Lecture 1 | New Revolutions in Particle Physics: Standard Model

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 or the quanta the quanta are the discrete indivisible units of energy that quantum 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 the oh 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 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 varies four kinds of field equations and we talked about how field equations can be generated from lagrangian's 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 or we haven't talked very much about specific particles tonight well I expected to spend the first half hour beating around the bush bush a little bit looks like I spend a few more minutes beating around the bush but then I want to come to really writing down what the particles are you know who are the players in the drama and start going through them more or less well I'm 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 how they come into 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 at 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 in the theory are 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 didn't know what it was you still wouldn't know more forces forces forces and in a certain sense forces force 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 give rise to gravitational forces it may be less obvious to you what the what the electron field electron has a field it also gives rise to forces and we'll talk about them a little bit so this kind of a correspondence that goes this way is a correspondence code 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 so this triangle really makes sense so I want to talk about that a little bit you know many of you know the idea but let's just discuss it for a moment ah we 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 and I want to know the force between them how do I calculate it well you could know the you could know the rule that the force is equal to the product of the charges times times 1 over R squared and so forth or you could try to calculate in a different way you could try to say what does the what do these two charges doom to space what they do to space is they create electric fields right the 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 are 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 all right 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 all right so we square this and we integrate it over all space the volume and that's the energy stored in this on 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 a 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 is 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 ok I don't want to belabor that now I 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 to the field energy would be the integral of e two 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 this this one is 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 the not energy let's call this energy e in h well let's not call it H energy just n on 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 e e 1 plus e1 e1 plus e2 e2 where these are the electric fields of particle 1 and particle 2 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 over space there are three terms the first term is e 1 squared e 1 squared gotten by squaring this the second term is plus e 2 squared e 2 squared and the third term is the interesting one it's the product of e 1 e 2 twice as a matter of fact times e 1 dot e 2 actually dot product alright what is this first term here 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 a 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 overlap at all you take one particle so far away that the Coulomb fields are hardly overlapping then this is going to be zero because we're every one is not zero e 2 will be zero or almost zero where every two is nonzero e 1 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 e 1 times e 2 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 at hours you might expect it's nothing but the Coulomb force 1 over R squared but I'd like to say it this way because it gives you with the following picture that putting in both charges taking them far apart they don't affect well Ledger 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 of particles it 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 set up or completely do it well actually a very completely different set up let's talk about molecular forces what the molecular forces come from I'll give you one source of them several four there are several origins of molecular forces but here's a set up I want to think about ah let's begin with a pair of protons and a single electron what is this 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 shrouding a 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 not 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 be pushed over to here that has exactly the same energy why because the two protons are the same kind and everything is completely symmetric over here so if the electron is in orbit well and quantum mechanical orbit around this proton of its room 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 which 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 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'll watch it from in here you'll ruin the phenomenon so the electron can hop back and forth hop back and forth simply means is 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 a equal probability of being over here and over here with a wavefunction looks 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 alright 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 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 proton 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 the if they were far apart they were infinitely far apart so if I were to plot the energy 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 a 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 pours pushes you towards decreasing 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 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 wavefunction sort of adjusting a little bit a little bit better than it would if you just add the two wave functions together um as I said that's the origin of covalent bonds sharing the sharing of electrons and in this case you can think of 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 in between the two protons what it does this possibility of the electron jumping back and forth lowers the energy relative so if you just had one proton and just one electron in the bound state there that means that there is an effective force and you know you can picture it this is this picture is a very 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 between the two protons now yeah could you think of it as being the electrons hopping back and forth positive charge 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 this was like Lex like what I used to say like black light wife's like I don't know no no no he was probably talking about the boza statistics of that photons like to like to be in the same state I don't know what he was talking about you saying he said like lights light like electrons like each other 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 the opposite of the exclusion principle for photons the boza statistics of them now because I don't know protons yeah that's because of their electric charge it does a little bit but not not very much and in fact the 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 that 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 places where 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 have the possibility one electron orbiting around this proton a second electron orbiting around this proton here now the two objects here they call atoms hydrogen atoms then neutral 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 binder bind and atom binding I molecule but even so a mistake in h2 plus is bound yeah yeah yeah it is bound but hmm yeah at small distances at small distances it is enough to overcome the Coulomb force that's right since creates and well it doesn't create a third force but it creates a sort of slightly nonlinear effect due to the cell with two to the two forces but there 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 though let's let's serve let's let's leave it at that there is this notion of the energy being lowered by the possibility of alternating between two quantum states not so much quantum entanglement that some it's related to what are called off diagonal elements in the Hamiltonian but which is 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 our very hot very very high temperatures this electron much higher well at high temperatures at high temperatures because it depends on the temperature at very very high temperatures all it will happen is the electron will get kicked out and you know 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 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 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 four centers and the possibility of the fault of the electron being in a superposition of states in other words of the 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 right that's what the Lagrangian of quanta of electrodynamics tells us it tells us about the probability for the emitting and absorbing 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 that is also emitting and absorbing photons so there's an equilibrium ok but every so often now this should be thought of in the language of Fineman diagrams every so often a photon which is emitted from here gets absorbed over here 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 Jo will grab Mo's of juggling objects okay 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 you 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 Fineman diagrams the emission of one photon by one particle and option of that same photon by another particle creates a force creates an energy which is not exactly the sum of the two energies and that energy is the Coulomb force between the between the charged particles so we have two distinct languages well apart from just the writing down the Coulomb force law we have two other ways of thinking about forces one of them is two classical field theory where you calculate the fields of objects and square them and the other way is through the exchange of particles Fineman diagrams where 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 any particle is also connected with a force when that particle can be exchanged or jump back and forth between two slits something else will describe some more examples but I did want before we move on to just discuss the relationship between particles and forces so a 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 so 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 comes that 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 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 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 really may be in the room but there'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 elect and and no particle whose name my 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 exists then there's got to be another one to match up with them in some appropriate way but in the end of the day um there are many more parameters many more different types of particles then there are known relationships between them which cut down the size of a problem okay the 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 in 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 o 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 part 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 and I'm not listing them in any particular order as it happens I'm if 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 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 it's 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 next particle of interest is the electron now the electron is a particle which has an anti particle it has an electric charge if it has an electric charge it must have an anti particle of the opposite charge and it is a convention whether we name the whether we think of the particle as the electron and the anti particle as the positron or whether we think of the positron as the particle and the electron is the anti particle the relation between them is mutual alright so when I like the electron I really mean the electron and positron and so we could write a here plus minus standing II - is the electron a plus is the positron the field of the electron is usually Sai and maybe you could put a little Eden stairs to indicate that it stands for the electron it 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 cool 10 minus 19 coulombs order yeah it's some very small charge but 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 challenge we'll just write as minus 1 for the electron and plus 1 for the positron so since we typically took think of the electron as a particle and the positron as the anti particle let's just call it minus one and remember that the positron has the opposite charge baryon number is zero and it's mass now we have to decide on units for mass units for mass are the same as units for energy e equals MC squared so we can either describe the mass as our mass and kilograms or an energy in joules or we can simply invent a new unit which is more appropriate for microscopic physics two atomic physics a 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 in a hydrogen atom is what thirteen point five electron volts an electron volt is how much energy you get if you pass an electron from a 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 the 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 is 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 point five one MeV and MeV stands for millions of electron volts an 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 know why no it's exactly 0.51 no it's not what's that pi 3 pi equals 3 right okay now we can start let 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 of them let me get a table we'll just make we'll just draw some pictures the basic arm 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 photon comes in from the past or whoops sorry you can even flip the electron legs around so that it looks like this electron going backward in time or 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 when 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 the phenomena that corresponds to the force between charges and in the language of particle exchange it's the photon on bouncing back and forth between charged particles which which creates that force yet another way to describe what's going on here is in terms of a Lagrangian or a term in the 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 Si electron it ki it creates it as the creation and annihilation operators in it an electron out and subside 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 Lagrangian appears the electric charge of the electron and that roughly speaking is associated with the amplitude for a electron to emit a photon an 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 ah but let's start adding a little bit to a particle list the next particles of interest these are of course familiar to you I'm sure right now if this were 1960 when I still when 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 call remind me to come back to this issue of the difference or what what it means to become positive 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 the 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 there are they go under they have names all right well why do they called what they are they called what they are just historically randomly people assigned the silly names to them and there's no logic to what they call no logic at all this first of all the up quark and that's called you the symbol is you well let's see we should write there a quarks here quarks and I suppose the symbol for quarks is Q all quarks or fermions will write down their charge later they have all baryon number of 1/3 now why 1/3 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 carrier counter that's covering one unit of a 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 we'll come to which are very similar to para 2 protons and neutrons they're also called baryons the prefix barrier I think means heavy and baryons we'll call baryons because there are 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 yeah I was the atomic weight yeah the atomic weight R is equal approximately equal to the total number of protons and neutrons and the total number of protons and neutrons and 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 and hmm you do have isotopes but still a number of protons plus neutrons doesn't change number of protons can change how the hell can a number of protons change 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 radioactivity in radioactivity one form of radioactivity a neutron decays into a proton plus an electron and an anti-neutrino 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 ah 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 or have to generalize it a little bit beyond protons and neutrons it's the 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 barrier number one antineutron baryon number minus one but clearly there's an element of convention exactly what you call them but once it was fixed that the barrier on them of a proton was one then the barrier number of a quark was a third because three quarks make a proton okay 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 what about an anti quark there are anti quarks barian number is minus 1/3 and so I won't write that down separately the number of corpses conserved number of quarks minus the number of anti quarks 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 like a king completely disappear its energy has to go someplace are there processes in nature where a proton might disappear and cut 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 decay is its half-life the 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 there's widely believed that the answer is yes but has never been demonstrated sadly how do you have you wait around for 10 to the 34 years for proton to decay you get 10 to the 34 you protons and you wait around for one of them and you see one now 10 to the 34 protons is a lot of protons no that that's not that that that's zero barian number begins goes to zero baryon number proton has baryon number one antiproton is barrier number -1 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 it 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 quirks by definition have one third of a unit one third of a unit as I said minus the third for anti quirks but in order to fill in the rest of this in particular electric charge and mass we 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 the 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 hmm what directions up and down up and down means in the Earth's gravitational field is nothing up EE or down e about them all right then it gets worse there are strange quarks which are no stranger than non strange works it gets more and silly there are charm quarks which are charming I suppose I don't know and then there are that this is if you don't you know if you're if you're squeamish or you know very give up quarks arm quarks bound works and then top quarks and 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 so bottom and top strange and charm how and under what circumstances these things when named is not 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 they're all free some sometimes Q sometimes sy q sometimes capital Q sometimes depending if you're talking about the individual types of them you'll just use UDS CBOT use the same names for the fields as used 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 - which is the same is not the same but which follows the same pattern the pattern of these two is similar to the pattern of these two similar where 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 ah all right so the down up system is very similar to the strange charm system is very similar to the bottom top position of the 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 1/3 and 2/3 that's the first example of particles in nature which have charges which are not integer multiples of the electric charge of electron okay however quirks 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 ok the strange and the charm exactly the same thing minus 1/3 and 2/3 bottom and top exactly the same minus 1/3 and 2/3 cannot be read they're just repetitions of the same thing what about the anti particles if I were to list the anti particles 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 yeah they're all baryon number one third right 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 are 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 89 1800 times the electron mass there is about 940 MeV this is a lot lighter than a proton the up quark about 5 MeV less than the vendor 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 to be the mass of a proton or neutron ok we'll come back to that point is of course there's more in a proton than just a it's quirks ok strange and charm strange is roughly order magnitude 100 MeV a strange and charm is little over about a thousand 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 a thousand twelve little more than that whoo sorry 100 mr. zero decimal creep okay a thousand mev and the bottom of cork 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 100 how much 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 but for sure if there wasn't one family we wouldn't be here cuz there would be no protons and neutrons but given that there's this one family of up quarks and down quarks why are the strange quarks and charm quarks or top quarks and bottom quarks nobody has a clue stupid question yeah when these quarks were found the story goes they were looking in a certain place because the mass said the mass should be certain notes they said they said that they went through the calculations and they knew that this is where it is going to be it was going to be somewheres around some a GeV they're going to foil the top quark yeah not a predicted it would be there before they yeah but not on the basis of you know abstract theory but on the basis of you know how the top quark would affect the road work its way into other particles and I was just sitting because you just said it nobody knows why and they're all over the ballpark and yet they seem to know that that's where they wanted to look for ya but not not because not because there was any basic underlying reason why the top quark had that mass what you could do is because they supposing the top quark had a certain mass and then calculate various Fineman diagrams involving the top quark in various ways finding 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 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 rather be consistent with how it all disappeared what will happen if ours the direction go ahead you're asking anything 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 marketing about jets produced well I don't know what you're talking about yeah we can talk about jets combine let's come back to it after we've after we price charge Nestle balance nose is that you're interested okay Semmy theory yeah some extent that that that is understood 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 it 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 question it's a melting the balance of this experiment works no relative abundance and where but what do you mean very little bonus meaning the world in the universe there are very there are 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 only alright first of all the only quarks which have any degree of stability are ups and bounds the rest of these decay to these so really 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 quirks of each type there are in a proton there are no neutrons or sorry of course there are neutrons there are neutrons and atoms are in nuclei so you have to know the relative abundance of protons and neutrons to know the relative abundance of it but that's all it is relative abundance of protons and neutrons okay so what do we know what is a proton and what is a neutron in this language and let's come over here a proton is three quarks 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 the down quark has charged minus 1/3 so 2/3 minus 1/3 minus another third this is electrically neutral charge equals zero that's good Neutron has charge 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 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 of the same thing except for an interchange of the up label and the down label you might then surmise that they are that their properties are almost 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 but it's not quite true because up quarks and down quarks don't have exactly the same mass all right they don't have exactly the same mass now ten 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 our particle physics and so to a 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 and 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 okay neutron is a little bit heavier than the proton and it's largely attributed to the AH 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 have exactly the same mass but you accounted for electromagnetism in other words the photon so 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 okay so the proton would be a little bit heavier because of the electric 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 ah and the reason is because the down quark is a little bit heavier than the up quark okay but other than that yeah neutron is about what 938 MeV and proton is about 939 MeV ER that was about 1.4 MeV MeV difference between them something like about 1.4 MeV difference between any 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 it's a little bit of excess energy in the neutrino which allows it to decay and it allows it in particular to decay with an electron to 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 them 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 analogue 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 at 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 so the same way but it's even better here ah so you can construct another kind of analogue it's called strange baryons strange baryons I forget their names lambdas and sighs they've got all kinds of me and I did you know it's been so long since I since I worked on these things that I can't even remember their names they have symbols like this associated with them like this and they're lambdas I don't remember which one is which not important but for example you can create the Lord's name is I 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 it down and put in an S and the s and the down have the same charge alright so this is also electrically neutral but it has a strange quark in it and it's called a strange baryon okay they're not stable they can decay we're going to discuss the the decay processes later but they're not completely stable so they evaporate then this one will turn into that one but yes they do exist likewise you can put in two strange quirks and an up quark what is the charge of that one same thing charge neutral again and likewise likewise for the proton you can replace it by up up and strange so there are all these strange baryons dangerous those became what what kind of process what products do you Oh perfect neutrons only photons in neutrons ah for Pyro's or things like an electron another chance what can't just in also only substituted strangers for boundaries no you can't know what this 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 all right now you can also oh in SCID ently these strange particles are a little bit heavier than the protons and neutrons because of this extra 90 MeV of erm extra 90 MeV 90 MeV isn't much all right so there's 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 and so they're not found in university lovers all those that you put up there so far can be constructed with any pork sausage oh yes yeah you'll have to take every particle and replace it by its anti particle then it becomes the antineutron the antiproton and the anti question mark people will be strange that's the strange this is not just another word for saying I have a strange wood but if you push you to the bottom for kidding okay then they become bottom then the bottom baryons yeah yeah yeah strange are they strange I don't know Abby they will call strange because you know people became familiar with protons and neutrons by the 1950s and then when they discovered these other things who has strange and unexpected the fans yeah we're soon to see listen master - what do you know Sophia that mess oh you mean if you just add it up the master the quirks right yeah that's right there's a lot missing so it must be something else in the proton in the Tron no no they're gluons you know no no no no attempt here to be dramatic ah but the gluons don't carry any interesting charge baryon number do they carry mass well they carry energy so as it's a form of binding energy here that's right it's binding energy energies don't add not relativistically I mean well mass is don't add the mass of an object is not necessarily the masses of constituents well the 20 was saying about beautifully with the bomb you're using the language of particles here to describe these and positive particles it seems more complicated at least the word language appeals how would you combine it it seems like you would combine everywhere not to be a particle through your field you want to know whether you can construct a field describing a proton down up as if they're particles you think Oh minuscule yeah they're everywhere and your modes of the field are combining to form these composite particles Oh in thinking yeah I mean in thinking about this particular aspect of things it's much easier to think about about particles than fields is we could think about it in terms of fields but it's much harder and question about the binding Eris's yeah so if you if this difference between the Corp energies and proton energy we're binding actually that's a big positive energy you know are not an integer that's not an integer energy oh I thought you said integer yeah usually negative right right not true here well yeah I mean we'll come to it but yeah sure ah yes yes let's let's yes there is yes there is but not yet let's talk first about mesons massan's are simply quark antiquark now why you know you could raise the question why do three quarks bind together to form something why don't two quarks far buying together to form something the the early days of core ecology this was a complete mystery why quarks always you could say oh it's in order to make the charge and integer multiple of the electron well that's a stupid answer and tell not to be that stupid but is it at this stage it's a stupid answer but yet that is the pattern that is the pattern that they combine together in 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 in two 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 alright 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 their core the combinations of quarks they must be made of quarks and antiquarks in fact they are quarks a quark and an antiquark there are quark and an antiquark and so let's 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 that doesn't take any energy and it doesn't take much energy in 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 massan's are typically pretty light they're an up quark at a down quarter and an anti or a quark and an antiquark and then you can start thinking about the different combinations this is an up bar quark and a down quark there's a down 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 quarter the offices no you can't do that don't they have to be the opposite time because it's one third of the thirds so it's not beef no ok let's 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 though this has charge minus one right minus 1/3 minus 2/3 that's fine charge minus one is like like an electronic all right what about this one this is the anti particle of this hmm this one's not this one is just the anti particle of this oh yes right right this one is the antha these two are anti particles of each other because they are related by changing particles into anti particles down bar and two down up aren't up and this has charge plus one so these are anti particles 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 right there are two combinations of these two they would tell you what they are they are up bar up Plus down bar down and what would I put in front of it to make it have total probability 1 1 over square root of 2 this is a quantum state and this is another this is the orthogonal quantum state up or up - down bar down you know what this is this is an entangled pair of quarks not entangled through this spin but entangled through there up Nisour down this if you thought of openness and boundness is 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 and tangled not through their spin but through their ISO spin through their upness and down this we haven't used the word iso spin look maybe I'll tell you what it means but not right now it is just this analogy between the spin directions and the up this or down this quantum number these two things individually are well-defined particles this one over here goes together with these two they are called the PI ons they go together for a good reason for a good mathematical reason but they go together we'll have the right ones yeah they go together because their mass is very close to each other it is believed there would be exactly the same mass if the up quark and down quark had the same exact mass if they were 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 PI on multiplet pi plus minus and 0 3 independent kinds of particles called pi ons 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 the non mathematics and the other combination is simply this one over here and this is called the ADA P so there's the PI plus 2 for states here really define 3 pi ons PI plus minus and 0 and the ADA mess on the a numbness on is similar to a PI on in many ways but it's heavier why is it heavier that is a complicated story it is not an elementary story it's a complicated story maybe we will come to it maybe we won't but as a matter of fact it's masked ok what are the masses the PI ons the masses of the PI ons are about 140 MeV the mass of a PI on a supply on M 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 summarized in this range in here not this heavy and the mass of the ADA is about three times heavier or something like that the mass of the ADA is about five hundred MeV I don't remember the precise number but that's about right why that is why the ADA sticks out as being different was a puzzle for a long time it's after not obvious not obvious even today it's a rather mad abstract mathematical fact but it is it is understood also truth they're relatively long compared to most they don't decay by strong interactions they decay by weakened electromagnetic interactions so they're longer lived then than many of these these other particles yes that is true right they are long with okay that those are the mezzo no I've ever had these by themselves they're really in combination with other some differences are there now definitely is that so it isn't something like the neutrino oscillations well in the sense that it's related to super quantum superpositions 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 our 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 massan's which are called strange mesons or what's the other name for them k massan's k massan's Armazones containing a strange or an anti strange quark replacing a down quark okay 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 charged plus one and minus one these two are called the charged K massan's these two are called the neutral change the the neutral came as ons so there are three kinds of pie ons one kind of Ada and four kinds of homies that make altogether let's see three pi yarns for K mesons and an ADA yeah there's more there's more there's more oh did we leave something out yeah we left out one we left out we left out some yeah we left out s Bar s huh yeah it's nothing right nine nine altogether the reason it's nine is simple there are three coins of quarks three kinds of anti quarks three times three is nine okay for more please visit us at stanford.edu

Channel: Stanford

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Keywords: science, theory, engineering, thermodynamics, math, formula, space, statistics, electric field energy, elementary composite particle, charge, mass, density, shrouding away function, probability, wave, covalent bond, ex

Id: Igl8hE3Eac0

Length: 97min 17sec (5837 seconds)

Published: Fri Apr 16 2010