Listener Questions 35: Exomoons, black holes and math!

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Speaker 1: Hey, Daniel, do people still write us with questions? You know, the inboxes overflowing like usual, overflowing? Don't you answer them? I do, but every time I send a response, it just seems to generate more questions. You're not giving them a good answer. Maybe, but even when they say, oh, now I get it, they always come back with but that makes me wonder about something else. You should try asking them a question you stopped them that might give them something to think about, A question like would you fund my research? Oh? Nobody will ride you back? Then the question to end all questions? Literally, Hi am or handmad cartoonist and the creator of PhD comments. Hi, I'm Daniel. I'm a particle physicist and a professor at U c 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 complain about how much time I spent 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 stopped 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's suddenly turned into a social cause. Here free Daniel's 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 this same time. Stop trying to measure the chuckle and let it be uncertain but welcome. For a podcast, Daniel and Jorge Explain the Universe, a production of I Heart 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 uh 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 nineteen seconds reading about the life cycle of some guinea pig, it's because some person has decided to devote their life to studying that mee pig and how it spends its time. But what you mean every time I spend nineteen seconds reading about a guinea pig? Often do you spend nineteen seconds reading about guinea pigs? Do I need to answer that question? That's a question I don't want to 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 nineteen seconds reading about their lives 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 nineteen seconds of bathroom reading, you get, you know, millions of seconds of bathroom reading. It's my goal as a scientist is just to get maximum number of seconds of bathroom 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 academis should be based on that? Just forget about you know, impact factors and h Indices and Nobel Prices have a new award called the Toilets 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 us scientists, 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 did 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 effects 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 pig, but maybe they do, and maybe they do have an ultimately question about how life on nurse is here, why we're here, why is the earth here, or 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 generate guinea pig questions, for example, how long would a guinea pig last on the surface of the moon, or on guinea meat 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 that 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 were just line in your back staring up at the stars and wondering what's going on at the heart of them? Right to us two questions. At Daniel and Jorge dot 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? 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? No, it is an exciting question. Also, it's about the very nature of reality and whether reality is based on that, And so it's tackled 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. In this system is a moon that could sustain human life. What would the day night cycle look like with the planet or other moons blocking the Sun? What kind of seasons would you go through with the passing of more or less massive moons disrupt gravity? And interesting ways could one of those moons support smaller satellites like Phobos and demos. M Thanks and I look forward to hearing your answer. Awesome, Thank you, Billie. 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 there are maybe like the size of the of Earth, and sometimes they even have water, and so diggussion 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 this guy look like? How long would the day be, what would you see in this 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, Well, you're really suspicious here. Do you think Billy just has an ulterior motive here? Can't you be asking out of cheer curiosity? Absolutely, maybe he is and 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 him and tens of thousands of people where you 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 it's it's sort of inhabitable soon, 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 own into space, and we're gonna try to send something through one of those plumes and see like is their 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 try 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 in 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 nights 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 your moon around Jupiter, for example, then what determines whether you're seeing the Sun or not. It's 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 the reason is Jupiter is huge, and so it's going to eclipse the Sun pretty often. Right half the time, You're gonna 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, um, 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 tidally locked, meaning that one side of them faces Jupiter and one side of them doesn't, just the way that like 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. But that doesn't necessarily mean that you're sort of going around the Earth at the same rate that the Earth is spinning, 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 the Earth sized moon around Jupiter. It takes like eighty five 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 eighty five hours to go around 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, and the outward facing side of the moon of Jupiter would see the sun, but the inner part of this, the 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 of 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 eighty five hour long day night cycles. So you have like forty two hours of sunlight and then forty two hours of darkness. And that's a big difference from what we have here. Right, we have twenty four hour long periods which are determined by the spin of the Earth. On Europa, the day night cycles to term 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 gotta 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, and be sort of like here, except just longer days. Yeah, it would be here, just longer days. And it depends on how close in your orbit. For example, gannymed it's pure it is like a hundred and seventy hours, and I owe its period is forty two hours. So it depends how close you are to the gas giant. You can 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 tidally 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 the regular day night cycle, and I guess also regular seasons, right, because then the season is 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 Sun's for example, so part of the year the northern hemisphere is closer to 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 tidally 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 all It's only three degrees, much less than Earth's tilt. So on Jupiter the seasons are more mild. The winter and summer are not as dramatic. So if you're on the XO 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 that you're saying that day and night cycle would be pretty dramatic, like the days would be super hot and the nights would be super cool. 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. For example, you're on Europa, then Jupiter would be like twenty 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. Would be like a giant thing blocking your 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 it will look like night, right, because Jupiter castle sich a huge shadow. 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 open 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 would be pretty dramatic. And also probably Jupiter would be spinning, so you would see different sides of it as well, like sometimes you see the red eye, sometimes you wouldn't. It would 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 and Jupiter that's facing Jupiter. Then you would basically like your day would be split into too many days, kind of like you would see the sunrise above your horizon, but then it would dip behind Jupiter then when it come out of Jupiter, and then it would sunset back to the horizon on the other side, right, and the sunset could be pretty dramatic as well. Right, you have like light bending around Jupiter. You have like sunsetting 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. Cool. So you would have to sunsets and in 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 other in another solar system, the like the probability is that the Moon will be tidally locked to the giant planet. Right. Yeah, it depends a little bit on how close it is. The closer moon gas planet, the stronger this effect is. You can also have more complex tidal relationships, like, for example, Mercury is technically tidally locked to the Sun, but the same side of Mercury doesn't face the Sun all the time. It's a complicated three to 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 Jupiter's big gas giants much closer to the Sun than our gas giants. So it's possible they have moons inhabitable zone. Yeah, and those moons would see a pretty regular day and night pycho, which might be an ingredient for life. Right, Like it's things were totally chiotic. If your days and nights were totally unpredictable. Maybe life wouldn't be able to thrive in a place like that. Yeah, it would 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. Be really amazing to see those experiments play out in reality. Yeah, everyone would be like the Spanish were like, what you don't take siesta? Everybody takes siesta, 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 extra 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. Alright, we were answering listener questions and we just answered one about what it's like to live on a moon of a gas giant in another solar system. This one has asked kind of a similar question, almost and it comes from Bobby Pelod annual Horge. My name is Bobby from Arizona. This question comes to you is kind of a two part Could a black hole have a surface in that if you gathered enough materials, let's say iron at a thousand 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 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, let 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 the 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. 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 it's kind of like you say, a boundary, but it is a three dimensional boundary, which kind of makes it a fear. Technically, 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 is 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 bendy 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, and that sort of counts as a surface, right. You said the word surface in the sense that maybe you wouldn't be able to tell us you're falling in, but maybe somebody from the outside would see you sort of fall into that surface, right where 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 a 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 you would hit something. And if there's a whole bunch of stuff in the hole you or like 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 is wondering, like, you know, the black holes have all this stuff inside of him. If you fell into the black hole, wouldn't you eventually hit this stuff? Yeah, And it's a great question when you 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 dot of infinite density. M hmmm. I think you're saying, like here on Earth and there's a bunch of stuff at the 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 corks 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 that gravity is so powerful it squishes 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 you 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, are you 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 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. It's sort of like an indication that the theory itself is breaking down because it predicts something kind of crazy, right, physicist, 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 solved 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 that. 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 it's what you're saying, or it would still be a hole. There just wouldn't be a pinpoint singularity in the middle. And 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 gonna get shredded apart to their basic constituents. Maybe even the protons will get pulled apart into their quarks. Maybe those quarks we have pulled apart into whatever they are made out of. We just don't know. From 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 flows ball in the middle, that means that the 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'll necessarily be able to walk around on a collapsing star unless you have like really good boots. Yeah you have dark Star shoes. But achnically 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, and that has a surface that you could stand on or throw things at, and that they would splat you stand on in sense that you could like be there on top of it. I don't know if he 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, It It sounds like people maybe want to test it first, you know, by throwing like an animal at it. What what kind of animal the people usually do experiments with first? Is it bananas? Hamsters? I can't remember bananas animals on other planets. Maybe exo bananas might be in the animal category. Oh my goodness, he'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? 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 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 were answering the listener questions, and our last question is about the nature of reality. It comes from Matthew. Hello, Daniel, and ho. 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 Web space telescope out there in Lagrange too. How the heck that was math? Right, Like somebody was like, oh, look, here's the 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 kind like 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 thirteen where they'll check their math and oh, my gosh, I gotta know more. All right, thank you Matthew for that awesome question. Also, I think, uh, I think that's my reaction to a lot of these things about the universe. What the heck? I can't? 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, is that he's asking what is the math up 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. What do you mean, Like, you can have mathods as one plus one equals two of it, but but maybe you could have a neverse 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 dimensionals. 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 how 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 find like a you know, a law of particles that follows that math. The maths is still there and it makes sense in this universe. Doesn't mean it it's part of the universe. Yeah, It's one of the deepest questions in the philosophy of math, like are those numbers real and the part of the universe? And then you get into weird things like well, what does it mean to be real? Because like those numbers, the number two, where is the number two? Right? Everything else that's real has like a location, it has behavior, can 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 like 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. Um. I would say there's two parts of 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 gonna 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 we have you saying because we have time and universe and time kind of implies change and we need calculus. But it's also I think a little bit maybe more fundamental, I wonder, because it calcula is also about how the rates of change the pend on each other, right, Like we seem to have found laws, for example, like F equals m A 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 changes of things, and that's why calculus is useful. Yeah, Calculus is useful because he 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 rate 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 of waves and 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 shorting your 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 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 a quantum mechanically, it also leads you add up different probabilities. So, for example, one important formulation of quantum mechanics by Feinneman 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 lest 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 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 the here that would describe the universe in more detailed 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 enliven. It's invented a few and 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 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 will have more powerful math that describes the universe even better, because there's lots of things that we still 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 is pretty good and we're going to stick with it, But maybe less 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 it's just our way of understanding it. This is the 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 that 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, like 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 like figure out how word works, and you could reverse engineering using some other programming language. Maybe it was written in Python and you figured out how to write it in C. Right now you have a description of this computer program in your own language. That doesn't necessarily mean that that's the per brand 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 ForWord 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 would that even look like if you wrote it down, that you have to write down something. While on page forty seven of his book without Numbers, for example, he talks about how to do this. It's pretty philosophically intricate. He like abuse 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 that 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 trying to rid the calculation of intermediate steps that need numbers to describe them, but all tim redly would and you have to write it down, And what do you eventually have to you know, have an equation or something you know in his formulation of Newton's gravity, there are new 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? Does this seem suspect or is this like an actual valid possibility for the universe. I think that most philosophers see its 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 quipple 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 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? Like a hundred fifty years ago, people have been doing math for thousands of years. About a hundred and fifty years ago, people were like, hold on a second, what are the basic rules of math? Anyway? And so there was a guy named Piano who showed that almost all of arithmetic can be boiled down to just a basic fuel 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 and 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 about 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, there's addition. Basically, it's just a group exactly. It's addition and its popularity. It's all clicks versus very elitist or it's all about clickbait. All right, Well, I think that answers Matthew's question, what is the math of the universe? Well, the answer is, so far calculus has been really useful in describing the universe, but um physicists are not sure if maybe even calculus is the fundamental way to describe the universe, or even the most fundamental um 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 in the heart of the universe and why it is even possible to describe it mathematically or to make sense of it with our little primate brains. So you're gonna 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. Ye, thanks for listening, and remember that Daniel and Jorge Explain the Universe is a production of I Heart Radio. For more podcast for my heart Radio, visit the I heart Radio app, Apple Podcasts, or wherever you listen to your favorite shows. Yeah.