Speaker 1: Hey, Daniel, do you ever do physics demonstrations at home
Speaker 1: with the kids or on the kids?
Speaker 2: We have a strict no experimenting on the kids policy
Speaker 2: without both parents' consent.
Speaker 1: Oh good, did you have a process?
Speaker 2: We had to create a process after one of us
Speaker 2: was winging it. But yeah, I love doing physics demonstrations
Speaker 2: at home, though usually they don't work.
Speaker 1: What do you mean do you break the laws of physics?
Speaker 2: Well, I remember, for example, trying to show the kids
Speaker 2: that everything falls at the same speed m.
Speaker 1: And the laws of physics didn't cooperate.
Speaker 2: Well, it was at the dinner table, and I used
Speaker 2: little bits of our dinner, and we have a dog,
Speaker 2: so only one piece actually made it to the floor.
Speaker 1: WHOA. I guess your dog was trying to challenge the
Speaker 1: laws of physics or just your physics demonstration.
Speaker 2: I think I didn't appreciate the gravity of such an
Speaker 2: experiment for my dog, but.
Speaker 1: I'm sure your dog heavily appreciated it.
Speaker 2: I got his massive thank you.
Speaker 3: Hi.
Speaker 1: I am Horhemrick, cartoonists and the author of Oliver's Great
Speaker 1: Big Universe.
Speaker 2: Hi. I'm Daniel. I'm a particle physicist and a professor
Speaker 2: at UC Irvine, and I think physics can help us
Speaker 2: understand the world around us.
Speaker 1: Yeah, physics is a powerful tool to help us look
Speaker 1: at the world, challenge the laws of it, and try
Speaker 1: to figure out how it all works. Because it's a
Speaker 1: pretty wonderful universe that's pretty amazing to discover and to appreciate.
Speaker 2: That's right, from the tiniest little particles to big baseballs
Speaker 2: and enormous black holes. There's lots of mysteries out there,
Speaker 2: lots of questions to ask, lots of puzzles to solve
Speaker 2: at all different scales. It's not just particle physics that's
Speaker 2: revealing the truth about reality.
Speaker 1: Yeah, they're big puzzles, like what will dogs eat pretty
Speaker 1: much anything? Will they eat dark matter?
Speaker 2: Well, I've seen them eat various dark matters for sure. Y.
Speaker 1: Yeah, I know it's coming in and out both ends.
Speaker 1: That's not good. But yeah, even dogs can be physicists
Speaker 1: if they also are trying to figure out how the
Speaker 1: universe works, how things fall, and what rate do they fall.
Speaker 1: And that's something that even physicists today are looking at
Speaker 1: and are puzzling about.
Speaker 2: That's right, And we're hoping that our dogs will help
Speaker 2: us figure it out and that it won't be too
Speaker 2: rough a journey.
Speaker 1: So welcome to our podcast, Daniel and Jorge Explain the Universe,
Speaker 1: a production of iHeartRadio.
Speaker 2: Where no pun is too corny, no mystery too grand,
Speaker 2: and no puzzle too deep for us to explore. We
Speaker 2: think that everything out there can be understood, and that
Speaker 2: you deserve to understand it. We want to make these
Speaker 2: ideas click together in your mind so you have that
Speaker 2: aham moment when it all makes sense.
Speaker 1: It's right because we are here to dis because the
Speaker 1: fundamental loss of the universe and also the fundamental laws
Speaker 1: of the universe testing its limits. Are there limits? I
Speaker 1: think we just hit that limit.
Speaker 2: If you compress too many dad jokes into a podcast,
Speaker 2: does it collapse into a black hole?
Speaker 1: Does it become a granddad podcast? Now?
Speaker 2: And there are physics questions about gravity that we ask
Speaker 2: that are not related to punts.
Speaker 1: Yeah. Gravity is one of the biggest mysteries in the universe.
Speaker 1: It basically holds everything together and makes all the stars
Speaker 1: and galaxies out their work. But there are a lot
Speaker 1: of big things about it that we still don't understand.
Speaker 2: It's one of my favorite things in physics where something
Speaker 2: right in front of you is a big mystery. You
Speaker 2: don't need a ten billion dollar particle collider to ask, like, well,
Speaker 2: why do things move? Or why am I sticking to
Speaker 2: the Earth, or why does the Earth go around the Sun?
Speaker 2: You just look at the world around you and ask
Speaker 2: these basic questions. And our understanding of how this very simple,
Speaker 2: everyday experience happens has changed over decades and centuries and millennia.
Speaker 1: Yeah, gravity is I kind of a big deal. It's
Speaker 1: a heavy topic. It's a massive question that physicists have
Speaker 1: about how the universe works. And it's not just in
Speaker 1: front of us. It's all around us, under us, low us,
Speaker 1: behind us, on top of us, but well, hopefully not
Speaker 1: too on top of us.
Speaker 2: If you're listening to this podcast, Deep Deep Underground, then yes,
Speaker 2: it's on top of you. And an important way to
Speaker 2: make progress in these big questions is to look for patterns.
Speaker 2: When Newton noticed that the same laws could be applied
Speaker 2: to the motions of things in the heavens as on Earth,
Speaker 2: he understood that his theory was more general than just
Speaker 2: describing planets, that a single idea encompassed all of it.
Speaker 2: So looking for clues means looking for patterns, finding apparent
Speaker 2: coincidences and digging into them to figure out what the
Speaker 2: underlying mechanism really is.
Speaker 1: Yeah, and sometimes in looking for patterns, physicists notice certain
Speaker 1: things match up in a very suspicious and interesting way,
Speaker 1: and so it makes them wonder is this a coincidence
Speaker 1: or does this reveal something fundamental about the universe?
Speaker 2: Like if you just lost two hundred bucks and then
Speaker 2: your friend is like, hey, I have an extra two
Speaker 2: hundred bucks to spend, you might think that there's an
Speaker 2: explanation that tells the whole story.
Speaker 1: Yeah, obviously you need better friends.
Speaker 2: Obviously, dinner's on your friend tonight.
Speaker 1: Yeah, obviously you're eating scrats with the dog tonight.
Speaker 2: Sounds like it.
Speaker 1: So today on the podcast, we'll be tackling the question
Speaker 1: what's the difference between inertial and gravitational mass.
Speaker 2: It turns out there's a massive conceptual difference, but almost
Speaker 2: no actual difference.
Speaker 1: All right, well, it sounds like it's a detail we're
Speaker 1: going to dig into here today. I guess the idea
Speaker 1: is that there are different kinds of masses in physics.
Speaker 2: There are different kinds of masses in physics, and that
Speaker 2: comes from just having different kinds of experience. You know,
Speaker 2: we live in the world, we describe what we see,
Speaker 2: and the job of physics is to boil down all
Speaker 2: of those experiences into as few concepts as possible, to say,
Speaker 2: can we explain static electricity and lightning with one idea?
Speaker 2: If possible, then that'd be a great success. And so
Speaker 2: we have lots of different experiences of masks and the
Speaker 2: goals to try to like boil it down into just
Speaker 2: one explanation, a holistic view that explains the entire universe.
Speaker 1: I wonder, is it kind of like having a separate
Speaker 1: space in your stomach for dessert, Like, is some of
Speaker 1: my mass due to dessert and some of it is
Speaker 1: due to regular food.
Speaker 2: Some of my mass is definitely due to dessert, for sure,
Speaker 2: and there's always room for dessert. I'm not sure if
Speaker 2: that's black hole creation in my stomach or what.
Speaker 1: And if you throw white chocolate into a black hole,
Speaker 1: what happens? Does it explode?
Speaker 2: The black hole does something magical? It turns the white
Speaker 2: chocolate dark, not into dark chocolate, unfortunately, but it just turns
Speaker 2: it into more black hole.
Speaker 1: That's how we're going to say that black hole spits
Speaker 1: out the white chocolate because it's so terrible.
Speaker 2: The only thing that can survive a black hole is
Speaker 2: a white chocolate. No, I wish that were true. That
Speaker 2: would be fascinating.
Speaker 1: And then I thought you were going to say, the
Speaker 1: only thing that can survive a white chocolate is a
Speaker 1: black hole.
Speaker 2: No, it'd be interesting if you threw a white chocolate
Speaker 2: into a black hole and somehow it's quantum information was preserved,
Speaker 2: so you could come along and tell if a black
Speaker 2: hole had had white chocolate thrown into it or not,
Speaker 2: if it had been tainted by the disaster that is
Speaker 2: white chocolate.
Speaker 1: I see, you could shame it later.
Speaker 2: Or maybe black holes are like quantum erasers, deleting the
Speaker 2: tragedy that is white chocolate from the universe and doing
Speaker 2: us all a favor.
Speaker 1: Interesting. I think that's what we all need. It's like
Speaker 1: an incognito mode for a diet.
Speaker 2: I can eat this, but the calories don't count.
Speaker 1: Yeah, nobody knows why did.
Speaker 2: You turn that off? Ever, I guess you do need
Speaker 2: some calories.
Speaker 1: To survive, you know, it's a dietary privacy. But anyways,
Speaker 1: we're talking about the difference between inertial and gravitational mass.
Speaker 1: It seems that these are two separate concepts perhaps in physics,
Speaker 1: and the question is are they the same or are
Speaker 1: they different things? So, as usually, we were wondering how
Speaker 1: many people out there had thought about the difference between
Speaker 1: inertial and gravitational mass.
Speaker 2: Thanks very much to our army of volunteers who answers
Speaker 2: these questions for your education and listening pleasure. If you'd
Speaker 2: like to add your voice to the choir, we'd love
Speaker 2: to have you. Just right to us two questions at
Speaker 2: Daniel Andandhorge dot com.
Speaker 1: So think about it for a second. Do you think
Speaker 1: inertial and gravitational mass are the same. Here's what people
Speaker 1: have to say.
Speaker 4: Inertial mass is the mass that the higes gives, and
Speaker 4: I think it's the mass involved in like the force
Speaker 4: to change, like an object's velocity. And then gravitational mass.
Speaker 4: I really never knew how to defer the too.
Speaker 5: Inertial mass is how much an object readsists moving through space,
Speaker 5: how much force it would take to accelerate it, And
Speaker 5: gravitational mass has more to do with in a gravitational field.
Speaker 2: But I believe that they are equivalent.
Speaker 6: Well, I think that inertial mass represents how hard it
Speaker 6: is to change the motion off the given body, and
Speaker 6: that the gravitational mass represents how much the formation I
Speaker 6: think they is based on fabric that samebody calls us.
Speaker 7: I think the difference between inertia and gravitational mass is
Speaker 7: on the inertia is on the between the particles or something.
Speaker 7: I think that started in here. We have no idea
Speaker 7: a book, and like, I think it's like the connecting
Speaker 7: of the quarks and stuff, and that's what creates most mass.
Speaker 7: So most mass is just a bonding energy, so I
Speaker 7: think that's what energies.
Speaker 3: Inertial mass is a measure of how hard it is
Speaker 3: for an object to change its velocity, whether in magnitude
Speaker 3: or direction. As for gravitational mass, it's a measure of
Speaker 3: how much an object distorted the space time around it.
Speaker 3: I know there is a conundrum in classical mechanics around
Speaker 3: the fact that both these values are numerically the same,
Speaker 3: and I believe relativity has an answer for that, but
Speaker 3: I'm not quite sure what it is. So I'm waiting
Speaker 3: for you guys to explain.
Speaker 1: All Right, it's some nice, yeah, pretty deep guesses here.
Speaker 1: I like the one that says you need a whole
Speaker 1: podcast for that done that's the answer.
Speaker 2: Not done yet, we're still doing it.
Speaker 1: Well, you're listening to this, we already finished.
Speaker 2: Oh that's true.
Speaker 1: Yeah, yeah, we're working in the future.
Speaker 2: But yeah, these are great answers. People definitely know about
Speaker 2: these concepts, and some people even have ideas about their relationship.
Speaker 4: Yeah.
Speaker 1: I saw mentions of the Higgs boson here, I saw
Speaker 1: mentions of acceleration and energy. Sounds like this is going
Speaker 1: to be a pretty dense podcast.
Speaker 2: We're going to overcome some massive misunderstandings in people's brains.
Speaker 1: Yeah, it's a pretty heavy topic, so let's dig into it. Daniel,
Speaker 1: what is mass to a physicist? The non religious physicists, the.
Speaker 2: Non denominational idea of mass, I mean, mass to a
Speaker 2: physicist is just like a more mathematical and precise description
Speaker 2: of our experience, right. Physics is not trying to describe
Speaker 2: a universe you don't understand or that isn't familiar to you.
Speaker 2: We're trying to describe our universe, our everyday understanding of
Speaker 2: what it's like to be in the world, and that
Speaker 2: means explaining our intuitive experience, you know, the way that
Speaker 2: we live and we have this feeling that like you
Speaker 2: can pick something up that is hard, and you pick
Speaker 2: something else up and it's easy. Or you push on
Speaker 2: something and it's hard to get it moving, you push
Speaker 2: on something else and it's easier to get it moving,
Speaker 2: and that somehow that that might relate to, like how
Speaker 2: much stuff there is to something. You put another watermelon
Speaker 2: in the shopping cart and it's a little bit harder
Speaker 2: to get it rolling.
Speaker 1: So you're saying, the intuitive definition of mass is just
Speaker 1: how much stuff there is to something.
Speaker 2: Yeah, I think that's the most accessible and intuitive idea
Speaker 2: of what mass is. We think of it like the stuffiness,
Speaker 2: you know, like this has more scoops of basic universe
Speaker 2: stuff than something else.
Speaker 1: Like a rock has more stuff stuffed into it. Then
Speaker 1: let's say an air balloon.
Speaker 2: Yeah, it certainly does. You know, there are more atoms,
Speaker 2: it's denser. If you add up the amount of stuff
Speaker 2: in all those atoms in a rock, then there's more
Speaker 2: in that than in a balloon, for example. Absolutely, the
Speaker 2: job of physics isn't to like rely on these fuzzy
Speaker 2: concepts and just accept our intuitive understanding. It's to make
Speaker 2: a more precise mathematical description of what's actually happening, so
Speaker 2: we can extract from that some understanding of like what
Speaker 2: the rules of the universe.
Speaker 1: Are, right, because I guess there are kind of two
Speaker 1: kinds of mass, right, Like there's a measure of how
Speaker 1: hard something is to push to get a going, and
Speaker 1: then also how hard it is to lift up from
Speaker 1: the ground.
Speaker 2: Exactly, there's two different things you can do to stuff. Right.
Speaker 2: You can push that shopping cart filled with watermelons, and
Speaker 2: you know, if you put more watermelons in it, it
Speaker 2: takes a bigger push. And then there's also like actually
Speaker 2: lifting the shopping card of watermelons over your head, and
Speaker 2: the more watermelons that are in there, the more force
Speaker 2: it takes. And those are actually two separate concepts, right,
Speaker 2: they're related in that more watermelons makes it harder. But
Speaker 2: if you're just pushing the watermelons, then you're not lifting
Speaker 2: them against gravity, right, You're just like speeding them up.
Speaker 2: And that's what we call inertial mass. It's just like
Speaker 2: how hard it is to get something going even in
Speaker 2: outer space. Right, things take a push to get moving
Speaker 2: even when there's no gravity.
Speaker 1: Right, Because the two things don't necessarily have to be
Speaker 1: the same, right, Like, you can't imagine a scenario where maybe,
Speaker 1: for example, there's a rock on Dolli with wheels in it,
Speaker 1: and it takes a certain amount of force to push
Speaker 1: it from side to side, but then it maybe takes
Speaker 1: no force to lift it up, or maybe take it's
Speaker 1: an extra bigger force to lift it up. Right, we
Speaker 1: could live in a universe where those two things are
Speaker 1: not the same.
Speaker 2: Yeah, or even just on a planet. Right, if you
Speaker 2: have a rock on Jupiter, then it takes a large
Speaker 2: force to counteract Jupiter's gravity, But it takes the same
Speaker 2: force to push its side to side on Jupiter as
Speaker 2: it does on Earth.
Speaker 1: All right, So then the two things are different, and
Speaker 1: so let's dig into it a little bit more. Talk
Speaker 1: about inertial mass.
Speaker 2: So inertial mass is just this sense that it takes
Speaker 2: a force to get something going. And this is basic
Speaker 2: Newtonian mechanics. Things tend to stay at the same velocity
Speaker 2: unless you give them a push. That push is a force,
Speaker 2: and so this is just f equals MAA. Right, you
Speaker 2: want something to speed up, you got to push on it,
Speaker 2: and the amount of speed up you get for that
Speaker 2: push depends on the thing's mass. So if it has
Speaker 2: a small mass, like if m is very very small,
Speaker 2: and you give it a big push, you get a
Speaker 2: big acceleration. But if it has a large mass, like
Speaker 2: the Earth or something, and you give it a push,
Speaker 2: then it gets a very small acceleration. F equals MA
Speaker 2: tells you that the larger the mass, the larger the
Speaker 2: force you need to accelerate something to speed it.
Speaker 1: Up, right, And so in this case, mass is the ratio.
Speaker 1: Like what happens You've divide the force you need to
Speaker 1: push on something to get it to a certain acceleration, right.
Speaker 2: Exactly, And this is a very familiar experience, right. Think
Speaker 2: about like firing a rifle. When you fire a rifle,
Speaker 2: it's pushing on the bullet to make it go fast,
Speaker 2: But the bullet is also pushing on the rifle. Why
Speaker 2: doesn't the rifle zoom the other way just as fast
Speaker 2: as the bullet. Well, because the rifle has more mass
Speaker 2: than the bullet. They have the same force applying on
Speaker 2: both of them, but the bullet is less mass, so
Speaker 2: it gets more acceleration.
Speaker 1: Or maybe think about it as like an asteroid in
Speaker 1: space that's not in a planet or anything. The more
Speaker 1: massive the asteroid is, the harder it is to get
Speaker 1: it moving, that's inertial mass.
Speaker 2: That's inertial mass exactly. So things that have this property
Speaker 2: we call it inertial mass, are harder to get moving,
Speaker 2: They're harder to speed up and harder to slow down.
Speaker 2: They have inertia. That's sort of what we mean by inertia,
Speaker 2: that we have inertial mass.
Speaker 1: All right, Now talk about gravitational mass.
Speaker 2: So gravitational mass is what control how much gravitational force
Speaker 2: is applied on you. And Newton also has a formula
Speaker 2: for this. It's gmm over R squared. We have two
Speaker 2: masses there because two things are pulling on each other,
Speaker 2: and more mass means more gravity. Like if you added
Speaker 2: mass to the Earth without changing its radius, if you
Speaker 2: made it more dense so got more massive, then it
Speaker 2: would be pulling on you harder. And so that's the
Speaker 2: gravitational mass. It's the mass that goes into the gravitational
Speaker 2: force formula.
Speaker 1: All right. Guess going back to our asteroid in space scenario,
Speaker 1: Like if you have an asteroid in space and it's
Speaker 1: close to a big planet, the big planet is going
Speaker 1: to pull the asteroid towards the planet, and so the
Speaker 1: mass of the asteroid is maybe a measure of our
Speaker 1: heart would it be to keep the asteroid from being
Speaker 1: pulled towards the planet? Like, if you're trying to prevent
Speaker 1: the asteroid from falling into the planet, how hard would
Speaker 1: it be? Depends that's gravitational mass exactly. More gravitational mass
Speaker 1: means more gravity. Imagine you're zooming next to two.
Speaker 2: Planets and one of them has more mass than the other,
Speaker 2: then you're going to feel it's gravity more strongly. Right,
Speaker 2: And this is a Newtonian picture of gravity, or gravity
Speaker 2: is a force and you can think about it sort
Speaker 2: of like the gravitational mass is like the charge for gravity.
Speaker 2: Two electrons will push on each other because they both
Speaker 2: have negative charge, and if you increase that charge, then
Speaker 2: their force would be stronger. Well, the force law for
Speaker 2: gravity is exactly the same structure as a force law
Speaker 2: for electromagnetism. Where you replace the charges with the masses.
Speaker 2: You increase the mass, you get more gravity.
Speaker 1: Right, Like a lightweight asteroid, you wouldn't a small lightweight asteroid,
Speaker 1: you wouldn't need to push very hard to keep it
Speaker 1: from falling into the planet. With a huge massive asteroid,
Speaker 1: you need to be superman basically to keep it from
Speaker 1: smashing into the planet. All right, Well, that's the basics
Speaker 1: of Newtonian inertial and gravitational mass. Now let's get into
Speaker 1: where it gets kind of tricky, and are these things
Speaker 1: the same or are they different? According to Einstein, So
Speaker 1: let's dig into those details. But first let's take a
Speaker 1: quick break. All right, we're asking a massive question here today.
Speaker 1: What's the difference between inertial and gravitational mass. Are they
Speaker 1: the same? Are they different? Are they just two sides
Speaker 1: of the same coin? Are there two coins? How many
Speaker 1: coins are there in the universe?
Speaker 2: An infinite number of coins, with an infinite number of sides,
Speaker 2: with infinite mass. Maybe it's made out of photons. Who knows.
Speaker 1: There we go, That would explain why money's so light
Speaker 1: in my pockets. All right, so we talked about kind
Speaker 1: of the basics of inertial and gravitational mass. I guess
Speaker 1: from a Newtonian perspective, so like a couple of hundred
Speaker 1: years ago that this is when you'dn figured out, is
Speaker 1: that you have something called inertial mass and you have
Speaker 1: something called gravitational mass. And he basically measured them to
Speaker 1: be the same thing, right, or he thought they were
Speaker 1: the same thing.
Speaker 2: He actually sort of treated them as different things, right.
Speaker 2: He wrote them down as if they were different numbers.
Speaker 2: Like he wrote two different formulas, and the masses in
Speaker 2: those two formulas didn't have to agree. Like in principle
Speaker 2: in Newtonian physics, mass in f egals ma could be
Speaker 2: different from mass in the gravitational force formula. So he
Speaker 2: allowed for the possibility that these were different.
Speaker 1: Wait, what do you mean. He didn't call them mass,
Speaker 1: he didn't call them m.
Speaker 2: Well, and Newton actually didn't write his equations down in
Speaker 2: terms of mathematics. Back then, the style was more pros
Speaker 2: so a lot of newton stuff is actually written out
Speaker 2: in sentences, so the exact notation can be a little different.
Speaker 2: But in our modern translation of Newton's formulas, technically there's
Speaker 2: a little I in front of the inertial mass and
Speaker 2: a little G subscript in front of the gravitational mass,
Speaker 2: and they don't necessarily have to be the same. In
Speaker 2: Newtonian physics, you have to go out and measure whether
Speaker 2: these things are the same.
Speaker 1: But did he do it? Did Newton measure it to
Speaker 1: be the same or did he measure it to be different?
Speaker 2: So Newton measured it using a pendulum, and lots of
Speaker 2: other people have done these measurements and we find that
Speaker 2: they are the same. And it's sort of a famous
Speaker 2: result that people learn about, you know, in elementary school,
Speaker 2: that two things, even if they have different mass, fall
Speaker 2: at the same speed. That's basically testing whether inertial and
Speaker 2: gravitational mass are the same thing. Something that has more
Speaker 2: mass takes a bigger force to get going, but if
Speaker 2: it has more gravitational mass also, then it gets a
Speaker 2: bigger force from the Earth. And so something that's low
Speaker 2: mass and something that's high mass will get accelerated the
Speaker 2: same way by the Earth. The Earth is pulling harder
Speaker 2: on the one with more mass, which takes more effort
Speaker 2: to get it going. So the two things perfectly balance out.
Speaker 1: I guess we're just lucky. Newton didn't have a dog
Speaker 1: when he ran his experiments, so it even ran this
Speaker 1: experiment and he measured it to be the same Did
Speaker 1: he then conclude that it was the same thing? Did
Speaker 1: he then start calling it the same thing?
Speaker 2: Newton's experiment was not super precise, so this is one
Speaker 2: hundreds of years ago, and the technology for timing things
Speaker 2: and measuring things precisely was much fuzzier. So he concluded
Speaker 2: these things were likely the same, but he had no
Speaker 2: proof theoretically that showed that they had to be the same,
Speaker 2: and he only had an experimental measurement which was kind
Speaker 2: of fuzzy. And so people continued on measuring these things,
Speaker 2: and they've been measuring it basically ever since. People are
Speaker 2: basically still measuring this to see if they can find
Speaker 2: any discrepancies.
Speaker 1: At some point, I guess in our scientific history, scientists
Speaker 1: sort of kind of concluded they were the same, didn't they.
Speaker 1: I mean, at least when you're in high school, you know,
Speaker 1: they just teach you M. They don't teach you M
Speaker 1: I and MG. They just teach you M.
Speaker 2: There is a sort of simplified version of it in
Speaker 2: high school. But in Newtonian physics, these are potentially different,
Speaker 2: which is why you know, astronauts on the Moon in
Speaker 2: the sixties did this experiment, you know, dropping a feather
Speaker 2: and hammer at the same time, and why in the
Speaker 2: last couple of decades people have made this even more
Speaker 2: precise with high tech torsion balances. The narrow this down
Speaker 2: to the one part in ten to the thirteen. But
Speaker 2: you know, from an experimental point of view that's not
Speaker 2: the same. That just says it's either the same or
Speaker 2: it's very very close together.
Speaker 1: But I guess I mean like sort of in I
Speaker 1: guess in our society and our culture, at least how
Speaker 1: they teach physics in high school, right in college at
Speaker 1: least in my time, people are just sort of assume
Speaker 1: they're the same thing.
Speaker 2: Well, I think there's a simplification there. It's sort of
Speaker 2: like when people tell you of the photon has no mass. Well,
Speaker 2: we're pretty sure the photon has either no mass or
Speaker 2: almost nos some very very small number, but we haven't
Speaker 2: exactly measured it to be zero. We've measured it to
Speaker 2: be close to zero within some tolerance. So it just
Speaker 2: depends on how precise you want to be with your language.
Speaker 2: According to these measurements, they seem like basically the same thing.
Speaker 2: But that's not the same as saying we understand why
Speaker 2: they have to be the same. Theoretically they're linked. It
Speaker 2: might just be a coincidence, all right.
Speaker 1: So then scientists have been sticking to it. They've been
Speaker 1: trying to do this experiment to see if these two
Speaker 1: things are the same. Would have the experiments found.
Speaker 2: The experiments have never found any discrepancy between gravitational mass
Speaker 2: and inertial mass. Galleo did this experiment with like things
Speaker 2: rolling down inclined planes. There's this apocryphal story of him
Speaker 2: dropping things off the leaning tower at Pisa, which I
Speaker 2: don't think ever happened. There really was this test on
Speaker 2: the Moon where they drop a hammer and a feather,
Speaker 2: because you know, this is only truth. There's no air resistance.
Speaker 2: Air resistance makes everything much more complicated. If the only
Speaker 2: force involved is a force of gravity and it just
Speaker 2: has to overcome the inertia, then those things should perfectly
Speaker 2: balance out if the inertial mass and the pavitational mass
Speaker 2: are the same. So nobody's ever found any violation of
Speaker 2: these two things being the same.
Speaker 1: Okay, So then I guess the question is are they
Speaker 1: actually the same or are they just being measured to
Speaker 1: be the same.
Speaker 2: Yeah, Like, is it a coincidence or is it really
Speaker 2: just two ways of looking at the same thing. And
Speaker 2: those are two very different ideas about how the world
Speaker 2: could work. It's sort of like the way the electron
Speaker 2: charge and the proton charge balance each other out. We think, exactly,
Speaker 2: does that mean that there's a fundamental relationship between the two,
Speaker 2: or do we live in a world where these two
Speaker 2: things just happen to balance, and that's why we live
Speaker 2: in this world. Right, Even if your experience of the
Speaker 2: world is the same and doesn't change any experiments, it's
Speaker 2: a very different story about how the world works, about
Speaker 2: which universe we live in.
Speaker 1: Okay, So what do we know about this question?
Speaker 4: So?
Speaker 2: Newton's answer is it's a coincidence. These are two different concepts,
Speaker 2: they appear in two different formulas, we measure them, they
Speaker 2: happen to be equal. End of the story. Newton says,
Speaker 2: there's no reason for these two things to be the same.
Speaker 2: They just happen to be. So. So Newton has two
Speaker 2: parameters and they just happen to be exactly the same value.
Speaker 2: But that seems like too delicious a clue. When we
Speaker 2: find coincidences like that in nature, we're like, hmm, maybe
Speaker 2: there's a simpler version of the story. Maybe we can
Speaker 2: explain these two sides of the coin in terms of
Speaker 2: one coin. And that's where Einstein comes in. Einstein has
Speaker 2: a very different explanation for why things always fall the
Speaker 2: same way, no matter how massive they are.
Speaker 1: Right to Einstein, gravity is not even a force, right that's.
Speaker 2: Right, and that's the basic answer. Einstein says, there is
Speaker 2: no gravitational force. You can never measure gravity. You can't
Speaker 2: feel gravity. The reason things fall is because they're actually
Speaker 2: just moving together to follow the shape of space. Einstein says,
Speaker 2: you're kind of asking the wrong question by saying why
Speaker 2: these two things equal. He says, there's only one thing.
Speaker 2: There is only inertial mass. There's no such thing as
Speaker 2: gravitational mass, because there is no such thing as a
Speaker 2: gravitational force.
Speaker 1: Right. According to Einstein, gravity is like the bending of
Speaker 1: space right, space time. That's what makes something fall to
Speaker 1: the ground or orbit around the planet or the sun.
Speaker 2: That's right. To Einstein, gravity is sort of like an illusion.
Speaker 2: You can never even feel it or sense it directly.
Speaker 2: Let's make sure we unpack that a little bit, because
Speaker 2: there are important ideas in there that we have to
Speaker 2: mentally import to understand what's going to happen next. I mean,
Speaker 2: what does it mean that there's no gravitational force. You
Speaker 2: can't measure gravity. Gravity kind of looks like a force.
Speaker 2: It certainly feels like we can measure it. Right. Gravity
Speaker 2: looks like a force because we can't see the curvature
Speaker 2: of space. We think things should move in straight lines
Speaker 2: because we don't see that space is curved. So when
Speaker 2: we see things move differently than we expect, Newton tells us, oh,
Speaker 2: there's a force there, But if you could see the
Speaker 2: curvature of space, you'd understand that it's just stuff moving
Speaker 2: along those curves. There's no force there. It's actually just
Speaker 2: free fall motion. So when you jump off a building,
Speaker 2: for example, and you fall towards the Earth, you're in
Speaker 2: free fall. There are no forces acting on you. From
Speaker 2: your point of view, the surface of the Earth is
Speaker 2: accelerating to towards you. And if you pulled out a
Speaker 2: gravitometer or an accelerometer like a scale, you would measure
Speaker 2: no acceleration. You're not accelerating. There is no force on
Speaker 2: you at all. F equals ma equals zero. Now standing
Speaker 2: on the surface of the Earth, you do measure acceleration.
Speaker 2: A gravitometer like a scale measures non zero acceleration. But
Speaker 2: that's not the force of gravity on you. That's the
Speaker 2: surface of the Earth accelerating up against the natural free
Speaker 2: fall motion of gravity. All acceleration is against the natural
Speaker 2: motion of gravity. So Newton says that the person on
Speaker 2: the surface is not accelerating and the falling person is
Speaker 2: being accelerated by the force of gravity. But Einstein says
Speaker 2: that the surface of the Earth is accelerating and the
Speaker 2: person falling has no acceleration. You will not sense any
Speaker 2: gravity there because there is no force there for you
Speaker 2: to measure with your accelerometer.
Speaker 1: Right, But I guess you still sort of have the
Speaker 1: concept of mass, right, because some things bend space time
Speaker 1: more than others. Like a feather, doesn't it bend space
Speaker 1: and time a little bit more or less than a
Speaker 1: bowling ball?
Speaker 2: Yes? Absolutely, But that's just the single concept of mass, right.
Speaker 2: That's like the inertial mass of the object. It controls
Speaker 2: how it bends space. But everything moves through bend space
Speaker 2: the same way, regardless of its mass. But that's just
Speaker 2: one concept in general relativity.
Speaker 1: What do you mean it's the same concept. So now
Speaker 1: Einstein said that the idea that they're identical doesn't matter.
Speaker 1: Beca is they're the same thing.
Speaker 2: He says, there essentially is only one idea here, the
Speaker 2: mass of the object, and that controls how it bends space.
Speaker 2: And it's the bending of space that controls essentially how
Speaker 2: these objects move.
Speaker 1: Right, But isn't there like a degree to which something
Speaker 1: bends space more than other things.
Speaker 2: Well, the bending of space actually doesn't come from mass,
Speaker 2: it comes from energy density. Mass doesn't have a unique
Speaker 2: property to bend space. It's really just the energy content
Speaker 2: of something which bends space. And you can bend space
Speaker 2: even if you don't have mass, like a box of photons,
Speaker 2: for example, can bend space.
Speaker 1: Right, right, I mean we've talked about this before in
Speaker 1: the podcast, that there really is no such thing as mass.
Speaker 1: There's really only energy. Right.
Speaker 2: That's a strong philosophical statement. I would say mass makes
Speaker 2: some sense, but in the end, when you look at it,
Speaker 2: it's basically another kind of energy. Yeah.
Speaker 1: Yeah, I mean I'm just going by what we wrote
Speaker 1: in our book.
Speaker 2: I don't think we said that mass doesn't exist. We've
Speaker 2: said that mass is internal stored energy.
Speaker 1: Yeah, so like all mass is energy, is what we said.
Speaker 1: But there is this weird property about energy that if
Speaker 1: you have concentrated energy bound to like a particle or something,
Speaker 1: then that particle is hard to move. Right. That's still
Speaker 1: what you would call inertial mass.
Speaker 2: But now when you say something is easier or harder
Speaker 2: to accelerate, you're adding in other forces to make that
Speaker 2: acceleration happen. If we're just talking about gravity, like the
Speaker 2: experiment of dropping a bowling ball or a feather, there
Speaker 2: is no way to accelerate it because gravity isn't the
Speaker 2: force and doesn't accelerate things. Things just move according to
Speaker 2: the curve of space. Other forces can provide acceleration. In fact,
Speaker 2: they are the only way to accelerate things. So they
Speaker 2: still have this concept of inertial mass that's separate from
Speaker 2: gravity for the other forces. But within gravity, there's just
Speaker 2: one concept of mass, the energy that helps bend space.
Speaker 2: That mass doesn't play a role in how things move
Speaker 2: through that space. So there's not a separate concept of
Speaker 2: inertial and gravitational mass in Einstein's relativity like there is
Speaker 2: in Newtonian gravity.
Speaker 1: Right, But then like more energy then also then bend
Speaker 1: space more around it.
Speaker 2: Yes, that's right, more energy density, bend space more around it.
Speaker 1: So what do you mean by Einstein said that it's
Speaker 1: all the same thing? Like it can all be explained
Speaker 1: by just the concentration of energy.
Speaker 2: In general relativity, these all flow from the same fundamental equations.
Speaker 2: Newton has two equations that are totally separate totally distinct,
Speaker 2: completely different descriptions. F equals ma a is one equation.
Speaker 2: F equals gmm over r squares the other. He has
Speaker 2: his law of inertia, and he has his law of gravity.
Speaker 2: For Einstein, these things all just flow from the concentration
Speaker 2: of energy density energy city bend space, and objects move
Speaker 2: through that bend space. But these things just all flow
Speaker 2: from the same set of equations. There's just one equation there.
Speaker 2: There's no room to like put in another equation with
Speaker 2: a separate value from mass. The separate equations are the
Speaker 2: other forces. Electromagnetism can accelerate objects, and that's a concept
Speaker 2: totally separate from gravity. It requires a concept of inertial mass.
Speaker 2: So if you involve the other forces, there are still
Speaker 2: two parameters there, but now there's only one for gravity
Speaker 2: thanks to Einstein.
Speaker 1: But I wonder if there's like a knob there, you know,
Speaker 1: like let's say I have I don't know, ten kilo
Speaker 1: jewels concentrated in a the size of a lemon. Now
Speaker 1: that amount of energy concentrated in one spot, it's going
Speaker 1: to be a little bit hard to move. That's inertial
Speaker 1: mass of the lemon. But then also that lemon is
Speaker 1: bending space time around it to a certain degree, wouldn't
Speaker 1: I call that gravitational mass, Like you can imagine ten
Speaker 1: kilo jewels of energy bending space a lot in one
Speaker 1: universe and bending space not much at all in another universe.
Speaker 2: So the lemon nd space and causes curvature. But from
Speaker 2: a gravitational point of view, it has no meaning to
Speaker 2: say it's hard to accelerate the lemon, because gravity doesn't
Speaker 2: accelerate things. The lemon and a pebble and a bowling
Speaker 2: ball all moved through that curved space the same way gravitationally.
Speaker 2: If you bring in other forces like rockets, then you've
Speaker 2: reintroduced inertial mass, but not gravitationally. There is another nub there.
Speaker 2: That's the gravitational constant, right, which appears in Newton's formula
Speaker 2: but also appears in general relativity. But that affects everything, right,
Speaker 2: That affects how much mass is going to bend space.
Speaker 2: So you crank G up and then the same amount
Speaker 2: of mass is going to bend space more right, But
Speaker 2: that's simultaneously automatically also going to change how things move,
Speaker 2: because things move just following the curvature of space. So
Speaker 2: That's the beautiful thing about GRS that it tells you
Speaker 2: that the way things move through space doesn't depend on
Speaker 2: their mass. It only depends on the geometry of space.
Speaker 2: It's purely geometric. So the reason, for example, that the
Speaker 2: feather and the hammer fall at the same rate is
Speaker 2: because they are both just following the curvature of space,
Speaker 2: regardless of what their mass is. So if you crank
Speaker 2: up g you get more curvature and that changes how
Speaker 2: everything moves.
Speaker 1: Right, But the bowling bustle has more inertial mass, right,
Speaker 1: So why does it move at the same rate as
Speaker 1: a feather.
Speaker 2: Because motion through space doesn't depend on your mass.
Speaker 3: Right.
Speaker 2: You have to get rid of this idea of inertial
Speaker 2: mass affecting how you're going to move. What affects how
Speaker 2: you move is just the curvature of space, just the
Speaker 2: geometry of space time. The way to look at it
Speaker 2: is not that both the bowling ball and the feather
Speaker 2: are being accelerated the same amount. That's Newtonian and requires
Speaker 2: gravitational forces balanced by inertia. The way to look at
Speaker 2: it is that the bowling ball and feather move the
Speaker 2: same way through space time. Neither of them is accelerating.
Speaker 2: They're both in free fall. What's accelerating is the surface
Speaker 2: of the Earth rushing up to them, so of course
Speaker 2: it reaches them at the same time.
Speaker 1: Well, maybe it would help to understand a little bit
Speaker 1: more how gravity causes things to move and this idea
Speaker 1: of pseudo forces. So what do you mean, Like gravity
Speaker 1: is a pseudo force.
Speaker 2: So electromagnetism is a real force. It like accelerates stuff, right,
Speaker 2: It pushes and it pulls. That's what we mean by
Speaker 2: a force. But a pseudo force is when something appears
Speaker 2: to move without a force being applied to it, right,
Speaker 2: And this is not unfamiliar to you. Like if you're
Speaker 2: in the back of a truck and there's a bowling
Speaker 2: ball there and somebody hits the gas, Then to you
Speaker 2: in your frame of the back of the truck, the
Speaker 2: bowling ball is going to move. They hit the gas,
Speaker 2: the bowling ball is going to move to the back
Speaker 2: of the truck. They hit the brakes, the bowling ball
Speaker 2: is going to move to the front of the truck.
Speaker 2: So you're seeing, like this ball move even though nobody's
Speaker 2: pushing on it, right, nobody's pulling on it, nobody's applying
Speaker 2: any force to it, but you're seeing the ball accelerate,
Speaker 2: so there's a pseudo force there. Something is happening to
Speaker 2: accelerate this thing even though there's no forces on it.
Speaker 2: And in the same way, for example, if you're out
Speaker 2: in space and you're in a rocket ship and your
Speaker 2: rocket ship is accelerating and you drop a ball, then
Speaker 2: that ball is going to fall to the floor. How
Speaker 2: you can get the appearance of gravity on a spaceship
Speaker 2: if you're accelerating, So that's a pseudo force, right. Basically, acceleration,
Speaker 2: any accelerating frame gives you a pseudo force. There's no
Speaker 2: gravity on the spaceship. It's just the floor is accelerating
Speaker 2: up to meet the ball that you've dropped it. All right,
Speaker 2: So that's the concept of a pseudo.
Speaker 1: Force, like in those space movies where they have like
Speaker 1: a rotating spaceship or something, and this interpretive force makes
Speaker 1: it feel like there's gravity around you.
Speaker 2: Exactly, that's right, yeah, but there's.
Speaker 1: No actual gravity happening.
Speaker 2: There's no actual gravity there. It's just acceleration that's creating
Speaker 2: this pseudo force. And so now Einstein says, well, curvature
Speaker 2: of space time, which is invisible to us, we can't see.
Speaker 2: It also causes pseudo forces. Like if you're out in
Speaker 2: space and you drop a ball and somewhere near the Earth,
Speaker 2: it's going to drift towards the Earth, and somebody watching
Speaker 2: you do this experiments from sort of far away is
Speaker 2: going to notice, hmm, there seems to be a force
Speaker 2: on this ball, and that's what Newton would call the
Speaker 2: gravitational force. But Einstein would say, no, there's no actual
Speaker 2: force there. It's moving because of a pseudoforce. It's moving
Speaker 2: because actually just following the curvature of space time. You
Speaker 2: can't see that curvature. It's not obvious to you, but
Speaker 2: the ball is following the curvature of space time, and
Speaker 2: to us it looks like there's a force on it,
Speaker 2: even though there's not. The ball is not actually accelerating.
Speaker 1: So you're saying, like what we think of it as
Speaker 1: gravity is really just pseudo gravity, right, kind of like
Speaker 1: when you have like a black hole and it's bending
Speaker 1: space time around it, it's sort of like causing acceleration
Speaker 1: around it or something. It's bending space time so that
Speaker 1: there's acceleration so that it feels like something is pulling
Speaker 1: us down.
Speaker 2: So yeah, masses definitely bend space time. But the issue
Speaker 2: of acceleration is a little bit subtle. Like if you
Speaker 2: are that ball that's falling towards the Earth, you don't
Speaker 2: feel any acceleration, just like if you jump off of
Speaker 2: a building. Before you hit the ground, you feel like
Speaker 2: you're in free fall. You feel weightless. Right, so you
Speaker 2: never actually experience gravity. You never feel gravity accelerating you.
Speaker 1: Okay, but to somebody standing far away, it does look
Speaker 1: like you're accelerating, right.
Speaker 2: That's right, that's where the pseudo force comes. Then somebody
Speaker 2: else in an inertial frame would say, oh, there's a
Speaker 2: force on you. You're falling down towards the center of the Earth,
Speaker 2: or you're falling in towards that black hole, and you're
Speaker 2: accelerating relative to them. They're seeing that pseudo force. But
Speaker 2: Einstein says, there's no force there. It's just things moving
Speaker 2: according to the curvature of space time. Right.
Speaker 1: All right, Well, let's dig a little bit more into
Speaker 1: this detail and how it compares to inertial force, how
Speaker 1: Einstein may be grappled with the idea of inertial mass,
Speaker 1: and maybe where mass even comes from. So let's dig
Speaker 1: into those details. But first, let's take another quick break.
Speaker 1: All right, we're talking about the difference between inertial and
Speaker 1: gravitational mass, and it's getting a bit hairy, Daniel, I
Speaker 1: feel like, because I feel like we're once again trying
Speaker 1: to explain really difficult general relativity special relativity topics on
Speaker 1: an audio podcast, and so it can be a little
Speaker 1: bit confusing. But it sounds like what you're saying is
Speaker 1: that Einstein sort of puts the whole question kind of
Speaker 1: in the nonsense category, like it doesn't make sense to
Speaker 1: even compare gravitational and inertial mass because to Einstein, there
Speaker 1: is no such thing as gravitational mass.
Speaker 2: Yeah, exactly. And it's sort of beautiful because he still
Speaker 2: does manage to sort of like explain what we see,
Speaker 2: Like we see these interesting things like a big ball
Speaker 2: and a little ball fall at the same rate, and
Speaker 2: he can still explain that and explain it in this
Speaker 2: gorgeous geometrical explanation, and he does so by saying that
Speaker 2: there is no ambiguity between the inertial and gravitational masses.
Speaker 2: There's just one mass.
Speaker 1: Well, Nick, if I can ask a question and maybe
Speaker 1: take us deeper into the black hole, rabbit hole here.
Speaker 1: So we're imagining this scenario where we have a bawling
Speaker 1: ball and a feather, and let's say they're near a
Speaker 1: black hole. Now you're saying that to somebody standing far
Speaker 1: away from this scenario, they're both going to accelerate and
Speaker 1: move towards the black hole at the rate. Because that's
Speaker 1: so gravity works.
Speaker 2: Right, because things move through space time regardless of their mass. Right,
Speaker 2: Your mass does not affect in general relativity how you
Speaker 2: move through space.
Speaker 1: Time, right, right, And even though the feather has less
Speaker 1: inertial mass than the bowling ball, the balling ball will
Speaker 1: we definitely for sure, right, I think it has more
Speaker 1: inertial mass.
Speaker 2: But even just saying the phrase inertial mass implies F
Speaker 2: equals MA. That's the formula that apears in so puts
Speaker 2: you in a Newtonian point of view, right, So, like
Speaker 2: the phrase inertial mass doesn't really belong in a conversation
Speaker 2: about general relativity. There's just mass.
Speaker 1: Well, like if I were to strap a rocket to
Speaker 1: my bowling ball and a strap a little rocket to
Speaker 1: my feather, I would need to expend more energy in
Speaker 1: that rocket to move the bowling ball than the feather.
Speaker 2: If you want to add in other forces electricity or
Speaker 2: rockets or whatever, then you bring back inertial mass. But
Speaker 2: for Einstein's gravity, there's just one mass, the one that
Speaker 2: bends space time. Think about your big ball and your
Speaker 2: little ball on the surface of the Earth, right, what's
Speaker 2: happening there, Well, both of them want to be sort
Speaker 2: of falling towards the center of the Earth to follow
Speaker 2: the natural motion of the Earth. Both of them are
Speaker 2: not because the Earth is pushing back up on them, right,
Speaker 2: And so really what's happening there is like their Earth
Speaker 2: is accelerating them up at the same rate so that
Speaker 2: they don't fall towards the center of the Earth.
Speaker 1: I guess maybe if we can go back to the
Speaker 1: feather and the bowling ball, Like, if I have the
Speaker 1: feather in the bowling ball in space, nothing around it,
Speaker 1: no black hole, no planet Earth, and I wanted to
Speaker 1: move them one meter, I would need more energy to
Speaker 1: move the bowling ball than the feather, right, I don't
Speaker 1: need a bigger force.
Speaker 2: Yeah, if you're out in deep space and there's no
Speaker 2: gravity in your by so space is totally flat, then
Speaker 2: these things just sit there if you don't apply force
Speaker 2: to them, And if you do apply force to them,
Speaker 2: then they will accelerate. That You can sort of use
Speaker 2: Newtonian mechanics in this context because there is no curvature
Speaker 2: to space. And if you want to apply other forces,
Speaker 2: ones that generate real acceleration, then you bring in inertial mass. Again,
Speaker 2: but that concept doesn't exist in gravity anymore.
Speaker 1: Right, and so in this case there is something calling
Speaker 1: our like it takes a bigger force to move the
Speaker 1: bowling ball on space.
Speaker 2: Takes a bigger force to move the bulling ball. Yes,
Speaker 2: Newton would say, that's inertial mass.
Speaker 1: That's inertial mass. Okay, Now let's put the feather and
Speaker 1: the bowling ball near a black hole and I let
Speaker 1: go of them. You're saying, because of Einstein and the
Speaker 1: way the black hole is bending space time around it,
Speaker 1: the feather and the bowling ball are going to fall
Speaker 1: towards a black hole at the same rate, because that's
Speaker 1: how space time is bent around.
Speaker 2: That's right, they both follow space time regardless of their mass.
Speaker 1: Right. But now let's say I put little rocket. It's
Speaker 1: in the feather and in the bowling ball, and I'm
Speaker 1: trying to prevent these things from falling into the black hole.
Speaker 1: To an outside observer far away from this catastrophic scenario.
Speaker 1: Don't I need to push the bowling ball harder or
Speaker 1: expand more energy in my rocket to keep the boiling
Speaker 1: ball from falling into the black hole than the feather?
Speaker 2: Yes, in general relativity, if you don't want to follow
Speaker 2: the curvature of space time, then you need a force, right,
Speaker 2: That's what forces are. Essentially, anytime you're accelerating, is accelerating
Speaker 2: to avoid just following the curvature of space time. And so, yeah,
Speaker 2: you need a force to push on these things. And yeah,
Speaker 2: I think you need a bigger force to push on
Speaker 2: the bowling ball than the feather.
Speaker 1: Okay, so you're saying that my rocket on my bowling
Speaker 1: ball needs to push harder than the rocket on the
Speaker 1: feather to keep it from falling into the black hole. Right,
Speaker 1: so's just more of something there that needs to happen
Speaker 1: in order to keep them from falling into the black hole. Now,
Speaker 1: is that more of that something or is that something
Speaker 1: that there's more for the bowling ball? Is that still
Speaker 1: inertial mass or is that a different amount related to
Speaker 1: how much the black hole is bending space time?
Speaker 2: Yeah, here we're talking about real acceleration opposing the natural
Speaker 2: motion according to the curvature of space, and that has
Speaker 2: to come from something other than gravity, which means a
Speaker 2: real force, and that brings in inertial mass. Again, yes,
Speaker 2: but again, there's no inertial mass in gravitational motion. The
Speaker 2: reason the bowling ball and the feather fall towards the
Speaker 2: black hole at the same rate without rockets.
Speaker 1: So it's the same as inertial mass.
Speaker 2: Then yeah, when you bring in the other forces, there
Speaker 2: will be inertial mass again, but within gravity itself there
Speaker 2: isn't one anymore. Like the reason that you do not
Speaker 2: fall towards the center of the Earth is because the
Speaker 2: surface of the Earth is pushing you up exactly the
Speaker 2: same way that rocket is accelerating the bowling ball away
Speaker 2: from the black hole. The surface of the Earth is
Speaker 2: pushing you up away from gravity. And if you drop
Speaker 2: a ball. Newton says, oh, that ball is accelerating towards
Speaker 2: the center of the Earth. Einstein says, no, when you
Speaker 2: drop the ball is when it stops accelerating. You are
Speaker 2: accelerating up away from the center of the Earth, like
Speaker 2: the bowling ball and the rocket, to avoid falling in
Speaker 2: and the ball is now in free falls now flowing
Speaker 2: naturally with gravity, it's stopped accelerating. That's why everything falls
Speaker 2: at the same rate, because it's really the Earth that's
Speaker 2: rushing up to meet it, rather than like the bowling
Speaker 2: ball or the feather that are falling. They're just like
Speaker 2: hanging out, not accelerating with respect to space.
Speaker 1: Right, And so in that sense, it's the same thing,
Speaker 1: like inertial mass is the same as gravitational mass. But
Speaker 1: I guess my question now leading up to this is,
Speaker 1: let's say we lived in a universe in which gravity
Speaker 1: were differently, Like the amount of space time bending that
Speaker 1: a black hole does is different in my universe and
Speaker 1: in your universe. Like in my universe, the black hole,
Speaker 1: if you constantly constant dam much energy into a spot,
Speaker 1: doesn't bend space time very much, like almost not at all.
Speaker 2: You're changing the value of G.
Speaker 1: Yeah, changing the value of G.
Speaker 2: Okay, you're making it the value of J, the whorege value.
Speaker 1: Okay, yeah, it's the J constant that's right, for which
Speaker 1: I'll get I'm sure i'll get an oval price. But
Speaker 1: in your universe G is huge. So like the black
Speaker 1: hole bends spacelime a lot, and so space in your universe,
Speaker 1: space is rushing towards the black hole a lot, super fast,
Speaker 1: a lot, And whereas in my universe, let's say it,
Speaker 1: it means even zero. So now wouldn't in my universe
Speaker 1: I would need less to spend less energy in my
Speaker 1: rockets to keep the balling well from falling into the
Speaker 1: black hole, whereas in your universe I would need a
Speaker 1: lot of energy to keep the bowling ball from falling
Speaker 1: into the black hole.
Speaker 2: Yes, the force you need does depend on the gravitational constant,
Speaker 2: because you're pitting gravity against non gravitational forces, which do
Speaker 2: have a concept of inertial map. And when you fight
Speaker 2: against the curvature with other forces than the relative strength
Speaker 2: of curvature and those forces matters.
Speaker 1: I guess maybe where I'm going with this is that
Speaker 1: you're sort of making it sound like there is no
Speaker 1: coincidence anymore with Einstein's relativity. But I wonder, and again
Speaker 1: I'm not an expert. I'm just kind of intuitively following
Speaker 1: my sense of intuition here. I wonder if it's still
Speaker 1: sort of a coincidence. You just move the coincidence somewhere else, I.
Speaker 2: Think, to me, the way to answer that question is
Speaker 2: just to think about the bowling ball and the feather
Speaker 2: without the other forces, because it's the fact that the
Speaker 2: bowling ball and the feather fall at the same rate that,
Speaker 2: in Newton's view, means these two things have to be equal, right,
Speaker 2: That's where the coincidence comes from. And Einstein says that
Speaker 2: the bowling ball and the feather have to follow the
Speaker 2: same rate because they're just following me the curvature of
Speaker 2: space time. Even if you crank up G. If you
Speaker 2: crank up G to the new Joorge value, so now
Speaker 2: everything is crazy curved, then the bowling ball and the
Speaker 2: feather are going to fall into the black hole at
Speaker 2: the same rate. They'll fall faster than in a universe
Speaker 2: without crazy G, but they will both fall into the
Speaker 2: black hole the same rate. If you relax G downs
Speaker 2: so that space is curved less by mass, it's harder
Speaker 2: to make black holes or whatever, then the bowling ball
Speaker 2: and the feather are going to fall in more slowly,
Speaker 2: but they're still going to fall at the same rate.
Speaker 2: Doesn't that answer the question?
Speaker 1: Okay, so you're saying that in your universe with the
Speaker 1: big G, the feather and the bowling bell would fall
Speaker 1: really fast towards a black hole, whereas in my universe
Speaker 1: with the little G they would fall slowly.
Speaker 2: Mm hmm.
Speaker 1: Okay, But in both universes, if there is no black hole,
Speaker 1: they would Both the feather and the bowling ball would
Speaker 1: have different inertial masses to each other, but they would
Speaker 1: The bowling ball in my universe would have the same
Speaker 1: inertial mass as the bowling ball in your universe.
Speaker 2: Yes, for the real forces, you still have inertial mass.
Speaker 2: But the coincidence within gravity is explained by Einstein since
Speaker 2: gravity now only has one mass instead of two.
Speaker 1: You see what I mean, Like there's inertial mas. I'm
Speaker 1: wondering if that inertial mass, which is the same in
Speaker 1: my universe in your universe, is different than the gravitational mass,
Speaker 1: which is different in my universe and your universe because
Speaker 1: we have different gs, or I wonder if maybe the
Speaker 1: answer Maybe what's confusing me is that in both universes,
Speaker 1: the one with big G and litogy, we would in
Speaker 1: both cases we would still be wondering about the same thing.
Speaker 1: Like I wonder if both universes it would they would
Speaker 1: seem like coincidences that inertial gravity and gravitational gravity in
Speaker 1: a Newtonian sense, are the same.
Speaker 2: I think in both the big G universe and the
Speaker 2: little G universe, you'd have a big Newton and a
Speaker 2: little Newton, which would have developed their own laws of
Speaker 2: Newtonian physics, which would seem like there was a coincidence
Speaker 2: between them because they have these two different concepts, one
Speaker 2: of gravitational force from some gravitational mass that explains the
Speaker 2: apparent force of gravity. But then Big Einstein and Little
Speaker 2: Einstein would have come along and explain that there is
Speaker 2: no force operating there, that there really is just the
Speaker 2: one mass. And if Big Einstein and Little Einstein could
Speaker 2: talk to each other and compare notes, if both the
Speaker 2: universes are relativistic, then they would see that both universes
Speaker 2: are following their laws of physics. I think it's interesting
Speaker 2: that in one universe you have like a stronger reaction
Speaker 2: to energy density in terms of the curvature space than
Speaker 2: in the other, which will definitely change how things move.
Speaker 2: But in that universe things always agree, right, Like the
Speaker 2: two objects moving through the same space time move the
Speaker 2: same way regardless of their mass is the key.
Speaker 1: Okay, it sounds sort of like the main idea is
Speaker 1: that sometimes so we think it is a coincidence, it's
Speaker 1: really just a different way of looking at how the
Speaker 1: universe works.
Speaker 2: Yeah, exactly, that you can bring two different ideas together
Speaker 2: and click them into one larger idea. Where you thought
Speaker 2: you had the freedom to twiddle two knobs to whatever
Speaker 2: values you want, but turns out they're connected in some way.
Speaker 2: There's a relationship between the knobs twidt the one you
Speaker 2: have to twiddle the other. So really there's just one knob.
Speaker 1: Or at least it's one knob, and maybe I don't know,
Speaker 1: there could still be other knobs in the universe, but
Speaker 1: like the ones that affect how things move and how
Speaker 1: things get attracted to larger objects through gravity. You're saying,
Speaker 1: in this universe they're sort of connected. It's like one knob,
Speaker 1: mm hmm.
Speaker 2: Exactly in our unit. First, at least you're right that
Speaker 2: there are other knobs for the other forces, and those
Speaker 2: still have the concept of inertial mass. But within gravity,
Speaker 2: the apparent coincidence between those two knobs gravitational and inertial
Speaker 2: mass is explained because there is no inertial mass in gravity,
Speaker 2: because it doesn't accelerate anything because it's not a force.
Speaker 1: So then to answer the question of the podcast, there
Speaker 1: is no difference between inertial or gravitational mass, or is
Speaker 1: the answer that this question doesn't make sense?
Speaker 2: The answer is that there is still inertial mass for
Speaker 2: other forces, but within gravity, there's just one concept of mass.
Speaker 2: There's no separation between gravitational and inertial mass. There is
Speaker 2: just mass, and we can still understand why things fall
Speaker 2: at the same rate even in that context. Right, we
Speaker 2: don't have to worry about this miraculous balance between inertia
Speaker 2: and gravity because they are just two sides of the
Speaker 2: same coin. Inertia and gravity are wrapped up by Einstein
Speaker 2: into one idea that controls how things move through space.
Speaker 1: All right, Well, it was a heavy topic, but I
Speaker 1: think we made it through to the other side, or
Speaker 1: at least we did not fall to a black hole
Speaker 1: well discussing it, although maybe we should just add more
Speaker 1: dad jokes and puns so that we, you know, reach
Speaker 1: the event horizon.
Speaker 2: Yeah, and to me, thinking about these examples really helps
Speaker 2: you get more intuition for thinking about gravity as just
Speaker 2: a geometric thing. Doesn't matter what your mass is, you
Speaker 2: move through space the same way mends on your velocity, certainly, right,
Speaker 2: And like a photon flying near a black hole is
Speaker 2: going to have a different trajectory than a grapefruit traveling
Speaker 2: at five meters per second. Your velocity definitely matters, but
Speaker 2: not your mass, which is just a very different way
Speaker 2: of thinking about the universe. And I love how the
Speaker 2: story of physics is explaining everything we see in all
Speaker 2: of our experiences with different stories, stories that update through
Speaker 2: time to give us a different picture of how the
Speaker 2: universe works.
Speaker 1: Yeah, although your dog had been there, may it would
Speaker 1: have eaten the grip and we'd still be back at uh,
Speaker 1: not understanding any of this.
Speaker 2: My dog will eat almost anything.
Speaker 1: All right. Well, we hope you enjoyed that. Thanks for
Speaker 1: joining us, See you next time.
Speaker 2: For more science and curiosity, come find us on social
Speaker 2: media where we answer questions and post videos. We're on Twitter, Discborg, Insta,
Speaker 2: and now TikTok. Thanks for listening, and remember that Daniel
Speaker 2: and Jorge Explain the Universe is a production iHeartRadio. For
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Speaker 2: or wherever you listen to your favorite shows.