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New Revolutions in Particle Physics: Standard Model | Lecture 6

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get back to SU 3 and S U 2 2 3 was CD as symmetry which Woodward said it acted vertically and our table it took us from 1 colored red Green In Bloom and mix them up what's just bear in mind sells about that they story may sells at a table this is a table not all elementary particles obviously but it's table of all week freely on table all of the fairly arms spin Vermont world and not so much because the firm but just happens that they're kind of constituents as constituent particles of the Adam in the nucleus just right and then begin our below the 6 different families of of quarks the family's refer cool wrote they were referred to the news media up-and-down that's called a family of Kobe up down family then is up to now charmed strange I guess you call the charm of estranged family and the top and bottom that's a horizontal structure whether they have red green and will have a quarter in each 1 of these slots Of the but stickers far away he borrowing because we here where working each 1 of these slots and the color symmetry S U 3 symmetry color which is associated with quite Cuomo dynamics is a symmetry group which acts on this trip here and mixes them up into each other that's symmetry group has generators those generators correspond to be infinitely small transformations but also corresponds to the blog on these symmetry group which thinks red green blue is associated with the existence of the lawns and the glow on when there is from 1 Corto another for example from red to green you create a red so ready Green on this transformation from red to green is simply 1 of the generally as you rate of generators rescued 3 the transformation on one-to-one correspondence with the emission of a blue or you could think of an admission of a blue as physical act which of physical phenomenon which does the same thing as the symmetry group which mixes of particles in the which other Bassett character of boards gage bows and arrows a manifestation of the symmetry group it would be and mission of the gage blows on really does change our particle from 1 thing to another in exactly the same pattern as the symmetry group change when they were knocked out that red Green and and when you perform 1 of these transformations you'd do it all of the court simultaneously you don't do it just them up pork or just kill family if you want the symmetry to be correct to either be real symmetry of the theory that you must do it simultaneously on all of the quarks and that corresponds to the statement that exactly the same Our say this is from up to upcourt to for a century on mission has not changed horizontally only changes vertically so for example the same glue 1 which would be involved in a meeting all which would be emitted when a rate up upcourt becomes a green work that's exactly the same as would be emitted when I say when a top rate court would be on top Marine Corps red green bar lower so the symmetry takes hold rose and mixes them into each other then huh it was the 2nd of the Freddy I know it's actually a 3rd symmetry talk about electrodynamics and what it does to the armed with what the emissions what these symmetries associated with electric dynamics but now encountering another cemetery which is usually called a flavor symmetry flavor symmetry or a rocket family symmetry somehow sometimes it takes up sit down at the same time that takes Chanter strange at the same time that it takes top about are key the color punching Solheim for example it will be processed seized in which and up Quark let's say all of the blue variety unix W. plus bows on W plus a in it becomes a value work also on the blue variety what has W. blows on it's a physical manifestation of the transformation what's sexual horizontally back for exactly the same W. plus would mediate would be made in the same kind of course would be when Our green state trial court because things a green strange quark St. W. plus and so forth be wants never move your horizontally W. bows on never move you vertically and that is also the character of the Symmetry Groups Symmetry Groups move your horizontally but as you to a dozen movies from here to hear from you to here it just moves you between up and down down up or at the same time charmed strange stirring charm for us the mathematical structure of S U 3 cross you to do your hair the photon the full-time positions is associated with the symmetry which changes the bane of every charge carrying field which I explained that last time every charge carrying field transforms with babies
under you want to you wear those together you have the basic ingredients of as you 3 across youth to cross you want crossed simply need better product structure with ASU Toulouse Dollar mixed up the colors and the S U 3 years don't mix up the up and down want product structure and that's where the terminology that's with I I guess of corporate our that to stay in the novel is a gage theory based on the age group as you play cross S you to cross you want now it is actually a little bit more complicated Shane were going to sort out the complications but roughly speaking as you 3 color as you tool for W mission a new 1 for elected electrodynamics now this is good did it slightly more complicated than that because saying is not a 100 percent consistent for reasons that will become clear about it all right they envision of the W on incidentally of course W HMOs answer only discovered relatively late in the game and our real postulated some time in the sixties but it really only achieved some real traction and seventies W. votes on the theory weak interactions goes for some aspects of the theory weak interactions goes back much earlier than that both the thirties of the family theory of weak interactions will discuss the relationship should be enough OK what about the coupling constant better involved in these various interaction B U 1 coupling constant here that's associated with the emission photon and the coupling constant simply electric charge the reason that emissions or the reasoned that the probability of the emission of what time is the fine structure constant is because this is the amplitude for the emotional photon you have the school where defined the probability for year the To be present so he square is basically the fine structure constant there has pies and things are important but he squared is basically fine structure constant and it's also the coupling constant or be mission I'll be quantum mechanical amplitude for emission I had a virtual emission of photon which means that at times Goodby reabsorb before it gets very far or if the electron was stripped out of the way than the real mission Tom these amplitude that is constant called electric charges a pure number editor number left well the fine structure constant itself square of this number it is as a told you about 1 over 130 set the pace of a small number are here the SCO 3 coupling constant that usually called Jedi what we can cause G strong G sub and that of course is associated with the emission of a global 1 and that's also a number that number is close to warn or a macro 1 is the big oddly corresponding thing corresponding to the fine structure constant would be more like about a 5th is a lot bigger than a world 437 so we missed another 1 is much much more probably event for glow quirks smacks of something it basically of 1 with a probability cost 1 almost always the glue 1 where the photon almost never admits of what they might think in view of the fact that the weak interactions of hold very weak in cold weak interactions and back from the fact that the decay rates on very much lower associated with weak interactions the weak interactions are indeed in many many ways very much weaker than either be Blahnik interaction of electromagnetic interaction but not because the coupling constant small coupling constant of the weak interactions is closely related to the coupling constant for quantum electrodynamics that's about the same order of magnitude bars related its related by some some simple numerical factor Burke marked a very different so that raises the question What is it about these prophecies evolving W arms that makes it so improbable so are unlikely that weak interaction will take place is unlikely after all it takes the neutron 12 minutes to the case it must be very unlikely process that's the next question but think about the decay of the neutron cave the neutron originates From a down quark inside the neutron them for me maybe a W minus and becoming an op court so it's in the works is another downpour and up for this isn't for us it a new try and popped into balance and this is a proton tulips and bound and a W goes off but we might but they W you can also become double-A-minus become an electoral and ended it by neutrino art school go back to the table you knew my more particles warfarin this Milan's on laptop let times come in basically the same pattern up then John strange top bottom but they do not carry color the meaning of that is they don't participate at all in the color interaction they 1st probably free they me wine and I'm perfectly free to say I don't know so our however is a pattern and the pattern use Knopf below it does have some structure but they were not tonight but at some point they do understands better almost as tho it were a 4th Carla 11 times no other laptop and do not have the same charges as the quarks summer just remind you of these this column would be the courts with charged to 3rd and this column would be the courts which aren't my theory
that this 1 has what more unit Of charge than this 1 the
difference of charge is when you're
right down left on time a rolling the different the same a strong here of course two-thirds minus 1 one-third two-thirds minus 1 3rd now and missed some W only cares about the difference of charge another words allowed W. can be needed if the difference of charge is the right thing I W plus W has a definite charge and to emit different charge of the initial and final me must be correct ISO so if we W. could be emitted when and neutrino becomes an electron only comes electron becomes a neutrino lead charged difference must be the same appeared in fact what goes here would be the nature of neutrino electron neutrino and electron the charge of difference is this has charge minus 1 charges you so the charge differences the same and it is mathematically consistent to say that a W bows on the same W bosons and can be emitted when neutrino Becomes Electra path in the next column on the charge under the charmed strange column calms neutrino associated with the new 1 and new on the new orders in every respect at least so far as we know essentially the same as electrons except it's guesses about 200 times larger again nor the reason for that present time and then on the topped by column the heaviest of the quarks is matched with the heaviest of electrons always that we don't know the details of the masses of the neutrinos well I think neutrino associated with cow that time and the tower time and Fowler foreign news quite a bit heavier than any other work on every lap time I understand was I don't remember right now now toward left but Greek stand for what light the now there are barium ahead him and his arms stand for something could have as spoke at the terminology historically was will be confused Mayor sons meant something in the middle barrier meant something heavy like protons and neutrons and electrons meant something like well because of that the new 1 was called the new missile because it was so midway between the proton electrons that terminology went away when it was realized just how different the new 1 was From the pipe which has comparable mess it was much more like electrons and I was like a pine summers on reserved for quirky back work Paris always both songs and new ones no longer have recalled the new US Army such as the historical amount OK now what he does what is the probability of this process it has it's a fight diagrams and refinement that Iran has some parts to it and the part consists 1st of all of vertices and propagate propagated on these elements which have to do with the emotion of particle from 1 point to another and this particular case the motion of the W from the point where it made it to the point where the electron neutrino or electronic neutrino are created I'm so this process 2 main ingredients but we can't isolated from the rest of it 1 of them it is 2 powers let's give the the coupling constant and the coupling constant for the emission of a W let's call it Gene W. G valuable awful week DQC QCD strong interaction coupling constant removing a a cool 1 recalled G strong this was G wheat as I said it's a number of about the same order of magnitude as electron charge so it's not enormously small it's not it's not the smallness Of this coupling constant which accounts for the improbable nature of weak interaction at 1st of all we get to powers G weaker squared that's analogous to 2 powers of electron charge if we explained the exchange of all time this is expected to be number of about 1 over 100 not exactly the fine structure constant within a factor of 3 or something that close fine structure constant were magnitude that's what this year but that is something else there is the propagator of Abdullah bows so we have to know a little bit about propagate in quantum field theory they other factors which are inserted in finding that ran to account for the motion of a particle from 1 point to another as such they are simply functions of these based time difference of the space time distance between mission and the adoption the functions if you like of the magnitude of proper time along with between this event and that but In any case the functions that propagator squalid distance between 2 points That's a function of the space-time differed distance between those points function distant and that has the following properties it depends crucially on the mass of the article works being exchanged depends on the following way if we would've if we were plot throughout the plant as a function of distance if we went all the mathematics of quantum field theory and worked out the propagator we would find that skull our stuff and Bessel functions complicated function but not a complicated but important aspect of it is that it is large and small distances it falls short groans where 1 over a distance of some power will distance squared between 2 points so it's very large small distances but then add and if the the particle had no man has it would just continue on its way cede power loss off to adjust fall off gradually with 1 universal behavior which we go like 1 or with the square of the distance between the point it as tho it would be here but the man's of this particles introduces a new ingredient entered this is ingredient which causes the propagator to decrease suddenly like that it decreases exponentially exponentially words the Apollo along gives rise to an exponential and the interesting questions the way does that happen where does that happen and what value of distance those that they have suddenly manifests itself and tell the particle hate you're out there you shouldn't be out here because you carrying what medicines known Mr. Kerry new carrying off some mass from from just as none you gotta get back that's not the thing about some of the story the propagated has an exponential decrease where it happened and is just dimensional analysis in in which peoples h Bora Bulls warned take such units man's man's poses romance has the same now when I write an equal I simply mean Unix what's the usual stay calm notation for units square bracket around the quantity a standard notation for the units an object that put a
bracket around a mess has saying units as an energy like that because he was MC Square receives equal to 1 etc. but they also have the same unit as it 1st lady length bake met has the same units in 1st later always said there was a 3rd quantity which has seen units of medicine was it at the momentum the same as momentum NetWare about momentum times districts where units of momentum resistance no uncertainty Uncertainty Principle think Uncertainty Principle momentum times distance is 8 buyer but age is dimensionless in these units so momentum and dissidents simply have inverse units to each other so that for the way it has inverse distance above may ask energy and also momentum and therefore we can say that the Red differently with right that length as units of inverse maps down 1 over maps or that tells us the horizontal axis he was distance D the mass of the particles In and that tells us that the distance at which it falls off like this the only way we can make a distance using the mass particle occurs at a distance Our 1 over the mass of the particle that's really Compton wavelength of the particle there would put back since he's age bars would be H. far over and see the provide forms a and see this at a at a distance Our order a farm of it and see the propagator suddenly died down and as an exponential the vertical axis is the size of the Delta the and 1 of his Is it square of the propagated is the probability that the particle go that far before the before you so this is saying is that there's a sudden shock turned off of the probability for particle of garlic given dissidents before converting white which is controlled by the massive particle in particularly the heavier than rest of the particle the less distance to go before it has give up its energy in the form of white now at Bombay you'll silly what's prescribed experiment is not the tool point with these events take place what's prescribing experiment is the moment of the particles you measure the momentum of the particles you measure the momentum of the incident particle P on proton not as neutron neutron you measure the momentum of the proton you know the momentum of the W on the momentum of the W on these different Of the momentum of the protons neutrons see another momentum the W goes on and of course that tells you the momentum of electron neutrino their momentum conservation you don't as a role was certainly not enough his experiments actually know the distance between those points you know the moment but a relationship between functions of momentum and functions of position of functions of this and that relationship is Fourier transform you can think of the propagator mind as a function of positions for a moment that you could think of it as a function of either position or momentum the position distance between here and he or the Fourier transform of this function for transformer is the amplitude 40 meeting a W will a given momentum so the question is what does the Fourier transform of a function like this look like I'm not gonna work it out this is something you can go and study for yourself a function which has power along and then a sudden decrease like that I will simply tell you what the Fourier transform of the propagator before it transformed as a function of the squalor of the momentum of the W bombs on any also parametric it depends on the mass of the W boss let's call it Del Valle twiddle twiddle stands for Fourier transform as a function where to recall momentum of the W its court case what is it looked like it's very simple 1 provided by case square plus the man's of verbal square that's it that's a factor press the fact that you put it if you know that momentum of the W how would you know by measuring the initial and final momentum of the proton and neutron you measure the momentum of the W and then you insert this factor In has 1 of the factors including amplitude for the mission of the W that's the rule as final rules that's it the in this all 1st of all let's talk about a photo if we amid a folk target has and while the case squared typically when you amid a photon in ordinary quantum electrodynamics the momentum of the photons pretty low by particle physics standards it's typically in fuel load of 200 electron volts or something like that very small Kenny and so the propagator for admitting the photon at momentum is rather large moment and this is a big numbers K goes to 0 the weak interactions we know that the probability of emissions is much much smaller Was it said it is not the coupling constant there so the only thing that can be the massive W. bows are a mess of the W blows on issues very large for whatever reason then this is always going to be small and fact the Big East it will ever be is what happens when Katie is equal to 0 . Keyes equal to 0 this propagated here is equal to just 1 0 MW squared and it's never bigger than that that's as big as it gets so the most likely thing that happens is too lenient a alone momentum doubled and if you do it cost you a probability amplitude equal to 1 divided by the mass of the W square the suspended quantum field theory in addition there are the coupling constants so all the net result is that the probability or ample probability amplitude for
remaining NEW and having a convert to an electron neutrino is GW square can't provide by him W square the MW Square is a factor in the spine and Byron W. Devoe from here to here orally steps the biggest share them with serious the thing about this is true this is true armed where OK so there we have to get a little more technical lover and that mostly comes into play Leon very little energy consumers and tuition like this and more momentum energy so it's mostly space flight which means possible we are reaction you would have to worry about this there were a few momentum of the Carmelite but not in that Russia all but still remained a news always small white is it small proton becomes a NATO innovative became the amount the momentum that's transferred from the proton could be from the neutron and proton is minuscule by comparison with massive W. blows minuscule doesn't matter whether it's positive or negative the case square 20 by comparison with mess of W saw net result is that weak interaction on May a week because of the large mass Of the double how large is about a hundred crimes the mess probe time so that means that go with that amplitude the amplitude for this process is going to have a factor relatively small factor from G. W. squared roughly defined structure constants in their 1 0 MW Square which is a tiny fraction squared messes W is a hundred times a proton man's that's a factor of 10 thousand but that's just the amplitude we have to square the whole thing defined the probability for the reaction that happen so that Bernard GW for divided by MW cover for that's a very small number that suitors more number the of the W law that's why weak interactions small not because the primordial coupling constant is small because the the W for whatever reason happens to be launched in nuclear physics on proton neutron type mess your usual units of nuclear physics of our old particle physics mess of the WTO said 1 million workers but G. W. square was about history of something in an hour on massive W is a hundred Proton units that had 4 millions at least for now and it from the weakness of the weak interaction right so right so originally also was known from experiment was this combination always known was a combination and it was called capital Jeannine family experimentally what you measure is neither or by now of course there are fancier experiments experiments in the old days off where you never have enough momentum to make this nominated very very much you didn't get to see the the demand that the Terminator why was was very with momentum all you saw was commerical constant and it was always the same W. bars on their didn't change from 1 reaction to another it was always a W votes are always and squared and so experimentally all you knew was this number G family which is a small number of very small number Arabs with American values its it carries dimensions so told you work it is somewhat tell you in units of the light years per unit there were small number on right so that's always known historically some time and the must then 19 fifties various theories Julian Schwimmer other people began the suspect look maybe the weak interactions are similar to other interactions and mediated by some sort of particle I don't know whether I don't know where the terminology W. came from probably stood for a week and I don't know which way the remark 1st used it but the idea of particle heavy enough that it would make this small number was introduced some time ago but it was recognized pretty much from the beginning that it it would take up a pretty heavy particle 100 times the part time and so it wasn't until accelerators came into being where you could generate that much energy mid seventies late seventies Our where accelerators which could create enough energy generated W particle actually detected measured it Javier W. particle really exist to commit produces getting flat that is at theaters should the residents by boat press this this process works as leaders of the of are the only suppresses the cost of energy conservation nothing or thing can happen In the energy available for half so that's another thing which controls rates pocket rates are controlled by 3 things about 3 things coupling constants man's is of particles he intermediate states like this and also available energy available energy has to do with the energy of the initial state in the final stage 3 different features coupling constants masses all property if you like structure propagated and how they depend on momentum and finally things can happen if there isn't enough energy and it will happen with very small probability of further the energy available small enough so you need be initial states that have as much energy as the final stage in order for crosses happened and the west of the ingredients there Have duel with be it or suppression of the Doerun 3 separate things got off a new the threat is Luo country with momentum distance scale so put but a real W. blows on laboratory has allowed I'll be waiting to let Montana mule deer with black then be electron
energy of the final state must be discerned been due initials but that means there isn't really enough energy to create the W boss he really isn't enough energy to create a W bows that's why there is no real process in where'd W bows on those flying off simply isn't enough energy that well so what does happen they W. blows on His produced virtually according to the rules of quantum mechanics a violation of our energy can take place as long as it takes place for sure enough time if fee amount of extra energy in here works call stock the energy time uncertainty principle set among other things than the parent an apparent violation of energy conservation of EU could only last for a time which cannot be bigger that smaller lenders case clocks you cannot have an apparent violation of energy in an intermediate state that lasts for a time longer than a healthy does of water each maybe another example of the sort of thing is you have a potential when I potential energy this potential energy could be the potential energy of an alpha-particle nucleus an alpha-particle stuck the nucleus can't get out why not because there are enough energy to get out of it has to go over a bump to to get out of the alpha-particle normally sits over here but it can't tunnel Kaunda mechanically From or our them Connecticut orgy particle is always positive right In here has a certain amount of energy it has a much higher potential energy over here this is a potential a preliminary potential function the potential energy is here the particle started arrested had no kinetic energy and had this much potential energy it has the same amount of potential energy over here and the same and is also when comes out of here also comes out arrest comes up here rest was arrest over here saying potential reducing potential energy so I can happen on the other hand if you look at it between it seems have a large potential energy much larger than have over here and I can't have less Connecticut June however over you the kinetic energy was already was over here the meaning of that is that it temporarily apparently violated energy conservation that if you went to measure the particle in here and check whether it was in here not you would destroy the of but if you just look on the outside you'll have to say it somehow the intermediate state electron had more interview was alpha-particle had more energy than was 1st I have who was a violation of energy conservation and apparent or how long can be alpha-particle last under this barrier here he answers it can last longer and the role is if the violation of energy conservation so he built EU then it had better get out from under there and the time which is less than a adultery this is a kind of familiar thing from elementary quantum mechanics apparent violations of energy conservation could take place as long as they last sufficiently short time same thing here Our there is the W boson is very heavy particle there is simply not enough energy in the new neutron to broke par neutron or anything else to create a W blows on let alone have enough energy woefully final particles that cannot happen with can happen use that temporarily for a very very short time period but the neutron candymaker W W minors become a proton but then but then it is as if the alpha-particle warned of the barrier W bars as I can last that long I better get rid of all our energy and could do with a number of white 1 Wakenda was getting really thought the other late in the race is by becoming electron which has a small energy and neutrino which also has a small John the intermediate state here very very heavy W. bows on is very much like the intermediate state in which the alpha-particle is under the battery only last a short time we did In him tissue world no no no no and in even energy conservation from Minnesota final status is always exact cartridge just the funeral for which it is sure that all this is that bad said also that everyone was lovely wasn't it buys that are too a itself also part part of that you know hello yeah never done leaders will became electron neutrinos but if you make a W with enough energy life time for a real W. became upset it's not it's not the uncertainty time there is a certain lifetimes W produced who eventually became but on the festival W is more kind violation will cause but we became later and later so real doubled up produced and real double it you produce things which whose a became the decay probability is controlled by their velocity and stand relativity Our well what health care very short very the W 3 times 10 to 20 27 security was not part of a new set out on that a of is that now a little time to hit rate this this is this is a template was is the amplitude of processed square the amplitude is a probability that this as a probability per unit time it's a probability per unit time ended so it's In verses related as related alive inversely related to a lifetime and that's why this is a very small number the life time is unusually large In particle physics units sold week lifetimes particles which can only decayed for reasons of another by a weak interactions have anomalously longer lifetimes and weighty trace it you trace of of them now if a process that what is
really was case squared plus MW squared off well on right if you have enough energy and enough momentum you can detect the fact eventually that these rates here will be momentum and turnover was effective constantly awhile becomes the 10 case and that of course has seen with great precision so they told lost yobbo to went and their Tricord detectable possibly as part of this is that at ship you could construct something called the loss it would be misleading to think of it the real signal its house is Is there any of if it have to have a staff of the W balls on for example and has a number of ways of became but 1 ticket indicate literally Tecate isn't electrons and banditry and you can calculate the fine diagrams describing it has strategy in it W minus a factor G and electron banditry know and you can calculate that end yes you could compute the lifetime of the we're at a reduced this is the single most indicators were in use it until the last 10 years period W where real W decays it produces an electrode trio with enormous kinetic energy Mary relativistic right it does W bows the rest will become and their mother became modes this is not the only became a condone you want and train on the number of different became awards but if the Cato lecture on train they would be very very real mystical staff that created a furor really really real particles are simply the ones May created initially over the particles which Keane and particles which went out of a small interaction region the virtual particles of mathematical constructs which the internal particles in the finding diagram you don't observe them if you went into that if you if you suddenly tried to observe that article How would you observe that particle the only way you could observe it would be sin something else into the system let's talk about trying to observe our particles of this nature at where even before that what about trying to observe what's happening to an alpha-particle as it moves on to while obviously you have only a very short time enough to want to observer of your Apple observers who want to know whether there was a particle on me here you have to interact with a on very very short time scale you have a very short time scale you if you won't find out for example by looking at it with a full time you'll have to send in I'm very very short wavelength photon ports in particular energy of that would have to be about that big that's of this energy time uncertainty principle set the scene energy time uncertainty principle gives you information about these Waverly and the energy of a photon that you would need if you wanted to have a higher resolution good enough to see what was going on in there as if you are actually see me most probably alpha-particle from here to here which last time don't take your half the fitted with a full-time whose energy was big enough that it actually would not really media alpha-particle into this region he you supply supplying energy and is 1 of these quantum mechanical complementarity things that you think something is impossible and so you try to detect and you find out in order to be packet you'll have to do it the system exactly that thing which you were trying to rule does not happen this is this is quite that it's always the same story and the same would be true of virtual particles virtual particles less small time if you want to get into the system and detect 1 you have to hit it with something with enough energy that would actually create that particle if you want to see the virtual hear how much time you have very short so you had it will default on a full-time sufficiently small wavelength guess what it's got enough energy actually not good W. out of the systems that you actually see a W but that's unsatisfying frustrating neutral in the April 1 thing that you had to do something the system which they do it exactly what you trying to prove didn't happen always at work that's that's quite McCann-Erickson much ground this year and I'm not sure not draw it to try to see for example OK sell arm let's let's 1st got something slightly different you ever get to see the virtual photon so that our presence in India Oregon electron but yes if he had elect not enough you'll knock out there will not be electron out in the bottom of the ocean so you don't get to see them and you don't get to see the virtual photons if you do exactly the experiment which puts enough energy to allow to see those which votes from the W sinking a stroke if you have a proton that Proton W and become a neutron and of course if is nothing else around that it doesn't became the W will have to come back and be reabsorb sickened think of a proton as a sort of equilibrium between a proton and neutron with W. bows on around constantly going back and forth between the 2 of them between the 2 things with very very very fast oscillation enormously fast oscillation between the 2 of you want to see that W. all you have to to do is part of the book on our that has a frequency which is large enough that it can resolve the short kind of W was out there and guess what if you don't hit a proton with a high energy photon yes you will not Gary W. so in that sense you get to see him but that of course becomes a different
process becomes a process in which the W is a final particle not an intermediate 1 rural the vote neutral most profound it could also have neutron goes to prop goes to neutron with W the differences but this 1 would be of W plots and this will be the next year they said they did not above pose free a music the office were language is 1 thing facts are factors at the end of the day there will be trouble you flying you want to interpret that as W that was before and but you knock out orders was in the newly created W well mathematics says but it will be a bubble you on 1 picture of it is that the W was there and you jerk the neutron out before it before we had a chance to get back and mathematics supports that there is a way of thinking about mathematics reps were high on other hand dues is true to vote for the Rajat wouldn't go what do say how well what is it that it build but for him but it look for what will be the 1st to lose there are hadn't plus somewhere the WTO voice at the others where you don't always W some W sometimes you get double sometimes it might get 3 W sometimes made with particle hard enough to get also to John Wheeler article really hard as both China and show you the other nite when used when you try to to think about what is elementary and what's not elementary it gets very confusing because if you take what he thought was a very elementary particle and you hit it really hard enough all kinds of junk comes out and among the juncture comes out might be chairs and tables will you need a hell of a lot of energy that but you had electron hard enough for the really really really hard being stay with much much more energy than for example a mess proton mess thousand protons for example and guess what out of it will come protons electrons all sorts of things every once in a while 1 of those electrons will stick to a proton so you will discover the inside an electron are inside a Proton was up as a hydrogen atoms we have lesson is dumped striker Thierry mental picture of what comes out of a system is necessarily what was in the air before who blew Qian Qichen says it back this in itself does this in itself but the Rebecca energy really has to do with diagrams returned disconnected from the rest just their vacuum but the presence of vacuum diagrams like this further so vacuum diagrams something which also Violet can we violates energy conservation but suppose for electron electron from to electrons necessarily have a certain minimum amount of energy the vacuum has no energy and so this is a violation of energy and that means that that pay only last for a short time OK I would like to see that there so you send in some very high frequency photon or pay very high frequency photons from opposite sides and guess what you sometimes make electron-positron pairs that should time so you not the the hell out of back and flocculation and you discover early discovered that we are a long not been knocked on temperature they they are dependent on particles in your colliding having a lot of energy types of it's a question Olatz say will do with temperature when you have a system at high temperatures it simply means that you have a lot of particles around high energy so that means that typically at high temperatures there are enough high energy particles to cause these things happen but just think of high-temperature resist just having a lot of high-energy particles around small number of high-energy particles you won't think of that as temperature you to say I have particles with large kinetic energy now an example of what temperature canoe is if you have the alpha-particle bound inside the nucleus like that and you put into a temperature back now I don't mean temper mean your bath water temperature that I mean temperatures which are many and he's fine which is zillions and zillions of degrees time but the effect of putting in a temperature you can either think of particles coming in colliding will you could just think of it as no vibrations closing this alpha-particle Jingle around give enough temperature and sure enough gigolo over the top sometimes so sold yes these virtual process be In goose but temperature but temperature resemble the way just what are is it that the the generation that lust the that has not be reviewed to to see any of us but it works
that way this the other plus some of which not shot that part of of it but that there place the W W in this diagram is a fluctuation but it's not fluctuation of the vacuum it's a fluctuation of the protons the approach armed sometimes flocculate and makes a W and neutron you know how half relative arms but not the same thing as sayings on electron In the neutrino and a W let's see that would be a W plus concerned torrents former vacuum fluctuations it's another process where there really isn't enough energy for a happened so what happens in his virtual cents for a short period of time and in that sense similar from different the same rules apply to it and only last for a short time therefore if you want to get into an observer Jack below with something which has very high energy because of the uncertainty principle and the result was the energy is always enough the energy is high enough to see in the air it will also behind enough To create post partners energy has released so get it now but another way of saying is a the basic interaction is always blue ones between electron neutrino NW but just there were pulled out of the How do you could go along he dropped it a always had entered the block now all I just want talk 1 when chopper OK so how much how what's the weight of a chocolate cake with a chocolate cake is really good chocolate cake stands at laser kilogram a kilogram 2 thousand brand switches and for 8 plonk masses and plant that's right if you could accelerate the error particles tend to be a punk messes With a very very very small probability you might get a chocolate cake but dream Michael graphic thing us ways warehouse he for an EU chair and a fair enough that it should be sure as possible with what he has said that book out for a corners which is about 10 to the minus 5 grams so would that people no not really not mess is not the heaviest I'm not a lot but if you're sure where are we you call articles of energy much larger than the plant what you get I was going to say 99 times out of a hundred which make it 99 . 9 and endlessly however were is the get a black hole but every once in a while we're a probability which is exponentially small In the entropy of a black hole that black holes will be made a chair instead of how I know that I know that because the process a big share fully told black hole front as possible and therefore by time reversal in the process of a black hole hitting it chair it it must be possible so it every once in a while a black hole but when I see every once in a while I mean very rare percentage of the time Institute do this experiment the black hole will behave statistically extremely unlikely way but all that entropy use because tricks and basically anything that can happen will happen eventually and so we have Everything that could come out of black hole if you do process of firms sold above so all this about energy scale has to do with Prague are usually food here is not to buy time for the 1st time they have urged I could hurt class this is out there were serious a 1st first-line ritual not succeed your Yamamoto who is largely a matter but not and say it out with a book on the real been you they interact with each other bird yeah but and don't well aware of the fact that both arms is they don't interact with each other or zones premier sale interact with no different in that respect the reason that a photon it doesn't seem to interact with other photons but super interested then photons could scatter now would merely in the laboratory to light beams scattered by photons could do the following a photon can come in another photon come in and they can create an electron-positron pairs of electrons you might wish he plots electron-positron pair well that can happen then the opposite can happen electron-positron pair could become pair of photons and in fact it can happen as a virtual process as virtual process similar to a pair of photons nor out but scatter by means of an intermediate state which is an electron-positron pair now why doesn't it happened in the laboratory with ordinary photo and the answer is it takes a certain it takes a certain amount of energy to Greek electron-positron Paris right each electron has a mass of always of Heffernan they said Our so these together taken immediate of energy if the pedal photons has energy very very much lower than that that there is not enough energy for the real creation of electron-positron pair but still it can happen virtually but what happens virtually there are
propagated in here and it's the same sort of deal as what happened here when your have to supply extra energy for the process that happened there was always cost probability typically the cost and probability is somehow inverse the amount energy that the need to make the process happen so what less process doesn't happen laboratory be cost In laboratory photon energies are always vastly smaller than the massive an electron photon energies or what an electron volts typical photon optical photons electron bolted to the mass electron is all water and the electron volts and so typically the photons don't have nearly enough energy for the process the happened if and when a process with intermediate process happens which has happened very fast comes and goes always Of cost of probability so this process scattering is a very low probability profits at low energies on the other hand the can't hit with enough energy to be able to create an electron-positron pair they really do interact with each other not forgot the original question what they had to do with the leader of arms for the same thing they views true W. blows on to interact each other if had a good rest all they are those arms yes but don't think interaction effectively bars the statistics arm well let's put it this way be effects of the statistics for meal hundreds of is only interesting when you have a situation where you create more than 1 part of it more than 1 particle Lepri knew each other pretty much the same state in most particle physics experiments you create particles Kong flying off in every direction and it's very rare that you have 2 particles Of the same kind going pretty much the same direction in such a way that it matters very much with from me on the Bulls arms but yes some they do interact statistically the same with times our W. balls arms will prefer to be in the same state the same sense of photons preferred principle you could make a laser more and Dr. not likely In principle we could make a system ladies but Stella coalition I can tell by had color now it's all knowledge always 3 quarks 1 red 1 green blue which makes a white what or colorless by black or white because uh this this is a start rarity Proton however the but so it's to reveal that Barry the produced respect much of the they were that is this place that it will Yao will get to it don't get to it in the context of the Higgs boson on young pigs balls on place where something like Moser condensation happens around I did have 1 nobody has asked me to bring you up myself what kind of group structure could reimagined which would mix be off Call it removed our report of quarterly underground work the charm quark strange quark just to get him just off court and work they go into each other by W. what group could we be be talking about other talking about to Lira 2 elements here and linking the the other at the symmetry of the year of the system for talking about us silver having generators is assumed to have that has 3 generators each generator be Bowl sons are in one-to-one correspondence with me would be generators somewhere worked 8 gage bows on illegal ones is 1 image generator 2 to 3 we only have to to gage bosons W plus W. mind but we're trying to postulate that this is the theory based on the symmetry as you tell missing something and Dili are missing 1 gage votes is not a photon it is not the photons figures closely related to the particle called busy on a 3rd member of the W family W. plants W. and they will come to an please streamlining begin to talk about the relationship between electric charge Zeeb ozone as you too so for that to come back but I around our I was going to talk about getting too late now that it's getting too late to do almost anything the other day I have to talk about tonight was spontaneous symmetry breaking let's talk a little bit about spontaneous symmetry breaking just qualitatively want tried quantitative just qualitatively was spontaneous Herbert on I think the best later describe it is but illustrating is a famous illustration which is in a sense of spontaneous symmetry breaking a birth the main thing is that helps you locate the factory somewhat correct on the famous example and people sit down to dinner and go around a large table and each person has the left of them a fork in the right of them personal after their arrival for nobody knows whether to go for of West West for right for you should vanish if they sit there and they can't decide what to do until all of a sudden 1 of them true motion for the right for work and they all go right for it was nothing asymmetric to to begin with but there was a kind of instability was a kind of instability Our 2 possibilities and instability and instability being such that instabilities kicked off the whole
universe speak suddenly goes 1 way instead of the other way so I will give you an example are mathematical example of felon magnet is an example of spontaneous symmetry breaking but let's think let's start with a very simple example a simple example is Pa a bunch of spins and spends can either be all out or sorry spends can even be be up or down for the moment it's not even important that we're talking about quantum mechanics these could be corn classical corn and army of the coins can be up put down their laid out on the table in lattice he is and as an interaction energy between neighboring coins and the interaction energy is such that the quality of the neighbors are opposite for example I heads and tails that cost energy another words as some kind of force between the particles In the course of coins so if are composed that cost of energy if parallel would cost less G so they like to be parallel energetically they like to be parallel but opening this way or this way and that Carlo this way for this work and that cost will reduce the apparel nothing about state of lowest energy What is the state of Lower standard the stay most energy is obviously all here or old payout period to states of lowest energy wall had all tales which 1 is the ground-state that both Gorham states but now I suppose weighty far away offer a hundred miles away 1 of the spins is known to be haze that will is asymmetric will normally under most circumstances you would say just 1 degree of freedom very very far away has no effect on 1 of the properties of the ground state are far away from that degree of freedom typical expectations usually true almost always true would narrow but in this case that 1 ahead will cause the ground-state energy to be different if the role heads and the role tales of all had been you'll save 1 unit of energy and so in seeking its ground state this system will tend toll heads rather than all tales once a hands then you could forget you couldn't I want to toil heads they start over again and say lot the legislative assistant was all heads will cost me some energy to put paid there because it has 4 neighbors which are a chance to make it had so the result is that this kind of system although it started with the symmetry starting with a cemetery had ghost tales at asymptotically very very far away boundary condition or just a very very distant degree of freedom tip any instability and put the system into 1 of the many possible in this case only 2 possible load ground states wanted a state then the properties of what goes on in here are determined by the ground state in particular I Taylor will cost you energy because of the presence of or where this is so full and primitive most from the example of a spontaneous symmetry breaking how was it different than just an ordinary symmetry breaking what ordinary symmetry breaking beat me or annually symmetry breaking or we could call an explicit symmetry breaking would be a symmetry breaking if heads headed different energy jails not paralyzed energies but just 1 hit by itself supposing that 1 hit by itself had less energy than the tail then of course it would be completely obvious that the system would be its lowest energy state be all heads and so it would be also the case all but they would be no 2nd grand state in which they were all pair it would be biased but energy will be biased by the energy not be 1 extra particle infinitely far away but by EU local things going on so that would be a on our on a bias situations where heads and tails were not equivalent to each other not energetically saying and it's not a spontaneous symmetry breaking its just no symmetry to begin with or explicit symmetry breaking is there is a difference between explicit symmetry breaking and spontaneous symmetry breaking yes there is there is 1 phenomena that can happen when this spontaneous symmetry breaking that will not happen if is exposed to breaking the phenomena is called domain walls the domain wall is what happens if fora layout here very very far away you insist along this line here that everybody's heads way out here assume that everybody tales what then is the state of lowest energy and this state of lowest energy issues Everybody on side tales everybody in this site heads an aide found in between where heads go from tells content from the boundary where you go from Paris to call domain so the presence of domain wall and this would not be the case if you had explicit symmetry breaking explicit symmetry breaking in the state of lowest energy which just be all heads Courier would care about would much that fewer so spontaneous symmetry breaking in this case the signal of it is existence under certain circumstances certain kinds of experimental setups would lead to the existence domain walls were on 1 side you have 1 thing on the other side you had the other than the presence of domain walls which would be the signal that there was a spontaneous symmetry breaking so this is a basic idea of spontaneous symmetry breaking a symmetry of the system but with instability a year instability that kickoff by going very far away just fiddling with something very far away and that will fix Everything said signal the signature of it is the existence of domain walls next time we'll talk about other kinds of spontaneous symmetry breaking our and come to the Higgs phenomenon are makes number is a number of spontaneous symmetry breaking will talk about so I just keep just keep this example in March for more
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Metadaten

Formale Metadaten

Titel New Revolutions in Particle Physics: Standard Model | Lecture 6
Serientitel Lecture Collection | Particle Physics: Standard Model
Teil 6
Anzahl der Teile 10
Lizenz CC-Namensnennung 3.0 Deutschland:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/15083
Herausgeber Stanford University
Erscheinungsjahr 2010
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Physik
Abstract (February 15, 2010) Professor Leonard Susskind delivers the sixth lecture for the course New Revolutions in Particle Physics: The Standard Model.

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