Daniel and Jorge Explain the UniverseDaniel and Jorge talk about the number that controls the strength of gravity and why it's so hard to measure.
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That's O do oo do quor Hey, 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.
Oh, that sounds like a good plan. Really lean into the dignity of aging.
I don't have a lot of dignity, but I am definitely aging about you. How's your transition going to full Einstein hairstyle mode.
I still have no silver hair. In fact, I'm thinking about dying my.
Temples, dyeing them, 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 gray hairs exactly.
I want to increase my gravitass, not just my personal gravity.
Yeah, I mean your problem is you're increasing in with and not with them.
That was a weighty bird.
I am poor Ham, 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 seed 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 twenty 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 thirties and people were calling 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 iHeartRadio, 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 in 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 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.
It's right, we're trying to find what the wise crack of the universe is. That kind of what the job of a physicist is.
I hope there will be some humor in these stories. You know, every good story has some comic relief in it, even mathematical stories.
But I guess it's within 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 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't even means something when you're out in space far away from any gravity.
Yeah, it is a pretty perplexing universe, and sometimes it's sort of it 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 consonants, lots of numbers 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. They're 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's sitting in front of like the control panel floor 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 Groning exactly, or because Homer Symptom isn't charge.
Yeah, either because there's a cartoonist who's the designer of the universe and we all know they can't be trusted.
Are you saying God is the ultimate cartoonists or cartoonists are the ultimate gods?
I'm saying if either of those are true, then we're screwed.
No, wouldn't you want to live in a cartoon like, 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 in 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. meEach episode, I'm trying to embarrass us to the poortant where we don't know what he got 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 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 three hundred thousand meters per second, but it could also be something else, And that's what you mean by a control not like somehow when the universe was created, somebody said that not to three hundred thousand meters per second, but it could have been something else.
YEA, Actually I think it is something else. It's three hundred million meters per second. Oh three, that's what I said. 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 we set it to a thousand times the wrong come out, all.
Right, Homer. But these constants are fascinating, and physicists look at them and they go, 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 seventy four bajillion or ten to the negative thirty two, 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 that they 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 esthetics. 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's even really a great argument that I could take for why you would prefer numbers close to one.
Well, they say one is the loneliest numbers, 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 eighties pop songs.
Yeah, there you go, or in the lyrics, right, maybe eighties pop stars are the gods of the universe.
Yeah, maybe it's all just about ice ice Baby.
Yeah, there wasn't there a group called Genesis back in the eighties? 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 own 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 nine point eight 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.
Mmm.
Do you think G has anyone askedjieve 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 g's and the big g's of the world.
Well that's what cartoonists are here for, to anthropo forum orphize everything, even physics, I guess, But I guess it's big G, like like you said, to distinguish it from the little G 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 nine point eight 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 g's are totally irrelevant number.
I 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 men is the OG. You know, 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 actual 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 too questions at Danielandjorge dot com. Everyone wants to hear your voice.
So think about it 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 and 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 true. The observation of planets, stars and other celes your bodies and coming to a number that adjusts that motion to our other units of measuring.
Probably something to do at the moon. See we can estimate its mass, estimate the Earth's mass, then see what's going on there, and we can probably find a G.
All right, Well, somebody here confusedly with little G. You know they do look alike.
I guess do theyre? Though big capital G and little G look pretty different. I sent this an email, so I wrote explicitly big G.
Hmmmm.
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.
And 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 pastcale 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 lot of 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. Lets 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 new tone and 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. Were 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 measured 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 what if Suton'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 and masses and huge differences in distances. So you 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 one point seventh square root of the distance between them nuts, it's like the square of the distance between them. And it's just like mass one times mass too. It's not like mass one plus seventeen divided by five point two, you.
Know, Yeah, it is 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 in 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 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 of our distance square. It 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 one point seventy two 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 at different accelerations. So it's not one over are squared, but one of our 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 gee, 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.
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All right, we're talking about the universal gravitational constant uppercase G that 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. It's 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 Newtont's right, Newtant'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 pulls in 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 that Einstein sort of derived 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 these 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 six point six seven times ten to the minus eleven, 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 ten to the minus eleven.
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 that have like much more powerful gravity, and they all collapse in the black holes a few seconds after being birthed. Are the universes out there with even weaker g's, and those universes still haven't even made stars because there isn't a 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 other forces.
Well, 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 charge, 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 ten to the thirty three 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 the things that you don't weigh more, or that you do weigh a lot.
Everything is somebody's fault, somebody else's 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 repulsion? And what you find is that they're not even close. Right, Like, gravity is weaker. It's not even a little bit weaker or a lot weaker. It's ridiculously weaker. It's ten to the thirty three 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. It's like thirty two 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 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 objects. 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 and 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 on 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 can you have positive and negative charges, and so you can shield things. You can like balance all the forces out so that 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 is in't like isolating it, it's more like it's super weak, right, because like you could do it to this experiment out in the satellite, right and you know the 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 their 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 election 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 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 them, you know, ten 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 that's 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 learning 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, Well, 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 electroweak force in this 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 billder baller 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. It's like a chicken and egg problem, like how do you measure gravity. To measure gravity, you need to know the mass of something. But the mass of something you need to weigh it, which you need 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 and 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. 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 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 appear in his works because Newton was working at a time before we expressed our theoretical 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 gonna 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. You know, he doesn't summarize at all in terms of mathematics. So he never actually wrote down big G. It wasn't until couple hundred years later that I 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 that 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 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 seventeen seventies. There's a mountain in Scotland and it's a good choice because it's like isolated from other mountains. It just sort of like sticks up and it has like a nice symmetrical shape, which means that it was not super complicated to 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, it could the maximum effect. And there's like a whole team of people that spent like years up there making very precise measurements of pendula 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 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 that resting position will not be straight down. If you follow the string up, it will not point perfectly towards the 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 m.
I guess you could use this to like measure people's masses too, Like if you walk around, have a bitter ball on the string and just kind of walk around and get it close to people, you could technically righte measure their mass.
Technically, yes, you could measure their mass.
And 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 seventeen hundreds, 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 twenty percent. So they measured this, which is I think pretty awesome, Like this is a hard piece of work. There's 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 delated the volume of each of those and add them all up. And you know, this is before computing and before any sort of modeling. This is in the seventeen hundreds. He's working by like lamp light and with a quill. But they got the right number within twenty percent. 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.
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All right, we're talking about the universal gravitational constant. 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, 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 our 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 seventeen hundreds, and they got within twenty 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 it's going to be a lot lot smaller. So instead of having one pendulum and a mountain, instead they basically have two pendula. 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 string 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 this string it's hanging from. So it's called a torsion balance.
Right, you're talking about a setup 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, like you make a mobile out of two Bilder balls where you like put them on a rod and then you hang the row 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 mass 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 with when the balls 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 a 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 seventeen hundreds, and how close did they get?
So Yeah, so this idea was by John Mitchell, a geologist. Unfortunately, John Mitchell built the 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 seventeen hundred murder mystery involving physics. It's a winning podcast episode.
True Crime Science exactly. Anyway, he got a very precise measurement. He measured it to within one percent 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 seventeen hundreds, and that was the most precise measurement for about one hundred years.
Wow, that's pretty impressive what happened at one hundred years later.
So for the next se of years, the folks who were using a 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 wasn't until people improved on his torsion balance method. But one hundred years later, a scientist named CV Boys was able to bring down the uncertainty, and people made a little bit of progress over the next few decades, so the like by the nineteen thirties, 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 one hundred or one part in a thousand is not very impressive. It's one of the worst measured physical constants in the universe.
Oh man, are you physics shaming those experimenters?
Now, 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, use a 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 ten of a percent off or ten percent off? Like, how do you know what it 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 ten or fifteen 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 point one percent, you're not saying that that it's off five point one percent. You're saying like their confidence in their measurement is down to zero point one percent. Like they think they're within that range, right, it's more like a measure of confidence.
Yeah, they usually quote and uncertainly 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 tie 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.
M we can't 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 point one percent, that means that any calculation that we make using G is also off by at least that zero point one percent, right.
Mm hmm, yeah, these days we're down to about five times ten to the negative five is 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 in 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, will 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 that for that, you also kind of need g and so there's a 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 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.
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 domin 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 ge whiz, I mean big g wheez I mean uppercase. All right, thanks for joining us, see you next time.
Thanks for listening, and remember that Daniel and Jorge Explain the Universe is a production of iHeartRadio. For more podcasts from iHeartRadio, visit the iHeartRadio app, Apple Podcasts, or wherever you listen to your favorite shows. When you pop a piece of cheese into your mouth, you're probably not thinking about the environmental impact, but the people in the dairy industry are. That's why they're working hard every day to find ways to reduce waste, conserve natural resources, and drive down greenhouse gas emissions. House US Dairy tackling greenhouse gases. Many farms use anaerobic digestors to turn the methane from manure into renewable energy that can power farms, towns, and electric cars. Visit us Dairy dot COM's Last Sustainability to learn more.
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