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Part 3! How did Einstein develop General Relativity? What does it mean for different kinds of masses to be equivalent? How does gravity do what it does? Why is curvature so important in understanding gravity? I discuss these questions and more in today’s Ask a Spaceman!
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I swear I'm gonna finish in this episode. No matter how long it takes, even if this episode is three and a half hours long, I'm going the distance because this is getting ridiculous. Part three, by the way, if you if you're just now joining the adventures, this is part three of a planned two part series, but turned into a three part series on general relativity, our modern conception of general relativity. And I know and I'm about to repeat myself again. I've repeated myself a lot in these past two episodes, and I'm taking it slow.
I'm really digging into the juicy details. I'm taking the roundabouts. I'm taking the I'm taking the backcountry roads in this. I'm not taking the freeway. No.
I pulled off a long time ago, and I'm taking the little unmarked, barely two lane road back through the backwoods to this journey because it's such a rich, juicy topic. It's such a complex topic, and general relativity is so easy to say, but it's another thing completely to really understand. And so I want us to just soak in this. I want us to take a bath in Einstein's brain and just let it soak into our skin so that we can get a hint of the understanding of this magnificent, beautiful contraption that we use to understand gravity in our universe. And it's been an incredible journey, hasn't it?
If you haven't listened to parts one and two, I strongly suggest you go and do that right now. It it was a torturous, twisting, confused path to go from the raw ideas that Einstein had to a full theory of relativity and to catch us up. And even if you've already listened, just listened to the past two, it's always good to have a refresher when it comes to the mind of Einstein. So that full theory of general relativity, that general relativity cake has three ingredients. Ingredient number one, the equivalence of free fall that locally, in any tiny patch of the universe wherever you are, in your tiny tiny little patch right around you, special relativity holds.
Space time, therefore, is the ultimate stage. The playground of our universe is space time, the four dimensional structure. We need that and it looks like because of the equivalence of free fall, it looks like gravity is going to be connected to space time somehow. The second ingredient is the equivalence of acceleration. That is not just gravity that generates acceleration, but acceleration generates gravity.
These two things are identical. These two things are the exact same thing. Acceleration and gravity, they are together. They are two sides of the same coin. And then the last ingredient is somehow weird geometries have to be involved, and that's because some accelerations, like a spinning merry-go-round, lead to what we call non Euclidean geometries, geometries of curved spaces.
So because of the equivalence of acceleration, in this that some accelerations lead to non Euclidean geometries, you get the connection that there's a relationship between acceleration slash gravity and non Euclidean geometry. And then you ask, well, non Euclidean geometry of what? What's the thing being curved? There's the first ingredient, the equivalence of free fall, telling you that gravity is related to space time. And somehow space time has to be involved.
And so you're able to thread all these together, and we finally get the big result. We finally get the one statement that defines what our universe is all about, and that is Patreon coming in early into the episode. Thank you so much for your contributions to keep this show and all my education outreach efforts going. Go to patreon.com/pmsutter to see how you can contribute. Just a couple bucks a month is all it takes.
And as a bonus, I'm tossing in a brief bump for a new AstroTurf. March of twenty nineteen, Frasier Cain and I are going to Costa Rica. Beautiful, gorgeous tropical, and full of some brilliant dark skies. You will be surprised. It's an adventure on both land and in the sky.
Go to astrotours.co/costarica to sign up now. Now we're really here. Now we're at the big result where we have Einstein's relativity. We have all the conceptual ideas that go into it, but physics isn't about ideas. It's about mathematics.
And the mathematics of general relativity, which is this is what Einstein took, like, nearly a decade to do, was to actually develop and motivate the mathematics and to prove it to be correct. And the mathematics are kind of a beast, and kind of as in exceedingly a beast. It's a beastly beast. It's a set of 10. 10 equations all connected together that all rely on each other.
On one side of the equations, you have to have all the ways that matter and energy can just sit there or move or twist or flex. All the mathematics have to capture the ways that matter can situate itself. And on the other side of the equations, you have all the ways that space time can react to the behavior of all that matter. And so there's a lot of ways that space time can bend and flex and warp and ripple, and that takes a lot of junk to put in to describe. It's not an easy thing.
And it's because the arrangement of matter and energy is so subtle and so complicated, you need a complicated set of equations to describe it all. This is why relativity is so much more complicated than Newton's equations for gravity, because now general relativity automatically bakes in all those subtleties that you need to add to Newton's equations to to get the full picture. How the curvature is generated from a particular arrangement of matter and energy is very complex, so you have to solve these 10 coupled nonlinear, in the jargon, differential equations, which is just nuts. It's so complicated that when someone does find a solution, we name the solution after them, and the person that finds that solution becomes famous in their own right. There's only, like, I don't know if I have the number right in front of me, but there's something like fifteen, twenty known full solutions to general relativity where you can actually write down the answer to a particular scenario.
All the rest, what we know from general relativity, has to take place in simulation on a computer. That's how nuts we're talking. So how the curvature is generated is very complex, but how the curvature influences further motion is super duper easy. It's just like one equation. And it's easy to stay tuned.
Just everybody is in free fall, wanting to do their own thing, not having a care in the world. They're trying to follow nice straight paths, but the ground underneath them or the space time underneath them is forcing them to change their minds. And another way to visualize this is imagine that beam of light racing through the vacuum of space, but now you you don't just have empty space. You can imagine space time kinda sitting, permeating space underneath that beam of light. And if space time itself is bent, well, the beam of light wants to go in a straight line, but it's gonna follow the dips in the valleys, in the hills, and it's gonna wiggle left and right because it has no other choice because that's exactly what space time is telling it to do.
So what goes for light goes for all other kinds of motion. Despite it being super complex and subtle and kind of unwieldy, it is a fully self consistent theory of gravity. It does describe gravity in our universe, and it agrees with special relativity in those local patches. You know, by construction, Einstein knew that wherever you are in your tiny, tiny, little patch, gravity has to disappear and you're back to your normal flat space time that you know and love in special relativity, and it has to agree with Newton in the low gravity, the weak gravity environment, like, say, the surface of the Earth, then you better get good old Newton. Otherwise, you're not gonna be able to predict, I don't know, like projectile motion.
And if you can't get projectile motion right, then what kind of theory of gravity do you think you are? Not a good one. Despite its complexity, despite its subtlety, general relativity is easy to summarize. What is gravity? Gravity is the geometry of space time.
There it is. It is the distortion. So I'll say it again because it's it's one of these deliciously simple and deceptively simple statements that we've come across in this series where just a few short words, when you unpack them, you realize how powerful they are, but it's so easy to say that you could put it on a t shirt. So I'll say it again. Gravity?
What is gravity? You ask, what is gravity? Someone asks you, hey. Hey. Hey.
What's gravity? You can say, gravity is the geometry of space time. That's it. Gravity is the geometry of space time. It is the geometry of space time.
The geometry of space time is gravity. Einstein's approach to this relatively simple statement was twisting and winding. One could say it was non Euclidean, but it was based on solid hunches and brilliant thought experiments. Right? And it but it's kinda hard for us to follow because we're just mere mortals.
It's hard for us to see how Einstein went from those very simple thought experiments to 10 coupled nonlinear differential equations that describe the curvature of space time and matters relationship to it. Like, that that that's that's kind of a big jump. So here's another path to getting general relativity, and, thankfully this path is shorter because we already laid a lot of the groundwork in following Einstein's path. So it's been, you know, a hundred years since Einstein walked that road. We've had some practice in pedagogy in being able to describe and develop and prove general relativity from its basic assumptions.
And so so we've got we've got some tricks up up our sleeves. So let's let's run a thought experiment. Let's say you're floating high above the Earth, you're an astronaut or whatever, and you brought a box of junk with you in its little pieces. You know, it it's it's bolts. It's some length.
It's, you know, some some chewing gum left over, maybe the wrapper is in there too. You know, like, you just took your junk drawer up into space, and then you just dump it out. You just shake it out, and then you see what happens. And this is a thought experiment, so we don't have to worry about destroying any satellites or anything like that, but we're just gonna follow these, what we call test particles. We're gonna see their motion.
We want to understand gravity. We know that these objects, these bits and pieces will be pulled down to the earth eventually. They'll go into orbit, etcetera, etcetera. So we can use their paths to trace out gravity. Now normally, when we're using test particles to trace the effects of a force, it's usually really complicated because the relationship between the force that we're trying to study and the motion of the object itself depends on lots of stuff like its electric charge or its velocity or etcetera, you know, whatever.
But with gravity, it's different. Gravity, we have a shortcut. Gravity, we have the equivalence principle, so all paths, I wanna make this clear, however path you take up the mountain to get to general relativity, your base camp is always going to be the equivalence principle. That is the fundamental starting assumption that gets you to general relativity. The equivalence principle appears to be one of the most fundamental concepts in our universe.
It's fundamental because it leads to something bigger and better, in this case, the full theory of general relativity. But by itself, it's already a powerful statement. And the equivalence principle here means that we can use the particles, these test particles, to trace out gravity without worrying about their individual masses. You can have a big chunk, a little chunk, a medium chunk, whatever it is, and because of the equivalence principle, because their inertial mass is equal, their gravitational masses, you know they will 100% faithfully trace out the effects of the force of gravity, and you don't have to worry about anything else. You don't need to know all the masses of the particles in advance.
You don't need to care about their electric charge. You don't need to care about their shape, and on and on and on. You can just dump them and see what happens. And some interesting things start to happen. Let's say some of the junk just starts out randomly, perfectly lined up horizontally, like in a row, left to right, and then they'll they gently fall to Earth nice and slow.
Now they'll fall straight down. Right? But they'll fall straight down in a little tiny bit inwards because each individual particle is really falling towards the center of the Earth. It's not falling to the surface, it's falling to the center. From high up, it doesn't look like much a big difference, but if you follow them long enough and you're very very good at observing junk falling to the Earth, you'll notice that over time, those bits of junk will slowly start to come together because they're each following a straight line, but that straight line for each particle points inwards towards the center of the Earth.
So eventually, they'll intersect. Okay. File that away. Let's look at another picture. Some pieces of junk, just randomly, will be perfectly lined up vertically, top to bottom, evenly spaced out.
And then as they fall, we are watching them fall to Earth, bye bye little bits of junk. The bits that are closest to the Earth get a little bit stronger acceleration because they're a little bit closer. Gravity is a little bit stronger. So they'll start to pull away from the pack. And then the ones that are furthest from the Earth have a little bit weaker gravity because they're a little bit further away.
They'll start to drift behind. So slowly over time, these four or these particles that were close together will now start to spread apart. So what is this telling us? What is this example and the other example telling us? It's telling us that paths that start out parallel.
You know, the four particles in a horizontal row start out perfectly parallel, the four particles in a vertical row start out perfectly lined up, but their paths change. For the horizontal particles, their paths converge to a point. And for the vertical particles, their paths diverge. They spread apart. What is what is this saying?
It's saying that because of the equivalence principle, we can follow these test particles, and the test particles trace out the effects of gravity, and paths that start out parallel end up diverging or converging. That's telling us something about geometry. That's telling us that geometry is the way to describe general relativity. That geometry, the language of geometry, is what we need to speak the words to write the book on gravity. The book of gravity is written in geometrical characters, if you will.
We need geometry. We need the geometry of curved surfaces, of curved spaces, of curved space times if we want to describe gravity. And then you do a bunch of math, and you get your own relativity. Maybe I should have just started with that. But there it is.
But there it is. There is the connection. You start with the equivalence principle. You watch how test masses behave. You end up with geometry, and you try to find the mathematical apparatus that it that gives you that entire picture.
Boom. That mathematical apparatus is what we call general relativity. And there's one major thing that this new thought experiment illustrates. It's not just curvature in space, and I really, really, really wanna emphasize that. We need to talk about the curvature of space time, the unified four dimensional framework of our universe.
Otherwise, we're lost. We're not really talking about general relativity. You need to include the dimension of time in the full description. And I'm sure you've all seen the typical science center demo or classroom demo or video demo or an image or a picture that says this is what general relativity looks like, and you see, like, a a rubber sheet or, you know, just a flexible, bendy sheet like a trampoline or something. I've even used this analogy.
Alright? So sue me. And it's stretched out over some supports, and then someone puts, like, a bowling ball or something in the middle, and it stretches down, and you see, wow, that that's a big well. And then you you can, like, start rolling, like, little ping pong balls or something smaller around that sheet, and you see how initially they go straight and then their paths get deflected because of the curvature in that sheet, and you're like, wow, that's pretty cool. That's general relativity.
But then you start asking questions. Questions like, okay, if that sheet is being bent down to give it its curvature, where is our space time being bent down into to give us our curvature? And is space time really a thing, like a fabric that general that that this demo suggests that it's something I could reach out and grab and touch and then I can I can stretch it and squeeze it and ball it up and I can use that to deflect trajectories of incoming ping pong balls? There are lots of questions that you get from this demo, so I want you to not think about the demo too much. I want you to take a break from the demo.
Sometimes demos are very, very useful for getting thoughts started and getting you thinking in the right direction, so I don't really have anything against the demo per se. But that demo is for kindergartners. Not physical kindergartners, but kindergartners when it comes to understanding general relativity, and you know you are well past kindergarten. It's time for middle school general relativity. We're going to a higher level where the demo itself is gonna cause more harm for you than good.
So stop thinking about the demo. When you think of general relativity, I don't want you to think about that demo anymore. I don't want you to think about stretch rubber sheets or trampolines or balls, have, you know, bowling balls placed in the middle and then ping pong ball. Just just knock it off. I want you to think of something else.
I want you abstract away from this, and I want you to think about the mathematics because physics is a mathematical description of reality, so here we are. The curvature in space time is intrinsic. It's built in. Our space time doesn't curve into anything else like the way a rubber sheet curves into or curves down. We don't have that.
We don't need that. The mathematics doesn't need it. That sheet is two dimensional, and it's curving down into a third dimension so that you could see the curvature in it. That's called extrinsic curvature, external curvature. We don't need that.
Our four dimensional space time doesn't need to be embedded into a five dimensional structure to give it curvature. The curvature is built in. Curvature is discovered and described by following the paths of parallel lines. Just shoot some lasers around. The lasers will tell you what the curvature is.
There doesn't need to be a down. And the curvature is four dimensions. It is a four dimensional curvature. Not only is space statically curved like the demo would suggest, but the dimension of time is curved as well. And this is how general relativity curves the dimension of time.
It does it by and I'm gonna toss out a phrase here, and then I'll I'll come I'll actually explain the phrase. It tilts the light cones. It tilts the light cones. What the heck does that mean? Well, okay.
I haven't spoken about light cones yet. I had an opportunity to when we talked about special relativity because that's where this concept comes from. It probably needs its whole entire episode to get dedicated just to that, so feel free to ask, what the heck is a light cone? A light cone, it's it's the set of possible places you can be in your future is one way to describe. There's a lot of different ways to describe it.
Here's an analogy. You know, you know those doggy cones that they put around their their collars, their necks when they're not supposed to, like, scratch or bite on on some wound or something? I want you to imagine that every particle, everything, every being in the universe, whatever it is, has a a doggy cone attached to it. And these doggy cones, if you can it it limits your view. Right?
Like, you can only see basically right in front of you, maybe a little bit off to your sides. And if it's in your field of view, then you can go there. So if your your doggy cone is pointed to a particular star or a particular restaurant or fire hydrant, I don't know, then you can go there. You see, I'm like, okay. I'm gonna head over there.
I can be there in my future. But if it's outside of your doggy cone, if it's outside of your field of vision, then you can't ever go there in your future. It it's it's it's too far away from you, so to speak. And, really, this cone exists in four dimensions of relativity, but I want us to use this example just to just to get a feel for it. And I'll do a whole other episode digging in if you want.
The doggy cone sets where you can be in your future, the possible future trajectories of based on where you are now, and it's limited by the speed of light. That sets the width of your cone as the speed of light. And what gravity does is it tilts the light cones. It alters what your future trajectories can be. It opens up some and it closes some others.
So if you're a beam of light racing by through space, you've got a little doggy cone attached to you, and you have a limited range. You have a certain amount you can look. You can say, okay. I can go there in the future if I want. I can go there in the future if I want.
And then you pass by the sun. The sun tilts your light cone towards the sun. That's what gravity does, and it changes what your future possible paths could be. So there might have been a star way off on the right or like a nebula or a really interesting object over there, and you're like, you know what? Someday I'd like to go there.
You know, when I retire, I'm gonna visit that place. And then you go by the sun and it swings you to the left a little and it passes outside of your light cone, you're never gonna go there. Sorry. Unless you swing by another star and it puts you back in your light cone. It's the combination, the full picture of general relativity is the combination of the static bending of space like you think of in the museum demo that you're not supposed to think of anymore.
That's part of the effect. And the other part of the effect is this dynamical shifting, redirecting, repointing, realigning of light cones, of the possible future trajectories. It's both, and you have to have both. Einstein, what tripped him up for two years was he didn't think that there would be the static curvature of space. He thought it would only affect the light cones, and he kept running into trouble because when he baked that into the equations, he couldn't he couldn't get the right answer.
He couldn't bring it back to Newton's laws in the low gravity environment. So he knew he was off, but he didn't know where because he was really resistant to this idea that space would be statically bent around a massive object. Once he let that go, he was able to get the full theory and able to make predictions and match up to Newton's gravity and low gravity. The the whole deal. The whole deal.
So interesting sidebar there that even that conception tripped up Einstein for a couple years. I told you way at the beginning, like, two months ago that there'd be three paths to general relativity. I've done one, Einstein's path, which took up most of the time here. I did briefly another route, you know, tracing out these test particles, orbiting around the earth, knowing the equivalence principle. There's a third way, and I'll just breathe through this one because I don't I don't wanna belabor the point.
But the path number three is like the pure mathematics way. And in fact, this is the way that's used in general relativity graduate classes to actually prove it that you start in mathematics. You can actually prove stuff. You start from basic assumptions, and then you lead that to conclusions, and you know the conclusions are absolutely true given your assumptions. None of this wiggle room fuzzy, oh, imagine a merry-go-round spinning close to the speed of light blah blah blah.
That's for the physicists. Alright? And that's for people like Einstein to to be crafty and and clever, but physics is about math and math is about proofs. You actually have to demonstrate. You have to show your work.
And the show, the work part was developed by a mathematician named David Hilbert, who was a super genius in his own right, and he worked on all sorts of problems. I don't even have close to enough time to give him justice. If you'd like to hear about David Hilbert, let me know. And he heard what Einstein was up to with his general relativity gravity game, and he decided to get in on it. He's like, hey.
That seems like a fun problem to crack. I got free afternoon. I'll give it a shot. And then Einstein learned that Hilbert was interested, and he started sweating because when you have the ultimate super uber genius mathematician of your time interested in a problem that you're working on, and, you know, you've been working on it for half a decade and you'd like to get some credit, but there's a solid chance he's gonna outsmart you because, you know, he's David Hilbert, it lights a fire under you. I'm just saying, it lights a fire under you even if you're Einstein.
You suddenly have a brand new motivation that you didn't have before to actually get this done. And there was an absolute race for two years between 1915 and 1917. Einstein knew that he couldn't beat David Hilbert at the math game. Just David Hilbert's raw mathematical ability outclassed Einstein's, outclassed, like, all of humanity at the time and probably even to the present day. But fortunately for Einstein, Hilbert wasn't a physicist.
Phil Hilbert wasn't interested or concerned with matching the equations to nature or trying to reproduce Newton's laws or trying to reconnect with special relativity and certain limits or being able to make testable predictions from the mathematics. Hilbert was just interested from a very abstract, very high level mathematical game. So the big e did have a leg up when it came to intuition for the usefulness of results to guide his work and his development. They were in constant communication. They were sending notes to each other.
They they published nearly simultaneously, I think, just two or three weeks apart. Hilbert did acknowledge that Einstein beat him to the punch, but Hilbert's derivation, because it's on pure mathematical grounds, is the one that's used today to prove that general relativity are the correct set of equations given the assumptions of things like the equivalence principle. So it's not just hand wavy arguments. It's real solid math, and there's basically no easy way to describe it. It's based on something called the principle of least action, which is perhaps the most important concept in all of physics, which again deserves its own episode.
If you'd like to learn about the principle of least action, you know to who to call. Not Neil deGrasse Tyson. Me. Just call me. Just I mean, yeah.
He'll tell you about it, but but call me, and I'll do a show on it. If you've ever wondered how we get things like conservation of momentum, it's via the principle of least action. They're derived from that principle. It is a cornerstone thing in the mathematics of, like, all of physics, and I'm not even exaggerating. The principle of least action, if you've ever heard of the path of least resistance, it's that but applied to much harder problems.
In this case, you start with any old way of describing curvature. If you just say, okay. We're gonna assume that gravity is described by curvature, and there's any old combination of matter, and then you try to connect the two, like, okay. I know matter is related to curvature, but I don't know exactly how. Like, what are the mathematical juicy bits that actually make that connection possible?
You run through this principle of least action and out pops the equations of general relativity. It's like the principle of least action is like a factory that makes physical theories. And in this case, you fed it some certain raw ingredients like the equivalence principle and the idea of curvature, and out pops from this wonderful machine the actual math of general relativity. I know I'm not doing this path justice at all, but I want you to know that there's some solid math derivations of general relativity out there. We're not just hand hand waving all the time.
So Einstein in 1917 finally developed these equations. It was a set of equations that seemed to have everything right, but seemed to have everything right is a far cry from actually having everything right. So we we actually need to test it. He needed to test it. We needed to test it.
Everyone needed to test it. You actually have to test this stuff because, you know, physics. The first thing Einstein noticed about his equations and that really convinced him that he was on to something special was the orbit of Mercury. There's something funny about the orbit of Mercury. It's an ellipse around the sun, and so sometimes Mercury is closer to the sun, sometimes it's farther.
And the point in space where Mercury is farthest from the sun isn't always the same place. Like, if if you mark it out like, okay. Mercury is farthest from the sun, and then you put, like, a little beacon or a little marker or a little flag, the next orbit Mercury won't be at that exact location. It'll drift a little. This is called precession of the orbit of Mercury, and it drifts very, very, very slow.
I mean, it's ridiculously slow. And most of that is due to very, very slight gravitational tugs from the other planets, mostly from Jupiter, but all the others get to participate. And when people first noticed that the orbit of Mercury was a little bit off, they started adding up all the gravitational effects of all the planets, were able to explain, like, 95 of it. But there's still just a little a little fuzz off. Like, if you took Newton's equations and applied it to the solar system, you didn't quite get Mercury's orbit, which is weird.
You know, by the late eighteen hundreds, early '19 hundreds, most people just thought, close enough. Who cares? We're just we're missing something. You know, maybe we just forgot to carry a two in the math, or there's something in the solar system, something wiggly we don't really understand, but it's not that big of a deal. And then Einstein came around and said, oh, by the way, I have a new theory of gravity that improves on Newton's laws, and I am actually able to predict precisely the orbital precession of Mercury.
And everyone's like, oh, okay. That's cool. Like, you know, a problem that you're swept under a rug because it's been a problem for, you know, a hundred fifty, two hundred years or whatever, and everyone just assumed would have some boring explanation turns out to be the first entry point into a brand new way of thinking about gravity, yeah, it got people's attention. That's what be that's what Einstein he's like, hey. Look.
I did something cool. And he was pretty proud of himself, and he told everyone that everyone's like, yeah. Okay. Maybe you have a point, Einstein. But we need to do more tests.
And the second test came with the Eddington expedition led by, you know, sir Arthur Eddington. He got to name his own expedition. And this was to look at a total solar eclipse, and not just because they're awesome, but because Einstein's theory predicted that the path of light would get bent on ground gravitating objects like the sun. Newton's theory predicts this too, but only by about half as much as Einstein's general relativity. And this is happening all the time, but usually the sun, you may have noticed, is kind of bright, and it's hard to look at stars very close to the edge of the sun where this effect might be most measurable.
So that's why Eddington sought out a solar eclipse so that the sun looks dark for a minute, and you can actually get some good work done. You can look at distant stars and see if their positions are different than what you know they are because their light has been bent around the edge of the sun. He did the observation. He did the measurement. It was super tough.
Good job, Arthur Eddington, for doing a good job, and it was exactly what Einstein predicted. Those two bits, Mercury and the Eddington expedition, really sold the scientific community on Einstein's work. Like, you gotta admit, he's he he has a good point when no one else is able to describe this bending of light except for Einstein, and he predicted it before it was observed. That's like, ah, that's like perfect science physics happening right there. More tests would come later like the redshift of light.
A beam of light traveling from the surface of the Earth to the upper atmosphere actually redshifts just a little bit. That's prediction of Einstein as it was demonstrated in the fifties. Even most recently, Einstein predicted the existence of gravitational waves. We see gravitational waves. We see it's like every time we try to test general relativity and I can do a whole other episode if you want on testing general relativity in the modern era.
You know, not talking about stuff from a hundred years ago. Happy to do an episode on that. Just ask. As far as we can tell, general relativity is a complete description of gravity in our universe, but we know it's incomplete. We know there are flaws.
We call those flaws singularities. They appear in the centers of black holes. They appear in the earliest moments of the universe in the big bang. We know it's not a quantum theory. We know it's not a fully accurate picture of the way gravity works in our universe, but it's so dang good.
It's passed every single test with flying colors. So despite it being a hundred years old, we haven't figured out how to move past it. That is a separate episode too. All this leads to the final question, which I think is maybe the most important question here. How if if if gravity is the curvature of space time, how does matter and energy actually bend space time?
Like, how's it how's it do it? Does it grab it? You know, does it just breathe on? Does does it blow on it? Like, what is the mechanism for matter and energy to bend space time?
If gravity is curvature, how is curvature, you know, accomplished? And I think here we need to step away from the kindergarten model. And, indeed, I think we need to step away from any visualization at all. I there's no picture that I can paint for you that shows you how matter and energy bend space time. That's because it's mathematical relationship.
The math provides the connection. The equations provide the connection. The presence of matter and energy, this is exactly what general relativity teaches us, is equal to the curvature of space time, and the curvature of space time is equal to gravity. I have another word of the day. The first episode, the word of the day was equivalence.
The second episode in this series, the word of the day was non Euclidean. In today's word of the day is geometrodynamics. Geometrodynamics. Not the car. Not the geometr.
Just geometrodynamics. The dynamics of geometry. Straight lines don't stay straight in four dimensional space time. That is our experience of gravity. The fact that straight lines don't stay straight in four dimensions is our experience of gravity.
The dynamics of geometry, geometry dynamics, geometric dynamics is gravity. We have when it comes to gravity, we have a set of observed phenomena. We identify quantities like mass. We see how it reacts when placed near other masses. We note that everything falls equally, that there's this quantity we call acceleration, etcetera, etcetera.
We try our best to summarize these effects in a way that we can make further predictions AKA a physical theory. We use the language of curved space time to explain the observed effects of gravity and to make predictions. I will say, and this is more of a philosophical stance, that it's a little bit dangerous to say that's what gravity is. Gravity is the set of observed phenomena. We use the language of curvature and acceleration and geometry to describe that phenomena.
Gravity just is. It's a thing we see in our universe. General relativity is our best attempt to model it, to explain it, to understand it, to be able to make predictions, which is all physics is. It's a set of models that describe the universe that we observe. In the picture of general relativity, gravity is the curvature of space time, geometrodynamics.
Outside of general relativity, because we know general relativity is incomplete, All physical models and theories are incomplete to some level. Gravity just is gravity. Thank you so much to all the amazing questions that led to this episode. Andrew p, Joyce s at Luft eight, Ben w, Colin e, Christopher f, Mariah a, Brett k, Brian guy, the fly guy, at Mark Greib, Kenneth l Ellison k, and at at Shrennick Shaw. So many good questions about gravity.
I hope I generated a lot more because this is such a rich, deep, interesting topic. There were lots of invitations in the past few episodes to dig deeper. Feel free to email me. Even if you think someone else has emailed me already or contacted me, askaspaceman@gmail.com. Go to ask a spaceman dot com.
You can find me on youtube.com/paulmsudder. You can find me on social media at paul matt sudder on all the channels. Even if you think someone's already asked, ask anyway because I would like to give you credit for thinking of a cool question. And, of course, thank you to my top Patreon contributors this month, Robert r, Justin g, Kevin o, Justin r, Chrissy, and Helgeb. It's you folks and all the fine contributors on patreon.com/pmcenter that keep this show going.
I greatly appreciate. You are enabling science communication as best as I can make it, and I can't give you enough thanks. Don't forget, there is a brand new Astro tour to Costa Rica, Astrotours Dot Co Slash Costa Rica. Me, Fraser Cain, awesome jungles, beautiful dark skies, what more can I say? And, hey, go to spacechariotersshow.com.
If you'd like to follow-up on any of these topics on the radio show, feel free. We can do that too. Have a conversation on the air. That's spaceradioshow.com. Thank you so much, and I will see you next time for more complete knowledge of time and space.