Daniel and Jorge Explain the UniverseWhat’s the difference between inertial and gravitational mass?
Daniel and Jorge talk about whether there are two or one kind of mass and the massive consequences.
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Hey Daniel, do you ever do physics demonstrations at home with the kids or on the kids?
We have a strict no experimenting on the kids policy without both parents' consent.
Oh good, these you have a process.
We had to create a process after one of us was winging it. But yeah, I love doing physics demonstrations at home, though usually they don't work.
But 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 laws 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 Jorgemrick, cartoonists 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 face 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 particles to 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, they're 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.
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 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 that it won't be too rough a journey.
So welcome to our podcast, Daniel and jorgeik 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 ah hum moment when it all makes sense.
It's right because we are here to discuse the fundamental loss of the universe and also the fundamental laws 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 their 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. We're something right in front of you is a big mystery. You don't need a ten billion dollar 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 in millennia.
Yeah, gravity is kind of a big deal. It's a heavy topic. It's a massive question that physicists have about how the universe works. And it's not just in front of us. It's all around us, under us, low us, behind us, on top of us, well 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 laws could be applied to the 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, fine 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 matchup 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 two hundred bucks and then your friend is like, Hey, I have an extra two hundred 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 scrats with the dog 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.
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'd be a great success. And so we have lots of different experiences of mass and the goals 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, 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 start white chocoling to black hole, what happens? Does it explode?
The black hole does something magical? It turns the white chocolate dark into dark chocolate, unfortunately, but it just turns it into more black hole that's.
What we'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 a white chocolate. No, I wish that were true. That would be fascinating.
And then I thought you were going to say, the leading that could survive a white chocolate is a black hole.
No, it'd be interesting if you threw a white chocolate into a black hole and somehow it's 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, you could 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 incognito 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, you.
Know, it's a dietary privacy. But anyways, 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 usually, we were wondering how many people out there had thought about the difference between inertial and gravitational mass.
Thanks very much do 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 two questions at Danielandjorge dot 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 HIGs gives, and I think it's the mass involved in like 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 reads us 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 the formation in the space time fabric that same body calls us.
I think the difference between inersia and gravitational mass is on the inergia is on the bonding between the particles or something. I think that started in here. We have no idea book, and like, 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 energia 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 distorted 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 best 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, 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 standard, 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 it is 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. Then 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, and there's more in that than in a balloon, for example. Well, absolutely. The job of physics isn't to like rely on these fuzzy concepts and just accept our intuitive understanding. It's to make 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. There's two different things you can do to stuff.
Right.
You can push that shopping cart 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 for as 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 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 Dolli 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 it 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 its 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 MAA. Right, you want something to be, you 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. A f eqals 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, if pushing on the bullet to make it go fast, but the bullet is also pushing 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.
All right, 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 heart 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. Right, And this is a Newtonian picture of gravity, or gravity is a force, and you can think about it 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 a 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 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.
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All right, we're asking a massive question here today. What's the differences 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's so light in my puckets. 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 Youdn figured it out, is that 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 egals ma could be different from mass in the gravitational force formula. So he allowed for the possibility that the were different.
Wait, what do you mean? He didn't call them mass, he didn't call them m.
Well, and Newton actually didn't write his equations down in terms of mathematics. Back then, the style was more pros 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, so 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 it even 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 one 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 MG, 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 sixties 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. The narrow this down to the one part in ten to the thirteen. 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 and our culture at least how they teach physics in high school, right in college, at least in my time, people are just sort of assumed they're the same thing.
Well, I think there's a simplification there. It's sort of like when people tell you of 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, but 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. Would have the experiments found. The experiments have never found any discrepancy between gravitational mass and inertial mass. Galleo did this experiment with like things rolling down inclined planes.
There is this apocryphal story of him dropping things off the leaning tower at Pisa, which I don't think ever happened. There really was this test on the Moon when 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, hmm, 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 is a very different explanation for why things always fall the same way, no matter how massive they are.
Right to 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 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. To 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. You can't measure gravity. Gravity kind of looks like a force. 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 or an accelerometer like a scale, you would measure no acceleration. You're not accelerating. There is no force on you at all. F equals MA 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, right, that's like the inertial mass of the object. It controls how it bends space. But everything moves through bend 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?
Well, 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 when you look at 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've 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 with in 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 Newtony and gravity.
Right, But then like more energy then also then bend space more around it.
Yes, that's right, more energy density, bend 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 fundamential equations. Newton has two equations that are totally separate, totally distinct, completely different descriptions. F equals ma a is one equation. F equals gmm over our squares the other. He has his 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 bend space, and objects move through that ben space. But these things just all flow from the same set of equations, just just one equation. Room to put in another equation with a separate value from mass. The separate equations are the other forces. Electromagnetism can accelerate objects, and that's a concept totally separate from gravity. It 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, ten kilo jeweles concentrated in a the size of a lemon. Now that amount of energy concentrated in one spot, it's 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 ten kilodeles 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 vity doesn't accelerate things. The lemon and a pebble and a bowling ball all moved 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 knub 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 GRS 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, 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 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 a pseudo force. So electromagnetism is a real force like accelerate stuff. 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. 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 flo 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 interpretive 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 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 it 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, masses 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 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. 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, how Einstein may be grappled with the idea of inertial mass, and maybe where mass even comes from. So let's dig into those details. But first, let's take another quick break.
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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 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 explain 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, if I can ask a question and maybe take us deeper into the black hole rabbit hole here. So we're imagining this in ere where we have a bawling ball and a feather, and let's say they're near a black hole. No 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 balling ball will we definitely for sure, right they think it has more inertial mass.
But even just saying the phrase inertial mass implies f equals ma. That's the formula it appears in, so puts you in 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 strap a little rocket to my feather, I would need to expand more energy in that rocket to move the bowling ball than the feather.
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 of 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 that 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 in 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 don't need a bigger force.
Yeah, if you're out in deep space and there's no gravity in nearby, so space is totally flat, then 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. That You can sort of use new Tonian 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.
It 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 of 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 a black hole at the same rate because that's how space time is spent around That's right.
They both follow space time regardless of their mass.
Right. But now let's say I put little rocket. It's 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, in general relativity, if you don't want to follow the curvatures, 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'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 for the bowling ball? Is that still inertial mass or is that a different amount related to 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 falls towards the black hole at the same rate without rockets.
So it's the same as inertial mass.
Then yeah, when you're bringing 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 falls, 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 work 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 constantly constant 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 whorege value.
Yeah, it's the J constant that's right, for which I'll get I'm sure i'll get an oval price. But in your universe G is huge. So like the black hole bends spacelame 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 it means even zero. So now wouldn't in my universe, I would need less to spend less energy in my rockets to keep the balling well 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 gravitation 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, than 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 follow the same rate because they're just following me the curvature of space time. Even if you crank up G. If you crank up G to the new Jhoorge value, so now everything is crazy curved, then the bowling ball and the feather are 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 the black hole, whereas in my universe with the little G, they would fall slowly. Mm hmm. 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 they would the bowling ball in my universe would have the same inertial mass as the boiling 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.
Do you see what I mean? Like there's inertial mas. I'm wondering if that inertial mass, which is the same in my universe in your universe is different than the gravitational mass which is different in my universe and your geniverse because we have different gs, or I wonder if maybe the answer of maybe what's confusing me is that in both universes, the one with big G and LITOG, we would in both cases we would still be wondering about the same thing like that. I wonder if both universes, it would 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 the 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 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 we think it 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 turns out they're connected in some way. There's a relationship between the knobs. Tow At one you have to twiddle the other. So really there's just one knob, or.
At least it's one knob, and 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 gravity, you're saying in this universe they're sort of connected.
It's like one knot mm hmm 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 inertial 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 or 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 there are 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 well 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. Mend on your velocity certainly, right, and 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 in all of our experiences, with different stories, stories at update through time to give us a different picture of how the universe works.
Yeah, although your dog had been there, maybe it would have eaten the grip, I we'ld still be back at uh not understanding any of this.
My dog will eat almost anything.
All right, Well, 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, Instant, 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.
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