Daniel and Kelly’s Extraordinary Universe - Listener Questions 35: Exomoons, black holes and math!

Episode Date: February 7, 2023

Daniel and Jorge answer questions from listeners like you! Write to us at [e-mail] See omnystudio.com/listener for privacy information.

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podcasts podcast oh overflowing don't you answer them i do people still write us with questions you know the inbox is overflowing like usual oh overflowing don't you answer them i do but Every time I send a response, it just seems to generate more questions. But you're not giving them a good answer. Maybe, but even when they say, ooh, now I get it, they always come back with, hmm, but that makes me wonder about something else.

Maybe you should try asking them a question. If you stop them, that might give them something to think about. A question like, would you fund my research? Oh, nobody will write you back then. The question to end all questions. Literally. Hi, I'm Jorge, I'm a cartoonist and the creator of PhD comics. Hi, I'm Daniel. I'm a particle physicist and a professor at UC Irvine, and I refuse to limit my chuckles.

Are people trying to limit your chuckles? Are you under the oppressive rule of an anti-chuckler? Well, we did have one person who wrote in and complained about how much time I'd spend chuckling on the podcast and then we talked about it on a recent episode and then I got an avalanche of emails from people who say never stop chuckling. All right, there you go. You got some support from the internet to keep chuckling. Somebody literally wrote to me this morning and said, chuckle to your heart's content, sir. So here I am chuckling away. It seems like a bit of an overreaction over one comment from the internet. It suddenly turned into a social cause here. Free Daniels chuckles. Now I'm self-conscious about it. I don't know if I'm chuckling on

purpose or chuckling to chuckle or what's going on. I got to get out of my own head. Oh, man. So they are being limited. They are shackled now. I think maybe it's like a quantum thing. We just shouldn't look at it so much and just let it be itself. Let it be both annoying and endearing at the same time. Stop trying to measure the chuckle and let it be uncertain. But welcome to our podcast, Daniel and Jorge explained the universe, a production of iHeart radio. In which we do try to measure the universe, or at least our understanding of it. Our goal is to use our minds to try to nail down everything that's happening out there in the universe from the tiniest little vibrating strings that might make up the very fabric of reality all the way up to cosmic black holes that

are swallowing the centers of galaxies we think it's a worthwhile way to spend your time to try to understand the universe and we exult in the joy of our curiosity and the chuckles that we find along the way yeah because it is a wonderful universe it's huge it's amazing it's fascinating it gives us a lot to think about and as you said sometimes a lot to chuckle about it's kind of a funny universe funny smelling

funny looking or funny weird it's got all the funnies it's quantum in that way as well it's both funny ha ha and funny at the same time it's a superposition of funnies it is pretty funny weird that's for sure

so many things we have discovered about the universe that make us go what that can't possibly be true and then we do the experiment and the universe says Oh yeah, that's exactly what's going on. And it makes us reformulate the way we think about the whole universe. For me, those are the best moments in science when the universe tells us that we've been thinking

about things the wrong way the whole time. And science is how we explore the universe and find out how things work and why they are the way they are. And the way we do that is with questions, right? Science is all based on questions. Science is basically just people asking questions. You might imagine that science is like some big building with columns where information gets turned out on like a ticker tape or something. But it's just a bunch of people being curious about the universe.

Every time you spend like 19 seconds reading about the life cycle of some guinea pig, it's because some person has decided to devote their life to studying that guinea pig and how it spends its time. Wait, what do you mean? Every time I spend 19 seconds reading about a guinea pig. How often do you spend 19 seconds reading about guinea pigs? Do I need to answer that question? That's a question I don't want an answer to. I'm not sure we want to go there.

It's just a hypothetical example. I want people to appreciate the time and devotion that goes into every single scientific bit of knowledge we have. Each one comes from some individual needing to know the answer to that question. So science is in the end just a bunch of people asking questions and deciding they got to know the answer. And then Daniel deciding he's only going to spend 19 seconds reading about their last. work. Well, there is this amazing asymmetry, right? In the same way you can spend decades doing research and somebody can just like skim it on their phone while they're in the bathroom and they go, oh, that's cool. And then they move on with their lives. Right. But think about the millions of

people that could be reading this on their phones. If you multiply, I guess those 19 seconds of bathroom reading, you get, you know, millions of seconds of bathroom reading. That's my goal as a scientist is just to get maximal number of seconds of bathroom reading. aim high or aim low you know just aim somewhere who cares about Nobel prizes or citation counts or fancy awards seconds of bathroom phone scrolling that's my new metric all right do you think academia should be based on that just forget about you know impact factors and H indices and noble prices have a new award called the toy lease To release. I do think it's important that we reach everybody out there. It's not important that they're on their toilet while we reach them. But I do think it's vital that science communicates outside of just academia and the rest of a scientist to everybody out there who's curious about the world and who's helping to pay for our studies and pay our salaries. This knowledge and this curiosity belongs to everyone, which is why we do these episodes where we talk about questions from not just from cutting edge scientists, but from people.

out there like you. That's right because science affects everybody and in fact everybody has questions about the universe, maybe not necessarily about guinea pigs or I'm sure people don't think they have questions about guinea pigs, but maybe they do. And maybe they do have an ultimately question about how life when Earth is here, why we're here, why is the Earth here, what would it be like to live in other planets? Are you saying there are people out there who don't have questions about guinea pigs? Are you serious? How many people do you know? Have you met people outside of your little bubble there? It's just so easy for your brain to like generate guinea pig questions, for example. How long would a guinea pig last on the surface of the moon or on

Ganymede or in outer space? Now you're sounding like a super villain. I'm not suggesting we do these experiments, but I would like to know the answer. People do have questions and sometimes we answer them here on the podcast. That's right. If you have a question about something that doesn't make sense to you or maybe you heard us talk about something on the podcast and it doesn't quite click in your brain or you are just lying on your back staring up at the star. and wondering what's going on at the heart of them, write to us to questions at danielanhorpe.com. We answer every single email and tweet

and we will answer your question as well. Wait, Daniel, you don't answer all of my emails. Answer all emails from listeners, absolutely. Do you listen to our podcast? I do listen to the podcast. Maybe I just need to frame it in the form of a physics question. There you go. But people do send questions to us and we answer them here.

And so today we have three great questions from listeners about exciting topics, like what's it like to live in a moon of Jupiter, a question about black holes and whether they have a surface, and also a question about math, which I guess maybe it's not as exciting as the first two. What if it's about guinea pig math? Would that make you more or less interested? Does that mean like a trial math for the universe? There you go. No, it is an exciting question. Also, it's about the very nature of reality and whether

reality is based on math. And so let's tackle this first question first, and this one comes from Billy. Hey, guys. I'm wondering what life would be like for humans on the moon of a gas giant. So suppose we find a Jupiter-like system within what we currently understand as the habitable zone of a star. And this system is a moon that can sustain human life. What would the day-night cycle look like with a planet or other moons blocking the sun?

What kind of seasons would you go through? Would the passing of more or less massive moons disrupt gravity in interesting ways? could one of those moons support smaller satellites like Phobos and Demos? Thanks, and I look forward to hearing your answer. Awesome. Thank you, Billy. That's a great question. Like, what's it like? Because we often hear about how the moons of other planets are maybe habitable and they're maybe like the size of Earth and sometimes they even have water.

And so the question is, like, what would it be like to live in a moon of another planet? It's a great question to put yourself on the surface of one of those moons and think about like, what would the sky look like? How long would the day be? What would you see in the sky? How many eclipses would there be? What would the seasons be like? It's a really fun question, especially, for example,

if you're writing a science fiction novel that's set on one of those planets, as I suspect Billy might be. Boy, you're really suspicious here. You think Billy just has an ulterior motive here? Can't you be asking out of sheer curiosity? Absolutely. Maybe he is. Maybe he isn't.

But after we give our answer, I think he'll be well set up to write that novel. And I'm looking forward to reading it. The hymn and tens of thousands of people. Better get typing fast, Billy. But it is an interesting question. What would it be like to live, for example, in a moon like Europa, which is a moon of Jupiter here in our solar system, which has water and is sort of in the habitable zone, right?

Yeah, and these moons are huge. Remember that Jupiter is much, much bigger than Earth. And so a moon of Jupiter can be basically the size of a planet. Yeah, and Europe in particular has liquid water in it, right? Europa has an icy crust and we think oceans of liquid water underneath. we're sending probes up there to sample those oceans because sometimes they crack and shoot geysers of crystallized water out into space and we're going to try to send something through one of those plumes

and see like, hmm, is there organic material in there? Maybe little frozen microbes. It's going to be pretty exciting. Yeah, and I think people have also talked about Titan, right, which is another moon in here in our solar system that might be livable. Yeah, a lot of these moons are pretty big and pretty rocky and might have liquid under the surface. So they might like naturally have their own life.

It's a great way to ask the question, like, how likely is life to evolve? Because it's like an independent way to sample whether life emerges from similar conditions to what we have on Earth. And there's another question, which is like, what would it be like for us if we tried to colonize these places and actually established bases there? What would your daily life be like on those surfaces? Yeah, and I guess that's the question, Billy had because I guess if you're on a moon, then you're orbiting another planet. and then that planet is presumably orbiting the sun of its solar system. And so the question is, would that make your days and night super wonky and unpredictable? Or would they make them maybe more predictable?

Or would you even have seasons, things like seasons? Yeah. It wouldn't make it less predictable, but it would make it very, very different from our experience. Earth, for example, currently just orbits the sun and we have a day-night cycle because of the Earth's spin. If you're a moon around Jupiter, for example, then what determines? whether you're seeing the sun or not, is not your spin, but how long it takes you to go around Jupiter? Wait, what do you mean? Why is it determined by your orbit around Jupiter? Wouldn't it also

depend on your inherent spin of the moon? There's a couple of reasons. One reason is Jupiter is huge, and so it's going to eclipse the sun pretty often, right? Half the time you're going to have Jupiter between you and the sun. And so because Jupiter is so big in your sky, you can have like hours long eclipses every day. Okay, maybe. Let's get down to specifics, like if I was in a moon of Jupiter, what should I expect to see in terms of day and night? How often would I see the sun? One key thing to understand is that these moons tend to be tidily locked, meaning that one side of them faces Jupiter and one side of them doesn't. Just the way that our moon faces the Earth.

So there's the near side of the moon and the far side of the moon. We always see the same side of the moon from Earth. That doesn't necessarily mean that we're sort of going around the Earth at the same rate that the Earth is space. Like the moon has a certain period around the Earth, but the Earth is also spinning. So it gets kind of complicated, right? That's right. The Moon sees different parts of the Earth, right? But the Earth always sees the same side of the Moon.

But now put yourself on Earth-sized Moon around Jupiter. It takes like 85 hours for Europa, for example, to go around Jupiter. So now your day-night cycle is determined by how long it takes you to go around Jupiter. Okay, so like if Jupiter was standing still, Europa would take 85 hours to go to orbit around Jupiter. That's what you're saying? Yeah, exactly. And so at any given time, if it's on the side of Jupiter that's facing the sun, then the outward facing side of the moon of Jupiter would see the sun.

But the inner part of the moon that's facing Jupiter would not see the sun. Yeah. So you have like two important hemispheres. You have the far side of Europa, the one that's facing away from Jupiter, and the inner side, the one that's facing towards Jupiter. On the far side, the outer side, that part never sees Jupiter. Jupiter never appears in the sky on the far side of Europa. But you do have 85 hour long day night cycles.

So you have like 42 hours of sunlight and then 42 hours of darkness. And that's a big difference from what we have here, right? We have 24 hour long periods which are determined by the spin of the Earth. On Europa, the day night cycles determine by how long it takes to go around Jupiter. And a longer day night cycle means higher temperatures during the day and colder temperatures at night. Yeah, you got to pack a heavier sweater, I guess. But I guess if you're on the outside of the outward-facing side of the moon, then life would be pretty regular, right?

It'd be sort of like here except just longer days. Yeah, it would be here just longer days. And it depends on how close in you orbit. For example, Ganymede, its period is like 170 hours. In I.O., its period is 42 hours. So it depends how close you are to the gas giant. You could have a much longer or a shorter day-night cycle. It depends on how long it takes to go around the gas giant

instead of how fast you spin. And all of those moons are tidily locked to Jupiter, like they're all always facing the same way towards Jupiter? Yeah, they are. Okay, so like half of the world or half of Europa just sees a regular day-night cycle. And I guess also regular seasons, right? Because then the seasons kind of depend on whether Jupiter is farther

or closer to the sun. Yeah, the seasons depend on the tilt of the planet, right? And so Earth's axis of rotation is tilted relative to the suns, for example. So part of the year of the northern hemisphere is closer to the suns. the sun and the other part of the year, the southern hemisphere is closer to the sun. If you have no tilt, then you don't have seasons. Every part of the year is the same. If you're on a moon of a planet that's tidily locked to that planet, then the moon's tilt is

connected to the planet's tilt. In the case of Jupiter, for example, the tilt is actually pretty small. It's only three degrees, much less than Earth's tilt. So in Jupiter, the seasons are more mild. The winter and summer are not as dramatic. So if you're on the exo moon of a planet that isn't tilted very much, then you're not going to have seasons. You could also imagine being on the moon of a planet that it tilted more. I see. So the seasons, for example, in Europe, at least in our case, where there isn't a lot

of tilt, the seasons would be pretty mild or like not a lot of variations in the seasons like we have here on Earth, but maybe you're saying the day and night cycle would be pretty dramatic. Like the days would be super hot and the nights would be super cold. And if you're on the inside surface of the moon, the one that's always facing Jupiter, then things are pretty dramatic because Jupiter would be huge in your sky. If, for example, you're on Europa, then Jupiter would be like 20 times as big in the sky as our moon is here on Earth.

It would be a huge thing. You'd see it all the time. It would be like a giant thing blocking your view, right? You see Jupiter like a huge thing in the sky. Yeah, and you would see eclipses basically every day, right? Because Jupiter would get between you and the sun every single day. And every time you get that eclipse, it will look like night, right? Because Jupiter casts such a huge shell.

Yeah. So you have this day night cycle, but then on the inside surface of the moon, you also have a daily eclipse, which is like a mini night in the middle of your day. So like everybody takes a siesta. Sounds great. Let's move to Europa. And if you think about it also, how much you see of Jupiter depends on its relationship to the sun. The same way that like our moon either looks full in the sky if the sun is shining straight on it or it can look dark if the sun is shining on the other side of it. The same thing will happen to Jupiter. You could have like a crescent Jupiter or a full Jupiter, right? It'd be pretty dramatic.

And also probably Jupiter would be spinning so you would see different sides of it as well. like sometimes you'd see the red eye sometimes you wouldn't it'd be pretty beautiful actually because jupiter is a gorgeous planet it's got so much texture on it it's frankly a lot better looking than our moon well it depends on your taste i guess but i guess we're saying that if you're on the side of the moon in jupiter that's facing jupiter then you'd basically like your day would be split into two many days kind of like you would see the sunrise above your horizon but then it would dip behind jupiter then it would come out of jupiter and then it would sunset back to the horizon on the other side, right?

And the sunsets could be pretty dramatic as well, right? You have like light bending around Jupiter. You have like sun setting behind Jupiter, which would be pretty dramatic because then the sun is being filtered through the jovian atmosphere, which would be pretty cool. And at night you might have a really dramatic auroras, like the northern lights and the southern lights. Oh, cool. So you would have two sunsets and two sunrises every day.

Yeah, exactly. You'd have one over the horizon of your own moon and one over the horizon of Jupiter. All right. Now, this sort of depends a lot on, like you said, the tilt. But it is maybe a pretty typical example if you have like a big gas giant and with moons, right? Like if that was somewhere out there in another solar system, the like the probability is that the moon will be tidily locked to the giant planet, right? Yeah, it depends a little bit on how close it is. The closer moon gets to the planet, the stronger this effect is.

You can also have more complex tidal relationships. Like, for example, Mercury is technically tidily locked to the sun. But the same side of Mercury doesn't face the sun all the time. It's a complicated 3-2-spin orbit resonance where it does like three flips every two times around the sun. So you can get even more complex relationships. But we do expect in other solar systems to see gas giants near the habitable zone. Like in our solar system, we have Jupiter and Saturn kind of far out compared to the Earth. But in many other solar systems we see in telescopes, we see what we call hot Jupiters, big gas giants much closer to

the sun than our gas giants. So it's possible they have moons in the habitable zone. Yeah. And those moons would see a pretty regular day and night cycle, which might be an ingredient for life, right? Like if things were totally chaotic, if your days and nights were totally unpredictable, maybe life wouldn't be able to thrive in a place like that. Yeah, it'd be really amazing to see life develop in other cycles.

Like, what would it be like to have a big night and a mini night? And how would that affect the development of life and reproductive cycles? It'd be really amazing to see those experiences. experiments play out in reality. Yeah, everyone would be like the Spanish. We're like, what? You don't take siestas? Everybody takes siestas.

Even the plants. Even the guinea pigs. Or I guess exo guinea pigs on that planet. Would they still be called guinea pigs? Well, I think that answer is a question for Billy. Life on an exo moon of a gas giant in another solar system would be most likely pretty regular. Now let's get to our next question. And this one is about black holes and whether they have a surface.

So we'll get to that question. But first, let's take a quick break. I'm Dr. Joy Harden Bradford, and in session 421 of therapy for black girls, I sit down with Dr. Ophia and Billy Shaka to explore how our hair connects to our identity, mental health, and the ways we heal. Because I think hair is a complex language system, right, in terms of it can tell how old you are, your marital status, where you're from, you're a spiritual belief. But I think with social media, there's like a hyper fixation. and observation of our hair, right? That this is sometimes the first thing someone sees

when we make a post or a reel is how our hair is styled. We talk about the important role hairstylists play in our community, the pressure to always look put together, and how breaking up with perfection can actually free us. Plus, if you're someone who gets anxious about flying,

don't miss session 418 with Dr. Angela Neil Barnett, where we dive into managing flight anxiety. Listen to therapy for black girls on the IHeart Radio app, Apple Podcasts, or wherever you get your podcast. The OGs of Uncensored Motherhood are back and badder than ever. I'm Erica. And I'm Mila. And we're the host of the Good Mom's Bad Choices podcast, brought to you by the Black

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And then everybody else wants. to get pissed off because the white said it was okay. Problem. My oldest daughter, her first day in ninth grade, and I called to ask how I was going. She was like, oh, dad, all they were doing was talking about your thing in class. I ruined my baby's first day of high school. And slumflower.

What turns me on is when a man sends me money. Like, I feel the moisture between my legs when the man sends me money. I'm like, oh, my God, it's go time. You actually sent it? Listen to the Good Mom's Bad Choices podcast every Wednesday on the Black Effect Podcast. network. The iHeart radio app, Apple Podcast, or wherever you go to find your podcast. I'm Dr. Scott Barry Kaufman, host of the Psychology Podcast. Here's a clip from an upcoming

conversation about exploring human potential. I was going to schools to try to teach kids these skills, and I get eye rolling from teachers or I get students who would be like, it's easier to punch someone in the face. When you think about emotion regulation, like you're not going to choose an adaptive strategy, which is more effortful to use. unless you think there's a good outcome as a result of it, if it's going to be beneficial to you. Because it's easy to say, like, go blank yourself, right? It's easy. It's easy to just drink the extra beer.

It's easy to ignore, to suppress, seeing a colleague who's bothering you and just, like, walk the other way. Avoidance is easier. Ignoring is easier. Denials is easier. Drinking is easier. Yelling, screaming is easy. Complex problem solving, meditating, you know, takes effort. Listen to the psychology podcast on the online.

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This one has asked kind of a similar question, almost, and it comes from Bobby. Hello Daniel and Jorge. My name is Bobby from Arizona. This question comes to you as kind of a two-part. Could a black hole have a surface in that if you gathered enough materials, let's say iron at 1,000 or billions of times the mass of the sun and it became a black hole? Would you be able to fall in that hole hypothetically and stand on the surface of that solid iron? Additionally, could this same black hole potentially gather enough materials around it to spark fusion? again within the black hole. All right. A little bit of a mind-bending question here is, can a black hole have a surface inside of its event horizon? And could you maybe like spark a sun inside of the hole? Man, I love that image of a sun hidden inside a black hole.

Like fusion burning away furiously, pumping out photons, which are forever trapped by the black hole. So thank you Bobby for this question. What do you think Bobby was thinking? I think Bobby, like many people, is wondering what's going on? on inside a black hole. When stuff falls inside a black hole, what happens to it? What does it do? What is the structure of matter in there? What kind of weird stuff does it form? I think that's sort of the heart of his question. And that's a question that many people have, including black hole

experts and cosmologists and astronomers. Basically, everybody wants to know what's going on inside a black hole. All right. Well, maybe let's dig into this and let's be maybe clear because black holes do kind of have a surface to them, right? They have an edge to them, which is kind of like where the black starts, basically. There's definitely like an edge to a black hole in the sense that we can say there's a point of no return. If you get closer to the black hole than this, then all paths lead towards the center. There's no escape, right? And that's what we call the event horizon. It's like a threshold. But it's not a surface in the sense that it's like a physical boundary. If you're falling into the black hole, you don't necessarily even notice when you pass the event horizon.

There's no like gatekeeper there or force field or anything. You can't even necessarily know whether you're past the event horizon. The only way to know if you're past the event horizon is to do the calculations and see if there's any path out for any particle even into the infinite future. So there is this distance from the center of the black hole we call the event horizon. That doesn't necessarily mean that that is a surface. It's a surface only in sort of a mathematical sense. Right. It's kind of like you say, a boundary, but it is a three-dimensional boundary, which kind of makes it a surface.

sphere technically. Mm-hmm. Yes. And that one, that's the mathematical event horizon. But that's not necessarily what we see when we look at pictures of a black hole. That's not necessarily like the black that we see in those pictures, right? That one's bigger than this event horizon. But that does sort of look like a surface.

Yeah. You're used to looking at something and seeing it the way it is because your mind is used to reconstructing objects in front of you assuming that light travels in straight lines, which is why your mind gets confused if you're looking at like a bent, the mirror or through some lenses, things look distorted, right? In the same way, space itself is distorted even outside the black hole and light doesn't travel in straight lines. It gets all twisted and bent. So what you see when you look at a black hole is not the actual physical extent of the black hole, but an image of the black hole that's been distorted by these weird

paths that light follows. So specifically, you see a black circle that's actually larger than the event horizon and includes not just the part of the event. horizon that's facing you, but also the part from behind, like photons that leave the event horizon from behind the black hole get bent around by the gravity and then back towards your eye. So you can see the entire surface of the black hole from any side of it. Right. So that sort of counts as a surface, right? You just said, use the word surface in the sense that maybe you wouldn't be able to tell

as you're falling in, but maybe somebody from the outside would see you sort of fall into that surface, right? Or they would see a surface relative to somebody falling in. Yeah, it's definitely a boundary. It's a surface mathematically. It's not a surface in the sense that you could like stand on it. There's nothing there to support you. You can't like walk around on the event horizon.

Right. So I think Bobby's question now here is whether or not a black hole has a surface in the sense of like having a physical hard surface on which you can actually like stand or into which you would crash if you fell into black hole. Because I imagine maybe he's thinking like a regular hole here on the ground on earth. It's a hole and you would fall in but eventually it would hit something. And if there's a whole bunch of stuff. in the hole, or like a trash or something, you would eventually fall into the hole, but then you would hit the pile of trash. And so I think maybe Bobby's wondering, like, you know, the black holes have all this stuff inside of them. If you fell into the black hole, wouldn't you eventually hit this stuff?

Yeah. And it's a great question. The way to think about this is in terms of the forces. So gravity is very powerful when things get very massive and things get very close. But it's not all powerful, right? Like, think about the huge ball of iron in the center of the earth. Why isn't that a black? hole. It's not a black hole because iron has internal structure, has enough internal structure to resist the gravitational collapse. Like the atoms pushing against each other that form this ball of iron, they resist gravity. But inside a black hole, gravity is much, much more powerful. It's more powerful than the structure of iron. It's more powerful than any sort of bond that we are aware of. We don't think there's anything that can overcome the power of gravity once you are inside the black

hole. So if you take a big blob of iron, as he said, a huge mass of iron like millions of times the mass of the sun and collapse it to a black hole, once all that iron is inside the black hole, it doesn't have the strength to resist the gravitational collapse. And that's why general relativity predicts a singularity. It says that things just keep compressing and compressing and compressing until you get a dot of infinite density. I think you're saying like here on Earth, there's a bunch of stuff at its center, but it's not collapsing because other forces are keeping gravity from collapsing further, you know, like the electromagnetic force between all of the electrons and the protons and the quarks inside of the atoms in Earth's core. But in a black

hole, like, we've sort of done something different. We've like accumulated so much stuff. The gravity is so powerful. It squeezes even the electromagnetic force. Like, it just squeezes everything down theoretically into an infinite point. Exactly. You can have a certain mass of iron and it can hold itself up. But if you make it too massive, gravity gets too strong and then it collapses. And that's how black holes form, right? Black holes form from stars that made too much heavy stuff at their core. So they're no longer able to resist gravity's collapse and then it turns into a black hole. So all that iron, according to general relativity, forms a singularity, a dot at the center of the black hole where all of that mass has accumulated. And so unless you can walk around on an infinitesimal

point, according to general relativity, there's not really a surface. inside the black hole. And there's no chemistry going on and no fusion or no anything else. Right. And you're saying at the center of a black hole, there's no surface, there's no pile of trash or iron. There's just an infinite dot. But what about the stuff getting to the dot? Isn't that stuff accumulated maybe? Yeah, that's a good point. It takes a finite amount of time once you pass the event horizon to reach the singularity. And so if the black hole is actively feeding, then you have a singularity surrounded by stuff that's still falling in. You know, sort of like a toilet bowl of stuff swirling around it.

And remember, this is according to general relativity. Einstein's equations predict this runaway effect that leads to a collapse that leads to a point. Because in Einstein's theory, space is smooth and continuous. It can be chopped up into infinitely small slices, and you can also know where everything is at all times. These assumptions are in total contradiction to what we know about the universe being quantum mechanical.

And so physicists don't take this prediction of singularity seriously. We don't see it as like an actual prediction of what's happening inside is sort of like an indication that the theory itself is breaking down because it predicts something kind of crazy. Right. This is something that maybe general relativity is wrong and you wouldn't get a singularity at the center of a black hole. You would maybe get like a quantum blob. Yeah, we think that something will prevent the singularity from happening because you can't confine particles to an infinitely small space without giving them effectively infinite energy because of the quantum uncertainty principle. And so there's a minimum quantum fuzz to the universe always.

So when you try to compress matter really, really far, there must be some quantum mechanical way that they resist becoming a singularity. You know, I think of them as sort of like layers of defense. Matter has many ways to protect itself from collapsing. First, there's like the chemical internal structure like the Earth. Or if you have a star, then it's fusion, which is pushing out and pumping out energy to prevent collapse. If you're like a neutron star, then there's like the neutron degeneracy.

We don't know what's going on inside a black hole. there might be something else quantum mechanical that matter can do to resist being compressed into a singularity. To know how that works, we'd have to have a theory of quantum gravity, which we just don't have. Though there's lots of fun ideas about what might be going on inside. Yeah, and so inside of a black hole, there might not actually be a hole, I think is what you're saying. Or it would still be a hole. There just wouldn't be a pinpoint singularity in the middle. It might be that the stuff inside of the hole is still holding together or, you know,

making a pile due to some other quantum force. Yeah. And it's very unlikely that if you throw a bunch of iron into a black hole, that it's going to stay iron. It's going to turn into some other completely different state of matter because the iron molecules are not going to be able to survive that intense experience. They're going to get shredded apart to their basic constituents. Maybe even the protons will get pulled apart into their quarks. Maybe those quarks will get pulled apart into whatever they are made out of. We just don't know.

From the outside, it still just looks like a black hole. You can't see beyond the event horizon. So gravitationally speaking, a singularity or a quantum blob with the same mass all acts the same from the outside. So as you say, it still looks like a hole. Yeah. But to Bobby's question, then, if there is a quantum fuzzball in the middle, that means that inside of a black hole, there would be a surface, right? Like a physical surface that you could maybe stand on if you could somehow survive or even think inside of a black hole, right? Yeah, perhaps. It depends a lot on that theory of quantum gravity. So what's going on inside it?

You know, we talked to the podcast once about the dark star theory that black holes are not actually black holes. They're just very slowly collapsing stars that will reach a minimum point from quantum mechanics and then bounce back out and turn into like white holes eventually. And so that's also not the kind of thing you would necessarily be able to walk around on a collapsing star unless you have like really good boots. Yeah, maybe you have dark star shoes. But technically it would have a surface, right? It would answer Bobby's question and the answer would be yes. There would be like a physical blob inside of a black hole that has a surface that you could stand on or throw things at and that they would splat. Yeah, stand on in sense that you could like be there on top of it.

I don't know if it would absorb you or pull you apart or melt you instantly. So I certainly wouldn't recommend it to anybody out there who's considering it. Sounds like we would maybe want to test it first, you know, by throwing like say a, An animal added. What kind of animal do people usually do experiments with first? Is it bananas? Hamsters? I can't remember.

Are bananas animals? On other planets, maybe exo bananas might be in the animal category. Oh, my goodness. I'll bring up all kinds of ethical issues for me there. Did I tell you, by the way, what my kids dressed up as for Halloween? No. Well, my son has become very long and lean, and so he dressed up as a banana. All right.

He's aspiring to the greatest fruit of it. on the planet. So we had a banana in the family. But I'm not throwing him into any black holes, no matter what he wears on Halloween. Yeah, I might get a little slippery. But I think that answers Bobby's question. Could a black hole have a surface?

The answer is yes. I mean, it has kind of a threshold surface. It has a visual surface, which is the part that looks black. And it may, if general relativity is wrong, and we think it most probably is, it does have maybe a physical surface inside of the hole. It certainly might.

It could be a dark star. It could be a fuzzball made of strings. It could be something else entirely we haven't yet imagined. If we could see inside a black hole, we could know what happens when you compress matter in these extreme circumstances and we could learn something about the fundamental nature of reality. All right. Well, thank you, Bobby, for that question.

And now let's get to our last question. This one's about the very nature of the universe and whether or not it all adds up. So we'll tackle that question. But first, let's take another quick break. All right, we're answering listener questions, and our last question is about the nature of reality. It comes from Matthew. Hello, Daniel and Jorge. I have a question about the math of the universe.

What is it? Trigonometry, algebra, calculus, the math of space exploration. I was thinking about the James Webb Space Telescope out there in LaGrange 2. How the heck? That was math, right? Like somebody was like, oh, look, here's some math. We can put this thing there and it'll stay put.

Because it's like circling the sun with the Earth and the moon, but then it's like doing little loop-de-loops in addition to the circling the sun. And another thing, how do they get it to stay focused on something a billion trillion miles away when it's doing all that motion. Are they constantly firing thrusters? Anyways, tell me about the math

of the universe. Like from the olden days to now. What the heck? Trigonometry? What is it? Like that scene in Apollo 13 where they all check their math and oh my gosh,

I got to know more. All right. Thank you, Matthew, for that awesome question. Also, I think that's my reaction to a lot of these things about the universe. What the heck? I can't anymore. It is amazing how the universe works

and how it seems to be so describable by math. It really is incredible. Yeah. And so that's Matthew's question. He's asking, what is the math of the universe? Is it trigonometry, algebra, calculus, long division? It is really interesting to wonder which parts of math describe the universe

because you can imagine that we could invent a whole bunch of math that doesn't describe the universe that isn't relevant necessarily. Wait, what do you mean? Like, you can have math that says one plus one equals two, but maybe you could have a universe where one plus one doesn't equal to? No, I mean that you can invent kinds of math

that don't have to reflect the physical universe. For example, you can invent weird kinds of geometry, you know, surfaces that live in eight dimensions, but the universe might not be eight-dimensional. So you can spend your whole life thinking about the mathematics of eight-dimensional objects, but that's not actually relevant to our universe, if our universe is just three-dimensional.

But, you know, we don't know. People spend, for example, decades developing ideas called group theory about how things relate to each other, then later it turns out to be totally relevant to particle physics. So you never know what math is going to be relevant. But it's definitely possible that there's kinds of math

which are not relevant to the universe. Right, but I guess it's kind of a tricky philosophical question because, like, if you can come up with math that makes sense, doesn't technically mean that it exists in the universe? even if you can't find like a, you know, a lot of particles that follows that math, the mass is still there and it makes sense in this universe. Doesn't that mean that it's part of the universe? Yeah, it's one of the deepest questions in the philosophy of math.

Like, are those numbers real of the part of the universe? And then you get into weird things like, well, what does it mean to be real? Because like the numbers, the number two, where is the number two? Right? Everything else that's real has like a location. It has behavior. It can like participate in experiments. you can talk about whether protons are real

and you can do tests on them. You can't do that for the number two. There's no way the number two can participate in experiments can cause effects. So if it's real, it's real in a different way than other things that are real. But I think maybe Matthew's question

is not so much about these big philosophical questions. I think maybe he's coming at it from a more intuitive point of view, which is like, you know, does the universe have a mathematical description? can you describe the universe with math? And if you can, what kind of math is it? Is it trigonometry, algebra, or is it just all addition, all the way down?

I would say there's two parts to that answer. One is what kind of math do we use to describe the universe? And the other is whether we could boil that down to one sort of like basic kind of math. So on the first one, we tend to use calculus a lot. Like calculus is often described as the language of physics. It's really a very, very powerful tool to describe what we see about the universe. That's because calculus is like the mathematics of change. If you have something flying through the air with a certain velocity, that's fine.

But now if you want to change, that's velocity. And you want to understand where it's going to go. You have to accumulate all those changes and figure out where it's going to land. That requires calculus. So the mathematics of change is really the mathematics of motion in our universe. So calculus is really fundamental. Right, because you're saying because we have time in the universe and time kind of implies change, then we need calculus. But it's also, I think, a little maybe more fundamental, I wonder, because it, calculus is also about how the rates of change depend on each other, right?

Like we seem to have found laws, for example, like F equals MA, that says that, you know, the rate of change depends on this force or that force or this situation. And so it seems like the universe has laws that govern over the rate of change. of things and that's why calculus is useful. Yeah, calculus is useful because it gives us these tools and we can express the laws of the universe that we discover in terms of those. So you're right, almost all the laws of physics like f equals M.A. That's an expression in calculus because A is a derivative. Acceleration is the rate of change of velocity. That's a differential. That's part of calculus.

Force is really change in momentum with respect to time, right? And so that's a differential. So you're absolutely right that most of the laws of physics can be expressed in terms of objects that were invented for calculus. But calculus also handles things that are not great of change with time. You know, calculus lets you integrate over space also. If you have an object that has like a varying density and you want to know it's total mass, you can integrate over the object over space in order to get the total mass if the density is varying. So calculus is the math of change of time or of space.

Yeah. And then what happens when you go down to the quantum level? First of all, does calculus still apply or does it get more into like quantum waves and functions and fields? Is calculus still useful there and maybe even appropriate because the world is quantized? It's absolutely still useful there. Like the Schrodinger equation, that's a differential equation. Absolutely. It's a wave equation which tells you how the wave changes in space and how that relates to how it changes in time.

So calculus super fundamental. And the basic theory of the standard model, which we call a quantum field theory, is full of calculus because calculus involves integrals and integrals allow you to add up over many, many different things. You can add up slices in time or slices in space. Quantum mechanically, it also led to add up different probabilities. So for example, one important formulation of quantum mechanics by Feynman says if you want to understand how a particle moves from A to B, you have to integrate over all possible paths of the particle. So calculus lets you consider multiple different possibilities simultaneously. So it's crucial to quantum field theory. Right. So calculus is pretty useful. So kids pay

attention to that class when you get to calculus. But I guess maybe a question here is, is calculus the theory to use for the university? Like it's useful and you definitely seem to be able to use it to describe a lot of the universe and even predict a lot of what happens in the universe. But maybe we're just kind of lucky. Like maybe calculus just sort of works most of the time. And so we think it's the way to go, but maybe there's a different math here that would describe the universe in more detail, the more we learn about it. Is that possible? It certainly is possible, and we're constantly improving on and developing new techniques in calculus.

It's not like calculus is a finished thing. It's not like Newton and Leibniz invented a few hundred years ago and now it's done. People are still working on it like today, figuring out ways to do complicated integrals and whole new techniques that makes previously unsolvable problems now solvable. So it's definitely a developing field and it's improving. And so that means that in the future, we'll have more powerful math that describes the universe even better. Because there's lots of things that we still like don't know how to do problems we can't solve, probably because we just don't have the mathematical tools for them yet.

You're saying calculus is pretty good and we're going to stick with it. But maybe as you were saying, the deeper question is whether or not this is just in general using math to describe the universe if that is something fundamental about the universe or is just our way of understanding it. This is a question the philosophers of math debate and have been debating for thousands of years and probably will keep debating for thousands more years. I'm not sure it's something they can really make progress on. They're really at the heart of it we're asking whether math describes the universe or whether it controls the universe. Like is the universe itself mathematical? Is math part of the universe itself or is it just our description of it is the way that we organize our thoughts?

Is it like a convenient way to think or is it really the source code? of the universe itself. And telling the difference between those things is pretty tricky. You mean the difference is kind of like whether the universe actually cares about math, right? Because maybe like in one scenario, the universe just does its thing and the universe doesn't even care about math or know what math is. The other scenario is that the universe is kind of beholden to math or somehow the universe is math at its core.

That's the difference, right? Yeah, that's a good way to think about it. Sometimes the way I think about it is in terms of like a computer program. Say somebody writes a computer program and then you use it, Microsoft Word, for example. And you could try to figure out how Word works and you could reverse engineer it using some other programming language. Maybe it was written in Python and you figured out how to write it in C. Now you have a description of this computer program in your own language. That doesn't necessarily mean that that's the program that's actually running inside of Word.

You might just have a description of it. Or it might be that you've discovered the actual source code for Word itself. In the same way, the math that we are building might be the actual code that the universe is following, or it could just be a good description of it. And there might be other possible descriptions that are equally valid. We just don't know. All right. Well, which is it then, I guess. I wish we knew.

One of my favorite philosophical attempts to answer this question came from Hartree Field. He said, let's see if it's possible to do science and physics specifically without any math, without any numbers at all. Like, can you devise laws of physics that don't have numbers in them? Wait, numbers or even like variables and symbols or none of that? None of that at all. He writes in his book like, I denied that numbers exist. He wrote this whole book called Science Without Numbers, where he was admitting that math is useful,

but he was trying to prove that it's not necessary by building up a new version of these theories that didn't use any numbers. What? What did that even look like? If you wrote it down, don't you have to write down something? Well, on page 47 of his book without numbers, for example, he talks about how to do this. It's pretty philosophically intricate. He, like, imbues points of space with certain kind of properties so that you don't ever have to do any calculations.

Like, most specifically, he thinks about gravity and how gravity work. And when we do gravitational calculations, we create all sort of abstract intermediate ideas, like the gravitational field. And we say that the earth is pulled on the sun because of the gravitational field of the sun. And he's like, you need numbers to describe that field, but what if that field wasn't there? You don't ever observe the field directly. You just observe the sun pulling on the earth. What if that's just something that space does and there is no field at all? That's an example of how he's trying to rid the calculation of intermediate steps that need numbers to describe them.

But ultimately, wouldn't you have to write it down and wouldn't you eventually have to, you know, you know, have a equation or something? No, in his formulation of Newton's gravity, there are no equations, there are no numbers, there is no mathematics. It's hard to imagine because we think that math is the answer, right? Like you do a calculation, you get a result. It says, oh, the force on the earth is this. For us, math is the language itself.

But he developed a way to perform these calculations to think about it that doesn't have math as the internal steps or either as the answer. And is this credible? Is this seem suspect or is this like an actual valid? possibility for the universe. I think that most philosophers see it as like a heroic effort to make the point that maybe math isn't necessary, but there's a lot of steps he took along the way, which people quibble with, and people don't think that this effort could be applied to like everything in physics. And so it's like, hey, cool point man, but it doesn't really work. It doesn't really

convince anybody that you don't need math to do science. I see. People are like, hey, there are a number of errors in your theory. And then he's like, wait, but there are no numbers. Ha ha. Exactly. I think that most people, most mathematicians and most physicists think that math is an inherent part of the universe. Right. But then I guess the larger question I was kind of alluding to is whether the universe cares if there's math or not. Or like, which came first? Math or physics? I don't know what it means for the universe to care about something. But I think there is another interesting aspect to Matthew's question, which is like which math is essential? Trigonometry, algebra, calculus. And that's interesting because you're like slicing up math now into different

categories, which are a little bit arbitrary, right? Like calculus uses trigonometry and algebra and all of these things. But there actually is a really interesting effort inside of math to try to like boil all of math down into the shortest list of rules you would need to build up all the rest of math, like to find the core axioms at the heart of it all. Oh yeah? Where is that coming from? From the math fields or from the physics fields? That comes from mathematics from like 150 years ago. People have been doing math for thousands of years. About 150 years ago, people were like, hold on a second. What are the basic rules of math anyway? And so there was a guy named P&O who showed that almost all of arithmetic can be boiled down to just a basic few rules. And then

people who came after him showed that most of math could be boiled down to arithmetic. And then later people showed that most arithmetic can be boiled down to something called set theory, which is math about like groups. What's in a group? What's out of a group? How do you combine groups? How do you overlap groups? So the current like idea by the very foundation of math is that in the end, it's all about sets. It's all about like what's in a group, what's out of group. From that, you can build arithmetic and from that you can build calculus. So fundamentally, we think that the description of the universe is mathematical and it's all set theory all the way down. That's kind of what I was saying, right? It's just addition. You're in the group or not in the

group? Exactly. It's addition and its popularity. It's all clicks. The universe is very elitist. Or it's all about clickbait. All right. Well, I think that answers Matthews. question, what is the math of the universe? Well, the answer is so far. Calculus has been really useful in describing the universe, but physicists are not sure if maybe even calculus is the fundamental way to describe the universe or even the most fundamental way to describe math itself. That's right, but that doesn't mean we don't like thinking about these questions and wondering about what's going on at the heart of the universe and why it's even possible to describe it mathematically or to make sense of it with our little primate brains. So you're going to keep going

until it all adds up or until you ask, what the heck, I can't even. Until we're part of the in-group that actually knows some answers. Until we're all guinea pigs. We're all test subjects in this universe. Living on the surface of some crazy exo moon. Or black hole.

All right, well, thank you to everyone who sent in their questions. We love answering questions. We hope you enjoyed that. Thanks for joining us. See you next time. Thanks for listening and remember that Daniel and Jorge Explain the Universe is a production of IHeartRadio. For more podcasts from IHeartRadio, visit the IHeartRadio app, Apple Podcasts, or wherever you listen to your favorite shows. Yes, come again.

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