Daniel and Kelly’s Extraordinary Universe - How can we measure the curvature of space?

Episode Date: March 9, 2023

Daniel and Jorge bend their minds (and yours) around the curvy topic of bent space.See omnystudio.com/listener for privacy information.

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I think it would have to be general relativity because it's super beautiful and gorgeous, but it's also really hard to actually wrap your mind. isn't that all relative though but i guess what makes it hard all the math there's a lot of math but fundamentally it's the concepts you know it's just such a different view of how to see the universe it says that space is like a thing and it's invisibly doing stuff that we're blind to yeah it's pretty wild and now we got like neutrinas dark energy dark matter seems like most of the universe is invisible to us we're definitely more clueless than clued in when it comes to the universe

It's all a giant game of clue, you know. It was the dark energy that killed the dark matter in the space library with the neutrinos. That might be the first time neutrinos ever killed anybody. Hi, I'm Horham, a cartoonist, and the creator of PhD comics. Hi, I'm Daniel. and a professor UC Irvine, and if I could choose the way I go out, I'd like it to be with neutrinos. Oh, yeah? Why is that? Because it sounds unique. You know, I'd like to be the first person ever killed by neutrinos. I don't even know if that's possible. Like, imagine the crazy

intense neutrino beam necessary to even heat you up a little bit, not to mention kill you. Sounds like you thought about this a lot, about how to use neutrinos to kill someone. Yeah, for about 10 seconds so far. I guess it is hard, but I guess with enough of them, they could be deadly, right? Yeah, if you have a powerful enough beam, they could actually deposit enough energy and you had to fry you just like a laser. Ooh, neutrino lasers.

But would it be like a neutral tan? It'd be like a little neutral tan, right? Because it's neutrino. Maybe our next product idea should be neutrino's blocking tree. Now, there's a science scam. Add the word quantum to it, and it'll sell, sell, sell.

Could have a rating of MPF 1000. Neutrino protection factor. But anyways, welcome to our podcast, Daniel, and Jorge explained the universe, a production of iHeard Radio. In which we try to beam into your brain all of the incredible mysteries and knowledge about the universe without toasting it. We try to protect that precious little blob of matter while also injecting ideas and questions and curiosity into it. We hope to stimulate your brain to think about the nature of the entire universe, what it looks like, what it seems like, what it's actually doing behind our backs without toasting it aggressively. Or at least neutrally toasting it because it is a fascinating universe full of amazing things out there.

And it's an ever-changing universe. It's a universe that's expanding and growing and shifting and moving and rotating space, doing all kinds of things. It is doing a whole lot of things. And as you mentioned, it's doing a lot of things that we can't see. Our senses are like tiny little portals into the vast and complex workings of the universe. Most of what's out there is really invisible to us. Yeah, and that's one of the wonderful things about the universe, that it doesn't reveal itself right away. We need to probe it, we need to think about it, we need to find clever ways to figure out what's going on out there.

And so the history of physics is filled with people noticing something weird, something they can't quite explain, something that doesn't quite fit. Usually that's a thread we can pull on to unravel an entire story about something going on in the universe we weren't even aware of. The discovery of neutrinos being pumped out from the sun. the discovery of vast quantities of dark matter floating out there in space and changing the way that galaxies spin and the entire universe is formed. And that's not the end of the invisible things that the universe is doing right under our noses. Yeah, maybe one of the most mind-blowing revelations about the universe that humans have discovered in the last hundred or so years

is this idea that space is not fixed. It's not this kind of emptiness that we are used to in our everyday lives as we move around in space. Space is actually bending and curved. Yeah, space has a lot more properties than Isaac Newton might have imagined. It can do stuff. It's not just there. It's not just the emptiness, the lack of stuff.

It is actually a physical, dynamical thing that has properties and can affect things in all sorts of important ways. Yeah, and so one of the most interesting facts about that is this idea that space can curve, that space is not just straight up emptiness with nothing in it. it can actually kind of bend. This idea that space can be described geometrically as having curvature is, of course, one of the great insights that underpin Einstein's theory of general relativity. We've had this idea for about 100 years and it completely reshapes the way we think about the universe, but it still can be pretty tricky to understand what it means.

What are we talking about here? If you have a chunk of space in front of you, what does it mean for it to be curved? and is it possible to actually see it? This is literally a mind-bending topic. If your mind is part of space, then yes, bending of space will also bend your mind. I do feel like my head is in outer space a lot of the time. Or out of space or outer space, both.

We want to blow your mind into outer space. With neutrino lasers? Is that where all this is going? Neutrino lasers are not really very useful for anything, except for joking about how Daniel wants to. to go out. Well, technically would they be called lasers or nasars? Yeah, good question. I guess it depends on the frequency, right? But it'd be pretty tricky to build an apparatus that could resonate or focus neutrinos, neutrino optics, which be quite challenging to design. It's even hard to make

x-ray lasers. So I think neutrino lasers are pretty far from our technological capability. So I can safely joke about using them to fry my brain. Well, they're also pretty far from the topic. I don't know how we just took a 90-degree turn here. We were almost on track there. We're talking about the curvature of space and how space is kind of bendy. And so today on the program, we'll be asking the question. Can we measure the curvature of space?

Maybe we should be measuring the curvature of the podcast. Like, can we actually keep a conversation going in a straight line? Or do we constantly bend off the topic into other areas like neutrino lasers? I think the experimental data says that we do bend a lot. Sometimes 90 degrees, sometimes 360 degrees. Yeah, and sometimes those are the best moments on the podcast when we talk about something totally unexpected and discover a fun little corner of physics.

Yeah, but let's maybe stick to the straight and narrow here and stay on the topic of the curvature of space. This is an interesting topic because, first of all, maybe a lot of people out there, at least maybe in the general public, don't know that space can curve. Yeah, spatial courage. is really the foundation of general relativity. It's the idea that gravity is not actually a force,

but that the reason things move as if there was gravity is because space is invisibly doing this thing. It's bending. It's curving. It's changing how things move through it. It really requires complete shift in your understanding of gravity and what the universe really is all about. Now, technically, Daniel,

don't we need to say that we're talking about the curvature of space time, right? Yes. Because space by itself doesn't really bend. more like a bending if you include time into it. Well, technically I think space does bend, but you're absolutely right that the equations and the important like conservation laws are expressed in terms of space time because relativity takes time and treats it as the fourth dimension of space.

So really it thinks about a four-dimensional object, not just 3D space. So yes, space time is the more accurate description. Right. Wait, are you saying that 3D space bends or it's only that we should really be using the word space time to mean like the 4D concept is what bends. Well, each dimension does bend, right? X bends, Y bends, Z bends. So space itself as XYZ does bend, but time also bends and they all sort of bend together.

And that's one thing that Einstein realized is that it makes much more sense to think of these as four components of one larger mathematical object. But each individual one does bend the way, for example, time bends, right? That's time dilation. He certainly does bend, but it also bends in conjunction with. the other dimensions. That's some of the beautiful mathematics of relativity, seeing how all four work together.

Cool. Well, as usual, we were wondering how many people out there had thought about the question of whether and how you can measure the curvature of space. So thanks very much to everybody who answers these questions for us. We'd love to hear your voice on the podcast as well. Write to me to Questions at Danielanhorpe.com, and I'll email you a batch of questions for future episodes. So think about it for a second.

How would you measure the curvature of space? Here's what people had to say. Yes, we can measure the curvature of space, I think. We did that gravitational wave detection recently, and I know at least the calculations work out, so I'm going to go away, yeah. I know we can detect distortions due to gravitational lensing from massive objects,

but I don't think that was what you mean. I don't know how we would detect the curvature of space while being within the space-time continuum, I would think you'd have to be outside of it to be able to see the curvature. Yes, I don't know exactly how it works, but probably we can measure it with a light, with photons, something,

but I don't know exactly how this might work. If we can't measure the curvature of space, what is general relativity all about? All right, everyone's seen pretty positive about the fact that you can do it. Yeah, it's definitely something we know is happening out there, right? Which is sort of cool philosophically and conceptually to accept that this thing is happening all around you, it's sort of invisible to you, but it's necessary to understand how things

work, right? To accept that a big fraction of the nature of the universe itself is invisible to us. Yeah, I guess it's kind of a weird question because like if space bent right here in front of me, I would probably be able to tell, right? Well, that's the question is how could you tell? Like imagine it was just space, no matter, no particles. Everything was totally empty. If you had a chunk of space in front of you,

how would you measure its curvature? Could you measure it without its influence on other things? Like you can't see it bent. The way you can look at a road and say, okay, I can see that the road is bending ahead of me. You can't do the same thing with space because its bending is not directly visible. What do you mean it's not directly visible?

Like if the space in front of me curved, wouldn't I be able to see it curve? Well, imagine an invisible road, right? If you can't see the road, but you can follow the cars moving along it, then that's the way you're seeing that the road curves. So that's a difference between a visible road where you can, for example, see that it's bendy even when there aren't any cars on it. And an invisible road, like at night, if you can't tell where the cars are on the mountain, but you can follow their headlights. So you can infer where the road must be. In the same way, space, we can't directly see its curvature.

Unless there's matter being influenced by that space, we can't directly tell what the curvature is. Oh, I see what you're saying. You're saying space by itself is invisible. You can't, like, see space. And so therefore, how do you know if it's bending or not? Yeah, exactly. And you might think, oh, that's obvious, right? We're talking about space.

Space is invisible because it's space, right? But remember that we now know that space is a thing. It has properties. So at each point in space, it has this property, this amount of curvature that's somehow stored in it. And yet we can't directly see it. So even though it's invisible, there is something. to it. All right. Well, let's dig into this topic. Daniel, step us through the basics of this. Like,

what do you mean by curvature? What does it mean for space to be curved? So first, let's dispense with a sort of common misunderstanding of curvature. A lot of people have seen this example of like a rubber sheet with a bowling ball in it and have been told that this is an example or an analogy for the curvature of space. And, you know, this is helpful in some ways because it makes you think about how space could be bendy, but it's also really misleading in some important ways. First of all, it treats our universe as if it was two-dimensional, just like the surface of the rubber sheet. And it suggests the bending is happening in some third dimension, up and down. So it suggests that bending is extrinsic, that it's like relative to some fixed external ruler.

But in our universe, we think that the bending of space is intrinsic. There is no external ruler, no fourth dimension where our space is sort of like bending out towards. The bending of space for us and in general relativity is intrinsic, which means it's. just changes the relative distances between things, like how far two points are apart. I guess that's weird to me because I think what you're saying is that curvature is something that happens within space, not relative to anything outside of it. But if it's not happening to anything relative outside of it and we're all in space, I mean, is that still curvature or is it just that's the way space is? You know what I mean? Like what's the difference

between a curve space and a non-curve space? Well, you can measure it. And what does it mean, right? Well, we know that space can be curved and it can also be not curved because we have chunks of space in our universe that are not curved that are like far from masses and energy and chunks of space that are highly curved near large masses or even so curved that they become like one directional inside a black hole. So it's definitely something that space can do and space can do differently. They can have different amounts of curvature. Well, I feel like you're now defining it relative to how it's not curved, right? You're saying it curves relative to how it's not curve, but isn't that also just like an external measure of it or an extrinsic definition of it? Well, I think it's still relative and you can use that definition, as we will talk about in this episode, to construct like ways to measure that curvature by, for example, passing matter through it and seeing the influence on it, right? In curve space, things that are not under acceleration don't appear to move in straight lines, whereas in flat space, they do.

So there's definitely a difference in the behavior of objects in flat space. and in curved space. And it all comes down to this definition of relative distances, right? This metric, which is the solution to Einstein's equations, tells you the amount of curvature every point, and that tells you how things move. And that basically tells you what the shortest path is between two points in space. And so it's all about the relative differences, not in reference to any external ruler. But yeah, it is relative to some internal ruler, right, which is flat space.

That's true. Right. So you're sort of comparing it to like a universe without any mass. or any energy in it, basically, right? Which is kind of like thinking about it as like the exterior measure of space, like relative to not space, which is kind of like an outside point of view, right? Well, I think it's a nice way to think about it as a benchmark. Compare curved space to flat space.

That's definitely a nice way to think about it. But that flat space doesn't have to be an external metric. It's not like our curved space is sitting inside some larger flat space that's being used to measure it. We can measure the curvature internally without right. referencing anything outside of our universe. Maybe that's what you mean by intrinsic is that you can measure this curvature without knowing what it would be like without any masses in it. Yeah, exactly.

And it's amazing that we can, that we can detect this in our universe. And in some sense, it's kind of obvious to us. Like we notice the effect of curvature all the time because we grew up experiencing it. Our experience of gravity turns out not to be due to some mysterious force of gravity as Newton described, but it's the effect of curvature. curvature changing how things move through space. So we experience the curvature space all the time.

It's not subtle. All right. So curvature is kind of a property of space itself. It's not relative to some outside space that space sits in. And so is it related to the force of gravity? Right. And so Newton's idea was, look, gravity is a force. I noticed the earth pulls on things like this apple or that bowling ball or my bowl of yogurt or whatever.

And so Newton explained this thing he observed that masses, tend to attract each other in terms of some force. And he didn't understand like a mechanism of it. He didn't understand deep down what's happening. He just described it and said, here's a mathematical description for what's happening. I have an equation that describes it. It all seems to work. So that was Newton's description.

But it turns out that gravity is not actually a force in our universe, the way, for example, electromagnetism is, or the strong force, or the weak force. It turns out it's an apparent force, something that seems to be a force, but is actually caused by something else. Wait, I feel like you're saying maybe the electromagnetic force is apparent. It's not a real force? It's an apparent force? No, I was saying the opposite.

That electromagnetism and the weak force and the strong force, those are real forces. But that gravity is different. Gravity is an apparent force. It's not actually a force in the universe. It's just caused by a curvature. And because we can't see the curvature, we need to invent this force in order to explain what we are seeing. Oh, right.

I got that backwards. So then the curvature space is gravity? Is there a curvature of space that's not gravity? So gravity is our way to explain the effect of the curvature of space because we didn't realize that space was curved. We didn't understand it was happening. Let's take a simple example of apparent forces we sort of invent to explain things. Say, for example, you're driving a truck and you got a tennis ball in the back.

Now, when your truck is not going anywhere or it's driving a constant speed, this tennis ball in your truck is just going to sit in the back. It's not going to roll forwards or backwards. But now if you hit the gas and the truck accelerates, then what happens to the tennis ball? It suddenly rolls to the back of the truck, right? But in your frame, the frame of the truck, why is the tennis ball rolling backwards?

There's no force on the tennis ball for somebody sitting in the back of the truck. They just see it roll backwards. Well, I guess, you know, if you were there in the truck, you would also feel that force, right? Yes. You were saying maybe like if you had a camera inside the truck filming this ball, someone looking at the footage,

would you see the ball suddenly start to move. Yeah, exactly. Somebody would see the ball suddenly start to move. And so they would say, where's this force coming from, right? There's nothing touching it. What is pushing on the ball? We know the answer is that the truck is accelerating, right? It's actually how you measure acceleration.

But in the frame of the truck, the camera that's sitting in the back, you can't explain it without adding some external force and saying, well, there must be some external force on this ball. Right. So you add this apparent force in order to explain the motion you see. It's the same thing is happening like on a merry-go-round. If you're on a merry-go-round that's spinning, you're you're going to. you feel this apparent force outwards, right? There's no real force pushing you off the merry-go-round.

It's just the fact that it's spinning, which again is a kind of acceleration, creates this apparent force. So if you wanna do like F equals M-A and you wanna explain all acceleration in terms of forces, you have to create this apparent force to explain what's going on when you accelerate the truck or when you're on the merry-go-round.

Those are just examples of other places where we've had to add apparent forces in order to explain the data dynamics that we're seeing. Well, I guess maybe I'm a little confused on this subtle point because, you know, in the case of the ball in the truck, there is a force going on, right? Like something is pushing the truck. But nothing is pushing the ball.

Yeah, but the truck is being pushed by the engine and the wheels and the friction with the road. What I'm seeing is the ball not being accelerated with the truck. But there is a force going on, right? There is a regular electromagnetic force pushing the truck. You're exactly right. And that's the key insight. There is a force on the truck.

And therefore, the whole frame of reference there is accelerating. So what you're really seeing there is that the frame of reference is accelerating, which makes it a non-inertial frame. And the equation F equals MA only works in inertial frames because there's no force on the ball. If you want to understand the acceleration of the ball from the point of view of your camera in the back of the truck, there is no force in the ball. Like nothing is touching it, nothing is pushing on it. Something instead is pushing the camera, which is attached to the truck. It's changing the frame of reference. So if you want to use F equals MA, you have to add in a force to compensate for that.

So the acceleration creates this apparent force on the ball, even though, again, nothing is actually pushing the ball. But you see it moving as if there was a force on it. Right. But I guess that's only because you don't know that the truck is accelerating. But if you did, you could figure it out. You could, you know, account for it because of the forces that are there, no? Exactly right.

There's two different ways to think about this to think, oh, I'm in an accelerating frame, so I shouldn't be using F equals MA. I have to account for the fact that I'm accelerating. But if you didn't know that the camera was accelerating, then you have to add a force to account for it. That would be an apparent force. And that's exactly our situation when it comes to curvature and gravity.

We can't see curvature. We don't know that it's out there. In fact, for hundreds or thousands of years, we didn't even know it was happening. And so in order to explain the motion of objects, as we saw them, we had to create this apparent force. We call gravity to explain the things that otherwise didn't have an explanation.

Now we know that space is curfew, like knowing that the truck was accelerating, and that can be our explanation instead of creating this apparent fictitious force. Let's dig more into this idea of curvature, and then finally, how do you even measure something that's invisible out there in space? But first, let's take a quick break.

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Tim McRaw. Tickets are on sale now at AXS.com. Get your tickets today. AXS.com. All right, we are bending our minds here with the curvature of space. And I have to say I got a little bit confused because I feel like we've talked about this for hours and hours on this podcast, but it's still kind of hard to process. It's kind of hard to tell the difference between like, hey, gravity is not really a force.

It's a space that bends. And the alternative point of view, which is like, hey, maybe if you just look at a different you can see it this way, that it's a bending of space. You know what I mean? Like, is it that we can see it as a bending of space or that it is a bending of space? Oh, yeah, great question, right? Is it just a philosophical distinction or is it actually a physical distinction? Doesn't matter.

The answer is that it does matter. We know that it is the bending of space, but most of the time it doesn't matter. Most of the time treating it like a force and treating it like the bending of space give exactly the same prediction for the earth going around the sun and for all sorts of things. In some edge cases, some corner cases, some extreme circumstances, they do give slightly different predictions. And that's how we know that Einstein's theory was right and then Newton's was wrong. What are some of these extreme cases? So there are a couple of examples. One is like spinning masses. Another is the effect on light. So Newton's theory predicts that

spinning masses have exactly the same gravity's masses that don't spin. Like if you're in outer space and the earth is spinning under you, the gravity from the earth is not affected by the fact that the Earth is spinning. It just depends on the amount of mass. But Einstein says actually there's a little effect there. If the Earth is spinning, it's like dragging the curvature of space with it. And this causes a weird little twisting effect

on things out in space. We talked about a really precise experiment called Gravity Probe B, which actually measured this and confirmed that this is happening. The other example is the bending of light. Newton's theory says that masses attract as a force of gravity between objects with mass. But photons have no mass.

And yet we see they are bent by massive objects. Einstein's theory was famously proven when we saw light being bent around the sun. This is gravitational lensing. And that's light moving through curved space. So there are some differences between the view that gravity is just a force like Newton said and that gravity is just an apparent force due to the bending of space. Right.

I know we talked about both of those cases before in the podcast. But I guess maybe a question, I wonder if other people have, is that, or that we're used to defining gravity only as, like, what happens between things with masses. But if, you know, mass is also energy, what have you just expand that definition of gravity to be what happens between things with energy? And so then you can include things like light, and that would also explain the bending of light, wouldn't it? Or, like, I wonder if, like, if you also include energy, then the spinning of the earth that could also be sort of like extra rotational energy. I don't know. I'm just making things out.

I'm just like, no, it's really cool. Could you add these features, these bells and whistles to Newton's theory to make them work? And there's a whole bunch of people trying to think about exactly how to bridge Einstein and Newton's theory to make Newton's theory like a special case of Einstein's theory to sort of put it as a point in a larger sort of Einsteinian space. And you can try to do that, but it doesn't quite work. You know, for example, treating photons as if they have energy and therefore gravity doesn't work because photons are the same frequency, bend through space the same amount.

It depends on the curvature of space, not on the energy of the photon. So it doesn't quite work. Because I guess photons can have different energies to them. Yeah, photons of different frequencies have different energies. But how much they bend depends on the curvature of space, not on the energy of the photon. Unless maybe there's something you're missing? Yeah, you can add more bells and whistles if you like. Potentially it's possible for somebody to come up with a modification to Newtonian gravity

to make it work like Einstein's and think about it as a force. you know, in some sense, we can never really know what's real out there and what is just our description of the universe. But we have a very compelling description of all of these effects using the concept of space being curved. It's very successful. And so we'd like to think that it's real. But ultimately, we never can know what's actually happening out there as compared to our mental image of the universe. All right. Well, then we have to sort of accept then that it's a real curvature like it really does bend. It seems to be a very accurate description of what's happening in the universe, so it's very tempting to say it's real.

You know, philosophically, what does it mean for it to be real? It means that, like, it's happening even if we don't look. Like, if humans weren't here to measure the curvature, space would still be bent. So that's a philosophical claim, not a scientific one. It's not something we could ever actually test. But, yeah, it's pretty convincing. When you have a theory that works this well, it feels like you've discovered how the universe is working rather than just describing it. Well, maybe one thing that's a little bit also confusing is that in terms of the curvature space,

it's sort of like you can't tell it's curved if you're in it. You can only tell its curve if somebody's watching you from the outside, right? Like if you were writing that light beam being bent through space, you wouldn't feel any forces, right? You would think you were going in a straight line. But to someone outside of you, you'd be like, oh, that light ray bent. Yeah, you're exactly right. Anything moving according to curvature feels no acceleration. Like if you built an accelerometer, and basically that tennis ball in the back of a truck is an accelerometer, something that measures whether there is acceleration.

Say you have an accelerometer with you and you're in a spaceship and you're flying through totally flat space at constant velocity. You're watching the accelerometer, nothing happens. No surprise there. Now say you're flying through curved space, as you say. Could you tell that you were flying through curved space just by looking at stuff inside your ship at your accelerometer? After all, you are bending, right? you're changing your direction. Well, the answer is no.

You do not feel any acceleration inside your spaceship. Your accelerometer does not register any acceleration because you're moving along the curvature of space. The accelerometer only measures sort of like forces against the curvature of space, like resisting gravity's flow. So yeah, the only way you can measure that curvature is by, like, for example, comparing your position to other objects out there. You mean as you were riding the light beam?

Yeah, as you're writing the light beam. This concept of freefall of moving through space without any other forces, just letting gravity control you is really important in general relativity. That's the sort of like concept of an inertial observer. Somebody who's like skydiving, they jump out of an airplane. They're in free fall. Ignore air resistance. Newton would say, oh, they're being pulled down by the force of gravity, right? And Einstein would say, no, they're just moving along the curvature of space.

There's no force on them. They're just in freefall. And Einstein's right that if you had like an accelerator, with you after you jumped out of the plane, it would not measure any acceleration. Right. Maybe this is where it gets sort of tricky and you kind of have to include the definition of time into it, right? Because I guess if you jumped out of an airplane, you would get moved, right?

Like your position in space would change. Yeah, exactly. Even though there's no acceleration, right? That's because in curved space time, you have to accelerate just to remain stationary. The airplane, for example, it's applying a force to stay up. It's actually accelerating upwards. When you jump out of the airplane, you are no longer accelerating. You are now in free fall.

So there are no forces on you. Because remember, gravity, not a force. You're just moving according to the curvature space. Just like that spaceship out in space, moving through bent space, it's not going to notice anything. You jump out of the airplane, you're not going to measure any acceleration. The airplane is staying up, hopefully. And so it's accelerating up, right?

Just like somebody who's standing on the surface of the Earth, in order to avoid moving down towards the center of the Earth, center of the earth, the earth is accelerating them upwards. It's providing a force. The ground is pushing them up. It's actually accelerating them all upwards. You are in free fall. You don't measure any acceleration. You measure everybody else accelerating upwards. Right. I think maybe this is where you kind of have to say the word space time, right? Because I mean, you can't just say like you're following the curvature of space because that only works if you also include time into the word. Absolutely. Yes. Time is crucial here because we're talking about motion. So you do kind of have to say

the word, really that it's a curvature of space time, right? Yeah, curvature of space time, absolutely. All right, like you said, it's kind of hard to know that space time is bending around you if you're in it, if you're being moved along, it's curvature. And so I guess the question is, how do you measure then that space is being bent? What are some of the ways that people do that? So the most straightforward way to test whether space is bent is to see its effect on stuff, right?

This famous description of general relativity is that matter tells space space. time how to bend. Space time tells matter how to move. So if you see stuff moving in straight lines, that tells you that space time in front of you is flat. If you're an inertial observer and you see things moving in curves, that tells you that space time in front of you is curved somehow. So you can just watch the motion of objects, just like looking at those cars descending down the mountain at night. Look at their headlights. You can tell if the road they're on is bent. So basically, you have to be kind of like an outsider observer or I guess you have to sit at a distance, imagine what that space in front of you would be like if there wasn't any

bending and if something moves through there differently than it would through empty space, then you know it's being a bent. Yeah. Say, for example, you didn't know the sun was there and you threw a planet into the solar system and it didn't fly right through. Instead, it bent and it ended up in an orbit, right? That's definitely. not the motion you expect through flat space. And so you can tell that space is curved because the object is not moving in a straight line. It's following the curvature of space. It's on what we call a geodesic. The path of particle follows if there's no acceleration on it. And so you can tell, for example, that the space in our solar system is curved because the

earth is not moving in a straight line. Right. I think we've talked about this before. Like if you took out the sun and you replaced it with a black hole with the same mass as the sun, it would be super tiny, right, I think, maybe around the size of a bowling ball or something like that, which you would never see from this distance, right? Because it's millions of miles away. But the planets would still keep orbiting the same way as it would before. Yeah, I think the sun would actually compress about three kilometers, but you're absolutely right on the point of gravity. Our Earth would move around it in the same way. And so if space was like invisibly bent by a black hole, then you could tell. And that's exactly what we do at the

part of our galaxy, we can tell that there's a black hole there, even though it's largely invisible, by the motion of the stars nearby. They whizz around as if there was some very massive object there, curving space. That's what I meant, like a three kilometer wide bowling ball. I want to see the pins. Yeah, yeah. But you still wouldn't see that from here, probably, right? Something in object, three kilometers, why? You probably wouldn't see that from here, would you? Especially if it's black in a black backdrop. I don't know if it's one of those, like swirly galaxy bowling balls might also bend into the background. Oh, yeah.

They do have those glow in the dark bowling balls. Yeah, exactly. And so that seems sort of obvious. And maybe that sounds like a cheat. Like we're just saying, oh, gravity is actually the curvature of space. So anywhere you see the effect of gravity, you're seeing the curvature of space. And therefore, you know that space is curved. But remember, we also talked about the curvature of space doing things that just Newton's

gravity can't do like bending light around the sun. And this was Einstein's famous test of general relative. He predicted that in an eclipse, we would be able to see the bending of light from distant stars as it goes around the sun. Right. Like during an eclipse, right? During an eclipse, you can see the light rays kind of bend around the eclipsing moon. Actually, the bending is of distant stars well behind the sun around the sun. And the reason we use the eclipse is not because we're looking for the light being bent around the moon, but just that then the moon mostly blocks out the sun's light. So it's easier to see these stars that are very close to the sun. In principle, you could see this at any time. Stars that are sort of just behind the sun or having their light bent by it,

but it's pretty hard to do when the sun is on. So basically we use the eclipse to turn the sun off to block it, and then we can see the stuff around it more easily. But also technically the sunrace are probably being bent by the moon in front of the sun. Oh, yeah. Awesome. Yeah, absolutely. A little bit, but maybe not noticeably.

Yeah, for sure. You put your hand up to block the sun. sun and your hand is bending the light rays of the sun, right? Because your hand curves a space. Everything with mass curved space. It's a pretty subtle effect. I mean, even the sun bends this light by like a thousandths of a degree. So it's pretty hard to see. All right. Well, I think what you're saying is that one way to know if curvature of space caused by a mass is to see if things that fly near it, including light, a bend. Yeah, exactly. And one time on the podcast, you made a really cool point that the best way to see this is actually use like two beams of light you like shine a

laser through space and see if they stay parallel right because if space is flat then they will stay parallel forever but if space is curved then they will bend and they may even cross okay so that's one way to measure how a space can bend is if you see things it the trajectory of things even including light bending around something you know that bending relative to what you're looking at that means that there's something there and it's bending space what are some other ways that we can measure the bending of space time. Yes, space time. Exactly.

Very good point. And time is also bent with space, as you've said, right? And so the curvature is not just in space, but in space time, which means the time is also curved. And that's this feature we call gravitational time dilation. The curvature of space makes clocks slow down. And this is really super fascinating and different from the kind of time dilation we're used to thinking about from velocity.

Like if you see somebody in a spaceship traveling. really, really fast, we know that your view of their clock sees their clocks slow down. Moving clocks run slow. That's one really cool effect, but it's actually totally separate from this kind of time dilation. This is time dilation just caused by the curvature of space. So if you're in a part of space that has a lot of curvature, your clock will run more slowly. And so if you look out into the universe and everybody else has clocks and you see their clocks running faster, that means that you are in curved space.

You look down at your clock and it seems to be running normally. Everybody else's clocks are running faster. They see your clock as running more slowly. So that's one way to detect the curvature of space. I think you mean like the example of like, you know, you can measure the curvature of space by seeing how they bend, how their trajectory bends in space that tells you there's something there. But like there might be a situation where you can't tell that space is bent,

even though there's something there. Like for example, if I shoot a laser straight at a black hole, I'm not going to see the path of the laser move or change, right? Just going to keep going in a straight line. I guess until it hits the black hole, but before that, you wouldn't be able to tell that space was bending unless you use something else like time. Yeah, good point.

If you shoot a laser beam directly at the heart of a black hole, like pointed bang on to the singularity, then its path wouldn't bend, right? Because it would be sort of moving along that curvature. But its time would bend, right? And so anything falling towards a black hole, its time gets dilated. And this is something we've actually measured.

But what would that mean for a laser there? Like, would you see the laser slow down? So this gets into very tricky territory and general relativity, but measuring velocity of distant things. If you are near those photons as they pass you, you measure them as having the velocity of the speed of light. If you are far away from them and they're moving through curved space, then the rule that light always travels at the speed of light no longer applies.

that only applies to flat space near inertial observers. So you can actually see light travel at all sorts of different weird velocities. You would see it slow down, yes. Interesting. It is pretty weird. You sort of have to need to plant the clock in that light laser beam in order to know that space was curved. Otherwise, would you know?

I suppose by measuring its velocity as a distant observer, you could measure the curvature of space there. But your right, time is a really cool way to measure the curvature as well. And this, I think, is really cool because these are experiments. we have done. We shot a laser into the heart of a black hole? Did I miss that headline? Unfortunately, nothing so cool because we don't have laser beams orbiting black holes to do

these experiments. We have to make do with measuring the curvature of space around our Earth. And so what we've done is built really, really precise clocks and see that they run differently at different altitudes, for example. And again, this is not velocity-based time dilation. This is not put a clock up in a spaceship and orbit the Earth really, really fast. They have, for example, a super precise atomic clock that they can raise and lower by like a foot

and they can see a difference in how fast it runs if they raise and lower it just by one foot because the curvature is different as you move further away from the surface of the earth. All right, well, let's get into some of the other ways that you can measure the curvature of space and then let's talk about what this all means, man. But first, let's take another quick break.

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We're talking about the curvature of space. It's bending my mind a bit. And how you might measure this bending of space if you didn't know, I guess, if space was being bent. I guess if it's not obvious, because space is invisible, technically. Yeah, if you can't see the, curvature directly, how can you tell that it's there? And I love this philosophical question of

even if you measure it, do you really know that it's there or if it's just some weird effect? Like, could somebody come up with another theory of physics that doesn't require the curvature space, but requires some other weird change in our understanding of reality that can also explain everything we see? Yeah, possibly. And then you might be forced to believe that that's how reality actually is. The space doesn't curve. It's actually this other thing that's happening. Yeah, so we're sort of along for the ride as physics is figuring it out. Is this shifting of the clocks in relatively, like this idea that time slows down maybe also another way to show that gravity is not like Newton imagined it, right?

Because there's nothing in Newton's laws that account for like time slowing down, right? Yeah, great point. Is there? I don't know. No, there is not. Newton thinks of space and time as absolute and universal, right? So this is another feature of relativity, connecting space and time together, tying it all up into one 4D mathematical object and accepting that they are related to each other. And in special relativity, space and time are all twisted up together.

How you measure clocks depends on where you are and how fast you're going. So they're definitely tied together in a way that Newton never anticipated. Right. All right. Well, we're talking about how to measure this invisible thing of an invisible thing. And so what are some of the other ways that you might measure the bending of space? One really cool way to measure the bending of space is to look at the geometry of objects. Like, you can tell if space is.

is curved by building triangles or by measuring the circumference of circles. And this is easiest to understand if you think about like what happens on the surface of a sphere versus like what happens out in space. If you're like out in space and you build a triangle and you measure its angles, you get 180 degrees. Now if you're on the surface of the earth

and you build like a really big triangle and you measure all of its angles and add them up, you'll discover that they don't actually add up to 180 degrees. They add up to a little bit more because the angles of a triangle add up to 180 degrees only on a flat surface, not on a curved surface. Well, I guess only if you kind of project that shape onto the surface of the earth, right?

You can still have a perfect triangle. It's just sitting on top of the earth in a weird way, isn't it? Yes. If you follow the curvature of the earth, then that triangle has an angle greater than 180 degrees. If you don't follow the curvature of the earth and your triangles like sort of awkwardly sitting on top of the earth, then yeah, it can still be flat. But if it follows the curvature, it won't have angles that add up to 180. That's one way that you can tell if that the surface of the earth is curved, right?

Yeah, exactly. You can measure the curvature of the earth. And that's sort of a famous example, but it applies to other objects too. And I think maybe people haven't heard about this. And I think it's really cool. You can also measure the curvature by measuring pie, right? Like draw a circle, measure the diameter and the circumference. The ratio is pie.

And on a flat surface, pie is 3.14159, et cetera, et cetera. But on a curved surface, it's not. And on a curved surface, the diameter gets longer. Instead of just being like straight across the circle, it's now like rising above the circle and coming back down. So pie changes as space gets curved. I think what you mean like is that if you drew a circle across the equator or if you thought of the equator as a circle

and then you try to measure its radius from the north pole, you wouldn't get pie. You would get something else because you're measuring the radius along the, surface of the earth right you're measuring this basically curvature the longitude basically line which are longer than if you just do a line through the center of the earth on that circle exactly so if you were like not aware that the earth was curved you draw this huge circle and you walk from one part of the equator across the north pole and then back down to your circle and measured that

then you would get an answer that's much longer than just drilling a hole through the center of the earth and so basically that's a measurement of pie and so pie is a measurement of curvature. And so if you go out in space and make a really big circle and then measure its diameter using a laser beam, you can measure the curvature of that space by comparing what you get to pie. But what if you make a giant pie the size of the equator? Wouldn't you still be measuring pie?

And fill it with neutrinos. I can't tell if you're joking or not. Are you talking giant pie P-I-E? Yeah, like you mean a giant apple pie. to say, right, with the diameter of the equator, wouldn't you still measure pie? Well, that's a good question. If you build a flat pie out in space

that's ignoring the curvature of space that's being held together by electromagnetic bonds, which are really strong, then it could still be flat, right? But if you're following the curvature of space, you're using like a laser beam to follow the curvature of space, then you would not get pie measured across your giant apple pie.

Which you would have to cut, I guess, with a neutrino laser beam because it'd be so big. What kind of ice cream do you serve with neutrino apple pie? I don't even know. Obviously, a dark ice cream. All right, so that's another way to measure the curvature space is using geometry, which is like a sixth grade subject, just measuring angles between things. If they don't come out to be what you would expect in flat space,

then you know your space is curved. What are some other ways that we can measure the bending of space? So I think one of the coolest ways is this experiment we talked about much earlier, which measures frame dragging. This is an effect that doesn't happen in Newtonian gravity at all. So as we said before, the Earth is spinning and as it spins, it sort of like drags space time with it a little bit. And so if you're an object out orbiting the Earth, you feel a different force because the Earth is spinning than you would if it wasn't spinning. What you feel is a little torque, like a little twist, not just a force inwards towards the center of the Earth, but like a little twist that spins you a little bit because how space is sort of flowing over you.

So there's these awesome experiments called Gravity ProB that built like the most spherical objects known to man, these super precise gyroscopes out in space that were like mined in Brazil and then polished by like German grandmothers for years and years and years. And these were able to measure this very, very small effect, but it's real. You know, we have a whole episode about this, but this is sort of related to tidal forces too, right? Like if you have an object out in space near Earth spinning, some things are sort of closer to it than others. And so there's some delay in how the gravity kind of goes from one end to the other. Yeah, exactly. This only happens on objects that are not points, that objects that have an extent.

Because as you say, they're experiencing space differently. And so it's that relative effect across the object that ends up causing the torque. So you're right. Conceptually, it is similar to tidal forces in that way. The effect is larger for bigger objects and zero for point-like objects. But this frame-dragging is a way to confirm that space. can curve, but you sort of need a giant spinning object to cause that kind of effect. Yeah, you don't get frame dragging around objects that are not spinning. So in one way, it's really

a test of Einstein's theory to say, is this effect that Einstein predicts, but Newton doesn't, is it real in our universe? And the answer is yes. And that's a consequence of all of Einstein's math and his concept that space is curved. This is a direct result of space being curved and how space reacts and how that curvature reacts to mass, especially spinning masses. And so in that sense, it's an indirect confirmation that space is actually curved. The scientists who work on this project, they think of this is like one of the most direct measurements of the curvature of space, because so many other measurements could be explained by Newton's theory. This one only can be explained by Einstein's theory. So they take it as really proof that Einstein was right and therefore

space is curved. Or space can curve, right? Yes. Can curve. Or more accurately, space time can curve. Yes. Space time has the ability to have curvature, which is really still boggles my mind. Yeah. So I guess maybe to wrap it all up, like let's say I wanted to tell if the space around our solar system or even the space around our galaxy was curved, maybe not due to the mass

of the galaxy, but just like overall, like are we living in a spherical universe or are we living in a cube universe or are we living in a donut universe, like, how do you tell that your space around you is curved? Would you be able to tell with any of these methods or do with some of these methods work and others not? So to measure the curvature space on like a cosmological scale, you could use this. Like if you could construct a giant triangle bigger than galaxies or shoot laser beams between galaxies in a big triangle, then you could use these methods to measure them. But that's not really practical, right? But what we can do instead is see the effect of space on things that are already out there.

For example, we looked at the cosmic microwave background radiation, this light left over from just after the Big Bang. And that light has like wiggles in it, has like hot spots and cold spots. And we know something about how big those hot spots should be because of like how much time things had to like even out and cool off. And then the curvature of space affects the size of those hot spots. as we see them. If space is curved in one way, then the spots get bigger. They get blown up by lensing. If space is curved in another way, they get shrunk. So we can actually measure like the overall curvature of space near us by looking at the size of hot spots in the cosmic microwave background radiation. Because I guess that light comes from really, really, really

far away, kind of, and all around it. Yeah, and all around us. It's been traveling for billions and billions of years. And so it's probing a really, really big space. It's like the oldest light that we can see. So it comes from like the very edge of the observable universe. What does that light say? Is the universe bending right or left? That light says that to within our accuracy to measure it, the universe is flat. There are little bendy spots here and there near galaxies, but that overall there is no curvature to the universe, that the universe seems to be mostly flat. That's sort of a weird result, though. I would maybe say maybe you're just wrong.

it's sort of like when you're trying to see if something is right or laugh and you say it's neither I'm like well how do you know you got it right yeah it's a good question and lots of people have done these experiments with lots of different technologies and looked at lots of different aspects of it so we're pretty confident but you know there's also statistical uncertainty there it's like flat to within about one percent and so there's a possibility that spaces a little bit bent one way or the other, sort of overall. But we know that space is bent near us, right?

Effect of all the mass of the galaxy and the solar system is definitely curving space in our neighborhood. What if we build a giant pie the size of the galaxy? I'm in. I don't need to hear anymore. I mean, well, technically you could also do that, right? That thing, that's what you meant earlier

by giant lasers. Like if you build a giant circle, the size of the galaxy, and measure pie by measuring the comference and radius, then you would be able to tell, right, that things are bent. Yes, galaxy size pie is a good experiment. In any case. Because even if it turns out to be inconclusive,

it might still be delicious. Fun, fun, fun, fund. All right, well, it sounds like there are many ways to measure the curvature of space, some of them more delicious and or dangerous than others. But the amazing fact is that space time does bend. been confirmed. And there are experiments you can do to measure it. That's right. And it is possible to get a grasp on what's going on with our universe, understanding it's otherwise invisible doings.

If we are clever enough, and if we follow the threads of all those weird little things, we can't otherwise explain. I wonder what people who think that the earth is flat think about this concept. Like, is this just too much for them? Or do you think there are people out there who say, yes, the earth is flat, but the universe is his curve? I don't know. I'm a flat universer. All right. Another exploration of how mind bending and also space time bending the universe is. I guess a good reminder that sometimes we think the universe is one way from our local experience.

But if you go out there into the universe or explore extreme situations, it turns out that the universe is different. You enjoyed that. Thanks for joining us. See you next time. Thanks for listening and remember that Daniel and Jorge Explain the Universe is a production of iHeartRadio. For more podcasts from iHeartRadio, visit the iHeartRadio app, Apple Podcasts, or wherever you listen to your favorite shows. Friday, and cancer free the next Friday. No chemo, no radiation, none of that. On a recent episode of Culture Raises Us podcast, I sat down with Warren Campbell,

Grammy-winning producer, pastor, and music executive to talk about the beats, the business, and the legacy behind some of the biggest names in gospel, R&B, and hip-hop. Professionally, I started at Death World Records. From Mary Mary to Jennifer Hudson, we get into the soul of the music and the purpose that drives it. Listen to Culture Raises Us on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. Welcome to Pretty Private with Ebeney, the podcast where silence is broken and stories are set free. I'm Ebeney, and every Tuesday I'll be sharing all new anonymous stories that would challenge your perceptions and give you new insight on the people around you. Every Tuesday, make sure you listen to Pretty Private from the Black Effect Podcast Network.

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