Daniel and Kelly’s Extraordinary Universe - What’s the difference between inertial and gravitational mass?

Episode Date: December 12, 2023

Daniel and Jorge talk about whether there are two or one kind of mass and the massive consequences.See omnystudio.com/listener for privacy information.

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What do you mean? Do you break the laws of physics? Well, I remember, for example, trying to show the kids that everything falls at the same speed. And the laws of physics didn't cooperate? Well, it was at the dinner table, and I used little bits of our dinner. And we have a dog, so only one piece actually made it to the floor. Whoa. I guess your dog was trying to challenge the loss of physics? Or just your physics demonstration?

I think I didn't appreciate the gravity of such an experiment for my dog. But I'm sure your dog heavily appreciated it. I got his massive thank you. Hi, I'm Jorge McCartunist and the author of Oliver's Great Big Universe. Hi, I'm Daniel. I'm a particle physicist and a professor at UC Irvine, and I think physics can help us understand the world around us. Yeah, physics is a powerful tool to help us look at the world, challenge the laws of it, and try to figure out how it all works. Because it's a pretty wonderful universe that's pretty amazing to discover and to appreciate. That's right. From the tiniest little part,

Particles, two big baseballs, and enormous black holes. There's lots of mysteries out there. Lots of questions to ask, lots of puzzles to solve at all different scales. It's not just particle physics that's revealing the truth about reality. Yeah, there are big puzzles like, what will dogs eat? Pretty much anything? Will they eat dark matter? Well, I've seen them eat various dark matters for sure.

Yeah, I know. It's coming in and out both ends. That's not good. But yeah, even dogs can be physicists if they also are trying to figure out how the universe works, how things fall and at what rate do they fall. And that's something that even physicists today are looking at and are puzzling about.

That's right. And we're hoping that our dogs will help us figure it out and then it won't be too rough a journey. So welcome to our podcast, Daniel and Jorge, explain the universe, a production of iHeartRadio. Where no pun is too corny, no mystery too grand and no puzzle too deep for us to explore. We think that everything out there can be understood and that you deserve to understand it.

We want to make these ideas click together in your mind so you have that aha moment when it all makes sense. That's right because we are here to discuss the fundamental loss of the universe and also the fundamental loss of the universe. Testing its limits. Are there limits? I think we just hit that limit. If you compress too many dad jokes into a podcast, does it collapse into a black hole? Does it become a granddad podcast? now. And there are physics questions

about gravity that we ask that are not related to puns. Yeah, gravity is one of the biggest mysteries in the universe. It basically holds everything together and makes all the stars and galaxies out there work, but there are a lot of big things about it that we still don't understand.

It's one of my favorite things in physics where something right in front of you is a big mystery. You don't need a $10 billion particle collider to ask like, well, why do things move? Or why am I sticking to the earth? Or Why does the earth go around the sun? You just look at the world around you and ask these basic questions

and our understanding of how this very simple everyday experience happens has changed over decades and centuries and millennia. Yeah, gravity is kind of a big deal. It's a heavy topic. It's a massive question that businesses have about how the universe works. And it's not just in front of us. It's all around us, under us, below us, behind us, on top of us. But we'll hopefully not too on top of us.

If you're listening to this podcast, deep, deep underground, then yes, it's on top of you. And an important way to make progress in these big questions is to look for patterns. When Newton noticed that the same loss could be applied to motions of things in the heavens as on Earth, he understood that his theory was more general than just describing planets, that a single idea encompassed all of it. So looking for clues means looking for patterns, finding apparent coincidences, and digging into them to figure out what the underlying mechanism really is. Yeah, and sometimes in looking for patterns, physicists notice certain things match up in a very suspicious and interesting way.

And so it makes them wonder, is this a coincidence or does this reveal something fundamental about the universe? Like if you just lost 200 bucks and then your friend is like, hey, I have an extra 200 bucks to spend. You might think that there's an explanation that tells the whole story. Yeah, obviously you need better friends. Obviously, dinner's on your friend tonight. Yeah, obviously you're eating scraps with the top. God tonight. Sounds like it.

So today on the podcast, we'll be tackling the question. What's the difference between inertial and gravitational mass? It turns out there's a massive conceptual difference, but almost no actual difference. All right. Well, it sounds like it's a detail we're going to dig into here today. I guess the idea is that there are different kinds of masses in physics. There are different kinds of masses in physics, and that comes from just having different kinds of experience. You know, we live in the world. We describe what we see. And the job of physics is to boil down all of

those experiences into as few concepts as possible to say, can we explain static electricity and lightning with one idea? If possible, then that would be a great success. And so we have lots of different experiences of mass and the goal is to try to like boil it down into just one explanation, a holistic view that explains the entire universe. I wonder, is it kind of like having a separate space in your stomach for dessert? Like, is some of my mass due to dessert and some of it is due to regular food? Some of my mass is definitely due to dessert for sure. Some, but not all. And there's always room for dessert. I'm not sure if that's black hole creation in my stomach or what. And if you throw white chocolate into black hole, what happens? Does it explode? The black hole does

something magical. It turns the white chocolate dark. Not into dark chocolate, unfortunately, but it just turns it into more black hole. That's how you're going to say that black hole spits out the white chocolate because it's so terrible. The only thing that can survive a black hole is white chocolate. No, I wish that were true. That would be fascinating. Then I thought you were going to say the only thing that can survive a white chocolate is a black hole. No, it would be interesting if you threw white chocolate into a black hole

and somehow its quantum information was preserved so that you could come along and tell if a black hole had had white chocolate thrown into it or not. If it had been tainted by the disaster that is white chocolate. I see. shame it later. Or maybe black holes are like quantum erasers deleting the tragedy that is white chocolate from the universe and doing us all a favor. Interesting. I think that's what we all need. It's like an incoctita mode for a diet. I can eat this, but the calories don't count. Yeah, nobody knows. Why did you turn that off ever? I guess you do need some calories to survive. Yeah, you know, it's a dietary privacy. But anyways, we're talking about the difference between

inertial and gravitational mass. It seems that these are two separate concepts. perhaps in physics, and the question is, are they the same or are they different things? So as usual, we were wondering how many people out there have thought about the difference between inertial and gravitational mass. Thanks very much to our army of volunteers who answers these questions for your education and listening pleasure. If you'd like to add your voice to the choir, we'd love to have you. Just write to us to questions at danielanhorpe.com. So think about it for a second. Do you think inertial and gravitational mass are the same?

Here's what people have to say. Inertial mass is the mass that the Higgs gives. I think it's the mass involved in the force to change like an object's velocity. And then gravitational mass, I really never knew how to defer the two. Inertial mass is how much an object resists moving through space, how much force it would take to accelerate it. And gravitational mass has more to do with in a gravitational field, but I believe that they are equivalent. Well, I think that inertial mass represents how hard it is to change the motion of the given body, and that the gravitational mass represents how much deformation in the space-time fabric that same body causes.

I think the difference between inertia and gravitational mass is on the inertia is on the bonding between the particles or something. I think that's edited in here, we have no idea book. And I think it's like the connecting of the quarks and stuff. and that's what creates most mass. So most mass is just a bonding energy. So I think that's what energy is. Inertial mass is a measure of how hard it is for an object to change its velocity, whether in magnitude or direction.

As for gravitational mass, it's a measure of how much an object distorts the space time around it. I know there is a conundrum in classical mechanics around the fact that both these values are numerically the same. And I believe relativity has an answer. for that, but I'm not quite sure what it is. So I'm waiting for you guys to explain. All right. Some nice, pretty deep guesses here. I like the one that says you need a whole podcast for that. Done. That's the answer. Not done yet. We're still doing it. Well, if you're

listening to this, we already finished. Oh, that's true. Yeah. Yeah. We're working in the future. But yeah, these are great answers. People definitely know about these concepts and some people even have ideas about their relationship. Yeah. I saw mentions of the Higgs boson here. I saw mentions of acceleration and energy sounds like this is going to be a pretty dense podcast we're going to overcome some massive misunderstandings in people's brains yeah it's a pretty heavy topic so let's dig into it daniel uh what is mass to a physicist the non-religious physicists the non-denominational idea of mass i mean mass to a physicist is just like a more mathematical and precise description of our experience right physics is not trying to describe a universe you don't understand

understand that isn't familiar to you. We're trying to describe our universe, our everyday understanding of what it's like to be in the world. And that means explaining our intuitive experience, you know, the way that we live and we have this feeling that like you can pick something up and it's hard and you pick something else up and it's easy or you push on something and it's hard to get it moving. You push on something else and it's easier to get it moving and that somehow that that might relate to like how much stuff there is to something. You put another watermelon in the shopping cart and it's a little bit harder to get it rolling. So you're saying the intuitive definition of mass is just how much stuff there is to something.

Yeah, I think that's the most accessible and intuitive idea of what mass is. We think of it like the stuffiness, you know, like this has more scoops of basic universe stuff than something else. Like a rock has more stuff stuffed into it than, let's say, an air balloon. Yeah, it certainly does. You know, there are more atoms. It's denser. If you add up the amount of stuff in all those atoms in a rock, there's more in that than in a balloon, for example. Absolutely. The job of physics isn't to like rely on these fuzzy concepts and just accept our intuitive understanding.

It's to make a more precise mathematical description of what's actually happening. So we can extract from that some understanding of like what the rules of the universe are. Right. Because I guess there are kind of two kinds of mass, right? Like there's a measure of how hard something is to push to get it going and then also how hard it is to lift up from the ground. Exactly. It's two different things you can do to stuff. Right. You can push that shopping card filled with watermelons. And you know, if you put more watermelons in it, it takes a bigger push. And then there's also like actually lifting the shopping card of watermelons over your head. And the more watermelons that are in there, the more force it takes.

And those are actually two separate concepts, right? They're related in that more watermelons makes it harder. But if you're just pushing the watermelons, then you're not lifting them against gravity, right? You're just like speeding them up. And that's what we call inertial mass. It's just like, how hard it is to get something going. Even in outer space, right, things take a push to get moving, even when there's no gravity. Right, because the two things

don't necessarily have to be the same, right? Like, you can't imagine a scenario where maybe, for example, there's a rock on dolly with wheels in it, and it takes a certain amount of force to push it from side to side, but then it maybe takes no force to lift it up or maybe takes an extra bigger force to lift it up.

Right? We could live in a universe where those two things are not the same. Yeah. Or even just on a planet, right? If you have a rock on Jupiter, then it takes a large force to counteract Jupiter's gravity. But it takes the same force to push it side to side on Jupiter as it does on Earth. All right. So then the two things are different. And so let's dig into it a little bit more. Talk about inertial mass. So inertial mass is just this sense that it takes a force to get something going. And this is basic Newtonian mechanics. Things tend to stay at the same velocity unless you give them a push. That push is a force. And so this is just F equals MA, right? You want a basic Newtonian mechanics. Things tend to stay at the same velocity unless you give them a push. And so this is just F equals MA, right? You want to something to speed up, you've got to push on it. And the amount of speed up you get for that push depends on the thing's mass.

So if it has a small mass, like if M is very, very small, and you give it a big push, you get a big acceleration. But if it has a large mass, like the Earth or something, and you give it a push, then it gets a very small acceleration. F equals MA tells you that the larger the mass, the larger the force you need to accelerate something to speed it up. Right. And so in this case, mass is the ratio.

Like what happens if you divide the force, you need. to push on something to get it to a certain acceleration, right? Exactly. And this is a very familiar experience, right? Think about like firing a rifle. When you fire a rifle, it's pushing on the bullet to make it go fast, but the bullet is also pushing it on the rifle. Why doesn't the rifle zoom the other way just as fast as the bullet?

Well, because the rifle has more mass than the bullet. They have the same force applying on both of them, but the bullet is less mass so it gets more acceleration. Or maybe think about it as like an asteroid in space. That's not in a planet. or anything. The more massive the aster it is, the harder it is to get it moving. That's inertial mass. That's inertial mass, exactly. So things that have this property, we call it inertial mass, are harder to get moving. They're harder to speed up and harder to slow down. They have

inertia. That's sort of what we mean by inertia, that we have inertial mass. All right. Now talk about gravitational mass. So gravitational mass is what controls how much gravitational force is applied on you. And Newton also has a formula for this. It's GMM over R squared. We have two masses there because two things are pulling on each other. And more mass means more gravity. Like if you added mass to the Earth without changing its radius, if you made it more dense, so it got more massive, then it would be pulling on you harder. And so that's the gravitational mass. It's the mass that goes into the gravitational force formula. Or I guess going back to our asteroid in space scenario, like if you have an asteroid in space and it's close to a big planet, the big planet

is going to pull the asteroid towards the planet. And so the mass of the asteroid is maybe a measure of how hard would it be to keep the asteroid from being pulled towards the planet? Like if you're trying to prevent the asteroid from falling into the planet, how hard would it be depends. That's gravitational mass. Exactly. More gravitational mass means more gravity. Imagine you're zooming next to two planets and one of them has more mass than the other. then you're going to feel it's gravity more strongly. And this is a Newtonian picture of gravity where gravity is a force. And you can think about it's sort of like the gravitational mass is like the charge for gravity.

Two electrons will push on each other because they both have negative charge. And if you increase that charge, then their force would be stronger. Well, the force law for gravity is exactly the same structure as the force law for electromagnetism where you replace the charges with the masses. You increase the mass, you get more gravity. right like a lightweight asteroid you wouldn't a small lightweight asteroid you wouldn't need to push very hard to keep it from falling into the planet with a huge massive asteroid you need to be Superman basically to keep it from smashing into the planet all right well that's the basics of Newtonian inertial and gravitational mass now let's get into where it gets kind of tricky and are these things the same or are they different according to Einstein so let's dig into those details but first let's take a quick break A foot washed up a shoe with some bones in it. They had no idea who it was.

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Neil Barnett, where we dive into to managing flight anxiety. Listen to Therapy for Black Girls on the IHeartRadio app, Apple Podcasts, or wherever you get your podcast. All right, we're asking a massive question here today. What's the difference between inertial and gravitational mass? Are they the same? Are they different?

Are they just two sides of the same coin? Are there two coins? How many coins are there in the universe? An infinite number of coins with an infinite number of sides. With infinite mass? Maybe it's made out of photons, who knows? There we go. That would explain why money is so light in my pockets.

All right, so we talked about kind of the basics of inertial and gravitational mass, I guess from a Newtonian perspective. So like a couple of hundred years ago, that this is what Newton figured out. He said you have something called inertial mass, and you have something called gravitational mass, and he basically measured them to be the same thing, right? or he thought they were the same thing. He actually sort of treated them as different things, right?

He wrote them down as if they were different numbers. Like he wrote two different formulas, and the masses in those two formulas didn't have to agree. Like in principle, in Newtonian physics, mass in F equals MA could be different from mass in the gravitational force formula. So he allowed for the possibility that these were different. Wait, what do you mean?

He didn't call them mass? He didn't call them M. Well, Newton actually didn't write his equations down in terms of mathematics. Back then, the style was more prose. So a lot of Newton's stuff is actually written out in sentences. So the exact notation can be a little different. But in our modern translation of Newton's formulas,

technically there's a little I in front of the inertial mass and a little G subscript in front of the gravitational mass. And they don't necessarily have to be the same. In Newtonian physics, you have to go out and measure whether these things are the same. But did he do it? Did Newton measure it to be the same? Or did he measure it to be different? So Newton measured it using a pendulum.

and lots of other people have done these measurements, and we find that they are the same. And it's sort of a famous result that people learn about, you know, in elementary school, that two things, even if they have different mass, fall at the same speed. That's basically testing whether inertial and gravitational mass are the same thing. Something that has more mass takes a bigger force to get going. But if it has more gravitational mass also, then it gets a bigger force from the Earth. And so something that's low mass and something that's high mass will get accelerated the same way. by the Earth. The Earth is pulling harder on the one with more mass, which takes more effort

to get it going so the two things perfectly balance out. I guess we're just lucky Newton didn't have a dog when he ran his experiments. So Newton ran this experiment and he measured it to be the same. Did he then conclude that it was the same thing? Did he then start calling it the same thing? Newton's experiment was not super precise. So this is hundreds of years ago and the technology for timing things and measuring things precisely was much fuzzier. So he concluded these things were likely the same, but he had no proof theoretically that showed that they had to be the same, and he only had an experimental measurement, which was kind of fuzzy. And so people continued on measuring these things, and they've been measuring it basically ever since. People are basically

still measuring this to see if they can find any discrepancies. And so at some point, I guess, in our scientific history, scientists sort of kind of concluded they were the same, didn't they? I mean, at least when you're in high school, you know, they just teach you M. They don't teach you M-I and M-G, they just teach you M. There is a sort of simplified version of it. in high school. But in Newtonian physics, these are potentially different, which is why, you know, astronauts on the moon in the 60s did this experiment, you know, dropping a feather and hammer at the same time. And why in the last couple of decades, people have made this even more precise with high-tech torsion balances that narrow this down to the one part in 10 to the 13. But, you know,

from an experimental point of view, that's not the same. That just says it's either the same or it's very, very close together. But I guess I mean like sort of in, I guess, in our society, in our culture and how they teach physics in high school, right? In college, at least in my time, people just sort of assume they're the same thing. Well, I think there's a simplification there. It's sort of like when people tell you, oh, the photon has no mass. Well, we're pretty sure the photon has either no mass or almost no mass,

some very, very small number. But we haven't exactly measured it to be zero. We've measured it to be close to zero within some tolerance. So it just depends on how precise you want to be with your language. According to these measurements, they seem like basically the same. thing. But that's not the same as saying we understand why they have to be the same. Theoretically, they're linked. It might just be a coincidence. All right. So then scientists have been sticking to it. They've been trying to do this experiment

to see if these two things are the same. What have the experiments found? The experiments have never found any discrepancy between gravitational mass and inertial mass. Galileo did this experiment with like things rolling down inclined planes. There's this apocryphal story of him dropping things off the leaning tower of Pisa, which I don't think ever happened. There really was this test on the moon where they drop a hammer and a feather because, you know, this is only true. There's no air resistance. Air resistance makes everything much more complicated. If the only force involved is the force of gravity and it just has to overcome the inertia, then those things should perfectly balance out if the inertial mass

and the gravitational mass are the same. So nobody's ever found any violation of these two things being the same. Okay. So then I guess the question is, are they actually the same or are they just being measured to be the same. Yeah. Like is it a coincidence or is it really just two ways of looking at the same thing? And those are two very different ideas about how the world could work. It's sort of like the way the electron charge and the proton charge balance each other out. We think exactly. Does that mean that there's a fundamental relationship between the two or do we live in a world where these two things just happen to balance? And that's why we live in this world, right? Even if your experience of the world is the same and doesn't change any experiments, it's a very different

story about how the world works, about which universe we live in. Okay. So what do we know about this question? So Newton's answer is, it's a coincidence. These are two different concepts. They appear in two different formulas. We measure them. They happen to be equal.

End of the story. Newton says there's no reason for these two things to be the same. They just happen to be so. So Newton has two parameters and they just happen to be exactly the same value. But that seems like too delicious a clue. When we find coincidences like that in nature, we're like, maybe there's a simpler version of the story. Maybe we can explain these two sides of the coin in terms of one coin. And that's where Einstein comes in. Einstein has a very different explanation for why things

always fall the same way, no matter how massive they are. Right. Einstein, gravity is not even a force, right? That's right. And that's the basic answer. Einstein says there is no gravitational force. You can never measure gravity. You can't feel gravity. The reason things fall is because they're actually just moving together to follow the shape of space. Einstein says you're kind of asking, asking the wrong question by saying why these two things equal. He says there's only one thing. There is only inertial mass. There's no such thing as gravitational mass because there is no such thing as a gravitational

force. Right. According to Einstein, gravity is like the bending of space, right? Space time. That's what makes something fall to the ground or orbit around a planet or the sun. That's right. To Einstein, gravity is sort of like an illusion. You can never even feel it or sense it directly.

Let's make sure we unpack that a little bit because. there are important ideas in there that we have to mentally import to understand what's going to happen next. I mean, what does it mean that there's no gravitational force that you can't measure gravity? Gravity kind of looks like a force and it certainly feels like we can measure it, right? Gravity looks like a force because we can't see the curvature of space. We think things should move in straight lines because we don't see that space is curved. So when we see things move differently than we expect, Newton tells us, oh, there's a force there. But if you could see the curvature of space, you'd understand that it's just stuff moving along those curves.

There's no force there. It's actually just free fall motion. So when you jump off a building, for example, and you fall towards the earth, you're in free fall. There are no forces acting on you. From your point of view, the surface of the earth is accelerating towards you. And if you pulled out a gravitometer, an accelerometer, like a scale, you would measure no acceleration. You're not accelerating. there is no force on you at all.

F equals M.A. equals zero. Now, standing on the surface of the Earth, you do measure acceleration. A gravitometer like a scale measures non-zero acceleration. But that's not the force of gravity on you. That's the surface of the Earth accelerating up against the natural free fall motion of gravity. All acceleration is against the natural motion of gravity. So Newton says that the person on the surface is not accelerating

and the falling person is being accelerated. by the force of gravity. But Einstein says that the surface of the earth is accelerating and the person falling has no acceleration. You will not sense any gravity there because there is no force there for you to measure with your accelerometer. Right, but I guess you still sort of have the concept of mass, right?

Because some things bend space and time more than others. Like a feather, doesn't it bend space and time a little bit more or less than a bowling ball? Yes, absolutely. But that's just the single concept of mass. mass, right? That's like the inertial mass of the object. It controls how it bends space. But everything moves through bent space the same way, regardless of its mass. But that's just one concept in general relativity. What do you mean? It's the same concept. So now Einstein said that

the idea that they're identical doesn't matter because they're the same thing. He says there essentially is only one idea here, the mass of the object, and that controls how it bends space. And it's the bending of space that controls essentially how these objects move. Right. But isn't there like a degree to which something bends space more than other things? The bending of space actually doesn't come from mass. It comes from energy density. Mass doesn't have a unique property to bend space. It's really just the energy content of something which bends space.

And you can bend space even if you don't have mass. Like a box of photons, for example, can bend space. Right, right. I mean, we've talked about this before in the podcast that there really is no such thing as mass. There's really only energy, right? That's a strong philosophical statement. I would say mass makes some sense.

But in the end, when you look at it, it, it's basically another kind of energy, yeah. Yeah, I mean, I'm just going by what we wrote in our book. I don't think we said that mass doesn't exist. We said that mass is internal stored energy. Yeah, so like all mass is energy is what we said. But there is this weird property about energy that if you have concentrated energy bound to like a particle or something, then that particle is hard to move, right?

That's still what you would call inertial mass. But now when you say something is easier or harder to, accelerate, you're adding in other forces to make that acceleration happen. If we're just talking about gravity, like the experiment of dropping a bowling ball or a feather, there is no way to accelerate it because gravity isn't the force and doesn't accelerate things. Things just move according to the curve of space. Other forces can provide acceleration. In fact, they are the only way to accelerate things. So they still have this concept of inertial mass that's separate from gravity for the other forces. But within gravity, there's just one concept of mass, the energy that helps bend

space. That mass doesn't play a role in how things move through that space. So there's not a separate concept of inertial and gravitational mass in Einstein's relativity like there is in Newtonian gravity. Right. But then like it's more energy than also then bend space more around it. Yes, that's right. More energy density bends space more around it. So what do you mean by Einstein said that it's all the same thing. Like it can all be explained by just the concentration of energy. In general relativity, these all flow from the same fundamental equations. Newton has two equations that are totally separate, totally distinct, completely different descriptions. F equals MA is one equation, F equals GMM over R squared, the other. He has this law of inertia and he has his

law of gravity. For Einstein, these things all just flow from the concentration of energy density. Energy density bends space and objects move through that bent space. But these things just all flow from the same set of equations. There's just one equation there. There's no room to, like, put in another equation with a separate value for mass. The separate equations are the other forces. Electromagnetism can accelerate objects, and that's a concept totally separate from gravity and requires a concept of inertial mass.

So if you involve the other forces, there are still two parameters there. But now there's only one for gravity, thanks to Einstein. But I wonder if there's, like, a knob there, you know, like, let's say I have, I don't know, 10 kilojoules concentrated in the size of a lemon. Now, that amount of energy concentrate in one spot is going to be a little bit hard to move. That's inertial mass of the lemon. But then also that lemon is bending space time around it to a certain degree. Wouldn't I call that gravitational mass?

Like you can imagine 10 kilojoules of energy bending space a lot in one universe and bending space not much at all in another universe. So the lemon bends space and causes curvature, but from gravitational point of view, It has no meaning to say it's hard to accelerate the lemon because gravity doesn't accelerate things. The lemon and a pebble and a bowling ball all move through that curved space the same way gravitationally. If you bring in other forces like rockets, then you've reintroduced inertial mass, but not gravitationally. There is another knob there. That's the gravitational constant, right?

Which appears in Newton's formula, but also appears in general relativity. But that affects everything, right? That affects how much mass is going to bend space. So you crank G up and then the same amount of mass is going to bend space more, right? But that's simultaneously automatically also going to change how things move because things move just following the curvature of space. So that's the beautiful thing about GR is that it tells you that the way things move through space doesn't depend on their mass. It only depends on the geometry of space. It's purely geometric.

So the reason, for example, that the feather and the hammer fall at the same rate, is because they are both just following the curvature of space, regardless of what their mass is. So if you crank up G, you get more curvature, and that changes how everything moves. Right, but the bowling bustle has more inertial mass, right? So why does it move at the same rate as a feather? Because motion through space doesn't depend on your mass, right? You have to get rid of this idea of inertial mass affecting how you're going to move. What affects how you move is just the curvature of space, just the geometry of space time.

The way to look at it is not that both the bowling ball and the feather are being accelerated the same amount. That's Newtonian and requires gravitational forces balanced by inertia. The way to look at it is that the bowling ball and feather move the same way through curved space time. Neither of them is accelerating. They're both in free fall. What's accelerating is the surface of the Earth rushing up to them. So, of course, it reaches them at the same time. Well, maybe it would help to understand a little bit more how gravity causes things

to move and this idea of pseudo forces. So what do you mean like gravity is the pseudo force? So electromagnetism is a real force. It like accelerates stuff, right? It pushes and it pulls. That's what we mean by a force. But a pseudo force is when something appears to move without a force being applied to it. Right. And this is not unfamiliar to you. Like if you're in the back of a truck and there's a bowling ball there and somebody hits the gas, then to you in your frame of the back of the truck, the bowling ball is going to move. They hit the gas, the bowling ball is going to move to the back of the truck. They hit the brakes. The bowling ball is going to move to the front of the truck. So you're seeing like this ball move even though nobody's pushing on it, right? Nobody's pulling on it.

Nobody's applying any force to it. But you're seeing the ball accelerate. So there's a pseudo force there. Something is happening to accelerate this thing even though there's no forces on it. And in the same way, for example, if you're out in space and you're in a rocket ship and your rocket ship is accelerating and you drop a ball, then that ball is going to fall to the floor. This is how you can get the appearance of gravity on a spaceship if you're accelerating. So that's a pseudo force, right? Basically, acceleration, any accelerating frame gives you a pseudo force. There's no gravity on the spaceship.

It's just the floor is accelerating up to meet the ball that you've dropped it. All right. So that's the concept of a pseudo force. Like in those space movies where they have like a rotating spaceship or something and this intributive force makes it feel like there's gravity around you. Exactly. That's right. Yeah.

But there's no actual gravity happening. There's no actual gravity there. It's just acceleration. that's creating this pseudo force and so now Einstein says well curvature of space time which is invisible to us we can't see it also causes pseudo forces like if you're out in space and you drop a ball and somewhere near the earth it's going to drift towards the earth and somebody watching you do this experiments from sort of far away is going to notice hmm there seems to be a force on this ball and that's what newton would call the gravitational force but Einstein would say no there's no there's no

actual force there. It's moving because of a pseudo force. It's moving because actually just following the curvature of space time. You can't see that curvature. It's not obvious to you, but the ball is following the curvature of space time. And to us, it looks like there's a force on it even though there's not. The ball is not actually accelerating. So you're saying like what we think of as gravity is really just pseudo gravity, right? Kind of? Like when you have like a black hole and it's bending space time around it, it's sort of like causing acceleration around it or something. It's bending space time so that there's acceleration so that it feels like something is pulling us down. So yeah, mass has definitely bend space time, but the issue of acceleration is a little bit subtle. Like if you are

that ball that's falling towards the earth, you don't feel any acceleration. Just like if you jump off of a building before you hit the ground, you feel like you're in free fall. You feel weightless, right? So you never actually experience gravity. You never feel gravity accelerating you. Okay, but to somebody standing far away, it does look like you're accelerating, right? That's right. That's where the pseudo force comes in. Somebody else in an inertial frame would say, oh, there's a force on you. You're falling down towards the center of the earth or you're falling in towards that black hole

and you're accelerating relative to them. They're seeing that pseudo force. But Einstein says there's no force there. It's just things moving according to the curvature of space time. Right. All right. Well, let's dig a little bit more into this detail and how it compares to inertial force. Einstein maybe grappled with the idea of inertial mass, and maybe where mass even comes from.

So let's take into those details. But first, let's take another quick break. A foot washed up a shoe with some bones in it. They had no idea who it was. Most everything was burned up pretty good from the fire that not a whole lot was salvageable. These are the coldest of cold cases, but everything is about to change. case that is a cold case that has DNA. Right now in a backlog will be identified in our lifetime. A small lab in Texas is cracking the code on DNA. Using new scientific tools, they're finding clues in evidence so tiny you might just miss it. He never thought he was going to get caught. And I just looked at my computer screen. I was just like, ah, gotcha.

On America's crime lab, we'll learn about victims and survivors. And you'll meet the team behind the scenes at Othrum, the Houston Lab that takes on the most hopeless cases to finally solve the unsolvable. Listen to America's Crime Lab on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts.

I had this overwhelming sensation that I had to call it right then. And I just hit call. I said, you know, hey, I'm Jacob Schick. I'm the CEO of One Tribe Foundation, and I just wanted to call on and let her know. There's a lot of people battling some of the very same thing you're battling, and there is help out there.

The Good Stuff podcast, season two, takes a deep look into One Tribe Foundation, a non-profit fighting suicide in the veteran community. September is National Suicide Prevention Month, so join host Jacob and Ashley Schick as they bring you to the front lines of One Tribe's mission. I was married to a combat army veteran, and he actually took his own life to suicide. One Tribe saved my life twice. There's a lot of love that flows through this place, and it's sincere. Now it's a personal mission.

Don't have to go to any more funerals, you know. I got blown up on a React mission. I ended up having amputation below the knee of my right leg and a traumatic brain injury because I landed on my head. Welcome to Season 2 of the Good Stuff. Listen to the Good Stuff podcast on the IHeart Radio app, Apple Podcasts, or wherever you get your podcast. Your entire identity has been fabricated.

Your beloved brother goes missing without a trace. You discover the depths of your mother's illness the way it has echoed and reverberated throughout your life, impacting your very legacy. Hi, I'm Danny Shapiro. And these are just a few of the profound and powerful stories I'll be mining on our 12th season of Family Secrets. With over 37 million downloads,

we continue to be moved and inspired by our guests and their courageously told stories. I can't wait to share 10 powerful new episodes with you, stories of tangled up identities, concealed truths, and the way in which family secrets almost always need to be told. I hope you'll join me and my extraordinary guests for this new season of Family Secrets. Listen to Family Secrets Season 12 on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. I'm Dr. Joy Harden Bradford, and in session 421 of Therapy for Black Girls,

I sit down with Dr. Ophia and Billy Shaka to explore how our hair connects to our identity, mental health, and the ways we heal. Because I think hair is a complex language system, right? In terms of it can tell how old you are, your marital status, where you're from, you're a spiritual belief. But I think with social media, there's like a hyperfixation and observation of our hair, right? That this is sometimes the first thing someone sees when we make a post or a reel is how

our hair is styled. You talk about the important role hairstyles play in our community. the pressure to always look put together and how breaking up with perfection can actually free us. Plus, if you're someone who gets anxious about flying, don't miss session 418 with Dr. Angela Neil Barnett, where we dive into managing flight anxiety. Listen to Therapy for Black Girls on the IHeart Radio app, Apple Podcasts, or wherever you get your podcast. All right, we're talking about the difference between inertial and gravitational mass, and it's getting a bit hairy, Daniel, I feel like,

because I feel like we're once again trying to explain really difficult general relativity, special relativity topics on an audio podcast. And so it can be a little bit confusing. But it sounds like what you're saying is that Einstein sort of puts the whole question kind of in the nonsense category. Like it doesn't make sense to even compare gravitational and inertial mass because to Einstein, there is no such thing as gravitational mass. Yeah, exactly.

And it's sort of beautiful because he still does manage to sort of like explain what we see. Like we see these interesting things like a big ball and a little ball fall at the same rate. And he can still explain that. And he explained it in this gorgeous geometrical explanation. And he does so by saying that there is no ambiguity between the inertial and gravitational masses. There's just one mass. Well, like if I can ask a question and maybe take us a deeper into. the black hole, a rapid hole here.

So we're imagining the scenario where we have a bowling ball and a feather, and let's say they're near a black hole. Now, you're saying that to somebody standing far away from this scenario, they're both going to accelerate and move towards the black hole at the same rate, because that's how gravity works, right? Because things move through space time regardless of their mass, right? Your mass does not affect in general relativity how you move through space time. Right, right.

And even though the feather has less inertial mass than the bowling ball. the bowling ball will be definitely for sure right they think it has more inertial mass but even just saying the phrase inertial mass implies f equals m a that's the formula it appears in so put you to a newtonian point of view right so like the phrase inertial mass doesn't really belong in a conversation about general relativity there's just mass well like if i were to strap a rocket to my bowling ball and a strap a little rocket to my feather i would need to expend more energy in that rocket to move the bowling ball than the better. If you want to add in other forces, electricity or rockets or whatever, then you bring back inertial mass. But for Einstein's gravity, there's just one mass, the one that bends space time. Think about your big ball and your little ball on the surface of the earth, right? What's happening there? Well, both of them want to be sort of falling towards the center of the earth to follow the natural motion to the earth. Both of them are not because the earth is pushing back up on them, right? And so really what's happening there is like their earth is

accelerating them up at the same rate so they don't fall towards the center of the earth. I guess maybe if we can go back to the feather and the bowling ball, like if I have the feather and the bowling ball in space, nothing around it, no black hole, no planet Earth, and I wanted to move them one meter, I would need more energy to move the bowling ball than the feather, right? I would need a bigger force. Yeah, if you're out in deep space and there's no gravity nearby, so space is totally flat, and these things just sit there if you don't apply a force to them. And if you do apply force to them, then they will accelerate.

You can sort of use Newtonian mechanics in this context because there is no curvature to space. And if you want to apply other forces, ones that generate real acceleration, then you bring in inertial mass again. But that concept doesn't exist in gravity anymore. Right. And so in this case, there is something called inertial mass. Like it takes a bigger force to move the bowling ball in space. Takes a bigger force to move the bowling ball. Yes. Newton would say that's inertial mass.

That's inertial mass. Okay. Now, let's put the feather and the bowling ball. near a black hole and I let go with them. You're saying because of Einstein and the way the black hole is bending space time around it, the feather and the bowling ball are going to fall towards the black hole at the same rate because that's how space time is bent around. That's right. They both follow space time regardless of their mass.

Right. But now, let's say I put little rocket in the feather and in the bowling ball and I'm trying to prevent these things from falling into the black hole to an outside observer far away from this catastrophic scenario. Don't I need to push the bowling ball harder or expand more energy in my rocket to keep the bowling ball from falling into the black hole than the feather? Yeah, so in general relativity, if you don't want to follow the curvature of space time, then you need a force, right? That's what forces are, essentially. Anytime you're accelerating is accelerating to avoid just following the curvature of space time. And so, yeah, you need a force to push on these things. And yeah,

I think you need a bigger force to push on the bowling ball than the feather. Okay. So you're saying that my rocket on my bowling ball needs to push harder than the rocket on the feather to keep it from falling into the black hole, right? So there's just more of something there that needs to happen

in order to keep them from falling into the black hole. Now, is that more of that something or is that something that there's more of for the bowling ball? Is that still inertial mass? Or is that a different amount related to like how much

the black hole is bending space time? Yeah, here we're talking about real acceleration, opposing the natural motion according to the curvature of space. And that has to come from something other than gravity, which means a real force. And that brings in inertial mass again, yes. But again, there's no inertial mass in gravitational motion. The reason the bowling ball and the feather fall towards the black hole at the same rate without rockets.

So it's the same as inertial mass then? Yeah. When you bring in the other forces, there will be inertial mass again. But within gravity itself, there isn't one anymore. Like the reason that you do not fall towards the center of the earth is because the surface of the earth is pushing you up, Exactly the same way that rocket is accelerating the bowling ball away from the black hole. The surface of the earth is pushing you up away from gravity. And if you drop a ball, Newton says, oh, that ball is accelerating towards the center of the earth.

Einstein says, no, when you drop the ball is when it stops accelerating. You are accelerating up away from the center of the earth, like the bowling ball and the rocket to avoid falling in. And the ball is now in free fall. It's now flowing naturally with gravity. It's stopped accelerating. That's why everything falls at the same rate because it's really, the earth that's rushing up to meet it rather than like the bowling ball or the feather

that are falling. They're just like hanging out not accelerating with respect to space. Right. And so in that sense, it's the same thing. Like inertial mass is the same as gravitational mass. But I guess my question now leading up to this is let's say we lived in a universe in which

gravity worked differently. Like the amount of space time bending that a black hole does is different in my universe and in your universe. Like in my universe, the black hole if you concentrate that much energy into a spot doesn't bend space time

very much like almost not at all you're changing the value of G yeah changing the value of G okay you're making it the value of J the Jorge value okay yeah it's the J constant that's right

for which I'll get I'm sure I'll get a noble price but in your universe G is huge so like the black hole bends space time a lot and so space in your universe space is rushing towards

the black hole a lot super fast a lot and whereas in my universe let's say it means even zero So now, in my universe, I would need less to spend less energy on my rockets to keep the bowling ball from falling into the black hole. Whereas in your universe, I would need a lot of energy to keep the bowling ball from falling into the black hole. Yes, the force you need does depend on the gravitational constant because you're pitting gravity against non-gravitational forces, which do have a concept of inertial mass. And when you fight against the curvature with other forces, then the relative strength of curvature and those forces matters.

I guess maybe where I'm going with this is that you're sort of making it sound like there is no coincidence anymore with Einstein's relativity. But I wonder, and again, I'm not an expert. I'm just kind of intuitively following my sense of intuition here. I wonder if it's still sort of a coincidence. You just move the coincidence somewhere else. I think to me the way to answer that question is just to think about the bowling ball and the feather without the other forces. Because it's the fact that the bowling ball and the feather fall at the same rate that in Newton's view means these two things have to be. equal, right? That's where the coincidence comes from. And Einstein says that the bowling ball

and the feather have to fall at the same rate because they're just falling with the curvature of space time. Even if you crank up G, if you crank up G to the new Jorge value, so now everything is crazy curved, then the bowling ball and the feather are going to fall into the black hole at the same rate. They'll fall faster than in a universe without crazy G, but they will both fall into the black hole at the same rate. If you relax G down so that space is curved less by mass, it's harder to make black holes or whatever, then the bowling ball and the feather are going to fall in more slowly, but they're still going to fall at the same rate.

Doesn't that answer the question? Okay, so you're saying that in your universe with the big G, the feather and the bowling well would fall really fast towards a black hole, whereas in my universe with the little G, they would fall slowly. Okay, but in both universes, if there is no black hole, they would both the feather and the bowling ball would have different inertial masses. To each other, but the bowling ball in my universe, would have the same inertial mass as the bowling ball in your universe.

Yes, for the real forces, you still have inertial mass. But the coincidence within gravity is explained by Einstein, since gravity now only has one mass instead of two. You see what I mean? Like, there's inertial mass. I'm wondering if that inertial mass, which is the same in my universe and your universe, is different than the gravitational mass, which is different in my universe and your universe because we have different Gs.

Or I wonder if maybe the answer, maybe what's confusing me is that, in both universes, the one with big G and little G, we would, in both cases, we would still be wondering about the same thing. I wonder if both universes, they would seem like coincidences that inertial gravity and gravitational gravity in the Newtonian sense are the same. I think in both the big G universe and the little G universe, you'd have a big Newton and a little Newton, which would have developed their own laws of Newtonian physics,

which would seem like there was a coincidence between them because they have these two different concepts, one of gravitational force from some gravitational mass that explains the apparent force of gravity. But then Big Einstein and Little Einstein would have come along and explain that there is no force operating there, that there really is just the one mass. And if Big Einstein and Little Einstein could talk to each other and compare notes, if both the universes are relativistic, then they would see that both universes are following their laws of physics. I think it's interesting that in one universe, you have like a stronger reaction to energy density in terms of the curvature of space than in the other,

which will definitely change how things move. But in that universe, things always agree, right? Like the two objects moving through the same space time move the same way regardless of their mass is the key. Okay. It sounds sort of like the main idea is that sometimes what we think is a coincidence. It's really just a different way of looking at how the universe works. Yeah, exactly. That you can bring two different ideas together and click them into one larger idea where you thought,

you had the freedom to twiddle two knobs to whatever values you want, but it turns out they're connected in some way. There's a relationship between the knobs. If you twiddle one, you have to twiddle the other. So really, there's just one knob. Or at least it's one knob, but maybe, I don't know. There could still be other knobs in the universe, but like the ones that affect how things move and how things get attracted to larger objects through gravity, you're saying in this universe,

they're sort of connected. It's like one knob. Exactly. In our universe, at least. You're right that there are other knobs for the other forces and those still have the concept of inertial mass, but within gravity, the apparent coincidence between those two knobs, gravitational and inertional mass is explained because there is no inertial mass in gravity because it doesn't accelerate anything because it's not a force. So then to answer the question of the podcast, there is no difference between inertial and gravitational mass or is the answer that this question doesn't make sense? The answer is that there is still inertial mass for other forces, but within gravity, there's just one concept of. mass. There's no separation between gravitational and inertial mass. There is just mass. And we can still

understand why things fall at the same rate, even in that context, right? We don't have to worry about this miraculous balance between inertia and gravity because they're just two sides of the same coin. Inertia and gravity are wrapped up by Einstein into one idea that controls how things move through space. All right. Well, it was a heavy topic, but I think we made it through to the other side, or at least we did not fall into a black hole while discussing it. Although maybe we should just add more dad jokes and puns so that we, you know, reach the event horizon. Yeah, and to me, thinking about these examples really helps you get more intuition for thinking

about gravity as just a geometric thing. It doesn't matter what your mass is. You move through space the same way. It depends on your velocity, certainly, right? Like a photon flying near black hole is going to have a different trajectory than a grapefruit traveling at five meters per second, your velocity definitely matters, but not your mass, which is just a very different way of thinking about the universe. And I love how the story of physics is explaining everything we see and all of our experiences with different stories,

stories that update through time to give us a different picture of how the universe works. Yeah. Although if your dog had been there, maybe it would have eaten the grapefruit. And we'd still be back at not understanding any of this. My dog will eat almost anything. All right. Well, we hope you enjoyed that. Thanks for joining us. See you next time. For more science and curiosity, come find us on social media where we answer questions and post videos.

We're on Twitter, Discord, Insta, and now TikTok. 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. Your entire identity has been fabricated. Your beloved brother goes missing without a trace. You discover the depths of your mother's illness.

I'm Danny Shapiro, and these are just a few of the powerful stories I'll be mining on our upcoming 12th season of Family Secrets. We continue to be moved and inspired by our guests and their courageously told stories. Listen to Family Secrets Season 12 on the I-Novely. My Heart Radio app, Apple Podcasts, or wherever you get your podcasts. It's important that we just reassure people that they're not alone, and there is help out there. The Good Stuff Podcast, season two, takes a deep look into One Tribe Foundation, a non-profit fighting suicide in the veteran community.

September is National Suicide Prevention Month, so join host Jacob and Ashley Schick as they bring you to the front lines of One Tribe's mission. One Tribe, save my life twice. Welcome to Season 2 of The Good Stuff. Listen to the Good Stuff podcast on the iHeartRadio app, Apple Podcasts, or wherever you get your podcast. Every case that is a cold case that has DNA. Right now in a backlog will be identified in our lifetime. On the new podcast, America's Crime Lab, every case has a story to tell.

And the DNA holds the truth. He never thought he was going to get caught. And I just looked at my computer screen. I was just like, ah, gotcha. This technology is already solving so many cases. Listen to America's Crime Lab on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. This is an IHeart podcast.