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Part 1! 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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EPISODE TRANSCRIPTION (AUTO-GENERATED)
So let's say you got a new job with, I don't know, let's call it evil genius corp for purposes of illustration. And it's your first day and you're so excited, you're super nervous, and you have a routine. Like, you you have exactly the same routine every single morning. The alarm goes off, you hit it, the alarm goes off again, you hit it again, then finally you get up, you take a shower, you brush your teeth, you you dress yourself, you get your coffee going, you eat breakfast, you you open up the door, you get in the car and you drive off, you do whatever. And your first day, totally normal.
You know, you got your excess keys. You got your computer. You put a picture up in your cubicle. You're happy. You finally have a job, and it doesn't matter if it's with Evil Genius Corp.
And then the next day rolls around. And the exact same routine, you get out of bed, you take a shower, you brush your teeth, you make your cup of coffee, you're a little bit nervous, you spill the coffee and it splashes down on the floor and you waste a little bit of time having to clean it up. And then you make a fresh pot of coffee and then you eat some breakfast And then you open up the door, and instead of your front yard that you're used to, it's the pure vacuum of space. It turns out your room, your entire house has been attached to an evil genius corp rocket that is currently blasting its way through the furthest most distances of the solar system. What's going on?
Let's play another little mind game. Let's say you're a construction worker working on a high rise building, thirty, fifty, a hundred stories. I don't know how tall skyscrapers get. Very tall. The tallest skyscraper in your world, and you're at the top floor, and you're, I don't know, welding or plumbing.
I have something to do with construction. And you're doing your normal thing. You've been working at this for years. The height doesn't bother you. It doesn't even nauseate you.
It's just totally normal routine. But in one very unlucky moment, something distracts you, A butterfly floats past you and you wonder, how the heck did a butterfly get this high? And in that moment, you trip and you fall and you have a few seconds until you become a puddle of goo on the ground. But in those few seconds, you notice something funny. You notice something funny.
Except for air resistance, you feel totally weightless. In fact, your your lunchbox that you carried up to the topmost floor that you were working on in the skyscraper was falling with you, And you can reach over. Just reach out your hand and grab your lunchbox and open it up and eat a snack. And it floats around, and you remember seeing pictures and videos of astronauts on the space station and their how they float around and they can juggle and and they have, you know, blobs of water that that, you know, blibble and blobble and just sort of all sorts of cool stuff and behaves like water on the Earth doesn't behave, and that's exactly what's all the stuff around you is behaving like. It feels like there's no gravity at all even though you're falling.
Let's look at another example. Let's say let's say you're in a car, just riding along in a car as a passenger, no big deal at all, nothing special. But out of nowhere, the driver of the car swerves left hard level. It just takes that wheel and jams on it like there's something wrong. And you feel pressed smack up against the door of the car next to you like you're glued up against it.
You know, you remember your physics lessons that this force you're feeling, this, centrifugal force is what we call a fictitious force. It's not really there. It's not like there's a hand reaching out from the ether and grabbing you and yanking you by the collar and pushing. No. You would just prefer to be going in a straight line, but because the car is turning, the car keeps getting in your way.
And so it's really the electric forces pressing up against you between the atoms and molecules of your body and the atoms and molecules of the car door that are rubbing up against each other and providing that force. What does it mean for a force to be fictitious if it's something real that you can feel? Last example. In Newton's picture of gravity, gravity is like a set of invisible strings threading the cosmos, connecting massive object to massive object. It connects me to the Earth, an apple to the Earth, the Earth to the sun, the moon to the Earth, the Jupiter to its moons, Jupiter to the sun, all these little strands.
This picture of a set of invisible threads was upgraded over the centuries, especially the ninth cent nineteenth century by a couple French dudes, Laplace and Poisson, who had evolved this picture of a bunch of invisible strands into what we call a field picture, where there is something called the gravitational field, which you you can imagine. You can think of electric and magnetic fields, which if I have an electric charge or a magnetic or a flowing electric charge, I create electric and magnetic fields, which are basically instructions for how other electric and magnetic objects are to behave in the vicinity of the original charge. It's a set of instructions that are written down all across the universe. It's the field. Well, there's a gravitational field in this picture where if I have a massive object like the sun or me or an apple or whatever, it sets up a gravitational field, which are a set of instructions throughout the universe that tell other objects how to behave, how to respond to that object's gravity.
But what if what if the sun were to just disappear or move or do something quite unsunlike? How would the other objects in the solar system react or behave if the sun disappeared or the sun shifted? Well, in this picture of Newton, Laplace, and Poisson, the field, the gravitational field that they set up, that they generate would change instantaneously. And a planet like the Earth, if the sun were to disappear, the planet like the Earth would be like that invisible thread between the sun and the Earth were to go snip, and it would just go flying off in a straight direction. Or in the language of Laplace and Poisson, the field would disappear, and there'd be no reason for the Earth to hang around anymore, and so off it would go.
But that would happen instantaneously, but we know that things can't happen instantaneously in our universe. Things are limited to the speed of light. How can gravity affect things faster than the speed of light? It's a good question. It's a good question.
These four scenarios get us thinking about the nature of gravity. And what's going on? You might have guessed this episode is about gravity because, you know, that's the title of the episode. And, of course, when we're talking about gravity, we're talking about general relativity. And I know for sure, without a doubt, I've just literally started recording this episode.
It's going to be two and possibly three episodes in this series. I I know it if I mean, it's general relativity, folks. This is not gonna be a twenty five, thirty five minute topic. This is a beast. Why is it a beast?
Why is general relativity such a big deal? Why can't I just talk about it in one episode? Because gravity is about motion. Think of a dance or a race or a football game or satellites in orbit. Gravity and motion are intimately connected in our everyday experience, and motion is exceedingly subtle.
Think of all the different ways you can move. Think of all the different ways you can arrange matter and energy in a scenario or in the entire universe. It's kind of complicated. Gravity must be equally complicated if we are to capture all the subtlety, all the nuance, all the hidden little corners of motion. And I could, if I wanted to, in this episode, just give a pithy summary of general relativity.
I'm sure you've heard before. You know, matter tells space time how to bend and space time tells matter how to move there. Book it done. Check mark. That is everything you need to know about gravity.
But you folks have some more detailed questions. Questions like Andrew p on email. How does general relativity work? Joyce s email. How does general relativity work?
Same exact question. At looft eight on Twitter. How does the bending of space work? Ben w via email. If general relativity produces solutions that don't exist, doesn't that make the whole equations wrong?
Colony on email. How does general relativity work? Christopher f. Email. How does general relativity work?
Are you sensing a theme here? Maria a email. Could you explain general relativity? Brett k email. What is gravity?
YouTube, Bry guy, the fly guy, said in all capital letters talk about g r. That's not technically a question, but I'll take it at Margrebe on Twitter. What is gravity? Kenneth l on YouTube. Is gravity really a force?
Allison k on email. What is gravity, and how does it work in the universe? And at Shrenik Shah on Twitter, how does gravity do what it does? Based on your questions, you don't just want the pithy summary. That is the summary you state after you've understood the guts, after you've gone in there, after you've been there, man.
Then at the other side, once you have this nirvana like understanding of the workings of gravity, then you go around saying, well, yes, of course. Matter tells space time how to bend and space time tells matter how to move. It's it's easy. You'll get to say that with an equal level of confidence and eyebrow lifting as I just did after this series, but we have to get in there. We have to go into the jungle.
We have to go into the weeds. We have to play this game of really understanding general relativity, which is going to be tough and which is why it's gonna be two or three episodes. Gravity, general relativity is one of these amazing things that is so easy to say in summary, but the summary raises so many questions, the questions you raised. Okay. Matter tells space time how to bend.
How does that work? The bending of space time tells matter how to move. How does that work? What do you how is this connection actually made? How are we to make sense of this connection?
So I doubt these episodes, two, possibly three are gonna be cleanly or logically separate. I have a whole SCAD of notes. I don't know what unit of scale a SCAD is, but it's vaguely a lot. I'm gonna start talking, and when I get tired, I'm gonna call it an episode, and then we'll move on from there. And so I need you.
We're gonna take this training together, folks. This is a marathon, not a sprint through general relativity. This is a journey. This is an exploration. This is a stop and smell the gravitational roses kind of set of episodes.
So make yourself a hot cup of cocoa. Get your favorite blanket out, and let's take a peek at good old Uncle Albert's masterpiece. And it really is a masterpiece. There is when you think of, like, a great artist producing something that just shocks and wows the world that is appreciated, that resonates through centuries, this is an equal achievement. When it comes to special relativity, Einstein gave us the foundations of special relativity in nineteen o five.
You could seriously argue that if we lived in a universe with no Einstein at all, someone else would have come up with it. And in fact, other people did. Other people were working on similar kinds of problems. Other people were looking at things like Maxwell's equations and noticing some funny business in there. People were thinking about the nature of space and time in their relationship.
Mickelson and Morley had were doing experiments that were showing that the speed of light appears to be constant. People had already written down actually a lot of the mathematics. It was Einstein that came in and gave us the perspective on it, the lens that we should truly appreciate about how space and time are really connected to each other. But other people probably would have come to the same conclusions. It was right there.
It was bubbling underneath the surface. But general relativity, general relativity, nobody was thinking along these lines. Don't get me wrong. There were a lot of smart people in the world at the time, people that were perhaps as smart or even smarter than Einstein. A lot of the physicists in the world at the time were studying quantum mechanics, the mechanics, the physics of the very, very small.
It's so cool how in parallel we're developing special relativity and general relativity, which leads us to modern cosmology at the exact same time we were studying quantum mechanics in the world of the very small. A lot of physicists were really focused on that. It was very fruitful, very exciting, very, very tough problems too. And in fact, Einstein dabbled in quantum mechanics. He did some very, very important work in quantum mechanics, but he preferred working on this.
And while I can pretty confidently say that at the time, early twentieth century, there were people on the planet, at least as smart and perhaps smarter than Einstein, I can say nobody thought about these problems the same way Einstein did. And that's really what sets him apart isn't necessarily his raw intellect, but the way he used his intellect. It was his thought process, and it's so great. General relativity took a long time to develop years. And we have records of that development.
We have publications that Einstein would put out year after year after year. We can see how he put together the pieces that would lead him down the road to general relativity. We have his private notebooks where he would sketch out ideas and bounce them around and try to figure them out and and and come up with new ways. And and so we get this peek into the mind of Einstein, and it's absolutely fascinating. When I say years, it took Einstein seven years to develop general relativity.
Holy moly. I can't even concentrate on a problem for seven minutes. And he's stuck at it for seven years. And this leads me to a brief, a brief, I promise this brief, rant about how Einstein is portrayed. One is he's portrayed as this super eccentric genius that probably forgets to brush his teeth, doesn't know how to tie his shoes, wears pants on backwards, but is absolutely brilliant.
No. Einstein was actually rather dapper until later in his life. You know, he he wears he wore some he wore some nice cuts, that guy. And he he worried about everyday problems. He worried about his his relationship with his wife wives.
He worried about his taxes. He worried about his house and, you know, he wanted to live in a decent era, etcetera, etcetera, etcetera. He worried about normalcy. He was a normal human being, but he was he was very, very smart, and he could apply this intelligence in some very, very creative ways. And then that's the second aspect, the popular presentation of Einstein.
Because we look at Einstein and we look at that raw intellect and we're like, holy crap. I can never be that smart. And, you know, that's probably true. But then he has these wonderful quotes, like imagination is more important than knowledge. And so we take that and say, okay.
Okay. Yeah. He's smart, but he's telling me a not so smart person, possibly a dumb person, that as long as I have imagination, I can make it in life. Well, yeah. Okay.
I mean, don't get me wrong. Imagination, creative thinking, critically important critically important to solving the challenges that life faces. You're right. To having a successful life, to being happy in your life. Don't get me wrong.
Imagination, creative thinking, absolute cornerstone of of science too, of analytic, but it has to be it has to be backed up. Critical thinking has to match the creative thinking. That imagination has to match the perseverance. You can't just have creative thoughts and imagination. You need analytic stills and perseverance to see through it.
That's the potent combination that Einstein had. And Einstein liked to downplay his mathematical skills, but he was exceedingly competent at mathematics. But when especially when it comes to g r, general relativity, there are basically, like, four people in the world at the time who understood the mathematics that Einstein needed to use to develop to general relativity. So he needed a lot of help. He needed a lot of help, and and I'll talk about that later.
And when we see this story of how Einstein developed general relativity, and we're gonna follow that story, he didn't know the right answer ahead of time. He didn't know what would come out of this thinking. He didn't know when would come out of this thinking. He had brilliant insights and huge leaps of understanding, leaps of logic that no one else was capable of making. But he also had blind alleys.
He had garden paths. He had misgivings. He had doubts. For example, for a while, he was convinced that the speed of light wasn't constant. In his early developments of trying to understand general relativity, one of the consequences was that speed of light was not constant.
And everyone was like, hey, Al. I thought you just made a big deal about the speed of light being constant, and now you're saying no. Never mind. What's what's going on? And he stuck at it for a few years until he realized a further nuance that put the speed of light back in its place.
He came in 1912, '19 '13. He came this close, and I'm holding my fingers really close together, this close to general relativity. Like, seriously, like, two lines away in the derivation. But he got stuck on some concept that he thought must be true that turned out to be wrong, and, again, I'll get to this in more detail later, that prevented him from fully realizing the equations, and it took him two years to overcome it. Two years to overcome it.
So we see this these two sides where, yes, there's creative thinking and thought experiments and imagination, which is absolutely beautiful and breathtaking in its scope and its power, and it's wonderful to behold. And then we also see these amazing analytic skills and mathematics that can back it up and the perseverance to see it out of how all these thoughts that he had, which ones slowly he winnowed them out so that the right ones would rise to the top over the course of years. There's no doubt Einstein was absolutely brilliant, and he could think like no other person at the time. And in fact, so much of his journey to general relativity over the course of these seven years was guided by instinct and gut feelings, some of which turned out to be wrong. And even today, we can't fully explain how he made the jumps he made.
It's crazy. It's crazy. He would just write in his notebook or he'd he'd declare in a paper. He'd say, like, this concept, like, you know, just random concept. I think it's important.
I think this one's a good one. I think this is a key. I think this is I feel good about this idea. And he wouldn't let it go. And then, you know, insert years of hard work and out pops general relativity.
And he couldn't even fully explain it. It's like, why do I think this concept is important? How do I just do? I got feeling about this one, boss. And he'd follow through.
And some of them would turn out to be wrong, and the mathematics would tell him when he went wrong, but some of them turned out to be right, and some of them led to general relativity. So one of the reasons this isn't going to be just one episode isn't because I just spent ten, fifteen minutes talking, not even haven't even gotten to general relativity yet, is that I'm gonna give you three paths. I'm gonna give you three roads to general relativity. Each one builds the final result in a slightly different way. And for me, it's only by thinking about all three approaches simultaneously.
At the same time, do I get some sort of sense of what's going on, of of wrapping my own head around this concept of general relativity, of what the math is telling me? Path a, path number one that we're gonna take is Einstein's path. The path from nineteen o five, started thinking about general relativity about nineteen o seven, path from nineteen o seven to 1914, '19 '15 or so. The good side of that path is there are tons of brilliant thought experiments and visual metaphors, like the examples of worker falling in an office building or living inside of a rocket. Yeah.
Those were Einstein's ideas. I totally stole them from them. So I don't have to come up with any new metaphors because Einstein already thought of them, and they're the best metaphors. The bad news is it's a twisting complicated path, and his insights don't 100% translate to the final form of general relativity because he made leaps that we don't understand. So he'd say he'd start with some scenarios like this is how I'm gonna think about general relativity and out pops the math.
And we're like, wait a minute. How'd you go from that from from a to b? No. I don't know. I just did because I'm Einstein.
Pretty sure he didn't talk like that. But it gives us a way of seeing inside his mind and seeing how this final theory shapes up. Path b, the second path, is the way it's taught to physicists in science school. In undergraduate, graduate courses on general relativity, we don't trace Einstein's footsteps. Instead, we we follow some more logical footsteps.
Steps. Some now that we already know the answer, now that Einstein already gave us the answer, the the answers in the back of the book, it's we can follow a more logical orderly path that's still based on physics and still gives us general relativity, follows a different approach than Einstein took. The good news is it's nice straightforward logic. Bad, it's there's not too many metaphors. It's hard to connect to the real world.
It's a little bit mathy. It's a little bit mathy, but we're gonna go there. And then path three, the final path at the very, very end of this series, who knows how far away that is, is the way a mathematician would derive it. If you just said, mathematician, give me general relativity. How would they do it?
Well, there's a way. There's a way. Good news is it's 100% bulletproof and logical. Like, this is general relativity. This is the way to explain gravity.
Bad news is it's, you know, pure mathematics. But I'm gonna present it to you especially at the end so we have some sense of of how general relativity is actually derived in practice and how the mathematics are used to enhance and extend general relativity so that we can test it. So let's start twenty minutes in. Let's start with Einstein's path. So the state of play got us soccer clocks back to nineteen o five.
'19 o '5, special relativity is on the scene. And if you haven't listened to the what is space time special relativity episodes yet, go now. I'll wait right here. Don't worry. Welcome back.
Now that you understand special relativity, we have to see it's gonna play a major, major role in the development of general relativity. In nineteen o five, nobody really understood its implications, but everyone understood it to be a big deal. Kind of like Patreon. Patreon dot com slash p m sutter is how you support the show with your contributions. A dollar a month, $5 a month, $25 a month, hundred dollars a month.
Whatever you can contribute helps keep this show going. I greatly appreciate it. That's patreon.com/pmsudder. Anyway, special relativity. Nobody really understood its implications.
And in fact, there was a conference, a big debate, and the organizers were trying to decide the topics. And someone brought up, like, hey. What about this whole special relativity thing? And the organizer said, I don't think there's two people in the world who understand special relativity enough to actually debate it. We can't have a debate.
It would just be Einstein lecturing to us. Even Einstein himself didn't fully understand the implications of special relativity. Like, the whole interwoven space time thing that we're used to, that wasn't Einstein's work. That was his teacher's work, Herman Minkowski. Einstein's own teacher had to tell him the implicate full implications of Einstein's work.
That's how new and fresh and radical it was. But, anyway, that's a different show. But everyone understood it'd be a big deal and pretty important. One of the reasons it's super important is that it's almost like a metatheory of physics. It's a theory about theories.
Special relativity talks about motion. Again, there it is motion in all its subtle glory and the relationship between space and time. It provides a stage for all the other theories, the interactions, the forces, and the fields, and the particles to play on. So all theories must agree with special relativity because special relativity is the backdrop. Special relativity is the stage.
All the other theories are the actors. If you write a play with no actors, you don't get to go on the stage. So you have to be compatible with special relativity in order to be a viable physics theory of the universe. Electromagnetism, electromagnetic theory automatically agrees with special relativity because Maxwell accidentally wrote down a theory compatible with special relativity without even knowing it. It was Einstein who recognized it for what it was.
People had already figured out that something fishy was going on with Maxwell's equations. Einstein was the one who finally connected the dots. Quantum mechanics was being developed at the same time. Quantum mechanics and special relativity would eventually become wedded with the officiant being Paul Adrienne Maurice Dirac. So there we go.
Thermodynamics, which, by the way, thermodynamics, statistical mechanics, huge major super important branch of physics. Please feel free to ask about that, about heat and motion and work and entropy and all that good stuff. Please send me those questions. I'd love to do episodes on those topics that those topics don't get a lot of love even though they're a cornerstone of the way we understand the world. But, anyway, you can massage the equations of thermodynamics to make them work with special relativity.
No biggie. But what about gravity? What about gravity? Newton's vision of gravity, even extended and modified by people like Laplace and Poisson, doesn't fit. It doesn't fit because Newton's gravity requires absolute reference frames.
It requires a master clock ticking away in the universe, a master ruler sitting out there somewhere that we can all measure motion against. And Newton's theory says all these effects, gravitational effects happen instantaneously, which is a no go in special relativity. So how do we fix it? How do we fix Newton's gravity to bring it up to date? We need a gravity two point o for the twentieth century.
Turns out turns out this is the craziest thing. You can relatively easily make adjustments to Newtonian gravity to make it compatible with special relativity. Yeah. Yeah. Yeah.
You can just add some tweaks to the math, like, fudge this a little, tweak that, add this term over here, and boom. You can make a fully compatible gravitational theory with a few minor adjustments, some gizmos and add ons and whatsits, and make it compatible with special relativity. But these lead to some very unsavory consequences, like different masses falling at slightly different rates, Or fall times also depending on the amount of horizontal travel. You remember under Newton gravity, say, on the Earth, gravity only acts down. So dropping a ball is no different than shooting a ball or throwing a ball.
The time it takes to hit the ground is the exact same no matter the case because gravity only acts in one direction, just down. But in these modified theories, that would change. It'd be a super tiny difference, super tiny change, but it'd still be a change. And, honestly, if it weren't for Einstein, we'd probably be stuck with one of these as our quote, unquote theory of gravity, where we just have these minor modifications that'd be very, very small. And we'd say, okay.
That's it. But then over the course of decades or a century, we would get better at measuring this stuff, and we wouldn't notice any differences. So perhaps, eventually, a hundred years later, we'd be forced to conclude something like general relativity would be afoot, but there's no guarantee because there is only one Einstein. There's only one person who is able to come up with this. So we'd probably have some kludge together, hodgepodge, horrible looking Frankenstein monster of a theory to explain gravity, and it would kinda sorta work, and we wouldn't really have any idea of how to go forward.
Gee, does that sound familiar? Instead, Einstein was drawn to some quark hidden inside of Newton's work, and this is a quark of mass. We're so familiar with this concept of mass, but, really, there are two definitions. There are two definitions of the word mass. Actually, there's more more than two.
But for this discussion, they'll just be two. There's inertial mass. You know, f equals m a, force equals mass times acceleration. Good old Newton. Well, the mass that appears in that equation is the inertial mass.
How much oomph does it take to shove you around? If there's something with low mass, it doesn't take much. I can just flick it, and it'll go scooting across the table. But if something's big, like a truck, has a lot of mass and I flick it, it's not going anywhere. It needs more oomph to shove it around.
It has greater inertial mass. And then there's also gravitational mass, which is almost like gravitational charge. How much does a particular object or body respond to the presence of a gravitational field? If I have more mass, I'll respond more strongly to a gravitational field or the gravitational influence of another object. And if I don't have a lot of mass, I'll barely respond at all.
Why do different masses of balls tossed out of the tower in Pisa fall at the same rate? They have different masses, but they hit the ground at the exact same time because it just so happens that inertial mass is the exact same as gravitational mass. If I have, say, twice the mass, if I double my mass, then the gravitational force that's pulling on me is twice as strong, So I ought to fall twice as quickly, but I have twice the initial mass. It's two times harder to move me, and so it perfectly cancels out. I end up hitting the ground the exact same rate no matter my mass.
Ignoring things like drag and air resistance, okay, just so we're all clear, in an ideal situation. It is a confusing thing. It's not an intuitive thing. It's not an obvious thing. Galileo first demonstrated.
Newton put it into his theory. But, like, what's going on? Why are these two masses the same? Just why? It confounded folks for centuries.
Seriously. People would write about it, study it, be like, I honestly don't know why is inertial mass the exact same thing as gravitational mass. It has to be for Newton's theories to work, but why is it true? And it confounded Einstein too. It confused him.
It puzzled him. It worried him. It stressed him out. But this is what makes Einstein Einstein. Instead of trying to grapple with it, he embraced it.
It's like, keep your friends close, put your enemies closer. If you don't understand something, make it a fundamental cornerstone of your belief system. Now that is a handy rule to live by. Einstein was really attracted to this concept of equivalence, the equality between inertial mass and gravitational mass. He raised he elevated this equivalence, this equality to the level of a principle.
He made it a fundamental rule of the universe. And if there's nothing else you take away from these episodes, if you if we end up not getting any more making any progress on general relativity, at least remember this, that the mass that determines the movement of an object, its inertia, is exactly the mass that responds to gravity. That is Einstein's first major thought. Einstein got on the road. He said, you know this thing that's confusing everyone?
I'm just gonna declare it to be true. You don't have to worry about it anymore because it's just it's just a rule. It's just a thing. It's a part of physical existence. He's gonna elevate it to the level of a principle.
He's gonna start from there and see where it goes. And Einstein realized this in his person falling down thought experiment. It's kinda dark, but whatever. Okay. We're gonna we're just following Einstein here.
Here's how it comes into play. Here's how we get started on the road to general relativity. Let's say you're falling down, ignoring air resistance. You feel totally weightless. You feel totally weightless.
It's exactly the same as if I were floating around the middle of nowhere away from all any gravitational source at all. Right? You look at an astronaut in the space station who are in a continual state of free fall, and they're floating around as if there were no gravity at all. Einstein's gonna say, there is no gravity at all in free fall. In the little patch, the little area, the little bubble of space surrounding that astronaut or you if you're falling off a a tall tower and in those few seconds you have to contemplate, you know, the nature of general relativity.
In those few moments, you feel weightless, you are weightless, there is no gravity. In fact, if you were to examine the space time around you, it would be perfectly flat. It would be the perfectly flat space time that we all know and love from special relativity in technical terms. In technical terms, it's called an inertial frame of reference. These are the frames of reference that special relativity, this is its bread and butter.
This is exactly the stage it operates at. You are in the stage of special relativity if you're in free fall. There is no gravity. This only works because of the equivalence principle. If inertial mass were not the same as gravitational mass, then this equality would break and you would not be in free fall, and this would not hold.
But because because of the equivalence principle, because inertial mass equals gravitational mass, when you are on free fall, when you are feeling weightless, there is no gravity. You have an inertial frame of reference. Your little bubble around you, your little patch of space time looks perfectly flat. By the way, as a side note, Einstein rarely ever used concept of space time. You know, that was invented by his teacher, Minkowski.
He just preferred algebra. Random tidbit. So that's a great starting point. Inertial mass is gravitational mass. A freely falling observer experiences no gravity at all despite gravity is acting on them, but they feel no gravity.
That's a great starting point, but that doesn't get us, you know, a theory of gravity. But that's gonna have to wait till next time. Thank you so much for listening. I will continue our journey. We have just barely begun this road to general relativity.
Thank you so much to my top Patreon contributors this month, Robert r, Justin g, Kevin o, Justin r, Chris c, and Helga b for your generous contributions. If you'd like to contribute too, go to patreon.com/pmsucher. And if you can't contribute, totally understood. No big deal. Could you give a review on iTunes?
Could you tell a couple friends about the show? Keep the momentum going. Keep those questions coming. We're on a long journey for GR, but don't worry. When we get there, there are plenty more questions to explore in the universe even though general activity might take us a while.
And, hey, if you haven't checked out Astro Tours, we have so many cool trips coming up. Ethan Siegel of Starts With A Bang, he's leading the next trip to Iceland. January Of Twenty Nineteen, he's going to Iceland. Go to astrotours.co to see the trip details. We've got trips coming out like crazy for 2019.
We're going to Costa Rica. We're going to the Rockies. We're going to the South American Southwest. We're going on a cruise this year. We might go to oh my gosh.
It's so exciting. Can't wait to go on all these trips you do. That's astrotours.coc0 for all the info. Visit askaspaceman.com for all the show notes. You can also post questions there.
Send me questions, hashtag ask a spaceman on Facebook and Twitter, or just email askaspaceman@gmail.com. Check out the YouTube channel, youtube.com/paulmsutter. And I'll see you next time for more adventures in general relativity, which means complete knowledge of time and space.