Science & Technology Q&A for Kids (and others) [Part 139]

Foreign. Hello, everyone. Welcome to another episode of Science and Technology, Q and A for kids and others. Sorry I'm starting slightly late today. We were just wrapping up our annual Wolfram Winter School, talking about our physics project, mostly for graduate students and others studying those kinds of things. Lots of interesting projects got done there. Okay, so let's talk about some things here. I see a question came in, asks, why is there matter at all in the universe? Why is the universe not just empty? It's a good question. Well, let's talk about that. They're different. I think we're in a better position to answer that question because of the progress we've made in understanding fundamental physics from our orphan physics project in the last few years. But let's give it a try. One question is, what is the universe fundamentally made of? The traditional view has been there's space. There's kind of the extent of space. You can move things around to different positions in space. And then there's things that you put in space, like atoms or electrons or photons or us or whatever else, that there are these two different kinds of things, that there's this sort of background of space. It's like you've got your blank sheet of paper that is the space in the universe. And then all of the sort of things we care about, the content of the universe, is the things you draw on that blank sheet of paper. So from that point of view, you could ask the question, well, why is there anything other than just the blank sheet of paper? In fact, in traditional models of physics, it gets even more. I don't think it's very easy to explain why there would be any matter in the universe, why the universe wouldn't just be pure, empty space. Now, there is a little bit of a footnote to that, even in traditional models of physics, because one of the phenomena we've known for 100 years happens is this phenomenon of quantum fluctuations. So in our typical sort of view of what's happening in the world, we sort of imagine that there are definite things happening in the world. But quantum mechanics, kind of the theory of sort of what happens at small scales says, actually, that isn't right. Definite things don't happen. There are always many different paths of history being followed. At least that's the interpretation of it that we have now in the last few years, that there are sort of many paths of history that are being followed. And when we humans observe the universe, and this is really my interpretation of this at this point, is that we humans are kind of aggregating we're putting together a bunch of these different paths of history, just as if we were differently set up. We might be able to observe every individual molecule bouncing around in the air, but as it is, we only observe sort of the aggregate, the average of the effects of lots and lots of molecules. So similarly, a little bit more difficult to understand. We're only observing kind of the average of many paths of history. Okay, but there's this phenomenon that on each different path of history, the detailed configuration of what electrons, antielectrons, et cetera, et cetera, et cetera, exist at any given place in space is different. And this leads to this idea of quantum fluctuations, vacuum fluctuations, the idea that at any moment there are always these kind of so called virtual particle antiparticle pairs being produced. So it's like an electron, a positron, the anti electron come into existence for a very short time, then they annihilate again. And that keeps on happening throughout the universe. So even if you believe that there is no matter in the universe, there is still. Well, in the traditional theory, one would always have some many pieces to this. Maybe the better thing to do is not to try and explain the traditional theory, which gets itself horribly tangled up when we start discussing the relationship of matter to gravity, to vacuum fluctuations, and so on in our models of physics. What is going on is that we don't distinguish sort of space and matter as separate kinds of things. Instead, the whole universe, what is really there is just this giant network. And each, the network represents connections between these very abstract elements. We can call them atoms of space. They're not atoms in the sense of hydrogen, helium, those kinds of atoms, they're just indivisible points, in effect, that represent the sort of smallest components of space. In our models, space has a definite structure. It's made of this giant graph that connects together these individual elements that sort of represent disembodied points in space. And all we know is kind of how these points are connected in this graph. And then the question is, well, what is matter? If that's, if the structure of space is determined by this big graph, what is matter? Well, matter is certain persistent features in the structure of this graph. This graph is continually getting rewritten. Every time there's a little piece of graph that has some particular form, it gets transformed into a piece of graph that has some other form. This keeps happening once, just sort of evolving this graph. And matter in this interpretation is kind of pieces of that graph that are somewhat stable through time. And that could happen. The analogy I Tend to give of this in a fluid with a bunch of molecules bouncing around underneath. You can still have an eddy that is kind of a spinning around piece of fluid that is fairly stable. You can see it sort of move along, you know, in basin of water or something like this. It has a certain identity that it maintains even though it's continually made from different, different molecules that are the ones that are actually contributing to the structure of that eddy. But the eddy itself has a continued existence. And that's what we think matters, how we think matter works in this model of the universe where there's this sort of underlying graph that represents the structure of everything, structure of space. But there are certain features of that graph that we interpret as matter. And matter, as far as we know right now has. We can sort of break down matter into particles like electrons and quarks and photons and so on. Everything that we think of as matter can be thought of as something which is a small lump of stuff that maintains its character as it travels through space and as it progresses through time. We can sort of think of all of matter as broken down into those kinds of lumps. In our model of physics. It's not absolutely necessary that everything that is persistent in time can be broken into lumps in that kind of way. And there might be other forms of matter that don't get sort of don't get decomposed as particles in the same way. In fact, for example, dark matter, something that has been known about for 100 years that has a gravitational effect, but seems to have no other effect. It's possible that that is a quotes form of matter that cannot be represented in terms of these sort of lumps of stuff that correspond to particles. So this question of why would there be matter in the universe? Why would there be anything that is sort of persistent in the universe, as opposed to just having space where the space is continually getting rewritten and changing and so on. Why is there anything that has stability that we can identify as matter? And I think that's that in our models becomes essentially a pure, in a sense, theoretical question. It's something which is a question. Can you derive in our models the fact that anything would be persistent? I suspect the answer is that it is inevitable that there will be things that are persistent in that sense. In our models there's sort of a. And this is getting deeply abstract. We're far down the rabbit hole here. In our models there's this idea of what we call the ruliad, which is, I've talked about this network and these rewrites of the network and so on. The RULIAD is what you get by looking at all possible rewritings of a system, all possible computations that sort of figure out what the next state of a system will be. And kind of the big idea is that we are observers of the ruliad and we are sampling particular possibilities in this set of all conceivable computations. And I think so my guess is that the reason that the samplings we take of the RULIAD that give us the laws of physics that we experience necessarily correspond to things that have a certain where we are identifying certain persistence, because we identify ourselves as having a certain persistence. Boy, this is deep in the rabbit hole. See, one of the things that is very non trivial about our way of experiencing the universe is that we believe that the universe has a certain persistence and what it does. But in order to detect that, we ourselves have to be persistent. And that's not a trivial assumption, because in these models of physics, at every successive moment of time, we're made of different atoms of space. It's like that eddy moving through the water. At every moment, it's made of different water molecules. Yet if you imagine that that eddy was a mind kind of, you know, if you made up a whole brain's worth of eddies interacting with each other and so on to those eddies, it would seem that they could say we persistently exist. We are maintaining our thoughts through time, so to speak, even though at the smallest scales there are different molecules being swapped in and out for what make up those eddies. And so it is, I think, with us that we believe we are persistent in time. We have a certain persistent set of activity, that we have a certain persistence to how we perceive things. That is a question of an assumption that we make. We assume that we are persistent in time, the thoughts we had a moment ago are connected to the thoughts we have now, and so on, even though the raw material from which those thoughts are made is different at every successive moment in time. So my guess is, boy, this got deep in the rabbit hole. My guess is that the fact that we have that persistence inevitably means that the kind of slice of the ruliad that corresponds to the universe as we perceive it also has certain persistence. And that's why we believe that there are persistent things in the world that we can describe as matter, and that that's sort of why matter exists for observers like us in the universe. That got incredibly philosophical. I'm sort of surprised at how philosophical the answer to that question gets that sort of the persistent things in the universe exist because we believe we are persistent in observing the universe. Let's see. Okay. Laurie asks a question. How does friction affect the motion of an object? Well, what is friction? You know, you, you have a thing and you're, you are trying to move one sort of block of wood across the floor or something, and there is resistance to motion. There is the block of wood doesn't want to slide. Well, what causes that resistance to motion? Actually, the details of how that works have been pretty confusing. And the basic law of how much friction force there is was discovered 400 years ago, but it still isn't really completely understood. What is that law? The law says the amount of friction, the amount of force that's going to push back on you trying to push something forwards, is proportional to essentially the weight of the object. The normal force, the force with which the object sort of pushes into the floor, multiplied by some factor called the coefficient of friction, usually denoted mu, Greek letter mu. So different kinds of materials have different coefficients of friction. Some slide very easily, like ice, for example, will have a low coefficient of friction. Things slide easily on ice. Some things have a very high coefficient of friction. It's very hard to get them to slide against each other. But what causes it to be hard to slide at all? Well, okay, let's talk about what a solid object is. A solid object has a bunch of atoms. If you looked at it at a small enough scale, it'd be made of a bunch of atoms. And those atoms are organized in some way so that they're more or less fixed in position. Two kinds of solid objects, crystals and so called amorphous materials. So in a crystal, the atoms are arranged in a very regular way. Like for example, in a salt crystal, they will be arranged in a cubic lattice. So it's just like you have a bunch of cubicle boxes and you stack them all up and you put atoms at the centers of those boxes, for example, or on the corners of those boxes. And that's the arrangement of atoms in the salt crystal. In something like glass, atoms are arranged in a much more random way. You're just packing in those silicon oxygen atoms and so on, just sort of packing them in. Just like if you took a bunch of balls, you threw them in a ball pit. That's how you get a so called amorphous solid. So now the question is, when we're talking about friction, the issue is what happens at the surface of the solid? Do you have, if you've got friction between Two things. You're saying, how does one surface of one solid slide against the surface of another solid? So in a crystal, for example, you can potentially cut the crystal in such a way that you're just cutting right down a plane of atoms so that it's very, very perfectly regular. That's something you see in so called cleavage planes for crystals. If you, if you pick the right angle, the crystal will sort of come apart and you'll have a perfectly flat face, almost perfectly flat face. Let's consider that case first. So let's say you've got two crystals and they've all been, they've been sort of perfectly cleaved and you're trying to slide them against each other. Well, the first thing that happens is if you do that in space, they'll stick. Typically those two surfaces, they'll just, they won't actually slide. They'll just those, the, the, the atoms of one surface will interact with the atoms of the other surface and they'll essentially make an extended solid. It's like the, the atoms on one side. If it's two pieces of metal that, let's say the same metal, it's like, well, you know, why would we distinguish the atoms that are in one piece of metal from the atoms in the other piece of metal? They just make a bigger crystal, so to speak. What happens on, you know, not. That's assuming that the, the surface of the crystal is just a perfect arrangement of these atoms. In practice, if you're, you know, out in the air and things like this, the surface of that crystal will have all kinds of air molecules that get stuck on it. And there'll be sort of chemical reactions that happen, little chemical reactions that happen that produce changes in that surface. And so it won't be this perfect, atomically perfect surface that would have this feature that it can sort of automatically weld to another surface. And so you're already seeing there's a big mess here because the details of how friction works depend on things like, well, how clean is the surface? Things like this, by the way, it's not surprising. It depends on how clean the surface is. We kind of know that lubrication with oil and things like this can affect how much things slide. And so details of the surface are going to affect it. The basic, the thing that's a bit surprising is if you push down harder, it becomes harder to slide things. Why does that happen? It's not really clear why that happens. Kind of a possible theory is that the surface of the material is always like kind of A mountainscape. And so what's happening is you're sort of pushing two mountainscapes together. And if you don't push terribly hard, the only things that are actually sort of against each other are the tips of the mountains. And when there are only a small number of tips of mountains, the amount of sort of frictional force associated with atoms pulling on each other is lower. If you push down, you're kind of crushing those mountain scapes. And so there's a larger area of contact between the two surfaces at the level of atoms. And so you have more frictional. So you have more. The surfaces are less prepared to slide against each other. But. That's kind of the story of, again, it's not very well understood. I mean, what fundamentally happens in friction? What fundamentally happens is when you push an object, all the atoms in that object are moving the way you push them. But what's going on is in the end, that motion is as you push those atoms and they interact with the atoms in the other surface. All the atoms are kind of getting moved around and wiggled around. And what's happening is that in the end that wiggling around of atoms produces heat in these surfaces. Heat is in fact just the microscopic motion of molecules. But and so what's happening in friction is you're going from this large scale mechanical process of sliding one block against the other to this small scale phenomenon of lots of sort of random motions of molecules down at the level of what's happening in these surfaces. So the big picture is friction is about turning systematic motion into heat. And the sort of, the amount of friction depends on many details of these surfaces. So I don't think there's any case where one can compute from sort of first principles the coefficient of friction. I think one always has to measure it. And I think that in what can happen without an atmosphere and things like that is you simply get sort of immediate welding of surfaces immediately. The surfaces just lock together, at least with crystals, not with amorphous materials. I think another phenomenon in, in friction is that the static coefficient of friction is larger than the dynamic one. And that means when you kind of are pushing on something, there'll be a moment when it sticks, and then once it started to move and there's a big resistance to it starting to move. Once it started to move, you have to push it less hard to keep it going. Then you have to push it to start it going in the first place. And that phenomenon of the sort of stick slip phenomenon is important because, for example, earthquakes are the result of that phenomenon because, you know, the rock is continually across a fault line in the earth. The rock is continually being sort of pushed. Two pieces of rock are being pushed relative to each other. And most of the time they don't move at all. But suddenly they start, they unstick and they start moving. And once they've started moving for that moment when the earthquake is happening, they find it easier to move than it took than it was for them to start moving in the first place. They're also when we talk about anti lock brakes for cars, when the car is sort of sliding on ice and so on, and there's sort of this question of whether you can make use of the fact that there's a higher resistance to starting to slide than there is to sliding once you are sliding, so to speak. Let's see. Well, there's a question here from, from Paula. What is the relationship between force, mass and acceleration? This was the great achievement of Isaac Newton in 1687. Kind of launched the serious kind of mathematical science of mechanics. And his second law says force is equal to mass times acceleration. And when you really take it apart, it's not clear quite from the outside what the second law means other than that it defines the notion of force. But let's talk about what these notions are. So what is acceleration? So when you have something moving, you can describe it as, oh, it's going at such and such a speed. That means the speed is the amount it changes its position in a certain amount of time. So let's say we're walking at 2 miles per hour. That means in we are going, we're changing our position by two miles in the course of one hour. Okay, but now the question is, that's velocity. That speed is how much we're changing our position in the course of time. Now the question is, do we change our speed in the course of time? Are we just going to constant speed or is our speed changing? So acceleration is the rate at which we are changing our speed. So for example, we might say, you know, we, we put our foot on the gas for a car and it accelerates because it changes its speed from being, let's say 0 miles per hour to 60 miles per hour. And the acceleration is the rate at which we are changing the speed of the thing. And we, we can keep going. You know, we can say, well, the, the velocity is the rate of change of position, acceleration is the rate of change of velocity. There's this thing that often is called jerk, which is the rate of change of acceleration. How much a thing Jerks. You know, the kind of human perception of that was a, you know, that, that, you know, you really jerked to a stop or something like this. That's looking at the change of acceleration typically. But in any case, acceleration is just defined as this thing about how things move and how the rate of change of position works. Well, so that's a thing that has a definite meaning. Now there's the question of mass. Well, what is mass? Well, there are actually two very different meanings, two very different things that correspond to the mass of an object. One is how difficult it is to make that object start to move. How much force you have to put to get that object to move at a certain speed. That's one sort of measure of mass, which is actually just comes from Newton's second law, force equals mass times acceleration. I told you this was a bit of a put up job and a sort of circular definitional thing. But so one version of mass is the thing that appears in that formula. Another version of mass is how much the thing is pulled by the force of gravity. So one can have the mass of something which is the so called inertial mass, the mass that is associated with the inertia of the object, how much, how much it takes to get the object moving in a certain way. Another thing one can look at is how much the object is pulled down to the ground, so to speak, by the force of gravity and the amount it's pulled down. One talks about the mass of an object which is associated with how difficult it is to get the object moving. Let's say it's on a frictionless table and you're just sort of getting the object to move around. The heavier it is, the, the harder you have to push it to get it to move. But now the next question is, well, the higher the mass is, the more you have to push it in that scenario. But the higher the mass, the more it's going to push down as a result of it being pulled by the force of gravity. And so there's another formula also due to Newton, which is the formula for law of gravity that says that the force associated with gravity is proportional to the mass. Okay? So it is a non trivial fact that the mass that is associated with sort of how hard you have to push the thing to get it moving is the same mass quantity that determines the force of an object produced by gravity. The equivalence between inertial and gravitational mass is a thing that is sort of a big feature of general relativity. It's the so called principle or equivalence that was developed in 1915 by Einstein. And actually in, well, this, in our models of physics, it is inevitably true. And it's also inevitably true in the kind of, in the framework for thinking about space time that general relativity has. But, so that's another piece to the picture is there's this parameter mass. There's this thing, force equals mass times acceleration. Okay, what is mass? Well, we can independently measure mass by saying that it is the amount that gravity pulls on something. That's an independent measurement. It's not obvious it'll be the same mass, but it turns out it is the same mass. So what is force? Well, force, I'm afraid it's very circular because force is kind of this thing that is quite an abstract thing that represents kind of whose effect is to make something accelerate. But force has all kinds of rules about it. Like, for example, if you have sort of, you can. Force is in a particular direction. You can have two forces that cancel. You can have something where, when, when. Whenever things are in equilibrium, whenever things aren't moving. If I have my two, two hands, so to speak, and I'm pushing one way with a force in this direction, I'm pushing force in that direction. If they're not going to move, that means those two forces have to be equal and opposite. That's the only way I can get the thing to not accelerate. If one hand was pushing harder than the other with more force, I would start accelerating in a particular direction. So actually, Newton's third law has to do with the idea that with every reaction, there's an equal. Every action is an equal and opposite reaction. And that is essentially the consequence of the fact that if you have forces pushing in two different directions, the only way that their effect is, can be canceled out is if the two forces are equal. By the way, just to fill in Newton's laws of motion, the first law is kind of a special case of the second law. It says if you have an object that is not acted on by any external force, then it will keep going at a constant speed in a particular direction. So by the way, in Newton's time to make that claim was not obvious because today we might easily be able to have some nice air hockey table or something where we can push a puck and we can see that it starts going and it just keeps going in that direction. But in Newton's time, the number of things that didn't have lots of friction associated with them wasn't large. So the claim that you could have a thing that would just once you push it in A particular direction, it will keep going. But in that direction, if it isn't acted on by a force, including the force of friction, that that would happen was not so obvious. It was important to Newton in what he was figuring out because he was trying to understand the motion of planets. And in that case he imagined that planets wouldn't have any force other than gravity acting on them, which is more or less correct. But so the fact that Newton was able to come up with this law of motion, force equals mass times acceleration and so on, the thing that was non trivial about that was just identifying what kind of a law one should try to come up with. In other words, to say we can distinguish a material object and we just have to talk about the motion of that object, we don't have to talk about what that object is doing. If the object is a person, when the person moves, the person is walking their legs and is moving around, or they're swimming and they're, you know, flapping their arms around and so on. You know, there's lots going on with the object. The fact that you could just have an inert object and you could talk about its motion and the effect of things on that motion, that was a non trivial realization that that was a thing about which you could make a theory. That's always one of the challenges in making up scientific theories is how do you concentrate on one particular thing and successfully idealize away everything else? How can you just say I'm going to concentrate on the motion of this one thing acted on by forces this, that and the other, rather than saying, well, I have to cover, I have to have a theory that describes how everything fits together. Let's see, Gorgola is asking, can you explain the difference between static and kinetic friction in the context of Newton's laws? No, Newton's laws do not address that. Newton's laws just say the law of friction says, in sort of Newton's law terms, it says there's a force, the law of friction says there's a force, its force is equal to mu times N, the coefficient of friction times the so called normal force, which is how much you're pushing down on the object, how much you're trying to push the object into the surface that you're sort of sliding it relative to. And so when you put that into Newton's laws of motion, what it's going to say is, well, the friction force is resisting motion. So that means that if force is equal to mass times acceleration, there's a force, the frictional force, that is Opposing the direction of motion. So the friction force will always make the thing slow down. It will always make there be an acceleration that's in the opposite direction. So the thing will slow down, and eventually it will come to rest. And so, in a sense, as you sort of substitute in the formula for frictional force Into Newton's second law, you get this result that says the effect of the frictional force Will be that the thing will eventually come to rest. Now, there are many pieces to this that are complicated. So, for example, friction, ordinary friction, Is a story about solid surfaces sort of rubbing against each other. But there's also an analog of friction in gases and liquids. So the analog of friction in a gas Is that there is a drag on an object moving through the gas. So if you throw a ball, the ball will not. If you throw a ball in space or on the moon or something like this, where there's no atmosphere, there's no air, the ball will only have. The only force acting on it will be gravity. If you throw a ball on the earth, not only will gravity be acting on it, but also there's a drag force that's essentially the analog of friction in the air. So what's happening? Well, the ball has to kind of slide through the air. There are all these air molecules that are bouncing around, and they're hitting the ball and so on. But what the ball has to do is to push those air molecules out of the way to make its way through the air. And as it pushes those air molecules out of the way, those air molecules change their motion. That's what it means for it to push it out of the way. The air molecule hits the ball. The ball is. The molecule is bounced away, so to speak, by the presence of the ball. Well, it turns out that you can work out that effect of the sort of the drag on the ball by having to move the air molecules. Same thing happens in water with liquids, for example, the liquid molecules out of the way, the molecules are always moving around. So they'll always be a part where the solid. The ball will just stop at the solid surface. You can't move those atoms in the solid, but with a gas or liquid, those atoms are always moving around. So you can always sort of find that with the ball. The ball can always push its way through the liquid or the gas. But as it does so, it has to rearrange the molecules. And what will happen when it rearranges the molecules? Well, it's kind of like what happens in the molecules when you're rubbing solid surfaces. You'll produce some sort of extra motion in those microscopic molecules which will turn into eventually heat, random motion of those molecules. So you throw a ball through the air, it has a certain drag and it's actually pretty complicated to work out the drag. If you're going through water, for example, I should explain that the amount of drag. There are four parameters that affect the actual force on an object going through air or water or a gas or a liquid. The four parameters are how big is the object, what is the density of the material? Like air has very low density, water has a higher density, means a higher mass per unit volume, how big is the object, what's the density of the material, how fast is the object going? And a fourth parameter, which is the so called viscosity of the material. So what is viscosity? Viscosity is the resistance. It's a little bit like a coefficient of friction, but it isn't defined the same way at all. It's kind of how much does the material resist being moved? So a typical measure of viscosity is you've got, let's see, you've got, for example, two plates and they've got fluid between them. And the question is, how much force does it take to move one plate relative to the other? Knowing that what you're really doing is the plates aren't touching, so there's no friction. But what's happening is there's fluid in between them and you're trying to slide, you're trying to make it so that the, so that the, let's say one plate is moving at a certain speed, the other plate is stationary. How much force is there that is associated with the molecules? So that the molecules in the fluid, they hit one plate, they just might say bounce straight up, they hit the other plate, they bounce in a different direction. How much does that bouncing in a different direction thing have the effect of sort of pulling you back as you slide these plates. And that the quantity that determines that is called viscosity. It's measured in units of, usually called centipoise. There's a poise as a unit of viscosity. It's actually a very big unit. So usually centipoise is what's used to determine viscosity. So if you pour water, you can see sort of how it pours and how it starts moving is determined by its viscosity. If you pour syrup treacle in British English, if you pour that, it pours much less easily. And that's because it has higher viscosity, it has a higher resistance to starting to move. So when you try and pour it and you've got that jug or something, and you're trying to get the liquid to not be in the jug, but to be moving and falling out of the jug, when you have higher viscosity, it's more difficult for it to do that. It flows less easily. What determines viscosity? It's a detailed. It's a matter of detailed properties of the material. In the case of a gas, there's a fairly simple formula for the viscosity. In the case of a liquid, it's been super difficult to work out viscosities and pretty much hasn't been done. Computing the viscosity of water is, I think, still undoable. From first principles, computing the viscosity of air is pretty easy. There's simply. I could even probably explain how one does. Just has to do with. When you're looking at these molecules, they're hitting one side, they're going to hit the other side, they hit other molecules a certain number of times in between, and you're sort of continually transferring momentum from one side to the other. And the rate at which that happens is essentially determined by the number of molecules that are there and their average speed. So anyway, there are these four quantities. The size of the object, the speed of the object, the density of the fluid it's going through, and the viscosity of the fluid it's going through. And it turns out those four quantities are the only things that the drag on an object or the kind of the form of, you know, essentially the drag on an object can depend on. When you look at the sort of the. As an object moves through a fluid, the fluid will make all sorts of eddies and all kinds of other shapes and so on behind it. And what determines that is just some combination of those quantities. So there's this neat trick called dimensional analysis, which says, okay, we got these quantities and they each have certain units. There's length, there's a length unit, there's a velocity, that's length per unit time, there's a density that's mass divided by length cubed and then viscosity. I believe the units of that are mass over length over time. I think, anyway, when you have these three quantities and you know that the properties that you get out are just. They don't depend on the overall size of the object, they only depend on some combination of those quantities. And turns out there's just one way of combining those quantities to make something that doesn't have units, doesn't have dimensions of length or something like this. It's a thing called the Reynolds number. And it is. Let's see, what is it? It's some. It is length times. Yeah, it's. It's size times velocity divided by viscosity over density, if I remember correctly. And so that means. What does that mean? That means if you decrease. If, if that. That's telling you that what mostly matters is the size of an object multiplied by velocity. It's going. And the, the, the. The. So, okay, what. What effect does that have? If you look at the pattern of fluid flow when you move your finger through some water, for example, you'll see. When you move it fairly slowly, you'll see these couple of eddies forming behind it and so on. If you were to look at. And there's a certain speed at which you'll see different form of flow. If you look at something really big like a ship. Well, you could compare the flow behind a ship, the flow behind an airplane. They're going at very different speeds. They're going. But they're going in materials, different materials. There will be a speed for the ship, size of ship, a speed for the airplane, size for the airplane, at which the form of the flow will be the same. Even though one is in air, one is in water, they're going at different speeds and so on. The flow is determined only by the Reynolds number. So in a first approximation, the Reynolds number is what determines, for example, whether the flow is smooth or laminar. Whether, in a sense, the fluid is just sort of sliding past the object or whether the fluid is kind of getting caught on the object and making all this sort of turbulent mess like you would see in a waterfall or something like this. And for many things, the sort of critical roundness number is about 100. Some other ones is about 1000. It depends a bit on the shape of the object. But that determines if you were to have a. A big thing going very slowly or a smaller thing going very fast. All that matters in determining the structure of the flow is the Reynolds number. Okay, so now why am I telling you all of this? We were talking about kind of the frictional effects of fluids on things moving through them. So you throw a ball and the ball has a certain drag force on it that's associated with having to move the air out of the way as the ball goes through. Okay? So that drag force is quite hard to compute if the ball is moving slowly enough. If you drop a little sphere through some thick mineral oil or something, or through syrup or Something like that. In that case, there's a lovely formula. It's called Stokes's law. And it says that the. See if I can get it right. It's 6 PI, eta av, I think, is the. The force is 6 PI times the viscosity times the. The radius of the sphere times the velocity. It's very simple formula. And that determines the. The. Essentially the. The force that's the drag force that's pushing back relative to the thing falling through the material or being thrown through the material. So that's what happens at very low Reynolds numbers. As soon as you get to the Reynolds numbers that correspond to throwing a ball through the air, there are much higher Reynolds numbers. There's turbulent flow behind the ball. And roughly in that Stokes's law thing, the drag force is proportional to the speed at which the thing is going through the. Through the fluid. As you get to larger speeds, larger Reynolds numbers or larger objects, the drag force becomes proportional to the square of the speed. And so that means things slow down more quickly, so to speak. Okay, what consequence does that have? Well, one consequence it has is if you have an object and you drop something out of an airplane, it'll fall through the air. If you're crazy enough to go and do skydiving or something, then, you know, you fall through the air at a certain speed, and what happens is there's a drag force. That's the air pushing back on you. The force of gravity is making you fall. The drag force is causing you to. Is trying to prevent you from falling. And that drag force, if you work out the equations, the thing that's making you go faster, if it wasn't for the air, you would just. The force of gravity is constant. So the force is constant. That means that you have a. According to Newton's second law, you have a constant acceleration. So your speed, which started off as zero when you were at least the vertical speed, started off a zero. When you're on the plane and you jump out of the plane and you start falling and you start falling. And as the longer you go, the faster you're falling. If there wasn't any air there, in fact you would go. The speed you would go at would increase with time, just linearly with time. So after one second, I happen to know, because I know the formulas, that you'd be going at 9.8 meters per second, and after two seconds, you'd be going at twice that speed. After three seconds, three times that speed, and so on, you just keep going faster. But that isn't how it really works because there's this drag force associated with you falling through the air. And eventually the drag force balances the force of gravity. And so you get to what's called the terminal velocity. You end up getting to a speed at which the force of gravity pulling you down is equal to the drag force pushing you up. And I think it's like 100 miles an hour or something. For a typical person, it depends on whether you can go faster if you make your area, your cross sectional area smaller by kind of diving through the air, so to speak, as opposed to making yourself as big as possible. And the limiting case of that is a parachute. Where the idea in a parachute is to make your area as big as possible so that the drag force increases with the area. And so when you have a big parachute, the drag force is very big. And so the terminal velocity is very small. Small enough that. Well, I don't think it's trivial even to land when you're using a parachute. You have to kind of be careful to not break your leg when you land and such like. But it is a reasonable speed rather than 100 miles an hour. And so that is determined by the terminal velocity associated with this great big parachute as compared to the terminal velocity associated with this smaller object. And so that's kind of the interpretation of sort of the analog of friction, the effect of friction, but not friction in solid objects grinding against each other, but this other friction like effect that is drag forces or viscosity in the air. But by the way, I should say that the. What drag is not only associated with viscosity. Viscosity is a microscopic phenomenon like friction of sort of individual molecules doing their thing. Drag is also sort of just the, the large scale pushing of the air out to the side. And that, that large scale effect, that's kind of a more inertial kind of effect. And that's a different effect from the viscosity effect. And sort of in the, the, particularly when you're going fast, the, that's the major effect is just you've got to push the air molecules out of the way. There are, there are other effects. And this is a complicated area. I mean, there are other places where you can ask about sort of Newton's laws, met's the real world. Another one, another complicated, messy area is this thing called the coefficient of restitution. So coefficient of friction is about sliding. We've got drag which is associated with pushing through something like the air. Another thing is you take a rubber ball, you drop it on the ground, it bounces up again. So what's happening there is the coefficient of restitution is kind of if the thing falls down and it hits the ground with a certain speed, it will then bounce back with. It will bounce up again. So we've reversed the velocity you've made it go. Instead of going down, it goes up. But how fast does it go up relative to the amount it went down? So the coefficient of restitution is the ratio of those things. So for example, a typical might be 0.3 or something. If you have a pretty good. If you have a super ball or whatever they're called, they'll bounce up almost as high as you drop them. And that means that their coefficient of restitution is close to one, which means when they hit the ground at a certain speed, they'll bounce back at about the same speed, which means they'll go up to the same height and so on. And what determines that coefficient of restitution? Oh boy, that's a mess. I mean, it is determined by kind of the solid object analog of viscosity. And yeah, it's just really complicated actually. And it's sort of an advanced end of solid mechanics that is mostly just you just measure it and see what comes out. It's hard to work out, but that's another piece. When you're solving Newton's equations and you're solving it for a bouncing ball, one of the things you have to do is figure out when it bounces, when it bounces back. How much does it bounce? When it bounces? And that's not something you can deduce from Newton's laws alone. That's something where you have to know lots of detailed properties of materials. And even then you can't compute it. You pretty much just have to measure it nowadays. Let's see. Well, there's another question here. You guys are really exercising my kind of. Can I actually explain, well, physics. But you know, the problem with explaining physics is that there are things that are very clear cut and well understood and you'll find in textbooks of high school physics. Then there are things that are often assumptions that are made there that are extremely not well understood. And when you ask questions about, I don't know, a bouncing ball, for example, you might find, well, yes, you can apply Newton's laws. And it's all great except, well, you've got this coefficient of restitution. What the heck is that? Well, that's really hard to compute. And that's a whole different story of physics. It's physics as well, but it's not sort of clear cut high school level physics. So Paula asks here, how do Newton's laws of motion apply to objects moving in circular motion? That sort of high school level physics and sort of more complicated. So the people you take, you have a string, you have something tied at the end of the string and you whirl it around. Everybody knows that the string will try and it'll try and pull itself away from you. And that is often referred to as centrifugal force that the thing will centrifugal, fugal comes from the Latin, I guess, to run away from. And that's running away from the center force. So it's, the thing is effectively pulling away from you. And then people will say in physics textbooks, no, no, no, you shouldn't talk about centrifugal force. You should only talk about centripetal force. And this is all gets very confusing. First point, okay. Newton's first law says if you don't act on something with a force, it'll just keep going in a straight line. It'll just keep going in the same direction forever at the same velocity, that is the speed in the same direction. Okay? So that means if you want to keep something going in a circle, you've got to put some, you've got to, you've got to exert a force on it. Otherwise just can keep going in a straight line. So for example, so that's why you know, when you're string, you have got to be pulling on that string to get the object not to just fly off in some direction. So that centripetal force is the force on the object that's pulling it in to keep it, to keep it a fixed distance. You know that the, the to, to keep it just the distance that this, that the taut string is rather than sort of whizzing off to infinity. And so that, and in order to keep it at that distance, you have to exert a certain force. And depending on how fast the thing is going around, that force will be higher the faster it's going around. And the, the basic point is what you've got to do is, okay, so here's the thing. Left to its own devices, the object will just keep going in a straight line. It would take its velocity, velocity, its speed in a certain direction would keep it constant. But what you've got to do is to change the velocity. You're not changing its overall speed, but you're changing the direction of the speed. And so that change, change of the direction of the Speed is again, a form of acceleration. One form of acceleration is just you are going in a certain direction. You change the speed at which you're going in that direction. But you could also be changing the direction of the speed. And in order to do that, you have to say, well, I was going at this speed in this direction, but now I want to reduce the amount that I'm going in that direction and instead go in this other direction. And that corresponds to changing the speed that corresponds to an acceleration. So that's why it's the necessity. If you want to keep the thing going in a circle. The necessity of changing its velocity means that it has to be accelerating. In order for it to accelerate, you have to exert a force on it. That's the force that you're pulling on it with a string with. And so what's an application of that? Well, if you have something being pulled towards the center of the Earth by gravity, and yet. And you want it, okay, so a spacecraft that was just tooling along in interplanetary, interstellar space, nowhere near any planets or stars or anything like that, is just going to keep going in a straight line in a first approximation. That's Newton's first law. If it gets near the Earth, the Earth will make. It will exert a force of gravity on it, and so it will pull it towards the Earth. But the whole point is that you can get a situation where you have an orbit where the thing has to be pulled by a certain force. It's being pulled by a certain force of gravity. It is that force is causing the thing to change its acceleration. I'm sorry, to change its velocity. And you can arrange things so that you've got at the right speed, there'll be a match between the acceleration that comes from the force being exerted by gravity and the acceleration needed to just sort of slip around the Earth in orbit. And so for low Earth orbit, that speed is about 17,000 miles an hour. If you're going at that speed, you will be the kind of. The force of gravity just matches what you need to change your velocity so that you just keep going around the Earth. And for different planets, that speed is different. And that's the. So that. That's kind of an application of kind of circular motion and forces in circular motion. The. Yeah, let's. Now, when. When it comes to. If you really want to get complicated, okay, we'll. We'll skip to something a much more complicated version of circular motion. A very confusing thing about the universe is how rotation works in the Whole universe. Maybe we won't get. Maybe we won't talk about that. We can talk about some. Well, there's a kind of a circular motion phenomenon in black holes that's pretty funky when usually the force of gravity just pulls things right into the center of. Like on the Earth. In a first approximation, the force of gravity just pulls everything towards the center of the Earth. It's not precisely the center of the Earth. There's usually one in a thousand deviation from it just going towards the center because the density of rock in different places is different and so on. But first approximation just pulls it in towards the center. Okay, there is an exception to this. There are black holes that were formed from the collapse of a star that was spinning around rapidly. Probably the details of exactly how that formation process works are not well understood. But probably that leads to black holes that are effectively spinning. I say effectively spinning because there's really nothing about the black hole that allows you to tell that it's spinning. Because a black hole, it's like having a perfect sphere. If you're just looking at the perfect sphere from the outside, and it's a perfect perfect sphere. It's just the fact that it might be turning around. You can't tell. It's just. There's a sphere there. You'd have to have some little bit on the surface that you can see. Oh, yeah, that got moved around. But if the sphere is really perfect, you can't tell that it's moving, that it's spinning from a distance. Okay, so. So it is with black holes. They're very perfect in their sort of perfect spheres. But there are a type of black holes called Kerr black holes that have the property that the, the, the. So in black holes, you. There's sort of a. A black holes, more or less. Most of what you talk about in black holes is the gravitational field in a black hole, what's inside it, and whether there's a crushed star inside it or whether there's something different inside it. You can't tell from the outside. All you can tell from the outside is what the gravitational field looks like, what the. What the force due to gravity looks like. Okay, so in these black holes that have this spin parameter, there's this weird thing that happens called frame dragging. And what happens is that everything that the force of gravity is not just going towards the center. The force of gravity is something that causes objects to get sort of dragged in a circular motion around this black hole. So that's a funky effect. And you can get, well, all kinds of all kinds of interesting things happening there. An example of another weird effect in circular motion is a photon. So photons of particles of light, they have, well, they have zero mass, but they can have a certain energy. One of the really funky things that can happen with black holes is that photons can orbit black holes. So normally you have a satellite orbiting the Earth. It's a massive object orbiting this massive planet. But one of the weirder things that can happen, particularly with these spinning black holes, is that you can have a photon that has. Does it happen with non spinning ones? I'm not sure. I think not. For some reason you can have photons that orbit the black hole. So you can have essentially light continually circulating around this black hole. It never escapes, it never goes off to infinity. It's just hanging out there, circulating around the black hole. Just another weird thing to a weird effect. All right, maybe one more question. We seem to be on a quotes elementary physics story here. Well, there was a meta question here. How would you structure a discussion on. On introduction of physics? So if you mean if you were going to explain physics without kind of from scratch, what would you talk about? You know, I think the thing is physics gives you kind of simple explanations. Elementary physics is about giving you simple explanations for certain kinds of things that happen in the world. And there are lots of things that happen in the world, but there isn't a simple explanation that can be given. There are lots of things in the world where maybe the microscopic rules that determine it are simple, but the actual phenomenon is quite complicated and you can't necessarily work out how it will work without just sort of following all those microscopic rules. So if you ask what can you say that's easy to talk about in physics there are different areas. There's mechanics, the story of motion, the story of forces, things like this. We just talked about a bunch of those kinds of effects. There's a certain distance you can go where you are able to talk about things in simple ways. When you have things like friction or coefficient of restitution or viscosity, something like that, the microscopic details of what produces those things is often very hard to explain. But if you just say and let's assume the coefficient of friction is 0.3, then you can work out the mechanics around that. That's one area. Another area is optics, properties of light. There's a bunch that you can see fairly easily with things like lenses and so on. Again, in a lens, light is bent due to the so called refractive index. The speed of light is different inside the glass than it is in the vacuum. If you say, why is it different? That can actually be worked out. The refractive index is not so hard to work out in at least certain simple cases. But again, it's much more complicated than sort of elementary physics to work out the refractive index. You just say, okay, okay, the refractive index of water is 1.33. We don't really know why, but if we assume that we know light goes 1.33 times slower in water than does in air, and we can make certain conclusions about refraction and so on from it. So there's a little slice of optics that you can work out. Optics is actually pretty good in this respect. There's a lot you can work out in optics where you're just following fairly simple formulas and so on. Electricity and magnetism, There are again certain things you can work out fairly easily, Mostly having to do with what electromagnetic fields do when they're not inside materials and so on. What happens when you have sort of working out when is there magnetism in a material? When is a material a superconductor or something? These are very hard to work out. But if you say, well, the material just has such and such a property, what consequences does it have for the electric field, the magnetic field? That's fairly easy to work out. The people long ago used to teach fluid mechanics a lot in physics. They don't teach it very much anymore, mostly because there's rather little that can be said simply about it. There are rather few formulas that work there. Mostly it's pretty hard to compute what happens, the flow of fluids around an airplane or something. Very hard to work out. You know, working out things like this drag coefficient. I think I told you the one formula that's sort of an easy to work out. Well, it's not so easy to work the formula out, although it's not undoable. But once a simple formula there. But fluid mechanics tends not to be taught so much in elementary physics. Let's see, the other big area is thermodynamics, the story of heat and temperature and so on. And again, if you assume certain properties of materials, you just say the specific heat of this is blah. Then you can do calculations. There's a sort of domain of calculations that are fairly easy to do. Like if you put certain, certain amount of heat into a substance, then the temperature will increase by something that's proportional to the so called specific heat. Well, the, the specific heat times the temperature gives you the heat that you have to put in to raise the thing by that temperature and so on. Then, of course, things complicated things happen. Like water can boil into steam. The process by which that boiling happens is very hard to work out. Still not completely understood, but you can just say, and by the way, at 100 degrees centigrade, at normal pressure, water will turn into steam. And you can work out things assuming that fact. But to work out that fact is hard and actually as yet undoable. So the story of elementary physics is a story of kind of navigating between these different things that are hard. And the fact that there is a path between the hard things is actually kind of interesting. It's the same thing happens in mathematics. There are questions you can ask in mathematics that you study in elementary mathematics that are askable. And then there are other questions where it's like, no, nobody knows the answer to that. Things like, you know, if you look at prime numbers and you look at twin primes, like, like 11 and 13 primes that are two apart, nobody knows whether there are an infinite number of twin primes. That's an elementary thing to ask, but it's very hard to answer. But there are questions in mathematics. You can say, for example, every number has a unique decomposition as a product of primes. That's something which for 2000 years, people have kind of actually, when was that proved? That was proved. Not sure that was proved. That was probably more recent than that. I don't think that was known to Euclid and people like that. But in any case, it's something you can work out. But so in mathematics, like in physics, there are things that are sort of elementarily workable out. There are things where we humans can readily see what's going on. And there are things kind of if we step off the path, we quickly go into the jungle and we quickly go into things where it's very hard to answer. And same happens in physics. So there are these particular areas of physics where it's been possible to kind of navigate through and get to easy answers. And there are general principles about how physics works where it isn't as easy to sort of do the exercise, work out the numbers and so on. And those are quite robust. And those are. Those are interesting areas to explain if you're explaining sort of physics. Now, you know, the other thing that the things I've just mentioned are kind of the main areas of elementary physics. Kind of the next big story is the story of how atoms work and how quantum mechanics works and so on. That tends to be sort of a more advanced discussion in physics. I'M hoping that it won't need to be more advanced. I'm hoping that as we understand more from our physics project about how quantum mechanics really works, that it will be possible to discuss that in almost as elementary a way as all these other things. And then we have. There are aspects of physics which are actually pretty easy to explain, but which tend not to get explained in elementary physics. Probably the most notable of those is particle physics, where the dynamics of how particles interact when they collide and all that kind of thing. Very complicated. But the basic statement that a proton has three quarks, roughly in it, two up quarks and a down quark, that's pretty easy to understand. A neutron has an up quark and two down quarks, and so on. And it's pretty easy. It's a matter of just simple arithmetic to say, okay, these quarks have these properties, these electric charges, et cetera. Etc. Etc. Etc. What consequence does that have for these particles? And there's a sort of zoo of particles, and it's pretty easy to work out what particles can exist on the basis of these different combinations of quarks and so on. It's always been surprising to me that because in the history of physics, all this stuff about particle physics got worked out through very sophisticated mathematics and so on, but the results do not require that. The results are pretty easy to explain. But yet, at least in the US it tends to be the case that there isn't really a discussion of those things in quotes, elementary physics, even though there certainly could be, because it actually isn't complicated. There's nothing you don't need to know. Fancy math, even though that was how people historically got there in the 1950s, 1960s and so on, you don't need to know that to understand it. Similarly, when it comes to things to do with gravity and black holes and so on, there's a fair distance you can get without fancy math. And I think actually our physics project gives you even further that you can get without fancy math. But it also shows you if you step far off the path, it's really a very dense jungle out there. And that dense jungle has a lot of things to say about what is predictable in the world and what's not. But actually, what of the things it does tend to say is that by the very fact that, you know, the jungle is dense, you know, there's lots of sort of randomness and complexity going on. Even that fact alone gives you certain simplifying consequences that allow you to make statements all right. Well, we should probably wrap up there, and so thanks for joining me, and bye for now.