Lecture 2 | New Revolutions in Particle Physics: Standard Model

[Music] Stanford University before we start we're going to talk about quantum chromodynamics today quantum chromodynamics and we're not going to talk about the deep mathematics of it and go into it we have basically one lecture to do quantum chromodynamics which is a huge subject it's a subject which easily takes a quarter to but I'll stick with the highlights and tell you what the basic intuitive picture is quantum chromodynamics is similar to quantum electrodynamics quantum electrodynamics is the theory of electrons and photons it's also the theory of the Coulomb force the quantum mechanical theory of the Coulomb force if applied to the problem of atoms in which you do not worry about the motion or the nature of the nucleus the structure of the nucleus you simply think of the nucleus as a fixed point creating an electric field then quantum electrodynamics is also the theory of atoms and the same sense quantum chromodynamics is the theory of quarks and gluons and the theory and the things that quarks and gluons make the things the quarks and gluons make a called hadron is h a d R o n s hadrian's or hadrons and they consist of things like protons and neutrons which are called baryons which have an it quark number or a net baryon number that means an imbalance of quarks and antiquarks three quarks for the proton three quarks for the neutron and mesons which are quark antiquark pairs and all of them are full of gluons gluons are the electrically neutral stuff which is the glue and the binding stuff that holds the quarks and gluons together much the same way that the electromagnetic field or a Coulomb field is the binding agent that holds atoms together atoms other electrostatically bound objects all right but before we go into it I want to remind you a little bit about the mathematics of spin because very first of all that particular mathematics will come up in another guise but also a simply related mathematics to it will also come up in the guise of a quantity called color or concept called color we're not going to do group theory in this class all right we'll try to finesse it but the basic mathematics of what we're talking about is group theory as I said I'm not going to use group theory or at least not not call it group theory as we use it for the four spin the theory of spin is the theory of a group a group if you don't know what a group is just ignore it all right but the group is the group of rotations of space the theory of spin is also the theory of the symmetry of physics with respect to rotations of space but we finish that by not talking about the theory of rotations but by talking about the theory of angular momentum I'll just remind you very quickly that we derived everything about angular momentum from some basic commuted commutation relations which one of the form LX with ly equals I times LZ I think there's an H bar in there but the other is an H bar in there where those are the components of angular momentum we work that out last quarter and we found some rather surprising and interesting things oh of course there are three other relations like this which I've gotten by permuting X to Y Y to Z and Z back to X I won't write them down but when we are worked out the consequences of this first of all we broke the symmetry now when I say we broke the symmetry I'm not talking about something some symmetry breaking in nature just we broke the symmetry in our mathematical description the symmetry being the symmetry of rotation or the symmetry which interchanges XY and Z and so forth we broke it in our heads maybe not in the real physics but just by focusing on the Z component of spin on the Z component of angular momentum we basically focused on it we cannot measure all three components simultaneously they don't commute with each other here they are they don't commute with each other at most one of them commutes with itself of course it commutes with itself and no two of them commute so most you can talk about one of them are or measuring one at a time and we arbitrarily chose LZ when we did that and use these commutation relations what we found was first of all that L is quantized and the difference between neighboring values of L was always one unit in units of h-bar number one number two we focused on a on spin and we described different spin possibilities the first set of spin possibilities were the half spin objects are the things which we call fermions those who are the object whose spin was centered about zero in such a way that the first level the first Z component of spin was 1/2 and the first one in the opposite direction was minus 1/2 three halves minus three halves and so forth those were fermions but right right now the main point was that the mathematics of spin or angular momentum gave rise to some multiplets there was first to spin half multiplet that was the multiplet with a spin minus 1/2 and it's been plus 1/2 like the spin of the electron that was associated with half spin particles and fermions bosons which for our purposes now just think integer spin the first one was just spin zero there are particles with spin zero they have no spin that's all they just have no spin at all then there are particles will spin one the photon is a spin one particle there are other spin one particles there are nuclei and atoms of spin one and they have three states plus one minus one in units of h-bar and zero and then the next interesting family has spin three-halves spin three-halves again goes on the half spin column here and that has 1/2 minus 1/2 three-halves minus three-halves r there are particles with spin three-halves there are certainly nuclei with spin three halves and atoms with spin three halves so these things also exist likewise what comes after spin one spin to spin to spin zero spin one spin minus one or the Z component of spin 1 minus 1 2 and minus 2 these labels here are the Z components of the spin okay now when you speak about an object of spin L L is the notation that denotes the highest value of Z component of spin so this would be or M you can use M ordinarily it's used in ah mrl doesn't matter let's let's use L let's yourself that was a little bit different than anything when you speak of spin L you're speaking about about an object whose maximum spin along the z axis is L so this would be spin 1/2 L equals 1/2 this one would be l equals 1 and so forth how many states are there how many independent states are there for a spin a particle with spin L 2 L plus 1 2 L plus 1 for example for spin 1/2 twice L is 1 plus 1 is 2 2 States if L is 1 twice 1 is what is to add one more that's 3 three states and so 2 L plus 1 is the number of states is the number of independent spin States for a given value of for a given value of L so that's where that's something I want you to remember now another thing if you have more than one particle such as an electron then you have two spins spins can be combined let's consider what you can make in the way of spin by combining together the spins of two electrons let's forget the fact that electrons can orbit around each other let's ignore what's usually called orbital angular momentum and just concentrate on the spin angular momenta what kind of angular momentum can you make for two half spin particles well the maximum value of the Z component of spin is what one if the O in units of h-bar let's forget h-bar now when I say unit and the maximum spin I mean in units of h-bar the maximum spin you can have along the z axis is 1 that's when both spins are pointing along the same when both spins are pointing upward along the z axis that axis is the z axis so you can have angular momentum one you can have angular momentum minus one and you can also have angular momentum or Z component of angular momentum zero but in fact you can have two states where the Z component of angular momentum is zero this one and that and that one this one and that one so there are two states two independent states whose Z component of angular momentum is zero how many states are there for a spin one object 312 plus one okay so there must be a spin one combination because we can make total spin up equal to one that's the maximum so there must be some where is there a some combination must correspond to spin one what does it spin one-half it has spin one along the axis spin minus one along the axis and spin zero but there are two states with spin zero with Z component of spin equal to zero they can't both be part of the spin one multiplet what could the extra one be it's got to be either spin zero spin one spin to spin three spin for spin a half spin - it's been a half spin three halves so here's what we found let's let's write them down this both spins up are both Z components of spin I'm going to stop saying Z components both spins up that's got Z component equal to one both spins down that's got Z component equal to minus one and then there seem to be two with Z component equal to zero but if I look at spin one it all has is plus minus and 0 there are only three of them so this cannot be a multiplet this these four states cannot all correspond to spin one what else could be there besides spin one it's been 0 can't be spin 2 because spin 2 has to have five space states the only other thing is has been 0 so there must be quantum states here 3 quantum states corresponding to spin 1 and 1 when you put the spins together and you ask what kind of angular momentum can you make you can make spin 1 and spin 0 the only combination the only question is what combination what quantum mechanical combination of these two correspond to spin zero and what combination correspond to spin 1 the missing spin 1 combination and I will tell you right now the answer is that the symmetric combination with a plus sign incidentally this state over here is symmetric between interchange you can think of it if you like as one spin over here one spin over here J labelled is 1 over here and the one over here the spin States if they're both up is symmetric that means the spin state is the same if you went to change the two spins obviously they're both up this one is also symmetric up down by itself is not symmetric if you interchange spin if you want to change the two of them this one goes to this one and this one goes to this one they swap but there's one linear combination one quantum mechanical combination which is symmetric under the interchange of the two plus minus plus minus plus this is the symmetric state what should you do to it to make it have total probability equal to one divided by the square root of SIL these are the three states which together form 0 1 and minus 1 if you rotate the axes they transform into each other this is a spin 1 up this is a spin 1 down where's the ones with spin 1 in the other directions it's made up out of this ok so this is the spin 1 multiplet and what about the other one we're missing a state there were 4 altogether here we have 3 linear combinations what's the other linear combination the other orthogonal linear combination with a minus 1 so there's another one here with up down - down up the square root of 2 this one this is these three correspond to l equals 1 this one corresponds to l equals 0 so these are the ways that you can put to spin half's together to make the two possible combinations this combination l equals 0 what is it like with respect to its angular momentum the answer is it doesn't have any angular momentum it's a thing without angular momentum as far as angular momentum goes it's like a nothing I mean it may have some energy and they have other things charged whatever but as far as angular momentum goes it's like empty space it's got nothing okay you might ask can a up spin and a down spin come together and annihilate and disappear well there's all kinds of reasons why electrons can't disappear but just for anger pure angular momentum reasons and we just worried about conservation of angular momentum and nothing else then which of these combinations can just disappear if as I said if we worried about nothing but angular momentum conservation can this disappear no because it has two units of angular momentum up about down how about this one yes or no let's take a vote how many think yes everything no ok the noes win because this one is not without angular momentum it looks like it has no Z component of angular momentum and it doesn't but the angular momentum about the X and y axis of this is not equal to zero it does not have l equals zero it has L equals 1 this is the missing thing that allows you to rotate the angular momentum into other directions what about this one yeah that one has angular momentum zero and if it was if the only consideration was angular momentum conservation it could decay it could just disappear now one way of thinking about it is you could say well um yeah that's good enough that's that's uh that's that's close enough this one here can disappear okay if your measure the angular America Z could get 1/4 - yes in which case no you get with along the z axis you would get 0 in either case you know along the z axis but if you measure the angular momentum along some other axis you would get 1 or minus 1 all right so that's that's the theory of angular momentum now why am i bringing that up now or the theory of spin in particular spin 1/2 spin 1/2 and how you build out of it other spins Oh incidentally let's spill let's try to build spin three-halves let's ask what happens if you put together on three spins well if they're all pointing upward in the same direction what's the and that would be the maximum or would you get three halves how many states are there with spin three halves so incidentally how many states are there altogether of of three spins each with spin 1/2 8 2 times 2 times 2 okay so there are eight states altogether how many states are there for a spin three-halves object four so how many left over for what can those other four be could they be another spin three-halves object No why not to be 0 on the other okay so let's go through it again if you have a spin three hands multiplet there will be one state which has Z component of spin three-halves and one with minus three-halves we've already used those up when we said there were four states which formed this through spin 3 has multiplet we use them up now all that's left now is spins whose maximum value is plus or minus 1/2 ok so what can be there what an addition can be there only spin only spin spin 1/2 anything else couldn't be no they can't be spin 0 because making 3 spin a half's can never make spin 0 all it can make is spin three-halves and spin 1/2 but we seem to have four states left over the implication is there are two distinct ways to make spin 1/2 so there are combinations which correspond to the spin three-halves the easiest ones are all three spins up or three spins down and then there are more complicated ones and then there are two distinct ways to make spin 1/2 which altogether adds up to four states all right so when you take three spins three half spins you get spin three-halves and you get spin one half twice two distinct ways of doing it let's keep that in mind okay now why am i talking about spin now what I really want to talk about is a concept called ISO spin isotopic spin isotopic spin was the first internal symmetry group that or the first internal quantum number the first analog of a spin which occurred in particle physics that did not have to do with the rotation of space but it had to do with the rotation of an imaginary space or an internal space or if you like it just gave rise to another set of quantum mechanical variables which were basically isomorphic completely similar to spin to spin a head to spin but it didn't have to do with spin it didn't have to do with the rotation of space you could imagine if you like that it had to do with the rotation of some internal directions internal directions imaginary directions of space mathematical directions so let me tell you where it comes from we've already actually described it although we haven't said it we talked about quirks and we talked about there's a whole variety of different kinds of quirks but most of the quirks were rather heavy they were an a heavy and had an appreciable mass in units of G V's or hundreds of M V's the natural mass scale for hadron physics is somewhere as hundreds of M V's the mass of a typical meson is a couple of hundred M V's the binding energy of particles is M V's milli ah sorry hundreds of em V's not many these hundreds of MeV is what object in nature has binding energies of order a few M V's nuclei nuclei nuclei things that hold protons and neutrons together but what holds a neutron together has three quarks has a binding energy of a few hundred MeV all right so the natural energy scale is a few hundred MeV and there were only two quarks which were very light but or whose masses were very light by comparison with that then they were the up quark and the down quark the other quarks are heavy and to make particles out of them there's a cost in energy and so for the lightest objects the most stable typically heavier objects will decay to lighter ones the light objects of nuclear physics the lightest objects the ones which are stable are the ones made of up and down quarks now up and down quarks have almost the same mass of course the down quark is about twice as heavy as the up quark but they both have very small mass by comparison with the hundreds of M V's of a of nuclear physics so in some first approximation you can say that the up quark and the down quark have no mass they're more important than masses are close to being equal that's a symmetry what does that mean that means if you took all up quarks and replace them by all down quarks everything would be pretty similar now of course the up quark is slightly more massive than the don't know the down quark is slightly more massive than the up quark so typically things made of down quarks would be a little more heavy than the things made of the corresponding up quarks but the difference is small for example a two up quarks and a down quark make a proton two down quarks in an up quark make a neutron the mass difference between a neutron and the proton is very small okay so that's an example of the almost symmetry between up quarks and down quarks so a first approximation you just forget the difference up quarks and down quarks are symmetric with respect to each other in the same way you're in the mathematically the same way that a spin up and a spin down are symmetric in the case of spin it really has to do with the symmetry of space rotating the axes in the case of up quarks and down quarks it's just a mathematical manufactured space that you can imagine where you take an up quark to a Down quark by flipping some direction in some imaginary direction in your head but all you're doing is interchanging up quarks and down quarks thinking of up quarks and down quirks as mathematically the same more mathematically isomorphic to up spins and down spins you come to the concept of isotopic spin isotopic spin is the analog of spin but not up and down in the sense of the z axis and the flipping spin but up and down in the sense of up quarks and bound quarks because there's nothing really up to up up or down about it it's just the interchange of two labels are quarks and down quarks and so when invents the concept of isotopic spin our and for all mathematical purposes the replacement of up quarks and down quarks is very analogous to the replacement by of an up spin by a down spin okay so the spin we have two states up and down and that defines spin for quarks we have up and down and that defines I so spin and certaintly what does this it what does the ISO come from isotope isotope we're going to see in a moment that isotopic spin interchanges and saying when when you interchange up quarks and down quarks you want to change proton and neutron of course if you interchange proton and neutron in the nucleus you'll wind up making an isotope of some of something so it comes from the word isotope isotopic spin but what it is is in nuclear physics in the old days it was just the replacement of the interchange of a proton by a neutron and thinking of the proton and neutron as a spin multiplet in a mathematical spin space it was traced eventually just to the fact that there are two quirks of quarks and down quarks that was the origin of it you did I suspend free day oh yeah that's good Eisenberg yeah what something is about the end of the charge yeah okay so isotopic spin is not a precise symmetry of nature it's not a precise symmetry of nature in that first of all the up quark and down quark don't have exactly the same mass but even if they did there would still be a distinction of physical distinction which would be which would make them different and that is their electric charge electric forces within the nucleus except for a big nucleus when a nucleus gets big electro electric forces become strong but for small nuclei and especially for protons and neutrons and hadrian's electromagnetic forces are negligible by comparison with the other forces holding protons and neutrons together so an approximation ignore the mass difference between protons and neutrons or ignore the mass difference between up quarks and down quarks and ignore the fact that they have electric charge altogether and concentrate on the other forces of nature in particular the strong interaction forces which will come too and then there is a precise symmetry relating up quarks to down quarks and that symmetry is very much like ordinary spin symmetry it is analogous to spin symmetry okay let's talk about what you can make supposing are well one quark by itself we will come to a understand is not a physical object that we can examine in the laboratory the simplest object that we can examine in the laboratory is three quarks and that's a proton or a neutron that's like having three spins what can you make out of three spins what you can make out of three spins is either spin three-halves or spin 1/2 and you can make the spin 1/2 and do two distinct ways but let's forget the two ways let's just say we can make spin three-halves and spin 1/2 in the same way taking 3 quarks we can make an object of isotopic spin 1/2 or an object of isotopic spin three-halves let's first concentrate on the object of isotopic spin 1/2 an object of isotopic spin 1/2 how many states should it have just by pure mathematical analogy with ordinary spin to a spin 1/2 object has two states so a nice have spin I said I so spin together is the right work is the simplified word an ISO spin state of 1/2 also would have two states what are those two states proton and neutron so let's write down what the proton and neutron are in quark language now let's let them that's that's really that's proton okay let's imagine that we've labeled the the quarks by label the quarks let's imagine they're really located at three distinct spots inside the proton this of course is not really true but I mean they move around but let's just simplify the story and say there are three distinct quarks and we're going to label them with three distinct labels here's a down quark and here's two up quarks all right the down quark might be the quark at position one all right so let's call it at position one the up quark might be at position two and the u k-- where the other up quark might be at position three so anything wrong with this state quarks are fermions right what's a fermions because because quirks are fermions their states should be anti-symmetric their States should be anti-symmetric okay now that suggests that may be the right combination for the U quarks is two anti symmetrize it and that would be correct that's not an important issue for us right now but I'm just being very precise that down quark and two up quarks in an anti symmetric state is a proton an anti symmetric state of two spins makes spin zero so this is an ISO spin zero object x and ISO spin 1/2 object that has I saw spin 1/2 but never mind this is this is a bit of mathematics it's a little too fancy we don't need to worry about it this is the proton it has charge plus 1/2 hat sorry 2 3 plus 2/3 is 4/3 and minus 1/3 makes charge 1 so that's the proton and it is the combination of 3 quarks which makes an ISO spin 1/2 state same as 3 spins making a spin 1/2 state so the proton is also a member of a spin I so spin 1/2 object and the other one is gotten by simply interchanging ups and downs and that's up down down let me not let me not belabor this point about the symmetry here and that's the neutron the proton and the neutron in this language are symmetric with respect to each other and they form an isotopic spin 1/2 double it in the same sense that you can put three spins together to make a spin 1/2 and there are only two such states so isotopic spin invades the theory of protons and neutrons and in this language just gives us another just like a quark has isotopic spin 1/2 so does the neutron and proton ok there's another object which is very similar to a proton Neutron in many ways it's also made of three quarks but it's the combination or incidentally what is the spin of the proton and the tri-axial spin 1/2 okay so you take is taking 3 quarks with the same spin sorry 3 quarks with spin and 3 quarks with I so spin and you've made a spin 1/2 and an ISO spin 1/2 ok now there's another object which has 3 quarks in it which has spin three halves and I so spin three halves if you like the three ordinary spins are lined up in it in the same direction and the three iso spins are lined up so what kind of thing are they well if the three iso spins are lined up that must mean that there are objects with three up quarks three up quarks three down quarks also the three spins are aligned just the ordinary spins the three spins are also aligned the form spin three halves or down or whatever three quarks up three quarks read up quarks or three down quarks this is not a neutron this doesn't this is not a neutron or proton this is a new object which is a little bit more massive than a proton or neutron it has a name it's called a delta it has ISO spin three halves and it has spin three halves so it's sometimes called the Delta three halves it has both ISO spin and spin three halves let's forget it's spin it spins it just aligned if we line them up all along the z axis then they're all aligned let's forget that what about this can this be all there is to an ISO spin three half state how many states does it does a spin three halves object have four right so there must be two more and there are two more there are two more Delta 3 half States two more of them and two more are u UD + UD d for States for objects all which are related by symmetries they all have very close to the same mass the only thing which distinguishes their mass is the little small difference between masses of up and down quarks and they're all very similar to each other I'm telling you this for a reason this said this played an important historical role and I'm going to tell you about in a moment these four states are called the Delta three-halves and what's that charges let's go through their charges what's the charge of this one since the symmetry that you you need give you all right let's look at the charges button that's wait what the third one done what's the mystery that the proton ah steady spinning spinning that's finished we have not spin one-half okay the I systems Z campano it has it's part of the multiplet which is an ISO spin three-halves object okay right ISO spin three-halves right so as both spin and I suspend three-halves but by looking at these two you couldn't tell that you have to know sorry you have to know a bit more about the nature of the way they're combined all right but they have a component of ISO spin just as the analog of the Z component of spin would be one half but the full isotopic spin would be three halves yeah remember every object which has a spin three halves comes in four states four states here they are one half one half minus three-halves minus three-halves same is true for ISO spin okay but let's concentrate on spin for a moment these two states they that's these two and the ones of maximum and minimum spin that's these two so it's got to be four of them we know that a thing with spin three-halves has four states z-component devices spin can be 1/2 and minus 1/2 but by analogy we'll ordinary spin there will have to be four of them ok but let's let's come to the to the importance points let's first of all label their charges this one has three charge 2/3 object it has charge to this one has charge minus 1 + u UD has charge plus 1 + charge what is this 1 0 so the charges are different well these two do have the same charges sorry did I get this right u UD no yeah yeah yeah these do happen to have the same charge as proton and neutron but these are different okay all four of these objects have to within a small discrepancy the same mass just as the proton and neutron have the same mass these have the same mass but that mass is not the same as the proton and neutron proton and neutron the mass is about 940 in units of MeV zillions of electron volts this is the mass of the proton and neutron with the neutron being slightly heavy and not by much okay the mass of the Delta is about 1200 MeV the Delta can decay it can decay into a proton and neutron and a PI on let's just see how that would work let's take the easy ones the easy ones have all three quarks the same up up up so here we have three up quarks moving along and how can that decay what does it was it going to decay into it's going to decay into a proton and new or neutron and a MS on Amazon is a quark antiquark pair let me just draw a have for you how this happens this would be up up up the two up quarks go off this up quark also goes off but quarks can separate like that quark and an antiquark appear in between like that the quark and the antiquark in between could either be a down quark or an up quark so one possibility is that this is another up quark and then this would be an anti up quark and this would be an up quark an up quark and an antiquark have zero charge this would be the decay of the Delta three-halves what do we have here this one no this one can't happen this one actually can't decay not possible we have to put it down quark here there's just not enough energy for it to happen this would be an anti down quark and an up quark so what would this thing be up up and down that would be a proton the proton is lighter than the Delta so there's enough leftover energy how much energy is left over let's see 260 MeV about right something like that 300 MeV roughly 300 MeV what's the mass of a pi on about 140 about 140 MeV so there's enough energy for this to happen and still leave over some kinetic energy for the PI on to fly away what kind of pie on is this with an up in a down bar what's its charge 2/3 and 1/3 so this is a pie plus and a proton total charge to this is the object with charge - so these Delta objects are not stable they all can decay into a proton or neutron and a pion and they're very short-lived their lifetime we could work out the numerical I'll tell you what their lifetime is order of magnitude order of magnitude it's the time that light would take to cross the proton so you can figure out that the proton is about ten to the minus thirteen centimeters what's the speed of light that 10 to the 10th centimeters per second so ten to the minus twenty third seconds or something they don't last long but they do last long enough to be identifiable as distinct objects when they produce these deltas these deltas and collisions particle collisions Delta's are produced and they're real objects but they are very very short-lived scheme as a matter of notation is making it if this which ordered no not enough not for purposes here no [Music] okay that's exactly what we have to come to now there's something wrong here something's rotten in the state of Denmark what is it well we have three up quarks whose spins are all in the same direction we could put those spins we could if we like choose those spins to be all up and make a delta three-halves with its spin ordinary spin up with all three in the same direction and they'd all be three up quarks you're not allowed to put two fermions in the same state ah if if you could fiddle around with the spin maybe you could do something with a spin but all the three spins are the same why are they the same because it has spin three-halves three quarks with spin three-halves have the same spin they also have the same ISO spin namely they're all up quarks so we seem to have found an object which consists of three identical up quarks that's a violation of the principle that you cannot put two fermions into the same state this was the clue that led eventually to what is called quantum chromodynamics it was realized that quarks have to have another property they must have another property or so that the three quarks in the Delta three-halves can be different from each other the fermion statistics the fermionic property of them requires that they be the friend so there must be a label another label that was hidden from view for some reason which um which is there but not apparent and experiments that label is called color color is again highly arbitrary term it has nothing whatever to do with ordinary color and it was just a label - - a name a name different in different places the three colors of quarks are different in some places they're red white and blue mostly in the southern parts of the United States other places are red green and blue red green and blue being the primary colors of light up that you see with your eyes I will use red green and blue I haven't heard red white and blue being used for a long time not for the last nine years or so but they're just labels they're just labels and in no sense of a physically different one from another and any sort of interesting measurable way the fact that there are three distinct ones and that they are that they are not the same is important they have exactly the same mass they have exactly the same properties so let's now write down what we know about the the labeling of quarks all the various quirks we know about there are up quarks down quarks so that's the lightest one then there are charm quarks strange quarks and after charm comes top quarks and bottom quarks they're not listed in order of mass the up is the lightest the down is next the charm is much heavier than the strange by a factor of about eight or something like that and the top is vastly heavier than the bottom but I've just put them in I've been perverse and put up on top of down I don't know why these are the six distinct types of quarks but now for each type of quark there is another label so quarks are labeled by two labels and the two labels are red green and blue as I said I don't want anybody to think they're really red green and blue but that's the label and where did that come from how did we know it was there well it's one of these things where physicists simply followed their noses they simply said look there's something wrong with this quark model you can't have three quarks all in the same state they must differ by something else now they could differ by position but it was known that for one reason or another that it didn't have to do with position and momentum that was that was known to be irrelevant for dynamical reasons for energetic reasons so that was not the issue there were three quarks all in the same state they must have it in fact the situation was actually quite similar to what happened in atomic physics spin was discovered by unum back in gouts MIT because of the because of atomic spectroscopy helium had two electrons in the same state no good violates the the Pauli principle well actually the timing here I think may be a little bit confused but it could have worked this way they could have said well paui tells us that you can't put two things in that maybe it did work that I can't remember now I wasn't around I don't remember but the reason or one of the reasons that gouts mitten olam BEC might have since I the history in detail might have invented spin was because in the helium atom there were two electrons apparently in the same orbital state so you've got to attach to the hill to the electron another quantum number another label and at work that works just fine it worked a second time history repeated itself and various people Nambu Nambu was the one who realized this your chair on Nambu Nambu japanese physicist japanese american physicist the Nambu realized that this called for another quantum number and he said every quark has to have another degree of freedom i don't think he called it color i suspect that was Gelman but i'm not sure many a good time good deal later and then what he said is look Oh what's going on here is that you put three quarks together one red one green and one blue and now you're in business no more violation of the Heisenberg uncertainty principle the same trick incidentally works for protons and neutrons are that you can understand the proton and neutron also as a red ultimate what I call is again red green and blue yes question so is there physical property that you measure or no no in every possible way they are the same except we know there are three distinct ones so if you had one you could tell the other why and anything you say if you say that maybe the crystals in the five Richard huh if you can't to take the difference right you can see if you have one you can tell the other one is different other that's that's that's a little bit complicated and in collisions you can tell that if you have one if you have two of them you can tell that they can't be the same in arctic observed the colors in the action you have well yeah the color is conserved but it's also always zero it's not only conserved but it's always zero so it's a little bit funny conservation law but look you could say the same thing about it doesn't quite tell you that you need all three of the colors for a uue game no but you need do need something to distinguish the two use yeah it gives you more than you need that's why that's why I historically the Delta three-halves played an important role it was looking at this guy here which was unambiguous three quarks parallel spin parallel iso spin something's wrong it would have been possible to analyze the protons and neutrons but it would have been less convincing when the Delta three-halves was interpreted in terms of quarks that really hit you over the head that so the ultimate resolution is and then we now know you know really experimentally extremely well with the three quarks that three different kinds of colors are really there you know even with ordinary spin what's the difference between spin up this way and spin that way there's no difference they have exactly the same property all you have to do is turn your head over Oh spin this way unless you'll have another one to set a direction or something to set a direction then then you can't tell the difference between them on the other hand if you have some object which picks out a direction and you bring a spin up to it you can tell whether the spin is a long a particular axis or not in the same way if you have a proton a proton being different than a neutron and proton and the neutron are identifiable objects I mean in laboratory if you have a proton it picks out a direction in this isoh spin state space it's up in the ISO spin direction not down and if you have another quark you can discover whether that quark is power has its ISO spin parallel to or anti parallel to the proton so yes you can tell not at ISO spin you can tell whether it's I said something wrong but close enough if you have one object it can provide a kind of frame of reference for the other ones and test whether they're the same or not but the mathematics of quantum chromodynamics simply requires that that you have these three different things you could say maybe it's a violation of the poly principle you could there's no known mathematical framework for discussing that and there's no quantum field theory that has anything but fermions and bosons so you'd have to be Vincent Lee knew mentor position and you can make a case that ice has been is a kind of observer absolutely what would be a totally observable much much more subtle much more subtle much more subtle let's come back to it I'll tell you we get there after we've talked a little bit about I just have the same session in a different form if you have a down up of a proton one of them one of the three quarks is green and since the down there's only one of I mean the question the question is how can you really associate with one color with one of the rocks no you have to think of quantum superpositions of states so you might write let's take the case of the proton up down down this could be green red blue but we have to write all possibilities all ways of combining them and to make a real proton so we have to use some quantum mechanics to symmetrize the wave functions and so forth symmetrize anti symmetries them appropriately but the the big advantage of this Delta three-halves you didn't have to do anything fancy just three all in the same direction no okay um sure you could say well maybe there was something wrong with our ideas about quantum field theory but by now the theory of quantum chromodynamics which is exactly baked chromel has to do with color color is the important quantity in quantum chromodynamics just like charge is the important quantity in an electrodynamics this theory is a highly accurate description of experimental data associated with the collision of patrons and its accuracy is you know way beyond what can be questioned now so the ultimate answer is that it works okay now let's talk about gluons the missing ingredient now we have the analog of electrons the quarks the fermions they have some attributes they have some electric charge like electrons they stick together not quite the way electrons stick to a nucleus perhaps a little more the way electrons stick to positrons but they stick together somehow what's missing is what sticks them together what sticks together atoms is the electrostatic field the electrostatic field is associated with photons we can either think of it in field language that every electron creates a field around it all we can think of it in particle language that electrons emit and absorb photons the exchange of photons back and forth between charged particles creates the the forces between them what about quarks what sticks them together particle very very similar to the two the photon at first it was a speculation maybe such objects exist then a theory was built a mathematical theory was built with quarks and gluons gluons being the analog of photons they're very similar to photons they have spin one just like the photon which means they have the same kind of polarization states they're massless like photons very similar but with one big difference that will come through and they jump back and forth or they go on one hand a quark is a source of the field that's associated with gluons the gluon field in the same sense that the electron is the source of the electromagnetic field on the other hand not the other hand but a similar hand the quarks can emit and absorb gluons what are gluons like what quantities do gluons have photons are pretty in a certain sense uninteresting except for the fact that they have a polarization they have a spin and they have a polarization they have a momentum and they have a polarization and that's about all they don't have any charge by itself a photon if it collides with another Photon there are no forces now that's not exactly true there are forces between photons but there's secondary effects they're not electrostatic forces because the photon is charged there are secondary effects which come from quantum electrodynamics and loops of quantum complicated finding diagrams involving electrons but the primordial interaction between photons is there is none they move freely past each other and that's why a beam of light moving in one direction will pass over pass through a beam of light moving in the other direction with no interaction Excelsior in some material okay so photons are not very interesting and in the sense that they don't interact with each other they are interesting from the point of view of their interaction with electrons and basically all of quantum electrodynamics is summarized by one diagram and that diagram which we've drawn several times is the emission of a photon from an electron electrons are drawn as having a directionality the direction along which the charge is moving you can flip lines around and every time you see an arrow going downward that indicates a pro a positron but it's all one basic vertex that's it and out of that you can build forces you can build collisions everything else all right just for the purposes are from bookkeeping think of a photon as having the same charge as an electron and a positron in fact a photon if it's given a hit and given a little extra energy can decay into an electron and a positron it's not that in any sense of photon is made of an electron and a positron that's not the point but it happens to have the same properties as an electron and a positron in particular it's electric charge it also has a angular momentum it has a spin a spin of 1 and with an electron and positron if you line up their spins you can also make a spin of one so in many ways a photon is similar to an electron and a positron that sometimes indicated by drawing by thinking of the photon as a fictitious composite of an electron and a positron and then this diagram this diagram of the emission of a photon can be drawn just by saying the electron comes along becomes an electron over here the electron over here was really a positron moving backward which turned around now there's no content in this other than to say without losing any electric charge you can emit a photon and you can see it directly you don't really certainly don't need this to see that an electron can emit a photon and that there's no violation of conservation that's totally obvious that an electron can emit an electrically neutral thing but nevertheless let's just draw the emission of a photon by thinking of the photon as a composite of an electron and positron it's it's not useful for electrodynamics the analog is quite useful for quantum chromodynamics okay now let's come to quarks electrons we're finished with and the important thing in quantum chromodynamics is the color so let's begin with quarks quarks can be red green or blue let's make a column vector out of them and use the language of quantum mechanics a quark can either be in the red state the green state or the blue state and make a column out of it an anti quark let's represent anti quarks by red bar green bar and blue bar a gluon first of all a gluon is an object that can be emitted by a quark if this is a quark and a cork goes off a gluon can be emitted but the interesting thing is the gluon behaves in some respects like a quark and an antiquark it's not a quark and an antiquark I'll tell you precisely in what sense it behaves like a quark and an antiquark but let's think of the gluon as a quark and an antiquark in the same way so how do we label if we label each quark by a color this now becomes a quark and an antiquark quark and an antiquark how many different kinds of quarks and antiquarks are there what did I hear nine yeah you're almost right right the logic was what I was looking for I wanted you to say nine there's a subtlety there's a subtlety which will come to there really only eight but but let's say nine to begin with what are those nine quarks well I started one of those nine gluons then the nine combinations that you can make by taking a quark and an antiquark in other words they make a matrix if quarks are like a column then and we might think of just for fun we might think of anti quarks as making a row red bar green bar blue bar then gluons would fill out a matrix all right in other words to label a gluon you would label it with two indices two colors and what would they be there would be red red bar red green bar red blue bar green red bar green green bar green blue bar what else PR bar be G bar be P bar to the diagonal sit again well the diagonal elements are not really indistinguishable but the but the point is that the sum of the diagonal elements is is not an independent quantum state all right so it would seem like there are nine gluons later on we will talk about a particular subtle PE which tells us the quantum mechanical superposition of red red bar plus green green bar plus blue blue bar is our nothing doesn't exist but for now for our purposes right now let's neglect that there are really only eight gluons but it really does look from this pattern here that there should be nine so let's let's play with it as if there were nine then what kind of Fineman diagrams can exist well a quark can become another kind of quark and emit a gluon all right so let's draw the diagram for that let's take the case of a red quark becoming a green quark and emitting a gluon what kind of blowing gets emitted red green bar where's red green bar here right here red-green bar and if you like you can draw that with a neat notation the notation is just a bookkeeping device really and here it's useful here it really is useful just think of the red is going through and the green also is going through except when you flip the green line over it becomes an anti green and a red so the gluon that's emitted is as if the red just went through and the green annihilated a green bar that's the basic vertex of quantum chromodynamics there's not just one of them there were nine of them or are actually only eight but but the pattern is quark goes to another kind of quark and gluon is emitted if a red cork goes to a red quark then it's a red red bar if a red cork goes to a blue quark then it's a red blue bar and so forth and so on okay now that's as I said the basic the basic phenomenon or the basic primitive building block of quantum chromodynamics you can build all sorts of sorry that's a half that's one of the building blocks there is another building block that isn't there for quantum electrodynamics as I said photons don't interact with each other in particular a photon can't emit a photon and another photon electron can emit a photon and stay an electron photons don't emit photons so photons don't interact with each other in any way except in materials yeah gluons are only in the with a change in port no they can no you can have I don't require I mean about this process and whether it change the weather does not change SS this is the only method aware which one that's right this is the only way in which gluons are emitted but there is something new that makes quantum chromodynamics first of all far more complicated and far more interesting than electrodynamics let's take a gluon moving along here's a gluon let's see let's take that glue on to be a red blue bar glue on that's a red blue bar glue on okay now can this happen I'm going to show you something that yes is really part of quantum chromodynamics maybe it's not too surprising once I draw it this is not really a quark but just imagine it's a fictitious quark making up the glue on all right fictitious quark goes off well if it's a fictitious quark it better not really go off but we'll see in a moment what happens to it and the blue bar keeps going but now if these really work works a quark and an antiquark could form what kind of quark antiquark ooh would you like to put there green let's put green there this would be green going this way and this would be anti green going this way and this would be red so red goes through blue bar goes through and green becomes anti green going that way well what do we have now now we have a basic vertex in which three gluons come together let's draw gluons as wavy lines similar to the photons we now have a vertex in which a red blue bar becomes a red green bar and a green blue bar we don't really have to remember what combinations are possible all we have to do is figure out which diagrams we can draw where all of the lines go through without being interrupted you can figure out what the various couplings or what the various possible fundamental diagrams there are connecting gluons this is the new thing what it means is that gluons interact with each other gluons exert forces on gluons in a way that would be unthinkable for photons photons cannot exchange photons between them gluons can exchange gluons between them so now let's come to forces the gluon behaves in a way which is similar to the photon and that's something which is similar to what the photon does it can be exchanged here's a diagram it's easy to draw diagrams where quarks interact with each other all right let's let's draw yeah let's draw a diagram in which an anti quark interacts with a quark all right here's a blue bar anti quark which emits a blue bar green gluon becomes a green blue arm and now the green glow on the green Werth sorry let's see this would be a green bar this would be a blue green bar glue on his green bar is blue but let's say that blue goes right through like that and what do we have here we have here now an exchange of a one between a blue bar and a blue making a green bar and a green that's a kind of force between quarks that creates a force between quarks in very much the same way that photons exchanged between electrons create forces oh you might want to make a force between a blue bar and blue bar supposing we wanted force between a blue bar and a blue then we would make this blue bar here alright so we can make all sorts of forces this way but what about forces between gluons all we have to do to this diagram is add an extra two lines let's what did I have this originally um blue bar let's make it blue bar green bar up here green up here let's put another line in here it's not another quark now it's really going to be representing a gluon and this one let's take to be red red goes right through let's put another line over here I don't know what that I take that one to be I think I took that one to be blue bar blue bar this is now a diagram which represents the exchange of a gluon between two gluons this is really something new this is something very very different than electrodynamics what does it lead to it leads to forces between gluons quarks can bind together because of the exchange of gluons and make hadrons but gluons can bind together and make objects there are objects in quantum chromodynamics which contain no quarks there are no bound are no bound States composite objects in quantum electrodynamics just made up out of photons there are objects which are just made up out of gluons and how do they happen they happen because gluons can exchange gluons back and forth we could just summarize this by saying there's a force due to the exchange of gluons between gluons this would also mean for example that if you had two waves of gluons going past each other they would interact with each other they would deform each other they wouldn't just go through each other just like two electromagnetic waves in fact even if you had a single gluon wave moving along the different parts of it would exert forces on each other and cause it to deform or do whatever it might do so the watchword is that the dynamics of gluons is nonlinear yeah do you have the same degrees you just have to make sure the lines follow through the diagram uninterrupted well that's what this that's what they're following the lines means where did I draw this wrong I might have drawn oh sorry this should be green bar this should be green bar Green a green bar yeah sorry the rule is follow the lines when a line turns around in time like that change it to an anti particle and that's basically the only rule of quantum chromodynamics that there are interactions between quarks and gluons and they they satisfy the let's call it the follow the line rule all right and there are interactions between gluons and gluons and they also follow the line any color problem in our genes what's he wear our g o5 r d RB bar this should be B bar in equity G know where it should be feed bar left I'm going this way this one should be G and this one should be P bar okay let's draw let's do it over wrap sorry I messed it up that way enough to do it over okay so I think I have blue bar over here red if I remember I don't remember red goes through so it stays red blue bar goes over here and then turns around so this must be blue this one was blue bar has to be a quark and an antiquark blue bar straight through blue bar here and now we have our choice what we want to put over here so I think I put green going this way green green green bar green goes right through the diagram okay now I think it makes sense every line just go straight through red go straight through that way blue bar goes straight through this way well we can put the arrow the other way to indicate ant that particle yeah yeah gluons always have the properties of quark antiquark earlier by analogy with the photon she said the gluons are massless yeah these diagrams with olie still they are masters we're going to come to what meaning of the mass of a quark and a gluon are all right yes they are massless in a technical and special sense I'll tell you right now with the special senses we're going to quit in a minute or two in fact right now I'll give you an example we're going to come we're going to study this theory one more one more week and we're going to talk about the confinement of quark so we're going to talk about the structure of hadron x' and so forth but let me just tell you in what sense a quark or a gluon does or does not have a mass or does or does not have the mass that we ascribe to it so let me imagine that I have a object of mass M a small object of mass M and the small object of mass M has attached to it a I don't know what it is it's whatever you want it to be some sort of Wiggly soft the piece of chewing gum or something that dangles off it now I want to move this object if I move the object with a very small force the force being so small that it doesn't deform that the acceleration is so slow that the whole thing moves off together what kind of mass does it have the answer is it has the mass of whatever you put here plus the mass of the a lot of chewing gum or whatever it happens to be we're thinking now purely non relativistically just to give you an analogy on the other hand supposing I shake this thing with a very high frequency and I ask what are the properties of the motion of the of the core of it over here when it's been subjected to a very very high frequency force of some sort what kind of mass does it have over here just the mass of this object alone right the rest of it doesn't have time to to adjust to the other forces it just stands still now maybe this sends out a wave all right but the very rapid oscillation here the response of this in here would be the response of an object of mass M so what is the mass of it is it the mass of the sum of them or is it the mass of the thing at the end the answer is ill-defined the answer depends on the frequency of the force that you that you exert on it masses of objects are frequency dependent or well in the sense in this sense the the mass of this object the observed mass of it that the that would respond with would depend on the frequency of the motion in the same sense the mass of a quark is frequency dependent if you shake a quark is some kind of object inside a hadron there are three of them and there's a bunch of mushy gluons stuff in there holding them together if you were to try to move the quark by itself but if you were trying to move the quark slowly if you grab the whole of that quark if you could do so and you moved it very slowly the whole thing would drag along and what would be the mass of it what would be the mass you would experience mass of the whole thing which could be the mass of the proton which is nine hundred and thirtysomething or others what about if you were to exert a very high frequency force on it well I'm not going to tell you what well the answer would be what we normally call the mass of the quark that's this 5 or 10 MeV for an up-or-down core up or down quark so the mass of the quark 1 is subjected to a very very high frequency only when it's hit very hard and you try to see how it flies off dragging this other stuff behind it the initial impulse that it gets and the initial velocity that goes off with will be sensitive to the to one value of the mass on the other hand if you hit it very slowly with a very gentle low-frequency force the whole thing would move off so the concept of what is the mass of a quark is somewhat ambiguous are and to keep the discussion simple let's say the mass that we usually ascribe to the fourth or the quark are these high frequency responses analogous to to the mass at the end of the wall of julyan not really this is a completely client in this case this is a completely classical phenomenon that you have a small little nut at the end of a Wiggly something-or-other you shake it very rapidly you see it accelerates with one kind of acceleration you accelerate it with a low frequency it absorbs that's a classical phenomena does not have to do with the last actually describe the electric charge charge like yeah yes yes yes yes lesson but that's exactly right the lesson is the parameters that we describe particles with are dependent on frequencies and wavelengths of the interactions that they engage in they're called running yeah oh is that the same story pause it does it does we have to sort out exactly what we mean by the charger or quirk but let's just put it this way it's one-third the charge of a proton but yes you're right we do have to define it carefully and that's a whole story into itself that's a big question right I don't know that's what we're going to talk about we go that's next right back yeah this stuff works here it's so hard with the fractional choices and Carter question this and that because you can look at individual products how did people figure this out oh that took time [Music] yeah well there was a number of clues there were a number of clues by the time I came into physics the idea of quarks was already established I mean by nineteen I was a graduate student in 1963 when Murray gell-mann announced the idea of quarks so and I dunno how he came to it but but the there were clues there are a lot of clues there were a lot of clues but there were also a lot of inconsistencies so it was a pattern of suggestion suggestive facts together with apparent inconsistencies such as the violation of Fermi statistics and and there was another fact which was very peculiar the other fact there will come through next time had to do with the fact that works are never produced in the laboratory that they're always permanently confined inside protons neutrons massan's that was another fact and it wasn't one person who put it together was a whole variety of people who put the whole thing together Nambu had the right idea in the early 60s he had the right idea but the whole thing got put together and you know nailed in place and the whole structure was put together over a period of 10 years yeah we will talk about that yes this theory is ignoring electrons now just like in quantum electrodynamics we ignore quarks I only have to put them together we have to put them together into some coherent thing in which quarks and electrons and photons and all of them form one bigger structure some of which has been done and some of it has not been so yeah it is a process of isolating I mean physics always works that where you isolate do you you know you divide and conquer and then you have to put it all together ok good let's say for more please visit us at stanford.edu

Channel: Stanford

Views: 91,770

Rating: 4.8921161 out of 5

Keywords: Science, physics, mathematics, atom, nucleus, electric field, protons, neutrons, antiquarks, mesons, spin, electron, bosons, fermions, half-spin particles, angular momentum, z component, isotopic spin, symmetry, up quarks, down quarks, spin up, spin down

Id: yy989li6xgY

Length: 98min 28sec (5908 seconds)

Published: Fri Apr 16 2010