What if the speed of light were slower?

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Speaker 1: Hey, Alry, when did you move to California? It was a long time ago. So was it like before or after the last ice age? How do you think, I am Daniel? Or do you mean like the time that the temperature drop below sixty degrees here in Los Angeles? We call that the California ice Age? Well, I mean that begs the question, did you move to California for the weather? Kind of? I mean I moved here for grad school and I actually had to choose between Stanford and Berkeley. Is there much of a weather difference on the other side of the Bay. There is, Actually there's a big difference. At least on the day that I made the decision, it was much sunnier at Stanford. I see. So you're saying Berkeley is cooler. I'm saying Berkeley is ice here and more frigid. Everybody who went to Stanford is definitely hot. It's hot place. Hi am Orhamedy cartoonist and the creator of PhD comics. Hi, I'm Daniel. I'm a particle physicist and a professor at U SEE Irvine, and I will always support Berkeley over Stanford. What about Berkeley over Irvine? Don't make me go there, man, are you pro where does it art varks or bears? Like? Which one would win in a fight? Do you think a bear or an art vark? Well, bear sleep a lot, so I think you know, while there's snooze in the art bark could just like slip in there and lick their face with its long tongue. Anyway, it's an ant eater and not an art bark. Is there a difference? Is there a difference? O? Gosh? Welcome to Creature feature the podcast about art varks and or college mascots one of the two. But anyways, welcome to a podcast. Daniel and Jorge Explain the Universe, a production of I Heart Radio in which we take you on a tour of the universe, regardless of where you went to college or if you went to college. The goal of this podcast is to get everybody on board with this journey of exploration, to wonder how the universe works, how it might have been, why it is the way that it is, and can it make sense to all of us? It's right because it is a pretty mysterious universe full of interesting phenomena for us to look at and gepe that and wonder about and there we importantly ask questions about I have a question for you, which is, you know, if Berkeley is the Golden Bear and Irvine is the ant eater, what is Stanford's mascot? Is it a tree? It's Silicon Valley? Money, piles of cash, piles of bitcoins probably these days. Yeah, well, we're not gonna let this go. Are we the Stanford Berkeley thing on this episode? Oh no, Man, Berkeley over Stanford all day every day. Maybe should discuss our after grad school school. So I went to Caltech and you went to EC Irvine. After grad school, actually went to the University of Pennsylvania, which is a private school. And yeah, then I did go to UC Irvine. And I've bounced back and forth between public and private institutions, but in the end, my heart really is in public institutions because they serve the public, and you know, to get off the jokes for a moment, like, I really do believe in the mission of educating the public and providing a path of mobility for people. California public college system from the cow States all the way up to the University of California's that they do an incredible public service. And I think that this podcast is part of that. We want to reach out and educate everybody about the mysteries of the universe, not just those that have piles of cash or stacks of bitcoin. Yeah, and that's why you renounced your undergraduate institution, right, no comment. I'm just kidding. But it is a pretty amazing universe full of things to discover that are there for everyone to wonder and to look in and to have questions about. Because people have questions. People do have questions, and they write to us with their questions. And the cross section of folks who write to us is just incredible. From seven year old wondering about black holes, to night guards at hospitals who listen to our podcast while they walk the halls, to pro bono attorneys from Alabama who listened to our podcast is a break from the craziness of their lives. Everybody out there wonders about the nature of the universe and how it works, and whether it's possible for it all to make sense to them. Yeah, that is pretty incredible to think that there are so many people listening to this and kind of thinking about the same topics at the same time. Makes us all sort of feel connected in a way like we're all wondering about the universe at the same time together. Yeah, we are all wondering about the universe, and I hope that means that we're also connected to like alien scientists who I think are probably wondering about the same universe. I like to fantasize about a whole galactic community of scientists wondering about the nature of this crazy cosmos, and we're just a tiny little piece of it. Well, I feel like you just stepped it up a notch there. I was going for some sort of human grandeur, but you took it to the galactic level. That's what we do on this podcast, man, take it to the galactic level every time. I don't know if I want to mind meld with aliens necessarily, though. Do you think we've enjoyed that experience? Well, you know, that's sort of the Berkeley approach. You know, we're all one with the universe. Man, I have to take any particular substances to kind of reach that state that I can approchase maybe at Berkeley Bananappeals for sure. Yeah. But yeah, people definitely have questions, and sometimes we get those questions here on the podcast. People send them to us over email or through social media. That's right. So if you have questions about the nature of the universe, or there's something we said on the podcast that you didn't quite understand, or there's just been something bugging you that you really need to get explained, please don't be shy right to us two questions at Daniel and Jorge dot com. We answer every single question. We will answer your question. Yeah, and sometimes the questions are so interesting that Daniel picks them to answer on the podcast. Yeah. Sometimes the questions make me go off and do a bit of a dive or research to get a solid answer. And sometimes I think it's a question that other people might want to hear the answer to. And sometimes I think this is be fun to laugh with Jorge about, make fun of or to laugh about what are your plans here? Well, you know, I try to be nice to Stanford grads who you know, went to a junior college after all, that's right, ideas who are are not physicists. So today on the podcast will be tackling listener questions number twenty five and also titled Jorhan Daniel keep Fighting about Berkeley and Stanford. You see, you really you're the ones SEO seems to be bringing it up more. No, I think that's probably true. I think Berkeley folks probably feel the Berkeley Stanford rivalry more than Stanford folks, who are like, what, who cares academy chip on the shoulder? I think so probably where the public university that could. I think the more interesting question is an art park the same as an an eater? I think the question is how did you get a Stanford education? And not know the answer to that? Well, I was in the engineering department. I didn't zoology one on one, right, Yeah, don't you like look to nature for inspiration? Well? I felt like the straw was already invented, so I didn't need to copy the ant eaters trunk. Oh, I see, all right, that's true to invent something. Yeah, and well, there's not much of a market for an ant eating robot anyway, or ant eating straw. But anyways, we're here to answer questions from listeners. And this is the twenty fifth episode that we've done this, and I feel like we don't do this enough. Daniel, I really like these episodes. Oh good, well, let's do some more of them. I think these are a lot of fun also, and today we have a question inspired by one of our previous listener question episodes. WHOA what We're going inception? Here we are deep diving like a question within a question episode. Yeah. Well, that's the wonderful thing about questions is that the answer is just raised more questions. They make people think in a way they had them before. They make people's brains go places they hadn't gone before without needing to buy anything on Telegraph Avenue. Yeah, but that optional, I guess. I mean it might make the podcast actually more interesting to some people exactly. That's what we've been talking about bananas the whole time. But we have three pretty awesome questions here today from listeners, and they have to do with the ice age here on planet Earth, about how photons move near black holes, and also what would happen if the speed of light changed. So thanks to those listeners who sent in their questions, and also we're willing to record their audio, and don't forget if you have a question, you can also get an answer right to questions at Daniel and Jorge dot com. Al Right, the first question we have here is from Carson, who has a question about the ice age. So I listened to the podcast about the asteroid and the dinosaurs, and I was wondering, what would happen if the ice age hadn't happened. Thanks for answering all my questions. Pretty cool question, Thank you, Carson. I guess Carson has a question is kind of like what if question, Like how different would the Earth be if certain things hadn't happened. It's a really fun question, and it gets to the heart of how our entire existence depends on so many tiny little factors, just like if an asteroid hadn't hit the Earth, or if the Earth hadn't warmed or cooled, so many chaotic events which could have been different were crucial to us being here right now, and so it's really fun to imagine alternative Earth's different scenarios where things might have turned out very differently. Yeah, I think Carson just wants us to talk about dinosaurs. But you know, you can't blame them. You know what young person doesn't want to talk about dinosaurs? Or maybe Carson's thinking about where to go to college and is wondering, you know, like Berkeley Stanford. You know, well, you're really not dropping this. Well, well, Carson, I have to tell you if there is another ice age, Berkeley's going to freeze first before Stanford. Just letting you know that it is a little bit more north and on the other side of the Bay, which gets colder, and therefore it will have a larger snowpack and better water reserves that lasted through the summer. Because we're not nice to the Bay area. I'm not sure where you're going directly thinking to me, this question is really fascinating because there are a lot of connections between ice ages and the physics of the Solar system. That is, you know, how the Earth goes around the Sun, and the variations in the Earth's orbit really do have a strong impact on how much sun we get and how much ice there is on the Earth. Yeah, it's pretty interesting the connection there, and it's amazing that Carson had been thinking about the ice age. I guess we've had several ice ages throughout the ages. We have had several ice ages, and if you cast your mind back, like really deep far into the history of the Earth, it's incredible how different the Earth looked like around six fifty million years ago. We were in the depths of an ice age, so cold that they think that ice reached all the way down to the equator, like it was basically a snowball Earth. Whoa, Yeah, Like if you took a picture of it, you would just see a big white ball, kind of like when you look at you know, some of the ice planets. So if you're an alien scientists visiting Earth for an interstellar physics conference and you arrived, you know, six million years too early, you wouldn't find anybody to talk to and you think, oh, that's just a frozen wasteland, or you might think, great ski here. Hello. Yeah, I hope that one day we like unfaw some big block of ice and find an alien skiing. That would be an incredible discovery. But then, you know, wouldn't their snowboards hover? Also? I mean, if they made it all the way here for a ski vacation, I wonder what would be in that flask. But anyways, ice ages are interesting, as you said, because they are connected to kind of the physics of our planet and the physics of our planet revolving around the Sun, like it's it's heavily tied to the orbit and the tilt of the planet. Right. There are a lot of factors that affect ice ages, from climates to continental drift, all sorts of things, and scientists don't have a complete understanding of what causes these things. There are still lots of big open questions. But one thing that we do know is that changes in how the Earth orbits the Sun, for example, whether the Earth's orbit is circular or whether it's become more elliptical, and changes in the earth tilt. These things can affect how much solar radiation falls on the Earth, and that affects the temperature for sure. Wow. Well, first of all, I guess maybe this is something I hadn't thought about. Is is the Earth's orbit not constant? Isn't it like a perfect circle or slight oval? And are you saying there's some variations in that trajectory. There are definitely variations in that trajectory. And it goes from being like almost a perfect circle to being more elliptical. And it becomes elliptical by having the semi minor axis get a little shorter. So it's not like the Earth gets further from the Sun but during parts of its orbit and then gets closer to the Sun. Wait, what so what determines these changes in our orbit? So if the Earth was alone in the Solar System, it would have a very simple, stable orbit around the Sun. But it's not, and there are other things in the Solar System, like Jupiter and other gravitational bodies. These things have very gentle tugs on Earth's orbit. We're into a whole episode soon about spin resonances and tidle locking the whole Solar systems. That an incredibly complicated Swiss watch, but it means that there are these cycles that change how the Earth tilts and also how the Earth orbits as it goes around the Sun based on these little gentle tugs from things other than the Sun. Wow, I guess there's still pretty small changes. Maybe, like if you look at the picture of it, maybe you couldn't tell the difference between the different orbits. Yeah, the orbital changes are not huge, or if you're looking from a distance you definitely could see anything. But you know, small changes in how much the Earth tilts towards the Sun or how far away it is from the Sun you really can have a strong impact on the amount of solar radiation. For example, if you look back over the last twenty or hundred thousand years, you see variations of up to twenty percent in the amount of solar radiation that hits the Earth based on these cycles. Wow. Yeah, I guess you can sort of look at the record, right, Like you can look at ice layers and rock layers and you can see that it used to be sunnier before or not. Yeah. They do these core samples where they dig down and layers of ice in Greenland or in other parts of the world, and they can see the global temperatures and there really is variation. And they do these calculations based on you know, solar system models and to understand the variations in the Earth's tilt and orbit. And there's a really nice alignment between these global temperatures and these Earth's orbital changes. Wow. And it's crazy because it's like small, even tiny, little changes can basically change the weather. Like if the Earth tilled three degrees or two degrees this way or that way a little bit more, then suddenly we have an ice age. It really is incredible. But this is just one effect. It's important to understand other things, like atmospheric effects can drown them out. For example, if we hadn't been pumping c O two into our atmosphere, scientists predicted we'd be due for like a big glaciation stage in about fifty thou years. Now that's sort of off the table because the amount of C O two that we pumped into the atmosphere, so we can override these effects with larger effects like the Greenhouse effect. Well, it's in doable. So we can actually like change the destiny of the Earth, like we could totally ruin it perhaps even yeah, exactly. And so I just don't want anybody out there to think that all of the change in the atmosphere is due to natural effects from the Earth's orbit. This is an effect, and it has contributed to glaciation into ice ages, but it's not the only effect, and it doesn't even have to be the dominant effect. And it also sort of impact as you said, how much radiation we get. Like if if our orbit but you know, flies a little bit closer to the Sun, it's going to get a little harder on Earth too. Yeah, And some of these things can be sort of dramatic, like you have different cycles based on the orbit and the tilt and all these things that are different cycles there which have different periods like twenty or forty or a hundred thousand years. Sometimes they all come together and happen all at the same time. You can get pretty dramatic shifts in temperature, like about thirteen thousand years ago when temperatures dropped dramatically in just a few decades, and then thirteen hundred years later, temperatures spiked like ten degrees celsius within just a few years. As like all of the effects swung one way and then swung the other way. These things can have really big effects on the Earth's climate. Ten degrees is huge. It seems like it's not totally unpredictable, right, Like, we have a certain model of the Solar system and our our atmosphere, and so you know, we should believe the signists when they say what's going to happen next. Yeah, this part is pretty predictable because we have good models for how the Earth's orbit is affected by the tug of Jupiter, etcetera, etcetera. The other parts, you know, climate resonances and what happens with the greenhouse gases, that's something we're working on, is not as well understood and can be more dramatic. You know, something I didn't realize was that the climate is even affected by the flow of the continents. As the continents move over the surface of the Earth, they change how water flows. Is there a water channel between these two continents or not, for example, And that affects how the atmosphere moves, and that can have significant effects on the climate as well. There's a lot going on. It's a big complicated system with a huge number of feedback cycles, you know, so if you get it a little bit wrong, then you can get it a lot wrong. But you know, climate scientists are doing a great job at modeling this stuff. Well, I guess Carson's question is what would have happened if we hadn't had the last ice age? And so let's talk maybe about how an ice age impacts the Earth. Yeah, so the most recent ice age, scientists say, lasted from about two and a half million years ago till about twelve thousand years ago, waited less than millions of years. Yeah, these ice ages can last millions of years and sometimes hundreds of millions of years. But within an ice age there are more variations, and they call these glacial periods where things can then the glaciers can retreat and come back. And so the most dramatic and the one that really affects sort of life on Earth and the way we live. It is the last glacial period, which lasted from about a hundred thousand years ago to about twelve thousand years ago. That's the most recent impact on sort of like human development and migration, because I guess the northern parts of the and southernmost parts of the Earth more covered in ice than usual, but not completely. You said that we only got completely covered millions of years ago. That's right. During this last glacial period, we had like Canada was an ice sheet, most of the northern United States with an ice sheet. There are lots of glaciers around the world at high altitudes. But you know, it's not like the whole Earth was an ice sheet. But you know it affected the humanity. Humanity, for example, mostly lived at lower latitudes during this stage until the ice retreated and then they could migrate to Eurasia and more northern latitudes. Like it was still sunny in the Equator. Yes, it was still sunny in the Equator and hotter cool It was cooler than it is today, but obviously it was hotter at the equator than it was at the pole. Still, what about Berkeley, Berkeley will always be cool man, very chill. Not as chill as you see Santa Cruz. Right, there are the chill ones. Yep, nobody can chill like bananas slugs. All right, well, let's get a little bit more into the impacts of the Ice Age on Earth and the Last Ice Age on Earth and what would happen if we hadn't had that ice age. First, let's take a quick break. All right, we are answering questions from listeners, and our first question was from Carson, who asked what would have happened if we hadn't had the I guess the Last Ice Age that's probably the one that Carson is most wondering about. And you know, the Ice Age has big impacts on geology because the glaciers can like grind mountains and create valleys. It also has a big impact on the flora and fauna that developed to adapt to that climate, and specifically it had a pretty big impact on where humans ended up and how we evolved. Yeah, it's it's sort of an interesting effect that maybe when I was younger, I hadn't thought about that, Like glaciers can really kind of like smooth over a landscape. I think a lot of the like the eastern United States has you know, more rolling hills rather than dramatic mountains because the glaciers basically like you know, crunched them all down. I'm not actually sure about that. I think that smoother mountains are just older mountains. They have been worn down by wind and rain and cycles of weather. The Rockies, for example, are sharper because they're younger. It's incredible in the history of the science is really fascinating as people realized that there was this incredible, powerful, dramatic force that happened very very slowly on Earth. These moving of these glaciers can really shape valleys and distribute boulders. It was the presence of these boulders that tip people off. People in the Alps were like, how did this rock get here? It's for much more northern climates, and people were wondering, like how to explain where all the rocks were, And very slowly they put together this crazy story about sheets of ice moving over the Earth and changing its shape. It's kind of bonkers and like boulders hitching a ride or like surfing the glacier wave. Yeah, glaciers break boulders off the mountains and then can carry them for hundreds of miles and deposit them somewhere else. Wow. Yeah, and said how stone hands got a bill. I think that was graffiti from the alien skiers. Actually the alien snowboarders came to a snowboard and piles on rocks like like the tourists usually do. I think that's another divide. We don't want to get into skiers versus snowboarders. But yeah, like you said, it really affects the trajectory not just of the landscape but also life on earth. Like if most of the Earth is covered in ice, it's gonna you know, determine what kinds of animals survive and which ones don't. And you know the kind of flora and fauna that we have. You know, the fact that we have like horses and cows, and a lot of the grains we eat are basically evolved grasses. That's due to the climate that we had. If we hadn't had an ice age, for example, the whole earth might be wetter, and it might be warmer, and it might be more covered in jungles and rainforests than grassy plains. And so the kind of farming practices we developed could have been totally different. Oh. Interesting, So that's one way, one specific way the Ice Age has you know, impacted us is we would have less fewer horses and cows and grasses, grasslands, and the whole concept of agriculture could be very different. A farm could be basically a piece of forest. You know, it's hard to imagine how civilization and how agriculture might have developed in the context of basically everybody living in the Amazon. Interesting. Yeah, because it might have also affected human development, right, absolutely. There are some theories that the harsh living conditions during the Ice Age basically forced humans to develop cognition, to evolve bigger brains so we could work together and develop tools, hunt willy mammoths, this kind of stuff. It's certainly had an impact on humans, although there's always the alternative reality game. They're like, sure that might have played a role. We don't really know what would have happened to humanity in other situations. Maybe we would have been even smarter. I see. The theory is sort of like, because it was we had these long winters, it kind of forced humans to plan ahead and to think about like crop since strategizing, which kind of pushed this to be smarter and to be and to be less procrastinators exactly. But these are always just explanatory stories, right, There's aren't really testable theories. It's very easy to look at the series events and say, oh, this makes sense, and I think this is why it happened. To really know, you'd have to run alternatives. You'd have to say, well, let's see what happens if I change things? And that's sort of a fascinating question. But one will never know the answer too, because we only have this one universe and we only see what happens to this Earth one time. Yeah, we need like a control Earth for every single conceivable experiment we do. We need the multiverse for that reason, so you can see, you know, what would happen if I had gone to Stanford? Would I be a different person today? You'd definitely be much cooler. Maybe I had or richer. Apparently, maybe you would have invented TikTok Daniel. If I had, it would have been a lot more boring than it is today. It would have been physics though exactly all right, Well, I think that answers Carson's question. If we hadn't had the ice age, things would be really different. Well, first of all, it sort of depends a lot on our trajectory in space and how close we get to the Sun and how and how tilted we are. But if we hadn't had the last one, maybe we would be eating different kinds of plants and fruits and animals and and or we might be a little bit different ourselves. Yeah, we might all be roasting banana slugs over the fire, and we might all be procrastinators instead of just some of us being procrastinators. Speaking of procrastination, let's get into our next question, and this one comes from Chris, who has a question about photons moving near black holes. Hi Danueine Horree, thank you so much for your show. I look forward to it every week. All right, here's my question about photons. So let's say we are on Miller's planet, the like the one in Interstellar, and we look up at the sky and we can see a star. So the photons coming off that sun. Let's say some of the photons missed the gravity of the planet and continue on to their destination. But a few of those photons get trapped or caught into the gravity of the planet. So from the perspective of somebody that's not in the gravity of the planet. Doesn't that photon travel slower than the other photons that moved on that didn't get caught in the gravity of the planet. Kind of confusing, all right, thanks, kind of confusing for sure. That's why we're here. I think there's a good summary of general relativity right there. Kind of confusing, I guess special realtivity. Chris, it's kind of confusing. But is there really excellent question he's asking It really difficult and subtle question about what it looks like to see a photon go near a very massive object, to be sucked into the gravity well of a black hole or a very dense planet. Right, Because we've talked about on this podcast, how when you have a lot of mass, like in a black hole or just like a heavy planet, it can bends the space time around it, and it actually sort of slows down time. I think that's maybe what he's trying to connect. Yeah, it can slow down time, and also it changes the path of these particles. It changes the fundamental geometry of space the way the particles move. At least two really confusing and sort of paradoxical ideas, Like one thing we say in the podcast a lot and that people talk about in physics A lot is light always moves at the speed of light, no matter who's measuring it, right, We say that a lot. On the other hand, we also say that like photons can't escape a black hole, and people might be puzzling about that, like what does that mean? How fast is a photon moving when he's trying to climb out of that gravity? Well, doesn't eventually get stopped by the gravity of the black hole. Had he reconciled those two ideas, Yeah, it's kind of confusing for sure, But I think maybe the scenario is I think he was trying to paint, is that like, let's say a star shoots off to photons and one photonogy goes clear through space, no, no, nothing in its path, But the other one flies like us, to a heavy planet or close to a black hole. Like, if you were looking at these two photons, but the one that goes near the black hole, would that one go slower? Yeah? Would you see a photon moving at less than the speed of light? And your instinct, physics wise, is to say no, absolutely, that can never happen. Problem is, that's not exactly true. Because when we say photons always travel at the speed of light, there's a qualifier there. There's a caveat that we almost never mentioned that's important in this particular case. And that caveat is that it's true that photons always travel at the speed of light. But that's only true if space is flat, that is, if there's no curvature to space, and only true for nearby observers. So the full statement is that photons only travel at the speed of light as measured locally by people nearby. In flat space, space is curved and you're far away from an object, the rule that photons have to travel at the speed of light no longer holds interesting. I think what you're saying is that, like, photons have to travel the speed of light in space right like to the photon, it's always going at the same speed. But you're saying you can't sort of squish and bend space itself, which might to a someone who's looking from far away, might make it actually go faster and slower than the speed of light. Yeah, and it goes one step deeper than that. And remember that you can't talk about velocity without talking about pairs of objects. Velocity is not a property of an object. Of ball flying through space doesn't have a speed. It only has a speed relative to observers. So whenever you talk about velocity, you can't think about a ship traveling near the speed of light. You always have to say a ship traveling at whatever speed relative to Earth, for example. So in this case, we're talking about photons relative to an observer nearby versus photons relative to an observer far away. The problem is that, in general relativity, that is the theory that tells us how to think about the universe as it curves and bends in response to mass, there is no well defined definition of velocity for something that's far away. It's like you can't even really sensibly talk about the speed of a photon that is very far away from you. Wait, what what do you mean? Like? I can see it, you know, one spot from from a distance, and then I see it in another spot from a distance a short time later. I can you know, measure with the distance between those two things and divide by the time. That would give me the its speed. Yeah, that sounds straightforward, but the problem is that you were using your local inertial reference frame to measure the path of something that's moving through curved space far away. So you're assuming that space is flat between here and there, and if it isn't, if space is curved, then the reference frame of someone else nearby those photons would be very different, and your measurement and velocity and there's won't agree. For example, a distant observer will see light near a black hole travel at all sorts of crazy speeds from less than the speed of light all the way down to zero, but a local observer near the black hole and near that photon will always measure that light moving at the speed of light. But this is more than just different reference frames having different values. We have that in special relativity and we know how to translate and compare, but because space is curved, there are many different ways to compare those measurements velocities in general relativity, So to translate between two different reference frames and curved space, now why is that? What you need to do in that case is compare its velocity to your own, right, you need relative velocity, and so you're making those measurements and so really what you're doing is you're comparing two different vectors there, like your velocity and its velocity, and that's something you can do if space is flat, but it's not something that we know how to do if space is curved. And it's useful to think about an analogy like making a measurement on the surface of the Earth. Say, for example, you have two runners and they're running a race. If they're next to each other, it's very simple to see who's faster. They're literally next to each other. Now, imagine you take one of the runs and one of them is in Paris and the other one is in Cape Town, South Africa or something. So they're like on different places in the Earth. Now they're not really running in the same direction, right, because the Earth is curved. One is running in one direction, the other one is running sort of in a different direction. So how do you compare their velocities? Right? Well, one thing you can do is to say, well, I'm gonna take the velocity vector of the Cape Town runner. I'm gonna bring it over to Paris and sort of like transported over to Paris, and then I'm going to compare the two velocities. I mean, like, if I'm floating in a space station looking at these two runners from space, you just want to compare these two, right, it doesn't matter really where you are from that perspective, You've got to bring those vectors close to each other. But why do I have to do that? I guess can I? I just, for example, from space in my space station, measure the length of the track that the American runner is in, and then measure from space the length of the track that the South African runners in. And then you know, as I see that, I start the clock when they both started running, and then I measure how long it took to get to the side of the track. Yeah, you could do that. You could ignore the curvage of the Earth and just measure their velocity relative to somebody in space. That's like, again, assuming everyone is in your local inertial frame and that space is flat. But we put people in this example on a curved surface as an analogy for what happens when space is curved. But when you're running a race, we really want the velocity along the Earth, right, not the velocity through space, which you one is the answer of if I brought the Cape Town runner to Paris, who would win this race? Right? And so the curvage of the Earth makes a difference there you can't just ignore it, alright, So you're saying that that it's hard to measure or compare velocities in curve space because things kind of get kind of wonky because spacetime is being curved. That's right, And the problem is that how you compare those two vectors depends on how you bring one vector close to the other vectors. This is called parallel transport in geometry. You want to compare two vectors, you've got to bring them near each other. In flat space, that's not a big deal because if move the vector from there it here doesn't change. In curved space, the vector changes as it moves through that curved space, and so there's an infinite number of different ways you can do it, and the answer you get depends on the path. So if you bring the Cape Town Guide to Paris along one path, is vector will be in one direction. If you do it along another path, IS vector will be in a different direction. And so this is all really important because it means that you can't define the difference between those two velocity vectors across curved space, and so that means that you can't talk about the relative velocity of things that are really really far apart, you can't define what happens to a photon, and that means that the rules of special relativity and no longer apply. So a photon moving around a black hole could appear to have a velocity not the speed of light, all the way down to apparently zero velocity as it tries to climb out of that gravity. Well, right, I think what you're saying is that if we were to run the experiment that Crisp wants us to run, which is like, shoot two photons and have one go into a black hole, like, we would see one of them just fly through space away and the other one we would see actually like kind of stop at the black hole, kind of like right, like it would just stop from our point of view. From our point of view, and according to our decision about how to measure that velocity, somebody else looking from another perspective might have a different definition of like, well, here's how I'm going to bring those velocity vectors together to compare them. They might get a different answer. What do you mean, Like if I'm moving maybe at a different speed, but if I just stand on the other side of the black hole, I'm probably going to see the same thing. Right, I'm going to see one photon keep flying off and the other one stop at the black hole. Right, But in order to measure the velocity of that photon, you need to talk about how to bring its velocity vector into your local space, and there's an infinite number of ways to do that, and the choice you make about how to transport that vector changes the answer. So you and I could be right next to each other looking at the same photon. But if you have a different definition of basically velocity in general relativity than I do, we could get different answers. So that's why people say it's not well defined, because there's an infinite number of arbitrar choices you can make that do affect your answer? All right, Well, then what would be the answer for Chris? So you would you see that photon move slower, the one that goes near the heavy mass. You would see it move slower exactly no matter where you are. You would see it move slower than the speed of light, almost no matter where you are. And you know, this might be confusing to people if they think, well, how can we not define the velocity of objects that are far away? Like we talk about galaxies moving really really fast away from us, and the galaxies are very far away. That's one reason we can talk about galaxies moving away from us faster than the speed of light. One way to think about it is that space is expanding between us and those galaxies. Another totally reasonable way to think about that is to attribute that velocity actually to the objects and not to the motion of space itself. Those are both arbitrary but reasonable choices. And that's why we say, like the velocity of objects isn't well defined in gr because it requires an arbitrary choice. It's kind of like how we've always said or set often on this podcast and in our books. It's like if Hussain Bold can only run so fast on land, but if there's like new land being made between us and him, he's gonna look like he's going faster than what he can actually run. Or if there's if like the continent he's on is actually moving towards us, he might appear to be moving slower exactly. And that's the standard choice and cosmology to think of the universe as expanding in a certain way and to think of motion relative to that expanding space, And that's a totally reasonable choice, and that's what we usually do when we talk about the expansion of the universe and the velocity of really distant objects. But you could make other choices. As an arbitrary choice, it is just sort of the one people typically make. You could make other choices, which is why these velocities of very distant objects technically not well defined. And that's why you can end up in situations where you say things like, oh, light is moving slower than the speed of light. It's because velocity of far away objects is not really well defined. If you're near a photon, it will always be moving at the speed of light relative to you, right right, Yeah, Like if you're falling into the black hole with the photon, the photon would just look like it's it's moving at the speed of light. But that's because also your time frame is also being slowed down right exactly it's near you, and so locally space is always flattened near you, and so if you're with the photon, it's moving through flat space at the speed of light. A distant observer, that's where the problem comes in because the definition of velocity for distant objects is bunky in general relativity, where its Chris says, kind of confusing. I think that's the real answer for Chris here to this question. It's kind not confusing. All right, Well, let's get into our last question, and this one is a little bit related. It's another question about light and it's speed, So let's get into that. But first let's take another quick break. All right, we are answering listener questions and also debating UM Berkeley versus Stanford. Apparently there's no debate, man, I mean, it's just talking about it. But I see, well, I think there's a debate about whether there is a debate. I think it's only really one side of that debate. Now we we're answering listener questions and our last question here comes from Dennis, who has a question about the speed of light. Hello Daniel Kay, First of all, I love your podcast. I was wondering what is the minimal speed of light to sort of hold a universe together? And what would happen if a light would only have a thousand kilometers per per second of speed? What was happened? Then? Okay, thank you? Alright, awesome question from Dennis here about the speed of light, and I guess this question is sort of like, because we've talked about on this podcast before and in our book also about the speed of light is a little bit arbitrary, Like you can it could have it's it's like three millions per second, but it could have been something different. It could have been three per second or three billion meters per second, and you could maybe still have like a functioning universe. Yeah, we don't really know if it could have been something else, but we don't know why it is what it is. We have no explanation for it being that number in particular, and that suggests that maybe it could have been something else. And there's lots of really interesting philosophical wrinkles there, like are there other versions of the universe out there in the multiverse with different speeds of light? Etcetera, etcetera. And it's a really great question to ask, like what speeds are allowed? Could the universe work if the speed of light was different? Yeah? Pretty cool And something I think we discussed recently in an podcast episode that was a little mind blowing for me was that you told me that a light the speed of light is not actually a fundamental like unit or value of the universe. That's right, The speed of light has units to it, right, meters per second, and so the actual number is really arbitrary because it depends on the units. So when we talk about the construction of the universe and the parameters that influence the way that it is, we try to focus on numbers that don't have units to them, dimensionless numbers, numbers like the cosmological constant which affects the expansion of the universe, or the ratio of masses of the electron to the muan, for example. And the speed of light does factor in because it's part of what we call the fine structure constant, which combines a bunch of these different constants blanks constant, the speed of light, strength of the electromagnetic force. Yeah, like this like like a ratio, right, like the speed of light divided by how quickly Berkeley students think two really big numbers. But I think the idea is that generally speaking, like you know, how fast light travels through space is sort of like a fundamental property of the universe that we currently can't really explain. Like it seems arbitrary, yeah, and it might be that it bubbles up from a deeper understanding of the nature of space time. You know if space, for example, is a quantum foam of little space pixels linked together by tiny wormholes. It could be that some property of those wormholes influences how information propagates from one space pixel to the other, and that determines the speed of light. We just don't know the sketch from maybe how you could get an answer to what the speed of light is, or it could just be a totally arbitrary It could be that as universes are created, to some random process that sets these parameters, and this is the one that we got, Like you get three hund a million per second, you get second exactly. And it's fun to think about what the universe would look like. And I love the way Dennis posed this question, which is like could the universe come together with the minimum speed of light for a universe to function? Yeah, it seems like he has he has a two part question. Actually, the first part is like, could we have a universe with a slower speed of light? And what would be the slowest speed of light that a universe would still hold together? Which is sort of an interesting way to put it, like could with the universe fall apart if the speed of light was slower. Well, you know, the way I think about this is in terms of light cones, something we talked about in the podcast once, which tells you what portion of the future of the universe you can influence and which portion of the past of the universe influences you. Because we have this maximum speed of information, it means that, for example, you can't affect things in a neighboring galaxy that are happening right now. You made a decision about something you wanted to happen in Andromeda, it would take millions of years for that decision to have any effect. That your light cone fraction of the universe in the future that you can influence, and the size of that cone, the slope of that cone is determined by the speed of light. So the speed of light was much much faster than you could influence Andromeda maybe tomorrow. If the speed of light was much much slower, that might take billions of years to affect Andromeda instead of millions. And so the size of that cone, the narrowness of that cone, is determined by the speed of light. Yeah, I mean it definitely, it would change the universe. But I think his maybe question was more like, is there something in the equations of the universe that we know about right now that if I, you know, start dialing the speed of light down, would at some point equations fail or become incoherent or illogical. Or is it really the fact that, you know, the speed of light could be one centimeter per second and you could still have a functioning universe. Yeah, as far as I know, there is no minimum speed. You would have completely different kind of universe. It would feel very, very different, and it might affect the structure of matter. You know, the orbits of the electrons, for example, are affected by the speed of light, and so you might not get hydrogen, you might get weird other forms of matter. But you would still have a universe even with a much slower or much faster speed of light. I see, like if you change the rules, the atoms and the corks and all that would just played played differently, but they could still play, They could still play exactly, and they would play differently, And the consequences of that are really hard to imagine and difficult to calculate. Also, you know, we don't really even have a great theory for like how corks come together to make protons and neutrons because it involves the strong force, which is a real pain to calculate. And so if the balance of all those forces changes, then a lot of things that are difficult to calculate would be different. So the whole universe could be very different. But you know, if the universe doesn't change that much, if the speed of light goes down by fifty or something, I think you'd largely get the same universe, but it would feel different, like you could see less of the universe out there, like our little bubble. The observable universe also depends on the speed of light, right well, but I think it's also maybe deeper, perhaps than just what we can see, because the speed of light doesn't just affect light and photons. It also sort of the term is how fast some of these fundamental particles can move, right, and also kind of like the range of their effect, right Like I'm thinking some of the force particles, if they could move faster or slower than there there, it wouldn't be a strong perhaps, that's certainly true. And the speed of light I think most directly affects the strength of the electromagnetic interaction because it goes directly into the fine structure constant, which appears in the coupling of photons to electrons and photons to other charge particles. So the speed of light was different, it would change also sort of the relative strength of electromagnetism to the other forces. All right, so, um, you said it would be different. So what are some of the ways that the universe would be different if the speed of light was slower. Well, if the universe was different, if the speed of light was slower, we couldn't have as large as structure forming in the universe. Like, in order to have a structure form, you need to have information go back and forth across it. You know, for a planet, for example, to coalesce gravitationally, you need information to propagate from one side of the planet to the other for it to be like a single object. You mean, like gravity. Even the force of gravity has a speed limit, and that speed limit is the same as the speed of light. Yeah. So if we're talking about like the speed of information through the universe, then if you're cutting the speed of information down, then gravity also transmits its information more slowly. Right, you would be basically slowing down gravity too. Yeah, you would be slowing down gravity and you would be limiting gravity in the size of the thing that it can build. You know, we think that there's like a biggest structure that can exist in the universe because it takes time for gravity to pull things together, and the universe hasn't existed for that long, so you know, the universe has been around fourteen billion years. That means you can't have a structure that's like fifty billion light years wide because it just hasn't been time for like one side of it to coordinate with the other side and like come into equilibrium with it. So there's a limit there on the biggest thing you can make, and that depends on the speed of light. Right, It's like trying to bring your kids together. If you're really slow person, you can't like if you slow down gravity, Like gravity would be trying to pull all those distant galaxies together, but maybe by the time it acts that the galaxies are long gone. Yeah. Or say, for example, you're trying to organize a family reunion. You can get in touch with much more distant relatives if you can email them rather than having to send snail mail or send a pony. Right, if you can only send a pony and you can organize a much more local family reunion, whereas if you can email people, you can get people from Singapore and people from Australia to come to your party. And so in that way, the universe would be sort of more local if the speed of light was smaller, right, Although I do know you, Daniel, and I know that a family union it would be you would organize it with ponies so that it maybe together as well. Like I put it on the back of an anteater. What's the problem you didn't get the invitation? Should have put it on the back of the tree. Banana's slug. But it's not just that it doesn't just affect the structure of the universe, right, Like if you slow down, gravity would also affect relativity to right, Yeah, a lot of the really weird effects from relativity times slowing down and things getting contracted, all that kind of stuff. We never see those effects because they only happen when you're going at very very high speeds relative to something else. So that's why it took us a long time to even discover that it's part of reality. But if the speed of light was slower, if it was like closer to human speeds, or speeds we could achieve on Earth, then we might have noticed these things because you would be able to see them, and we might have like intuition for relativity would like make sense to us in a way that right now it doesn't. Well, I wonder though, like if you slow down gravity and lights and basically how everything can propagate in the universe, wouldn't sort of time also slow down or wouldn't it feel slower as well, to the point where you know it's almost like if you're near a black hole, you know your time is moving slower, but you don't notice it. It's a great question, and this sort of goes to the heart of why we talk about dimensionless constants instead of dimension full constants like the speed of light, because for example, you could change the speed of light, but then if you tweaked a bunch of other numbers at the same time, nothing effectively would change in the universe. I think that's what you're talking about, if you tweaked a bunch of these numbers in such a way that none of the dimension list constants change. For example, if you change the speed of light, but you also change planks constant, and you change the strength of the electromagnetic force, and you wouldn't notice anything because you have look no absolute ruler to compare it to. It's sort of like if you got bigger and your ruler got bigger, you wouldn't notice any difference, right, Yeah, I think you know what I mean. It's like if you slow down the speed of light and slow down gravity put in that also maybe affect how fast you can think. Would you technically be thinking slower? Oh? Your perception of time? Oh that's fascinating from a neurobiological point of view, that's a great question. I don't know that our thinking, though, is limited by the speed of light. I think it's more affected by whether you went to Berkeley or Stanford. No, that's a great question. I don't know the answer to that. Whether the speed of your brain is actually affected by the speed of light, and whether I like our internal sense of time is affected by the speed of light. I suspect that it isn't that they're biological processes are very very slow. But I'm really just speculating there. Well, but I mean chemical reactions in your brain depend on the electromagnetic force, right, which would be slower as well. Yeah, that's true. Those bonds would have a different strength. We'll ask Katie Golden next time she's on, since she's an expert. She went to Harvard East Coast. West Coast just got complicated, all right, Well, at least team West Coast is representing today. That's right. We should unite against the true enemy, Annual the East Coast. All right, Well, it also might have a very direct impact on our everyday lives if the speed of light was slower, as specifically as you're listening to this podcast, right, Yeah, the Internet would be slower if the speed of light was slower. We relied these days on being able to like stream HD videos from around the world, downloading gigabyte files from Australia, etcetera. But the Internet moves at the speed of light and so like the bandwidth would be the same, but the latency would be longer. Like if you wanted to pin a computer in Australia and the speed of light was a thousand kilometers per second instead of three hundred million meters per second, then you would notice the different About half of our listeners are going and that's not a universe I want to live in. Forget it. Let's not even dwell on that everybody wants to live in the universe where the speed of light is faster and they get their downloads more quickly. Yeah, we all want optical fiber at the current speed. All right, Well, I think that answers the question for Dennis. There is no minimum speed of light that would hold the universe together. We could literally be like point zero zero zero zero, there is zero one per second, and you could still have a universe. It just would be super duper different. Yes, in ways that are probably impossible to predict. So hey, let's give it a try and find out. No, I want my fast internet, Daniel, I want my family reunions tomorrow. All right, Well, thank you to all of our question askers. We hope that was interesting for all of us. I think it was interestingful. It makes you kind of think about, you know, how the universe could have been different, in the Earth could have been different, all these interesting what if questions, And sometimes the hardest question is the deepest ones, the most insightful ones are the ones that everybody asks. You don't have to be an academic physicist or a working cartoonist to think deeply about the universe and ask fascinating questions, So please engage your brain and think about the universe. And if you have a question you don't know the answer to, don't be shy to write to us two questions at Daniel and Jorge dot com. Yes, and there's your questions, even if they are a little confusing. Hope you enjoyed that. Thanks for joining us, See you next time. Thanks for listening, and remember that Daniel and Jorge explained The Universe is a production of I Heart Radio. Or more podcast from my heart Radio visit the I heart Radio app, Apple Podcasts, or wherever you listen to your favorite shows.