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I like to think sometimes about what it was like to be a caveman or cave one. You know, they probably didn't travel nearly as much as we do, and so they just didn't have a global sense for where they lived in the world. They just saw a little patch and all they could do was wonder about what lay beyond. Now, of course, we know so much more about the world, and so we can look at the bones of Stone Age people and feel like we might know more about their world than they did. There might have been people who lived near the ocean but never saw it, things that were right around the corner they didn't even know about. But aren't we still cave men and cave women in that way? We still see our little patch of the universe, and we don't know what's around the corner. What if there's some crazy, awesome thing, but it's just a little bit further than we can see. And so that makes me wonder will future humans look back at us in the same way, chuckling to themselves about how clueless we are? I sure hope so, because it means physicists have been doing their jobs.

I like to think sometimes about what it was like to be a caveman or cave one. You know, they probably didn't travel nearly as much as we do, and so they just didn't have a global sense for where they lived in the world. They just saw a little patch and all they could do was wonder about what lay beyond. Now, of course, we know so much more about the world, and so we can look at the bones of Stone Age people and feel like we might know more about their world than they did. There might have been people who lived near the ocean but never saw it, things that were right around the corner they didn't even know about. But aren't we still cave men and cave women in that way? We still see our little patch of the universe, and we don't know what's around the corner. What if there's some crazy, awesome thing, but it's just a little bit further than we can see. And so that makes me wonder will future humans look back at us in the same way, chuckling to themselves about how clueless we are? I sure hope so, because it means physicists have been doing their jobs.

Hi.

Hi.

I'm Daniel. I'm a particle physicist, and welcome to the podcast Daniel and Jorge Explain the Universe our production of iHeartRadio Today in the podcast is just me. Jorge can't be here today to join us, and so I'm going to be taking you on a tour of all the amazing things in our universe, all the incredible things that we want to understand, all the distant places that we can just barely probe with our telescopes, all the tiny particles that we seek to understand. This podcast is about all of those things and everything. We want to explain the entire universe in a way that makes you come away thinking hmmm, I get it, and maybe once or twice even makes you chuckle. And one of the things that we cherish on this podcast is not just the things that science has been working on, but the things that you have been wondering about, because physics is not something which belongs to a tiny group of people who happen to get to be professors of physics, but it's something we can all do. Every time you wonder about the universe, every time you think to yourself, how does that work? Every time you hear two things you don't quite know how to fit them together in your mind, you are doing physics. You are being a physicist, and we love that here on the podcast, and we want to encourage that. And one way that we do that is by answering your questions. So if you have questions about the way the universe works, you have lots of ways to get in touch with us. You can send us an email to questions at Danielanjorge dot com. You can engage with us on Twitter at Daniel and Jorge, or you can come and ask me in person. Come to one of my public office hours where I hang out on zoom and answer questions from anybody and everybody about physics. For information on that, go to my website to sites dot UCI dot edu slash Daniel and you'll find all the relevant connection information. Sometimes I'll get emailed the question from a listener and it's such a good question, such a fun topic, that I think I'm not just gonna write back and send them the answer. I want to talk about this on the podcast, So I'll ask them to send me an audio clip of themselves asking the question, because I think all of you might be interested in the answer. And that's exactly what we're going to do on today's episode. Today, I'll be catching up with our backlog of listener questions while Jorge is on a break and answering questions from real people. Questions about physics, questions about which corner of the universe we're in, questions about how mirrors work, questions about photons and gravity, the kind of things that thinking people wonder about when they try to understand the world around them. All right, so let's get to it. First. Up is a question about the universe.

I'm Daniel. I'm a particle physicist, and welcome to the podcast Daniel and Jorge Explain the Universe our production of iHeartRadio Today in the podcast is just me. Jorge can't be here today to join us, and so I'm going to be taking you on a tour of all the amazing things in our universe, all the incredible things that we want to understand, all the distant places that we can just barely probe with our telescopes, all the tiny particles that we seek to understand. This podcast is about all of those things and everything. We want to explain the entire universe in a way that makes you come away thinking hmmm, I get it, and maybe once or twice even makes you chuckle. And one of the things that we cherish on this podcast is not just the things that science has been working on, but the things that you have been wondering about, because physics is not something which belongs to a tiny group of people who happen to get to be professors of physics, but it's something we can all do. Every time you wonder about the universe, every time you think to yourself, how does that work? Every time you hear two things you don't quite know how to fit them together in your mind, you are doing physics. You are being a physicist, and we love that here on the podcast, and we want to encourage that. And one way that we do that is by answering your questions. So if you have questions about the way the universe works, you have lots of ways to get in touch with us. You can send us an email to questions at Danielanjorge dot com. You can engage with us on Twitter at Daniel and Jorge, or you can come and ask me in person. Come to one of my public office hours where I hang out on zoom and answer questions from anybody and everybody about physics. For information on that, go to my website to sites dot UCI dot edu slash Daniel and you'll find all the relevant connection information. Sometimes I'll get emailed the question from a listener and it's such a good question, such a fun topic, that I think I'm not just gonna write back and send them the answer. I want to talk about this on the podcast, So I'll ask them to send me an audio clip of themselves asking the question, because I think all of you might be interested in the answer. And that's exactly what we're going to do on today's episode. Today, I'll be catching up with our backlog of listener questions while Jorge is on a break and answering questions from real people. Questions about physics, questions about which corner of the universe we're in, questions about how mirrors work, questions about photons and gravity, the kind of things that thinking people wonder about when they try to understand the world around them. All right, so let's get to it. First. Up is a question about the universe.

Hi, Daniel n Jorte. My name is Elia, and I'm a big fan of your podcast. I've always wondered whether or not it is possible to know which corner of the universe we're in, depending upon what we believe the shape of the universe is, and if it's shaped like a donut, for example, is it possible to cross through the donut hole and re enter the universe provided inflation suddenly stopped. Thank you so much for teaching and inspiring us.

Hi, Daniel n Jorte. My name is Elia, and I'm a big fan of your podcast. I've always wondered whether or not it is possible to know which corner of the universe we're in, depending upon what we believe the shape of the universe is, and if it's shaped like a donut, for example, is it possible to cross through the donut hole and re enter the universe provided inflation suddenly stopped. Thank you so much for teaching and inspiring us.

All right, thanks very much, Ilia for that super fun question. I like this question a lot, not just because it talks about donuts and that makes me hungry, and it makes me wonder, was Ilia eating a donut when he's asked me this question. Why a donut? Why not like a pastry shaped universe or you know, a pie shaped universe. But we'll dig into that and take a bite out of that part of the question. But I also love this question because they touch is on something really deep and fascinating not just about the shape of the universe, but about where we are in the universe. Are we in an interesting part of the universe? Are we near the center of the universe? Are we near some weird edge or corner of the universe? I love when you take a deep question about the universe, how big is it? What shape is it? And you make it a personal question, like where are we in the universe? So let's dig into it. Where are we in the universe? What corner of the universe are we in? And you're totally right ilia that the answer to this question depends a lot on what we think about the shape and the size of the universe. So let's answer it in a few different ways. Let's start with the most likely configuration for the universe and imagine that the universe is infinite. That means that it goes on forever in every direction. There's no edge, there's no point at which the universe stops. It just goes on forever. And it's sort of euclidian in a sense that you can go on forever without looping around on yourself, and the two parallel lines will go on forever without crossing. Why do I say this is the most likely scenario, the most likely setup for a universe. I just think it's the most natural because it has no edges, because it's sort of simple. If you have an edge, then you have to explain why that edge. If you have an edge, you have to answer why is this edge over here and not somewhere else. You need a special case. And I like explanations that don't have special cases, that are simple and that are universal. And so this one that the universe just sort of goes on forever in every direction is nice because it makes no place in the universe special. Every point in the universe has an infinite amount of universe in every direction, and so it's very similar everywhere. And that's the key thing. That's a crucial idea in cosmology recently, this cosmological principle, the one that says that every location in the universe is equivalent. There's no center, there's no edge, there's no corners. Every place in the universe is basically like every other place in the universe. Now, let's unpack that a tiny little bit. What do we really mean when we say every place in the universe is like every other place in the universe, Because my house is not the same as your house, and the Earth is not the same as Jupiter. And there are galaxies, and there are places where there are no galaxies. So like at the very microscopic level, it's not true that every place in the universe is the same as every other place in the universe. What we mean when we say that is that the laws of physics are the same, that they always apply in the same way. That you don't have different laws and different constants over there than you have over here. Now, if you have the same laws of physics, how is it that you can even have any difference. How is it that you can have a planet here and not a planet there, where you have all these galaxies over here and no galaxies over there. Well, the current understanding is that this comes from quantum randomness. In the very early universe, when it was hot and dense but still infinite, right, still goes on in every direction, but hotter and denser and younger. That there were quantum fluctuations that made some spots in the universe more dense, with stuff in some spots less dense. Now, does that mean that those spots are different from the other spots, Well, they got different random numbers, but they had the same opportunity. They were playing the same game, they just had a different outcome. And quantum mechanics is amazing because the rules are the same. It gaves the same probability distribution for every scenario that's identical, but individual outcomes can be different. Quantum mechanics tells us that if you poke a particle the same way one hundred times, you might get one hundred different outcomes. Or you might have a scenario where half the time it goes left and half the time it goes right, even if the initial conditions are exactly the same. So that's what's happening in the very early universe. The initial conditions, this great energy density is the same everywhere, but different things can happen in different places. They are following the same rules, so there's no special place, but they have a different outcome. And then those little pockets of over density get expanded into massive macroscopic effects which seed the structure of the universe when the universe expanded very rapidly in the early Big Bang. So you have hot, dense stuff in the very early universe. Random quantum fluctuations make some of it a little bit more dense. Inflation expands those tiny little microscopic things into big macroscopic things, and then gravity takes over. So that's how you can have a universe where the rules of physics are the same everywhere, but you don't actually have the same outcome everywhere. You have galaxies here and no galaxies over there. So in that scenario, the universe is the same everywhere. There's no corners, there's no center, and everywhere in the universe follows the same rules. And so where are we in the universe? Well, we're here, but here is sort of the same as there, so here or there there or here. It sounds sort of like a Doctor Seuss book, right, but it's actually real. And this I think is the most prevalent idea for where we are in the universe because it doesn't require any special cases. Now, for those of you who are thinking back about how I described the Big Bang and thinking, hold on a second, wasn't the Big Bang? At a certain point? I described it as a moment when the universe was hot and dense and young. Right, that doesn't mean that it was hot and dense and localized. The way I think about the Big Bang is not as a tiny dot which then exploded out to fill up the universe with stuff. The more modern view of the Big Bang is that it was a change from high density to low density. I'm using different words there because I mean something different. I mean that the universe was high density but still infinite, So not a tiny little dot of stuff like many people used to describe the Big Bang, but an infinite universe filled with hot dense stuff which then expanded. So now that hot dense stuff becomes cold and dilute, right, it spreads out. Space itself is expanded. You create new space between stuff in order to go from a hot dense universe to a cold, dilute universe. So the Big Bang was not an explosion as much as an expansion of space. It stretched space everywhere. So the Big Bang happened everywhere, all at once. So that's the answer in the scenario that the universe is infinite, that it goes on forever in every direction, And in that scenario, doesn't really make sense to talk about where we are in the universe because everywhere is the same place. But as we've talked about on the podcast a few times, we don't know that the universe is infinite. We can't know that the universe is infinite. We could only see a finite patch of the universe. Just like ancient peoples who thought about the universe but never traveled very far from their home, they only saw a tiny little path. They could only imagine what was beyond the edge of their knowledge. In the same way, there's a patch of the universe about ninety billion light years across that we can see. We call this the observable universe, and beyond it, we don't know what's there. Why can't we see it, Well, it's a physical limitation. It's because of the speed of light. Light just hasn't had enough time to get to us from there since the beginning of the universe. It's on its way. It's been flying our direction the whole time. The universe has been doing its universe thing. But it started out so far away that even though it's traveling at light speed, it hasn't reached us yet. And it will. And every year that goes by the size of the observable universe, the portion of the universe that we can see gets bigger and bigger, and we can see more and more stars and more planets around them, and all sorts of amazing, interesting stuff. And of course, first we see the stuff that's happened fourteen billion years ago, because that's when the light left it to get to us. So as we look further out into the universe, we actually see the past more than we see the present. So if there was something crazy happening just past the edge of the observable universe, we wouldn't see it for a while. If it's just happening now, if there's some crazy dancing banana party happening on a planet just past the edge, it's going to take billions of years before those awesome images get to us, so we can embarrass the aliens by posting them on social media. So what lies beyond the edge of the observable universe we don't know, and that's one reason why we don't know the shape of the universe. There are a few scenarios for how the universe could be shaped. One of course, is that it's infinite. Another is that it's not infinite, but it doesn't have an edge, something like the surface of a sphere. As you walk along the Earth, you're not aware of there being any edges. I mean, there are oceans and all sorts of stuff and walls and fences, but sort of geomegically only. Imagine yourself walking just on the surface of a perfect sphere. You wouldn't know in the edges. You could go on forever without bumping into anything, and eventually you could even come back to where you started. So that's a universe that's not infinite as a finite amount of area the surface of a sphere. So make sort of the leap from the two dimensional surface of a sphere where you're walking around on it now into three dimensional space. How does that work? Are we saying that three dimensional space is sort of like plastered onto the surface of a four dimensional sphere. No, we're just saying that the universe could be connected differently. We don't know if our three dimensional space is like embedded in some higher dimensional space four or eleven or twenty six, though, if you're interested in that kind of stuff. We have a whole podcast episode about how many dimensions there are in space. But even if we just assume that space has three dimensions, it's still possible for it to curve because space can be bent and connected in weird ways. It can loop around itself, it can have all sorts of distortions. And we'll talk about this actually later today in this same podcast. But you can imagine space being complex in such a way that bits of it are connected to each other, so that if you did embed them in a four dimensional space, it would look like a weird shape. It would look like the surface of a sphere, or it would look like a donut or a banana or a pastry or something else. And now I'm getting too hungry to continue answering this question. But we just don't know the shape that all of these things are possible, because we just can't see enough of the universe to rule some of this out. Now, it's also possible that the universe isn't infinite and that it does have some weird edge. Remember, space is not something that we understand very well. Only for the last one hundred years or so have we even understood that space is a thing that it can bend and distort and expand and grow and do all sorts of weird stuff. So we're at really the very beginning of our understanding of the nature of space. And it might be that space has some weird edge beyond which there is no more space. What would be there beyond space? Is that nothing? Is that a thing without space? We just don't know. But it's possible for space to have weird connections so that if you get to the edge of it, you just can't go that way anymore. You might think, well, what does that mean? How is that possible? Well, remember that in black holes, for example, space can be distorted so that you can only move in one direction. Inside a black hole, space is so distorted that every motion takes you towards the center. It's an example of a non simple arrangement of space. So now imagine the edge of the universe where there just is no direction out. There's no direction you can go that would take you beyond the edge of the universe. There's only directions in towards the universe, sort of like when you're in a black hole. There is no path out of the universe, but there is an edge to the black hole, there is an event horizon. So it is possible to have these weird edges, these discontinuities in space, places where you just cannot go. Is the universe like that? We just don't know. Maybe future societies, as they eat their donuts, will laugh at us for thinking that this was real, or maybe future societies, as they eat their healthy snack will be thinking, boy, they were really onto something. They should have dug even deeper. All right, So let's get to the last part of Ilia's question, which is about the donut hole. What if the universe is not infinite and it's not like the surface of a sphere where you can sort of move around in every direction. What if it's connected like a donut. You know, the surface of a donut is connected differently from the surface of a sphere. Right. On a sphere, if you go north, you come back to where you started, and if you go east, you come back to where you started. On the surface of a donut, it's a little bit different because on the surface of a donut, if you go north, for example, you come back to where you started, but you don't get to the other side of the donut. To do that, you have to go east right, So there's no trivial mapping from a surface of a donut to the surface of a sphere. Right, donut has a hole in the middle, and a sphere just doesn't. So Ilia's awesome question is is it possible to go through the donut hole? Is it possible to get to the other side of the universe without going the long way around. Well, I think to answer your second question, first, you could get to the other side of the universe using a wormhole. Right. If the universe is topologically complex, then you can allow other wrinkles. Instead of just being sort of hooked together like a bunch of chain links, but in the shape of a donut, you could have a connection directly between one side of the donut and the other. That's what a wormhole would be. That's exactly what a wormhole is. It's a connection between two points in space that are otherwise very distant, and so you can imagine using a wormhole to get from one side of the donut to the other. Could you actually be inside the donut? Could you like leave the universe and fly through the donut hole to get to the other side. I think, unfortunately, the answer to this question is no. Even just imagining the universe as having a hole in the middle, that that donut hole is a real thing means that you're taking this analogy one step too far. You're imagining the universe is embedded in some high dimensional space where that hole exists. Remember that this donut is an analogy. It's an analogy of a two D universe that's sort of painted onto the surface of a three D donut. But our universe is three dimensions, and again we don't think that it's painted onto the surface of a four D universe. We just think that the connections between the points in the three D universe might resemble the relationships of the surface of a three D donut. Right, And so if you want to visualize it, you can imagine putting it into four D space to sort of arrange it in your head and think, oh, and in that four D space you get a three D donut. But that doesn't mean that four D space exists, And so that doesn't mean that that place, the whole inside the donut, is a real thing. Right, said another way, if the universe is a donut, then the hole in the inside doesn't exist as a place you can go any more than the part of the outside of the donut exists. There's no space there, there's no way to be there, there's no way you can go there, and so it just doesn't exist. So sorry, Iliat, you can't take a short cut across the donut hole, no matter how many donuts you eat. All right, that was a super fun question, Thanks very much, Ilia. I want to answer some more questions, but first let's take a quick break. With big wireless providers, what you see is never what you get. Somewhere between the store and your first month's bill, the price you thought you were paying magically skyrockets. With mint Mobile, you'll never have to worry about gotcha's ever again. When Mint Mobile says fifteen dollars a month for a three month plan, they really need it. I've used mint Mobile and the call quality is always so crisp and so clear. I can recommend it to you. So say bye bye to your overpriced wireless plans, jaw dropping monthly bills and unexpected overages. You can use your own phone with any Mint Mobile plan and bring your phone number along with your existing contacts. 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All right, thanks very much, Ilia for that super fun question. I like this question a lot, not just because it talks about donuts and that makes me hungry, and it makes me wonder, was Ilia eating a donut when he's asked me this question. Why a donut? Why not like a pastry shaped universe or you know, a pie shaped universe. But we'll dig into that and take a bite out of that part of the question. But I also love this question because they touch is on something really deep and fascinating not just about the shape of the universe, but about where we are in the universe. Are we in an interesting part of the universe? Are we near the center of the universe? Are we near some weird edge or corner of the universe? I love when you take a deep question about the universe, how big is it? What shape is it? And you make it a personal question, like where are we in the universe? So let's dig into it. Where are we in the universe? What corner of the universe are we in? And you're totally right ilia that the answer to this question depends a lot on what we think about the shape and the size of the universe. So let's answer it in a few different ways. Let's start with the most likely configuration for the universe and imagine that the universe is infinite. That means that it goes on forever in every direction. There's no edge, there's no point at which the universe stops. It just goes on forever. And it's sort of euclidian in a sense that you can go on forever without looping around on yourself, and the two parallel lines will go on forever without crossing. Why do I say this is the most likely scenario, the most likely setup for a universe. I just think it's the most natural because it has no edges, because it's sort of simple. If you have an edge, then you have to explain why that edge. If you have an edge, you have to answer why is this edge over here and not somewhere else. You need a special case. And I like explanations that don't have special cases, that are simple and that are universal. And so this one that the universe just sort of goes on forever in every direction is nice because it makes no place in the universe special. Every point in the universe has an infinite amount of universe in every direction, and so it's very similar everywhere. And that's the key thing. That's a crucial idea in cosmology recently, this cosmological principle, the one that says that every location in the universe is equivalent. There's no center, there's no edge, there's no corners. Every place in the universe is basically like every other place in the universe. Now, let's unpack that a tiny little bit. What do we really mean when we say every place in the universe is like every other place in the universe, Because my house is not the same as your house, and the Earth is not the same as Jupiter. And there are galaxies, and there are places where there are no galaxies. So like at the very microscopic level, it's not true that every place in the universe is the same as every other place in the universe. What we mean when we say that is that the laws of physics are the same, that they always apply in the same way. That you don't have different laws and different constants over there than you have over here. Now, if you have the same laws of physics, how is it that you can even have any difference. How is it that you can have a planet here and not a planet there, where you have all these galaxies over here and no galaxies over there. Well, the current understanding is that this comes from quantum randomness. In the very early universe, when it was hot and dense but still infinite, right, still goes on in every direction, but hotter and denser and younger. That there were quantum fluctuations that made some spots in the universe more dense, with stuff in some spots less dense. Now, does that mean that those spots are different from the other spots, Well, they got different random numbers, but they had the same opportunity. They were playing the same game, they just had a different outcome. And quantum mechanics is amazing because the rules are the same. It gaves the same probability distribution for every scenario that's identical, but individual outcomes can be different. Quantum mechanics tells us that if you poke a particle the same way one hundred times, you might get one hundred different outcomes. Or you might have a scenario where half the time it goes left and half the time it goes right, even if the initial conditions are exactly the same. So that's what's happening in the very early universe. The initial conditions, this great energy density is the same everywhere, but different things can happen in different places. They are following the same rules, so there's no special place, but they have a different outcome. And then those little pockets of over density get expanded into massive macroscopic effects which seed the structure of the universe when the universe expanded very rapidly in the early Big Bang. So you have hot, dense stuff in the very early universe. Random quantum fluctuations make some of it a little bit more dense. Inflation expands those tiny little microscopic things into big macroscopic things, and then gravity takes over. So that's how you can have a universe where the rules of physics are the same everywhere, but you don't actually have the same outcome everywhere. You have galaxies here and no galaxies over there. So in that scenario, the universe is the same everywhere. There's no corners, there's no center, and everywhere in the universe follows the same rules. And so where are we in the universe? Well, we're here, but here is sort of the same as there, so here or there there or here. It sounds sort of like a Doctor Seuss book, right, but it's actually real. And this I think is the most prevalent idea for where we are in the universe because it doesn't require any special cases. Now, for those of you who are thinking back about how I described the Big Bang and thinking, hold on a second, wasn't the Big Bang? At a certain point? I described it as a moment when the universe was hot and dense and young. Right, that doesn't mean that it was hot and dense and localized. The way I think about the Big Bang is not as a tiny dot which then exploded out to fill up the universe with stuff. The more modern view of the Big Bang is that it was a change from high density to low density. I'm using different words there because I mean something different. I mean that the universe was high density but still infinite, So not a tiny little dot of stuff like many people used to describe the Big Bang, but an infinite universe filled with hot dense stuff which then expanded. So now that hot dense stuff becomes cold and dilute, right, it spreads out. Space itself is expanded. You create new space between stuff in order to go from a hot dense universe to a cold, dilute universe. So the Big Bang was not an explosion as much as an expansion of space. It stretched space everywhere. So the Big Bang happened everywhere, all at once. So that's the answer in the scenario that the universe is infinite, that it goes on forever in every direction, And in that scenario, doesn't really make sense to talk about where we are in the universe because everywhere is the same place. But as we've talked about on the podcast a few times, we don't know that the universe is infinite. We can't know that the universe is infinite. We could only see a finite patch of the universe. Just like ancient peoples who thought about the universe but never traveled very far from their home, they only saw a tiny little path. They could only imagine what was beyond the edge of their knowledge. In the same way, there's a patch of the universe about ninety billion light years across that we can see. We call this the observable universe, and beyond it, we don't know what's there. Why can't we see it, Well, it's a physical limitation. It's because of the speed of light. Light just hasn't had enough time to get to us from there since the beginning of the universe. It's on its way. It's been flying our direction the whole time. The universe has been doing its universe thing. But it started out so far away that even though it's traveling at light speed, it hasn't reached us yet. And it will. And every year that goes by the size of the observable universe, the portion of the universe that we can see gets bigger and bigger, and we can see more and more stars and more planets around them, and all sorts of amazing, interesting stuff. And of course, first we see the stuff that's happened fourteen billion years ago, because that's when the light left it to get to us. So as we look further out into the universe, we actually see the past more than we see the present. So if there was something crazy happening just past the edge of the observable universe, we wouldn't see it for a while. If it's just happening now, if there's some crazy dancing banana party happening on a planet just past the edge, it's going to take billions of years before those awesome images get to us, so we can embarrass the aliens by posting them on social media. So what lies beyond the edge of the observable universe we don't know, and that's one reason why we don't know the shape of the universe. There are a few scenarios for how the universe could be shaped. One of course, is that it's infinite. Another is that it's not infinite, but it doesn't have an edge, something like the surface of a sphere. As you walk along the Earth, you're not aware of there being any edges. I mean, there are oceans and all sorts of stuff and walls and fences, but sort of geomegically only. Imagine yourself walking just on the surface of a perfect sphere. You wouldn't know in the edges. You could go on forever without bumping into anything, and eventually you could even come back to where you started. So that's a universe that's not infinite as a finite amount of area the surface of a sphere. So make sort of the leap from the two dimensional surface of a sphere where you're walking around on it now into three dimensional space. How does that work? Are we saying that three dimensional space is sort of like plastered onto the surface of a four dimensional sphere. No, we're just saying that the universe could be connected differently. We don't know if our three dimensional space is like embedded in some higher dimensional space four or eleven or twenty six, though, if you're interested in that kind of stuff. We have a whole podcast episode about how many dimensions there are in space. But even if we just assume that space has three dimensions, it's still possible for it to curve because space can be bent and connected in weird ways. It can loop around itself, it can have all sorts of distortions. And we'll talk about this actually later today in this same podcast. But you can imagine space being complex in such a way that bits of it are connected to each other, so that if you did embed them in a four dimensional space, it would look like a weird shape. It would look like the surface of a sphere, or it would look like a donut or a banana or a pastry or something else. And now I'm getting too hungry to continue answering this question. But we just don't know the shape that all of these things are possible, because we just can't see enough of the universe to rule some of this out. Now, it's also possible that the universe isn't infinite and that it does have some weird edge. Remember, space is not something that we understand very well. Only for the last one hundred years or so have we even understood that space is a thing that it can bend and distort and expand and grow and do all sorts of weird stuff. So we're at really the very beginning of our understanding of the nature of space. And it might be that space has some weird edge beyond which there is no more space. What would be there beyond space? Is that nothing? Is that a thing without space? We just don't know. But it's possible for space to have weird connections so that if you get to the edge of it, you just can't go that way anymore. You might think, well, what does that mean? How is that possible? Well, remember that in black holes, for example, space can be distorted so that you can only move in one direction. Inside a black hole, space is so distorted that every motion takes you towards the center. It's an example of a non simple arrangement of space. So now imagine the edge of the universe where there just is no direction out. There's no direction you can go that would take you beyond the edge of the universe. There's only directions in towards the universe, sort of like when you're in a black hole. There is no path out of the universe, but there is an edge to the black hole, there is an event horizon. So it is possible to have these weird edges, these discontinuities in space, places where you just cannot go. Is the universe like that? We just don't know. Maybe future societies, as they eat their donuts, will laugh at us for thinking that this was real, or maybe future societies, as they eat their healthy snack will be thinking, boy, they were really onto something. They should have dug even deeper. All right, So let's get to the last part of Ilia's question, which is about the donut hole. What if the universe is not infinite and it's not like the surface of a sphere where you can sort of move around in every direction. What if it's connected like a donut. You know, the surface of a donut is connected differently from the surface of a sphere. Right. On a sphere, if you go north, you come back to where you started, and if you go east, you come back to where you started. On the surface of a donut, it's a little bit different because on the surface of a donut, if you go north, for example, you come back to where you started, but you don't get to the other side of the donut. To do that, you have to go east right, So there's no trivial mapping from a surface of a donut to the surface of a sphere. Right, donut has a hole in the middle, and a sphere just doesn't. So Ilia's awesome question is is it possible to go through the donut hole? Is it possible to get to the other side of the universe without going the long way around. Well, I think to answer your second question, first, you could get to the other side of the universe using a wormhole. Right. If the universe is topologically complex, then you can allow other wrinkles. Instead of just being sort of hooked together like a bunch of chain links, but in the shape of a donut, you could have a connection directly between one side of the donut and the other. That's what a wormhole would be. That's exactly what a wormhole is. It's a connection between two points in space that are otherwise very distant, and so you can imagine using a wormhole to get from one side of the donut to the other. Could you actually be inside the donut? Could you like leave the universe and fly through the donut hole to get to the other side. I think, unfortunately, the answer to this question is no. Even just imagining the universe as having a hole in the middle, that that donut hole is a real thing means that you're taking this analogy one step too far. You're imagining the universe is embedded in some high dimensional space where that hole exists. Remember that this donut is an analogy. It's an analogy of a two D universe that's sort of painted onto the surface of a three D donut. But our universe is three dimensions, and again we don't think that it's painted onto the surface of a four D universe. We just think that the connections between the points in the three D universe might resemble the relationships of the surface of a three D donut. Right, And so if you want to visualize it, you can imagine putting it into four D space to sort of arrange it in your head and think, oh, and in that four D space you get a three D donut. But that doesn't mean that four D space exists, And so that doesn't mean that that place, the whole inside the donut, is a real thing. Right, said another way, if the universe is a donut, then the hole in the inside doesn't exist as a place you can go any more than the part of the outside of the donut exists. There's no space there, there's no way to be there, there's no way you can go there, and so it just doesn't exist. So sorry, Iliat, you can't take a short cut across the donut hole, no matter how many donuts you eat. All right, that was a super fun question, Thanks very much, Ilia. I want to answer some more questions, but first let's take a quick break. With big wireless providers, what you see is never what you get. Somewhere between the store and your first month's bill, the price you thought you were paying magically skyrockets. With mint Mobile, you'll never have to worry about gotcha's ever again. When Mint Mobile says fifteen dollars a month for a three month plan, they really need it. I've used mint Mobile and the call quality is always so crisp and so clear. I can recommend it to you. So say bye bye to your overpriced wireless plans, jaw dropping monthly bills and unexpected overages. You can use your own phone with any Mint Mobile plan and bring your phone number along with your existing contacts. 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AI might be the most important new computer technology ever. It's storming every industry and literally billions of dollars are being invested, so buckle up. The problem is that AI needs a lot of speed and processing power, So how do you compete without cost spiraling out of control. It's time to upgrade to the next generation of the cloud. Oracle Cloud Infrastructure or OCI. OCI is a single platform for your infrastructure, database, application development, and AI needs. OCI has four to eight times the bandwidth of other clouds, offers one consistent price instead of variable regional pricing, and of course nobody does data better than Oracle. So now you can train your AI models at twice the speed and less than half the cost of other clouds. If you want to do more and spend less, like Uber eight by eight and Data Bricks Mosaic take a free test drive of OCI at Oracle dot com slash Strategic. That's Oracle dot com slash Strategic, Oracle dot com slash Strategic.

If you love iPhone, you'll love Apple Card. It's the credit card designed for iPhone. It gives you unlimited daily cash back that can earn four point four zero percent annual percentage yield. When you open a high yield savings account through Applecard, apply for Applecard in the wallet app, subject to credit approval. Savings is available to Applecard owners subject to eligibility. Apple Card and Savings by Goldman Sachs Bank USA, Salt Lake City Branch Member FDIC, terms and more at applecard dot com. All right, we're back and this is daniel and I'm answering listener questions. We talked about the universe as a donut, and I hope that during that break you all went off and got a snack, healthy or unhealthy. Up to you. And now we're back and we're talking more physics. And here's an awesome question from another listener.

If you love iPhone, you'll love Apple Card. It's the credit card designed for iPhone. It gives you unlimited daily cash back that can earn four point four zero percent annual percentage yield. When you open a high yield savings account through Applecard, apply for Applecard in the wallet app, subject to credit approval. Savings is available to Applecard owners subject to eligibility. Apple Card and Savings by Goldman Sachs Bank USA, Salt Lake City Branch Member FDIC, terms and more at applecard dot com. All right, we're back and this is daniel and I'm answering listener questions. We talked about the universe as a donut, and I hope that during that break you all went off and got a snack, healthy or unhealthy. Up to you. And now we're back and we're talking more physics. And here's an awesome question from another listener.

Hey, Danielle and Rock explained the universe. Amazing program you have there, always always inspiring. I was wondering the other day how mirrors work, and then I remember that everything at the smallest scale it's even weirder. So how do mirrors actually work at the quantum level? Our photons bouncing off a mirror or are they being absorbed and remeded? How does that work? Thank you love your podcast, Say yeah.

Hey, Danielle and Rock explained the universe. Amazing program you have there, always always inspiring. I was wondering the other day how mirrors work, and then I remember that everything at the smallest scale it's even weirder. So how do mirrors actually work at the quantum level? Our photons bouncing off a mirror or are they being absorbed and remeded? How does that work? Thank you love your podcast, Say yeah.

All right, this is a really fun question because it digs really deep into understanding what light actually is. And I love the whole spirit of this kind of exercise of looking at things around us in the world and wondering what's really going on at the microscopic level. I mean, that's why I'm a particle physicist, because I have this feeling like everything around us in the world is not the true world, sort of built up of tiny little things which, acting together in vast amounts in aggregate, make these weird effects, these effects like people and weather and bananas. But that's not the true stuff of the universe, right, Bananas are not fundamental to the universe, no matter how much Woorhey likes to snack on them. The true universe is made out of the smallest, tiniest things. And it's my sense that if you understood the universe, the smallest, the tiniest bits, then you're understanding the deep truth, and you could always work your way up from that deep truth to anything else like supernovas and bananas. And that's why every time I see something weird in the world, I want to understand it in terms of the microscopic effects, like what's going on at the particle level that makes this happen. And so I think that's the motivation for this question, this question about how a mirror works, because you could imagine it like, well, what if light is just sort of like photons, and you think of photons as particles, and what happens when a photon hits a mirror? It bounces off And you have an image in your head of like a tennis ball bouncing off of a wall, and it bounces off and it sort of reflects off the wall. You know, big deal, right, But why not really happens microscopically because if you zoom in, you realize, well, the wall is not smooth, right, The wall is man out of a lattice of atoms, and the photon is also small, and so it's sensitive to these little defects. The wall is not perfectly smooth, So how can it bounce off of it, And what is bouncing really mean for a photon? Because what happens when a photon approaches the wall is that it like interacts with the electrons and the atoms in that lattice of the wall, right. And photons don't like touch the wall. They don't bounce off the wall the way a tennis ball bounces off the wall. The only way a photon can bounce or touch anything is through its interactions. That means that it like gets absorbed by the atom and then gets re emitted. And if it's getting absorbed and re emitted, how can it bounce off in the right direction?

All right, this is a really fun question because it digs really deep into understanding what light actually is. And I love the whole spirit of this kind of exercise of looking at things around us in the world and wondering what's really going on at the microscopic level. I mean, that's why I'm a particle physicist, because I have this feeling like everything around us in the world is not the true world, sort of built up of tiny little things which, acting together in vast amounts in aggregate, make these weird effects, these effects like people and weather and bananas. But that's not the true stuff of the universe, right, Bananas are not fundamental to the universe, no matter how much Woorhey likes to snack on them. The true universe is made out of the smallest, tiniest things. And it's my sense that if you understood the universe, the smallest, the tiniest bits, then you're understanding the deep truth, and you could always work your way up from that deep truth to anything else like supernovas and bananas. And that's why every time I see something weird in the world, I want to understand it in terms of the microscopic effects, like what's going on at the particle level that makes this happen. And so I think that's the motivation for this question, this question about how a mirror works, because you could imagine it like, well, what if light is just sort of like photons, and you think of photons as particles, and what happens when a photon hits a mirror? It bounces off And you have an image in your head of like a tennis ball bouncing off of a wall, and it bounces off and it sort of reflects off the wall. You know, big deal, right, But why not really happens microscopically because if you zoom in, you realize, well, the wall is not smooth, right, The wall is man out of a lattice of atoms, and the photon is also small, and so it's sensitive to these little defects. The wall is not perfectly smooth, So how can it bounce off of it, And what is bouncing really mean for a photon? Because what happens when a photon approaches the wall is that it like interacts with the electrons and the atoms in that lattice of the wall, right. And photons don't like touch the wall. They don't bounce off the wall the way a tennis ball bounces off the wall. The only way a photon can bounce or touch anything is through its interactions. That means that it like gets absorbed by the atom and then gets re emitted. And if it's getting absorbed and re emitted, how can it bounce off in the right direction?

Right?

Right?

And so I think that's the underlying question here. How do we understand reflection? How do we understand how mirrors bounce photons off in the right direction? If mirrors are just collections of particles and photons are just streams of particles. So I think to understand this question and to keep your handle around it at the microscopic level, there are two important things to understand, two effects that we have to have in our minds to make a clear picture of what's going on. And the first is what's going on between the photon and this particle in the mirror, this bit of the mirror that it's interacting with. So photon approaches the mirror, and you can think of a photon as a particle, or you can think about it as a wave. Doesn't really matter. But remember if you're thinking about it as a particle, its motion is determined by its quantum wave. So it's really the wave like effects that dominate here. Now I'm not saying a photon is a wave. I'm not saying it's a particle. If you've been listening to the podcast, you know that I think it's neither a particle nor a wave. It's some weird other quantum mechanical thing which can't be perfectly described by anything we have intuition for. But sometimes some pictures are more useful than others. So what happens when the photon approaches the bit of the mirror. Well, photons can only really do one thing, which is that they can get absorbed by charged particles and then they can get re emitted. And in this case it's mostly the electrons. Like there are charges also in the atomic nucleus, but the nucleus is surrounded by electrons, and so when the photon ofpproaches. The surface of the mirror really just sees the electrons. It sees this like wall of electrons, and that's okay. Photons can talk to electrons. They're happy to do that. But the only way for that to happen is for the electron to absorb the photon. Then it has more energy and then it can give off that photon. It emits that photon, and then the question is how does it know which direction to emit that photon? When an electron which is spinning around an atom gives off a photon, doesn't it just emit it sort of randomly? And you can imagine all of these atoms is just like tiny little sources of light because they've absorbed the photon. Now it's theirs. Why don't they just shine them all in different directions? Well, that is the right way to think about it. You can think about each of these atoms which receives a photon as a little sort of point source. It's giving off a little bit of light. And this happens in lots of other examples too. For example, when light goes through a little slit, as it famously does in the double slit experiment, when it comes out of that slit, it's not going ness sarily in the same direction as when it went into the slit. Now it's like a little point source at the slit. And that's what you need to have, like interference between two slits. You need the lights to be coming out in lots of different directions so we can add up constructively or destructively. And that same picture also works for what's happening at the surface of a mirror. The photon is absorbed by an atom, and then the atom emits, and it emits in all directions. So why does the photon end up bouncing at the correct angle, right, Because if the photon comes in at a very steep angle, it comes out at a steep angle. If photons come in a very shallow angle to come out at a shallow angle, well, the way it works is that the photon comes out not just with the direction, but also with a phase. So the quantum wave function of the photon that determines where it's going has a number in it called the phase, sort of like how much it's spun. And the atom actually emits photons in all directions, but with different phases, and those phases deter whether or not. The photons at up constructively or destructively, and the phase that comes out depends on the angle that the photon came in. And so what happens is photon comes in, gets absorbed by the atom, and the atom emits photons sort of in every direction belt with different phases, and only in the right direction, in the direction that sort of corresponds to the angle the photon came in. Do those photons not cancel each other out, so you get destructive interference for all the other directions in constructive interference in the direction that corresponds to the same angle that came in. And that's what mirrors do. They bounce photons off, so the angle they leave at is the same as the angle they came in. If you're coming at ninety degrees, you leave it ninety degrees. If you come in at two degrees, you leave a two degrees in the other direction. So the atom is absorbing that photon and then it is sort of emitting in every direction, but there is one direction where the phase is right for the photons to get canceled out on top of each other. So that's why one direction dominates. And you can think about that either in terms of like lots of photons coming in in parallel hitting the surface and then sprang out all different directions, and the ones that are sort of in the wrong directions end up canceling each other out, and that's why you only get photons coming out in parallel. Or you can actually also think about it in terms of one photon. This is sort of mind blowing the same way that the double slit experiment is. The single photon hitting a mirror doesn't have like neighboring photons on either side to do the destructive and constructive interference for it. So how does that happen? Well, when a photon is absorbed by the atom and then emitted, there's a probability distribution there for where it's going to go, and it's those probabilities that can interfere with each other. Just like a single particle going through the double slit experiment has probabilities to go through either slit, a single photon hitting a mirror has probabilities to go in lots of different directions, and those probabilit interfere with themselves. So single particles probabilities interferes with itself, and that what determines the direction that the particle can go in, all right, So I said that there were two things you had to understand to figure out how mirrors work. One, we just talked about how atoms absorb and re emit the light and how it ends up going in the correct direction because the quantum mechanical phase of the wave function ensures that that direction is the only one that doesn't get destructive interference. The second is that conductors make better mirrors than non conductors. Things that do conduct the electricity make good mirrors. That's why metals, for example, make good mirrors a good sheet of aluminum, and the reason for that is that conductors don't let photons penetrate deep into their surface, and instead they mostly reflect it just from the very very thin sheet of the surface, which gives you a coherent image. If a particle went deep into a material and was absorbed before being re emitted, like a a centimeter inside the material, it might never emerge, and if it did, it might not be as coherent because they will have interactive with lots of different atoms. To get a nice, really crisp picture, you want to reflect just off the very surface of the material, so you're reflecting from a very flat plane, not getting the distortions you would get if you deflect it off of a surface that was not smooth. And so if particles can penetrate different levels of the material, you're basically reflecting off a not smooth mirror and you get a muddled mess. So metals are very good mirrors because they don't let photons penetrate very far into them. And that's because they are conductors, because they can rearrange their electrons to basically cancel out any electric field. If you have an electric field and you put a conductor in it, it will move its electrons around to balance that electric field because electric fields act on those electrons, and if you have a positive voltage in one direction, it will pull electrons in that direction to cancel it out. And so conductor, because they have these electrons to sort of slosh around inside them and reconfigure pretty easily, can cancel any electric field inside of them. That's why, for example, it's very difficult to get a phone call inside an elevator. Right in an elevator, you're surrounded by a metal box, and a phone call is just radio waves. It's a fluctuation in the electromagnetic spectrum, and that will just induce electrons inside the elevator walls to move around to cancel it. So a Faraday cage is nothing but a metal box and it can pretty effectively cancel almost any electromagnetic signal. The other side of that is that mirrors don't allow photons to go very deep into the material because they can rearrange the electrons to avoid those em fields going into the material. And that makes them good reflectors because the photons reflect just from the surface rather than deep in the material where the image might get muddled. All right, So next time you're looking in the mirror and you're wondering, wow, why am I so good looking, it's because of quantum mechanics and because of electrons zooming around to give you a nice, crisp, clear picture of your smiling face. All right, I hope that answered your question. I have one more question I really want to get to. But first, let's take another break. 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And so I think that's the underlying question here. How do we understand reflection? How do we understand how mirrors bounce photons off in the right direction? If mirrors are just collections of particles and photons are just streams of particles. So I think to understand this question and to keep your handle around it at the microscopic level, there are two important things to understand, two effects that we have to have in our minds to make a clear picture of what's going on. And the first is what's going on between the photon and this particle in the mirror, this bit of the mirror that it's interacting with. So photon approaches the mirror, and you can think of a photon as a particle, or you can think about it as a wave. Doesn't really matter. But remember if you're thinking about it as a particle, its motion is determined by its quantum wave. So it's really the wave like effects that dominate here. Now I'm not saying a photon is a wave. I'm not saying it's a particle. If you've been listening to the podcast, you know that I think it's neither a particle nor a wave. It's some weird other quantum mechanical thing which can't be perfectly described by anything we have intuition for. But sometimes some pictures are more useful than others. So what happens when the photon approaches the bit of the mirror. Well, photons can only really do one thing, which is that they can get absorbed by charged particles and then they can get re emitted. And in this case it's mostly the electrons. Like there are charges also in the atomic nucleus, but the nucleus is surrounded by electrons, and so when the photon ofpproaches. The surface of the mirror really just sees the electrons. It sees this like wall of electrons, and that's okay. Photons can talk to electrons. They're happy to do that. But the only way for that to happen is for the electron to absorb the photon. Then it has more energy and then it can give off that photon. It emits that photon, and then the question is how does it know which direction to emit that photon? When an electron which is spinning around an atom gives off a photon, doesn't it just emit it sort of randomly? And you can imagine all of these atoms is just like tiny little sources of light because they've absorbed the photon. Now it's theirs. Why don't they just shine them all in different directions? Well, that is the right way to think about it. You can think about each of these atoms which receives a photon as a little sort of point source. It's giving off a little bit of light. And this happens in lots of other examples too. For example, when light goes through a little slit, as it famously does in the double slit experiment, when it comes out of that slit, it's not going ness sarily in the same direction as when it went into the slit. Now it's like a little point source at the slit. And that's what you need to have, like interference between two slits. You need the lights to be coming out in lots of different directions so we can add up constructively or destructively. And that same picture also works for what's happening at the surface of a mirror. The photon is absorbed by an atom, and then the atom emits, and it emits in all directions. So why does the photon end up bouncing at the correct angle, right, Because if the photon comes in at a very steep angle, it comes out at a steep angle. If photons come in a very shallow angle to come out at a shallow angle, well, the way it works is that the photon comes out not just with the direction, but also with a phase. So the quantum wave function of the photon that determines where it's going has a number in it called the phase, sort of like how much it's spun. And the atom actually emits photons in all directions, but with different phases, and those phases deter whether or not. The photons at up constructively or destructively, and the phase that comes out depends on the angle that the photon came in. And so what happens is photon comes in, gets absorbed by the atom, and the atom emits photons sort of in every direction belt with different phases, and only in the right direction, in the direction that sort of corresponds to the angle the photon came in. Do those photons not cancel each other out, so you get destructive interference for all the other directions in constructive interference in the direction that corresponds to the same angle that came in. And that's what mirrors do. They bounce photons off, so the angle they leave at is the same as the angle they came in. If you're coming at ninety degrees, you leave it ninety degrees. If you come in at two degrees, you leave a two degrees in the other direction. So the atom is absorbing that photon and then it is sort of emitting in every direction, but there is one direction where the phase is right for the photons to get canceled out on top of each other. So that's why one direction dominates. And you can think about that either in terms of like lots of photons coming in in parallel hitting the surface and then sprang out all different directions, and the ones that are sort of in the wrong directions end up canceling each other out, and that's why you only get photons coming out in parallel. Or you can actually also think about it in terms of one photon. This is sort of mind blowing the same way that the double slit experiment is. The single photon hitting a mirror doesn't have like neighboring photons on either side to do the destructive and constructive interference for it. So how does that happen? Well, when a photon is absorbed by the atom and then emitted, there's a probability distribution there for where it's going to go, and it's those probabilities that can interfere with each other. Just like a single particle going through the double slit experiment has probabilities to go through either slit, a single photon hitting a mirror has probabilities to go in lots of different directions, and those probabilit interfere with themselves. So single particles probabilities interferes with itself, and that what determines the direction that the particle can go in, all right, So I said that there were two things you had to understand to figure out how mirrors work. One, we just talked about how atoms absorb and re emit the light and how it ends up going in the correct direction because the quantum mechanical phase of the wave function ensures that that direction is the only one that doesn't get destructive interference. The second is that conductors make better mirrors than non conductors. Things that do conduct the electricity make good mirrors. That's why metals, for example, make good mirrors a good sheet of aluminum, and the reason for that is that conductors don't let photons penetrate deep into their surface, and instead they mostly reflect it just from the very very thin sheet of the surface, which gives you a coherent image. If a particle went deep into a material and was absorbed before being re emitted, like a a centimeter inside the material, it might never emerge, and if it did, it might not be as coherent because they will have interactive with lots of different atoms. To get a nice, really crisp picture, you want to reflect just off the very surface of the material, so you're reflecting from a very flat plane, not getting the distortions you would get if you deflect it off of a surface that was not smooth. And so if particles can penetrate different levels of the material, you're basically reflecting off a not smooth mirror and you get a muddled mess. So metals are very good mirrors because they don't let photons penetrate very far into them. And that's because they are conductors, because they can rearrange their electrons to basically cancel out any electric field. If you have an electric field and you put a conductor in it, it will move its electrons around to balance that electric field because electric fields act on those electrons, and if you have a positive voltage in one direction, it will pull electrons in that direction to cancel it out. And so conductor, because they have these electrons to sort of slosh around inside them and reconfigure pretty easily, can cancel any electric field inside of them. That's why, for example, it's very difficult to get a phone call inside an elevator. Right in an elevator, you're surrounded by a metal box, and a phone call is just radio waves. It's a fluctuation in the electromagnetic spectrum, and that will just induce electrons inside the elevator walls to move around to cancel it. So a Faraday cage is nothing but a metal box and it can pretty effectively cancel almost any electromagnetic signal. The other side of that is that mirrors don't allow photons to go very deep into the material because they can rearrange the electrons to avoid those em fields going into the material. And that makes them good reflectors because the photons reflect just from the surface rather than deep in the material where the image might get muddled. All right, So next time you're looking in the mirror and you're wondering, wow, why am I so good looking, it's because of quantum mechanics and because of electrons zooming around to give you a nice, crisp, clear picture of your smiling face. All right, I hope that answered your question. I have one more question I really want to get to. But first, let's take another break. When you pop a piece of cheese into your mouth or enjoy a rich spoonful of Greek yogurt, you're probably not thinking about the environmental impact of each and every bite, but the people in the dairy industry are. US Dairy has set themselves some ambitious sustainability goals, including being greenhouse gas neutral by twenty to fifty. That's why they're working hard every day to find new ways to reduce waste, conserve natural resources, and drive down greenhouse gas emissions. Take water, for example, most dairy farms reuse water up to four times the same water cools the milk, cleans equipment, washes the barn, and irrigates the crops. How is US Dairy tackling greenhouse gases. Many farms use anaerobic digestors that turn the methane from maneuver into renewable energy that can power farms, towns, and electric cars. So the next time you grab a slice of pizza or lick an ice cream cone, know that dairy farmers and processors around the country are using the latest practices and innovations to provide the nutrient dense dairy products we love with less of an impact. Visit usdairy dot com slash sustainability to learn more.

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All right, we are back today. It's just me, Daniel, the particle of physicist, answering your questions about the nature of the universe. Whether the universe is as shapely and as hasty as a donut, Whether photons bounce off a mirror in the same way that a tennis ball bounces off a wall, and how it does that all work? And now we're going to get to the last question of the day, which is a classic, a question I love talking about. So here it is.

All right, we are back today. It's just me, Daniel, the particle of physicist, answering your questions about the nature of the universe. Whether the universe is as shapely and as hasty as a donut, Whether photons bounce off a mirror in the same way that a tennis ball bounces off a wall, and how it does that all work? And now we're going to get to the last question of the day, which is a classic, a question I love talking about. So here it is.

Hello, Daniel and Ja. Hey. My name is David Somerville. I live in fort Worth, but I am originally from Yorkshire in England. I love the way you guys bound stuff off each other on the podcast. Really works well, so please keep up the good work. I got a question for you. Black holes are known to have such huge gravitational pull then nothing can escape, not even the light. However, photons are massless, so how can the gravitational force of a black hole have any effect on light at all? No matter whether you use F equals M or f eqals gmm over our squad, if the mass of the photon is zero, then it means the net force on the light is zero, meaning it will carry on on its merry way unaffected. Obviously this is wrong, but I don't understand why. If you could explain that on the podcast, I would really appreciate it.

Hello, Daniel and Ja. Hey. My name is David Somerville. I live in fort Worth, but I am originally from Yorkshire in England. I love the way you guys bound stuff off each other on the podcast. Really works well, so please keep up the good work. I got a question for you. Black holes are known to have such huge gravitational pull then nothing can escape, not even the light. However, photons are massless, so how can the gravitational force of a black hole have any effect on light at all? No matter whether you use F equals M or f eqals gmm over our squad, if the mass of the photon is zero, then it means the net force on the light is zero, meaning it will carry on on its merry way unaffected. Obviously this is wrong, but I don't understand why. If you could explain that on the podcast, I would really appreciate it.

Thank you, all right, thank you very much for this wonderful question. This is a great question, not just because it's fun to talk about black holes and photons and all that, but because it shows somebody being a physicist in action. You're taking one idea black hole with crazy power for gravity, and then applying your understanding of gravity to it and saying, hold on a second, this doesn't work. This doesn't connect in my head. These two ideas clash, and so help me understand it. And that's what we're here for. We are here to help you understand the universe and resolve all of these ideas in your head. So the short answer to your question is that you're right, it doesn't work because you're using Newton's physics, Newton's law of gravity, which cannot describe what happens inside a black hole, and you got to upgrade to Einstein's theory of gravity, which can describe it. All right, but let's talk a little bit more about what that means. You were walking through your explanation and your question, and you were thinking, well, gravity is a force, and it's a force between things that have mass. Right, that's what we typically think about, is gravity. You are held on the Earth because the Earth has a lot of mass and you have mass, and gravity is a force between objects with mass. That was Newton's picture of gravity. That was Newton's description, and he formulated it mathematically. Force of gravity is big G, which is just a number sometimes the two masses involved divided by the distance between them squared. So what does that tell us. That's analyze that for a moment. It means that the more mass you have, the more force of gravity. F equals gmm over R squared. The bigger the m's, the bigger the F and so the more force you have. And that's why, for example, you feel a stronger pulled towards a heavier object like the Earth than you do to a grapefruit that's even closer to you. The one in the bottom though, the bit on the bottom of the equation is the one over R square, and that tells you that gravity gets weaker as you get further and if you're twice as far away, it gets four times weaker because it's an R squared. So you're right that if you use Newton's idea of gravity and you plug in the mass of a photon being zero, then you get zero force no matter what the other mass is the other mass is ten billion suns. It doesn't matter according to Newton, because Newton thought that gravity was just a force between two objects. But Newton was wrong in a couple of really important ways. One is that he thought that gravity was instantaneous. He thought that information about gravity traveled through the universe with no delay. He thought, for example, if the Sun disappeared, you would stop feeling its gravity just like that, there would be no delay. Now, of course, we know that it takes time for all information to propagate through the universe, and that if the Sun disappeared, you wouldn't feel it for eight minutes, because that's the maximum speed of information through the universe. So that's one thing about gravity that Newton got wrong. He thought it was instantaneous, and Einstein showed us that it can't be. But Einstein also showed us something much much deeper. He showed us that the right way to think of about gravity is not that it's a force at all. Instead that it's a bending of space. And it's this bending of space that affects the way things move in such a way that it looks as if there was a force we call gravity. Now, you may have heard that a few times, but I don't want to really sync that into your brain. I want to make sure you guys really understand what that means. So let's walk through a little analogy. Say, for example, you're on the surface of the Earth and you're on the equator and your friend is somewhere else on the equator, and you both have perfect compasses, and you say, all right, we're going to head north. Everybody walk north. Now, if you're walking north and your friend is also walking north, then you're walking in parallel directions.