Latest / Daniel and Kelly’s Extraordinary Universe / Why can't two electrons be in the same place?

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Why can't two electrons be in the same place? · Daniel and Kelly’s Extraordinary Universe

0:08
Speaker 1: Hey, Joe, if you could only eat one flavor of
0:11
Speaker 1: ice cream for the rest of your life, would it
0:14
Speaker 1: be chocolate or vanilla? Who do I have to choose?
0:18
Speaker 1: Can I do like a quantum superposition of the tooth flavors? No,
0:21
Speaker 1: you are not a quantum Jorge, so you can only
0:24
Speaker 1: be in vanilla or chocolate. States It's a classic dilemma
0:28
Speaker 1: of classical physics, isn't it is? And so does your
0:31
Speaker 1: wave function collapse to vanilla or chocolate? Obviously vanilla my
0:35
Speaker 1: favorite flavor. Are you telling me for real you'd give
0:38
Speaker 1: up chocolate ice cream forever? What if I break the
0:41
Speaker 1: loss of physics? Can I do something like a swirl?
0:44
Speaker 1: Then you go to physics jail whether they don't have
0:46
Speaker 1: either flavor of ice cream? It haves swirls in physics jail,
0:50
Speaker 1: not even for my last meal. All they have in
0:52
Speaker 1: physics jail is physics homework problems. That seems a little inhumane,
0:56
Speaker 1: the ice cream part, not the homework part. I am
1:13
Speaker 1: more hammy cartoonist and the creator of PhD comics. Hi,
1:16
Speaker 1: I'm Daniel. I'm a particle physicist and a professor at
1:19
Speaker 1: UC Irvine, And I choose the chocolate ice cream in
1:22
Speaker 1: one hundred out of one hundred multiverses. Big fan of chocolate, huh,
1:28
Speaker 1: there's just no comparison. I mean, chocolate is delicious, but
1:31
Speaker 1: chocolate ice cream, it just elevates it beyond understanding, No,
1:34
Speaker 1: I think. I guess My question is when you say
1:36
Speaker 1: chocolate I thing for the rest of your life. Do
1:38
Speaker 1: you mean like you only get to eat chocolate ice
1:41
Speaker 1: cream for all your meals? Or is this like only
1:44
Speaker 1: for desserts subtimes? I think even I would get tired
1:47
Speaker 1: of chocolate ice cream if I ate nothing but that breakfast,
1:50
Speaker 1: ludge and dinner, eventually it would get old. Though. You
1:53
Speaker 1: know this milk chocolate ice cream is dark chocolate ice cream.
1:56
Speaker 1: There's chocolate and salt. There are lots of variations there.
1:59
Speaker 1: But that's what I was going to ask, Like what
2:01
Speaker 1: kind of chocolate? There's so many the flavors to choose from. Yeah,
2:04
Speaker 1: and chocolate from all around the world. You know, Madagascar chocolate,
2:07
Speaker 1: and then it's whale and chocolate. They're all subtly different. Now,
2:10
Speaker 1: what's your stand on Like chips like chunks of chocolate
2:14
Speaker 1: in your ice cream? Honestly, I think that ruins the texture.
2:16
Speaker 1: You know, a frozen blob. It's like chewing on a pebble,
2:19
Speaker 1: Like nobody wants to eat rocks, right, right, right, So
2:22
Speaker 1: you're you're against some chocolate ice cream. I'm saying chocolate
2:25
Speaker 1: chunks ruined the chocolate ice cream experience. Let's just have
2:29
Speaker 1: pure ice cream and not chunks. But then now you've
2:31
Speaker 1: got to define a size limit, like what sized limit
2:34
Speaker 1: of chocolate particle are you willing to tolerate? Chocolate ice
2:38
Speaker 1: cream is fundamental, man, It's not composite. It's so important
2:42
Speaker 1: to the universe. There's a chocolate ice cream field that
2:45
Speaker 1: permeates the whole universe. I see, I see, But I mean,
2:49
Speaker 1: I'm sure there's this size of chocolate particle that will
2:52
Speaker 1: fly under your radar. Yeah, you know. I think this
2:54
Speaker 1: calls from more experiments for sure. And I actually did
2:56
Speaker 1: a little Twitter experiment myself. I was wondering if our
2:59
Speaker 1: support orders sided with the obviously correct me on the
3:03
Speaker 1: chocolate camp or the obviously incorrect you on the vanilla camp.
3:06
Speaker 1: So I went out into the little pole to ask
3:08
Speaker 1: people chocolate versus vanilla? But did you say chocolate vanilla? What?
3:12
Speaker 1: I didn't? I just said chocolate versus vanilla? Important science question.
3:16
Speaker 1: Oh yeah, it sounds like an ill designed experiment, Danny,
3:20
Speaker 1: I would expect more from a scientist. Well, I didn't
3:22
Speaker 1: want to be over specific. I wanted a sample, you know,
3:24
Speaker 1: people's general vibe about these flavors, the word chocolate and vanilla. Yeah, exactly.
3:30
Speaker 1: It wasn't a question of like, which one you preferred
3:31
Speaker 1: to spell? Obviously, it's about the flavor. And anyway, the
3:35
Speaker 1: Internet came down on my side, chocolate fifty eight percent
3:38
Speaker 1: to vanilla forty two percent. Wow, that's relatively closed, I
3:42
Speaker 1: would say, don't you think I actually was surprised. I
3:45
Speaker 1: thought chocolate was going to blow vanilla out of the
3:47
Speaker 1: water a little bit more. Here you go, Hey, you
3:49
Speaker 1: know I'll take a twenty point differential. Well, we all
3:52
Speaker 1: know that whatever the Internet things is the best choice
3:55
Speaker 1: for anything. Well, I would say whatever our listeners thing
3:59
Speaker 1: is definitely you know, sampling the truth of the universe.
4:02
Speaker 1: I see, did you have everyone to sign a little
4:04
Speaker 1: like waiver to testify that they're listeners? This is getting
4:07
Speaker 1: more unscientific by the moment. By the way, they all
4:09
Speaker 1: follow us on Twitter. Why would somebody follow us on
4:11
Speaker 1: Twitter and not listen to the podcast that just makes
4:14
Speaker 1: no sense exactly. If they're already listening to us in
4:17
Speaker 1: our podcast, why would they follow us on Twitter for
4:20
Speaker 1: important science questions like chocolate versus Vanilla, the chance to
4:23
Speaker 1: weigh in on the ultimate debate in the universe. Well,
4:26
Speaker 1: I guess if you'd like to go with the majority,
4:28
Speaker 1: you know, the mainstream, I guess that's your thing, right.
4:31
Speaker 1: Vanilla is definitely not the boring, middle of the road choice,
4:33
Speaker 1: for sure. Vanilla is the rebel choice. Yeah, it's the
4:37
Speaker 1: indie minority choice. But anyways, welcome to our podcast Daniel
4:41
Speaker 1: and Horry Explain the Universe, a production of iHeartRadio in
4:44
Speaker 1: which we appreciate all of the flavors of the universe,
4:48
Speaker 1: the quantum, the classical, the things that make sense, the
4:51
Speaker 1: things that don't make sense. We blend them all together
4:54
Speaker 1: into chunks so tiny and so smooth that you can
4:57
Speaker 1: appreciate them without having to chew on a intellectual pebbles.
5:01
Speaker 1: It's right because it is a delicious universe, full of
5:03
Speaker 1: amazing textures and flavors and temperatures of treats. And so
5:07
Speaker 1: there's a lot to talk about it in a lot
5:09
Speaker 1: to try to explain to everyone, And there's a wonderful
5:11
Speaker 1: and long history of trying to understand the universe, just
5:14
Speaker 1: sort of looking at the stuff around us, seeing if
5:16
Speaker 1: it makes sense, breaking into smaller pieces and seeing those
5:19
Speaker 1: pieces make sense, digging in even deeper to smaller and
5:23
Speaker 1: smaller pieces, until eventually we get the stuff that seems
5:27
Speaker 1: to follow weird and different rules, rules that surprise and
5:31
Speaker 1: confuse us. The universe is full of rules, interesting rules
5:34
Speaker 1: that are sometimes helpful, like Newton's laws or general relativity
5:38
Speaker 1: by Einstein. But sometimes there are rules that kind of
5:40
Speaker 1: don't quite make a lot of sense, at least to
5:43
Speaker 1: a human because our tendency is to think about things
5:46
Speaker 1: in terms of the things we know. When we discover
5:49
Speaker 1: a new object, we think, oh, maybe it's a little
5:51
Speaker 1: bit like a grain of sand, or maybe it's a
5:53
Speaker 1: little bit like a basketball. Can I apply the rules
5:55
Speaker 1: of waves to this thing? Can I apply what I
5:57
Speaker 1: know about bananas to this new discovery? So when we
6:00
Speaker 1: unearthed quantum particles, our first guests is to think, oh,
6:03
Speaker 1: these are like tiny little dots that follow the rules
6:06
Speaker 1: of classical physics. Maybe they move through space, they have
6:09
Speaker 1: velocity and position, they're just super duper tiny. But what
6:12
Speaker 1: we've discovered is that they are not like anything we
6:15
Speaker 1: have ever seen before. They're not tiny little dots of
6:18
Speaker 1: sand just like baseballs, but much much smaller. They're not
6:21
Speaker 1: even just like waves. There's something else, something weird, that
6:25
Speaker 1: follows a new set of rules that we have to
6:27
Speaker 1: discover and savor. Yeah. I feel like whenever we start
6:30
Speaker 1: to talk about things that don't make sense, it probably
6:33
Speaker 1: means that we're going to the quantum realm, that we're
6:36
Speaker 1: going to talk about quantum things. Yeah, but this is
6:38
Speaker 1: our experience every time we extrapolate from our intuitive experience,
6:42
Speaker 1: from our understanding of the world around us, not just
6:45
Speaker 1: the tiny and the quantum, but also the very very
6:47
Speaker 1: big right thinking about the universe as a whole, and
6:50
Speaker 1: maybe having an edge or having a beginning. All those
6:53
Speaker 1: things defy our understanding because they're not part of our experience,
6:57
Speaker 1: so we don't have like a natural vocabulary, a way
6:59
Speaker 1: of thinking about them that's comfortable. Instead, we have to
7:02
Speaker 1: rely on mathematics to bridge us into a new language,
7:06
Speaker 1: a new way of thinking about the world. Yeah, but
7:08
Speaker 1: I guess it's part of that is I wonder if
7:10
Speaker 1: it's just like the context in which we came up
7:13
Speaker 1: in as a species, like our size that we just
7:15
Speaker 1: happen to evolve into. Like if we were much much
7:18
Speaker 1: tinier as a living thing, you know, maybe the quantum
7:23
Speaker 1: rules of the universe would make more sense than the
7:25
Speaker 1: classical rules of the universe. I think that's probably true,
7:28
Speaker 1: And one day we might meet like microscopic aliens whose
7:32
Speaker 1: scientists of all finding quantum mechanics we totally intuitive and
7:36
Speaker 1: classical physics to be very very weird. Of course, they
7:39
Speaker 1: wouldn't call it classical physics. They would call it like,
7:41
Speaker 1: you know, huge physics or something. They would think it's
7:44
Speaker 1: very strange that if you take ten to the twenty
7:47
Speaker 1: nine quantum particles, they somehow come together to act like
7:50
Speaker 1: one big particle. That's an interesting question. I wonder, like,
7:53
Speaker 1: what's the smallest living sentient thing you can have? Like
7:57
Speaker 1: can you make a being out of straight up of
8:00
Speaker 1: a few quarks, you know what I mean? Or the
8:02
Speaker 1: strings inside of quarks. It's a really fun question. And
8:05
Speaker 1: Max Tegmark, who's a physicist at MIT, has this really
8:08
Speaker 1: fun paper about where consciousness comes from, and he thinks
8:12
Speaker 1: it's actually a state of matter. We're going to dig
8:14
Speaker 1: into it in a future podcast episode. But it might
8:17
Speaker 1: be that everything in the universe is aware, and that
8:20
Speaker 1: even small combinations of objects can somehow do calculations and
8:24
Speaker 1: maybe even be conscious. Dude, they gonna have to smoke
8:28
Speaker 1: some special things in order to get into that topic. Bananappeals,
8:33
Speaker 1: for sure, Well, the quantum universe is full of interesting
8:36
Speaker 1: and weird rules, sometimes rules that don't seem to make sense,
8:39
Speaker 1: or that even seem kind of fair, And as we
8:41
Speaker 1: explore the quantum universe we discover these rules. A lot
8:44
Speaker 1: of the time, these rules are just descriptive. They just
8:46
Speaker 1: describe what we see. They don't always fundamentally explain it.
8:50
Speaker 1: But sometimes we can actually find a reason for it.
8:53
Speaker 1: So that's sort of the strategy is like, look out
8:55
Speaker 1: in the universe, see what's going on, see what's not
8:57
Speaker 1: going on, so we can understand what the dues and
9:00
Speaker 1: don't have other particle world and then try to extract
9:03
Speaker 1: from that some fundamental reason why the universe is this
9:06
Speaker 1: way and not some other way. So to the other podcast,
9:09
Speaker 1: we'll be tackling the question why can't two fermions be
9:17
Speaker 1: in the same quantum state. Now, first of all, Danny,
9:21
Speaker 1: let me just say that I'm glad you're a bored
9:23
Speaker 1: with the faith the quantum realm? Have you sold out
9:25
Speaker 1: to the Marvel corporate machine yet to ching? No, it's true.
9:29
Speaker 1: I have the new ant Man movie on the brain.
9:31
Speaker 1: Can't wait to see it. Oh really, you're excited even
9:34
Speaker 1: though they're jumping into the quantum realm and finding all
9:37
Speaker 1: kinds of things inside of it. M Yeah, absolutely, I
9:39
Speaker 1: like those movies. I mean, they are scientifically mostly nonsense,
9:43
Speaker 1: but they also don't take themselves too seriously, and they
9:46
Speaker 1: have fun with it, and I think they're really creative.
9:48
Speaker 1: The first couple had some really beautiful visuals of like
9:51
Speaker 1: what the quantum realm might look like or what it
9:53
Speaker 1: might be like to visit the quantum realm, so I
9:56
Speaker 1: think they're a lot of fun. Oh wow, I feel
9:58
Speaker 1: like you are getting paid by Marvel, right, You're like,
10:01
Speaker 1: is this the Daniel? I know what science you like?
10:05
Speaker 1: The random use of the word quantum. No, I don't
10:08
Speaker 1: only like hard science fiction. I dislike hard science fiction
10:11
Speaker 1: that gets it wrong. You know, if you want to
10:13
Speaker 1: pretend to be serious about your science and then you
10:15
Speaker 1: get it wrong, then you get the merits from me.
10:17
Speaker 1: But if you're going to make fun of yourself along
10:19
Speaker 1: the way and just have a good time. Then let's
10:21
Speaker 1: go for it. Well, in this case, we're asking a
10:23
Speaker 1: kind of an interesting question here about the quantum nature
10:27
Speaker 1: of things. So why can't two fermions be in the
10:29
Speaker 1: same quantum state? No, I imagine this is maybe not
10:32
Speaker 1: a question most people have thought about before. This is
10:35
Speaker 1: something people run into in high school chemistry when they're
10:38
Speaker 1: like learning about electrons and electron orbitals. But it's a
10:41
Speaker 1: really deep and important concept in particle physics theory that
10:45
Speaker 1: relates to how particles operate, what it means for particles
10:48
Speaker 1: to be identical, what it means to like swap particles
10:51
Speaker 1: from one state to another. Turns out to be a
10:54
Speaker 1: really deep and important concept in particle physics, and something
10:57
Speaker 1: a couple of listeners wanted to know more about. How
10:59
Speaker 1: does it actually work and why does it happen? Maybe
11:02
Speaker 1: it'll be the plot of the next ant Men movie.
11:04
Speaker 1: You can't have two ant Men in the same place
11:06
Speaker 1: at the same time. Yeah, I think they have multiple
11:10
Speaker 1: ones in this latest movie, So maybe that's the plotline
11:14
Speaker 1: is toasted, Or maybe it just means ant Man is
11:16
Speaker 1: a Boson and not a Fermion, Or maybe he's an
11:19
Speaker 1: ant t particle. I wasped right into that was usually
11:27
Speaker 1: we were wondering how many people out there had thought
11:29
Speaker 1: about this rule that applies to fermions or electrons, and so,
11:33
Speaker 1: as usual, Danny went out there to ask the internet, right,
11:36
Speaker 1: that's right. Thank you very much to everybody who participates
11:40
Speaker 1: for this segment of the podcast, and if you would
11:41
Speaker 1: like to share your thoughts for our education and entertainment,
11:45
Speaker 1: please don't be shy write to us two questions at
11:48
Speaker 1: Daniel and Jorge dot com. So think about it for
11:50
Speaker 1: a second. Do you know why two fermions can't be
11:54
Speaker 1: in the same quantum state? Here's would be glad to say.
11:58
Speaker 1: I'm not sure of the terminology. I think there is
12:02
Speaker 1: an exclusion principle something that says that they can't occupy
12:06
Speaker 1: the same state or same space. I don't know if
12:09
Speaker 1: it's called the poly exclusion principle. I'm not sure. So
12:12
Speaker 1: I think the fermions are the force caring ones. Why
12:17
Speaker 1: can't they be in the same quantum state? You know,
12:20
Speaker 1: maybe they're all entangled with each other and so they
12:23
Speaker 1: all have to have like opposing states of some sort.
12:26
Speaker 1: I am merely guessing that two fermions cannot have the
12:29
Speaker 1: same quantum state because they have different properties. Well maybe
12:34
Speaker 1: because they have the same charges, and then they need
12:37
Speaker 1: to find more stable spots to be related to some
12:41
Speaker 1: other opposite charge particle. I think deferments cannot be in
12:45
Speaker 1: the same quint of state for the same reason that
12:48
Speaker 1: a magnet cannot have a same pool in booth sides.
12:52
Speaker 1: I'm a bit fuzzy on what fermions are, but if
12:57
Speaker 1: they can't be in the same quantum state, I think
13:01
Speaker 1: it might be to do with the fact that's kind
13:04
Speaker 1: of like magnets, where you need in order for them
13:08
Speaker 1: to be magnetic, you have to have one pole opposite
13:11
Speaker 1: to the other. Something similar like that, where the one
13:13
Speaker 1: needs to spin up one needs to spin down. All right,
13:17
Speaker 1: A lot of fun answers here. Nobody mentioned Paul Rudd.
13:21
Speaker 1: Nobody else out there is a shill from Marble like
13:23
Speaker 1: I am. Apparently you keep bringing it up. You rather,
13:28
Speaker 1: Paul Rudd. I want in on this. By the way,
13:31
Speaker 1: if you if you have a hook up with Marvel,
13:33
Speaker 1: I'm totally in. All right, sounds good now. These answers
13:36
Speaker 1: are pretty good. They're sort of all over the place.
13:38
Speaker 1: I was a little surprised. I thought we'd hear more
13:40
Speaker 1: mentions of the poll exclusion principle. More people need to
13:44
Speaker 1: take or remember their high school chemistry. You mean you
13:47
Speaker 1: were expecting more people to mention the poll exclusion principle. Yeah. Absolutely,
13:50
Speaker 1: I thought it was something people knew pretty well. I
13:53
Speaker 1: mean I remember suffering through it in high school chemistry.
13:56
Speaker 1: I imagine a lot of other people have. Well, let's
13:58
Speaker 1: step into it, Danny. What is the poly exclusion principle
14:01
Speaker 1: and how does it apply to quantum states and fermions.
14:05
Speaker 1: So the poly exclusion principle basically just says that you
14:08
Speaker 1: cannot have two fermions in the same quantum state, right,
14:12
Speaker 1: It's basically a statement of the problem. Of course, it
14:14
Speaker 1: references these particles fermions, named after Enrico Fermi. But these
14:19
Speaker 1: are the particles that make up matter. So quarks and
14:21
Speaker 1: electrons are fermions, and this is why, for example, you
14:25
Speaker 1: can't have two electrons in the same state around a
14:28
Speaker 1: hydrogen atom. The poly exclusion principle forbids it. Okay, so
14:33
Speaker 1: let me go back a little bit to a fermion.
14:35
Speaker 1: It's what you call the matter particles, right, Yeah, we
14:37
Speaker 1: have two different kinds of particles. In the standard model,
14:40
Speaker 1: we have the particles that make up matter, so the electron,
14:43
Speaker 1: the quarks, for example, and that of that you can
14:45
Speaker 1: build protons and neutrons, from which you can make the nucleus.
14:49
Speaker 1: At electrons you get atoms. Buy them all together, you
14:51
Speaker 1: get molecules. We're basically built out of those things. There
14:55
Speaker 1: are also other particles. These are the force particles. The
14:58
Speaker 1: particles like the photon that bind the electron to the nucleus,
15:02
Speaker 1: and the w and the z bosons for the weak force,
15:05
Speaker 1: and the gluons for the strong force. These particles are
15:08
Speaker 1: the force particles. There's an interesting difference between these two
15:11
Speaker 1: kinds of particles. The first one the fermions. You can
15:14
Speaker 1: never have two of them in the same state. Two
15:16
Speaker 1: electrons can never be in the same state. But the
15:18
Speaker 1: other group, the force carrying particles, these bosons. There's no limit,
15:23
Speaker 1: Like you can have two photons in the same state,
15:25
Speaker 1: ten photons in the same state, a million photons all
15:28
Speaker 1: piled on top of each other. So fermions can never
15:31
Speaker 1: be in the same state. Those are the matter particles,
15:34
Speaker 1: and bosons can be in the same state. That's this
15:37
Speaker 1: weird division Okay, now let's maybe define for people what
15:40
Speaker 1: is a quantum state, Like what does it mean to
15:43
Speaker 1: have a state, and what can those states be? So
15:45
Speaker 1: what can quantum particles do well. They can be in
15:48
Speaker 1: some location. They can also have a certain amount of energy,
15:51
Speaker 1: They can have a certain kind of spin, like some
15:54
Speaker 1: of these particles can have spin up or spin down
15:57
Speaker 1: or other various weird kinds of spin. So basically, anything
16:00
Speaker 1: that describes the particle is part of its quantum state.
16:04
Speaker 1: A quantum state is just a description of the particle,
16:07
Speaker 1: Like you mean, like where is it and what's it doing? Yeah, exactly,
16:11
Speaker 1: that's what a state is. The way you might describe
16:13
Speaker 1: like a classical object by saying where is it, how
16:16
Speaker 1: fast is it going? What is it? Location and velocity?
16:19
Speaker 1: That describes the classical object. A quantum state is just
16:22
Speaker 1: a description of the quantum particle. Like the state of
16:24
Speaker 1: a baseball might be like it's over here, it's moving
16:27
Speaker 1: in this direction, and it's also spinning in place, and
16:30
Speaker 1: maybe also like it's temperature. Would that be kind of
16:33
Speaker 1: like what you need to describe a baseball. Imagine, for example,
16:36
Speaker 1: we live in a simulation and you're the programmer of
16:39
Speaker 1: the simulation. What details do you need to keep track
16:42
Speaker 1: of to run your simulation? That's the quantum state of
16:46
Speaker 1: a particle. I see. Well, I'm not sure how many
16:48
Speaker 1: people out there know how to program, but I think
16:52
Speaker 1: maybe it's sort of like a list that identifies everything
16:55
Speaker 1: that we know about a particle. That's kind of what
16:58
Speaker 1: you're saying, right, And so for small particles that list
17:01
Speaker 1: it's not like an infinite list, right, Like it's a
17:03
Speaker 1: list of maybe like five things exactly. It depends a
17:05
Speaker 1: little bit on where that particle is. An electron in
17:08
Speaker 1: free space doesn't have energy levels the way an electron
17:11
Speaker 1: around a hydrogen atom does. Wait, what it depends on
17:15
Speaker 1: the situation. So like, if I have just have a
17:16
Speaker 1: particle out there in space by itself, what are its
17:19
Speaker 1: quantum state variables? A particle just out there in space
17:22
Speaker 1: with like no potential, no forces on anything, a free particle,
17:26
Speaker 1: then the quantum states are just the location and the
17:29
Speaker 1: energy and the energy. What do you mean by energy, Well,
17:31
Speaker 1: it's velocity, right, it's kinetic energy, and it's spin as well. Yes, absolutely,
17:36
Speaker 1: and it's spin. But remember out there in free space,
17:39
Speaker 1: the kinetic energy can have any value. Electrons are quantized
17:43
Speaker 1: into energy levels around a hydrogen atom because they're confined.
17:47
Speaker 1: The quantization only comes from the confinement. Electrons at in
17:50
Speaker 1: free space don't have like energy levels, whereas electrons around
17:53
Speaker 1: a hydrogen atom, for example, do. So there's an important
17:56
Speaker 1: distinction there about the quantum state of these particles. Are space,
18:00
Speaker 1: you would just say the energy around the hydrogenontom, you
18:03
Speaker 1: would say the energy level. But when it's out in
18:05
Speaker 1: space you also count like the spin of it too, Right,
18:07
Speaker 1: are there any other quantum variables? I guess each kind
18:10
Speaker 1: of particle has different kind of variables attached to it. Yeah, exactly.
18:13
Speaker 1: And electrons can have two different kinds of spin, spin
18:16
Speaker 1: up and spin down. Photons can have three different kinds
18:19
Speaker 1: of spin. The Higgs boson doesn't have any spin at all,
18:22
Speaker 1: So it depends a little bit on a kind of
18:24
Speaker 1: particle and also the situation that it's in. Okay, So
18:26
Speaker 1: now the rule here is that no two particles can
18:30
Speaker 1: have the same quantum state. Now what does that mean
18:33
Speaker 1: for like particles out there in the open floating around
18:35
Speaker 1: space like that means that no two electrons can be
18:38
Speaker 1: in the same spot with the same velocity in the
18:41
Speaker 1: same spin. So the rules not that no, two particles
18:44
Speaker 1: can be in the same state, but no, two fermions number.
18:46
Speaker 1: Half of the particles we call them fermions, they can't
18:49
Speaker 1: be in the same state. The other half we call
18:51
Speaker 1: them bosons. They have no problem being in the same state.
18:54
Speaker 1: So electrons and quarks they can't pile up on top
18:57
Speaker 1: of each other in the same state, whereas photons can.
19:00
Speaker 1: Question is, like, what happens out there in empty space? Well, yeah,
19:02
Speaker 1: two electrons cannot be in the same state, meaning it
19:05
Speaker 1: can't be in the same location with the same spin
19:07
Speaker 1: and the same energy. That's just not possible. Well that's interesting,
19:10
Speaker 1: Like that just seems to be like a rule the
19:13
Speaker 1: universe has, right, Like that's something that you think can't happen.
19:17
Speaker 1: But I guess is anyone actually tried to see if
19:19
Speaker 1: you can fit to electrons in the same spot. Oh yeah,
19:22
Speaker 1: the universe tries to do it all the time. Remember,
19:24
Speaker 1: the universe likes to have things relax down to the
19:27
Speaker 1: lowest energy. That's really what forces are. Forces are things
19:30
Speaker 1: that push things down to lower energy configurations. So think
19:33
Speaker 1: about what happens when you put electrons around an atom, Right,
19:37
Speaker 1: the first one goes down to the lost energy level,
19:39
Speaker 1: and then the second one can't go down to the
19:41
Speaker 1: lost energy level because that's filled. Right. It's sort of
19:44
Speaker 1: like playing connect for you put one piece in, the
19:46
Speaker 1: next one can't slot into that lowest level anymore. It
19:49
Speaker 1: has to go to energy level two. I guess I'm
19:51
Speaker 1: trying to understand like this rule on the free space
19:55
Speaker 1: situation first, and then maybe we can get into the
19:58
Speaker 1: going around an atom situation and after that because like electrons,
20:02
Speaker 1: for example, don't have a volume to them, right, they
20:04
Speaker 1: don't have a solidness to them. So technically, like you
20:07
Speaker 1: could have an electron on top of another electron, but
20:10
Speaker 1: you're saying the universe somehow, for some reason, doesn't like that. Yeah. Well,
20:13
Speaker 1: I think the free space example is a little artificial
20:15
Speaker 1: because you bring two electrons together, they will have a
20:18
Speaker 1: force between them. They will try to repel each other,
20:20
Speaker 1: so they're no longer free electrons, right, So that examples
20:23
Speaker 1: a little bit artificial. I think you know, out in space,
20:27
Speaker 1: the universe does try to compress electrons down into tiny dots.
20:30
Speaker 1: We'll talk later about what happens. For example, in white dwarfs.
20:34
Speaker 1: White dwarfs don't collapse into black holes because the electrons
20:37
Speaker 1: resist being put on top of each other, and the
20:40
Speaker 1: forces are strong enough to overcome this electrostatic repulsion, but
20:43
Speaker 1: they're not strong enough to overcome this quantum resistance to
20:46
Speaker 1: electrons being on top of each other. But it's not
20:49
Speaker 1: exactly out in free space, because again, electrons on top
20:52
Speaker 1: of each other there are pushing away against each other.
20:54
Speaker 1: There is potential energy there. I guess I think that
20:58
Speaker 1: let's talk about two electrons out there in free space,
21:00
Speaker 1: and I know they repel each other by the electromagnetic
21:03
Speaker 1: force because they're both the same charge. But let's say
21:05
Speaker 1: you manage to overcome that. You're saying, like, there's something
21:08
Speaker 1: else pushing these two electrons from being on top of
21:11
Speaker 1: each other. Yes, exactly. The universe will not allow you
21:14
Speaker 1: to do that, will not allow you to put two
21:16
Speaker 1: electrons right on top of each other because of this
21:18
Speaker 1: weird exclusion principle. And again, two photons and no problem,
21:21
Speaker 1: even two W bosons, which do have a charge, right,
21:24
Speaker 1: so they would resist each other to W boson's no
21:27
Speaker 1: problem to electrons problem. Interesting. Okay, so you can put
21:31
Speaker 1: two photons and two of each other, and you can't
21:33
Speaker 1: put to W bosons on the top of each other,
21:36
Speaker 1: even though like the w boson they have mass. Right,
21:39
Speaker 1: so even things with substance skin exists on top of
21:41
Speaker 1: each other. But somehow electrons that's a no go. Yeah, exactly,
21:45
Speaker 1: And is there a reason why. There's definitely a reason why,
21:48
Speaker 1: and it's connected to the particles spin. Electrons have spin
21:52
Speaker 1: one half, and photons and ws and zs have spin
21:55
Speaker 1: one and so there's a fun and subtle reason for why.
21:58
Speaker 1: That means they can't be on top of each other.
22:00
Speaker 1: All right, well, let's spin into that answer and figure
22:03
Speaker 1: out where exactly this rule comes from and how does
22:06
Speaker 1: it impact the rest of the universe. But first, let's
22:09
Speaker 1: take a quick break. All right, we're talking about the
22:25
Speaker 1: intricate rules of the quantum universe, and one of those
22:28
Speaker 1: rules is that two fermions can't be in the same
22:31
Speaker 1: quantum state at the same time. Somehow the universe has
22:35
Speaker 1: a problem with two fermions to matter particles. Tohow, I guess,
22:40
Speaker 1: I don't know, being in sync, being in the same
22:42
Speaker 1: place at the same time, and being totally identical. Yeah, exactly.
22:45
Speaker 1: It has an issue with fermions having essentially the identical
22:49
Speaker 1: setup is not allowed. It's like one per slot. You
22:53
Speaker 1: already filled your slot. You got to go to the
22:55
Speaker 1: next slot. You've got to find another way to be
22:57
Speaker 1: I guess for the idea of too electrons out in space, like,
23:01
Speaker 1: it's probably, first of all, very hard for two electrons
23:03
Speaker 1: to be in exactly the same space, but it seems
23:06
Speaker 1: like the universe just resists two electrons being really close
23:10
Speaker 1: to each other. Even Yeah, if you have some volume
23:12
Speaker 1: out there and then a bunch of electrons, then the
23:15
Speaker 1: universe likes each electron to be like in its own
23:17
Speaker 1: little volume, you know, like v over end something like that,
23:21
Speaker 1: and so it resists electrons overlapping too much. Oh, so
23:26
Speaker 1: the rule is more like it can be in the
23:28
Speaker 1: same state, but also like the universe doesn't even like
23:31
Speaker 1: for the states to be close to each other. Yeah, exactly,
23:34
Speaker 1: because remember, electrons have like a wavelength, and so as
23:37
Speaker 1: those wavelengths start to overlap, then the universe resists it. Technically,
23:41
Speaker 1: if you keep squeezing, it'll let them get closer and
23:43
Speaker 1: closer and closer, but fundamentally it resists them being right
23:46
Speaker 1: on top of each other. Okay, so the universe has
23:48
Speaker 1: has this problem for emeons apparently, and the weight kind
23:51
Speaker 1: of comes into effect that affects most people is as
23:55
Speaker 1: you were saying, when electrons start to orbit around the
23:59
Speaker 1: new of atoms, right exactly, And this has a huge
24:03
Speaker 1: effect on basically all of matter. Right. It's the reason
24:06
Speaker 1: that we have energy levels in atoms. It's a reason
24:08
Speaker 1: why we have the periodic table. It's a reason why
24:10
Speaker 1: atoms behave the way they do. The universe would be
24:13
Speaker 1: totally different if electrons could all like slot down to
24:16
Speaker 1: the lowest energy level. Now what I said earlier wasn't
24:19
Speaker 1: exactly correct. It was one little nuance, which is you
24:22
Speaker 1: can't have two electrons per energy level because they can
24:24
Speaker 1: have different spins, but the er electrons have to be
24:27
Speaker 1: in different states. So you can have like one electron
24:30
Speaker 1: around a hydrogenom no problem. For helium. You have two electrons.
24:34
Speaker 1: They can both be in the lowest energy level, but
24:36
Speaker 1: they have to have different spins because they can't be
24:38
Speaker 1: in the same state. Then when you go to lithium
24:41
Speaker 1: you have another electron. They can't fit in that lowest
24:43
Speaker 1: energy level. There's already two electrons in there, one spin up,
24:46
Speaker 1: one spin down. There's no other way to separate the electrons.
24:49
Speaker 1: There's no other label to distinguish it, so it has
24:52
Speaker 1: to go in the next energy level, goes in the
24:54
Speaker 1: second energy level, so that electron has more energy than
24:57
Speaker 1: the lowest level. Well, I guess I just wonder how
24:59
Speaker 1: many people out there are familiar with this idea of
25:02
Speaker 1: energy levels in electrons orbiting the nuclei of atoms. Maybe
25:07
Speaker 1: can you connect for us this idea of like, Okay,
25:10
Speaker 1: two electrons in space can't be in the same quantum state.
25:14
Speaker 1: They can to be one on top of each other.
25:16
Speaker 1: But now you know, if they're orbiting around the nucleus
25:19
Speaker 1: of an atom, I feel like there's a budge of
25:21
Speaker 1: space there. Why can't they kind of orbit at the
25:24
Speaker 1: same time. What does this mean about the energy levels? Well,
25:27
Speaker 1: if you have an electron and it's around a nucleus,
25:29
Speaker 1: you've already confined it to a very small space, right,
25:32
Speaker 1: And so in order to have two electrons basically being
25:35
Speaker 1: on top of each other from the point of view
25:36
Speaker 1: of the universe, those two electrons are on top of
25:38
Speaker 1: each other. If they're orbiting the same nucleus, they have
25:41
Speaker 1: to have some way to distinguish between themselves so they're
25:43
Speaker 1: not in the same state. As that means having different
25:45
Speaker 1: spin or having different energy, and around an atom, you
25:49
Speaker 1: can't just have any arbitrary energy out in free space.
25:52
Speaker 1: An electron can have any energy at once. When an
25:54
Speaker 1: electron is captured by a nucleus, when it's in some
25:57
Speaker 1: quantum state that's settled into the potential around an then
26:00
Speaker 1: it has certain energy levels it can be in that quantization.
26:04
Speaker 1: The fact you have an energy ladder rather than a
26:06
Speaker 1: full continuous spectrum comes from capturing the electron. It's the
26:10
Speaker 1: confinement that produces those energy levels. And so now instead
26:14
Speaker 1: of like being able to have two electrons with slightly
26:16
Speaker 1: different energy, now the electrons have like discrete options energy
26:20
Speaker 1: level one, energy level two, energy level seven. You can't
26:23
Speaker 1: have energy like one point two around the atom. It's
26:26
Speaker 1: not a solution to the Shortinger equation, is it. I
26:28
Speaker 1: wonder if it's a little bit like the Earth orbiting
26:30
Speaker 1: the Sun. Like you know, if Earth is out there
26:33
Speaker 1: in space, it can go as fast as it once
26:35
Speaker 1: in any direction at once. But if you're sort of
26:37
Speaker 1: requiring the Earth to go around the Sun and do
26:41
Speaker 1: it forever in a consistent way, there's only so many
26:44
Speaker 1: velocities it can have. Any's only so many energy levels
26:48
Speaker 1: it can have well, but gravity isn't quantized to our knowledge,
26:50
Speaker 1: like we think maybe eventually we will quantize gravity. So
26:53
Speaker 1: the Earth could exist at any radius around the Sun.
26:56
Speaker 1: It just has to have the right velocity. And so
26:59
Speaker 1: there is an infinite number of potential orbits for the Earth,
27:02
Speaker 1: whereas for a quantum object it really is different. It's
27:05
Speaker 1: determined by the shortening your equation, and they're just are
27:08
Speaker 1: quantized solutions to that. Okay, so now we've applied the
27:12
Speaker 1: rule to electrons orbiting in nuclei, and that tells you
27:16
Speaker 1: that two fermions can orbit at the same level unless
27:19
Speaker 1: they have a different spin. Exactly why is that? What
27:23
Speaker 1: does the spend that lets them occupy the same orbit?
27:26
Speaker 1: So the key thing is that they have to have
27:29
Speaker 1: different quantum states, and the spin is part of that
27:32
Speaker 1: quantum state. It's like one of the labels. So when
27:34
Speaker 1: you have electrons around an atom, you have four of
27:36
Speaker 1: these labels. You have N which tells you the energy
27:39
Speaker 1: level you have, L, which tells you like the sub
27:42
Speaker 1: level that you're in, and which tells you which of
27:44
Speaker 1: those ls you're in, and then finally the spin. And
27:47
Speaker 1: so the spin place two rolls one is like, it's
27:49
Speaker 1: another quality that the electron can have that lets it
27:51
Speaker 1: distinguish itself from something else. But also the electron having
27:55
Speaker 1: spin one half is the reason why electrons cannot do this.
28:00
Speaker 1: Photons have spin one which is why they can pile
28:02
Speaker 1: on top of each other, and electrons have spin one half,
28:05
Speaker 1: which is why they cannot pile on top of each other.
28:08
Speaker 1: It all comes down to these particles spin well before
28:14
Speaker 1: we spend that way. I guess maybe it tells a
28:16
Speaker 1: little bit about what would happen if we didn't have
28:18
Speaker 1: this rule, Like if we didn't have the poly exclusion principle,
28:22
Speaker 1: what would happen to like electron orbitals and atoms and
28:26
Speaker 1: the things the molecules in our body. So if we
28:28
Speaker 1: didn't have this, then electrons would all relax down to
28:30
Speaker 1: the lowest state. There would all be in the lowest
28:33
Speaker 1: energy level, because that's what the universe likes to do.
28:35
Speaker 1: It likes to spread energy out. It doesn't like to
28:37
Speaker 1: have little dense depositions of energy. So for example, if
28:40
Speaker 1: you zap an electron and you give it extra energy,
28:43
Speaker 1: so it jumps up the ladder to like you know,
28:45
Speaker 1: energy level ten, and you just wet a few moments,
28:47
Speaker 1: then it will radiate a way that energy and relax
28:50
Speaker 1: back down. So everything likes to sort of flow downhill
28:53
Speaker 1: to the lowest energy levels. And if you didn't have
28:56
Speaker 1: the poly exclusion principle, they would all just pile up
28:59
Speaker 1: at the lowest energy level, and that would make a
29:01
Speaker 1: big difference for like the size of these atoms. You know,
29:05
Speaker 1: the size of the atom is determined by the electron orbitals,
29:08
Speaker 1: and they get bigger and bigger and bigger as you
29:11
Speaker 1: get more and more electrons. Gold, for example, has like,
29:14
Speaker 1: you know, dozens of electrons, and so it's much larger
29:17
Speaker 1: than hydrogen. Hygen just has one electron, and so, like,
29:21
Speaker 1: the very structure of matter depends on the volume of
29:23
Speaker 1: these atoms. If somebody like turned off the poly exclusion principle,
29:27
Speaker 1: we would all collapse to be much much smaller. You mean,
29:30
Speaker 1: we would all go into the quadic realm, and man, no,
29:34
Speaker 1: we'd all be about the size of a chocolate chip,
29:36
Speaker 1: I think. But also it would change chemistry, right, The
29:39
Speaker 1: way that atoms bond together depends on these orbitals, the
29:42
Speaker 1: way that they interact all their properties, like how they're
29:45
Speaker 1: metallic or how they glow, the energy they can absorb
29:48
Speaker 1: all of this stuff depends on the poly exclusion principle,
29:51
Speaker 1: and so the whole universe would be totally different if
29:54
Speaker 1: electrons could pile up at the lowest levels. Okay, I
29:57
Speaker 1: think I see what you're saying. Like, if I just
29:59
Speaker 1: have the nuclear of an atom without any electrons, just
30:03
Speaker 1: sitting there, and I threw an electron into it, it
30:05
Speaker 1: would kind of snap into a certain orbit or kind
30:09
Speaker 1: of place or some sort of you know, cloud or
30:11
Speaker 1: function around that nucleus. Now, if I threw another electron,
30:15
Speaker 1: if he didn't have the poly exclusion principle, it would
30:18
Speaker 1: also fall into that lowest kind of orbit. But because
30:21
Speaker 1: you have the inclusion principle, the electron can't like get
30:25
Speaker 1: that close to the nucleus, and so it kind of
30:27
Speaker 1: forms another kind of orbit that is kind of maybe bigger,
30:31
Speaker 1: you mean, maybe bigger and more fragile too, Yeah, exactly.
30:35
Speaker 1: Then that controls the volume of the atom, but also
30:37
Speaker 1: controls how these things operate, you know, how they build
30:40
Speaker 1: themselves into crystals and then how electrons can flow through
30:44
Speaker 1: those crystals. Like why are metals conductors Because they have
30:47
Speaker 1: a bunch of electrons in this conduction band they're forced
30:50
Speaker 1: to be up there in their higher energy level bands
30:52
Speaker 1: flowing around semiconductors for the same reason. So the reason
30:56
Speaker 1: we have all these complex structures and complex behavior, periodic
31:00
Speaker 1: table and all that interesting chemistry comes from electron orbitals,
31:04
Speaker 1: which only are interesting because electrons populate them, and they
31:08
Speaker 1: only do that because of the Pauly exclusion principle. Otherwise
31:12
Speaker 1: they would always just be in the lowest energy level. Interesting.
31:15
Speaker 1: Now that we know what it is, let's maybe dig
31:17
Speaker 1: into the reason. Why Why does it have an issue
31:19
Speaker 1: with two fermions being on top of each other, Like
31:22
Speaker 1: it doesn't seem to have a problem with some of
31:24
Speaker 1: the other particles like the Higgs boson or photons or
31:27
Speaker 1: w particles being at each other. Why does it have
31:31
Speaker 1: this bias against electrons? Court, don't be so negative about it.
31:36
Speaker 1: You know, maybe you could think about it like a
31:38
Speaker 1: special property. You know, the electrons can like stand on
31:41
Speaker 1: top of each other to achieve things electrons could otherwise
31:44
Speaker 1: never do. Right, It's like an ability instead of a bias.
31:47
Speaker 1: I feel like the word exclusion is never good. That's true,
31:52
Speaker 1: everyone should be as inclusive as possible. Well, the issue
31:55
Speaker 1: really does have to do with the quantum nature of
31:57
Speaker 1: these things. So fermions, electrons, and even protons which are
32:01
Speaker 1: built out of quarks. These things have a really weird
32:03
Speaker 1: property that we've never seen in classical physics, and it
32:07
Speaker 1: has to do with what happens when you swap two
32:09
Speaker 1: of them. So imagine just you have two particles, particle
32:12
Speaker 1: one and particle two, and maybe they're in different states.
32:16
Speaker 1: You call one state A and one state B. Doesn't
32:18
Speaker 1: really matter. Now, imagine what happens if you swap them. Right,
32:21
Speaker 1: you take particle one, which used to be in state A,
32:23
Speaker 1: and I say, now you're in state B. In particle two,
32:26
Speaker 1: which used to be in state B, and say now
32:27
Speaker 1: you're in state A. All right. And so you have
32:30
Speaker 1: two particles and you sort of swap their arrangements. The
32:33
Speaker 1: universe says, and quantum mechanics says that when you do that,
32:37
Speaker 1: the wave function that describes what happens and tells you
32:40
Speaker 1: what's allowed, that wave function gets a negative sign, and
32:42
Speaker 1: that doesn't happen for bosons. For bosons, the wave function
32:45
Speaker 1: doesn't get a negative sign, and that has really really
32:48
Speaker 1: important consequences. I think you're talking about like a mathematical operation,
32:52
Speaker 1: or are you talking about like if I physically take
32:55
Speaker 1: two particles and I swapped their states mathematically the sign
32:59
Speaker 1: of the whole how the two particles somehow gets a negative.
33:03
Speaker 1: Is that kind of what you think? Yeah, we're talking
33:04
Speaker 1: about the wave function, which is like the thing that
33:07
Speaker 1: determines what happens. Right. Remember, you take the wave function
33:10
Speaker 1: and you square it, and that tells you the probability
33:13
Speaker 1: of various things happening. If you're talking about like Shortinger's cat,
33:16
Speaker 1: there's a wave function for it to be alive and
33:18
Speaker 1: a wave function for it to be dead. Those are
33:20
Speaker 1: two different possible outcomes, And the way that you've discover
33:23
Speaker 1: the probability of one versus the other is you take
33:25
Speaker 1: the wave function for that outcome and you square it.
33:28
Speaker 1: That's the rule. Now, a wave function is like a
33:31
Speaker 1: mathematical concept or construct that describes what something is doing
33:36
Speaker 1: or going to do. Yeah, it's the solution to the
33:38
Speaker 1: Shortinger equation. That doesn't help me. We don't really know
33:41
Speaker 1: what the way function is. It's problematic philosophically, like it's
33:44
Speaker 1: a part of our calculations. We use it to make predictions.
33:48
Speaker 1: Nobody really knows, like, is the wave function a real
33:51
Speaker 1: thing out there in the universe or is it just
33:52
Speaker 1: sort of like something in our heads. That's an intermediate
33:55
Speaker 1: step that we are using, but it definitely seems to
33:58
Speaker 1: be important, and it's part of the way we think
34:00
Speaker 1: about quantum physics. Like maybe if you have a baseball
34:02
Speaker 1: and you're throwing a baseball, you might describe it using
34:05
Speaker 1: a vector, like a vector from here from the pitcher
34:09
Speaker 1: to the baseball that describes the ball. Wave function is
34:12
Speaker 1: kind of like that for quantum particles, right, yeah, exactly.
34:15
Speaker 1: And the wave function is weird because it can also
34:18
Speaker 1: be negative, and it can also be like complex, right,
34:21
Speaker 1: it can have imaginary numbers like one plus two I. Right.
34:25
Speaker 1: The wave function is really weird. It's not physical in
34:27
Speaker 1: that way. But the interesting thing is that that all
34:30
Speaker 1: goes away usually when you use the wave function to
34:33
Speaker 1: make a prediction, because they square it and the imaginary
34:35
Speaker 1: parts go away and the negative signs go away. Nobody
34:37
Speaker 1: really cares about the wave function being negative usually, but
34:40
Speaker 1: in this one particular case it turns out to be
34:42
Speaker 1: weirdly really important because what happens if you have two
34:45
Speaker 1: fermions which are identical like two electrons, and they're in
34:48
Speaker 1: exactly the same state. Maybe they're both around a hydrogen
34:51
Speaker 1: atom and they're in the same energy level and they
34:53
Speaker 1: have all the same spin. Right, now, what happens, Well,
34:56
Speaker 1: take those two particles, particle one particle two. They're interesting, right,
35:00
Speaker 1: They're in the same state, and you swap them, right,
35:03
Speaker 1: swap them from one to the other. Now, really that
35:06
Speaker 1: has no effect because you had two identical particles in
35:09
Speaker 1: the same state, you swap them, nothing should change. But
35:12
Speaker 1: the universe says if you do that, you get a
35:14
Speaker 1: negative sign for the wave function. You mean, swap them,
35:17
Speaker 1: like pick them up and change their you know, like
35:20
Speaker 1: move them around, like swap their positions, or swap them hypothetically,
35:24
Speaker 1: like ask what would the wave function be if this
35:27
Speaker 1: particle was over here and that particle was over there.
35:29
Speaker 1: Don't actually do it, you just say, like, hypothetically, what
35:32
Speaker 1: would the wave function be if you had them in
35:33
Speaker 1: the opposite configuration? But they're the same configuration. Well, they're
35:37
Speaker 1: in the same state, but one of them has this
35:38
Speaker 1: label one. You know, one of them is particle one
35:40
Speaker 1: and one of them is particle two. Though they're in
35:42
Speaker 1: the same state, so you can't really distinguish them. Right,
35:44
Speaker 1: they're identical. They have the same orbit, the same spin,
35:47
Speaker 1: everything is the same, and if you swap them, as
35:49
Speaker 1: you're imagining, nothing changes because they're the same particle in
35:52
Speaker 1: the same state, so it should be the same. But
35:54
Speaker 1: the universe says, well, the wave function has to get
35:57
Speaker 1: a negative sign if you do this for fermions. So
35:59
Speaker 1: the only way to satisfy both of those requirements to say, well,
36:02
Speaker 1: it has to be the same if you swap them,
36:04
Speaker 1: and it has to get a negative sign if you
36:06
Speaker 1: swap them is for the way function to be zero.
36:09
Speaker 1: So if the way function is zero, then when you
36:11
Speaker 1: swap it, zero is negative zero. It's the only number
36:14
Speaker 1: that is its own negative, and so from that you
36:17
Speaker 1: can conclude that this is impossible. The universe just doesn't
36:20
Speaker 1: do this. The wave function for two fermions being in
36:22
Speaker 1: the same state is always zero. That way, it can
36:25
Speaker 1: satisfy both rules that swapping two identical particles doesn't change
36:29
Speaker 1: anything and that the wave function gets a negative sign.
36:32
Speaker 1: And you're saying earlier that this is because of their spin,
36:35
Speaker 1: Like if because they have a certain spin when you
36:38
Speaker 1: try to do this swapping, then some weird things happen
36:41
Speaker 1: exactly because this doesn't happen for particles of a different spin,
36:44
Speaker 1: like with photons, not an issue. Photons, the universe says, yeah,
36:48
Speaker 1: if you have two photons in the same state and
36:50
Speaker 1: you swap them, you don't get a negative sign. It
36:53
Speaker 1: only happens for fermions. And it's that negative sign that
36:56
Speaker 1: makes this impossible. It's a negative sign, which is why
36:59
Speaker 1: fermions can't be in the same state and bosons the
37:02
Speaker 1: universe doesn't have a problem with and it just operates
37:05
Speaker 1: differently on bosons than it does on fermions. Then you
37:08
Speaker 1: might ask, well, like, where does that negative sign come from?
37:11
Speaker 1: Why do fermions get a negative sign when you swap them.
37:14
Speaker 1: That's weird, right, Like why should you get a negative sign?
37:17
Speaker 1: You're just swapping two identical particles, it's basically the same setup.
37:20
Speaker 1: Why would you expect the wave function to be the opposite?
37:23
Speaker 1: And this is the weird thing that these quantum fermons
37:26
Speaker 1: can do that classical particles can't do. There's like no
37:30
Speaker 1: classical analog to this. There's no example in the natural
37:34
Speaker 1: world that you can think about with baseballs or coffee
37:36
Speaker 1: cups that is like this. It's most closely connected to
37:40
Speaker 1: rotating things, like if you take your coffee cup and
37:43
Speaker 1: you spin it around three hundred and sixty degrees, it's
37:46
Speaker 1: the same coffee cup. That makes sense, right, And the
37:48
Speaker 1: same thing is true for photons. If you take photons
37:51
Speaker 1: and you rotate them by three hundred and sixty degrees,
37:53
Speaker 1: you get the same photon. Electrons don't do that. Electrons,
37:57
Speaker 1: if you rotate them by three hundred and sixty degrees,
37:59
Speaker 1: you get the negative wavefunction than the original electron. So
38:03
Speaker 1: there's something weird and different about fermions that picks up
38:06
Speaker 1: this extra negative sign that's very different from anything we
38:09
Speaker 1: know about before. And you said it has to do
38:11
Speaker 1: with the quantum spin, but I guess don't some other
38:14
Speaker 1: fermions have no spin? Or do all fermions all of
38:18
Speaker 1: these matter particles have spin, and do they have the
38:20
Speaker 1: same spin? And that's why they have this rule against them? Exactly,
38:24
Speaker 1: all fermions have the same spin. They all have spin
38:27
Speaker 1: one half. And that's sort of what it means to
38:29
Speaker 1: be a fermion. I mean, some people say, no, fermions
38:32
Speaker 1: are things that do this that don't overlap with each other.
38:35
Speaker 1: They follow the poll exclusion principle, and it's because they
38:37
Speaker 1: have spin one half. Other people say, no, fermions are
38:41
Speaker 1: all particles that have spin one half. But it's the
38:43
Speaker 1: spin one half that makes them do this. And it's
38:47
Speaker 1: too mathematical to explain, but if you like dig into
38:49
Speaker 1: the quantum field theory, this comes out of that mathematics
38:52
Speaker 1: or the quantum field theory. The particles that have fields
38:55
Speaker 1: that have spined one half, when you rotate them, you
38:58
Speaker 1: get this extras sign, or when you swam them, you
39:00
Speaker 1: get this extra minus sign. It's called the spin statistics theorem.
39:03
Speaker 1: And that's fundamentally where this comes from. So it's the
39:07
Speaker 1: one half spin nature of these particles that means that
39:10
Speaker 1: they can't pile up on top of each other, whereas
39:12
Speaker 1: particles with spin one or spin two could totally pile
39:15
Speaker 1: up on top of each other and be in the
39:17
Speaker 1: same quantum state no problem. Or I'm getting the sense
39:20
Speaker 1: that maybe you gave him spin one half because they
39:23
Speaker 1: can't be in the same place at the same time,
39:26
Speaker 1: you know what I mean, Like, like, which game for
39:30
Speaker 1: is the chicken or the egg? The spin or or
39:32
Speaker 1: the exclusion principle? Oh, that's a great question. Actually, this
39:35
Speaker 1: is how electron spin was discovered, That's what I mean. Yes, no, absolutely,
39:40
Speaker 1: this is why spin was invented to explain this, right,
39:44
Speaker 1: and the story is actually really fun. People were looking
39:47
Speaker 1: at electron orbitals back in their early days, like nineteen
39:49
Speaker 1: thirties and trying to understand why the electrons filled up
39:52
Speaker 1: the orbitals the way they did, and they had this
39:55
Speaker 1: idea of the exclusion principle, but they didn't understand, like,
39:57
Speaker 1: why you could have two electrons in the lowest level,
40:00
Speaker 1: what's going on? And in the next level, why could
40:03
Speaker 1: you have eight instead of four? There was this weird
40:05
Speaker 1: factor of two that nobody could explain, and Paully wrote
40:09
Speaker 1: a letter to some other physicists about it, and he
40:11
Speaker 1: said that electrons have a two valuedness, not describable classically.
40:17
Speaker 1: He just meant like they have some physical property that
40:20
Speaker 1: has two options, like an up and a down, or
40:22
Speaker 1: a zero and a one, or you know, a switch
40:25
Speaker 1: that you could flip. There's something else about the electrons
40:28
Speaker 1: that let them distinguish each other, so you can have
40:30
Speaker 1: two of them in the lowest energy level. That's how
40:33
Speaker 1: we discovered that electrons actually do have spin, or at
40:36
Speaker 1: least you called spin, because you quite have another name
40:40
Speaker 1: for it. Right. To explain this phenomenon exactly. And there
40:43
Speaker 1: was two young Dutch physicists, Gaussmidt and Uhlenbeck, who read
40:47
Speaker 1: this letter from Pauli and they were like, oh, wait,
40:50
Speaker 1: maybe electrons are spinning. So they did a bunch of
40:52
Speaker 1: calculations and they're like, oh, electrons are spinning. This is
40:55
Speaker 1: really awesome. And they wrote this paper and they sent
40:57
Speaker 1: it off and then they showed it to another famous
40:59
Speaker 1: Dutch physicist, Lorenz, and Lorenz was like, y'all are totally wrong.
41:02
Speaker 1: Electrons can't spin. Their services would be moving faster than
41:06
Speaker 1: the speed of light. So then they realized, oh my gosh,
41:08
Speaker 1: our paper was wrong, and they try to retract it,
41:10
Speaker 1: but it was too late. It had already been published.
41:13
Speaker 1: And then it turns out that electrons do spin, but
41:16
Speaker 1: not in the way that they expected. They have this
41:18
Speaker 1: weird property quantum spin, which is not spin in the
41:22
Speaker 1: same way that like a baseball spins. It's some other
41:25
Speaker 1: weird kind of angular momentum. So the history of like
41:27
Speaker 1: the discovery of electron spin is pretty funny. Oh Man,
41:31
Speaker 1: particle physics are pretty catty. That we're short. Anger's cat
41:35
Speaker 1: came from exactly what. I love this story of two
41:38
Speaker 1: guys inventing spin for the wrong reasons trying to retract
41:41
Speaker 1: it and then ended up being right, sort of accidentally interesting.
41:44
Speaker 1: All right, Well, the universe us to have this rule,
41:47
Speaker 1: and it seems to be embedded in some of the
41:50
Speaker 1: mathematics that maybe makes the universe works. Let's talk about
41:54
Speaker 1: that Thorney philosophical question and also some of the consequences
41:58
Speaker 1: of this poly exclusion inciple on the rest of the universe.
42:01
Speaker 1: But first, let's take another quick break. All right, we're
42:16
Speaker 1: talking about the question of why can't two fermions be
42:19
Speaker 1: in the same quantum state? And what this means is
42:22
Speaker 1: that no two electrons or no two quarks can be
42:25
Speaker 1: kind of on top of each other, not out there
42:28
Speaker 1: in free space and not orbiting around an atom, which
42:31
Speaker 1: is what gives us the wonderful chemistry that makes us
42:35
Speaker 1: who we are. And we talked a little bit about that.
42:37
Speaker 1: The reason that two fermions or two electrons or two
42:40
Speaker 1: quarks can't do this is because it messes up the math.
42:44
Speaker 1: Now my question is, like, does that mean that the
42:46
Speaker 1: universe is mathematical? Like does the universe care about math?
42:50
Speaker 1: Like why does the universe care about math? Like? If
42:53
Speaker 1: I were the universe, I'd be like, I'm the universe.
42:55
Speaker 1: I don't care about math. Peoples two equals five? Why not? Well,
43:00
Speaker 1: I don't know, but it seems like the universe does
43:03
Speaker 1: follow mathematical laws, and the universe is self consistent, right,
43:07
Speaker 1: the universe doesn't have like two things going on at
43:09
Speaker 1: the same time or things that contradict each other. So
43:12
Speaker 1: it might just be that you can have lots of
43:14
Speaker 1: different universes out there, but only the ones that are
43:16
Speaker 1: self consistent that follow mathematical laws are the ones where
43:19
Speaker 1: you have, like people evolved with brains that to make
43:22
Speaker 1: sense of these things and study them. So we don't
43:26
Speaker 1: really understand it, but our universe does seem to follow
43:29
Speaker 1: mathematical laws, and when you find a mathematical principle, it
43:32
Speaker 1: seems to manifest itself in nature. Right. What we're talking
43:35
Speaker 1: about are the laws of how quantum feels operate, how
43:38
Speaker 1: they wiggle, how they transfer energy between them, the rules
43:42
Speaker 1: that they follow, and those rules seem to have like
43:44
Speaker 1: consequences way down the line that affect us and ice
43:49
Speaker 1: cream and stars. I guess what's kind of weird is
43:53
Speaker 1: that I'm sure math has a bunch of other rules
43:56
Speaker 1: that it likes to do it doesn't like you do.
44:00
Speaker 1: But maybe not all of them are represented in a
44:03
Speaker 1: physical thing, right, Like not all of them have a
44:06
Speaker 1: physical manifestation of those principles. But this is a case
44:09
Speaker 1: where you know, you have something that doesn't work in
44:11
Speaker 1: the math and it actually has like a physical, a tangible,
44:18
Speaker 1: you know, solid representation of that math. Yeah, exactly. It's
44:21
Speaker 1: certainly true that there are more sort of mental universes
44:24
Speaker 1: in mathematics than exist in the physical universe. Like you
44:27
Speaker 1: could dream up all sorts of universes that don't exist
44:30
Speaker 1: out there. But once you think about just our universe,
44:33
Speaker 1: if you think about the mathematical laws that describe it,
44:36
Speaker 1: the universe basically does everything that the math allows. Like
44:40
Speaker 1: if it's possible for an electron to radiate a photon
44:43
Speaker 1: or you know, a Higgs boson or something, it will.
44:46
Speaker 1: So the universe does everything that's mathematically allowed. And so
44:49
Speaker 1: if something is mathematically forbidden, if something doesn't happen, it's
44:52
Speaker 1: probably because it's mathematically forbidden. That's like one way that
44:56
Speaker 1: we figure out what the rules are. We look and
44:58
Speaker 1: we say, how muans don't just turn into electrons sometime?
45:02
Speaker 1: What's going on there? And it turns out there's a
45:04
Speaker 1: mathematical rule that describes why that can't happen. It often
45:09
Speaker 1: reveals some like underlying physical principle, and so that's why
45:12
Speaker 1: it's so fun to find these rules, describe them mathematically,
45:15
Speaker 1: and then step back and think, why is the universe
45:17
Speaker 1: this way? Would it be possible to have a universe
45:19
Speaker 1: without this rule, or is this rule necessary for the
45:22
Speaker 1: universe to like make sense at all? Well, I guess
45:25
Speaker 1: what's weird too, is that, you know, like it I'd
45:27
Speaker 1: be fine if the universe had this rule that said, oh, no,
45:30
Speaker 1: you can't have the two electrons kind of on the
45:32
Speaker 1: same spot at the same time. I'd be like, okay, fine,
45:34
Speaker 1: that never happens. But it's almost like the universe resists
45:38
Speaker 1: even getting close to that possibility. Like if you take
45:41
Speaker 1: as we were talking about earlier, if you take two
45:43
Speaker 1: electrons and you try to squish them together and you
45:46
Speaker 1: can overcome the electromagnetic force that repels them, there's another
45:50
Speaker 1: force almost in the universe that kind of resists that
45:54
Speaker 1: squishing them together. Right, It's like the universe is like
45:57
Speaker 1: kind of freaking out a little bit, like, ah, you're
45:58
Speaker 1: getting close to a logical inconsistency keep those two things away, yeah, exactly.
46:04
Speaker 1: And some listeners have written in to ask about that.
46:07
Speaker 1: They're like, what's the mechanism of that? Which of the
46:10
Speaker 1: forces is the thing that keeps the electrons or being
46:13
Speaker 1: on top of each other because they imagine that like
46:15
Speaker 1: otherwise they would, And so in order to change the
46:18
Speaker 1: direction of electron or something, you need to have some
46:20
Speaker 1: force that operates there. And if you try to read
46:23
Speaker 1: about it, it's a little bit confusing because there is
46:25
Speaker 1: a description of this, like Fermi pressure or this effective
46:29
Speaker 1: force that describes it. But if you think about forces
46:31
Speaker 1: in terms of like the fundamental forces, you know, the
46:34
Speaker 1: weak force, a strong force, the electromagnetic force. This is
46:37
Speaker 1: like an emergent force. This is something that comes out
46:40
Speaker 1: of observing these things and trying to describe the energy
46:43
Speaker 1: levels that they fall into and that they don't fall into. Really,
46:46
Speaker 1: there's no force that's doing this. It's just something the
46:49
Speaker 1: universe doesn't do. Like an electron just can't go there,
46:52
Speaker 1: you know, it's just like not an option for the electron.
46:55
Speaker 1: So is there like some sort of force pushing these
46:58
Speaker 1: two things apart that is working kind of on behalf
47:01
Speaker 1: of the firmi exclusion principle. Is there so as you think,
47:03
Speaker 1: or is it more sort of like a quantum probability
47:06
Speaker 1: or improbability that keeps two things apart. There's not a
47:09
Speaker 1: fundamental force, but they's sort of like an effective force.
47:12
Speaker 1: I mean, think about like having a bunch of electrons
47:15
Speaker 1: and trying to squeeze them down into the same place. Well,
47:18
Speaker 1: what's really going on is that you can't have the
47:21
Speaker 1: electrons in the same state, and so the electrons resist
47:25
Speaker 1: that by having different energies, you know, the same way
47:27
Speaker 1: they're like electrons around a nucleus will fill up the
47:30
Speaker 1: ladder of energies, so some of them have more energy
47:33
Speaker 1: than otherwise. Right, you're trying to squeeze a bunch of
47:35
Speaker 1: electrons down to a tiny little blob. They will resist
47:38
Speaker 1: it because some of them will have higher energy than otherwise,
47:42
Speaker 1: because they're forced into it, forced to stay in those
47:45
Speaker 1: higher energy states because of the ladder. And effectively that
47:48
Speaker 1: means that they're pushing back if they have more energy.
47:51
Speaker 1: They're like bouncing off the walls of your box with
47:54
Speaker 1: more momentum, they're pushing on that box. And so the
47:57
Speaker 1: fact that the electrons can't all go to the lowest state,
48:00
Speaker 1: means they have more energy, which means effectively they're pushing
48:03
Speaker 1: back on you as you try to squeeze them down.
48:06
Speaker 1: So that's like an effective pressure, right. It's not like
48:08
Speaker 1: the electrons are pushing against each other or like there's
48:11
Speaker 1: a force between the electron and the walls of your box.
48:14
Speaker 1: But as you try to squeeze electrons down, you'll notice
48:17
Speaker 1: this effective pressure that wouldn't happen if you did the
48:20
Speaker 1: same thing with photons. Oh, I see what you're saying.
48:22
Speaker 1: It's more like if you try to get an electron
48:26
Speaker 1: to collapse to the lowest possible, for example, orbit around
48:30
Speaker 1: in a nucleus, but there's already an electron there. It's
48:34
Speaker 1: not like the electron pushes back against you to try
48:37
Speaker 1: to collapse it. It's just that the electron doesn't give up.
48:40
Speaker 1: It's the energy that it has. Yeah, Like, in order
48:42
Speaker 1: to squeeze it down to the lowest it needs to
48:45
Speaker 1: give up that energy. But because it can, like, the
48:47
Speaker 1: electron hold onto that energy. And that's basically the same
48:50
Speaker 1: as like pushing back against you exactly, And that's the
48:53
Speaker 1: mechanism for it to push back. And we actually see
48:56
Speaker 1: that happen out there in the universe, and for example,
48:59
Speaker 1: white dwarf worse, are these really really dense blobs of
49:03
Speaker 1: super hot metal if they're left over For at the
49:05
Speaker 1: end point of a star, a star has done all
49:07
Speaker 1: the burning that it can, and it's blown up maybe
49:10
Speaker 1: and left behind its core. They're just sitting there, hot
49:13
Speaker 1: and glowing and eventually cooling down. These things are incredibly
49:17
Speaker 1: dense and the gravity is very very strong. So you
49:20
Speaker 1: might wonder, like, why doesn't the whit dwarf collapse into
49:22
Speaker 1: a black hole? The thing that keeps a star from
49:23
Speaker 1: collapsing into a black hole is that it still has
49:26
Speaker 1: fusion happening. It's like radiating out energy, it's like blowing up.
49:29
Speaker 1: But a white dwarf isn't doing that anymore. So it's
49:31
Speaker 1: just like a blob of mass. Why isn't it collapsing
49:34
Speaker 1: into a black hole? And the answer is electron degeneracy.
49:37
Speaker 1: These electrons resist getting pushed on top of each other,
49:41
Speaker 1: and they prevent this thing from turning into a black hole.
49:43
Speaker 1: They're like one of the last barriers of defense against
49:46
Speaker 1: gravitational collapse. Well, it's pretty cool. Would you say white
49:49
Speaker 1: dwarfs are pretty awesome? Are they more awesome than chocolate dwarfs?
49:53
Speaker 1: I think the fate of the universe is for all
49:55
Speaker 1: the white dwarves to cool down and become black dwarves,
49:58
Speaker 1: which means black dwar are cooler than white dwarfs, just
50:01
Speaker 1: like chocolate is cooler than vanilla. Well, sure, if you
50:04
Speaker 1: leave astro about, nobody wants. Nobody's gonna want to eat
50:06
Speaker 1: that ice cream eventually. But you know, if you add
50:09
Speaker 1: more mass to this white dwarfs, the gravity gets stronger.
50:12
Speaker 1: You can actually overcome this electron degeneracy pressure. And what
50:16
Speaker 1: happens is not that the electrons give up and then
50:18
Speaker 1: like pile on top of each other. They're just not
50:20
Speaker 1: allowed to do that. What happens is the electrons combine
50:23
Speaker 1: with the protons to turn into neutrons, so they give
50:27
Speaker 1: up and become not electrons anymore, and then you can
50:30
Speaker 1: get things a little bit denser. M you mean at
50:33
Speaker 1: some point like they just become pure energy and then
50:36
Speaker 1: they squeeze together. Yeah, well, the proton and the electron
50:39
Speaker 1: together can do like an reverse beta decay and become
50:42
Speaker 1: a neutron, and then you have a neutron star, which
50:45
Speaker 1: is just a big blob of neutrons, and those neutrons
50:48
Speaker 1: get squeezed together by gravity, and the neutrons are also fermions.
50:53
Speaker 1: One of the fascinating things about fermions is it's not
50:55
Speaker 1: just fundamental particles. You can put quarks together in various
50:58
Speaker 1: arrangements to make fermion. So like the proton is a fermion,
51:02
Speaker 1: the neutron is a fermion, and then the neutrons are
51:05
Speaker 1: resisting also because they're also fermions. The reason a neutron
51:09
Speaker 1: star doesn't collapse is because of the neutron degeneracy pressure.
51:14
Speaker 1: The same principle that kept the white dwarf alive is
51:16
Speaker 1: now keeping the neutron star from becoming a black hole.
51:19
Speaker 1: But then as you add more and more mass to
51:21
Speaker 1: that neutron star, it's denser and denser, and eventually even
51:24
Speaker 1: the neutrons degeneracy pressure is overcome, but again not by
51:28
Speaker 1: the neutrons violating this rule of the universe. Instead they
51:32
Speaker 1: just turn into something else. We've talked about the heart
51:35
Speaker 1: of neutron stars before. Nobody really knows what's going on,
51:38
Speaker 1: but it's not neutrons anymore. It's something else crazy that's happening,
51:41
Speaker 1: And to understand how you can keep adding mass and
51:43
Speaker 1: a black hole conform at the heart of it would
51:45
Speaker 1: require like a theory of quantum gravity that we just
51:48
Speaker 1: don't even have yet. You mean, like we have this
51:51
Speaker 1: exclusion principle, this rule about the universe. It says you
51:54
Speaker 1: can't squish two fermions together. But at some point, if
51:56
Speaker 1: you try hard enough, you can sort of bypass this
51:59
Speaker 1: rule because suddenly the things you're trying to squeeze together
52:02
Speaker 1: are no longer electrons or neutron state, just kind of
52:05
Speaker 1: become pure energy or pure quantum potential, and then they
52:08
Speaker 1: become something else. Yeah, exactly. We see those examples in
52:11
Speaker 1: all sorts of situations, like even when it's not at
52:13
Speaker 1: the heart of a neutron star. Superconductivity works this way.
52:17
Speaker 1: Electrons are fermions, right, they can't be in the same state.
52:20
Speaker 1: But if you get two electrons together and you sort
52:22
Speaker 1: of tie them up together into a single quantum object,
52:26
Speaker 1: they become a boson. They're two spin one half states
52:29
Speaker 1: combined to a spin one state, and this is called
52:31
Speaker 1: a Cooper pair, and it's a key to superconductivity because
52:35
Speaker 1: now these electrons can like flow and slide in the
52:38
Speaker 1: way that bosons can in lower energy states and make
52:42
Speaker 1: things move more quickly. So we can see fermions like
52:44
Speaker 1: exploiting this loophole by becoming bosons, by pairing up. So yeah, absolutely,
52:49
Speaker 1: you can avoid this rule of the universe by squeezing
52:52
Speaker 1: things down or tying things together. I think what you're
52:55
Speaker 1: saying is that the universe has principles, but if you
52:57
Speaker 1: put enough pressure on it, it totally without those principles
53:00
Speaker 1: out the door. Exactly. Even if I've agreed to eat
53:04
Speaker 1: chocolate ice cream for the rest of my life, I
53:06
Speaker 1: might sneak a sample of vanilla sometime just for variety
53:10
Speaker 1: under enough pressure pressure at the heart of a neutron star.
53:15
Speaker 1: Only then we eat no. I love vanilla. Did you
53:19
Speaker 1: know that vanilla beans are actually more expensive pound for
53:23
Speaker 1: pound than gold. I didn't know that, but it doesn't
53:25
Speaker 1: surprise me because vanilla is the best. I'll eat vanilla
53:29
Speaker 1: anytime over a goal. All right, Well, it sounds like
53:33
Speaker 1: the universe has these strange rules about it, although under
53:37
Speaker 1: enough pressure or there's certain circumstances, it seems to throughout
53:41
Speaker 1: these or it finds loopholes around these principles. But that
53:45
Speaker 1: it's thanks to these principles that we have things like chemistry,
53:48
Speaker 1: and we have chemistry the way it is, and so
53:51
Speaker 1: without these rules, we wouldn't be here talking about these rules. Yeah, exactly.
53:55
Speaker 1: It's the reason we even have a delicious dilemma between
53:58
Speaker 1: chocolate and vanilla, which I still thinking you can solve
54:01
Speaker 1: by just having a swirl. That's the loophole, that's right, Yeah,
54:04
Speaker 1: transforming it into something else, rocky road. It's called rocky
54:08
Speaker 1: rock for it already. Just spin it, spin it in
54:11
Speaker 1: a different way. All right. Well, we hope you enjoyed that.
54:15
Speaker 1: Thanks for joining us, See you next time. Thanks for listening,
54:25
Speaker 1: and remember that Daniel and Jorge explain the Universe is
54:28
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54:32
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54:37
Speaker 1: to your favorite shows.