New Revolutions in Particle Physics: Standard Model | Lecture 1
Susskind, Leonard
(January 11, 2010) Leonard Susskind, discusses the origin of covalent bonds, Coulomb's Law, and the names and properties of particles.
 Stanford University. Okay, so we've talked about a lot of things so far. Fields, quanta of fields, the relationship between fields and particles. That's the relationship between fields and their quanta. What are the quanta? The quanta are the discrete, indivisible units of energy that quanta mechanics implies for waves, for waves and waves of course are fields. Fields and waves are more or less the same thing. We've discussed the properties, not the properties of individual particles very much, but we've discussed some general properties, the properties of having energy, momentum, the properties of having spin, and the property of either being a fermion or a boson. Every particle is either a fermion or a boson. Fermions are the particles that don't like to live together in the same state. Bosons are the particles that do like to congregate and do condense into the same state. We've talked about wave equations on occasion or the field equations if you like, more generally. There is a kind of field equations. And we talked about how field equations can be generated from Lagrangians, from action principles. The quantum mechanical version of the Lagrangian is a kind of tool for codifying or codifying, whatever the right word is, codifying the interactions between particles. Various terms in the Lagrangian, things like, for example, products of fields represent processes which we can call vertices where particles come in and other particles go out. That would, for example, be a term in the Lagrangian which would have four powers of a field in it. So we've talked about these general things. We haven't talked very much about specific particles. Tonight, well, I expected to spend the first half hour beating around the bush a little bit. I'm going to spend a few more minutes beating around the bush. But then I want to come to really writing down what the particles are, who are the players in the drama, and start going through them more or less, well, not quite one by one, but in groups, and trying to give them some personality, give them some names, some properties, and also what it is they do and how they come into physics, into ordinary physics. Okay, but before I do that, there's kind of a triangle of concepts that we've discussed two legs of, but not the third leg very much. The triangle is particles or field quanta, particles, fields, and in modern physics, pretty much for every elementary particle. Now, we're going to have to think very hard in the future, not tonight. What is an elementary particle and what is a composite particle? We will come back to that. And you might think, I mean, everybody here probably has some answer if I were to ask you, how do you distinguish a composite particle from an elementary particle? And you will always be frustrated. You will always find some slippery reason that your definition didn't work. But for the moment, let's nevertheless imagine that there are elementary particles and that the elementary particles are the quanta of elementary fields, fundamental fields in the theory. And so they're more or less than one-to-one correspondence. But there's a third leg to this triangle. Anybody know what it is? Of course, you don't know what I'm thinking, so even if you did know what it was, you still wouldn't know it. Forces, forces, forces. So you can sense forces, forces. Okay, basically for every field there is a particle. For every field there is a force. Electric field gives rise to electric forces. Gravitational field gives rise to gravitational forces. It may be less obvious to you what the electron field, the electron has a field. It also gives rise to forces, and we'll talk about them a little bit. So there's kind of a correspondence that goes this way, there's a correspondence which goes this way. There must also be a correspondence which goes this way, a way of thinking about forces which is not based on fields, but which based on particles. If this correspondence or this triangle really makes sense. So I want to talk about that a little bit. Many of you know the idea, but let's just discuss it for a moment. Let me first discuss it in the context of electrodynamics. How forces come out of thinking, now this is classical electrodynamics for the moment, the complete field view of things. Supposing I put two charges into space, I want to know the force between them. How do I calculate it? Well, you could know the rule that the force is equal to the product of the charges times one over r squared and so forth. Or you could try to calculate it a different way. You could try to say, what do these two charges do to space? What they do to space is they create electric fields. Essentially that's the thing they do. They create an electric field that fills space. And I don't want to write down the details of what that electric field is. But let's just say this is the electric field. Let's forget the second particle and just write down the electric field due to the first particle, whatever it is. The electric field due to the first particle, incidentally it's proportional to the electric charge of the first particle. So let's explicitly put that in. E of the first particle times the electric field divided by the electric charge. This electric field here, I've divided out the electric charge. Maybe I shouldn't call it E. Let's call it E without the factor of the electric charge in it and put a little hat over it. That's this electric charge. And what is the field energy? Anybody know what the formula for the field energy is in an electric field? Electric fields have energy. They store their energy as a distribution of energy in space. And the field energy, the density of field energy, is the square of the electric field. So we square this and we integrate it over all space, the volume, and that's the energy stored in the electric field of the particle. Now, this energy does not depend on where we put the particle, right? The field will move. If we move the particle, the field will move with it, but the field energy will always be the same. The electric field will adjust to the position of the charge. The field will always give rise to exactly the same field energy. And this field energy here, remember E equals MC squared, that field energy is part of the mass of the particle. It contributes, the field contributes to the energy of the particle, and therefore it contributes to the mass of the particle. There's another way of thinking about a bit of renormalization, that there's some extra mass there because the field surrounds the particle in this way. Okay, I don't want to belabor that now. What about the second particle? Supposing the first particle wasn't there, but the second particle was there. This, of course, is the energy E, not the electric field. This is the energy. If there was only particle two, the field energy would be the integral of E2 times the electric field of the second particle squared. Now, if the two particles are not at the same place, well, let's not worry about the two particles. This one would also be independent of the position of this particle here. What about the energy if I have both particles? If I have both particles, then I have to add up the field first before squaring it. So the electric field, if I have two particles, will be the sum of the two electric fields, electric field, not energy. Let's call this energy En. Well, let's not call it H. Energy, just En. The energy, first of all, the electric field. The electric field will be the sum of the two electric fields. The electric field will be E1 plus E1, E1 plus E2, E2. Where these are the electric fields of particle one and particle two. This will be the total electric field. Incidentally, the electric fields are vectors, and so we might put little vector signs above them. The field energy you get by squaring this whole thing. So the field energy is the integral of a space. There are three terms. The first term is E1 squared, E1 squared. It's gotten by squaring this. The second term is plus E2 squared, E2 squared. And the third term is the interesting one. It's the product of E1, E2, twice as a matter of fact, times E1 dot E2. Actually, dot product. All right. What is this first term here? It's the self-energy. It's the self-energy of one particle by itself. It doesn't depend on the position of the particle. It's just a number. It's part of the mass of the particle. Let's forget it. It's already there as part of the mass of the particle. What about this one? Also, part of the self-energy of the second particle. What about this one here? This one is not the energy of either particle separately. It's proportional to the product of the charges. And it's proportional to the product of the fields. What if the particles were infinitely far away, so far away that their Coulomb fields hardly overlapped at all? You take one particle so far away that the Coulomb fields are hardly overlapping. Then this is going to be zero because wherever E1 is not zero, E2 will be zero, or almost zero. Wherever E2 is non-zero, E1 will be close to zero. So this will be very, very small as you take the particles apart. But what about when you bring them together? When you bring them together, the product of E1 times E2 will not be small. Nearby, where the particles are, both fields will be appreciable, and you will get a contribution from this. What is that contribution? That contribution as a function of distance, well, first of all, it's proportional to the product of the charges. It depends on the distance. And of course, if you work it out, as you might expect, it's nothing but the Coulomb force, one of our R squared. But I like to say it this way because it gives you the following picture that putting in both charges, taking them far apart, they don't affect, well, they're simply just independent objects. As you bring them together, they deform and distort the field in a way that depends on the distance between them, and the distortions of the field in between them, that field energy. That field energy, which is the contribution because both of them are there, that's the force law. So that's a purely field point of view of forces. A purely field point of view of forces. But if fields are nothing but collections of quanta, and quanta are particles, there must also be a way to think about forces in terms of particles. So let's talk about that a little bit. Before discussing electrodynamics in this way, let's talk about a slightly different setup. We're actually a very completely different setup. Let's talk about molecular forces. What do molecular forces come from? I'll give you one source, there are several origins of molecular forces. But here's a setup I want to think about. Let's begin with a pair of protons and a single electron. What is this? A proton over here, a proton over here, and a single electron. If this proton were very far away, then the ground state of the electron in the presence of the proton would just be the hydrogen atom ground state. It would be governed by some sort of Schrodinger wave function. Let's draw the Schrodinger wave function. The ground state would be the ground state of the hydrogen atom. And in the ground state, if this proton weren't there at all, not there at all, the electron in its ground state would certainly be found in the position nearby this proton. Now what if there are two protons over here? One proton over here, another proton over here, pretty far away, but not infinitely far away. Then there is another possible state of the electron with exactly the same energy where the electron is not over here, but it's over here with the corresponding wave function pushed over to here. It has exactly the same energy. Why? Because the two protons are of the same kind, and everything is completely symmetric over here. So if the electron is in orbit, well, a quantum mechanical orbit around this proton, or if it's in quantum mechanical orbit around this proton, the ground state energy will be exactly the same as if there was only one proton. But it's not quite true. Why isn't it exactly true? Well, if the protons are not infinitely far away, there are processes that could happen which could not happen if they were infinitely far away. Anybody know what the process is that can happen to the electron if the two... Tunneling effect. Tunneling effect. Yeah, the tunneling effect. The electron placed over here into its ground state can, with a small probability, suddenly appear in this atom over here. That's called quantum mechanical tunneling. It has to overcome an energy barrier in between the two. It takes some energy to pull the electron out of this atom. It'll get that energy back when it drops into this atom, but it has to go over this hill. Can it go over the hill? Classically it can't, but quantum mechanically it can tunnel from one place to another. Don't stand there and try to watch the tunneling. What happens if you try to watch for the electron going back and forth? Like anything else in quantum mechanics, watching it ruins it. You can watch over here. You can say, well, you can stand over here and wait for the electron to appear over here, but if you watch it from in here, you'll ruin the phenomenon. So the electron can hop back and forth. Hop back and forth simply means that there's a tunneling transition, a tunneling rate or a tunneling probability that if you put it over here, it can appear over here. If it appears over here and you wait a while, it will reappear over here and so forth. Okay, this process sets up a kind of equilibrium, long-term equilibrium in which the electron has an equal probability of being over here and over here with a wave function which looks like the sum of the two wave functions. Well, the sum divided by the square root of two in order for probability to add up to one. All right, so it looks like the sum of the two wave functions, which I didn't draw very well, but in the middle over here, it's slightly different. You might draw the exact wave function of the electron orbiting particle one as if particle two were not there. Same thing for particle two. And then add them up. Well, the correct tunneling wave function, the correct equilibrium wave function, is not exactly the sum of these two wave functions. It's a little bit different in here, a little bit, not much. But the point is the energy of the system is not exactly what it would be if the two protons were infinitely far away from each other. If they were infinitely far away from each other, you could put the electron over here, it would have a certain energy, or over here and it would have exactly the same energy. When you put them closer together, the energy of the electron is not exactly the same as it would be if they were far apart, if they were infinitely far apart. So if I were to plot the energy as a function of the distance between them, when they're very, very far apart, the energy of that electron is simply the energy of the electron with only one proton, and the other one just not there at all. At large distances, the energy would just be whatever it was. But as you bring the protons together, the energy of that two protons plus electron is a little bit less, turns out to be a little bit less, and that little bit less is a function of the distance between them. So now we have a situation when the system is in equilibrium with the electron tunneling back and forth and in equilibrium between the two, the energy is a function of the distance between them. What's the relationship between force and energy? You can think of this as potential energy. You can think of this as a potential energy between the two protons. The derivative of the energy. So the derivative of the energy, the energy has a gradient in here, force always pushes you toward decreased energy, and so this effectively creates an attraction between the two protons. That attraction is a kind of covalent bond. It's a kind of force between the two of them, which is due to the sharing of an electron, or to the fact that the electron can be in a superposition of quantum states in the two wells, in the two potentials of these two things here. Now, does that mean that a proton and another proton with an electron between them, which has this attractive force, will bind together? Not quite, because there's another force around. What's the other force around? The electrostatic force. The system doesn't have zero charge altogether, and so there's a repulsion force, and the repulsion force can overwhelm the attraction force, but nevertheless there is a force between two protons if there is an electron around, which is due, in a sense, to the jumping back and forth of the electron, or to the diminishing of the energy by the wave function sort of adjusting a little bit, a little bit better than it would if you just added the two wave functions together. As I said, that's the origin of covalent bonds, sharing of electrons, and in this case you can think of it, you can draw a picture. Now, the picture may or may not do anything for you. You have a proton over here, that's the world line of a proton, another world line of a proton, and the electron might start out being bound to this proton, hop across to this proton, hop back across to this proton. You shouldn't take this too literally, because if you stood in the middle, as I said, you would disrupt the process, but it's a description of the quantum mechanical state of the electron between the two protons, what it does, this possibility of the electron jumping back and forth, lowers the energy relative to if you just had one proton and just one electron in a bound state there. That means that there is an effective force, and you can picture it. This picture is like any analogy, it's often very, very misleading, but the presence of the electron in between the two protons creates an attractive force. It's called particle exchange, it's called particle exchange or electron exchange between the two protons. Now, yeah. So, is it as being the electrons hopping back and forth as reducing the effective positive charge of it? No, I don't think that that is quite the right picture. It doesn't really depend on the electric charges. It just depends on the fact that you can find, by adding together two wave functions, you can find a wave function with a little bit lower energy than either one separately. Is this what the magnet referred to as life-like-slide? That's what the magnet used to say, like, like, like. Like, like, like, I don't know. No, no, no, no, he was probably talking about the Bose's statistics of that photons like to be in the same state. I don't know what he was talking about. He made the same thing, he said that light, likes, like, like. Electrons like each other, photons. No, no, electrons hate each other. They don't like to be in the same state. Photons like each other, they love to be in the same state. I think he was probably talking about the opposite of the exclusion principle for photons, the Bose's statistics of them. Of course, I don't know. Protons have a tendency to be a cow. Protons. Yeah, that's because of their electric charge. Right, now what happens if we put the electron between them? Is that reducing the impulse? It does a little bit, but not very much. In fact, the force due to the electron jumping back and forth is a much shorter range force than the electrostatic attraction. So this force would only be important at relatively small distances, whereas the Coulomb force would fall off much more slowly. So the Coulomb force would be a longer range force. But, you know, it is there. It is there. The reason why it shows up is if you have a neutral system. I mean, it shows up better if you have a neutral system. If you have two electrons so that the total charge of the system is zero, then of course you'll have the possibility one electron orbiting around this proton, a second electron orbiting around this proton here. Now, the two objects here, they're called atoms, hydrogen atoms, and they're called electrons. So if you have a neutral system, there is no electrostatic force between them, but you still have this possibility of electrons jumping across. Electrons can jump across, a tunnel across, and then it does create an attractive force which can bind an atom, bind a molecule. Yeah, yeah, yeah, it is bound, but... Yeah, at small distances. At small distances, it is enough to overcome the Coulomb force. That's right. Yeah. Is there a possibility between the two protons that creates some kind of tension between them that creates some third force that the electrons kind of orbit around? Well, it doesn't create a third force, but it creates a sort of slightly nonlinear effect due to the two forces. But it's just a solution of the Schrodinger equation in the presence of the two forces does not have the energy that it would have if it was just one of those charges there. But let's leave it at that. There is this notion of the energy being lowered by the possibility of alternating between two quantum states. Is this thing all related to quantum entanglement? Not so much quantum entanglement. It's related to what are called off-diagonal elements in the Hamiltonian, but it's not too closely related to entanglement, I would say. For entanglement, normally you need two electrons. You only need one electron for this. For very, very, very high temperatures, does the electron move between the protons from a much higher probability? Well, at high temperatures, because it depends on the temperature, at very, very high temperatures, all that will happen is the electron will get kicked out and go to Alpha Centauri, and it won't even remember the fact that there was a proton around. If it gets hit hard enough by a very hot photon, but if the temperature is not that extreme, what it can do is cause, even if you only had a single atom, it could cause the electron to occupy higher levels. Now, higher levels have bigger wave functions, so the overlap between the higher wave functions could be larger, and it would certainly have some effect on the force. But that's a kind of special effect. All right, we have a concept that we see in the classical electrodynamics that the effect of having two charges changes the energy in between relative to what it would have been if you only had one, and it creates a force. Similar kind of thing here. If you have two force centers and the possibility of the electron being in a superposition of states, in other words, of the equilibrium being in a quantum superposition of the two states, the two states being over here or over here, that also lowers the energy and creates a force. Is there a way to think about the Coulomb force here in quantum mechanics where it is in some sense similar to this jumping back and forth of the electron? Yeah, there is. Let's come back to a single proton. A single proton is interacting with the electromagnetic field. That means it's interacting with the field whose quanta are photons. Classically, we might just describe it by solving the field equations for the electric field in the presence of a charged particle. Quantum mechanically, we think about it differently. Particularly in quantum field theory, we think about it as the emission and absorption of photons. That's what the Lagrangian of electrodynamics tells us. It tells us about the probability for the emitting and absorption of photons. So one way of thinking about the electron is that the actual physical electron is a quantum mechanical superposition of states in which, first of all, there are no photons. A superposition of a state with no photons. A superposition of states in which a photon has been emitted, and therefore there's a photon present. So it's a charged particle together with a photon around. Two photons can be emitted. The photon can be reabsorbed. The net effect in the end is some kind of equilibrium distribution, quantum mechanical equilibrium distribution of photons surrounding the electron. And you can measure those photons. I mean, a little bit different than measuring free photons. These photons are sort of trapped at the electron. They're emitted and reabsorbed. And if I have another electron over here, it is also emitting and absorbing photons. So there's an equilibrium. But every so often, now this should be thought of in the language of Feynman diagrams, every so often a photon which is emitted from here gets absorbed over here. And I always think about it as two jugglers, each juggling balls. And every so often, if they happen to be close enough together, a mistake will be made. And Joe will grab Mohr's juggling objects. Really what you really want to do is you really want to calculate the energy due to the electromagnetic field or due to the quantum superposition of photons that are present. You want to calculate that energy as a function of the distance between the charged particles. When they're very far apart, the two energies just add. They just get the sum of the energy of one charged particle and another charged particle. But as they get closer together, the charges begin to influence each other or in the language of Feynman diagrams, the emission of one photon by one particle and the absorption of that same photon by another particle creates a force. Creates an energy which is not exactly the sum of the two energies. That energy is the Coulomb force between the charged particles. So we have two distinct languages. Well, apart from just writing down the Coulomb force law, we have two other ways of thinking about forces. One of them is through classical field theory where you calculate the fields of objects and square them. And the other way is through the exchange of particles. Feynman diagrams with particles are exchanged back and forth. Any particle can be exchanged in some context or another. So every kind of particle in one way or another produces a force. In molecular physics, it's the exchange of electrons which create forces. In electrodynamics, it's the exchange of photons back and forth which create forces. So any particle is also connected with a force when that particle can be exchanged or jump back and forth between two something else. We'll describe some more examples, but I did want, before we move on, to just discuss the relationship between particles and forces. So we more or less have a one-to-one-to-one correspondence. Particles, fields for which those particles are the quanta, and forces which are associated with exchange processes where that particular kind of particle can bounce or jump back and forth. That's an important theme. So when people say that there are four forces in nature, now there's a force for every possible kind of particle. And we will discuss some of them as we go along. Okay, I think it's time now to start naming the particles, listing them, listing their properties, and discussing what they can do, what kind of processes they can engage in. And I could write down a big long list of all the elementary particles and then give you a test next week to see whether you memorized it or not. That wouldn't be fun at all. I think it's probably better to divide them up into small groups, which are in some way simply related to each other, get familiar with them a little bit and what they can do before we try to write down the whole damn standard model of particle physics, which is a monstrosity. I mean, you know, it's not my fault, certainly not my fault, that the standard model of elementary particle physics is an ugly monstrous mess. It's not Steve Weinberg's fault. It's nobody's fault, or if it is somebody's fault, that person, well, he may be in the room, but he's a little bit diffuse. Frankly, we don't understand why the particles are what they are. We don't understand why there is an electron and no particle whose name slips my mind because nobody's ever named it, because it doesn't exist, but nevertheless, why some particles exist and why other kinds of particles don't exist, we largely, by and large, don't know. We do understand some relationships between particles. If this one and that one and that one exist, then there's got to be another one to match up with them in some appropriate way. But in the end of the day, there are many more parameters, many more different types of particles than there are known relationships between them, which cut down the size of the problem. Okay, the mathematics and the relationships cut down the size of the problem somewhat, factor of two, factor of three or something like that, but there are hundreds of particles. So it is, honestly, a mess. If you want to understand what people are hoping for in the next round of experiments and so forth, you'll have to understand some of that mess and what the puzzles are about it. So let's begin. Let's name the particles. We begin with the most obvious ones. Let's make a table. Let's see, we need some columns. We can put the name of the particle over here. I'll put the symbol for the particle over here. I'll put the particle type over here. Now, what do I mean by type? I simply mean whether it's a fermion or boson. I'll put the electric charge over here. There's another quantity which characterizes particles. We'll call it the baryon number. I'll tell you what it is as we go along. And there are other properties. At the moment, I'm not listing them. And we'll put the mass over here. All right. The first one, of course, said I'm not listing them in any particular order. As it happens, I am writing down the lightest one first. The lightest one is, of course, the photon. The standard symbol for a photon is a gamma, like for a gamma ray. It has a field associated with it. The gamma particle is the quantum of a field. In most cases, or many cases, the field carries the same symbol as the particle itself. But for the photon, the field is called A. And it's really the vector potential of the electromagnetic field. You could use electric or magnetic fields, but you can also use the vector potential, which is another way of describing the electromagnetic field. It has a boson. I didn't write down the spin, but the spin is one unit of spin. The electric charge is zero. The baryon number, whatever that is, is zero. And the mass is zero. So that's the first particle. The next particle of interest is the electron. Now, the electron is a particle which has an antiparticle. It has an electric charge. If it has an electric charge, it must have an antiparticle of the opposite charge. And it is a convention, whether we think of the particle as the electron and the antiparticle as the positron, or whether we think of the positron as the particle and the electron as the antiparticle. The relation between them is mutual. So when I write the electron, I really mean the electron and positron. And so we could write E here plus minus. Standing E minus is the electron. E plus is the positron. The field of the electron is usually psi. And maybe you could put a little E downstairs to indicate that it stands for the electron. It's made up out of creation and annihilation operators for electrons. Electrons are fermions. It's charged. Okay? It's charged in what units now? Well, the standard particle physics or quantum mechanical unit for electric charge, believe it or not, is the electric charge of an electron. It's a good unit to work in terms of. You can go look it up in coulombs. It's 10 to the minus, what, 23 coulombs? 10 to the minus 19th coulombs, or yeah. It's some very small charge. But it's not useful to think about it in coulombs. All particles in nature have electric charges which are integer multiples of the electron charge. This could not true of quarks, but quarks are not observable particles. All right. So the charge we'll just write as minus one for the electron and plus one for the positron. So since we typically think of the electron as the particle and the positron as the antiparticle, let's just call it minus one and remember that the positron has the opposite charge. Variant number is zero and it's mass. Now we have to decide on units for mass. Okay? Units for mass are the same as units for energy. E equals mc squared. So we can either describe the mass as a mass in kilograms or in energy in joules, or we can simply invent a new unit which is more appropriate to microscopic physics to atomic physics. In fact, the unit that we use comes originally historically out of atomic physics. It is the unit in which the ionization energy of an electron and a hydrogen atom is what? 13.5 electron volts. An electron volt is how much energy you get if you pass an electron across a capacitor plate of one volt. It's a very, very small amount of energy, some tiny fraction of a joule. But one electron volt is the standard unit that came historically out of atomic physics, theory of electrons and so forth. It's going to wind up being too small a unit for us. Particle physics energies are larger than atomic physics energies, but for historical reasons we have the electron volt as our unit of energy. And the mass of an electron measured in electron volts is of order a million electron volts, one MeV. In fact, it's a half an electron volt. Not exactly. I think it's.51 MeV, and MeV stands for millions of electron volts. And MeV will be too small a unit for many other purposes. As I said, the particle physics is a mess, and the masses of particles extend all over the map. And so in trying to search for a useful unit, you're always frustrated. The useful unit will always be too small for the next... No, why? No, it's exactly.51. No, it's not. What's that? Pi 3. Pi equals 3. Pi equals 3. Right. Okay, now, quantum electrodynamics is the theory of electrons and photons, and we've talked about it a little bit, more than a little bit. And just we could also write down over here a table of the various... I don't want to make it a table. We'll just draw some pictures. The basic elementary process that takes place in quantum electrodynamics, photons and electrons, is the emission of a photon by an electron. Electron, electron photon, and as I've showed you several times, you can rearrange the legs of this diagram so that this could represent not the emission of a photon, but the absorption of a photon. A photon comes in from the past, or... Oops, sorry. You can even flip the electron legs around so that it looks like this. Electron going backward in time. Well, what does that mean? That really means a positron emitting a photon. So the basic building block for building up processes and interactions is this vertex with two electrons, electron, positron, whatever coming... one going in, one going out, and a photon coming out of it, or going into it. Out of that, you build up all of the various processes of quantum electrodynamics, but in particular, the process or the phenomenon that corresponds to the force between charges, and in the language of particle exchange, it's the photon bouncing back and forth between charged particles, which creates that force. Yet another way to describe what's going on here is in terms of a Lagrangian or a term in a Lagrangian. The Lagrangian describing this process here describes one electron in, one electron out, and one photon out, and so you build that out of the field operators. One electron in is psi electron. It creates, it has the creation of annihilation operators in it. An electron out is psi dagger of the electron, and a photon emitted is the field operator for the photon, and if you plug in all the creation and annihilation operators, you will find in here, buried in here, terms where a photon is emitted, an electron absorbed, another electron emitted, and so forth. And this codifies, this describes all of the various basic processes that can happen in quantum electrodynamics. Now, there's a parameter in the Lagrangian that appears the electric charge of the electron, and that, roughly speaking, is associated with the amplitude for a electron to emit a photon. The electron, let's say you hit the electron or whatever, the electron plows into the side of a x-ray machine. What's the probability that a photon will be emitted? Well, the amplitude is the electric charge, and the probability is proportional to the square of the electric charge. So all of this here is a way of describing all of these basic processes, and when they're combined together, they produce forces, they produce processes where photons are emitted, the whole world of quantum electrodynamics flows out of this, basically, one expression here. We won't try to go through that again now, but let's start adding a little bit to our particle list. The next particles of interest, these are, of course, familiar to you, I'm sure. Now, if this were 1960, when I was, well, I was, 1962, when I went to graduate school, probably the next particles I might write down would be protons and neutrons. Protons and neutrons are now subsumed by quarks. It is widely believed that, in some sense, protons and neutrons are composites of quarks, although we will come, remind me to come back to this issue of the difference, or what it means to be composite versus elementary. It's a very interesting story, but naively, quarks are smaller than protons and neutrons, and so protons and neutrons, which are big fat globs, are made up out of quarks. So, next thing are quarks. There's a lot of quarks. We won't even get to all of them tonight, or the whole set of distinctions between them, I don't think we will, but there's more than one type of quark. There are six types of quarks, six distinct particles, all of which are very similar to each other in some respects, very different from each other in different other respects. So, let's list them. They go under, they have names, all right? Well, why do they call what they are? They call what they are just a historically randomly people assigned silly names to them, and there's no logic to what they're called, no logic at all. There's, first of all, the up quark, and that's called U. The symbol is U. So, let's see, we should write there are quarks here, quarks. And I suppose the symbol for quarks is Q. All quarks are fermions. We'll write down their charge later. They have all baryon number of one-third. Now, why one-third? Well, the reason is very simple. The baryon number is basically the counting of the number of protons and neutrons. Each proton is counted as having one unit of baryon number. Each neutron is counted as having one unit of baryon. Baryon is just a word for protons and neutrons, and a somewhat generalization of protons and neutrons. Nucleon is a word for protons and neutrons. There are other particles which will come to which are very similar to protons and neutrons. They're also called baryons. The prefix barry I think means heavy. And baryons were called baryons because they're a lot heavier than electrons. But counting up the number of protons and neutrons, what do you call the number of protons plus neutrons in an atom? Atomic weight. Atomic weight, yeah. The atomic weight, yeah. Is equal, approximately equal to the total number of protons and neutrons. And the total number of protons and neutrons in nuclear physics never changes. Protons can turn into neutrons. Neutrons can turn into protons plus other things. But the number of protons plus neutrons never changes. You do have isotopes. But still, the number of protons plus neutrons doesn't change. Number of protons can change. How can the number of protons change? No, I'm just saying that different types of protons have different numbers than neutrons. Oh, yeah. Indeed they do. But are there processes with number of protons and neutrons change? Protons, not plus neutrons, but protons and or neutrons change? Beta decay. Beta decay, radioactivity, radioactivity, one form of radioactivity, a neutron decays into a proton plus an electron and an antinutrino. Okay, so in that process, the number of protons changes by one. The number of neutrons changes by one. But the number of protons plus neutrons doesn't change. There's a generalization of that in all of nuclear physics and particle physics. There's a certain quantity, which for ordinary nuclear physics is just the number of protons plus neutrons. And that number is sometimes called the Baryon number. We'll have to generalize it a little bit beyond protons and neutrons. It's a Baryon number. And it could have been defined to be two for the proton or seven for the proton or pi for the proton. But whatever it is, it has to be defined as twice as much for two protons, three times as much for three protons. So it's a convention that you say the Baryon number of the proton is one. Incidentally, what's the Baryon number of the antiproton? Minus one. Minus one. Proton has Baryon number plus one. Antiproton, Baryon number minus one. Neutron, Baryon number one. Anti-neutron, Baryon number minus one, but clearly there's an element of convention in exactly what you call M. But once it was fixed that the Baryon number of a proton was one, then the Baryon number of a quark was a third, because three quarks make a proton. So it's just a historical glitch that the Baryon number of the most fundamental thing in nuclear physics is one third and not one. So if you look out at an antiquark, there are antiquarks. Baryon number is minus a third. So I won't write that down separately. The number of quarks is conserved? Number of quarks minus the number of antiquarks is conserved. Now, whether or not that is an absolute conservation law, it is not believed to be an absolute conservation law. What do I mean by absolute conservation law? Can a proton disappear? It can't completely disappear. Its energy has to go someplace. Are there processes in nature where a proton might disappear and become something that is neither a proton or a neutron or anything else that you would call a Baryon? For example, without violating charge conservation, a proton could become a positron and a photon. So a proton could decay into a positron and a photon. Does it? Well, you can wait. If you have a single proton and you sit there and wait, you will wait a long, long time before that proton decays. It's half life to decay that way is at least 10 to the 33 or 10 to the 34 years. So this is not something that happens very regularly. Does it happen at all? The thinking is yes, it does, but this is one of the very, very interesting questions of particle physics of whether the proton can decay. And when you say can it decay, you mean decay into something that does not carry a Baryon number. And it is widely believed that the answer is yes, but it's never been demonstrated. Incidentally, how do you have you wait around for 10 to the 34 years for a proton to decay? You get 10 to the 34 protons and you wait around for one of them to see one. Now 10 to the 34 protons is a lot of protons. If you have protons, then it's protons. No, that's not that. That's zero Baryon number because it goes to zero Baryon number. One has Baryon number one anti proton has Baryon number minus one. So that's not a Baryon. We call them Baryon violating processes, processes in which the Baryon number is not conserved. Nobody has ever witnessed such a process in the laboratory or anyplace else. Can they happen? There does not seem to be any reason why they cannot happen built into the mathematics of what we know. So we leave this as an open question, but empirically and at least to a very, very high precision, Baryon number is conserved and quarks by definition have one third of a unit. One third of a unit. As I said, minus a third for anti quarks. But in order to fill in the rest of this, in particular, electric charge and mass, we don't have to label which kind of quark we're talking about. And there are lots of different kinds of quarks. So let's put in a list of different kinds of quarks. This is not new particles which are not quarks. This is just a subheading here, quarks and then things underneath. There are up quarks, down quarks. Why are they up and down and not up and down? There's nothing up and down about them. What directions? Up and down? Up and down means in the Earth's gravitational field. There's nothing up and down here about them. Then it gets worse. There are strange quarks which are no stranger than non-strange quarks. It gets more and silly. There are charmed quarks which are charming, I suppose. And then there are, now this is, if you're squeamish or very, bottom quarks, bottom quarks, bottom quarks, and then top quarks. The symbols are of course exactly the same. I just didn't feel like writing the words. Up, down, strange, charm, bottom, top. Same as bottom and top. I got a little pretentious beauty in truth. Bottom and top, strange and charm. How and under what circumstances these things were named is not interesting. I don't know, I do know, but never mind. They're all fermions. Okay, the symbols are just what I wrote here. Sometimes q, sometimes psi q, sometimes capital Q. Sometimes, depending if you're talking about the individual types of them, you'll just use U, D, S, C, B, or T. Use the same names for the fields as you use for the particles. And there's no completely coherent convention that everybody sticks to. All right, they're all fermions. The whole lot of them are fermions, as I said. But now comes the charges. So it's useful to divide them into groups of two. These groups of two are sort of repetitions of each other. This group of two, in many ways, is isomorphic, not exactly, to this group of two, which is not the same, but which follows the same pattern. The pattern of these two is similar to the pattern of these two. Oh, I got them upside down. Excuse me, wait. If I want to keep the pattern, let me see. I think I want to put down, up. Down, up, strange. Down, up. Strange, charm, bottom top. Yeah. All right, so the down, up system is very similar to the strange, charm system. It's very similar to the bottom top system. So let's write down what the electric charges are, and you can see them. You can see this similarity. The down, up system has charge minus a third and two thirds. That's the first example of particles in nature which have charges which are not integer multiples of the electric charge of the electron. However, quarks by themselves do not exist freely in nature. They're always bound into other structures, protons, neutrons, and so forth, and those particles do have integer charges. Okay, the strange and the charm, exactly the same thing, minus a third and two thirds. Bottom and top, exactly the same, minus a third and two thirds. Can that be read? They're just repetitions of the same thing. What about the antiparticles? If I were to list the antiparticles over here, they would just have exactly the same charges as the particles except opposite sign. So this is simply replication. For some reason, nobody understands. Nobody even has any idea why nature replicated itself this way. Are they still all bearing on number one-third? Yeah, they're all bearing on number one-third. Okay, and then the masses, the masses are not similar to each other. The masses wildly vary. I'm going to put down estimates for them because the precise value, well, there are precise values of the masses, but you can go look them up on Google or wherever you want. The down quark is about 10 MeV. So it's 50 times heavier than the electron. A lot lighter than the proton. Incidentally, what's the proton mass? About 1,800 times the electron mass. In other words, about 940 MeV. This is a lot lighter than a proton. The up quark, about 5 MeV, less than the, than the down quark. And protons are made only out of up quarks and down quarks. So it doesn't look like there's nearly enough mass in quarks to be the mass of a proton or neutron. Okay, we'll come back to that. The point is, of course, there's more in a proton than just its quarks. Okay, strange in charm. Strange is roughly order of magnitude 100 MeV. That's strange. And charm is a little over about 1,000 MeV. Now notice that the down quark is heavier than the up quark. But the strange quark, which is analogous to the down quark, is lighter than the charm quark. So there's some pattern of inversion here of the masses. Again, nobody understands at all why that's true. Yeah, charm is about 1,012. A little more than that. Oh, sorry. 100, Mr. Zero. Decimal creep. Okay, 1,000 MeV. And the bottom quark is about 5,000. Oh, this is called a GEV, giga electron volt. The bottom quark, see, we keep changing units. That's about 5 GEV. And the top quark is about 170 GEV. So how much heavier is the top quark than the up quark? Can anybody do that calculation? How much? 30,000. 30,000? A lot. A lot. All right. So on the one hand, these particles are extremely similar to each other. They do the same things. They have the same properties. And yet they have masses which wander all over the map. Does anybody understand why? No. Are there any ideas? Yes. Do any of them work? No. We don't even have a clue about why there's... First of all, we don't even understand, of course, why there's even one of them. One family. These are called families. Why is there one family? Well, we don't know. We're not sure if there wasn't one family who wouldn't be here because there would be no protons and neutrons. But given that there's this one family of up quarks and down quarks, why are there strange quarks and charm quarks, or top quarks and bottom quarks, nobody has a clue. And that question is a stupid question. Yeah. When these quarks were found, the story goes that they were looking in a certain place because the math said the math should be a certain amount. I'm not talking about this. No, they said that they went through the calculations and they knew that this is where it was going to be, that it was going to be somewhere around some AGEV that they were going to find. Oh, the top quark. Yeah. And I was not sure if they predicted that it would be there before they went to the top quark. Yeah, but not on the basis of abstract theory, but on the basis of how the top quark would affect the work its way into other particles, top and bottom. I was just saying because you just said that the numbers nobody knows why and they're all over the ballpark, but yet they seem to know that that's where they wanted to look for it. Yeah, but not because there was any basic underlying reason why the top quark had that mass. What you could do is you could say, supposing the top quark had a certain mass and then calculate various Feynman diagrams involving the top quark in various ways, Feynman diagrams involving ordinary particles, not the top quark, but which had top quarks running around in the interior of diagrams. Okay? You calculate those diagrams. Those diagrams have an effect on processes involving other particles that you know very well, and then you say, how and what does the mass of this top quark have to be in order that it does the right thing for these other particles? Right? So it was not in any sense a deep understanding of why the mass of the top quark was what it was. It was simply an observation that you needed that particular value of the top quark mass in order that it be consistent with... Yeah, right. So you can't observe the quark, but you can predict how it will disappear, what will happen if there is one kind of showers and directions and various particles will be included. Okay. Go ahead. You're asking me the same. Yeah, that's what that was. To say that you can't detect the quark becomes us to a certain extent a matter of definition, what it means to detect the quark. You can certainly detect evidence of quarks. What you can't do is create an isolated quark in isolation from other things and then examine it. But we'll come. We're going to come to the question. I think you're probably remarking about jets produced. Well, I don't know what you're talking about. Yeah, we can talk about jets. Let's come back to it after we talk more about quarks. Does it act that some quarks have twice the charge of the absolute value as far as... Is that from theory or is that just a bookkeeping? It's semi-theory. Yeah, to some extent that is understood. I'm not going to explain it now, but now I'm telling you the facts. We can talk about how much of this is explained and how much of it... How much of the pattern is... The right question is how much of this pattern is required for theoretical mathematical consistency. But we haven't gotten any yet. Some of this pattern is required. Yeah, some of this pattern is required, but not much of it. Very little of it is required by mathematical consistency. Question? No. It's the relative abundance of the six kinds of quarks. Relative abundance in where? But what do you mean by relative abundance? You mean in the world? In the universe, yeah. Neutrons are unstable. They decay. Protons are stable. They exist in intergalactic space and everything else. They're all... Yeah, the only thing that has any appreciable abundance... All right, first of all, the only quarks which have any degree of stability are ups and downs. The rest of these decay to these. So the real abundance of real particles in the universe are all ups and downs. Okay? Now, what's the relative abundance of ups and downs? That's determined by how many quarks of each type there are in a proton. There are no neutrons. Oh, sorry, of course there are neutrons. There are neutrons in atoms, in nuclei. So you have to know the relative abundance of protons and neutrons to know the relative abundance of... But that's all it is, relative abundance of protons and neutrons. Okay, so what do we know? A proton and what is a neutron in this language? And let's come over here. A proton is three quarks and a neutron is three quarks. Now, as I said, I'm now in the business of telling you facts about these particles, not at this point trying to understand why these are the facts. We can't do everything at once. A neutron is two down quarks and an up quark. Let's just check that. An up quark has charged two-thirds and a down quark has charged minus a third. So two-thirds minus a third minus another third. This is electrically neutral. Charge equals zero. That's good. Neutron has charged zero. Proton. Proton is exactly the same as a neutron except with an interchange of up quarks and down quarks. Two up quarks and a down quark. Okay? Now, up quarks and down quarks are a lot alike except for their electric charge. The electric charge has to do with the interaction with photons. Let's forget photons. Let's forget about the existence of photons for the moment and just talk about quarks and the other particles which are important inside the nucleus and so forth. Then it would almost seem that a neutron and a proton are the same thing except for an interchange of the up label and the down label. You might then surmise that their properties are exactly the same if, for some reason, the electric charge is unimportant. In other words, supposing we don't have to worry about the interaction with photons, just forget photons, then it would seem that protons and neutrons should be identical because what's the difference? You just replaced up quarks by down quarks. It's not quite true because up quarks and down quarks don't have exactly the same mass. They don't have exactly the same mass. Now, 10 MeV by comparison with the mass of a proton is small. It's almost negligible. It is very small and it's almost negligible in nuclear physics or in particle physics. To some precision, to the extent that you can ignore the masses of the quarks, which are, after all, smaller by far than the masses of protons and neutrons, neutrons and protons are a good deal alike. The only difference is the slight difference in mass between the up quarks and the down quarks. Which one is going to be heavier, the neutron or the proton? Of course, it's going to be the one with more down quarks because down quarks are a bit heavier than up quarks. Down quarks are a bit heavier than up quarks and so it's likely that the neutron is heavier than the proton and it is. Neutron is a little bit heavier than the proton and it's largely attributed to the fact that the neutron has more down quarks. Now, that's not all there is to the difference between protons and neutrons. If the down quarks and the up quarks had exactly the same mass, but you counted for electromagnetism, in other words the photon, you said, okay, the photon is not completely unimportant, then which would be heavier? The proton or the neutron? Why? Yes, because it has some electrostatic self-energy because it's charged. So the proton would be a little bit heavier because of the self-energy of the electromagnetic field, the electric field, one would expect the proton to be a little bit heavier. In fact, the neutron is a little bit heavier and the reason is because the down quark is a little bit heavier than the up quark. Okay, but other than that... You're going to give us the mathes? Of course. Neutrons and protons. Yeah, neutron is about what, 938 MeV and proton is about 939 MeV or... What's about 1.4 MeV difference between them? Something like about 1.4 MeV difference between them. There's enough energy between them, there's enough energy separating them that the neutron can afford a little bit of energy to when it decays into a proton plus an electron plus a neutrino. There's a little bit of excess energy in the neutrino which allows it to decay. And allows it in particular to decay with an electron to an electron. Okay, so that's the very, very rough story of protons and neutrons. We'll come back to it. But now there are also these strange quarks. Let's forget charm quarks for a moment. There's an interesting question. Can you replace... Notice that in every respect, the down quarks and the strange quarks are similar to each other except for the fact that the mass is different. So you might ask, can you construct an analog of the proton and neutron where you pull out a down quark and replace it by a strange quark? Or perhaps two strange quarks. Pull out a down quark and replace it by a strange quark? The answer is yes. Of course you can because in every respect, the up quarks and the down quarks are the same. It's sort of almost like an isotope. You pull out a proton and put it in a neutron and it sort of sticks together sort of the same way. But it's even better here. So you can construct another kind of analog. These are called strange baryons. Strange baryons, I forget their names. Lambdas and XIs, they've got all kinds of names. And it's been so long since I worked on these things that I can't even remember their names. There are symbols like this associated with them, like this and the lambdas. I don't remember which one is which. Not important. But for example, you can create, I don't know what its name is, pull out a down quark and create a strange and a down and an up. What's the mass of this one over here? Sorry, not the mass. What is the charge of this one? Well, it's exactly the same as a neutron because you pulled out a down and put it in S. And the S and the down have the same charge. So this is also electrically neutral. But it has a strange quark in it and it's called a strange baryon. They're not stable. They can decay. We're going to discuss the decay processes later. But they're not completely stable. So they evaporate. And this one will turn into that one. But yes, they do exist. Likewise, you can put in two strange quarks and an up quark. What is the charge of that one? Same thing. Charge neutral again. And likewise, for the proton, you can replace it by up, up and strange. So there are all these strange baryons. When those decay, what kind of products do you have? What kind of what? Products. Oh, protons and neutrons. Only protons and neutrons? Yeah, well, no, no. You get some protons and pions and other things like the electrons and other things. Of course, you can't just say protons. It's a matter of the hour. And you are. You also only substituted the changes for balance. Yeah. And not ups or... No, you can't... No, this is... Well, the rules of what you can exchange are a little bit complicated. But at the moment, you can always exchange one for a similar one of the same charge. Now, you can also... Oh, incidentally, these strange particles are a little bit heavier than the protons and neutrons because of this extra 90 MeV of... Oh, no, yeah, an extra 90 MeV. 90 MeV isn't much. So they're somewhat heavier than the ordinary protons and neutrons. But in every respect, they're similar. The main difference of importance is because they're heavier, they can decay to the protons and neutrons. And so they're not found in the universe and in the abundance. All of those that you put up there so far can be constructed with the heading for it also. Oh, yes. Yeah, you'll have to take every particle and replace it by its antiparticle. Then it becomes the anti-neutron, the antiproton, and the anti-question mark. Excuse me. You call these strange baritons. The strangeness is not just another word for saying they have strange quarks. But if you put it... what if you put it at the bottom before it could... Okay, then they become bottom. Then they're bottom baritons. Then they're bottom baritons. Strange baritons, as you put it in essence. Yeah, yeah, yeah. Are they strange? I don't know. They were called strange because people became familiar with protons and neutrons by the 1950s. And then when they discovered these other things, they said, oh, that's strange. And the unexpected things. Yeah. Where's the missing masto from the proton and neutron? The missing masto, what do you mean by that? Well, if you had the mast of the... Oh, you mean if you just added up the mast of the quarks. Right. There's a lot missing. Yeah, that's right. There's a lot missing. So there must be something else in the proton and neutron. No, no, they're gluons. Yeah. No, no, no attempt here to be dramatic. But the gluons don't carry any interesting charge, baryon number. Do they carry mass? Well, they carry energy. So... Okay, so actually what you were saying there is it's binding energy. It's a form of binding energy, yeah. That's right. It's binding energy. Energies don't add. Not relativistically. I mean, well, masses don't add. The mass of an object is not necessarily the mass of its constituents. Well, the 20-year thing about the Kovalev bomb type thing. Mm-hmm. Mm-hmm. Right. You're using the language of particles here to describe these composite particles. It seems more complicated if you use the word language of fields. How would you combine a field and upfield? It seems like you would combine everywhere and not be a particle. See what you're saying. Field. Do you want to know whether you can construct a field to describe a proton? Yeah, you're using down and up as if they're particles. Yeah. And there's fields and they're everywhere and their modes of the field are combining these composite particles. Well, in thinking, yeah, I mean, in thinking about this particular aspect of things, it's much easier to think about particles than fields. We could think about it in terms of fields, but it's much harder. Question about the binding energies. Yeah. So if this difference between the quark energies and the proton energy or binding energy, that's a big positive energy. No, not an integer. It's not an integer. It's a big positive energy. Energy. Oh, I thought you said integer. Yeah. And usually when you think of things being bound. Usually negative. Negative. Right. Not true here. Well, yeah, I mean, we'll come to it, but yeah, sure. You talked about the three Gs or three thousandths of the N. Yes. Yes. Yes, there is. Yes, there is, but not yet. Let's talk first about mesons. Mesons are simply quark and anti-quark. Why, you know, you could raise the question, why do three quarks bind together to form something? Why don't two quarks bind together to form something? In the early days of quarkology, this was a complete mystery. Why quarks? Oh, you could say, oh, it's in order to make the charge an integer multiple of the electron. Well, that's a stupid answer. And not to be that stupid, but at this stage, it's a stupid answer. But yet, that is the pattern. That is the pattern that they combine together and forms in which this is not the only rule, but this is one of the rules of nature. We do understand it and we do understand where it comes from, but a rule, a rule of thumb at the present time, is the way things bind. They always bind into combinations which have integer multiple of the electron charge. Okay, so you can take that as a working rule temporarily until we have a deeper understanding of it. All right, mesons are also particles, composite particles, which also have the property that their charge is integer multiple of the electron charge, but they have zero baryon number. They do not have baryon number, which means that they must be made, that they're quark, they're combinations of quarks. They must be made of quarks and anti-quarks. In fact, they are quarks, a quark and an anti-quark. They're a quark and an anti-quark, and so let's write down. There are, first of all, the ones that you can make only out of ups and down quarks. Ups and down quarks are special, not in any deep sense, but they're special because they're much lighter than the other particles. They don't decay, or they don't decay as rapidly if they do decay. They're abundant in nature, and more than that, it doesn't take much energy and collisions to make them, so of course they were the first particles to be discovered, things made up of only up quarks and down quarks. The up quarks and down quarks are pretty light, and the mesons are typically pretty light. They're an up quark and an anti-quark, and then you can start thinking about the different combinations. There's an up bar quark and a down quark. There's an up quark and a down bar quark. There's an up bar and an up quark, and there's a down bar and a down quark. I think I got them all. Any quarks at the opposite spin? No, you can't do that. Don't they have to be the opposite time because it's one-third or two-thirds? So it's not going to be. No. Okay, let's work out what their electric charges are. The electric charge of an up quark is minus two-thirds, and this one is minus one-third, and this has charge minus one, right? Minus a third, minus two-thirds. That's fine. Charge minus one is like an electron. What about this one? This is the antiparticle of this. This one's not. This one is just the antiparticle of this. Oh, yes, right. This one is the antiparticles of each other because they are related by changing particles into antiparticles, down bar into down, up bar into up, and this has charge plus one. So these are antiparticles of each other. Up bar up, that's electrically neutral, obviously, and charge equals zero. Now in fact, neither one of these two by themselves corresponds to distinct particles. Remember we're doing quantum mechanics. Each one of these states can be thought of as a quantum state. Think of it as a quantum state. The quantum state consisting of an anti-up quark and an up quark. The quantum state consisting of an anti-down quark and a down quark. One of the things you can do in quantum mechanics is to superpose states. If you have states, you can add them. You can superpose them. Superposing them means making combinations that have a probability for being either this one or this one. There are two combinations of these two. I'll tell you what they are. Up bar up, plus down bar down, and what would I put in front of it to make it have total probability one? One over square root of two. This is a quantum state, and this is the orthogonal quantum state. Up bar up, minus down bar down. You know what this is? This is an entangled pair of quarks. Not entangled through their spin, but entangled through their upness or downness. If you thought of upness and downness as about being similar analogous to the spin direction of a particle, up or down, and that's where this terminology came from, then these would be two entangled states entangled not through their spin, but through their isospin, through their upness and downness. We haven't used the word isospin. Maybe I'll tell you what it means, but not right now. There's just this analogy between the spin directions and the upness or downness quantum number. These two things individually are well-defined particles. This one over here goes together with these two, and they are called the pions. They go together for a good reason, for a good mathematical reason, but they go together because their mass is very close to each other. It is believed they would be exactly the same mass if the up quark and down quark had the same exact mass. If the masses were the same. All three of these are virtually indistinguishable except for a small difference in their mass and they have different charges. 0 plus 1 and minus 1, and this is called the pion multiplet pi plus minus and 0. Three independent kinds of particles called pions, and as I said, and we can discuss why nature chose these particular combinations to be analogous to each other, but now I'm telling you facts and not mathematics. And the other combination is simply this one over here, and this is called the eta. So there's the pi plus, the four states here really define the three pions, pi plus minus and 0, and the eta meson. The eta meson is similar to a pion in many ways, but it's heavier. Why is it heavier? That is a complicated story. It's not an elementary story. It's a complicated story. Maybe we'll come to it, maybe we won't, but as a matter of fact, it's massed. What are the masses of the pions? The masses of the pions are about 140 MeV. The mass of a pion, mass of pion, and pi is about 140 MeV. So in other words, it's not too different from, question? Yeah, it's about 140 MeV. So it's somewhere in this range in here, not this heavy, and the mass of the eta is about three times heavier or something like that. The mass of the eta is about 500 MeV. I don't remember the precise number, but that's about right. Why that is, why the eta sticks out as being different was a puzzle for a long time. Not obvious, not obvious. Even today, it's a rather abstract mathematical fact, but it is understood. Isn't it also true that they're relatively long, half-wise? I'm going to compare it to most of them. The numbers of orders and magnitude difference. They don't decay by strong interactions. They decay by weak and electromagnetic interactions. So they're longer lived than many of these other particles. Yes, that is true. They are long lived. Okay, those are the mesons. Did you give the name for the up bar, down, down bar? Yeah, those are pipe numbers. No, they don't have names by themselves. They're linear combination, which are the sum and differences of them, and have definite names. Oh, I suppose they do. Yes, those are. Is that similar to, is that something like the neutrino oscillations? Well, in the sense that it's related to quantum superposition of states, yes, but it's got more to do with spin combinations of two half-spin particles. There are two ways that you can entangle. Well, we'll come to one next time. The last thing I simply want to tell you is that you can make strange mesons. You can take any d-quark and replace it by a strange quark, strange bar quark, and so forth. That makes new mesons which are called strange mesons, or, what's the other name for them? K mesons. K mesons are mesons containing a strange or an anti-strange quark, replacing a down quark. There are four of them, up bar strange, up strange bar, down bar strange, down strange bar. These two have charge zero. Charge zero, and these have charge plus one and minus one. These two are called the charged K mesons. These two are called the neutral change, the neutral K mesons. So there are three kinds of pions, one kind of eta, and four kinds of, how many does that make all together, let's see. Three pions, four K mesons, and an eta, yeah. There's more, there's more, there's more. Did we leave something out? Yeah, we left out one, we left out some. Yeah, we left out S bar S, huh? Yeah, there's nine. Nine, nine altogether. The reason it's nine is simple. There are three quines of quarks, three kinds of anti-quarks, three times three is nine. All right, okay. For more, please visit us at stanford.edu.
 Stanford University.  Okay, so we've talked about a lot of things so far.  Fields, quanta of fields, the relationship between fields and particles.  That's the relationship between fields and their quanta.  What are the quanta?  The quanta are the discrete, indivisible units of energy that quanta mechanics  implies for waves, for waves and waves of course are fields.  Fields and waves are more or less the same thing.  We've discussed the properties, not the properties of individual particles very much,  but we've discussed some general properties, the properties of having energy, momentum,  the properties of having spin, and the property of either being a fermion or a boson.  Every particle is either a fermion or a boson.  Fermions are the particles that don't like to live together in the same state.  Bosons are the particles that do like to congregate and do condense into the same state.  We've talked about wave equations on occasion or the field equations if you like, more generally.  There is a kind of field equations.  And we talked about how field equations can be generated from Lagrangians, from action principles.  The quantum mechanical version of the Lagrangian is a kind of tool for codifying or codifying,  whatever the right word is, codifying the interactions between particles.  Various terms in the Lagrangian, things like, for example, products of fields represent processes  which we can call vertices where particles come in and other particles go out.  That would, for example, be a term in the Lagrangian which would have four powers of a field in it.  So we've talked about these general things.  We haven't talked very much about specific particles.  Tonight, well, I expected to spend the first half hour beating around the bush a little bit.  I'm going to spend a few more minutes beating around the bush.  But then I want to come to really writing down what the particles are, who are the players in the drama,  and start going through them more or less, well, not quite one by one, but in groups,  and trying to give them some personality, give them some names, some properties,  and also what it is they do and how they come into physics, into ordinary physics.  Okay, but before I do that, there's kind of a triangle of concepts that we've discussed two legs of,  but not the third leg very much.  The triangle is particles or field quanta, particles, fields,  and in modern physics, pretty much for every elementary particle.  Now, we're going to have to think very hard in the future, not tonight.  What is an elementary particle and what is a composite particle?  We will come back to that.  And you might think, I mean, everybody here probably has some answer if I were to ask you,  how do you distinguish a composite particle from an elementary particle?  And you will always be frustrated.  You will always find some slippery reason that your definition didn't work.  But for the moment, let's nevertheless imagine that there are elementary particles  and that the elementary particles are the quanta of elementary fields,  fundamental fields in the theory.  And so they're more or less than one-to-one correspondence.  But there's a third leg to this triangle.  Anybody know what it is?  Of course, you don't know what I'm thinking, so even if you did know what it was,  you still wouldn't know it.  Forces, forces, forces.  So you can sense forces, forces.  Okay, basically for every field there is a particle.  For every field there is a force.  Electric field gives rise to electric forces.  Gravitational field gives rise to gravitational forces.  It may be less obvious to you what the electron field,  the electron has a field.  It also gives rise to forces, and we'll talk about them a little bit.  So there's kind of a correspondence that goes this way,  there's a correspondence which goes this way.  There must also be a correspondence which goes this way,  a way of thinking about forces which is not based on fields,  but which based on particles.  If this correspondence or this triangle really makes sense.  So I want to talk about that a little bit.  Many of you know the idea, but let's just discuss it for a moment.  Let me first discuss it in the context of electrodynamics.  How forces come out of thinking,  now this is classical electrodynamics for the moment,  the complete field view of things.  Supposing I put two charges into space,  I want to know the force between them.  How do I calculate it?  Well, you could know the rule that the force is equal to the product of the charges  times one over r squared and so forth.  Or you could try to calculate it a different way.  You could try to say, what do these two charges do to space?  What they do to space is they create electric fields.  Essentially that's the thing they do.  They create an electric field that fills space.  And I don't want to write down the details of what that electric field is.  But let's just say this is the electric field.  Let's forget the second particle and just write down the electric field  due to the first particle, whatever it is.  The electric field due to the first particle,  incidentally it's proportional to the electric charge of the first particle.  So let's explicitly put that in.  E of the first particle times the electric field divided by the electric charge.  This electric field here, I've divided out the electric charge.  Maybe I shouldn't call it E.  Let's call it E without the factor of the electric charge in it  and put a little hat over it.  That's this electric charge.  And what is the field energy?  Anybody know what the formula for the field energy is in an electric field?  Electric fields have energy.  They store their energy as a distribution of energy in space.  And the field energy, the density of field energy,  is the square of the electric field.  So we square this and we integrate it over all space, the volume,  and that's the energy stored in the electric field of the particle.  Now, this energy does not depend on where we put the particle, right?  The field will move.  If we move the particle, the field will move with it,  but the field energy will always be the same.  The electric field will adjust to the position of the charge.  The field will always give rise to exactly the same field energy.  And this field energy here, remember E equals MC squared,  that field energy is part of the mass of the particle.  It contributes, the field contributes to the energy of the particle,  and therefore it contributes to the mass of the particle.  There's another way of thinking about a bit of renormalization,  that there's some extra mass there because the field surrounds the particle in this way.  Okay, I don't want to belabor that now.  What about the second particle?  Supposing the first particle wasn't there, but the second particle was there.  This, of course, is the energy E, not the electric field.  This is the energy.  If there was only particle two, the field energy would be the integral of E2 times the electric field of the second particle squared.  Now, if the two particles are not at the same place, well, let's not worry about the two particles.  This one would also be independent of the position of this particle here.  What about the energy if I have both particles?  If I have both particles, then I have to add up the field first before squaring it.  So the electric field, if I have two particles,  will be the sum of the two electric fields, electric field, not energy.  Let's call this energy En.  Well, let's not call it H. Energy, just En.  The energy, first of all, the electric field.  The electric field will be the sum of the two electric fields.  The electric field will be E1 plus E1, E1 plus E2, E2.  Where these are the electric fields of particle one and particle two.  This will be the total electric field.  Incidentally, the electric fields are vectors, and so we might put little vector signs above them.  The field energy you get by squaring this whole thing.  So the field energy is the integral of a space.  There are three terms.  The first term is E1 squared, E1 squared.  It's gotten by squaring this.  The second term is plus E2 squared, E2 squared.  And the third term is the interesting one.  It's the product of E1, E2, twice as a matter of fact, times E1 dot E2.  Actually, dot product.  All right.  What is this first term here?  It's the self-energy.  It's the self-energy of one particle by itself.  It doesn't depend on the position of the particle.  It's just a number.  It's part of the mass of the particle.  Let's forget it.  It's already there as part of the mass of the particle.  What about this one?  Also, part of the self-energy of the second particle.  What about this one here?  This one is not the energy of either particle separately.  It's proportional to the product of the charges.  And it's proportional to the product of the fields.  What if the particles were infinitely far away, so far away that their Coulomb fields  hardly overlapped at all?  You take one particle so far away that the Coulomb fields are hardly overlapping.  Then this is going to be zero because wherever E1 is not zero,  E2 will be zero, or almost zero.  Wherever E2 is non-zero, E1 will be close to zero.  So this will be very, very small as you take the particles apart.  But what about when you bring them together?  When you bring them together, the product of E1 times E2 will not be small.  Nearby, where the particles are, both fields will be appreciable,  and you will get a contribution from this.  What is that contribution?  That contribution as a function of distance,  well, first of all, it's proportional to the product of the charges.  It depends on the distance.  And of course, if you work it out, as you might expect,  it's nothing but the Coulomb force, one of our R squared.  But I like to say it this way because it gives you the following picture  that putting in both charges, taking them far apart,  they don't affect, well, they're simply just independent objects.  As you bring them together, they deform and distort the field  in a way that depends on the distance between them,  and the distortions of the field in between them, that field energy.  That field energy, which is the contribution because both of them are there,  that's the force law.  So that's a purely field point of view of forces.  A purely field point of view of forces.  But if fields are nothing but collections of quanta,  and quanta are particles, there must also be a way to think about forces  in terms of particles.  So let's talk about that a little bit.  Before discussing electrodynamics in this way,  let's talk about a slightly different setup.  We're actually a very completely different setup.  Let's talk about molecular forces.  What do molecular forces come from?  I'll give you one source, there are several origins of molecular forces.  But here's a setup I want to think about.  Let's begin with a pair of protons and a single electron.  What is this? A proton over here, a proton over here,  and a single electron.  If this proton were very far away, then the ground state of the electron  in the presence of the proton would just be the hydrogen atom ground state.  It would be governed by some sort of Schrodinger wave function.  Let's draw the Schrodinger wave function.  The ground state would be the ground state of the hydrogen atom.  And in the ground state, if this proton weren't there at all,  not there at all, the electron in its ground state would certainly be found  in the position nearby this proton.  Now what if there are two protons over here?  One proton over here, another proton over here, pretty far away,  but not infinitely far away.  Then there is another possible state of the electron with exactly the same energy  where the electron is not over here, but it's over here with the corresponding  wave function pushed over to here.  It has exactly the same energy.  Why? Because the two protons are of the same kind,  and everything is completely symmetric over here.  So if the electron is in orbit, well, a quantum mechanical orbit around this proton,  or if it's in quantum mechanical orbit around this proton,  the ground state energy will be exactly the same as if there was only one proton.  But it's not quite true.  Why isn't it exactly true?  Well, if the protons are not infinitely far away,  there are processes that could happen which could not happen  if they were infinitely far away.  Anybody know what the process is that can happen to the electron if the two...  Tunneling effect.  Tunneling effect. Yeah, the tunneling effect.  The electron placed over here into its ground state can,  with a small probability, suddenly appear in this atom over here.  That's called quantum mechanical tunneling.  It has to overcome an energy barrier in between the two.  It takes some energy to pull the electron out of this atom.  It'll get that energy back when it drops into this atom,  but it has to go over this hill.  Can it go over the hill?  Classically it can't, but quantum mechanically it can tunnel from one place to another.  Don't stand there and try to watch the tunneling.  What happens if you try to watch for the electron going back and forth?  Like anything else in quantum mechanics, watching it ruins it.  You can watch over here.  You can say, well, you can stand over here and wait for the electron to appear over here,  but if you watch it from in here, you'll ruin the phenomenon.  So the electron can hop back and forth.  Hop back and forth simply means that there's a tunneling transition,  a tunneling rate or a tunneling probability that if you put it over here,  it can appear over here.  If it appears over here and you wait a while, it will reappear over here and so forth.  Okay, this process sets up a kind of equilibrium,  long-term equilibrium in which the electron has an equal probability  of being over here and over here with a wave function  which looks like the sum of the two wave functions.  Well, the sum divided by the square root of two in order for probability to add up to one.  All right, so it looks like the sum of the two wave functions, which I didn't draw very well,  but in the middle over here, it's slightly different.  You might draw the exact wave function of the electron orbiting particle one  as if particle two were not there.  Same thing for particle two.  And then add them up.  Well, the correct tunneling wave function, the correct equilibrium wave function,  is not exactly the sum of these two wave functions.  It's a little bit different in here, a little bit, not much.  But the point is the energy of the system is not exactly what it would be  if the two protons were infinitely far away from each other.  If they were infinitely far away from each other,  you could put the electron over here, it would have a certain energy,  or over here and it would have exactly the same energy.  When you put them closer together, the energy of the electron is not exactly the same  as it would be if they were far apart, if they were infinitely far apart.  So if I were to plot the energy as a function of the distance between them,  when they're very, very far apart, the energy of that electron is simply the energy of the electron  with only one proton, and the other one just not there at all.  At large distances, the energy would just be whatever it was.  But as you bring the protons together, the energy of that two protons plus electron  is a little bit less, turns out to be a little bit less,  and that little bit less is a function of the distance between them.  So now we have a situation when the system is in equilibrium with the electron  tunneling back and forth and in equilibrium between the two,  the energy is a function of the distance between them.  What's the relationship between force and energy?  You can think of this as potential energy.  You can think of this as a potential energy between the two protons.  The derivative of the energy.  So the derivative of the energy, the energy has a gradient in here,  force always pushes you toward decreased energy,  and so this effectively creates an attraction between the two protons.  That attraction is a kind of covalent bond.  It's a kind of force between the two of them,  which is due to the sharing of an electron,  or to the fact that the electron can be in a superposition of quantum states  in the two wells, in the two potentials of these two things here.  Now, does that mean that a proton and another proton with an electron between them,  which has this attractive force, will bind together?  Not quite, because there's another force around.  What's the other force around?  The electrostatic force.  The system doesn't have zero charge altogether,  and so there's a repulsion force, and the repulsion force can overwhelm the attraction force,  but nevertheless there is a force between two protons  if there is an electron around,  which is due, in a sense, to the jumping back and forth of the electron,  or to the diminishing of the energy by the wave function  sort of adjusting a little bit, a little bit better  than it would if you just added the two wave functions together.  As I said, that's the origin of covalent bonds,  sharing of electrons,  and in this case you can think of it, you can draw a picture.  Now, the picture may or may not do anything for you.  You have a proton over here, that's the world line of a proton,  another world line of a proton,  and the electron might start out being bound to this proton,  hop across to this proton, hop back across to this proton.  You shouldn't take this too literally,  because if you stood in the middle, as I said, you would disrupt the process,  but it's a description of the quantum mechanical state of the electron  between the two protons,  what it does, this possibility of the electron jumping back and forth,  lowers the energy relative to if you just had one proton  and just one electron in a bound state there.  That means that there is an effective force,  and you can picture it.  This picture is like any analogy, it's often very, very misleading,  but the presence of the electron in between the two protons  creates an attractive force.  It's called particle exchange,  it's called particle exchange or electron exchange  between the two protons.  Now, yeah.  So, is it as being the electrons hopping back and forth  as reducing the effective positive charge of it?  No, I don't think that that is quite the right picture.  It doesn't really depend on the electric charges.  It just depends on the fact that you can find,  by adding together two wave functions,  you can find a wave function with a little bit lower energy  than either one separately.  Is this what the magnet referred to as life-like-slide?  That's what the magnet used to say,  like, like, like.  Like, like, like, I don't know.  No, no, no, no, he was probably talking about the Bose's statistics  of that photons like to be in the same state.  I don't know what he was talking about.  He made the same thing, he said that light, likes, like, like.  Electrons like each other, photons.  No, no, electrons hate each other.  They don't like to be in the same state.  Photons like each other, they love to be in the same state.  I think he was probably talking about the opposite  of the exclusion principle for photons,  the Bose's statistics of them.  Of course, I don't know.  Protons have a tendency to be a cow.  Protons.  Yeah, that's because of their electric charge.  Right, now what happens if we put the electron between them?  Is that reducing the impulse?  It does a little bit, but not very much.  In fact, the force due to the electron jumping back and forth  is a much shorter range force than the electrostatic attraction.  So this force would only be important at relatively small distances,  whereas the Coulomb force would fall off much more slowly.  So the Coulomb force would be a longer range force.  But, you know, it is there.  It is there.  The reason why it shows up is if you have a neutral system.  I mean, it shows up better if you have a neutral system.  If you have two electrons so that the total charge of the system is zero,  then of course you'll have the possibility one electron orbiting around this proton,  a second electron orbiting around this proton here.  Now, the two objects here, they're called atoms, hydrogen atoms,  and they're called electrons.  So if you have a neutral system, there is no electrostatic force between them,  but you still have this possibility of electrons jumping across.  Electrons can jump across, a tunnel across,  and then it does create an attractive force which can bind an atom, bind a molecule.  Yeah, yeah, yeah, it is bound, but...  Yeah, at small distances.  At small distances, it is enough to overcome the Coulomb force.  That's right.  Yeah.  Is there a possibility between the two protons that creates some kind of  tension between them that creates some third force that the electrons kind of orbit around?  Well, it doesn't create a third force,  but it creates a sort of slightly nonlinear effect due to the two forces.  But it's just a solution of the Schrodinger equation in the presence of the two forces  does not have the energy that it would have if it was just one of those charges there.  But let's leave it at that.  There is this notion of the energy being lowered by the possibility  of alternating between two quantum states.  Is this thing all related to quantum entanglement?  Not so much quantum entanglement.  It's related to what are called off-diagonal elements in the Hamiltonian,  but it's not too closely related to entanglement, I would say.  For entanglement, normally you need two electrons.  You only need one electron for this.  For very, very, very high temperatures, does the electron move between the protons  from a much higher probability?  Well, at high temperatures, because it depends on the temperature,  at very, very high temperatures, all that will happen is the electron will get kicked out  and go to Alpha Centauri, and it won't even remember the fact that there was a proton around.  If it gets hit hard enough by a very hot photon,  but if the temperature is not that extreme, what it can do is cause,  even if you only had a single atom, it could cause the electron to occupy higher levels.  Now, higher levels have bigger wave functions,  so the overlap between the higher wave functions could be larger,  and it would certainly have some effect on the force.  But that's a kind of special effect.  All right, we have a concept that we see in the classical electrodynamics  that the effect of having two charges changes the energy in between  relative to what it would have been if you only had one, and it creates a force.  Similar kind of thing here.  If you have two force centers and the possibility of the electron being in a superposition of states,  in other words, of the equilibrium being in a quantum superposition of the two states,  the two states being over here or over here,  that also lowers the energy and creates a force.  Is there a way to think about the Coulomb force here in quantum mechanics  where it is in some sense similar to this jumping back and forth of the electron?  Yeah, there is.  Let's come back to a single proton.  A single proton is interacting with the electromagnetic field.  That means it's interacting with the field whose quanta are photons.  Classically, we might just describe it by solving the field equations for the electric field  in the presence of a charged particle.  Quantum mechanically, we think about it differently.  Particularly in quantum field theory, we think about it as the emission and absorption of photons.  That's what the Lagrangian of electrodynamics tells us.  It tells us about the probability for the emitting and absorption of photons.  So one way of thinking about the electron is that the actual physical electron  is a quantum mechanical superposition of states in which, first of all, there are no photons.  A superposition of a state with no photons.  A superposition of states in which a photon has been emitted, and therefore there's a photon present.  So it's a charged particle together with a photon around.  Two photons can be emitted.  The photon can be reabsorbed.  The net effect in the end is some kind of equilibrium distribution, quantum mechanical equilibrium distribution  of photons surrounding the electron.  And you can measure those photons.  I mean, a little bit different than measuring free photons.  These photons are sort of trapped at the electron.  They're emitted and reabsorbed.  And if I have another electron over here, it is also emitting and absorbing photons.  So there's an equilibrium.  But every so often, now this should be thought of in the language of Feynman diagrams,  every so often a photon which is emitted from here gets absorbed over here.  And I always think about it as two jugglers, each juggling balls.  And every so often, if they happen to be close enough together, a mistake will be made.  And Joe will grab Mohr's juggling objects.  Really what you really want to do is you really want to calculate the energy due to the electromagnetic field or due to the quantum superposition of photons that are present.  You want to calculate that energy as a function of the distance between the charged particles.  When they're very far apart, the two energies just add.  They just get the sum of the energy of one charged particle and another charged particle.  But as they get closer together, the charges begin to influence each other or in the language of Feynman diagrams,  the emission of one photon by one particle and the absorption of that same photon by another particle creates a force.  Creates an energy which is not exactly the sum of the two energies.  That energy is the Coulomb force between the charged particles.  So we have two distinct languages.  Well, apart from just writing down the Coulomb force law, we have two other ways of thinking about forces.  One of them is through classical field theory where you calculate the fields of objects and square them.  And the other way is through the exchange of particles.  Feynman diagrams with particles are exchanged back and forth.  Any particle can be exchanged in some context or another.  So every kind of particle in one way or another produces a force.  In molecular physics, it's the exchange of electrons which create forces.  In electrodynamics, it's the exchange of photons back and forth which create forces.  So any particle is also connected with a force when that particle can be exchanged or jump back and forth between two something else.  We'll describe some more examples, but I did want, before we move on, to just discuss the relationship between particles and forces.  So we more or less have a one-to-one-to-one correspondence. Particles, fields for which those particles are the quanta,  and forces which are associated with exchange processes where that particular kind of particle can bounce or jump back and forth.  That's an important theme.  So when people say that there are four forces in nature, now there's a force for every possible kind of particle.  And we will discuss some of them as we go along.  Okay, I think it's time now to start naming the particles, listing them, listing their properties,  and discussing what they can do, what kind of processes they can engage in.  And I could write down a big long list of all the elementary particles and then give you a test next week to see whether you memorized it or not.  That wouldn't be fun at all.  I think it's probably better to divide them up into small groups,  which are in some way simply related to each other, get familiar with them a little bit and what they can do  before we try to write down the whole damn standard model of particle physics, which is a monstrosity.  I mean, you know, it's not my fault, certainly not my fault, that the standard model of elementary particle physics is an ugly monstrous mess.  It's not Steve Weinberg's fault.  It's nobody's fault, or if it is somebody's fault, that person, well, he may be in the room, but he's a little bit diffuse.  Frankly, we don't understand why the particles are what they are.  We don't understand why there is an electron and no particle whose name slips my mind because nobody's ever named it,  because it doesn't exist, but nevertheless, why some particles exist and why other kinds of particles don't exist,  we largely, by and large, don't know.  We do understand some relationships between particles.  If this one and that one and that one exist, then there's got to be another one to match up with them in some appropriate way.  But in the end of the day, there are many more parameters, many more different types of particles than there are known relationships between them,  which cut down the size of the problem.  Okay, the mathematics and the relationships cut down the size of the problem somewhat,  factor of two, factor of three or something like that, but there are hundreds of particles.  So it is, honestly, a mess.  If you want to understand what people are hoping for in the next round of experiments and so forth,  you'll have to understand some of that mess and what the puzzles are about it.  So let's begin.  Let's name the particles.  We begin with the most obvious ones.  Let's make a table.  Let's see, we need some columns.  We can put the name of the particle over here.  I'll put the symbol for the particle over here.  I'll put the particle type over here.  Now, what do I mean by type?  I simply mean whether it's a fermion or boson.  I'll put the electric charge over here.  There's another quantity which characterizes particles.  We'll call it the baryon number.  I'll tell you what it is as we go along.  And there are other properties.  At the moment, I'm not listing them.  And we'll put the mass over here.  All right.  The first one, of course, said I'm not listing them in any particular order.  As it happens, I am writing down the lightest one first.  The lightest one is, of course, the photon.  The standard symbol for a photon is a gamma, like for a gamma ray.  It has a field associated with it.  The gamma particle is the quantum of a field.  In most cases, or many cases, the field carries the same symbol as the particle itself.  But for the photon, the field is called A.  And it's really the vector potential of the electromagnetic field.  You could use electric or magnetic fields, but you can also use the vector potential,  which is another way of describing the electromagnetic field.  It has a boson.  I didn't write down the spin, but the spin is one unit of spin.  The electric charge is zero.  The baryon number, whatever that is, is zero.  And the mass is zero.  So that's the first particle.  The next particle of interest is the electron.  Now, the electron is a particle which has an antiparticle.  It has an electric charge.  If it has an electric charge, it must have an antiparticle of the opposite charge.  And it is a convention, whether we think of the particle as the electron  and the antiparticle as the positron,  or whether we think of the positron as the particle  and the electron as the antiparticle.  The relation between them is mutual.  So when I write the electron, I really mean the electron and positron.  And so we could write E here plus minus.  Standing E minus is the electron.  E plus is the positron.  The field of the electron is usually psi.  And maybe you could put a little E downstairs to indicate that it stands for the electron.  It's made up out of creation and annihilation operators for electrons.  Electrons are fermions.  It's charged.  Okay? It's charged in what units now?  Well, the standard particle physics or quantum mechanical unit  for electric charge, believe it or not, is the electric charge of an electron.  It's a good unit to work in terms of.  You can go look it up in coulombs.  It's 10 to the minus, what, 23 coulombs?  10 to the minus 19th coulombs, or yeah.  It's some very small charge.  But it's not useful to think about it in coulombs.  All particles in nature have electric charges which are integer multiples of the electron charge.  This could not true of quarks, but quarks are not observable particles.  All right.  So the charge we'll just write as minus one for the electron and plus one for the positron.  So since we typically think of the electron as the particle and the positron as the antiparticle,  let's just call it minus one and remember that the positron has the opposite charge.  Variant number is zero and it's mass.  Now we have to decide on units for mass.  Okay?  Units for mass are the same as units for energy.  E equals mc squared.  So we can either describe the mass as a mass in kilograms or in energy in joules,  or we can simply invent a new unit which is more appropriate to microscopic physics to atomic physics.  In fact, the unit that we use comes originally historically out of atomic physics.  It is the unit in which the ionization energy of an electron and a hydrogen atom is what?  13.5 electron volts.  An electron volt is how much energy you get if you pass an electron across a capacitor plate of one volt.  It's a very, very small amount of energy, some tiny fraction of a joule.  But one electron volt is the standard unit that came historically out of atomic physics,  theory of electrons and so forth.  It's going to wind up being too small a unit for us.  Particle physics energies are larger than atomic physics energies,  but for historical reasons we have the electron volt as our unit of energy.  And the mass of an electron measured in electron volts is of order a million electron volts, one MeV.  In fact, it's a half an electron volt.  Not exactly.  I think it's.51 MeV, and MeV stands for millions of electron volts.  And MeV will be too small a unit for many other purposes.  As I said, the particle physics is a mess, and the masses of particles extend all over the map.  And so in trying to search for a useful unit, you're always frustrated.  The useful unit will always be too small for the next...  No, why?  No, it's exactly.51.  No, it's not.  What's that?  Pi 3.  Pi equals 3.  Pi equals 3.  Right.  Okay, now, quantum electrodynamics is the theory of electrons and photons,  and we've talked about it a little bit, more than a little bit.  And just we could also write down over here a table of the various...  I don't want to make it a table.  We'll just draw some pictures.  The basic elementary process that takes place in quantum electrodynamics, photons and electrons,  is the emission of a photon by an electron.  Electron, electron photon, and as I've showed you several times,  you can rearrange the legs of this diagram so that this could represent  not the emission of a photon, but the absorption of a photon.  A photon comes in from the past, or...  Oops, sorry.  You can even flip the electron legs around so that it looks like this.  Electron going backward in time.  Well, what does that mean?  That really means a positron emitting a photon.  So the basic building block for building up processes and interactions  is this vertex with two electrons, electron, positron, whatever coming...  one going in, one going out, and a photon coming out of it, or going into it.  Out of that, you build up all of the various processes of quantum electrodynamics,  but in particular, the process or the phenomenon that corresponds to the force between charges,  and in the language of particle exchange, it's the photon bouncing back and forth  between charged particles, which creates that force.  Yet another way to describe what's going on here is in terms of a Lagrangian  or a term in a Lagrangian.  The Lagrangian describing this process here describes one electron in,  one electron out, and one photon out,  and so you build that out of the field operators.  One electron in is psi electron.  It creates, it has the creation of annihilation operators in it.  An electron out is psi dagger of the electron,  and a photon emitted is the field operator for the photon,  and if you plug in all the creation and annihilation operators,  you will find in here, buried in here,  terms where a photon is emitted, an electron absorbed,  another electron emitted, and so forth.  And this codifies, this describes all of the various basic processes  that can happen in quantum electrodynamics.  Now, there's a parameter in the Lagrangian that appears the electric charge of the electron,  and that, roughly speaking, is associated with the amplitude for a electron to emit a photon.  The electron, let's say you hit the electron or whatever,  the electron plows into the side of a x-ray machine.  What's the probability that a photon will be emitted?  Well, the amplitude is the electric charge,  and the probability is proportional to the square of the electric charge.  So all of this here is a way of describing all of these basic processes,  and when they're combined together, they produce forces,  they produce processes where photons are emitted,  the whole world of quantum electrodynamics flows out of this, basically, one expression here.  We won't try to go through that again now,  but let's start adding a little bit to our particle list.  The next particles of interest, these are, of course, familiar to you, I'm sure.  Now, if this were 1960, when I was, well, I was,  1962, when I went to graduate school,  probably the next particles I might write down would be protons and neutrons.  Protons and neutrons are now subsumed by quarks.  It is widely believed that, in some sense, protons and neutrons are composites of quarks,  although we will come, remind me to come back to this issue of the difference,  or what it means to be composite versus elementary.  It's a very interesting story, but naively, quarks are smaller than protons and neutrons,  and so protons and neutrons, which are big fat globs, are made up out of quarks.  So, next thing are quarks.  There's a lot of quarks. We won't even get to all of them tonight,  or the whole set of distinctions between them, I don't think we will,  but there's more than one type of quark.  There are six types of quarks, six distinct particles,  all of which are very similar to each other in some respects,  very different from each other in different other respects.  So, let's list them. They go under, they have names, all right?  Well, why do they call what they are?  They call what they are just a historically randomly people assigned silly names to them,  and there's no logic to what they're called, no logic at all.  There's, first of all, the up quark, and that's called U.  The symbol is U.  So, let's see, we should write there are quarks here, quarks.  And I suppose the symbol for quarks is Q.  All quarks are fermions. We'll write down their charge later.  They have all baryon number of one-third.  Now, why one-third? Well, the reason is very simple.  The baryon number is basically the counting of the number of protons and neutrons.  Each proton is counted as having one unit of baryon number.  Each neutron is counted as having one unit of baryon.  Baryon is just a word for protons and neutrons,  and a somewhat generalization of protons and neutrons.  Nucleon is a word for protons and neutrons.  There are other particles which will come to which are very similar to protons and neutrons.  They're also called baryons.  The prefix barry I think means heavy.  And baryons were called baryons because they're a lot heavier than electrons.  But counting up the number of protons and neutrons,  what do you call the number of protons plus neutrons in an atom?  Atomic weight.  Atomic weight, yeah.  The atomic weight, yeah.  Is equal, approximately equal to the total number of protons and neutrons.  And the total number of protons and neutrons in nuclear physics never changes.  Protons can turn into neutrons.  Neutrons can turn into protons plus other things.  But the number of protons plus neutrons never changes.  You do have isotopes.  But still, the number of protons plus neutrons doesn't change.  Number of protons can change.  How can the number of protons change?  No, I'm just saying that different types of protons have different numbers than neutrons.  Oh, yeah.  Indeed they do.  But are there processes with number of protons and neutrons change?  Protons, not plus neutrons, but protons and or neutrons change?  Beta decay.  Beta decay, radioactivity, radioactivity, one form of radioactivity, a neutron decays into a proton plus an electron and an antinutrino.  Okay, so in that process, the number of protons changes by one.  The number of neutrons changes by one.  But the number of protons plus neutrons doesn't change.  There's a generalization of that in all of nuclear physics and particle physics.  There's a certain quantity, which for ordinary nuclear physics is just the number of protons plus neutrons.  And that number is sometimes called the Baryon number.  We'll have to generalize it a little bit beyond protons and neutrons.  It's a Baryon number.  And it could have been defined to be two for the proton or seven for the proton or pi for the proton.  But whatever it is, it has to be defined as twice as much for two protons, three times as much for three protons.  So it's a convention that you say the Baryon number of the proton is one.  Incidentally, what's the Baryon number of the antiproton?  Minus one.  Minus one.  Proton has Baryon number plus one.  Antiproton, Baryon number minus one.  Neutron, Baryon number one.  Anti-neutron, Baryon number minus one, but clearly there's an element of convention in exactly what you call M.  But once it was fixed that the Baryon number of a proton was one, then the Baryon number of a quark was a third,  because three quarks make a proton.  So it's just a historical glitch that the Baryon number of the most fundamental thing in nuclear physics is one third and not one.  So if you look out at an antiquark, there are antiquarks.  Baryon number is minus a third.  So I won't write that down separately.  The number of quarks is conserved?  Number of quarks minus the number of antiquarks is conserved.  Now, whether or not that is an absolute conservation law, it is not believed to be an absolute conservation law.  What do I mean by absolute conservation law? Can a proton disappear?  It can't completely disappear.  Its energy has to go someplace.  Are there processes in nature where a proton might disappear and become something that is neither a proton or a neutron or anything else that you would call a Baryon?  For example, without violating charge conservation, a proton could become a positron and a photon.  So a proton could decay into a positron and a photon.  Does it?  Well, you can wait.  If you have a single proton and you sit there and wait, you will wait a long, long time before that proton decays.  It's half life to decay that way is at least 10 to the 33 or 10 to the 34 years.  So this is not something that happens very regularly.  Does it happen at all?  The thinking is yes, it does, but this is one of the very, very interesting questions of particle physics of whether the proton can decay.  And when you say can it decay, you mean decay into something that does not carry a Baryon number.  And it is widely believed that the answer is yes, but it's never been demonstrated.  Incidentally, how do you have you wait around for 10 to the 34 years for a proton to decay?  You get 10 to the 34 protons and you wait around for one of them to see one.  Now 10 to the 34 protons is a lot of protons.  If you have protons, then it's protons.  No, that's not that.  That's zero Baryon number because it goes to zero Baryon number.  One has Baryon number one anti proton has Baryon number minus one.  So that's not a Baryon.  We call them Baryon violating processes, processes in which the Baryon number is not conserved.  Nobody has ever witnessed such a process in the laboratory or anyplace else.  Can they happen?  There does not seem to be any reason why they cannot happen built into the mathematics of what we know.  So we leave this as an open question, but empirically and at least to a very, very high precision,  Baryon number is conserved and quarks by definition have one third of a unit.  One third of a unit.  As I said, minus a third for anti quarks.  But in order to fill in the rest of this, in particular, electric charge and mass,  we don't have to label which kind of quark we're talking about.  And there are lots of different kinds of quarks.  So let's put in a list of different kinds of quarks.  This is not new particles which are not quarks.  This is just a subheading here, quarks and then things underneath.  There are up quarks, down quarks.  Why are they up and down and not up and down?  There's nothing up and down about them.  What directions?  Up and down?  Up and down means in the Earth's gravitational field.  There's nothing up and down here about them.  Then it gets worse.  There are strange quarks which are no stranger than non-strange quarks.  It gets more and silly.  There are charmed quarks which are charming, I suppose.  And then there are, now this is, if you're squeamish or very,  bottom quarks, bottom quarks, bottom quarks, and then top quarks.  The symbols are of course exactly the same.  I just didn't feel like writing the words.  Up, down, strange, charm, bottom, top.  Same as bottom and top.  I got a little pretentious beauty in truth.  Bottom and top, strange and charm.  How and under what circumstances these things were named is not interesting.  I don't know, I do know, but never mind.  They're all fermions.  Okay, the symbols are just what I wrote here.  Sometimes q, sometimes psi q, sometimes capital Q.  Sometimes, depending if you're talking about the individual types of them,  you'll just use U, D, S, C, B, or T.  Use the same names for the fields as you use for the particles.  And there's no completely coherent convention that everybody sticks to.  All right, they're all fermions.  The whole lot of them are fermions, as I said.  But now comes the charges.  So it's useful to divide them into groups of two.  These groups of two are sort of repetitions of each other.  This group of two, in many ways, is isomorphic, not exactly, to this group of two,  which is not the same, but which follows the same pattern.  The pattern of these two is similar to the pattern of these two.  Oh, I got them upside down.  Excuse me, wait.  If I want to keep the pattern, let me see.  I think I want to put down, up.  Down, up, strange.  Down, up.  Strange, charm, bottom top.  Yeah.  All right, so the down, up system is very similar to the strange, charm system.  It's very similar to the bottom top system.  So let's write down what the electric charges are, and you can see them.  You can see this similarity.  The down, up system has charge minus a third and two thirds.  That's the first example of particles in nature which have charges which are not  integer multiples of the electric charge of the electron.  However, quarks by themselves do not exist freely in nature.  They're always bound into other structures, protons, neutrons, and so forth,  and those particles do have integer charges.  Okay, the strange and the charm, exactly the same thing, minus a third and two thirds.  Bottom and top, exactly the same, minus a third and two thirds.  Can that be read?  They're just repetitions of the same thing.  What about the antiparticles?  If I were to list the antiparticles over here, they would just have exactly the same charges  as the particles except opposite sign.  So this is simply replication.  For some reason, nobody understands.  Nobody even has any idea why nature replicated itself this way.  Are they still all bearing on number one-third?  Yeah, they're all bearing on number one-third.  Okay, and then the masses, the masses are not similar to each other.  The masses wildly vary.  I'm going to put down estimates for them because the precise value, well, there are precise values  of the masses, but you can go look them up on Google or wherever you want.  The down quark is about 10 MeV.  So it's 50 times heavier than the electron.  A lot lighter than the proton.  Incidentally, what's the proton mass?  About 1,800 times the electron mass.  In other words, about 940 MeV.  This is a lot lighter than a proton.  The up quark, about 5 MeV, less than the, than the down quark.  And protons are made only out of up quarks and down quarks.  So it doesn't look like there's nearly enough mass in quarks to be the mass of a proton or neutron.  Okay, we'll come back to that.  The point is, of course, there's more in a proton than just its quarks.  Okay, strange in charm.  Strange is roughly order of magnitude 100 MeV.  That's strange.  And charm is a little over about 1,000 MeV.  Now notice that the down quark is heavier than the up quark.  But the strange quark, which is analogous to the down quark, is lighter than the charm quark.  So there's some pattern of inversion here of the masses.  Again, nobody understands at all why that's true.  Yeah, charm is about 1,012.  A little more than that.  Oh, sorry.  100, Mr. Zero.  Decimal creep.  Okay, 1,000 MeV.  And the bottom quark is about 5,000.  Oh, this is called a GEV, giga electron volt.  The bottom quark, see, we keep changing units.  That's about 5 GEV.  And the top quark is about 170 GEV.  So how much heavier is the top quark than the up quark?  Can anybody do that calculation?  How much?  30,000.  30,000?  A lot.  A lot.  All right.  So on the one hand, these particles are extremely similar to each other.  They do the same things.  They have the same properties.  And yet they have masses which wander all over the map.  Does anybody understand why?  No.  Are there any ideas?  Yes.  Do any of them work?  No.  We don't even have a clue about why there's...  First of all, we don't even understand, of course,  why there's even one of them.  One family.  These are called families.  Why is there one family?  Well, we don't know.  We're not sure if there wasn't one family who wouldn't be here  because there would be no protons and neutrons.  But given that there's this one family of up quarks and down quarks,  why are there strange quarks and charm quarks,  or top quarks and bottom quarks, nobody has a clue.  And that question is a stupid question.  Yeah.  When these quarks were found, the story goes that they were looking  in a certain place because the math said the math should be a certain amount.  I'm not talking about this.  No, they said that they went through the calculations  and they knew that this is where it was going to be,  that it was going to be somewhere around some AGEV that they were going to find.  Oh, the top quark.  Yeah.  And I was not sure if they predicted that it would be there before they went to the top quark.  Yeah, but not on the basis of abstract theory,  but on the basis of how the top quark would affect the work its way into other particles, top and bottom.  I was just saying because you just said that the numbers nobody knows why  and they're all over the ballpark,  but yet they seem to know that that's where they wanted to look for it.  Yeah, but not because there was any basic underlying reason  why the top quark had that mass.  What you could do is you could say,  supposing the top quark had a certain mass  and then calculate various Feynman diagrams involving the top quark in various ways,  Feynman diagrams involving ordinary particles, not the top quark,  but which had top quarks running around in the interior of diagrams.  Okay?  You calculate those diagrams.  Those diagrams have an effect on processes involving other particles that you know very well,  and then you say, how and what does the mass of this top quark have to be  in order that it does the right thing for these other particles?  Right?  So it was not in any sense a deep understanding of why the mass of the top quark was what it was.  It was simply an observation that you needed that particular value of the top quark mass  in order that it be consistent with...  Yeah, right.  So you can't observe the quark, but you can predict how it will disappear,  what will happen if there is one kind of showers and directions  and various particles will be included.  Okay.  Go ahead.  You're asking me the same.  Yeah, that's what that was.  To say that you can't detect the quark becomes us to a certain extent a matter of definition,  what it means to detect the quark.  You can certainly detect evidence of quarks.  What you can't do is create an isolated quark in isolation from other things and then examine it.  But we'll come.  We're going to come to the question.  I think you're probably remarking about jets produced.  Well, I don't know what you're talking about.  Yeah, we can talk about jets.  Let's come back to it after we talk more about quarks.  Does it act that some quarks have twice the charge of the absolute value as far as...  Is that from theory or is that just a bookkeeping?  It's semi-theory.  Yeah, to some extent that is understood.  I'm not going to explain it now, but now I'm telling you the facts.  We can talk about how much of this is explained and how much of it...  How much of the pattern is...  The right question is how much of this pattern is required for theoretical mathematical consistency.  But we haven't gotten any yet.  Some of this pattern is required.  Yeah, some of this pattern is required, but not much of it.  Very little of it is required by mathematical consistency.  Question?  No.  It's the relative abundance of the six kinds of quarks.  Relative abundance in where?  But what do you mean by relative abundance?  You mean in the world?  In the universe, yeah.  Neutrons are unstable.  They decay.  Protons are stable.  They exist in intergalactic space and everything else.  They're all...  Yeah, the only thing that has any appreciable abundance...  All right, first of all, the only quarks which have any degree of stability are ups and downs.  The rest of these decay to these.  So the real abundance of real particles in the universe are all ups and downs.  Okay?  Now, what's the relative abundance of ups and downs?  That's determined by how many quarks of each type there are in a proton.  There are no neutrons.  Oh, sorry, of course there are neutrons.  There are neutrons in atoms, in nuclei.  So you have to know the relative abundance of protons and neutrons to know the relative abundance of...  But that's all it is, relative abundance of protons and neutrons.  Okay, so what do we know?  A proton and what is a neutron in this language?  And let's come over here.  A proton is three quarks and a neutron is three quarks.  Now, as I said, I'm now in the business of telling you facts about these particles,  not at this point trying to understand why these are the facts.  We can't do everything at once.  A neutron is two down quarks and an up quark.  Let's just check that.  An up quark has charged two-thirds and a down quark has charged minus a third.  So two-thirds minus a third minus another third.  This is electrically neutral.  Charge equals zero.  That's good.  Neutron has charged zero.  Proton.  Proton is exactly the same as a neutron except with an interchange of up quarks and down quarks.  Two up quarks and a down quark.  Okay?  Now, up quarks and down quarks are a lot alike except for their electric charge.  The electric charge has to do with the interaction with photons.  Let's forget photons.  Let's forget about the existence of photons for the moment and just talk about quarks  and the other particles which are important inside the nucleus and so forth.  Then it would almost seem that a neutron and a proton are the same thing except for an interchange  of the up label and the down label.  You might then surmise that their properties are exactly the same if, for some reason,  the electric charge is unimportant.  In other words, supposing we don't have to worry about the interaction with photons,  just forget photons, then it would seem that protons and neutrons should be identical  because what's the difference?  You just replaced up quarks by down quarks.  It's not quite true because up quarks and down quarks don't have exactly the same mass.  They don't have exactly the same mass.  Now, 10 MeV by comparison with the mass of a proton is small.  It's almost negligible.  It is very small and it's almost negligible in nuclear physics or in particle physics.  To some precision, to the extent that you can ignore the masses of the quarks,  which are, after all, smaller by far than the masses of protons and neutrons,  neutrons and protons are a good deal alike.  The only difference is the slight difference in mass between the up quarks and the down quarks.  Which one is going to be heavier, the neutron or the proton?  Of course, it's going to be the one with more down quarks because down quarks are a bit heavier than up quarks.  Down quarks are a bit heavier than up quarks and so it's likely that the neutron is heavier than the proton and it is.  Neutron is a little bit heavier than the proton and it's largely attributed to the fact that the neutron has more down quarks.  Now, that's not all there is to the difference between protons and neutrons.  If the down quarks and the up quarks had exactly the same mass,  but you counted for electromagnetism, in other words the photon,  you said, okay, the photon is not completely unimportant, then which would be heavier?  The proton or the neutron?  Why?  Yes, because it has some electrostatic self-energy because it's charged.  So the proton would be a little bit heavier because of the self-energy of the electromagnetic field,  the electric field, one would expect the proton to be a little bit heavier.  In fact, the neutron is a little bit heavier and the reason is because the down quark is a little bit heavier than the up quark.  Okay, but other than that...  You're going to give us the mathes?  Of course.  Neutrons and protons.  Yeah, neutron is about what, 938 MeV and proton is about 939 MeV or...  What's about 1.4 MeV difference between them?  Something like about 1.4 MeV difference between them.  There's enough energy between them, there's enough energy separating them that the neutron can afford a little bit of energy to when it decays into a proton plus an electron plus a neutrino.  There's a little bit of excess energy in the neutrino which allows it to decay.  And allows it in particular to decay with an electron to an electron.  Okay, so that's the very, very rough story of protons and neutrons.  We'll come back to it.  But now there are also these strange quarks.  Let's forget charm quarks for a moment.  There's an interesting question.  Can you replace...  Notice that in every respect, the down quarks and the strange quarks are similar to each other except for the fact that the mass is different.  So you might ask, can you construct an analog of the proton and neutron where you pull out a down quark and replace it by a strange quark?  Or perhaps two strange quarks.  Pull out a down quark and replace it by a strange quark?  The answer is yes.  Of course you can because in every respect, the up quarks and the down quarks are the same.  It's sort of almost like an isotope. You pull out a proton and put it in a neutron and it sort of sticks together sort of the same way.  But it's even better here.  So you can construct another kind of analog.  These are called strange baryons.  Strange baryons, I forget their names.  Lambdas and XIs, they've got all kinds of names.  And it's been so long since I worked on these things that I can't even remember their names.  There are symbols like this associated with them, like this and the lambdas.  I don't remember which one is which.  Not important.  But for example, you can create, I don't know what its name is, pull out a down quark and create a strange and a down and an up.  What's the mass of this one over here?  Sorry, not the mass.  What is the charge of this one?  Well, it's exactly the same as a neutron because you pulled out a down and put it in S.  And the S and the down have the same charge.  So this is also electrically neutral.  But it has a strange quark in it and it's called a strange baryon.  They're not stable. They can decay.  We're going to discuss the decay processes later.  But they're not completely stable.  So they evaporate.  And this one will turn into that one. But yes, they do exist.  Likewise, you can put in two strange quarks and an up quark.  What is the charge of that one?  Same thing. Charge neutral again.  And likewise, for the proton, you can replace it by up, up and strange.  So there are all these strange baryons.  When those decay, what kind of products do you have?  What kind of what?  Products.  Oh, protons and neutrons.  Only protons and neutrons?  Yeah, well, no, no. You get some protons and pions and other things like the electrons and other things.  Of course, you can't just say protons.  It's a matter of the hour.  And you are. You also only substituted the changes for balance.  Yeah.  And not ups or...  No, you can't...  No, this is...  Well, the rules of what you can exchange are a little bit complicated.  But at the moment, you can always exchange one for a similar one of the same charge.  Now, you can also...  Oh, incidentally, these strange particles are a little bit heavier than the protons and neutrons  because of this extra 90 MeV of...  Oh, no, yeah, an extra 90 MeV.  90 MeV isn't much.  So they're somewhat heavier than the ordinary protons and neutrons.  But in every respect, they're similar.  The main difference of importance is because they're heavier, they can decay to the protons and neutrons.  And so they're not found in the universe and in the abundance.  All of those that you put up there so far can be constructed with the heading for it also.  Oh, yes.  Yeah, you'll have to take every particle and replace it by its antiparticle.  Then it becomes the anti-neutron, the antiproton, and the anti-question mark.  Excuse me.  You call these strange baritons.  The strangeness is not just another word for saying they have strange quarks.  But if you put it... what if you put it at the bottom before it could...  Okay, then they become bottom.  Then they're bottom baritons.  Then they're bottom baritons.  Strange baritons, as you put it in essence.  Yeah, yeah, yeah.  Are they strange?  I don't know.  They were called strange because people became familiar with protons and neutrons by the 1950s.  And then when they discovered these other things, they said, oh, that's strange.  And the unexpected things.  Yeah.  Where's the missing masto from the proton and neutron?  The missing masto, what do you mean by that?  Well, if you had the mast of the...  Oh, you mean if you just added up the mast of the quarks.  Right.  There's a lot missing.  Yeah, that's right.  There's a lot missing.  So there must be something else in the proton and neutron.  No, no, they're gluons.  Yeah.  No, no, no attempt here to be dramatic.  But the gluons don't carry any interesting charge, baryon number.  Do they carry mass?  Well, they carry energy.  So...  Okay, so actually what you were saying there is it's binding energy.  It's a form of binding energy, yeah.  That's right.  It's binding energy.  Energies don't add.  Not relativistically.  I mean, well, masses don't add.  The mass of an object is not necessarily the mass of its constituents.  Well, the 20-year thing about the Kovalev bomb type thing.  Mm-hmm.  Mm-hmm.  Right.  You're using the language of particles here to describe these composite particles.  It seems more complicated if you use the word language of fields.  How would you combine a field and upfield?  It seems like you would combine everywhere and not be a particle.  See what you're saying.  Field.  Do you want to know whether you can construct a field to describe a proton?  Yeah, you're using down and up as if they're particles.  Yeah.  And there's fields and they're everywhere and their modes of the field are combining  these composite particles.  Well, in thinking, yeah, I mean, in thinking about this particular aspect of things, it's  much easier to think about particles than fields.  We could think about it in terms of fields, but it's much harder.  Question about the binding energies.  Yeah.  So if this difference between the quark energies and the proton energy or binding energy, that's  a big positive energy.  No, not an integer.  It's not an integer.  It's a big positive energy.  Energy.  Oh, I thought you said integer.  Yeah.  And usually when you think of things being bound.  Usually negative.  Negative.  Right.  Not true here.  Well, yeah, I mean, we'll come to it, but yeah, sure.  You talked about the three Gs or three thousandths of the N.  Yes.  Yes.  Yes, there is.  Yes, there is, but not yet.  Let's talk first about mesons.  Mesons are simply quark and anti-quark.  Why, you know, you could raise the question, why do three quarks bind together to form  something?  Why don't two quarks bind together to form something?  In the early days of quarkology, this was a complete mystery.  Why quarks?  Oh, you could say, oh, it's in order to make the charge an integer multiple of the electron.  Well, that's a stupid answer.  And not to be that stupid, but at this stage, it's a stupid answer.  But yet, that is the pattern.  That is the pattern that they combine together and forms in which this is not the only rule,  but this is one of the rules of nature.  We do understand it and we do understand where it comes from, but a rule, a rule of thumb  at the present time, is the way things bind.  They always bind into combinations which have integer multiple of the electron charge.  Okay, so you can take that as a working rule temporarily until we have a deeper understanding  of it.  All right, mesons are also particles, composite particles, which also have the property that  their charge is integer multiple of the electron charge, but they have zero baryon number.  They do not have baryon number, which means that they must be made, that they're quark,  they're combinations of quarks.  They must be made of quarks and anti-quarks.  In fact, they are quarks, a quark and an anti-quark.  They're a quark and an anti-quark, and so let's write down.  There are, first of all, the ones that you can make only out of ups and down quarks.  Ups and down quarks are special, not in any deep sense, but they're special because they're  much lighter than the other particles.  They don't decay, or they don't decay as rapidly if they do decay.  They're abundant in nature, and more than that, it doesn't take much energy and collisions  to make them, so of course they were the first particles to be discovered, things made up  of only up quarks and down quarks.  The up quarks and down quarks are pretty light, and the mesons are typically pretty light.  They're an up quark and an anti-quark, and then you can start thinking about the different  combinations.  There's an up bar quark and a down quark.  There's an up quark and a down bar quark.  There's an up bar and an up quark, and there's a down bar and a down quark.  I think I got them all.  Any quarks at the opposite spin?  No, you can't do that.  Don't they have to be the opposite time because it's one-third or two-thirds?  So it's not going to be.  No.  Okay, let's work out what their electric charges are.  The electric charge of an up quark is minus two-thirds, and this one is minus one-third,  and this has charge minus one, right?  Minus a third, minus two-thirds.  That's fine.  Charge minus one is like an electron.  What about this one?  This is the antiparticle of this.  This one's not.  This one is just the antiparticle of this.  Oh, yes, right.  This one is the antiparticles of each other because they are related by changing particles  into antiparticles, down bar into down, up bar into up, and this has charge plus one.  So these are antiparticles of each other.  Up bar up, that's electrically neutral, obviously, and charge equals zero.  Now in fact, neither one of these two by themselves corresponds to distinct particles.  Remember we're doing quantum mechanics.  Each one of these states can be thought of as a quantum state.  Think of it as a quantum state.  The quantum state consisting of an anti-up quark and an up quark.  The quantum state consisting of an anti-down quark and a down quark.  One of the things you can do in quantum mechanics is to superpose states.  If you have states, you can add them.  You can superpose them.  Superposing them means making combinations that have a probability for being either this  one or this one.  There are two combinations of these two.  I'll tell you what they are.  Up bar up, plus down bar down, and what would I put in front of it to make it have total  probability one?  One over square root of two.  This is a quantum state, and this is the orthogonal quantum state.  Up bar up, minus down bar down.  You know what this is?  This is an entangled pair of quarks.  Not entangled through their spin, but entangled through their upness or downness.  If you thought of upness and downness as about being similar analogous to the spin direction  of a particle, up or down, and that's where this terminology came from, then these would  be two entangled states entangled not through their spin, but through their isospin, through  their upness and downness.  We haven't used the word isospin.  Maybe I'll tell you what it means, but not right now.  There's just this analogy between the spin directions and the upness or downness quantum  number.  These two things individually are well-defined particles.  This one over here goes together with these two, and they are called the pions.  They go together for a good reason, for a good mathematical reason, but they go together  because their mass is very close to each other.  It is believed they would be exactly the same mass if the up quark and down quark had the  same exact mass.  If the masses were the same.  All three of these are virtually indistinguishable except for a small difference in their mass  and they have different charges.  0 plus 1 and minus 1, and this is called the pion multiplet pi plus minus and 0.  Three independent kinds of particles called pions, and as I said, and we can discuss why  nature chose these particular combinations to be analogous to each other, but now I'm  telling you facts and not mathematics.  And the other combination is simply this one over here, and this is called the eta.  So there's the pi plus, the four states here really define the three pions, pi plus minus  and 0, and the eta meson.  The eta meson is similar to a pion in many ways, but it's heavier.  Why is it heavier?  That is a complicated story.  It's not an elementary story.  It's a complicated story.  Maybe we'll come to it, maybe we won't, but as a matter of fact, it's massed.  What are the masses of the pions?  The masses of the pions are about 140 MeV.  The mass of a pion, mass of pion, and pi is about 140 MeV.  So in other words, it's not too different from, question?  Yeah, it's about 140 MeV.  So it's somewhere in this range in here, not this heavy, and the mass of the eta is about  three times heavier or something like that.  The mass of the eta is about 500 MeV.  I don't remember the precise number, but that's about right.  Why that is, why the eta sticks out as being different was a puzzle for a long time.  Not obvious, not obvious.  Even today, it's a rather abstract mathematical fact, but it is understood.  Isn't it also true that they're relatively long, half-wise?  I'm going to compare it to most of them.  The numbers of orders and magnitude difference.  They don't decay by strong interactions.  They decay by weak and electromagnetic interactions.  So they're longer lived than many of these other particles.  Yes, that is true.  They are long lived.  Okay, those are the mesons.  Did you give the name for the up bar, down, down bar?  Yeah, those are pipe numbers.  No, they don't have names by themselves.  They're linear combination, which are the sum and differences of them, and have definite  names.  Oh, I suppose they do.  Yes, those are.  Is that similar to, is that something like the neutrino oscillations?  Well, in the sense that it's related to quantum superposition of states, yes, but it's got  more to do with spin combinations of two half-spin particles.  There are two ways that you can entangle.  Well, we'll come to one next time.  The last thing I simply want to tell you is that you can make strange mesons.  You can take any d-quark and replace it by a strange quark, strange bar quark, and so  forth.  That makes new mesons which are called strange mesons, or, what's the other name for them?  K mesons.  K mesons are mesons containing a strange or an anti-strange quark, replacing a down  quark.  There are four of them, up bar strange, up strange bar, down bar strange, down strange  bar.  These two have charge zero.  Charge zero, and these have charge plus one and minus one.  These two are called the charged K mesons.  These two are called the neutral change, the neutral K mesons.  So there are three kinds of pions, one kind of eta, and four kinds of, how many does that  make all together, let's see.  Three pions, four K mesons, and an eta, yeah.  There's more, there's more, there's more.  Did we leave something out?  Yeah, we left out one, we left out some.  Yeah, we left out S bar S, huh?  Yeah, there's nine.  Nine, nine altogether.  The reason it's nine is simple.  There are three quines of quarks, three kinds of anti-quarks, three times three is nine.  All right, okay.  For more, please visit us at stanford.edu.
Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_0_8555.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_8556_9431.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_9432_9935.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_9936_10607.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_10608_10763.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_10764_11159.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_11160_11351.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_11352_12071.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_12072_12143.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_12144_12503.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_12504_16115.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_16116_20219.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_20220_21131.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_21132_22475.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_22476_23195.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_23196_23303.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_23304_23435.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_23436_29747.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_29748_31895.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_31896_31943.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_31944_33443.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_33444_36119.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_36120_37115.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_37116_38099.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_38100_38279.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_38280_39431.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_39432_42203.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_42204_44531.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_44532_47675.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_47676_48215.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_48216_49247.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_49248_51611.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_51612_51803.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_51804_53483.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_53484_54407.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_54408_55487.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_55488_56783.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_56784_57623.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_57624_58067.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_58068_58367.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_58368_60527.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_60528_62543.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_62544_63971.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_63972_64991.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_64992_65111.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_65112_65159.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_65160_65603.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_65604_67139.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_67140_67391.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_67392_67727.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_67728_69851.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_69852_70139.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_70140_71507.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_71508_71651.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_71652_71999.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_72000_72275.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_72276_72707.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_72708_73271.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_73272_73499.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_73500_73859.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_73860_73943.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_73944_74027.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_74028_74855.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_74856_74915.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_74916_75011.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_75012_75227.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_75228_75527.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_75528_81683.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_81684_81875.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_81876_82139.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_82140_82883.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_82884_85619.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_85620_86279.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_86280_88655.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_88656_90011.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_90012_91619.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_91620_93839.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_93840_94007.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_94008_94871.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_94872_95891.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_95892_96071.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_96072_97403.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_97404_97667.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_97668_101123.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_101124_101183.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_101184_101303.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_101304_101483.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_101484_101735.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_101736_102059.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_102060_102131.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_102132_104579.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_104580_107627.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_107628_107975.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_107976_108887.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_108888_109415.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_109416_110183.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_110184_113015.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_113016_113927.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_113928_113975.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_113976_115775.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_115776_116447.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_116448_117815.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_117816_119399.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_119400_119639.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_119640_119759.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_119760_126827.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_126828_126923.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_126924_129551.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_129552_130235.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_130236_132335.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_132336_134291.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_134292_134531.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_134532_137171.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_137172_137495.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_137496_139883.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_139884_140243.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_140244_140387.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_140388_143615.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_143616_143663.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_143664_144983.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_144984_145535.png Lecture_1___New_Revolutions_in_Particle_Physics__Standard_Model__480p__flash9_145536_145915.png
Stanford University. Okay, so we've talked about a lot of things so far. Fields, quanta of fields, the relationship between fields and particles. That's the relationship between fields and their quanta. What are the quanta? The quanta are the discrete, indivisible units of energy that quanta mechanics implies for waves, for waves and waves of course are fields. Fields and waves are more or less the same thing. We've discussed the properties, not the properties of individual particles very much, but we've discussed some general properties, the properties of having energy, momentum, the properties of having spin, and the property of either being a fermion or a boson. Every particle is either a fermion or a boson. Fermions are the particles that don't like to live together in the same state. Bosons are the particles that do like to congregate and do condense into the same state. We've talked about wave equations on occasion or the field equations if you like, more generally. There is a kind of field equations. And we talked about how field equations can be generated from Lagrangians, from action principles. The quantum mechanical version of the Lagrangian is a kind of tool for codifying or codifying, whatever the right word is, codifying the interactions between particles. Various terms in the Lagrangian, things like, for example, products of fields represent processes which we can call vertices where particles come in and other particles go out. That would, for example, be a term in the Lagrangian which would have four powers of a field in it. So we've talked about these general things. We haven't talked very much about specific particles. Tonight, well, I expected to spend the first half hour beating around the bush a little bit. I'm going to spend a few more minutes beating around the bush. But then I want to come to really writing down what the particles are, who are the players in the drama, and start going through them more or less, well, not quite one by one, but in groups, and trying to give them some personality, give them some names, some properties, and also what it is they do and how they come into physics, into ordinary physics. Okay, but before I do that, there's kind of a triangle of concepts that we've discussed two legs of, but not the third leg very much. The triangle is particles or field quanta, particles, fields, and in modern physics, pretty much for every elementary particle. Now, we're going to have to think very hard in the future, not tonight. What is an elementary particle and what is a composite particle? We will come back to that. And you might think, I mean, everybody here probably has some answer if I were to ask you, how do you distinguish a composite particle from an elementary particle? And you will always be frustrated. You will always find some slippery reason that your definition didn't work. But for the moment, let's nevertheless imagine that there are elementary particles and that the elementary particles are the quanta of elementary fields, fundamental fields in the theory. And so they're more or less than one-to-one correspondence. But there's a third leg to this triangle. Anybody know what it is? Of course, you don't know what I'm thinking, so even if you did know what it was, you still wouldn't know it. Forces, forces, forces. So you can sense forces, forces. Okay, basically for every field there is a particle. For every field there is a force. Electric field gives rise to electric forces. Gravitational field gives rise to gravitational forces. It may be less obvious to you what the electron field, the electron has a field. It also gives rise to forces, and we'll talk about them a little bit. So there's kind of a correspondence that goes this way, there's a correspondence which goes this way. There must also be a correspondence which goes this way, a way of thinking about forces which is not based on fields, but which based on particles. If this correspondence or this triangle really makes sense. So I want to talk about that a little bit. Many of you know the idea, but let's just discuss it for a moment. Let me first discuss it in the context of electrodynamics. How forces come out of thinking, now this is classical electrodynamics for the moment, the complete field view of things. Supposing I put two charges into space, I want to know the force between them. How do I calculate it? Well, you could know the rule that the force is equal to the product of the charges times one over r squared and so forth. Or you could try to calculate it a different way. You could try to say, what do these two charges do to space? What they do to space is they create electric fields. Essentially that's the thing they do. They create an electric field that fills space. And I don't want to write down the details of what that electric field is. But let's just say this is the electric field. Let's forget the second particle and just write down the electric field due to the first particle, whatever it is. The electric field due to the first particle, incidentally it's proportional to the electric charge of the first particle. So let's explicitly put that in. E of the first particle times the electric field divided by the electric charge. This electric field here, I've divided out the electric charge. Maybe I shouldn't call it E. Let's call it E without the factor of the electric charge in it and put a little hat over it. That's this electric charge. And what is the field energy? Anybody know what the formula for the field energy is in an electric field? Electric fields have energy. They store their energy as a distribution of energy in space. And the field energy, the density of field energy, is the square of the electric field. So we square this and we integrate it over all space, the volume, and that's the energy stored in the electric field of the particle. Now, this energy does not depend on where we put the particle, right? The field will move. If we move the particle, the field will move with it, but the field energy will always be the same. The electric field will adjust to the position of the charge. The field will always give rise to exactly the same field energy. And this field energy here, remember E equals MC squared, that field energy is part of the mass of the particle. It contributes, the field contributes to the energy of the particle, and therefore it contributes to the mass of the particle. There's another way of thinking about a bit of renormalization, that there's some extra mass there because the field surrounds the particle in this way. Okay, I don't want to belabor that now. What about the second particle? Supposing the first particle wasn't there, but the second particle was there. This, of course, is the energy E, not the electric field. This is the energy. If there was only particle two, the field energy would be the integral of E2 times the electric field of the second particle squared. Now, if the two particles are not at the same place, well, let's not worry about the two particles. This one would also be independent of the position of this particle here. What about the energy if I have both particles? If I have both particles, then I have to add up the field first before squaring it. So the electric field, if I have two particles, will be the sum of the two electric fields, electric field, not energy. Let's call this energy En. Well, let's not call it H. Energy, just En. The energy, first of all, the electric field. The electric field will be the sum of the two electric fields. The electric field will be E1 plus E1, E1 plus E2, E2. Where these are the electric fields of particle one and particle two. This will be the total electric field. Incidentally, the electric fields are vectors, and so we might put little vector signs above them. The field energy you get by squaring this whole thing. So the field energy is the integral of a space. There are three terms. The first term is E1 squared, E1 squared. It's gotten by squaring this. The second term is plus E2 squared, E2 squared. And the third term is the interesting one. It's the product of E1, E2, twice as a matter of fact, times E1 dot E2. Actually, dot product. All right. What is this first term here? It's the self-energy. It's the self-energy of one particle by itself. It doesn't depend on the position of the particle. It's just a number. It's part of the mass of the particle. Let's forget it. It's already there as part of the mass of the particle. What about this one? Also, part of the self-energy of the second particle. What about this one here? This one is not the energy of either particle separately. It's proportional to the product of the charges. And it's proportional to the product of the fields. What if the particles were infinitely far away, so far away that their Coulomb fields hardly overlapped at all? You take one particle so far away that the Coulomb fields are hardly overlapping. Then this is going to be zero because wherever E1 is not zero, E2 will be zero, or almost zero. Wherever E2 is non-zero, E1 will be close to zero. So this will be very, very small as you take the particles apart. But what about when you bring them together? When you bring them together, the product of E1 times E2 will not be small. Nearby, where the particles are, both fields will be appreciable, and you will get a contribution from this. What is that contribution? That contribution as a function of distance, well, first of all, it's proportional to the product of the charges. It depends on the distance. And of course, if you work it out, as you might expect, it's nothing but the Coulomb force, one of our R squared. But I like to say it this way because it gives you the following picture that putting in both charges, taking them far apart, they don't affect, well, they're simply just independent objects. As you bring them together, they deform and distort the field in a way that depends on the distance between them, and the distortions of the field in between them, that field energy. That field energy, which is the contribution because both of them are there, that's the force law. So that's a purely field point of view of forces. A purely field point of view of forces. But if fields are nothing but collections of quanta, and quanta are particles, there must also be a way to think about forces in terms of particles. So let's talk about that a little bit. Before discussing electrodynamics in this way, let's talk about a slightly different setup. We're actually a very completely different setup. Let's talk about molecular forces. What do molecular forces come from? I'll give you one source, there are several origins of molecular forces. But here's a setup I want to think about. Let's begin with a pair of protons and a single electron. What is this? A proton over here, a proton over here, and a single electron. If this proton were very far away, then the ground state of the electron in the presence of the proton would just be the hydrogen atom ground state. It would be governed by some sort of Schrodinger wave function. Let's draw the Schrodinger wave function. The ground state would be the ground state of the hydrogen atom. And in the ground state, if this proton weren't there at all, not there at all, the electron in its ground state would certainly be found in the position nearby this proton. Now what if there are two protons over here? One proton over here, another proton over here, pretty far away, but not infinitely far away. Then there is another possible state of the electron with exactly the same energy where the electron is not over here, but it's over here with the corresponding wave function pushed over to here. It has exactly the same energy. Why? Because the two protons are of the same kind, and everything is completely symmetric over here. So if the electron is in orbit, well, a quantum mechanical orbit around this proton, or if it's in quantum mechanical orbit around this proton, the ground state energy will be exactly the same as if there was only one proton. But it's not quite true. Why isn't it exactly true? Well, if the protons are not infinitely far away, there are processes that could happen which could not happen if they were infinitely far away. Anybody know what the process is that can happen to the electron if the two... Tunneling effect. Tunneling effect. Yeah, the tunneling effect. The electron placed over here into its ground state can, with a small probability, suddenly appear in this atom over here. That's called quantum mechanical tunneling. It has to overcome an energy barrier in between the two. It takes some energy to pull the electron out of this atom. It'll get that energy back when it drops into this atom, but it has to go over this hill. Can it go over the hill? Classically it can't, but quantum mechanically it can tunnel from one place to another. Don't stand there and try to watch the tunneling. What happens if you try to watch for the electron going back and forth? Like anything else in quantum mechanics, watching it ruins it. You can watch over here. You can say, well, you can stand over here and wait for the electron to appear over here, but if you watch it from in here, you'll ruin the phenomenon. So the electron can hop back and forth. Hop back and forth simply means that there's a tunneling transition, a tunneling rate or a tunneling probability that if you put it over here, it can appear over here. If it appears over here and you wait a while, it will reappear over here and so forth. Okay, this process sets up a kind of equilibrium, long-term equilibrium in which the electron has an equal probability of being over here and over here with a wave function which looks like the sum of the two wave functions. Well, the sum divided by the square root of two in order for probability to add up to one. All right, so it looks like the sum of the two wave functions, which I didn't draw very well, but in the middle over here, it's slightly different. You might draw the exact wave function of the electron orbiting particle one as if particle two were not there. Same thing for particle two. And then add them up. Well, the correct tunneling wave function, the correct equilibrium wave function, is not exactly the sum of these two wave functions. It's a little bit different in here, a little bit, not much. But the point is the energy of the system is not exactly what it would be if the two protons were infinitely far away from each other. If they were infinitely far away from each other, you could put the electron over here, it would have a certain energy, or over here and it would have exactly the same energy. When you put them closer together, the energy of the electron is not exactly the same as it would be if they were far apart, if they were infinitely far apart. So if I were to plot the energy as a function of the distance between them, when they're very, very far apart, the energy of that electron is simply the energy of the electron with only one proton, and the other one just not there at all. At large distances, the energy would just be whatever it was. But as you bring the protons together, the energy of that two protons plus electron is a little bit less, turns out to be a little bit less, and that little bit less is a function of the distance between them. So now we have a situation when the system is in equilibrium with the electron tunneling back and forth and in equilibrium between the two, the energy is a function of the distance between them. What's the relationship between force and energy? You can think of this as potential energy. You can think of this as a potential energy between the two protons. The derivative of the energy. So the derivative of the energy, the energy has a gradient in here, force always pushes you toward decreased energy, and so this effectively creates an attraction between the two protons. That attraction is a kind of covalent bond. It's a kind of force between the two of them, which is due to the sharing of an electron, or to the fact that the electron can be in a superposition of quantum states in the two wells, in the two potentials of these two things here. Now, does that mean that a proton and another proton with an electron between them, which has this attractive force, will bind together? Not quite, because there's another force around. What's the other force around? The electrostatic force. The system doesn't have zero charge altogether, and so there's a repulsion force, and the repulsion force can overwhelm the attraction force, but nevertheless there is a force between two protons if there is an electron around, which is due, in a sense, to the jumping back and forth of the electron, or to the diminishing of the energy by the wave function sort of adjusting a little bit, a little bit better than it would if you just added the two wave functions together. As I said, that's the origin of covalent bonds, sharing of electrons, and in this case you can think of it, you can draw a picture. Now, the picture may or may not do anything for you. You have a proton over here, that's the world line of a proton, another world line of a proton, and the electron might start out being bound to this proton, hop across to this proton, hop back across to this proton. You shouldn't take this too literally, because if you stood in the middle, as I said, you would disrupt the process, but it's a description of the quantum mechanical state of the electron between the two protons, what it does, this possibility of the electron jumping back and forth, lowers the energy relative to if you just had one proton and just one electron in a bound state there. That means that there is an effective force, and you can picture it. This picture is like any analogy, it's often very, very misleading, but the presence of the electron in between the two protons creates an attractive force. It's called particle exchange, it's called particle exchange or electron exchange between the two protons. Now, yeah. So, is it as being the electrons hopping back and forth as reducing the effective positive charge of it? No, I don't think that that is quite the right picture. It doesn't really depend on the electric charges. It just depends on the fact that you can find, by adding together two wave functions, you can find a wave function with a little bit lower energy than either one separately. Is this what the magnet referred to as life-like-slide? That's what the magnet used to say, like, like, like. Like, like, like, I don't know. No, no, no, no, he was probably talking about the Bose's statistics of that photons like to be in the same state. I don't know what he was talking about. He made the same thing, he said that light, likes, like, like. Electrons like each other, photons. No, no, electrons hate each other. They don't like to be in the same state. Photons like each other, they love to be in the same state. I think he was probably talking about the opposite of the exclusion principle for photons, the Bose's statistics of them. Of course, I don't know. Protons have a tendency to be a cow. Protons. Yeah, that's because of their electric charge. Right, now what happens if we put the electron between them? Is that reducing the impulse? It does a little bit, but not very much. In fact, the force due to the electron jumping back and forth is a much shorter range force than the electrostatic attraction. So this force would only be important at relatively small distances, whereas the Coulomb force would fall off much more slowly. So the Coulomb force would be a longer range force. But, you know, it is there. It is there. The reason why it shows up is if you have a neutral system. I mean, it shows up better if you have a neutral system. If you have two electrons so that the total charge of the system is zero, then of course you'll have the possibility one electron orbiting around this proton, a second electron orbiting around this proton here. Now, the two objects here, they're called atoms, hydrogen atoms, and they're called electrons. So if you have a neutral system, there is no electrostatic force between them, but you still have this possibility of electrons jumping across. Electrons can jump across, a tunnel across, and then it does create an attractive force which can bind an atom, bind a molecule. Yeah, yeah, yeah, it is bound, but... Yeah, at small distances. At small distances, it is enough to overcome the Coulomb force. That's right. Yeah. Is there a possibility between the two protons that creates some kind of tension between them that creates some third force that the electrons kind of orbit around? Well, it doesn't create a third force, but it creates a sort of slightly nonlinear effect due to the two forces. But it's just a solution of the Schrodinger equation in the presence of the two forces does not have the energy that it would have if it was just one of those charges there. But let's leave it at that. There is this notion of the energy being lowered by the possibility of alternating between two quantum states. Is this thing all related to quantum entanglement? Not so much quantum entanglement. It's related to what are called off-diagonal elements in the Hamiltonian, but it's not too closely related to entanglement, I would say. For entanglement, normally you need two electrons. You only need one electron for this. For very, very, very high temperatures, does the electron move between the protons from a much higher probability? Well, at high temperatures, because it depends on the temperature, at very, very high temperatures, all that will happen is the electron will get kicked out and go to Alpha Centauri, and it won't even remember the fact that there was a proton around. If it gets hit hard enough by a very hot photon, but if the temperature is not that extreme, what it can do is cause, even if you only had a single atom, it could cause the electron to occupy higher levels. Now, higher levels have bigger wave functions, so the overlap between the higher wave functions could be larger, and it would certainly have some effect on the force. But that's a kind of special effect. All right, we have a concept that we see in the classical electrodynamics that the effect of having two charges changes the energy in between relative to what it would have been if you only had one, and it creates a force. Similar kind of thing here. If you have two force centers and the possibility of the electron being in a superposition of states, in other words, of the equilibrium being in a quantum superposition of the two states, the two states being over here or over here, that also lowers the energy and creates a force. Is there a way to think about the Coulomb force here in quantum mechanics where it is in some sense similar to this jumping back and forth of the electron? Yeah, there is. Let's come back to a single proton. A single proton is interacting with the electromagnetic field. That means it's interacting with the field whose quanta are photons. Classically, we might just describe it by solving the field equations for the electric field in the presence of a charged particle. Quantum mechanically, we think about it differently. Particularly in quantum field theory, we think about it as the emission and absorption of photons. That's what the Lagrangian of electrodynamics tells us. It tells us about the probability for the emitting and absorption of photons. So one way of thinking about the electron is that the actual physical electron is a quantum mechanical superposition of states in which, first of all, there are no photons. A superposition of a state with no photons. A superposition of states in which a photon has been emitted, and therefore there's a photon present. So it's a charged particle together with a photon around. Two photons can be emitted. The photon can be reabsorbed. The net effect in the end is some kind of equilibrium distribution, quantum mechanical equilibrium distribution of photons surrounding the electron. And you can measure those photons. I mean, a little bit different than measuring free photons. These photons are sort of trapped at the electron. They're emitted and reabsorbed. And if I have another electron over here, it is also emitting and absorbing photons. So there's an equilibrium. But every so often, now this should be thought of in the language of Feynman diagrams, every so often a photon which is emitted from here gets absorbed over here. And I always think about it as two jugglers, each juggling balls. And every so often, if they happen to be close enough together, a mistake will be made. And Joe will grab Mohr's juggling objects. Really what you really want to do is you really want to calculate the energy due to the electromagnetic field or due to the quantum superposition of photons that are present. You want to calculate that energy as a function of the distance between the charged particles. When they're very far apart, the two energies just add. They just get the sum of the energy of one charged particle and another charged particle. But as they get closer together, the charges begin to influence each other or in the language of Feynman diagrams, the emission of one photon by one particle and the absorption of that same photon by another particle creates a force. Creates an energy which is not exactly the sum of the two energies. That energy is the Coulomb force between the charged particles. So we have two distinct languages. Well, apart from just writing down the Coulomb force law, we have two other ways of thinking about forces. One of them is through classical field theory where you calculate the fields of objects and square them. And the other way is through the exchange of particles. Feynman diagrams with particles are exchanged back and forth. Any particle can be exchanged in some context or another. So every kind of particle in one way or another produces a force. In molecular physics, it's the exchange of electrons which create forces. In electrodynamics, it's the exchange of photons back and forth which create forces. So any particle is also connected with a force when that particle can be exchanged or jump back and forth between two something else. We'll describe some more examples, but I did want, before we move on, to just discuss the relationship between particles and forces. So we more or less have a one-to-one-to-one correspondence. Particles, fields for which those particles are the quanta, and forces which are associated with exchange processes where that particular kind of particle can bounce or jump back and forth. That's an important theme. So when people say that there are four forces in nature, now there's a force for every possible kind of particle. And we will discuss some of them as we go along. Okay, I think it's time now to start naming the particles, listing them, listing their properties, and discussing what they can do, what kind of processes they can engage in. And I could write down a big long list of all the elementary particles and then give you a test next week to see whether you memorized it or not. That wouldn't be fun at all. I think it's probably better to divide them up into small groups, which are in some way simply related to each other, get familiar with them a little bit and what they can do before we try to write down the whole damn standard model of particle physics, which is a monstrosity. I mean, you know, it's not my fault, certainly not my fault, that the standard model of elementary particle physics is an ugly monstrous mess. It's not Steve Weinberg's fault. It's nobody's fault, or if it is somebody's fault, that person, well, he may be in the room, but he's a little bit diffuse. Frankly, we don't understand why the particles are what they are. We don't understand why there is an electron and no particle whose name slips my mind because nobody's ever named it, because it doesn't exist, but nevertheless, why some particles exist and why other kinds of particles don't exist, we largely, by and large, don't know. We do understand some relationships between particles. If this one and that one and that one exist, then there's got to be another one to match up with them in some appropriate way. But in the end of the day, there are many more parameters, many more different types of particles than there are known relationships between them, which cut down the size of the problem. Okay, the mathematics and the relationships cut down the size of the problem somewhat, factor of two, factor of three or something like that, but there are hundreds of particles. So it is, honestly, a mess. If you want to understand what people are hoping for in the next round of experiments and so forth, you'll have to understand some of that mess and what the puzzles are about it. So let's begin. Let's name the particles. We begin with the most obvious ones. Let's make a table. Let's see, we need some columns. We can put the name of the particle over here. I'll put the symbol for the particle over here. I'll put the particle type over here. Now, what do I mean by type? I simply mean whether it's a fermion or boson. I'll put the electric charge over here. There's another quantity which characterizes particles. We'll call it the baryon number. I'll tell you what it is as we go along. And there are other properties. At the moment, I'm not listing them. And we'll put the mass over here. All right. The first one, of course, said I'm not listing them in any particular order. As it happens, I am writing down the lightest one first. The lightest one is, of course, the photon. The standard symbol for a photon is a gamma, like for a gamma ray. It has a field associated with it. The gamma particle is the quantum of a field. In most cases, or many cases, the field carries the same symbol as the particle itself. But for the photon, the field is called A. And it's really the vector potential of the electromagnetic field. You could use electric or magnetic fields, but you can also use the vector potential, which is another way of describing the electromagnetic field. It has a boson. I didn't write down the spin, but the spin is one unit of spin. The electric charge is zero. The baryon number, whatever that is, is zero. And the mass is zero. So that's the first particle. The next particle of interest is the electron. Now, the electron is a particle which has an antiparticle. It has an electric charge. If it has an electric charge, it must have an antiparticle of the opposite charge. And it is a convention, whether we think of the particle as the electron and the antiparticle as the positron, or whether we think of the positron as the particle and the electron as the antiparticle. The relation between them is mutual. So when I write the electron, I really mean the electron and positron. And so we could write E here plus minus. Standing E minus is the electron. E plus is the positron. The field of the electron is usually psi. And maybe you could put a little E downstairs to indicate that it stands for the electron. It's made up out of creation and annihilation operators for electrons. Electrons are fermions. It's charged. Okay? It's charged in what units now? Well, the standard particle physics or quantum mechanical unit for electric charge, believe it or not, is the electric charge of an electron. It's a good unit to work in terms of. You can go look it up in coulombs. It's 10 to the minus, what, 23 coulombs? 10 to the minus 19th coulombs, or yeah. It's some very small charge. But it's not useful to think about it in coulombs. All particles in nature have electric charges which are integer multiples of the electron charge. This could not true of quarks, but quarks are not observable particles. All right. So the charge we'll just write as minus one for the electron and plus one for the positron. So since we typically think of the electron as the particle and the positron as the antiparticle, let's just call it minus one and remember that the positron has the opposite charge. Variant number is zero and it's mass. Now we have to decide on units for mass. Okay? Units for mass are the same as units for energy. E equals mc squared. So we can either describe the mass as a mass in kilograms or in energy in joules, or we can simply invent a new unit which is more appropriate to microscopic physics to atomic physics. In fact, the unit that we use comes originally historically out of atomic physics. It is the unit in which the ionization energy of an electron and a hydrogen atom is what? 13.5 electron volts. An electron volt is how much energy you get if you pass an electron across a capacitor plate of one volt. It's a very, very small amount of energy, some tiny fraction of a joule. But one electron volt is the standard unit that came historically out of atomic physics, theory of electrons and so forth. It's going to wind up being too small a unit for us. Particle physics energies are larger than atomic physics energies, but for historical reasons we have the electron volt as our unit of energy. And the mass of an electron measured in electron volts is of order a million electron volts, one MeV. In fact, it's a half an electron volt. Not exactly. I think it's.51 MeV, and MeV stands for millions of electron volts. And MeV will be too small a unit for many other purposes. As I said, the particle physics is a mess, and the masses of particles extend all over the map. And so in trying to search for a useful unit, you're always frustrated. The useful unit will always be too small for the next... No, why? No, it's exactly.51. No, it's not. What's that? Pi 3. Pi equals 3. Pi equals 3. Right. Okay, now, quantum electrodynamics is the theory of electrons and photons, and we've talked about it a little bit, more than a little bit. And just we could also write down over here a table of the various... I don't want to make it a table. We'll just draw some pictures. The basic elementary process that takes place in quantum electrodynamics, photons and electrons, is the emission of a photon by an electron. Electron, electron photon, and as I've showed you several times, you can rearrange the legs of this diagram so that this could represent not the emission of a photon, but the absorption of a photon. A photon comes in from the past, or... Oops, sorry. You can even flip the electron legs around so that it looks like this. Electron going backward in time. Well, what does that mean? That really means a positron emitting a photon. So the basic building block for building up processes and interactions is this vertex with two electrons, electron, positron, whatever coming... one going in, one going out, and a photon coming out of it, or going into it. Out of that, you build up all of the various processes of quantum electrodynamics, but in particular, the process or the phenomenon that corresponds to the force between charges, and in the language of particle exchange, it's the photon bouncing back and forth between charged particles, which creates that force. Yet another way to describe what's going on here is in terms of a Lagrangian or a term in a Lagrangian. The Lagrangian describing this process here describes one electron in, one electron out, and one photon out, and so you build that out of the field operators. One electron in is psi electron. It creates, it has the creation of annihilation operators in it. An electron out is psi dagger of the electron, and a photon emitted is the field operator for the photon, and if you plug in all the creation and annihilation operators, you will find in here, buried in here, terms where a photon is emitted, an electron absorbed, another electron emitted, and so forth. And this codifies, this describes all of the various basic processes that can happen in quantum electrodynamics. Now, there's a parameter in the Lagrangian that appears the electric charge of the electron, and that, roughly speaking, is associated with the amplitude for a electron to emit a photon. The electron, let's say you hit the electron or whatever, the electron plows into the side of a x-ray machine. What's the probability that a photon will be emitted? Well, the amplitude is the electric charge, and the probability is proportional to the square of the electric charge. So all of this here is a way of describing all of these basic processes, and when they're combined together, they produce forces, they produce processes where photons are emitted, the whole world of quantum electrodynamics flows out of this, basically, one expression here. We won't try to go through that again now, but let's start adding a little bit to our particle list. The next particles of interest, these are, of course, familiar to you, I'm sure. Now, if this were 1960, when I was, well, I was, 1962, when I went to graduate school, probably the next particles I might write down would be protons and neutrons. Protons and neutrons are now subsumed by quarks. It is widely believed that, in some sense, protons and neutrons are composites of quarks, although we will come, remind me to come back to this issue of the difference, or what it means to be composite versus elementary. It's a very interesting story, but naively, quarks are smaller than protons and neutrons, and so protons and neutrons, which are big fat globs, are made up out of quarks. So, next thing are quarks. There's a lot of quarks. We won't even get to all of them tonight, or the whole set of distinctions between them, I don't think we will, but there's more than one type of quark. There are six types of quarks, six distinct particles, all of which are very similar to each other in some respects, very different from each other in different other respects. So, let's list them. They go under, they have names, all right? Well, why do they call what they are? They call what they are just a historically randomly people assigned silly names to them, and there's no logic to what they're called, no logic at all. There's, first of all, the up quark, and that's called U. The symbol is U. So, let's see, we should write there are quarks here, quarks. And I suppose the symbol for quarks is Q. All quarks are fermions. We'll write down their charge later. They have all baryon number of one-third. Now, why one-third? Well, the reason is very simple. The baryon number is basically the counting of the number of protons and neutrons. Each proton is counted as having one unit of baryon number. Each neutron is counted as having one unit of baryon. Baryon is just a word for protons and neutrons, and a somewhat generalization of protons and neutrons. Nucleon is a word for protons and neutrons. There are other particles which will come to which are very similar to protons and neutrons. They're also called baryons. The prefix barry I think means heavy. And baryons were called baryons because they're a lot heavier than electrons. But counting up the number of protons and neutrons, what do you call the number of protons plus neutrons in an atom? Atomic weight. Atomic weight, yeah. The atomic weight, yeah. Is equal, approximately equal to the total number of protons and neutrons. And the total number of protons and neutrons in nuclear physics never changes. Protons can turn into neutrons. Neutrons can turn into protons plus other things. But the number of protons plus neutrons never changes. You do have isotopes. But still, the number of protons plus neutrons doesn't change. Number of protons can change. How can the number of protons change? No, I'm just saying that different types of protons have different numbers than neutrons. Oh, yeah. Indeed they do. But are there processes with number of protons and neutrons change? Protons, not plus neutrons, but protons and or neutrons change? Beta decay. Beta decay, radioactivity, radioactivity, one form of radioactivity, a neutron decays into a proton plus an electron and an antinutrino. Okay, so in that process, the number of protons changes by one. The number of neutrons changes by one. But the number of protons plus neutrons doesn't change. There's a generalization of that in all of nuclear physics and particle physics. There's a certain quantity, which for ordinary nuclear physics is just the number of protons plus neutrons. And that number is sometimes called the Baryon number. We'll have to generalize it a little bit beyond protons and neutrons. It's a Baryon number. And it could have been defined to be two for the proton or seven for the proton or pi for the proton. But whatever it is, it has to be defined as twice as much for two protons, three times as much for three protons. So it's a convention that you say the Baryon number of the proton is one. Incidentally, what's the Baryon number of the antiproton? Minus one. Minus one. Proton has Baryon number plus one. Antiproton, Baryon number minus one. Neutron, Baryon number one. Anti-neutron, Baryon number minus one, but clearly there's an element of convention in exactly what you call M. But once it was fixed that the Baryon number of a proton was one, then the Baryon number of a quark was a third, because three quarks make a proton. So it's just a historical glitch that the Baryon number of the most fundamental thing in nuclear physics is one third and not one. So if you look out at an antiquark, there are antiquarks. Baryon number is minus a third. So I won't write that down separately. The number of quarks is conserved? Number of quarks minus the number of antiquarks is conserved. Now, whether or not that is an absolute conservation law, it is not believed to be an absolute conservation law. What do I mean by absolute conservation law? Can a proton disappear? It can't completely disappear. Its energy has to go someplace. Are there processes in nature where a proton might disappear and become something that is neither a proton or a neutron or anything else that you would call a Baryon? For example, without violating charge conservation, a proton could become a positron and a photon. So a proton could decay into a positron and a photon. Does it? Well, you can wait. If you have a single proton and you sit there and wait, you will wait a long, long time before that proton decays. It's half life to decay that way is at least 10 to the 33 or 10 to the 34 years. So this is not something that happens very regularly. Does it happen at all? The thinking is yes, it does, but this is one of the very, very interesting questions of particle physics of whether the proton can decay. And when you say can it decay, you mean decay into something that does not carry a Baryon number. And it is widely believed that the answer is yes, but it's never been demonstrated. Incidentally, how do you have you wait around for 10 to the 34 years for a proton to decay? You get 10 to the 34 protons and you wait around for one of them to see one. Now 10 to the 34 protons is a lot of protons. If you have protons, then it's protons. No, that's not that. That's zero Baryon number because it goes to zero Baryon number. One has Baryon number one anti proton has Baryon number minus one. So that's not a Baryon. We call them Baryon violating processes, processes in which the Baryon number is not conserved. Nobody has ever witnessed such a process in the laboratory or anyplace else. Can they happen? There does not seem to be any reason why they cannot happen built into the mathematics of what we know. So we leave this as an open question, but empirically and at least to a very, very high precision, Baryon number is conserved and quarks by definition have one third of a unit. One third of a unit. As I said, minus a third for anti quarks. But in order to fill in the rest of this, in particular, electric charge and mass, we don't have to label which kind of quark we're talking about. And there are lots of different kinds of quarks. So let's put in a list of different kinds of quarks. This is not new particles which are not quarks. This is just a subheading here, quarks and then things underneath. There are up quarks, down quarks. Why are they up and down and not up and down? There's nothing up and down about them. What directions? Up and down? Up and down means in the Earth's gravitational field. There's nothing up and down here about them. Then it gets worse. There are strange quarks which are no stranger than non-strange quarks. It gets more and silly. There are charmed quarks which are charming, I suppose. And then there are, now this is, if you're squeamish or very, bottom quarks, bottom quarks, bottom quarks, and then top quarks. The symbols are of course exactly the same. I just didn't feel like writing the words. Up, down, strange, charm, bottom, top. Same as bottom and top. I got a little pretentious beauty in truth. Bottom and top, strange and charm. How and under what circumstances these things were named is not interesting. I don't know, I do know, but never mind. They're all fermions. Okay, the symbols are just what I wrote here. Sometimes q, sometimes psi q, sometimes capital Q. Sometimes, depending if you're talking about the individual types of them, you'll just use U, D, S, C, B, or T. Use the same names for the fields as you use for the particles. And there's no completely coherent convention that everybody sticks to. All right, they're all fermions. The whole lot of them are fermions, as I said. But now comes the charges. So it's useful to divide them into groups of two. These groups of two are sort of repetitions of each other. This group of two, in many ways, is isomorphic, not exactly, to this group of two, which is not the same, but which follows the same pattern. The pattern of these two is similar to the pattern of these two. Oh, I got them upside down. Excuse me, wait. If I want to keep the pattern, let me see. I think I want to put down, up. Down, up, strange. Down, up. Strange, charm, bottom top. Yeah. All right, so the down, up system is very similar to the strange, charm system. It's very similar to the bottom top system. So let's write down what the electric charges are, and you can see them. You can see this similarity. The down, up system has charge minus a third and two thirds. That's the first example of particles in nature which have charges which are not integer multiples of the electric charge of the electron. However, quarks by themselves do not exist freely in nature. They're always bound into other structures, protons, neutrons, and so forth, and those particles do have integer charges. Okay, the strange and the charm, exactly the same thing, minus a third and two thirds. Bottom and top, exactly the same, minus a third and two thirds. Can that be read? They're just repetitions of the same thing. What about the antiparticles? If I were to list the antiparticles over here, they would just have exactly the same charges as the particles except opposite sign. So this is simply replication. For some reason, nobody understands. Nobody even has any idea why nature replicated itself this way. Are they still all bearing on number one-third? Yeah, they're all bearing on number one-third. Okay, and then the masses, the masses are not similar to each other. The masses wildly vary. I'm going to put down estimates for them because the precise value, well, there are precise values of the masses, but you can go look them up on Google or wherever you want. The down quark is about 10 MeV. So it's 50 times heavier than the electron. A lot lighter than the proton. Incidentally, what's the proton mass? About 1,800 times the electron mass. In other words, about 940 MeV. This is a lot lighter than a proton. The up quark, about 5 MeV, less than the, than the down quark. And protons are made only out of up quarks and down quarks. So it doesn't look like there's nearly enough mass in quarks to be the mass of a proton or neutron. Okay, we'll come back to that. The point is, of course, there's more in a proton than just its quarks. Okay, strange in charm. Strange is roughly order of magnitude 100 MeV. That's strange. And charm is a little over about 1,000 MeV. Now notice that the down quark is heavier than the up quark. But the strange quark, which is analogous to the down quark, is lighter than the charm quark. So there's some pattern of inversion here of the masses. Again, nobody understands at all why that's true. Yeah, charm is about 1,012. A little more than that. Oh, sorry. 100, Mr. Zero. Decimal creep. Okay, 1,000 MeV. And the bottom quark is about 5,000. Oh, this is called a GEV, giga electron volt. The bottom quark, see, we keep changing units. That's about 5 GEV. And the top quark is about 170 GEV. So how much heavier is the top quark than the up quark? Can anybody do that calculation? How much? 30,000. 30,000? A lot. A lot. All right. So on the one hand, these particles are extremely similar to each other. They do the same things. They have the same properties. And yet they have masses which wander all over the map. Does anybody understand why? No. Are there any ideas? Yes. Do any of them work? No. We don't even have a clue about why there's... First of all, we don't even understand, of course, why there's even one of them. One family. These are called families. Why is there one family? Well, we don't know. We're not sure if there wasn't one family who wouldn't be here because there would be no protons and neutrons. But given that there's this one family of up quarks and down quarks, why are there strange quarks and charm quarks, or top quarks and bottom quarks, nobody has a clue. And that question is a stupid question. Yeah. When these quarks were found, the story goes that they were looking in a certain place because the math said the math should be a certain amount. I'm not talking about this. No, they said that they went through the calculations and they knew that this is where it was going to be, that it was going to be somewhere around some AGEV that they were going to find. Oh, the top quark. Yeah. And I was not sure if they predicted that it would be there before they went to the top quark. Yeah, but not on the basis of abstract theory, but on the basis of how the top quark would affect the work its way into other particles, top and bottom. I was just saying because you just said that the numbers nobody knows why and they're all over the ballpark, but yet they seem to know that that's where they wanted to look for it. Yeah, but not because there was any basic underlying reason why the top quark had that mass. What you could do is you could say, supposing the top quark had a certain mass and then calculate various Feynman diagrams involving the top quark in various ways, Feynman diagrams involving ordinary particles, not the top quark, but which had top quarks running around in the interior of diagrams. Okay? You calculate those diagrams. Those diagrams have an effect on processes involving other particles that you know very well, and then you say, how and what does the mass of this top quark have to be in order that it does the right thing for these other particles? Right? So it was not in any sense a deep understanding of why the mass of the top quark was what it was. It was simply an observation that you needed that particular value of the top quark mass in order that it be consistent with... Yeah, right. So you can't observe the quark, but you can predict how it will disappear, what will happen if there is one kind of showers and directions and various particles will be included. Okay. Go ahead. You're asking me the same. Yeah, that's what that was. To say that you can't detect the quark becomes us to a certain extent a matter of definition, what it means to detect the quark. You can certainly detect evidence of quarks. What you can't do is create an isolated quark in isolation from other things and then examine it. But we'll come. We're going to come to the question. I think you're probably remarking about jets produced. Well, I don't know what you're talking about. Yeah, we can talk about jets. Let's come back to it after we talk more about quarks. Does it act that some quarks have twice the charge of the absolute value as far as... Is that from theory or is that just a bookkeeping? It's semi-theory. Yeah, to some extent that is understood. I'm not going to explain it now, but now I'm telling you the facts. We can talk about how much of this is explained and how much of it... How much of the pattern is... The right question is how much of this pattern is required for theoretical mathematical consistency. But we haven't gotten any yet. Some of this pattern is required. Yeah, some of this pattern is required, but not much of it. Very little of it is required by mathematical consistency. Question? No. It's the relative abundance of the six kinds of quarks. Relative abundance in where? But what do you mean by relative abundance? You mean in the world? In the universe, yeah. Neutrons are unstable. They decay. Protons are stable. They exist in intergalactic space and everything else. They're all... Yeah, the only thing that has any appreciable abundance... All right, first of all, the only quarks which have any degree of stability are ups and downs. The rest of these decay to these. So the real abundance of real particles in the universe are all ups and downs. Okay? Now, what's the relative abundance of ups and downs? That's determined by how many quarks of each type there are in a proton. There are no neutrons. Oh, sorry, of course there are neutrons. There are neutrons in atoms, in nuclei. So you have to know the relative abundance of protons and neutrons to know the relative abundance of... But that's all it is, relative abundance of protons and neutrons. Okay, so what do we know? A proton and what is a neutron in this language? And let's come over here. A proton is three quarks and a neutron is three quarks. Now, as I said, I'm now in the business of telling you facts about these particles, not at this point trying to understand why these are the facts. We can't do everything at once. A neutron is two down quarks and an up quark. Let's just check that. An up quark has charged two-thirds and a down quark has charged minus a third. So two-thirds minus a third minus another third. This is electrically neutral. Charge equals zero. That's good. Neutron has charged zero. Proton. Proton is exactly the same as a neutron except with an interchange of up quarks and down quarks. Two up quarks and a down quark. Okay? Now, up quarks and down quarks are a lot alike except for their electric charge. The electric charge has to do with the interaction with photons. Let's forget photons. Let's forget about the existence of photons for the moment and just talk about quarks and the other particles which are important inside the nucleus and so forth. Then it would almost seem that a neutron and a proton are the same thing except for an interchange of the up label and the down label. You might then surmise that their properties are exactly the same if, for some reason, the electric charge is unimportant. In other words, supposing we don't have to worry about the interaction with photons, just forget photons, then it would seem that protons and neutrons should be identical because what's the difference? You just replaced up quarks by down quarks. It's not quite true because up quarks and down quarks don't have exactly the same mass. They don't have exactly the same mass. Now, 10 MeV by comparison with the mass of a proton is small. It's almost negligible. It is very small and it's almost negligible in nuclear physics or in particle physics. To some precision, to the extent that you can ignore the masses of the quarks, which are, after all, smaller by far than the masses of protons and neutrons, neutrons and protons are a good deal alike. The only difference is the slight difference in mass between the up quarks and the down quarks. Which one is going to be heavier, the neutron or the proton? Of course, it's going to be the one with more down quarks because down quarks are a bit heavier than up quarks. Down quarks are a bit heavier than up quarks and so it's likely that the neutron is heavier than the proton and it is. Neutron is a little bit heavier than the proton and it's largely attributed to the fact that the neutron has more down quarks. Now, that's not all there is to the difference between protons and neutrons. If the down quarks and the up quarks had exactly the same mass, but you counted for electromagnetism, in other words the photon, you said, okay, the photon is not completely unimportant, then which would be heavier? The proton or the neutron? Why? Yes, because it has some electrostatic self-energy because it's charged. So the proton would be a little bit heavier because of the self-energy of the electromagnetic field, the electric field, one would expect the proton to be a little bit heavier. In fact, the neutron is a little bit heavier and the reason is because the down quark is a little bit heavier than the up quark. Okay, but other than that... You're going to give us the mathes? Of course. Neutrons and protons. Yeah, neutron is about what, 938 MeV and proton is about 939 MeV or... What's about 1.4 MeV difference between them? Something like about 1.4 MeV difference between them. There's enough energy between them, there's enough energy separating them that the neutron can afford a little bit of energy to when it decays into a proton plus an electron plus a neutrino. There's a little bit of excess energy in the neutrino which allows it to decay. And allows it in particular to decay with an electron to an electron. Okay, so that's the very, very rough story of protons and neutrons. We'll come back to it. But now there are also these strange quarks. Let's forget charm quarks for a moment. There's an interesting question. Can you replace... Notice that in every respect, the down quarks and the strange quarks are similar to each other except for the fact that the mass is different. So you might ask, can you construct an analog of the proton and neutron where you pull out a down quark and replace it by a strange quark? Or perhaps two strange quarks. Pull out a down quark and replace it by a strange quark? The answer is yes. Of course you can because in every respect, the up quarks and the down quarks are the same. It's sort of almost like an isotope. You pull out a proton and put it in a neutron and it sort of sticks together sort of the same way. But it's even better here. So you can construct another kind of analog. These are called strange baryons. Strange baryons, I forget their names. Lambdas and XIs, they've got all kinds of names. And it's been so long since I worked on these things that I can't even remember their names. There are symbols like this associated with them, like this and the lambdas. I don't remember which one is which. Not important. But for example, you can create, I don't know what its name is, pull out a down quark and create a strange and a down and an up. What's the mass of this one over here? Sorry, not the mass. What is the charge of this one? Well, it's exactly the same as a neutron because you pulled out a down and put it in S. And the S and the down have the same charge. So this is also electrically neutral. But it has a strange quark in it and it's called a strange baryon. They're not stable. They can decay. We're going to discuss the decay processes later. But they're not completely stable. So they evaporate. And this one will turn into that one. But yes, they do exist. Likewise, you can put in two strange quarks and an up quark. What is the charge of that one? Same thing. Charge neutral again. And likewise, for the proton, you can replace it by up, up and strange. So there are all these strange baryons. When those decay, what kind of products do you have? What kind of what? Products. Oh, protons and neutrons. Only protons and neutrons? Yeah, well, no, no. You get some protons and pions and other things like the electrons and other things. Of course, you can't just say protons. It's a matter of the hour. And you are. You also only substituted the changes for balance. Yeah. And not ups or... No, you can't... No, this is... Well, the rules of what you can exchange are a little bit complicated. But at the moment, you can always exchange one for a similar one of the same charge. Now, you can also... Oh, incidentally, these strange particles are a little bit heavier than the protons and neutrons because of this extra 90 MeV of... Oh, no, yeah, an extra 90 MeV. 90 MeV isn't much. So they're somewhat heavier than the ordinary protons and neutrons. But in every respect, they're similar. The main difference of importance is because they're heavier, they can decay to the protons and neutrons. And so they're not found in the universe and in the abundance. All of those that you put up there so far can be constructed with the heading for it also. Oh, yes. Yeah, you'll have to take every particle and replace it by its antiparticle. Then it becomes the anti-neutron, the antiproton, and the anti-question mark. Excuse me. You call these strange baritons. The strangeness is not just another word for saying they have strange quarks. But if you put it... what if you put it at the bottom before it could... Okay, then they become bottom. Then they're bottom baritons. Then they're bottom baritons. Strange baritons, as you put it in essence. Yeah, yeah, yeah. Are they strange? I don't know. They were called strange because people became familiar with protons and neutrons by the 1950s. And then when they discovered these other things, they said, oh, that's strange. And the unexpected things. Yeah. Where's the missing masto from the proton and neutron? The missing masto, what do you mean by that? Well, if you had the mast of the... Oh, you mean if you just added up the mast of the quarks. Right. There's a lot missing. Yeah, that's right. There's a lot missing. So there must be something else in the proton and neutron. No, no, they're gluons. Yeah. No, no, no attempt here to be dramatic. But the gluons don't carry any interesting charge, baryon number. Do they carry mass? Well, they carry energy. So... Okay, so actually what you were saying there is it's binding energy. It's a form of binding energy, yeah. That's right. It's binding energy. Energies don't add. Not relativistically. I mean, well, masses don't add. The mass of an object is not necessarily the mass of its constituents. Well, the 20-year thing about the Kovalev bomb type thing. Mm-hmm. Mm-hmm. Right. You're using the language of particles here to describe these composite particles. It seems more complicated if you use the word language of fields. How would you combine a field and upfield? It seems like you would combine everywhere and not be a particle. See what you're saying. Field. Do you want to know whether you can construct a field to describe a proton? Yeah, you're using down and up as if they're particles. Yeah. And there's fields and they're everywhere and their modes of the field are combining these composite particles. Well, in thinking, yeah, I mean, in thinking about this particular aspect of things, it's much easier to think about particles than fields. We could think about it in terms of fields, but it's much harder. Question about the binding energies. Yeah. So if this difference between the quark energies and the proton energy or binding energy, that's a big positive energy. No, not an integer. It's not an integer. It's a big positive energy. Energy. Oh, I thought you said integer. Yeah. And usually when you think of things being bound. Usually negative. Negative. Right. Not true here. Well, yeah, I mean, we'll come to it, but yeah, sure. You talked about the three Gs or three thousandths of the N. Yes. Yes. Yes, there is. Yes, there is, but not yet. Let's talk first about mesons. Mesons are simply quark and anti-quark. Why, you know, you could raise the question, why do three quarks bind together to form something? Why don't two quarks bind together to form something? In the early days of quarkology, this was a complete mystery. Why quarks? Oh, you could say, oh, it's in order to make the charge an integer multiple of the electron. Well, that's a stupid answer. And not to be that stupid, but at this stage, it's a stupid answer. But yet, that is the pattern. That is the pattern that they combine together and forms in which this is not the only rule, but this is one of the rules of nature. We do understand it and we do understand where it comes from, but a rule, a rule of thumb at the present time, is the way things bind. They always bind into combinations which have integer multiple of the electron charge. Okay, so you can take that as a working rule temporarily until we have a deeper understanding of it. All right, mesons are also particles, composite particles, which also have the property that their charge is integer multiple of the electron charge, but they have zero baryon number. They do not have baryon number, which means that they must be made, that they're quark, they're combinations of quarks. They must be made of quarks and anti-quarks. In fact, they are quarks, a quark and an anti-quark. They're a quark and an anti-quark, and so let's write down. There are, first of all, the ones that you can make only out of ups and down quarks. Ups and down quarks are special, not in any deep sense, but they're special because they're much lighter than the other particles. They don't decay, or they don't decay as rapidly if they do decay. They're abundant in nature, and more than that, it doesn't take much energy and collisions to make them, so of course they were the first particles to be discovered, things made up of only up quarks and down quarks. The up quarks and down quarks are pretty light, and the mesons are typically pretty light. They're an up quark and an anti-quark, and then you can start thinking about the different combinations. There's an up bar quark and a down quark. There's an up quark and a down bar quark. There's an up bar and an up quark, and there's a down bar and a down quark. I think I got them all. Any quarks at the opposite spin? No, you can't do that. Don't they have to be the opposite time because it's one-third or two-thirds? So it's not going to be. No. Okay, let's work out what their electric charges are. The electric charge of an up quark is minus two-thirds, and this one is minus one-third, and this has charge minus one, right? Minus a third, minus two-thirds. That's fine. Charge minus one is like an electron. What about this one? This is the antiparticle of this. This one's not. This one is just the antiparticle of this. Oh, yes, right. This one is the antiparticles of each other because they are related by changing particles into antiparticles, down bar into down, up bar into up, and this has charge plus one. So these are antiparticles of each other. Up bar up, that's electrically neutral, obviously, and charge equals zero. Now in fact, neither one of these two by themselves corresponds to distinct particles. Remember we're doing quantum mechanics. Each one of these states can be thought of as a quantum state. Think of it as a quantum state. The quantum state consisting of an anti-up quark and an up quark. The quantum state consisting of an anti-down quark and a down quark. One of the things you can do in quantum mechanics is to superpose states. If you have states, you can add them. You can superpose them. Superposing them means making combinations that have a probability for being either this one or this one. There are two combinations of these two. I'll tell you what they are. Up bar up, plus down bar down, and what would I put in front of it to make it have total probability one? One over square root of two. This is a quantum state, and this is the orthogonal quantum state. Up bar up, minus down bar down. You know what this is? This is an entangled pair of quarks. Not entangled through their spin, but entangled through their upness or downness. If you thought of upness and downness as about being similar analogous to the spin direction of a particle, up or down, and that's where this terminology came from, then these would be two entangled states entangled not through their spin, but through their isospin, through their upness and downness. We haven't used the word isospin. Maybe I'll tell you what it means, but not right now. There's just this analogy between the spin directions and the upness or downness quantum number. These two things individually are well-defined particles. This one over here goes together with these two, and they are called the pions. They go together for a good reason, for a good mathematical reason, but they go together because their mass is very close to each other. It is believed they would be exactly the same mass if the up quark and down quark had the same exact mass. If the masses were the same. All three of these are virtually indistinguishable except for a small difference in their mass and they have different charges. 0 plus 1 and minus 1, and this is called the pion multiplet pi plus minus and 0. Three independent kinds of particles called pions, and as I said, and we can discuss why nature chose these particular combinations to be analogous to each other, but now I'm telling you facts and not mathematics. And the other combination is simply this one over here, and this is called the eta. So there's the pi plus, the four states here really define the three pions, pi plus minus and 0, and the eta meson. The eta meson is similar to a pion in many ways, but it's heavier. Why is it heavier? That is a complicated story. It's not an elementary story. It's a complicated story. Maybe we'll come to it, maybe we won't, but as a matter of fact, it's massed. What are the masses of the pions? The masses of the pions are about 140 MeV. The mass of a pion, mass of pion, and pi is about 140 MeV. So in other words, it's not too different from, question? Yeah, it's about 140 MeV. So it's somewhere in this range in here, not this heavy, and the mass of the eta is about three times heavier or something like that. The mass of the eta is about 500 MeV. I don't remember the precise number, but that's about right. Why that is, why the eta sticks out as being different was a puzzle for a long time. Not obvious, not obvious. Even today, it's a rather abstract mathematical fact, but it is understood. Isn't it also true that they're relatively long, half-wise? I'm going to compare it to most of them. The numbers of orders and magnitude difference. They don't decay by strong interactions. They decay by weak and electromagnetic interactions. So they're longer lived than many of these other particles. Yes, that is true. They are long lived. Okay, those are the mesons. Did you give the name for the up bar, down, down bar? Yeah, those are pipe numbers. No, they don't have names by themselves. They're linear combination, which are the sum and differences of them, and have definite names. Oh, I suppose they do. Yes, those are. Is that similar to, is that something like the neutrino oscillations? Well, in the sense that it's related to quantum superposition of states, yes, but it's got more to do with spin combinations of two half-spin particles. There are two ways that you can entangle. Well, we'll come to one next time. The last thing I simply want to tell you is that you can make strange mesons. You can take any d-quark and replace it by a strange quark, strange bar quark, and so forth. That makes new mesons which are called strange mesons, or, what's the other name for them? K mesons. K mesons are mesons containing a strange or an anti-strange quark, replacing a down quark. There are four of them, up bar strange, up strange bar, down bar strange, down strange bar. These two have charge zero. Charge zero, and these have charge plus one and minus one. These two are called the charged K mesons. These two are called the neutral change, the neutral K mesons. So there are three kinds of pions, one kind of eta, and four kinds of, how many does that make all together, let's see. Three pions, four K mesons, and an eta, yeah. There's more, there's more, there's more. Did we leave something out? Yeah, we left out one, we left out some. Yeah, we left out S bar S, huh? Yeah, there's nine. Nine, nine altogether. The reason it's nine is simple. There are three quines of quarks, three kinds of anti-quarks, three times three is nine. All right, okay. For more, please visit us at stanford.edu.
properties, not the properties of individual that's the origin of covalent bonds, sharing of quarks and the other particles which are