Daniel and Kelly’s Extraordinary Universe - How do we measure the gravitational constant?

Episode Date: April 20, 2023

Daniel and Jorge talk about the number that controls the strength of gravity and why it's so hard to measure.See omnystudio.com/listener for privacy information.

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Hey, Jorge, have you found your first gray hair yet? I have. I have quite a few of them, yeah. Although I like to think of them as silver, not gray. Ooh, that sounds like a good plan. Really lean into the dignity of aging. Well, I don't have a lot of dignity, but I am definitely aging. How about you?

How's your transition going to full Einstein hairstyle mode? I still have no silver hair. In fact, I'm thinking about dyeing my temples. Dying them, you mean like bleaching them to get gray hairs? Yeah, so people take me a little bit more seriously. Oh, I see. You want to look like one of those senior. established physicists with gray hairs exactly i want to increase my gravitas not just my personal

gravity yeah maybe your problem is you're increasing in width and not wisdom that was a weighty burn Hi, I'm Jorge. I'm a cartoonist and the creator of PhD comics. Hi, I'm Daniel. I'm a particle physicist and a professor at UC Irvine. And I was once accidentally C-Ced on an email where I was described as young-ish. Oh, all right. Yeah, that's good. But how long ago was this? Was this like 20 years ago? In which case, it was true back then.

Yeah, long enough that I shouldn't be telling that story anymore. Right. You're like, I was in my 30s and people were called me youngish. That's a better adjective than many other adjectives people can call you. Absolutely. I'd rather be youngish than oldish or stinkish. But anyways, welcome to our podcast, Daniel and Jorge, Explain the Universe, a production of IHeart Radio. In which we dig into the mysteries of this oldish universe

and our youngish attempts to understand it. We think that the universe should make sense to humans. We should be able to go out there and measure things about it, to figure it out, to unravel its mysteries and to explain it to each other. and that's our job on this podcast to unravel as many of those mysteries as possible and to explain them to you. That's right. It's our job to increase the gravity of your brain. Hopefully all of this amazing knowledge about the universe is maybe making more connections than the neurons in your brain and making your brain grow a little bit and also increasing the wisdom in there.

Because I guess knowing about the universe sort of increases your wisdom, right? If you know how the world works, that's sort of the definition of wisdom. Yeah, what other kind of wisdom is there other than knowing how the world works? if you lump like people and animals and society and all that kind of stuff into the world. And that's exactly what we're trying to do. We're trying to describe the world. And the way we do it is by telling these mathematical stories. We say there are relationships between these things.

We notice if you push on this thing a certain way, it goes a certain speed, or they don't move. If you don't push on them, all of these things are mathematical stories that we use to describe the universe that's out there. We hope to boil it down to a bunch of equations, which in the end, they're just describing what we see out there in the universe. That's right. We're trying to find the, what, the wisecrack of the universe? Is that kind of what the job of a physicist is? I hope there would be some humor in these stories.

You know, every good story has some comic relief in it, even mathematical stories. But I guess is wisdom the same as common sense? Do you think the universe has common sense? Absolutely not. Intuitive ideas about the universe. What makes sense to us from our limited experience here on Earth are not always reflective of what's really happening.

happening in the universe. You know, it made sense to Aristotle that things fell down, but that doesn't mean that everything always falls down or that down even means something when you're out in space far away from any gravity. Yeah, it is a pretty perplexing universe. And sometimes it sort of seems like it does things that don't make sense. And in fact, you can sort of ask the question whether humans will ever make full sense of the universe or if there are just some things about it that are sort of random, right? Or arbitrary. Yeah, there's lots of layers there. Are humans smart? enough to describe the workings of the universe in terms of our mathematics.

Is our mathematics actually the language of the universe itself or just our description of what we see? And philosophically, we aren't even sure if there is a single mathematical prescription that describes everything that happens out there in the universe. A whole group of philosophers believe in disunity that there might not be a single holistic description of the universe. So it's pretty complicated. But we do our best. We find these mathematical stories, which are equations. They relate things like force and acceleration or force and mass, all sorts of things. But they're not just equations.

The equations also have numbers in them, constants that describe the way the universe works. Yeah, the universe seems to have lots of constant and lots of numbers in them, like pi and I guess the expansion of the universe is also defined by a number. Yeah, that's right. The speed of light. All sorts of things seem to control the way that the universe works. And in lots of cases, we don't know why they have this value and not some. other value. Why is the universe expanding at this rate? Why is the speed of light not faster or slower?

Why are some of the forces strong and some of them are powerful? It seems like there's a control panel somewhere on the universe and all these things are just parameters. There's just like knobs on the control panel and you could have twirled them one way or another way and still gotten a universe. One very different from ours, but we don't know if there's a reason why the parameters have the values they do. I feel like every time you say that the universe has a control panel, I always imagine, for some reason, the Simpsons, you know, the opening scene with Homer sitting in front of like the control panel for the nuclear plant that he works at. I always always imagine that when you say the control panel of the universe. Like, is there a Homer Simpson about to spill some coffee or donuts onto the fabric of our universe?

Well, you know, that would explain maybe why the universe seems so crazy and bonkers sometimes because maybe there's an idiot in charge. Because it was designed by bad groaning. Exactly. Or because Homer Simpson is in charge. Yeah, either because there's a cartoonist who's the designer of the universe and we all know they can't be trusted. Man, are you saying God is the ultimate cartoonist or cartoonists are the ultimate gods? I'm saying if either those are true, then we're screwed.

No, wouldn't you want to live in a cartoon? Like if the universe was controlled by cartoon physics, I mean, wouldn't that be more fun? Wouldn't your job be more fun? my job would be impossible because there is no physics and cartoons. There don't seem to be any laws that anybody follows. It's just like make it all up as you go. So science is basically out the window. Is that your goal?

Well, to put you out of a job? Mech episode, I'm trying to embarrass us to the point where we don't know what he got as this anymore. But it does seem like there are these laws that describe what's out there. And sometimes in these laws, there are just numbers. Like if you look at Maxwell's equations or how electromagnetic radiation propagates to the universe, there are a couple constants in there. The permittivity of free space, for example.

All those things determine the speed of light. But these are just numbers that we measure in the universe. We don't have like a theoretical reason to say why it should be this number or the other number. It's just like an unknown parameter in the equations that we have to go out and do experiments to discover. Yeah, like you were saying, like the speed of light, it is 300,000 meters per second. but it could also be something else. And that's what you mean by a control knob. Like somehow when the universe was created,

somebody set that knob to 300,000 meters per second, but it could have been something else. Yeah, actually, I think it is something else. It's 300 million meters per second. Oh, that's what I said. There you go. Somebody fell asleep on the control panel, and the speed of light is slower over there in Pasadena

than it is down here, apparently. Well, there you go. Don't put me in charge of the knob because obviously I would set it to a thousand times the wrong amount. All right, Homer. But these constants are fascinating, and physicists look at them and they go, hmm, why this number? Why not some other number? Especially when the numbers are weird.

The numbers are like one or two. People are like, yeah, cool, that makes sense. But if the numbers are like 74 bajillion or 10 to the negative 32, people are like, that's really strange. It's got to be a story there. Right, because I guess if it's one, then that means that something canceled out, sort of, right? This is a really controversial way of thinking in theoretical physics to say that like numbers like one are natural, make sense that you know two things are related by a factor or close to one that means that it's a natural relationship and if the factor is really really big then you got to ask why what's going

on so why didn't things cancel out why are these things not in balance it's really kind of aesthetics it's not really driven by any deep principle in theoretical physics it's just like wondering why numbers are not close to one just preferring numbers close to one there isn't even really a great argument that I could make for why you would prefer numbers close to one. Well, they say one is the loneliest number. So maybe you're an introvert that sounds like the best number. Maybe the secrets to the universe are actually hidden in the names of 80s pop songs. Yeah, there you go.

Or in the lyrics, right? Maybe 80s pop stars are the gods of the universe. Yeah, maybe it's all just about ice, ice, baby. Yeah. Wasn't there a group called Genesis back in the 80s? There you go. Well, so there are all these amazing numbers that. seem to sort of control how the universe behaves and what it does and what the particles in

it all do. But we don't understand some of these constants. And in some cases, we don't even know exactly what they are, right? That's right. Sometimes we can do experiments to measure them very, very precisely. But some of these are a little slippery. Some of them are very difficult to actually nail down, especially one of the most fundamental constants in the universe. Yeah. So today on the program, we'll be asking the question. How do we measure the gravitational constant? G, uppercase G, that's how you call it? In physics, we call it Big G or the universal gravitational constant

because we want to distinguish it from little G, which is the acceleration due to gravity here on Earth, 9.8 meters per second squared, which everybody uses in their freshman physics class. And Big G is the number that appears in like Newton's equation for gravity. Do you think G has anyone asked G if it minds being called Big G? I'm glad that you're always thinking about these things from the point of view of the subject. You know, in physics we tend not to anthropomorphize everything, but I'm glad that somebody out there is looking out for the little Gs and the big Gs of the world.

Well, that's what cartoonists are here for, to anthropomorphize everything, even physics, I guess. But I guess it's big G, like you said, to distinguish it from the liturgy that I think most people are familiar with from like high school physics, right? Little G is the one that tells you the acceleration of gravity here on Earth. Like if you drop a ball, it's going to accelerate at 9.8 meters per second square. That's little G. Uppercase G is the more general gravitational constant. That's right. Little G is only relevant on the surface of the Earth.

If you go up in an airplane and you go deep down into the Earth, you're going to feel a different acceleration due to gravity because you're going to have a different amount of mass of the Earth or be a different distance from the Earth. And on other planets or in other solar systems, little Gs are totally irrelevant. number. You mean, there's like a medium G and a smallish G? There's a G junior and a G the third and all sorts of Gs, man. There's the OG, you know. There's a G whiz. But Big G is universal. It's supposed to reflect something about the universe itself and be independent of anything that happens on Earth or the size of the Earth or your distance from the Earth. It's something about the universe, not something about our neighborhood. Right. So this is like the G that relates to the action. force of gravity. Exactly. It's the number that controls really the strength of gravity in the

universe. Well, as usually, we were wondering how many people out there had thought about the uppercase G of the universe and how we might measure it. So thank you very much to everybody who answers these questions for this fun segment of the podcast. We love hearing your thoughts. And if you would like to share your thoughts for a future segment, please write to me to questions at Daniel and Jorge.com. Everyone wants to hear your voice. So think about it for For a second, how do you think the universal gravitational constant G is measured? Here's what people have to say. I assume gravitational constant G is unique to planet Earth, which exerts gravity upon us.

To calculate that constant, I would try to figure out how much force is necessary for us to go against the gravitational force of Earth, and then we know what the gravitational force itself is. I think we measure the gravitational constant by measuring how quickly galaxies are moving away from us, and stretching the space in between. This is an easy one for me to answer because I don't know what the gravitational constant G is, but I'm looking forward to hearing and finding out.

I guess it's through the observation of planets, stars, and other celestial bodies, and coming to a number that adjusts that motion to our other units of measuring. Probably something to do with the moon. See, we can estimate its mass, estimate the Earth's mass, then see what's going on there,

We can probably find a G. All right. Well, somebody here confused with little G. You know, they do look like, I guess. Do they, though? Big capital G and little G look pretty different. I sent this in an email, so I wrote explicitly Big G. I'm not giving a lot of partial credit on that one.

Oh, boy. There's pointage involved here? Do you get a grade? I'm handing out degrees over here. I don't think that's going to encourage people to call it. Well, look, if you want to get your PhD in podcast science, then, you know, you got to take it for credit. none of this past scale stuff i see i see but everyone gets an a though right yeah i'm a softy i'm not going to give you a little a or a capital a i give everyone a big a plus i'm a softy in the end all right

but some interesting answers here like some people are saying you can measure the gravitational constant by looking at planets and stars and how things move around in space yeah those are interesting ideas but fundamentally they don't work because they don't let you establish what g is because you don't know what the masses of those planets are and so there's too many unknowns in that equation. And somebody said it has something to do with the moon? Like maybe you can measure G using the moon. Yeah.

And again, you could measure G using the moon and the Earth if you knew very, very precisely the mass of the Earth and the mass of the moon. But if you don't, then you can't use that to measure G. All right, let's dig into it. Let's first of all define for our audience. What is the gravitational constant G? So the gravitational constant G is the number that defines the strength of gravity. and it appears in Newtonian gravity in his equation for the force between two objects that have mass.

So Newtonian gravity says that the force is big G times one mass, times the other mass, divided by the distance squared. So GMM over R squared. And that number G is the one that controls it. If G was bigger, you would have a larger force between objects. And if G was smaller, you would have a smaller force between objects of the same mass and at the same distance. So it's really just this like tunable parameter. And it's kind of what determines how strong the gravity is between two things, basically, right? Like what's the basic Newtonian formula for gravity?

Exactly. The Newtonian formula for gravity has big G in it. It's just GMM over R squared. And it's a similar structure to other forces, right? Like the electrostatic repulsion between two objects, like two electrons or whatever, has the same structure. And it also has a constant in front of it. It's a different constant. So each of the forces you can write using this kind of equation and each one has a constant in front of it that tells you how powerful the force is.

So like if you had two things floating out there in space, a mass one and a mass two, you can compute the force that attracts them together using this formula, right? You take the mass of one thing and then take the mass of the other thing. You multiply together. You divide by the square of the distance between them and then you take the number and that's what you multiply by G to get the force of gravity between them. Exactly. And if we lived in a universe where G was twice as big, or if the cartoonist at the control panel fell asleep on the knob and doubled big G, then all the forces of gravity would be twice as big. And if you divided G by a factor of two, if you made it twice as small, then the force of gravity would be twice as small. Yeah. And so that's why it's called the universal gravitational constant because it's supposed to be the same all over the universe, right? Like if you measure the gravity between two things here or in another planet or in another part of the galaxy,

you should be able to use the same constant G to calculate that force. Exactly. And one of Newton's great achievements was using this to describe gravity here on Earth between fairly small masses and small distances and gravity between planets and stars and moons to show that it works in lots of different settings over huge differences in masses and huge differences in distances. So he sort of unified the heavens and the Earth. in that sense. So yeah, it's supposed to be universal. Yeah, and it's pretty amazing that the formula is so simple.

If you think about it, right? It's like one multiplication, one division, and one squared. And boom, you can, like, decipher the workings of the universe, you know? Like, it's not like the 1.7th square root of the distance between them. No, it's like the square of the distance between them. And it's just like mass 1 times mass 2. It's not like mass 1 plus 17 divided by 5.2, you know. Yeah.

kind of cool and the structure sort of makes sense like first of all it has to be symmetric it can't be like mass one times mass two squared right because it needs to be the same force between mass one and mass two and mass two and mass one right it shouldn't matter which one you call mass one or mass two so it has to be symmetric it also makes sense that it's one over the distance squared because as things get further and further apart the force gets diluted over a larger and larger area and the surface area of that sphere grows with the distance squared. So it's the same way like if you have a light source like a star and you're twice as far away from it, then the same number of photons are now distributed over a larger sphere. That

sphere has four times the area. And so one over a distance squared really makes sense. And I think that's why it appears in all of the force laws, not just the one for gravity. The one for electromagnetism also has a one over distance squared. Right. It makes sense, but it didn't have to be that way, right? It could have been R to the 1.72 or something like that, right? Yeah, it could have been and there are actually theories of gravity that do change that that suggest that gravity changes at very small distances maybe or different accelerations. So it's not one over R squared. But one over R squared is also the simplest. But you're right. The universe didn't have to make sense and it doesn't have to be simple. It could be crazy complicated. All right. Well, that's the universal gravitational

constant uppercase G, which tells you the strength of the force of gravity in the universe. But as we know, gravity is not quite a force. And also, maybe this constant can change. So let's dig into that. But first, let's take a quick break. December 29th, 1975, LaGuardia Airport. The holiday rush, parents hauling luggage, kids gripping their new Christmas toys. Then, at 6.33 p.m., everything changed. There's been a bombing at the TWA terminal. Currently, the explosion actually impelled metal glass.

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All right, we're talking about the universal gravitational constant uppercase G. It basically kind of tells you the general strength of the force of gravity in the universe, right? Like if G was much bigger, then the gravity would be much stronger in the universe. If it was smaller, gravity would be much weaker. Exactly. And we don't know why it has this value. There's nothing in physics that says it should be this number. There's no set of equations you can use to like derive it or predict this value.

just something we have to go out and measure and discover in the universe. Right. So the origin of this constant is that it came from Newton's, right? Newton's laws about the force of gravity between like planets and the sun and things like that. But nowadays we think of gravity more like a bending of space. Does the gravitational constant G still come into play then? It actually does. The same constant G also appears in Einstein's equation.

So we've replaced Newtonian physics that says that there's a force. between masses and that pulls them together by saying actually there's no force there it just looks like a force what's really happening is that masses are bending space and when they move through that bent space it looks like there's a force on them and Einstein gives us equations that describe how that space is bent when mass is around and those equations the Einstein field equations also have constants in them and one of those constants is big G the same exact number and that shouldn't be a surprise because Einstein's field equations also reproduce all the predictions of Newtonian physics. Like Einstein and Newton agree about the force on the earth from the sun, for example.

Because, you know, Newtonian physics got a lot of stuff right. So it wouldn't make sense if they had totally different constants. Now, did Einstein sort of derive this constant independently? Or did he like start with Newton's equations and kept it in? You can't derive this constant, right? If we didn't have Newton and we just started with Einstein, he would have come up with his field equations and said, okay, but there's a number in it, and I don't know what that number is. Let's go out and measure it. In the same way that when we first got Newton's equations, there's a constant in there, and we have to go out and measure it. And Newton actually suggested some ways to go and measure this. So Einstein just sort of inherited this constant from Newton.

Interesting. All right, well, then what's the current value of what we think G or uppercase G is? So it's a really tiny number. It's 6.67 times 10 to the minus 11. And the units on it are kind of weird. It's meters cubed divided by kilograms times seconds squared. It's this very small number, like 10 to the minus 11. Whoa. So that's one of the reasons kind of why gravity is so weak, too, right? Because the G is such a small number.

That's exactly the reason why gravity is so weak. If G was much, much bigger, gravity would be much more powerful. And so this number is the number for G in our universe, and we don't know. Are there other universes out there with different values for G? have much more powerful gravity and they all collapsed into black holes a few seconds after being birth. Are the universes out there with even weaker Gs and those universes still haven't even made stars because there isn't powerful enough gravity to pull that stuff together? We just don't know if there are other options for this thing and why we have this value, but you're right,

it completely controls the strength of gravity and what's super weird about it being so small is that the other forces have much bigger constants, which is why gravity is so much weaker than all of the the other forces. I feel like you're blaming the gravitational constant here, but it could also just be like things don't have enough mass. Like maybe things were more massive. Do you know what I mean? And then the force of gravity would be stronger.

Yeah, exactly. There's a subtlety there in how you compare different forces. Like how do you compare electromagnetism and gravity? Well, you take objects that have mass and have charged like protons and you hold them apart at a certain distance and you calculate their relative strengths. And so, for example, if you hold two protons, like a centimeter apart, then you discover that gravity is 10 to the 33 times weaker than the electromagnetic force. But you might say, hold on a second. That's just because protons have

almost no mass and a big charge. If we lived in a universe where protons had tiny charge and huge masses, then you would say gravity is stronger. And yeah, you're absolutely right. But the kind of things that exist in our universe tend to have a certain amount of mass per charge. And that means that gravity ends up being really, really weak compared to electromagnetism. So, yeah, blame it on the constant or blame it on the particles, but it's somebody's fault. It's somebody's fault that they think that you don't weigh more or that you do weigh a lot. Everything is somebody's fault. Somebody else is the fault, right?

In this case, I think it is a fair comparison to say typical particles in the universe, what is their relative gravity versus their relative electromagnetic propulsion? And what you find is that they're not even close, right? And like gravity is weaker. It's not even a little bit weaker or a lot weaker. It's ridiculously weaker. It's 10 to the 33 times weaker. It's like negligible compared to the force of electromagnetism.

And that's due to this constant. Like electromagnetism has its own constant and it's just a much bigger number. Right. I think what you mean is like if I had two protons out there in space and I bring them close together, like the force of electromagnetism that's going to be repelling them is like 32 orders of magnitude more than the force of gravity bringing them together. Exactly. All right, well, let's dig into what it takes to measure the gravitational constant G.

It's pretty hard, right? Because as we're saying, gravity is super weak. Yeah, there's like three reasons why measuring big G is actually really, really hard. Number one is what you said, that gravity is weak. You know, it's not easy to measure these things because you need big masses. You can't really measure the gravity between two protons. It's so small that you could never really measure it. So you need bigger and bigger.

And that brings you to the second reason why it's so difficult, which is that it's hard to shield gravity from other things. Like you're always going to be feeling the gravity of everything else around you, you know, like your laboratory in the mountains and the earth. So it's hard to get like an isolated system to study gravity. What do you mean isolated? Like, because the earth is pulling you down with gravity, but you can still maybe measure gravity side to side, right? Like if I just put two balls in my table, technically they are being attracted to each other by gravity. Couldn't I measure that? Yeah, you certainly could, but they're also being attracted by the gravity of your wall

and the gravity of the tree outside and the gravity of the mountains nearby. And that's not true for other forces. Like for electromagnetism, you have positive and negative charges. And so you can shield things. You can balance all the forces out. So the electromagnetism is effectively zeroed out and study it at small scales. But for gravity, there's no way to shield your laboratory from the gravity of your surroundings, unless you get like really, really far away from everything.

What do you mean? Like I can't just conduct my experiment on a really tall tower or, you know, at the top of a mountain or maybe even on a satellite. Yeah, on a satellite would be great. The further you can get from other masses, the better you could do this experiment. So if you did your experiment measuring the gravitational strength between two objects, like out in the middle of a super bubble far away from everything, that would be great. But that's one of the challenges, right?

We don't have the way to do that experiment out in the middle of space. We have to do our experiments here in the vicinity of Earth, which has its own gravity. Well, it sounds like maybe the difficulty isn't like isolating in it. It's more like it's super weak, right? Because like you could do this experiment out in a satellite, right? And, you know, as it goes around the earth, things would cancel out anyways, right? Yeah, it's just one reason why it's difficult. The primary reason, I think, is that gravity is just so weak.

You know, you're trying to measure a very, very small effect. And it's swamped by all sorts of other effects. You know, if you have, for example, two masses and you want to measure the gravity between them, then you have to hope that there are no other forces bigger than the gravitational force also operating on those masses that would just swamp your measurement. You know, if there's like a tiny residual electric charge on these masses because you touch them and you got static electricity on them, it will be so much more powerful than the gravitational force you're trying to measure that it will just swamp your measurements.

Well, maybe we should paint a picture here for people. Like, how would you even design an experiment like this? Like, let's say I'm proposing to you, Daniel, that we go out up in the space shuttle or we go out in a rocket out to the International Space Station. I'm going to take two billard balls, put him, you know, 10 centimeters apart. And then I'm going to watch how long it takes them to get attracted to each other by gravity. What's wrong with that experiment? Yeah, you could do that. That would work.

Nothing is wrong with that experiment except that it requires going up to space. And also you have to account for all the other masses nearby, right? Like the space station is also going to be tugging on these things. And the space station is probably a lot more massive than the balls you brought. You can't bring super duper heavy balls up into space because you have limitations on the expense due to the launches. You mean, like I said, I have those two balls floating in front of me. They're being pulled together by the gravity they have with each other.

But maybe they're also being pulled apart a little bit by the space station around them, right? Or like if my fellow astronauts, it's to the right of me or to the left of me, it might influence how those two balls come together. Exactly. And because you're trying to measure something very, very small, then you need to be very, very accurate about your measurements and small changes in your results can lead to large changes in the results that you get. What if I just do it a lot? Or what if I tell everyone to stay still, not move in the space station? Wouldn't that give me

a pretty good experiment? Yeah, that would measure it. I don't think that would come close to the precision we have today. And also it would be really expensive. Everything out in space is very expensive and very complicated. All right. What are some of the other reasons that make it difficult? I think the last reason is just that there's no like relationship to the other constants. You know, the other forces, we think there might be some relationship with them. Electromagnetism and the weak forces can get bundled together into the electro weak force

and there's some unity there. We have theories about how the strong force might connect with that. And so we have like a unity of the forces. But gravity is by itself. We don't know how to bring gravity into quantum physics. So we have no like way to predict. or like constrain the value of this force you really just have to go out and measure it

there's no other way to analyze it right I always thought the hard thing about measuring the gravitational constant was that you know to get a measurement of it you sort of need to know like in our biller ball example you sort of need to know exactly what the masses of those biller balls are but it's hard to know what the mass of something is

if you don't already know the gravitational constant right isn't that one of the big problems like a chicken and egg problem like how do you measure gravity you need to know the mass of something, but to know the mass of something, you need to weigh it, for which you need to know the gravitational constant. Yeah, in the end, it comes down to what do you know first? If you know the masses of two objects, you can measure the force between them, and then you get Big G.

If you know Big G in the forces, then you can measure the masses between them. So the basic story of measuring Big G is finding a scenario where we already, for other reasons, know the masses of two objects that we can use to measure Big G. Big G. That's the struggle. That's why we can't, for example, have looked at the Earth and the Sun hundreds of years ago and used those to determine Big G because we didn't know the masses of the Earth and the Sun. To derive the masses of the Earth and the Sun from like their relative motion, you have to know the force between them and you'd have to know Big G. Well, maybe step us through then, like what's the history of trying to measure this universal

constant? So it goes all the way back to Newton, right? Newton described this relationship between stuff and there was a constant there and he suggested how you might measure this constant he said maybe if you had for example like a pendulum basically a heavy ball on a string and you brought it near something massive like a mountain then you might be able to measure the deflection of that ball as it's like tugged on by the mountain interesting bit of history though is that newton didn't write down big g he never wrote that down doesn't like appear in his works because newton was working in a time before we expressed our laws in terms of algebraic expressions. Back then, all of our physics was done in terms of sentences rather than in terms of algebra.

I thought you were going to say he did it in a time before we started body shaming our letters. No, so if you go back and like read the Principia, you know, he expresses his law of gravity in terms of a sentence. You know, he says they will be mutually gravitating towards each other at a rate relative to the reciprocal, the square of their distances. is, you know, he doesn't summarize it all in terms of mathematics. So he never actually wrote down Big G. It wasn't until a couple hundred years later that it started being called Big G.

But Newton had the basic idea. He's like, if you know the mass of a mountain and the mass of a pendulum, maybe you could make this measurement. Right. But again, that's kind of the problem. You don't really know the mass of the mountain. Well, what you could do is measure the mass of the mountain. You could say, I know the density of rock and I could measure the volume of the mountain.

And so from that, I could estimate the mass of the mountain. And this is actually what people did. The first measurements of Big G come from holding a pendulum near a mountain in Scotland and seeing how it deflected. No way. This actually works? This actually works. Yes. It was a huge project.

This was done in the 1770s. There's a mountain in Scotland. And it's a good choice because it's like isolated from other mountains. It just like sticks up. And it has like a nice symmetrical shape, which means that it was not super complicated to just. describe its shape and calculate its volume. And also it's like got really steep slopes. So you get kind of close up to its center of mass. Take the maximum effect. And there's like a whole team of people that spent like years up there making very precise measurements of pendulum with heavy

masses on them and measuring their deflection and surveying the mountain to try to estimate its volume as precisely as possible. It's a huge project. Wait what? So like if I hang a billard ball from a string, right? And hold it in front of me. It's going to hang straight down. But as I walk towards a big mountain, it's going to start to lean or get pulled and actually start swinging that way. Yeah, it will get pulled towards that mountain. So its resting position will not be straight down. If you follow the string up, it will not point perfectly towards zenith. It will be slightly deflected. And the bigger the mass of the mountain or the bigger the value of big G, the stronger that deflection. So if you know the mass of the mountain, then you can

measure big G. So this is the whole game is knowing the masses of two things and then measuring the forces between them. There's a fun little wrinkle here though. You might think that you also need to know the mass of the earth because that's also pulling on your pendulum. But if you know the volume of the mountain and the volume of the earth, which we do, then the angle of deflection of the pendulum depends on the relative densities of the earth and the mountain, which one is denser. So really, the experiment measures the density of the earth, which wasn't known at the time. Of course, knowing the density of the earth and the volume lets you calculate the mass of the earth and therefore let you get Big G.

I guess you could use this to like measure people's masses too. Like if you walk around a bitter ball on the string and just kind of walk around and get it close to people, you could technically, right, measure their mass. Technically, yes, you could measure their mass. You'd be like, hey, big Daniel. I mean, uppercase Daniel. If somebody had like accidentally ingested a lot of heavy metal, you could detect it. Yeah, absolutely.

All right. So that was in the 1700 and they did this and what did they find? What value did they come up with? So they made a measurement of this thing and they got the number right to within about 20%. So they measured this, which is I think pretty awesome. Like this is a hard piece of work. There was one guy who spent just like years calculating the volume of this mountain from all these survey measurements. He like turned it into prisms and calculated the volume of each of the.

those and add them all up. And, you know, this is before computing and before any sort of modeling. This is in the 1700s. He's working by like lamp light and with a quill. But they got the right number within 20%. So it's pretty impressive. And that also means that they made the first real measurement of the density of the earth. They found that it was four and a half times the density of water and almost twice the density of that mountain in Scotland. That was a bit of a surprise because we didn't know the internal structure of the earth. In Newton's time, some people thought the earth was like a huge hollow shell. So this number so much higher than the density of the mountain was a really fascinating early

clue that the earth has a really very dense core. It's a really very cool result with pretty basic tools. Wow, pretty cool. And so let's get maybe into some of the other ways that people have measured this, as well as maybe the most recent measurements and see how they measure. up and it's weigh them together. But first, let's take another quick break. December 29th, 1975, LaGuardia Airport. The holiday rush, parents hauling luggage, kids gripping their new Christmas toys.

Then, at 6.33 p.m., everything changed. There's been a bombing at the TWA terminal. Apparently, the explosion actually impelled metal glass. The injured were being loaded into ambulances, just a chaotic, chaotic scene. In its wake, a new kind of enemy emerged, and it was here to stay. Terrorism. Law and order, criminal justice system is back. In season two, we're turning our focus to a threat that hides in plain sight.

That's harder to predict and even harder to stop. Listen to the new season of Law and Order Criminal Justice System on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. I had this overwhelming sensation that I had to call it right then. And I just hit call. I said, you know, hey, I'm Jacob Schick. I'm the CEO of One Tribe Foundation. And I just wanted to call on and let her know there's a lot of people battling

some of the very same things you're battling. And there is help out there. Good Stuff Podcast Season 2 takes a deep look into One Tribe Foundation, a non-profit fighting suicide in the veteran community. September is National Suicide Prevention Month, so join host Jacob and Ashley Schick as they bring you to the front lines of One Tribe's mission. I was married to a combat army veteran, and he actually took his own life to suicide. One Tribe saved my life twice. There's a lot of love that flows through this place, and it's sincere. Now it's a personal mission.

Don't have to go to any more funerals, you know. I got blown up on a React mission. I ended up having amputation below the knee of my right leg and a traumatic brain injury because I landed on my head. Welcome to Season 2 of the Good Stuff. Listen to the Good Stuff podcast on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. A foot washed up a shoe with some bones in it.

They had no idea who it was. Most everything was burned up pretty good from the fire that not a whole lot was salvageable. These are the coldest of cold cases. But everything is about to change. Every case that is a cold case that has DNA right now in a backlog will be identified in our lifetime. A small lab in Texas is cracking the code on DNA.

Using new scientific tools, they're finding clues in evidence so tiny you might just miss it. He never thought he was going to get caught. And I just looked at my computer screen. I was just like, ah, got you. On America's Crime Lab, we'll learn about victims and survivors. And you'll meet the team behind the scenes at Othrum, the Houston Lab that takes on the most hopeless cases

to finally solve the unsolvable. Listen to America's Crime Lab on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. Hola, it's HoneyGerman, and my podcast, Grasias Come Again, is back. This season, we're going even deeper into the world of music and entertainment, with raw and honest conversations with some of your favorite Latin artists and celebrities.

to audition? No, I didn't audition. I haven't auditioned in like over 25 years. Oh, wow. That's a real G-talk right there. Oh, yeah. We've got some of the biggest actors, musicians, content creators, and culture shifters sharing their real stories of failure and success. You were destined to be a start. We talk all about what's viral and trending with a little bit of chisement, a lot of laughs, and those amazing vivras you've come to expect. And of course, we'll explore deeper topics dealing with identity, struggles, and all the issues affecting our Latin community. You feel like you get

a little whitewash because you have to do the code switching? I won't say whitewash because at the end of the day, you know what I'm me? Yeah. But the whole pretending and you know, it takes a toll on you. Listen to the new season of Grasasasas Come Again as part of My Cultura Podcast Network on the IHart Radio app, Apple Podcast, or wherever you

get your podcast. All right, we're talking about the universal gravitational constant. We know that it's kind of weak compared to the other forces, but it's super monumentally important in the universe because it basically determines how stars and planets form, how galaxies form. It basically determines the whole structure of the universe. Yeah, exactly. It's one of the parameters on that control panel of the universe that tells us why a universe is this way and not some other way.

And so we're talking about how you actually measure this because it's tricky because A, gravity is so weak. But also, B, you need to know the masses of things before you can measure this constant. But to measure the masses of things, you sort of need to know the constant. And so people have tried different ways. They did it first in the 1700s and they got within 20 percent. What was the next step? So that method holding a pendulum near a mountain worked, but it was pretty imprecise because the mountain is like a big fuzzy object. We don't really have a strong handle on its density.

You know, is it all the same rock all the way through? What exactly is the volume of it? And so people decided to shrink the experiment down to something smaller that they could control. But then you need a lot more precision because then the effect is going to be a lot, lot smaller. So instead of having one pendulum and a mountain, instead they basically have two pendulum. But if you just have like two billiard balls hanging near each other, the force between them is so small that you're not going to be able to measure any sort of deflection. So there was a geologist, John Mitchell, who came up with a really clever way to measure a very, very tiny force between two billiard balls, essentially.

How'd they do it? So what they do is they have a pair of these balls on a rod, and then they hang that rod from a string. And then they bring two other massive balls closer to these two balls on the rod, and they measure how strongly the rod is attracted to these other massive balls by measuring how far the strings twists. So instead of measuring like the deflection from the vertical, which is a tiny, tiny amount, they can measure like how far this thing has twisted the string it's hanging from. So it's called a torsion balance. Right. You're talking about a set of that's like, what do you call those like ornaments you hang them from your ceiling?

It's a mobile. A mobile, yeah. That's kind of what you're talking about, right? Like you make a mobile out of two billar balls where you like put him on a rod and then you hang the raw from the center of it on a string from the ceiling. and then you sort of see how this mobile swings or turns when you put bigger masses next to or near the two builder ball. Exactly.

And so now you're measuring the angle of rotation of your mobile, basically, as it turns towards the other balls. And that's a little bit easier to measure than the deflection relative to some vertical where you need to like calibrate it to the stars. Here you know how much force it takes to twist this string. You can calibrate that when the ball is all. aren't around and then you bring the balls in and you see like how much do they twist the string?

What is the like equilibrium position between the force that's trying to bring the mobile back to its resting position and the force from the balls that's pulling on it in the other direction? The twisting of the string also tends to want to bring it back to a neutral position, right? Exactly. If you just like twisted this thing up and let it go, they would spin back eventually to its resting position. And so just the way like a pendulum is deflected by the mountain, here this whole balance is twisted a little bit by the presence of these other masses. Interesting. And so they did this kind of at the end of the 1700s and how close it they get. So yeah, so this idea was by John Mitchell, a geologist. Unfortunately, John Mitchell built a whole

experiment and then died before he could really use it. And it was Cavendish who inherited this thing and did a bunch of really, really careful experiments. And he's the one for whom this experiment is known. Unfortunately, Mitchell sort of lost line. Sounds very suspicious. Yeah, lost. to history. But, you know, Cavendish... And 1700 murder mystery involving physics? That's a winning podcast episode. True crime science, exactly. Anyway, he got a very precise measurement. He measured it to within 1% of the true value.

And this was a big elaborate thing. It was like a two meter wide box that this whole thing was in. And it had to be enclosed in there to avoid like air currents. He could only observe it through these tiny little holes through which there were lenses. So it's a really elaborate setup. But it worked. And this is in the late 1700s. And that was the most precise measurement for about a hundred years.

Wow, that's pretty impressive. What happened a hundred years later? So for the next hundred years, the folks who were using the mountain method tried to beat Cavendish but failed. They kept trying like different mountains and different surveys and they spent lots of money and lots of time. And sometimes they drank too much and actually like burned down their whole facility. It's a very colorful history if you look into it. But they never succeeded in beating Cavendish. And it wasn't until people improved on his torsion balance method.

But a hundred years later, a scientist named C. V. Boys was able to bring down the uncertainty and people made a little bit of progress over the next few decades so that like by the 1930s we had a measurement of it to within a tenth of one percent and that sounds pretty good right but remember like this is a fundamental constant of the universe other constants we've measured to like one part in a billion so having this down to like one part in a hundred or one part in a thousand is not very impressive it's one of like the worst measured physical constants in the universe. Oh, man. Are you physics shaming those experimenters?

No, I'm doing exactly the opposite. I'm saying, this is so hard. It's a really, really difficult measurement. You know, in order to do this, you have to completely isolate your setup from everything else. You have to come up with clever ways to account for everything, to measure the bias in your experiment. You know, the more recent measurements people have been doing in the last few decades involve clever tricks like put a mirror on the wire. And instead of measuring the angle of the balls, which is really small, shine a laser on the mirror and use the motion of the laser spot to measure how much the wire has twisted. These kind of tricks and all sorts of other techniques to reduce the electrostatics on these balls. It's really impressive amount of

work. I guess my main question is you're saying like we're getting closer to the true measurement or the true value of this constant, but how do you know what the true value is? Like how do you know you're only 10th of a percent off or 10% off? Like how do you know what actually is supposed to be? Yeah, that's a great point. And we don't know what it's supposed to be. There's no prediction, right? So any number could be the right number. And in the history, these measurements, typically what happens is you have a first measurement,

which is sloppy and rough, and then you improve it and you get more and more precision. So if you look at these things over time, they tend to converge towards one value, which we say, oh, that must be the true value. In reality, it doesn't always work like that. We have some cases in history where the value seems to converge to one number and then it shifts. And that's because people know about the previous results and they sort of want to reproduce the previous results. So if like one of the first results was off by a bit, then there's like an implicit bias in people's experiments. They tend to like find mistakes and bugs until their

number agrees with the previous number. It takes a little bit more bravery and courage to disagree with an established measurement. So you see those sort of like jumps sometimes in the history of a measurement. This one is particularly interesting because as the measurements have gotten more and more precise, like in the last 10 or 15 years has been a real cottage industry of making these measurements, they've started to disagree. So now we have a bunch of measurements of the gravitational constant with fairly small uncertainties that disagree with each other by more than the uncertainties. Interesting. So I think maybe when you say like they got within 0.1%, you're not saying that it's off by 0.1%. You're saying like their confidence in their measurement is down to 0.1%. Like they think

they're within that range, right? It's more like a measure of confidence. Yeah, they usually quote uncertainty. They say it's this number within a certain range, but we can also compare their measurement to our current best understanding of what the value is. So we can analyze their historical accuracy by comparing it with modern measurements. And so is there no way to like derive this from the equations of the universe or to, you know, tied back to some other more fundamental thing, like the mass of an electron, for example, or something? No, there is not. There's no way to derive this. It's totally unrelated to every other physical constant and every other process in the universe. The gravitational constant doesn't just control gravity. It only controls

gravity. It doesn't determine anything else in the universe. So there's no other way to figure it out. The only way to do it is to measure the force of gravity between two things. And to do that, you got to know their masses. We can't like tell by, you know, how light bends around a black hole or something like that or around the sun. Yes, actually. As our calculations in general relativity get more and more precise, we may be able to do things. like seeing how space is bent in the vicinity of strong gravity, which might be able to give us a new handle on how to measure this constant. Pretty cool.

But I guess until then, that means like if our measurement of G is off by 0.1%, that means that any calculation that we make using G is also off by at least that 0.1%. Right? Yeah. These days we're down to about 5 times 10 to the negative 5 as a fractional uncertainty on big G. So, you know, like a few hundred parts per million, which is much more precise than historically, but still by far the worst measured constant. And you're right. It means that we can't make very precise predictions about what happens near Black Hole because they depend on Big G. So you need

super precise measurements to nail Big G so we can then make super precise predictions. It kind of sounds like maybe we'll never know the true value of G. It might be because the true value of G has an infinite number of digits in it. In that sense, we'll never know the true value of anything, even like, you know, the mass of an electron or any other parameter because it has an infinite number of digits and you can't have an infinite amount of experiments or an infinite number of graduate students to measure them. But I guess what I mean is like at some point, you do need to know the masses of the things involved in your experiment.

And so, but for that, you also kind of need G. And so there's always maybe going to be a little uncertain because of that. There's always going to be uncertainty, exactly. And because we don't know this one very well, it makes everything in gravity more uncertain. All right. well, sounds like there's still a lot of room for people to come up with some interesting experiment to measure this. Exactly.

You might think it's a historical quantity, but people have been measuring these things in the last five, ten years. It's like an area of active research, understanding Newton's constant for gravity. So I guess the next time you weigh yourself and you're like, what, I weigh this much, you can maybe blame it on the uncertainty of the gravitational constant. That's right. Blame Newton. But I guess that still doesn't help you explain why you're getting.

old or why you're getting more silver all right well we hope you enjoyed that and maybe thought a little bit more about what we know about the universe and we still don't know and how we still don't know very basic things about it like how much you weigh or how much how hard the earth is pulling down on you so for those of you looking to crack a deep secret of the universe this is one of those frontiers maybe you'll find a reason why g has to be a certain value or maybe you'll come up with a super clever experiment to nail it down very precisely and then everyone will go Gee whiz. I mean, big G whiz. I mean, uppercase Gwit. All right, thanks for joining us. See you next time. December 29th, 1975, LaGuardia Airport. The holiday rush, parents hauling luggage, kids gripping their new Christmas toys. Then everything changed. There's been a bombing at the TWA terminal.

Just a chaotic, chaotic. scene. In its wake, a new kind of enemy emerged. Terrorism. Listen to the new season of Law and Order Criminal Justice System on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. Have you ever wished for a change but weren't sure how to make it? Maybe you felt stuck in a job, a place, or even a relationship. I'm Emily Tish Sussman, and on she pivots, I dive into the inspiring pivots of women who have taken big leaps in their lives and careers. I'm Gretchen

Whitmer, Jody Sweetie. Monica Patton. Elaine Welteroff. Learn how to get comfortable pivoting because your life is going to be full of them. Listen to these women and more on She Pivots. Now on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. I was diagnosed with cancer on Friday

and cancer free the next Friday. No chemo, no radiation, none of that. On a recent episode of Culture Raises Us podcast, I sat down with Warren Campbell, Grammy-winning producer, pastor, and music executive to talk about the beats, the business, and the legacy behind some of the biggest names in gospel, R&B, and hip-hop. Professionally, I started at Death World Records. From Mary Mary to Jennifer Hudson, we get into the soul of the music and the purpose that drives it. Listen to Culture raises us on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts.

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