
Speaker 1: that it likes to do it doesn't like you do.

871
00:44:00,360 --> 00:44:03,759
Speaker 1: But maybe not all of them are represented in a

872
00:44:03,840 --> 00:44:06,240
Speaker 1: physical thing, right, Like not all of them have a

873
00:44:06,239 --> 00:44:09,680
Speaker 1: physical manifestation of those principles. But this is a case

874
00:44:09,719 --> 00:44:11,920
Speaker 1: where you know, you have something that doesn't work in

875
00:44:11,960 --> 00:44:17,919
Speaker 1: the math and it actually has like a physical, a tangible,

876
00:44:18,239 --> 00:44:21,560
Speaker 1: you know, solid representation of that math. Yeah, exactly. It's

877
00:44:21,560 --> 00:44:24,919
Speaker 1: certainly true that there are more sort of mental universes

878
00:44:24,960 --> 00:44:27,920
Speaker 1: in mathematics than exist in the physical universe. Like you

879
00:44:27,920 --> 00:44:30,840
Speaker 1: could dream up all sorts of universes that don't exist

880
00:44:30,880 --> 00:44:33,640
Speaker 1: out there. But once you think about just our universe,

881
00:44:33,719 --> 00:44:36,600
Speaker 1: if you think about the mathematical laws that describe it,

882
00:44:36,920 --> 00:44:40,279
Speaker 1: the universe basically does everything that the math allows. Like

883
00:44:40,400 --> 00:44:43,040
Speaker 1: if it's possible for an electron to radiate a photon

884
00:44:43,560 --> 00:44:45,959
Speaker 1: or you know, a Higgs boson or something, it will.

885
00:44:46,320 --> 00:44:49,400
Speaker 1: So the universe does everything that's mathematically allowed. And so

886
00:44:49,480 --> 00:44:52,600
Speaker 1: if something is mathematically forbidden, if something doesn't happen, it's

887
00:44:52,640 --> 00:44:56,239
Speaker 1: probably because it's mathematically forbidden. That's like one way that

888
00:44:56,280 --> 00:44:58,600
Speaker 1: we figure out what the rules are. We look and

889
00:44:58,640 --> 00:45:02,560
Speaker 1: we say, how muans don't just turn into electrons sometime?

890
00:45:02,880 --> 00:45:04,799
Speaker 1: What's going on there? And it turns out there's a

891
00:45:04,840 --> 00:45:08,920
Speaker 1: mathematical rule that describes why that can't happen. It often

892
00:45:09,000 --> 00:45:12,440
Speaker 1: reveals some like underlying physical principle, and so that's why

893
00:45:12,440 --> 00:45:15,160
Speaker 1: it's so fun to find these rules, describe them mathematically,

894
00:45:15,200 --> 00:45:17,240
Speaker 1: and then step back and think, why is the universe

895
00:45:17,280 --> 00:45:19,520
Speaker 1: this way? Would it be possible to have a universe

896
00:45:19,520 --> 00:45:22,480
Speaker 1: without this rule, or is this rule necessary for the

897
00:45:22,520 --> 00:45:25,719
Speaker 1: universe to like make sense at all? Well, I guess

898
00:45:25,760 --> 00:45:27,960
Speaker 1: what's weird too, is that, you know, like it I'd

899
00:45:27,960 --> 00:45:30,120
Speaker 1: be fine if the universe had this rule that said, oh, no,

900
00:45:30,200 --> 00:45:32,160
Speaker 1: you can't have the two electrons kind of on the

901
00:45:32,200 --> 00:45:34,320
Speaker 1: same spot at the same time. I'd be like, okay, fine,

902
00:45:34,360 --> 00:45:38,120
Speaker 1: that never happens. But it's almost like the universe resists

903
00:45:38,200 --> 00:45:41,359
Speaker 1: even getting close to that possibility. Like if you take

904
00:45:41,719 --> 00:45:43,279
Speaker 1: as we were talking about earlier, if you take two

905
00:45:43,280 --> 00:45:46,120
Speaker 1: electrons and you try to squish them together and you

906
00:45:46,160 --> 00:45:50,640
Speaker 1: can overcome the electromagnetic force that repels them, there's another

907
00:45:50,920 --> 00:45:54,040
Speaker 1: force almost in the universe that kind of resists that

908
00:45:54,360 --> 00:45:56,920
Speaker 1: squishing them together. Right, It's like the universe is like

909
00:45:57,080 --> 00:45:58,880
Speaker 1: kind of freaking out a little bit, like, ah, you're

910
00:45:58,920 --> 00:46:04,520
Speaker 1: getting close to a logical inconsistency keep those two things away, yeah, exactly.

911
00:46:04,560 --> 00:46:06,920
Speaker 1: And some listeners have written in to ask about that.

912
00:46:07,000 --> 00:46:10,040
Speaker 1: They're like, what's the mechanism of that? Which of the

913
00:46:10,160 --> 00:46:13,239
Speaker 1: forces is the thing that keeps the electrons or being

914
00:46:13,280 --> 00:46:15,440
Speaker 1: on top of each other because they imagine that like

915
00:46:15,480 --> 00:46:18,200
Speaker 1: otherwise they would, And so in order to change the

916
00:46:18,280 --> 00:46:20,839
Speaker 1: direction of electron or something, you need to have some

917
00:46:20,960 --> 00:46:23,319
Speaker 1: force that operates there. And if you try to read

918
00:46:23,360 --> 00:46:25,960
Speaker 1: about it, it's a little bit confusing because there is

919
00:46:25,960 --> 00:46:29,359
Speaker 1: a description of this, like Fermi pressure or this effective

920
00:46:29,360 --> 00:46:31,760
Speaker 1: force that describes it. But if you think about forces

921
00:46:31,760 --> 00:46:34,040
Speaker 1: in terms of like the fundamental forces, you know, the

922
00:46:34,080 --> 00:46:37,400
Speaker 1: weak force, a strong force, the electromagnetic force. This is

923
00:46:37,440 --> 00:46:40,080
Speaker 1: like an emergent force. This is something that comes out

924
00:46:40,120 --> 00:46:43,080
Speaker 1: of observing these things and trying to describe the energy

925
00:46:43,160 --> 00:46:46,800
Speaker 1: levels that they fall into and that they don't fall into. Really,

926
00:46:46,840 --> 00:46:49,279
Speaker 1: there's no force that's doing this. It's just something the

927
00:46:49,360 --> 00:46:52,759
Speaker 1: universe doesn't do. Like an electron just can't go there,

928
00:46:52,920 --> 00:46:55,680
Speaker 1: you know, it's just like not an option for the electron.

929
00:46:55,920 --> 00:46:58,279
Speaker 1: So is there like some sort of force pushing these

930
00:46:58,280 --> 00:47:01,000
Speaker 1: two things apart that is working kind of on behalf

931
00:47:01,040 --> 00:47:03,439
Speaker 1: of the firmi exclusion principle. Is there so as you think,

932
00:47:03,520 --> 00:47:06,200
Speaker 1: or is it more sort of like a quantum probability

933
00:47:06,520 --> 00:47:09,640
Speaker 1: or improbability that keeps two things apart. There's not a

934
00:47:09,719 --> 00:47:12,360
Speaker 1: fundamental force, but they's sort of like an effective force.

935
00:47:12,600 --> 00:47:15,200
Speaker 1: I mean, think about like having a bunch of electrons

936
00:47:15,480 --> 00:47:18,640
Speaker 1: and trying to squeeze them down into the same place. Well,

937
00:47:18,640 --> 00:47:21,279
Speaker 1: what's really going on is that you can't have the

938
00:47:21,320 --> 00:47:25,160
Speaker 1: electrons in the same state, and so the electrons resist

939
00:47:25,239 --> 00:47:27,920
Speaker 1: that by having different energies, you know, the same way

940
00:47:27,960 --> 00:47:30,120
Speaker 1: they're like electrons around a nucleus will fill up the

941
00:47:30,200 --> 00:47:33,160
Speaker 1: ladder of energies, so some of them have more energy

942
00:47:33,200 --> 00:47:35,040
Speaker 1: than otherwise. Right, you're trying to squeeze a bunch of

943
00:47:35,040 --> 00:47:38,760
Speaker 1: electrons down to a tiny little blob. They will resist

944
00:47:38,800 --> 00:47:42,440
Speaker 1: it because some of them will have higher energy than otherwise,

945
00:47:42,520 --> 00:47:45,120
Speaker 1: because they're forced into it, forced to stay in those

946
00:47:45,200 --> 00:47:48,719
Speaker 1: higher energy states because of the ladder. And effectively that

947
00:47:48,760 --> 00:47:51,120
Speaker 1: means that they're pushing back if they have more energy.

948
00:47:51,160 --> 00:47:53,960
Speaker 1: They're like bouncing off the walls of your box with

949
00:47:54,080 --> 00:47:57,279
Speaker 1: more momentum, they're pushing on that box. And so the

950
00:47:57,320 --> 00:47:59,919
Speaker 1: fact that the electrons can't all go to the lowest state,

951
00:48:00,280 --> 00:48:03,040
Speaker 1: means they have more energy, which means effectively they're pushing

952
00:48:03,080 --> 00:48:05,760
Speaker 1: back on you as you try to squeeze them down.

953
00:48:06,000 --> 00:48:08,759
Speaker 1: So that's like an effective pressure, right. It's not like

954
00:48:08,760 --> 00:48:11,319
Speaker 1: the electrons are pushing against each other or like there's

955
00:48:11,320 --> 00:48:14,440
Speaker 1: a force between the electron and the walls of your box.

956
00:48:14,760 --> 00:48:17,560
Speaker 1: But as you try to squeeze electrons down, you'll notice

957
00:48:17,800 --> 00:48:20,200
Speaker 1: this effective pressure that wouldn't happen if you did the

958
00:48:20,200 --> 00:48:22,839
Speaker 1: same thing with photons. Oh, I see what you're saying.

959
00:48:22,920 --> 00:48:25,759
Speaker 1: It's more like if you try to get an electron

960
00:48:26,080 --> 00:48:30,080
Speaker 1: to collapse to the lowest possible, for example, orbit around

961
00:48:30,080 --> 00:48:34,520
Speaker 1: in a nucleus, but there's already an electron there. It's

962
00:48:34,520 --> 00:48:37,359
Speaker 1: not like the electron pushes back against you to try

963
00:48:37,400 --> 00:48:40,560
Speaker 1: to collapse it. It's just that the electron doesn't give up.

964
00:48:40,600 --> 00:48:42,799
Speaker 1: It's the energy that it has. Yeah, Like, in order

965
00:48:42,800 --> 00:48:44,960
Speaker 1: to squeeze it down to the lowest it needs to

966
00:48:45,000 --> 00:48:47,600
Speaker 1: give up that energy. But because it can, like, the

967
00:48:47,640 --> 00:48:50,760
Speaker 1: electron hold onto that energy. And that's basically the same

968
00:48:50,800 --> 00:48:53,360
Speaker 1: as like pushing back against you exactly, And that's the

969
00:48:53,400 --> 00:48:56,000
Speaker 1: mechanism for it to push back. And we actually see

970
00:48:56,040 --> 00:48:59,400
Speaker 1: that happen out there in the universe, and for example,

971
00:48:59,480 --> 00:49:03,000
Speaker 1: white dwarf worse, are these really really dense blobs of

972
00:49:03,040 --> 00:49:05,440
Speaker 1: super hot metal if they're left over For at the

973
00:49:05,600 --> 00:49:07,799
Speaker 1: end point of a star, a star has done all

974
00:49:07,840 --> 00:49:10,360
Speaker 1: the burning that it can, and it's blown up maybe

975
00:49:10,360 --> 00:49:13,440
Speaker 1: and left behind its core. They're just sitting there, hot

976
00:49:13,480 --> 00:49:17,240
Speaker 1: and glowing and eventually cooling down. These things are incredibly

977
00:49:17,320 --> 00:49:20,040
Speaker 1: dense and the gravity is very very strong. So you

978
00:49:20,120 --> 00:49:21,960
Speaker 1: might wonder, like, why doesn't the whit dwarf collapse into

979
00:49:22,000 --> 00:49:23,880
Speaker 1: a black hole? The thing that keeps a star from

980
00:49:23,960 --> 00:49:26,000
Speaker 1: collapsing into a black hole is that it still has

981
00:49:26,040 --> 00:49:28,880
Speaker 1: fusion happening. It's like radiating out energy, it's like blowing up.

982
00:49:29,200 --> 00:49:31,359
Speaker 1: But a white dwarf isn't doing that anymore. So it's

983
00:49:31,360 --> 00:49:34,440
Speaker 1: just like a blob of mass. Why isn't it collapsing

984
00:49:34,480 --> 00:49:37,799
Speaker 1: into a black hole? And the answer is electron degeneracy.

985
00:49:37,840 --> 00:49:41,120
Speaker 1: These electrons resist getting pushed on top of each other,

986
00:49:41,160 --> 00:49:43,799
Speaker 1: and they prevent this thing from turning into a black hole.

987
00:49:43,960 --> 00:49:46,480
Speaker 1: They're like one of the last barriers of defense against

988
00:49:46,480 --> 00:49:49,120
Speaker 1: gravitational collapse. Well, it's pretty cool. Would you say white

989
00:49:49,160 --> 00:49:52,680
Speaker 1: dwarfs are pretty awesome? Are they more awesome than chocolate dwarfs?

990
00:49:53,040 --> 00:49:55,239
Speaker 1: I think the fate of the universe is for all

991
00:49:55,280 --> 00:49:58,240
Speaker 1: the white dwarves to cool down and become black dwarves,

992
00:49:58,640 --> 00:50:01,920
Speaker 1: which means black dwar are cooler than white dwarfs, just

993
00:50:01,960 --> 00:50:04,279
Speaker 1: like chocolate is cooler than vanilla. Well, sure, if you

994
00:50:04,360 --> 00:50:06,640
Speaker 1: leave astro about, nobody wants. Nobody's gonna want to eat

995
00:50:06,640 --> 00:50:09,680
Speaker 1: that ice cream eventually. But you know, if you add

996
00:50:09,719 --> 00:50:12,720
Speaker 1: more mass to this white dwarfs, the gravity gets stronger.

997
00:50:12,800 --> 00:50:16,239
Speaker 1: You can actually overcome this electron degeneracy pressure. And what

998
00:50:16,360 --> 00:50:18,600
Speaker 1: happens is not that the electrons give up and then

999
00:50:18,600 --> 00:50:20,560
Speaker 1: like pile on top of each other. They're just not

1000
00:50:20,640 --> 00:50:23,680
Speaker 1: allowed to do that. What happens is the electrons combine

1001
00:50:23,760 --> 00:50:27,080
Speaker 1: with the protons to turn into neutrons, so they give

1002
00:50:27,160 --> 00:50:30,520
Speaker 1: up and become not electrons anymore, and then you can

1003
00:50:30,560 --> 00:50:33,480
Speaker 1: get things a little bit denser. M you mean at

1004
00:50:33,480 --> 00:50:36,520
Speaker 1: some point like they just become pure energy and then

1005
00:50:36,520 --> 00:50:39,240
Speaker 1: they squeeze together. Yeah, well, the proton and the electron

1006
00:50:39,320 --> 00:50:42,200
Speaker 1: together can do like an reverse beta decay and become

1007
00:50:42,200 --> 00:50:45,359
Speaker 1: a neutron, and then you have a neutron star, which

1008
00:50:45,400 --> 00:50:48,760
Speaker 1: is just a big blob of neutrons, and those neutrons

1009
00:50:48,800 --> 00:50:52,839
Speaker 1: get squeezed together by gravity, and the neutrons are also fermions.

1010
00:50:53,120 --> 00:50:55,319
Speaker 1: One of the fascinating things about fermions is it's not

1011
00:50:55,400 --> 00:50:58,560
Speaker 1: just fundamental particles. You can put quarks together in various

1012
00:50:58,640 --> 00:51:01,840
Speaker 1: arrangements to make fermion. So like the proton is a fermion,

1013
00:51:02,160 --> 00:51:05,399
Speaker 1: the neutron is a fermion, and then the neutrons are

1014
00:51:05,440 --> 00:51:09,320
Speaker 1: resisting also because they're also fermions. The reason a neutron

1015
00:51:09,400 --> 00:51:13,840
Speaker 1: star doesn't collapse is because of the neutron degeneracy pressure.

1016
00:51:14,040 --> 00:51:16,160
Speaker 1: The same principle that kept the white dwarf alive is

1017
00:51:16,200 --> 00:51:19,200
Speaker 1: now keeping the neutron star from becoming a black hole.

1018
00:51:19,320 --> 00:51:21,560
Speaker 1: But then as you add more and more mass to

1019
00:51:21,600 --> 00:51:24,839
Speaker 1: that neutron star, it's denser and denser, and eventually even

1020
00:51:24,880 --> 00:51:28,520
Speaker 1: the neutrons degeneracy pressure is overcome, but again not by

1021
00:51:28,560 --> 00:51:32,160
Speaker 1: the neutrons violating this rule of the universe. Instead they

1022
00:51:32,200 --> 00:51:35,200
Speaker 1: just turn into something else. We've talked about the heart

1023
00:51:35,239 --> 00:51:38,000
Speaker 1: of neutron stars before. Nobody really knows what's going on,

1024
00:51:38,080 --> 00:51:41,280
Speaker 1: but it's not neutrons anymore. It's something else crazy that's happening,

1025
00:51:41,320 --> 00:51:43,480
Speaker 1: And to understand how you can keep adding mass and

1026
00:51:43,520 --> 00:51:45,479
Speaker 1: a black hole conform at the heart of it would

1027
00:51:45,520 --> 00:51:47,920
Speaker 1: require like a theory of quantum gravity that we just

1028
00:51:48,080 --> 00:51:50,960
Speaker 1: don't even have yet. You mean, like we have this

1029
00:51:51,080 --> 00:51:54,040
Speaker 1: exclusion principle, this rule about the universe. It says you

1030
00:51:54,040 --> 00:51:56,960
Speaker 1: can't squish two fermions together. But at some point, if

1031
00:51:56,960 --> 00:51:59,239
Speaker 1: you try hard enough, you can sort of bypass this

1032
00:51:59,400 --> 00:52:02,400
Speaker 1: rule because suddenly the things you're trying to squeeze together

1033
00:52:02,400 --> 00:52:05,360
Speaker 1: are no longer electrons or neutron state, just kind of

1034
00:52:05,400 --> 00:52:08,799
Speaker 1: become pure energy or pure quantum potential, and then they

1035
00:52:08,840 --> 00:52:11,239
Speaker 1: become something else. Yeah, exactly. We see those examples in

1036
00:52:11,239 --> 00:52:13,560
Speaker 1: all sorts of situations, like even when it's not at

1037
00:52:13,600 --> 00:52:17,239
Speaker 1: the heart of a neutron star. Superconductivity works this way.

1038
00:52:17,320 --> 00:52:20,360
Speaker 1: Electrons are fermions, right, they can't be in the same state.

1039
00:52:20,600 --> 00:52:22,799
Speaker 1: But if you get two electrons together and you sort

1040
00:52:22,800 --> 00:52:25,800
Speaker 1: of tie them up together into a single quantum object,

1041
00:52:26,000 --> 00:52:29,200
Speaker 1: they become a boson. They're two spin one half states

1042
00:52:29,200 --> 00:52:31,759
Speaker 1: combined to a spin one state, and this is called

1043
00:52:31,760 --> 00:52:35,759
Speaker 1: a Cooper pair, and it's a key to superconductivity because

1044
00:52:35,800 --> 00:52:38,239
Speaker 1: now these electrons can like flow and slide in the

1045
00:52:38,239 --> 00:52:42,080
Speaker 1: way that bosons can in lower energy states and make

1046
00:52:42,160 --> 00:52:44,799
Speaker 1: things move more quickly. So we can see fermions like

1047
00:52:44,920 --> 00:52:49,600
Speaker 1: exploiting this loophole by becoming bosons, by pairing up. So yeah, absolutely,

1048
00:52:49,640 --> 00:52:52,400
Speaker 1: you can avoid this rule of the universe by squeezing

1049
00:52:52,400 --> 00:52:55,440
Speaker 1: things down or tying things together. I think what you're

1050
00:52:55,480 --> 00:52:57,799
Speaker 1: saying is that the universe has principles, but if you

1051
00:52:57,840 --> 00:53:00,880
Speaker 1: put enough pressure on it, it totally without those principles

1052
00:53:00,880 --> 00:53:04,560
Speaker 1: out the door. Exactly. Even if I've agreed to eat

1053
00:53:04,640 --> 00:53:06,640
Speaker 1: chocolate ice cream for the rest of my life, I

1054
00:53:06,960 --> 00:53:10,280
Speaker 1: might sneak a sample of vanilla sometime just for variety

1055
00:53:10,480 --> 00:53:14,200
Speaker 1: under enough pressure pressure at the heart of a neutron star.

1056
00:53:15,640 --> 00:53:19,880
Speaker 1: Only then we eat no. I love vanilla. Did you

1057
00:53:19,920 --> 00:53:23,239
Speaker 1: know that vanilla beans are actually more expensive pound for

1058
00:53:23,360 --> 00:53:25,840
Speaker 1: pound than gold. I didn't know that, but it doesn't

1059
00:53:25,880 --> 00:53:29,040
Speaker 1: surprise me because vanilla is the best. I'll eat vanilla

1060
00:53:29,080 --> 00:53:33,080
Speaker 1: anytime over a goal. All right, Well, it sounds like

1061
00:53:33,280 --> 00:53:37,720
Speaker 1: the universe has these strange rules about it, although under

1062
00:53:37,840 --> 00:53:41,400
Speaker 1: enough pressure or there's certain circumstances, it seems to throughout

1063
00:53:41,480 --> 00:53:44,960
Speaker 1: these or it finds loopholes around these principles. But that

1064
00:53:45,120 --> 00:53:48,239
Speaker 1: it's thanks to these principles that we have things like chemistry,

1065
00:53:48,280 --> 00:53:50,960
Speaker 1: and we have chemistry the way it is, and so

1066
00:53:51,080 --> 00:53:55,080
Speaker 1: without these rules, we wouldn't be here talking about these rules. Yeah, exactly.

1067
00:53:55,080 --> 00:53:58,480
Speaker 1: It's the reason we even have a delicious dilemma between

1068
00:53:58,520 --> 00:54:01,040
Speaker 1: chocolate and vanilla, which I still thinking you can solve

1069
00:54:01,080 --> 00:54:04,719
Speaker 1: by just having a swirl. That's the loophole, that's right, Yeah,

1070
00:54:04,760 --> 00:54:08,000
Speaker 1: transforming it into something else, rocky road. It's called rocky

1071
00:54:08,080 --> 00:54:11,600
Speaker 1: rock for it already. Just spin it, spin it in

1072
00:54:11,600 --> 00:54:14,400
Speaker 1: a different way. All right. Well, we hope you enjoyed that.

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00:54:15,040 --> 00:54:25,640
Speaker 1: Thanks for joining us, See you next time. Thanks for listening,

1074
00:54:25,719 --> 00:54:28,440
Speaker 1: and remember that Daniel and Jorge explain the Universe is

1075
00:54:28,440 --> 00:54:32,720
Speaker 1: a production of iHeartRadio. Or more podcast from my heart Radio.

1076
00:54:32,880 --> 00:54:37,000
Speaker 1: Visit the iHeartRadio app, Apple Podcasts, or wherever you listen

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00:54:37,080 --> 00:54:38,240
Speaker 1: to your favorite shows.