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New Revolutions in Particle Physics: Standard Model | Lecture 10

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yards but but just for a moment stopped and their world next time I'm not tonight I will get 2 1 of the key puzzles purchase called the gate hierarchy we may I have branded my notes we may get to a specially since I'm getting rid of the year the review on but next quarter I want to study some of these paradoxes paradoxes but difficulties of the theory and how things like supersymmetry related how supersymmetry may or may not solve some of these Our puzzling features of the theory how unification what unification right now we have as you 3 we have as you to Italy have you want I'm talking now about the forces weak electromagnetic and a strong these somehow sit in some bigger structure is they were groped for example which contains the subgroups you 3 you too if you want I haven't told you what a subgroup is but you could imagine our is there a bigger structure bigger mathematical structures that contains as you 3 as you to a new 1 that is a subgroup there's a group called S fine and those a lot of interesting evidence that this whole structures described so far it's very very neatly into an as you find structure which quirks and let times are all part of the same multiplex will talk about that supersymmetry unification and the various puzzles that arise and I will tell you a little
bit about what LHC is
cooked up to discover about 1 thing the Galaxy was cooked up originally to discover was of
course the Higgs boson our Biggs bows on discovering the Higgs boson I'm not just discovering the Higgs boson for example the West is more than just discovering the existence of a particle also involves our whole hold a bunch of properties of this particle which are all related to the fact that it is a big smiles on for example I showed I think the last time how they Hague father-son Hanks phenomena is related to be masses of so we looked at the Dirac equation instead of looking at the Dirac equation we might have looked at the grungy and for the Dirac equation I idled off Weaver wrote down the Lagrangian for the Dirac equation I don't think we get let me right back to yell we did decline for the Milan bound for you operatives see refer strikebound direct equation 5 derivative with respect 2 x knew of the perimeter with respect the kind of society was a minus plus I don't remember plus derivative with respect to O X Y where X a body x y z kind how 580 SIA be off I have here I was set that equal what times the maps right hand side that was a Dirac equation let more everything over the left hand side but added value migrate my greatest mathematical discovery in only the equal sign Rashid I feel that discovery of I will call tho or lack of repair but this is the Dirac equation no surpassing I wanted the right this Dirac equation by variation with respect for something in particular it happens to be but area with respect to very easy way of constructing a Lagrangian such that when you very with respect size star is the Dirac equation which out all you have to do but multiply Dirac equation by sigh star site of sigh star ballots not now it's not yet still 0 but there but now it is not the Dirac equation it's still a Burundian the Dirac field where they have lived it has turned loose sigh dagger derivatives aside those are the kinds of things which moved a particle from 1 point sure enough members the client Gordon equation the candidate turned was associated with the hopping of the particle from 1 point to another that's what these terms are it absorbs a particle and moves to a new point of space time that's what the derivatives to move it to a new point of space time at the same time they do go it's been a certain way that's that's what kinetic things are and the terms it is just a term which takes a particle absorbed that any makes it from a point of space with no derivatives at all because it is more absorbs it and it's from the same spot that's still a grungy and for the Dirac equation up and its young the but no no no no brokers our guards you asked me if I had use that language but I will now use that language now but just for those who are curious the local variant language if you take site and you multiply by data that gives you something that's called a sidebar if you want to get back from sidebar society you multiply by beta white because data squares equal toward so you can write this you could rewrite this in the following way you're right sigh bar data at pesticide Debye IDT and then he'll always have then we will have a plus sign by alphasub piety derivative with respect to x abiding sigh and they about this 1 over here but they got this 1 is going be dagger at Vader and sigh what were the shit sidebar In the site and sigh Boren and plus and sidebar site now we're fighting the of these symbols Wickham call they Gammon not why not because it's connected with you know what usually refers to tie B for coordinator time of 0 component and 1 2 3 4 space says 1 called Gannon not is sometimes called the fact most frequently in modern physics the Alpha Beta notation mostly abandoned and use gamma so this becomes sigh Darren North beauty and this 1 now in a change the name they had tightened Alpha just a product they that turned out far off or the Caltech sidebar cannot citing plus and sidebars best on June and now has a very very neat for you could think of gamma nor Beebe IDT is being gamma North Deeb IDX nor is gamma or debate BXI that looks like a nice cold variant so far for vector product of gamma matrices times derivatives Nova were to correct the whole thing in the form of sidebar gamma new Deeb IDX new quality baby meal now new goes from 1 before plus end sigh OK that that's Mike Shaw the more elegant than the original form the Dirac were down is also the officer invaders a call Barak matrices began as a role so-called direct so I wore here were auto factory all you have to remember those at sidebars not side Decker its site dagger with extra Gammon but this is the the elegant form for the equation In fact sidebar side he happens to be a scalar and sigh sidebar gamma society is a force that has index mule so this is a more elegant way presented Dirac equation do Dracula grungy and the Dirac equation is just setting this equal to 0 Dirac Lagrangian looks like now from this point of view let's just examined well let's examine the various terms in the 5th direct
matrix anybody know what's called gimme a fire but missing cannot for his knowledge of what the heck that it's a a which is another 1 more gamma matrix which is called again 5 which happens to be the problem of gamma nor demo 1 endemic to gamma rays modem of behind our happens to be 1 more matrix and in fact the eigenvectors of Gamma gamma 5 also we put the 1 it has the wagon value plus 1 minus 1 and a 2 0 eigenvectors eigenvalues correspond left him the right-handedness were of the particles gamma fibers called Hill city Excuse me because around beat him there's a role for him a cut where was a Greek word for him Cairo on Cairo's kind of some of the current series CHI are around identified as called chi Rallidae amicably plus a minus 1 and co-sponsor the handedness of 2 particles now if you work it out if you work at the various things you'll find that this show that he does not couple the left-handed and right-handed components of cyber left in their right here into components of size means the things will eigenvalue plus 1 and minus 1 Gamma tried but just think of them electron guns or particles with right he did the Silver City are left-handed helicity these 2 0 here are these for here do not multiply left him times right here just happens they don't work out from by yourselves this would does sigh bark time sigh happens to be happens to to be happens to be society dagger left side right lost dagger right so I that's what so the Mets he mixes up the left-handed and right-handed particles that's what mess is a Dirac masses terminal of seemed weird that it said had anything to do with our with them inertia it's eternally which causes a left-hander Fermi Hunter flipped or writing the firm flipped off left-handed for me and so forth and that's what where he and the other terms don't do that so that means a massless fermionic has a definite Chi rowdy the flips the Cairo back and forth back for what column yacht I'd we talked about a class of interaction of the weak interactions let's put that particular focus on a Z in the emission and absorption of Z both times that is purely left-handed for some odd reason for some odd reason our busy bows on only as by left-handed particles not by writing articles is not sure the photon this is only true busy bars I'm sorry B W bows busy bows out of the little more kinky it there those has asymmetric couplings left him right on but let's focus on W Tuesday coupled so only the left-handed there are degrees of freedom so that means that In effect with respect to the charges with respect to the transformation properties under the SU tool connected with W with W. balls on the left-handed for me honest charged and the writing in different eras you not allow to put in Lagrangian something like this which would take a charge particle 2 women charged particle would mean a process in which a charged particle we come in get absorbed and on charged particle while violates charge conservation so this would not be a legal term in a Lagrangian that having a gage symmetry which only coupled the left-handed particles are right and the question is how do you get a mass of and we know that electrons in their quirks they'll have messes something wrong here is where the Higgs boson on comes into play the haze bars also plays the role of rate charged object with respect to the S U 2 of the weak interaction in fact it's a double it just like electron neutrino are doubly the Higgs bosons also a public I didn't emphasized that I'm not going to emphasize that skirted around it saw the Higgs boson on also transforms under as you and roughly speaking on the way to make this until will legitimate interaction Mr. multiplied by the appropriate Higgs Barzani on field here the Higgs boson if you like fairies carries a week charge which is in the same opposite depending on which comply with talking about as leader as two-week charge of work save electron before talking about electrons to the right here in the particle has no charge with respect with respect to the weak interactions so we have to do is put a hand bars on here and he daggers he this means the emission of a pig's bows on ammunition and that he expose on like with the Higgs boson carried off the charge the left-handed particles when it became the right particle so we introduce until a year into the Lagrangian something which takes a left-handed fermionic emits a right-hander from but also allows a Higgs bows on the be admitted in such a way that weak charge of quirk or whatever it is 5 escapes in the form of bags bars on the Higgs Dublin that would be the end of the story except for the spontaneous symmetry breaking which has to do with the Higgs field of getting an expectation value the Higgs field mobile we call the fire last time and in course of 5 continued to qualify William edify particle here that won't be the end of the story except that for whatever reason nature Harris chosen the energetics of the Higgs field is fine here have 1 of these Mexican Hat potential energy White did it do that why did nature do that we don't know the very lucky that it otherwise In chemistry regard and turn things would be very very unpleasant but with 1 of these upside down Mexican Hat potentials that means the fog is equal for a number of just the the magnitude of the Higgs field here which recalled death plus of fluctuation fluctuation away from that value and that fluctuations will we actually called the Higgs field
so let's go back now where evidence this tournament what happens to these terms in the Lagrangian they break up into 2 basis a piece of places but these 2 pieces 1 of them is all I left out 1 thing would leave this expression the numerical number G new-car coupling what's corgi so why and different G sub each firmly on these 2 should be saying IG symbolizes the number a pure number carries no dimensions the court you Yukon or couplings and where they came from somebody wiser than me into Lagrangian so who they are now let's use the fact that former is equal Poland fluctuating part was recalled for the month fluctuating part we could have done and for the fluctuating part we called it she the Higgs both that's not my notation that that's standard notation service becomes GUY f times dagger left side right plus so better right side left plus GUY Higgs field I'm just saying saying the same thing OK now we have a prediction for what the number f where that came from from the number F we obtain same number ever went into the massive boats on the shift of the Higgs field also determined the of disease W. wants to measure the mass of the CNW bows this was done in a long time ago they were measured messes measured about of water a hundred GDV 90 duties that solved that told us work at 4 that told what with the number at 4 hours as his a number of about minute 200 GUV for F pace that's a number of summer has units of message F. has units of met 200 but once we know that From W 4 6 then from the masses of the firmly on the Camilo what you call couplings are once we know for example electronic power coupling is some very very small number wide because the electron much lighter than his Ian W. B. you call coupling for the top quark that's a large white because top court is so heavy so the is over works wind-up being is you can't couplings fund S and Southall we've really gotten now no more than we put it that no only put we got death from well with a little bit more but basically masses of Z W system we got F and dated from the masses of the Fermi aren't we got Yukawa couplings of that was we were put in as much as we got out but now we also have something else we have GYA Higgs times things like that's just coincided that these terms in Lagrangian which take a Fermi and this could be electronic could be a whatever happens to be which take a fermionic absorb it and readmit it plus a Higgs boson so these event process to use let's say electron or it could be new 1 or it could be a pound or it could be sought quirk you mix any Higgs vows it could be a explores aren't coming along and Dick Cheney until an electron positron saying diagram so wants the Higgs boson materializes as a particle in a laboratory we should know what the various Tecate decay rates are referred to decay of the different kinds of electron-positron electrons new ones and that new 1 or whatever we know all of the interactions between the Higgs boson on and from and of predictable decay rates although Higgs boson decay rates obviously it'll prefer to dictate heavier particles close enough energy because these Yukon cup wins a larger color couplings of the coupling constant for the Higgs break up and cooler its constituents it into its decay products so at the moment I mean Higgs ology is a year is a pure feeling and sense that predicted by the theory there seems to be no other way to make it mathematically consistent but neither the Higgs nor the direct couplings these particles so of detected that will happen what I hope will happen is a lot of predictive power also are already has an enormous amount of predictive powers predictive power in the interactions of this season double which are experimentally detected the interactions disease W is not only with respect to the firm eons but with respect to each other sees it a town that law that the couple plan you calculate a finding diagram Our you could just think of it as elementary quantum mechanics this gives you a turn in the Hamiltonian which takes the Higgs boson onto a pair of particles and it just gives you the transition amplitude which square I want to squared you integrated or summit although although a final states integral to do and our vectors used to Kittery it's a standard calculation that it is basically a finding diagram if you like this gives you the amplitude square the amplitude to get the decay rate squaring the amplitude you could do do but putting is right on top of it so that he and the amplitude square and that becomes a finding by calculate the fine diagram but finds rules and 1 of the things that comes out case so what this a more thorough to hear that have to do so it's it's a very very definite calculation in standard quantity of the calculators you would be doing since 1930 quite what they are things that you have to put in which the values of the coupling constant masses of particles OK so that was the less a firm eons investors are via Ian W. bows out and all of them being proportional to its constant f where we talk about the air of a Higgs itself spoke about the dynamics of the Higgs boson the dynamics is really
all contained but In this Mexican Hat potential the minimum of the Mexican Hat potential tells you how much the field shifted and it tells you what effort you can't make up different potentials her have is a favorite 1 which actually has most important theoretical significance but and it goes as follows a let's go to the origin over here at the origin of the Higgs potential is a sort of upside down parabola let's forget what it does far from the origin let's just concentrate on near the art an upside-down parabola means something like mine let's call it news Court 3rd 5 square and its traditional put it to him just traditional might miss because it's an upside-down parabola remember it was fast you sweat as good a bicycle it what would you close you call this time the mass of the Higgs boson our Newark all new mass of the Higgs boson Will you really called New Square the square of the mass of the Higgs laws making it negative is a little bit weird it's as if there was an imaginary mass for of the Higgs boson but don't want nothing wrong with it it's perfectly OK that a potential which is upside down and the only thing which is unusual about it is putting the field at the origin is not a stable position it tends to Rohloff roll down the hill whereas if maelstrom was positive it would oscillate about the part about essential position he thought the field was not oscillate about power because of this my script now if William I was minus square with Rivera and down and down and the field which is run away to infinity it would be no ground state system it would be no vacuum Iowa Back in his state of lowest energy bill would be no state of lowest energy so it put in something to keep it from running away to infinity we better put something turned it off both thanked turned up this class Lander land that is just the number of pure number times fight fighter before why do I wanna but in fire when the flight fight the vise of the 5th 1 out odd powers because you are the keepers symmetric on both sides this was an important aspect of this potential was to keep it nice symmetric fighter before symmetric 5 Cuba's not this is the next thing you concluded Yukon put all sorts of things the higher powers here is not so important but not so important the most important ones by the 4th and expanding the potential on a power series it don't put in more but this is the most important thing fact it's also traditional perform over here you'll see why in a moment a tour here in a 4 over here what is this number this number is called a quartic coupling constant quartic because fight former if shares it is dimensionless it's a pure number we think we know something about that pure number not from direct experimental the evidence but from a lot of indirect evidence and what we know about that number from somewhat indirect properties of a weak interactions is that it's small but not absurdly small probably about a 1 per cent probably about an hour 1 . 0 1 or something like that compared to the numbers will be thinking about later this is a number which is of order of magnitude 1 is not enter the miners 20 and minus 15 are anything like that so just think of it as a number for the moment of order a warm and it's also dimensionless mule is not dimensional dimensionless has units of a man OK now China find out what that is the position of the minimum he always have to do is minimized this with respect fight we cooked up so that would have a minimum 80 rapidly falling quadratic terms and then taken over by incidentally near the origin this is smaller than a strike fighter the the more of them by square near the origin so this was not got much effect New York it picks up speed and eventually becomes much bigger than 5 squared large fire so that turned back OK let's just find a minimum of 5 sorry the minimum of b With respect a and that will tell us how much the you shifted but that's easy we just differentiate with respect defying the derivative of 5 squared to fight that heats up the food down he slept with the Sudan that minors New Square fight is is a derivative of vie with respect the fight plus land which is a member of order of magnitude 1 fight Hugh Elsa support before down here so it would kill for when a differentiated with respect to fight before set that equaled a 0 0 right now we can divide by fight divide clarifying supply squared away we get we get fired where there is equal to from New Square overland again land that is an ordinary number I don't think of it as very big are very small this is the value of flight at the minimum it's also called f was also the shift the field f SOS squared becomes New squared over land again emphasize land that is not the interesting numbers here it's the common garden variety number like go like go 1 10 or something like that that's not very big that's for sure on is controlled by a new NF is also approximately the mess overseen the balls busy W. Barzani on it's also the thing which comes in the mass Of the fermionic where are they all of the particles have NASA's proportional half square so it's mule or ask for new which is the controlling factors which controls all of these matters while all this is what will particles we know about focus that raises an interesting question wine follow all of the particles that we know of our controlled by the same phenomenon namely why aren't they particles which have masses with spontaneous symmetry breaking can certainly make up a fury of such particles for example just make up a particle was left-handed and right-handed components both have weak charge that we have no reason to put the fight and we would but the fire and you could put any mass that you like in front of perfectly
symmetric so if there was a particle on which was was left them right here in their components both interacted with the weak interactions the same way they could have a man's which was not proportional all kinds of other particles gold particles that don't have any weak interactions role if was such particles could have a could have masses which are not controlled by the general thinking which will come to which will come to explain why the general thinking is that the natural scale for particle physics is enormous much much higher than the masses of any of the ordinary elementary particles it's thought that only this 1 number that is the unusual number in physics very very small mass scale Jose origins present on not but was thought know are explained as we this quarter next quarter various points the idea that really only only mass parameter only small mass parameter in nature this heater and those particles what would by necessity have proportional to white because it's in the nature of their mathematics that they would have to be nasalis if there was no shift of only those particles of light enough to be detected at present that's the believe that's a very widespread belief that there is a good reason why all the particles and masses proportional because any that don't probably have masses which are much much larger but still have to explain the smallness of F for small compared to what well that's an interesting question small compared with what what is natural Ms. Gale of elementary particle physics so that's where I think uh we want to go next at 1 possible men's yes yes our pilot certificate brokered a break in 2 minutes but yes 1 possible mess which will talk about a few minutes after breakers plant mass another so-called unification that's ritual sure your on these masses are typically 16 or 17 orders of magnitude to rally around 15 orders of magnitude heavier than the mass than the at 15 orders of magnitude heavier than his bows on for example so what were left with then is a puzzle why is F. court to be sought more once we can understand why of quantity is so small it drags down the masses of all the other particles it trades and then known simply because they cannot have our other than proportional that they would naturally be worse in a world without bumping his record-breaking yes given that yet that's right effort is a number of about 100 GVT like that says a lot of of Mass be other mass scales which come particle physics which we know about the other possibly much more fundamental mass scales much much heavier than 15 orders of magnitude but there's but no no we discovered obviously no yes of course was predicted for why do we predict and 15 orders amounted to higher the shortest when now when I say that there are than their skills it we know that we know about the question is where we know all about that but we've never seen never seen them we see particles of man's will talk about that at the break In incident the capture of dead cannibals also said that worried about himself he might get yards right sir you U.S. about both countries so a bows a condensation or more precisely super fluidity which is similar Tobosa condensation that condensation of helium atoms helium atoms if helium atoms of course not elementary particles but on some scale they are elementary particles tourist you're interested in in the scales of water molecular size helium nucleus is an elementary particle and they can be described by a field that field naturally in ordinary vacuum has the value 0 discussed funding to know helium atoms present spontaneous symmetry breaking can happen which can shift the value of the year of the helium field when that happens in the same way that f was a shift the video of the Higgs field what happens at roughly speaking a called a Bose condensation Moser condensation happened spontaneously breaks a certain symmetry and as called and preach superfluid but if we helium Adam were charged if the healing nothing Ewing Oakley helium and if helium Adam were charged it would behave like pigs bows on and make a mess for the photo now ever happened anything like it never happened yes it does in a superconductor electrons pair up and bind together in the superconductor very weakly bound pairs and those pairs of electrons have charged to the not helium atoms in neutral here the Adams a call Cooper pairs and had bound configurations of electron electron-positron electron such a they are not very far separate space separate the opposite ends of surface right not think of particles 1st approximation think of them as particles that charged particles and then they condemn they dance which means the field for this pair of particles that shifted you would think of that period field is really just being the product of electron field with itself describing to electrons play the think no object which carries charged to when that field shifted it creates a condensate of Cooper pairs it creates a kind of superfluid before the prepares but it's now a superfluid of charged particles becomes a Higgs phenomena course superconductor man the Butler Ind Center every possible way behaves like the Higgs photons gets mass start trainee training because the the scales of so terribly different but Beyond Compton wavelength of the year of the a photon becomes finite end it behaves very very much like this like spontaneously shifted Higgs field and factor phenomenal was 1st discovered in the context of Our superconductors and was really discovered entirely independently by by pigs and other people OK let's break when you
begin the prime ordeal description of elementary particles you begin with Lagrangian and in the grounds in their of parameters such as masses of particles charges of particles and their the input on the other hand they're very rarely if ever the actual measured quantities measured quantities but you actually measure are usually the product of all kinds of interactions of things take place I love between high-frequency modes of the system and low-frequency modes of the system which renormalize or change the values of the parameters that you associate with experimental observations as an example His electric charge so let's talk about that and how charge between normal life is not going to to do any calculations calculations you have to go and get a book In Bourchier forward but the amount of among others it is a fairly simple warned reps well not it occurs condensed matter physics infected just occurs in classical over on electricity and magnetism associated with our electorate what's it called the high electric thank with a dielectric materials and conductors how beat actual observable Sharp normally are observed charge of an object is defined by the Ghulam law but the law at large separations the asymptotic can't force between 2 charges when they're far apart and that forces you well know it the product the charges of course you want to look at 2nd to be equal charges and particularly suppose they have the charge of electron just simple as he squared divided by are square adorned the potential energy just escorted by I think that charge as far apart as measure charge related reserve force between them and 5 Any Given distant it will not be precisely given by this formula but you asymptotically seperate them and you find asymptotically with respect the are the force between them the potential energy between them goes like he squared off attractive floor opposite charges repulsive for what charges authorities if you like the charger particles called long had spatially very large separation now if the material you do this you take charges in a material or even just a and you separate them and see what we forced will find that's not exactly given by the formula in which you go to the particle physics table of particle physics table particle properties reel off the electric charge of those system typically you want to read off the electric charge of with chunk of material but you might happen electrons Armenia and any excess protons electrons are in it so you might know it's charge in units the charge of electron upon a new discoveries no the force always a little bit less than always a little bit less than that unless you're an absolute vacuum an absolute vacuum completely empty space by definition electric charge forward to measure by measuring the force of a large distance know what it happens in material are let's begin with the conductor With electric after what happens to a charge of put into the conductor well the charge creates some electric field examples deposits plus charge it creates an outward electric chair electric field the electric field creates a kind the current uh the current starts charges movie and still the charges completely discharged into its completely discharge in other words until current tour charge has gone out of the boundary of the conductor Abacha bath the floor charge was stopped full charge follows entail he charged objects strongly charged object over here charged flood flows away from it collects on the boundary but with put the boundary off an Office of Tourism place course an opposite charge was plus an opposite charge cloud is found around it it completely discharges it so that outside normal electric overall and no more reason for the charges to flop that these charges are of course bound to the charge the positive charge the whole thing forms a neutral structure that you take another negative charge over here at exactly the opposite thing will happen to it will create some past charge around the same deal the charges will flow until it's completely neutralized and they take these 2 charges you thought you had the charges to begin with you evaluate or measures the force between them at large distances and you find out that there is not so the charge that you put In to begin with is not the experimental charge at the end of the day the experimental charged today in this case just . 0 no I happens and you start willing to charges but suppose they really small and you start moving them closer and closer together pieces it must be body really small and particularly the smaller than the clouds around them the former clouds around them are controlled by various properties of metal and so forth the electrons moving the metal matter making these charges even smaller we bring them really close together we bring them so close together but the screening cloud that please get between typically a scale for screening quarrel its control of love by dynamics of electrons in a year and a half in the system and the screening cloud of particles making up the screening Clark typically have a certain distance between them and that distance controls the size of a screening cloud when you bring these 2 particles closer than the screening cloud longer screen actually feel each other's role basic charge and you see that physical long force between them which is usually a squared off so you could say that the charge of electron of a charge the particle in this case is really a function of distant in the case of the conductor he of Oregon Zero and very large its whatever they would be charged the particle is a very small arms and the 4th instead of being just plain he squared of hands he squared files all are divided by the definition of these quite a lot of like I don't put anything new into it by calling 80 square of but it does stamped with it's called the running charge running as a function of distance between OK now what happens if you have something less extreme than a year a conductor for example of dielectric dialectic of you like has electron which are bound to the Adams electrons are bound to the Adams but they're free to shift a little bit like an almost think of
electrons as being on Springs where we 1 end of the spring electrons attached to it the other end of the spring on movie of the ion positively charged I'm
on attached and ordinarily electron moves symmetrically vibrates symmetrically Of course is not really a good picture of the matter but it's good enough for our purposes electron oscillate vibrates back-and-forth symmetrically about years so on average the dipole moment of these Adams 0 but now put the adamant to an electric field and what happens is the electron clouds shifts a little bit just a little bit leaving the dipole left all of our offer current doesn't flow charge just shifts a little bit because they're bound to be a radio ad OK so now what happens if you put a charge into a dielectric while a very similar phenomena happened but suppose we put a knife discharging all the ions are heavy didn't move very much but the electrons which abound them by Springs move out away from me are from the central at what is leave that leaves a little bit of plus charge but doesn't completely screen the charge screens some fraction of the charge so that if you look very very far away from the charged particle you'll find that be Field electric field is diminished by a certain fraction but it doesn't go to 0 very far away the fraction controlled by dielectric constant dielectric constant will tell you were how what these with discreet so again you'll find that a large separation plus charge in charge don't satisfy the expected Coolong you might expected from the actual but call the Bayer charge of these particles but it's diminished by this but this effect could
diminish the global mark is correct but with a diminished value of the charge so in this case you will also have a square of our of again if you bring the charges very close together so that they within the screening cloud then you feel the full strength of their charge so again he square is a function of arms in this case it would go to 0 infinity it would just go to some constant fraction of the original charge again the concept of a running charge right now exactly this really is exactly the amount happens quantum field theory of the origin of it is the payers but quantum electrodynamics quantum let the dynamics of the vacuum is full of electron-positron pairs of final diagrams where electrons positrons created by photons you just you just electron-positron loops with no with no photons and they inhabit the factor if you like the other way you could think about was you could think about in terms of their acts negative energy see vacuum is filled with this negative energy states or you could imagine that there are electron-positron pairs where happens when electric field comes along the electric field will shift the positrons warmly and shift electrons the other way so that every little virtual PARIS electron-positron pair will become polarized polarized exactly the same way that Adams become polarized by electric field plus charges shift in 1 way the minus charges shifting the other way that's what happens in the vacuum when you put an electric field of 5 OK that that's a step warns that number will cost you put in what you thought was an original bear charge of magnitude he charges in the vacuum rearrange a little bit of vacuum is basically a dielectric it's basically a dielectric charges shift a little bit in such a way that negative charges are screened by a little bit of positive charge from these virtual Perez and positive charges of screened by a little bit of negative charge the upshot is the chives felt that a large distance is not the same as the numerical value of the charge you put in Lagrangian which is usually called the bear electric charge but again you start moving electrons closer and closer to to each other and at some point they get closer and the size of the screening cloud but 1 difference in this case in this case is theory it is no set distant that electron-positron tend to be from be separated by the Reichstag is that the separation between electron-positron Paris depends on their energy half behind the energy of the virtual pair of closer they will be so there will be electron-positron pairs which form relatively big what's called Adams and not Adams what's called a comic crowed neutral system they will be 1 of higher virtual energy which is smaller ones of yet higher virtual energy which are even smaller ones which are higher energy which are even small pocket so what happens when you put the charge on and and bring another charge closer and closer and closer at 1st you will bring them close enough that they'll be within a distance of the low-energy virtual pairs the low-energy virtual pairs will no longer be able to screen the charge so the charge will look a little bit smaller so I'm a little bit bigger than would when they were far apart why when they were far apart they were completely screen that completely screen but they were screened by all possible virtual pairs bring little bit closer the low-energy virtual Paris which has a large separation between and you bring that charges closer than that of the low-energy virtual pairs on a longer important and screening but the higher energy virtual pairs a spilled screen to bring a little closer beach higher energy pairs fall out of the the equation because they are too far apart And yet higher energy once a store where the effect is that that East squared up all art is a function which keeps changing in changing in changing with Our it doesn't stop changing at some small acts in particular small distance the closer and closer you bring electron together the larger of the charge will appear to be so if you with the plot B by virtue of the fact that they appears at every possible energy in the back so at a plot electric charge as a function of radial separation let plotted as a function of inverse radial separation in most real separation is like energy closer things aren't together behind their energy so let's plotted as a function of our universe separation 1 art which is also related to energy momentum whoever then electric charge accused city will increase increase very slowly and factor very slowly logarithmic increase it doesn't increase rapidly that's why it's very hard to see an experiment some logarithmic gradually increase of the size of the size of an electric charge as you study smaller and more distant phenomena that's also true for example electric charge comes into calculations of scattering electronic scatter electrons at a low-energy they only get within a certain distance of each other behind the energy use can this closer those electrons can get to reach other by virtue of the uncertainty principle and when you do the calculations you have to put in the running short or if you count refused scatter electrons of enormously Holly energy they behave as if they had a larger charge there were small so that brings us for the idea of Running charge what is the fundamental charge what is the most fundamental value of the charges in the 1 of long distance is not that's the 1 that controlled by all of this complicated screening taking place as you get as you get the small and small distances you sort of peel away the screening cloud and smaller and smaller distances you peel away more and more of the screening Clark so freely at the smallest distances where the basic parameters parameters of the deployment of
Lagrangian the Area charge manifests itself yacht love Well you start seeing the measurable effect and but a high-precision measurable effect and a few times at about company wavelength of electron so upset Kendall minus 11 cent Compton wavelength of electrons sound of electron Heffernan EVE so Oh that's by 10 to the minus 11 centimeters and the miners let you start to see you start to see the running of the charge photo for a while it would keep going on if the physics did change them very small this we don't know what the physics at all factors right that's the we don't know what happened responsibly can only extrapolated not a roof wants study of the end got us where that's a more complicated phenomena more complicated phenomena that closely connected with the fact that blue ones interact with blue 1 and because once interact with glue on very nonlinear kind of way the effect is actually the opposite is I you got the infinitely small distances measured infinitely small distances the interaction of their electric charge but you'll never get that fairly small distances because I no it doesn't asymptotic greatest kid growing growing growing up the right right going on until something happens that was not taken into account by these calculation what could be a smallest dissidents in the world plant there's been something else happens and from experimental physics we don't know what terminates this we certainly believe it's terminated a plot point this physics certainly doesn't make sense a plot but if EU concocted to you could change that Lane and also at the same time change too cold the Bayer charge it would compensate so at any given level you could terminate a call the bare charge at battling or change the length scale if you appropriately injudiciously change the value of their charged with comes out of the low-energy on so that's the phenomenon renormalization changing things in such a way as to keep the physics that furniture if for year and a closer and closer distances now of course we don't do that experimentally so we do not allow mind how Rios travel we have to change the physics of small and small distances to keep it fixed experimentally accessible How we have to cheat electric charges we got small small distances in order to keep the physics fixed at any given Waverly so what this is telling us is that we got a smaller and smaller more and more refined description more and more fine-grained description the value of electric charge that we have to put into the Bears description has to grow now as a step that will change at some point with a physics the of quantum elected banner missed his widow something else so Oh that's electric a say that I have a way quite a difference among who will prompt would perhaps from totally OK let's talk about the strong interactions the strong interactions things more complicated when they remind you of what we learned about the Force between quarks the 1st law between quirks does not behave like he squared overhaul what happened some no phenomena will be flops lines that out of course is unhappy electromagnetic flux wise what forms of QCD cold from electric flocks Lorenz attract each other they attract
each other in a way that does not happen like that the South interaction between lower end that has the effect of turning be cool loan for you Long's pool blank structures which was squeezed by the vacuum and of his long like structures the effect of this is as you separated quirks the energy grows linearly with a separation between between you create this Turkish Taffy gooey stuff and between them and the energy of it grows simply as a lane of the buoy things between that means that the Forest Law energy grows linearly was a 4 skyward rights were tracked down so going said the energy drawing like East squared although are it says that it just grows linearly with our so this is the wrong formula we should have put here perhaps square or something like he squared times what's not court there something times are well we can either say we had completely the wrong theory or awaken say that he squared is growing like are squared we can say the picture from electrodynamics charges us green simply the opposite happens that he squared grows with separation something happens in the nonlinear effect here which is quite the opposite and so squared grows with separation incidentally and very small distances in distance to adjust so small smaller than the size of these folks owned it revert back to to square of our pace revert back their gold call but another way of saying it is but instead he squares as a function of distance getting larger with distance it actually gets smaller with he squared getting smaller not starting with the interest is getting smaller with university larger with distance smaller with inverse so therefore plot the quantum chromodynamics coupling constant it will fall as a function immersed on that was not the 1 for the weak interactions while we kinda acts as a sort of in between the sort between our similarities with both there in between go Libby now was that if it 8 arresting quite remarkable for that if you actually take the standard model and you work out how the charges 1st of all you need to know what the various coupling constants are In a laboratory those are the ones that control physics at whatever scales you've done your experiment a 100 GTV or whatever and put in their values and then you run in using just the standard model really polarization of the vacuum and all properties from the standard model of these 3 numbers more or less come together at a common moralist come together a common point now in aid will our NATO allies in the supersymmetric version of the theory which we will talk about next time that next Porter they come together with wrap high-precision about 1 per cent or person become together about 1 person that looks like there's something happening at Summit Energy which is unifying these forces there coupling constants scene To be the scene at some high energy if you just extrapolate these curves occurs a calculable of course you have to assume that no no physics comes in no no physics from or if no physics comes in you have to take into account no visits my shift is curves will bet in the supersymmetric version of the theory these 3 numbers come together very nicely told about 1 per cent at an energy of about take me to the 16th GTV wines energy Solheim because he's courage Mary logarithmically very slowly things very slowly very slowly so it takes Our warm we ensure of scales before they come together and they come together at about 10 the 16th GUT 10 of 14
times larger than the mess of W I'm sort of huge energy it looks from these curves that some kind of unification is taking place now is is good enough to they exist it's a relatively high precision agreement in the supersymmetric theory on supersymmetric theory it's not such high-precision agreement but it's tantalizing evident arresting our that this is repairman chief White if this is correct you might guess that the fundamental link scale of particle physics of the standard model is up at this time of the 15 GB 20 input seems to be simple as simple as that of the 3 coupling constants seemed to be saying Oh talk about what that means mathematically it has a very deep that could have a very deep mathematical meaning but for the moment it's just an observation about numbers they come together Our a particular energy now that energy also happens to be the place to work the plot the strain of gravitational forces gravitational forces are very weak at large distances from wine a moment they get stronger and stronger and stronger at small distances not only because the usual what are square before but above and beyond that the forces of gravitational become stronger and stronger there she will coal layer on top of that our but see the forces of gravitation would become stronger small distance so that would mean the gravitational forces which are credibly week at long distances but would do something like that and they don't quite all costs at the same place but they crossed within factory removes a logarithmic curves they crossed within a couple of orders of magnitude gravitational weak electromagnetic and strong interaction cross all within a couple of decades of energy of each other a couple of decades of length scale at about somewhere between 16 17 18 the Jedi so what all this means especially the gravitational side of it we don't know but there is a unification scale and if this really does correspond some unity between the 3 forces it looks like it happens at a scale which is not too different plant scale plant scale the scale where gravity would become comparable the force so let's talk a little bit about gravitational forces and why I gravity gets stronger at small distances are ordinarily no Manitoba what happens to gravitational forces as you very scale and the only point here is that when you understand how gravity depends on gray-scale you find out gravity falls on the same nite our ballpark where the other forces at scales which are very small gravity is really no weaker than other forces OK so understand this refers after racer blackboard remove but I don't but I will use the thinking met the 1st law of gravity is during World War square your call be surprised if I targets really wanna what are cube very small distances it wouldn't be surprised the Jordan hookers go through wiped 1 of our view of the the reason is rewrite there would right for us but what was what the forces turned work of prevented before it was out of a total of force is equal to an end 5 2 particles NASA's on our squared and Newton's constant threats of force between 2 particles right now this is a nonrelativistic formula visit formula for particles arrest when particles have a height energy or objects have a high-energy its energy gravity and not enough next not rest on a moving object will gravitate more than object at rest if you take a box full of high energy particles of high energy particles will gravitate more than they would if they were brought to rest with the box so the right formula for a more correct formula more correct formula it is the put here but the Beatles M C squared or an end that I'm square feet of Times Square or better yet and he was theocracy squared and put in here energy of particles he oversees oversee for whatever right policy for but sold this is a formula which is more accurate when the particles a relativistic OK now got the corner mechanics and imagined bringing to particles very close together much closer together than it Compton wavelength because of the uncertainty principle of we brought them closer together and we know that the close together that means that momentum is extremely Unser the same at the momentum is extremely uncertain you could say that momentum is very laws probably speaking if you brought them to within a distance aura of each other the momentum of them must be at least of order Wednesday on a 12 are right OK now where about the energy of these particles we these particles you might think
well of energy of a particle arrest as MC Square there has a little bit of velocity you had plus one-half and square 1 and square but what happens when the momentum gets really large when argued very small when August very small these particles become highly relativistic White the momentum gets much larger than any precise number when they get very close together what he energy other particle relativistic particle With momentum p relativistic means is moving with almost speed of light the Merrimack with so that no that's relativistic replace your now the energy Pete times speed of light Peter and speed of light start we can now say he is age and now I can plug this into the forest between particles stores it ever is equal to 8 squared with just their little of the particles come close together what's assume that both have the same energy perception so that's H. bar squared C squared of are squared that's just T-square here you 1 times us is factor yet was a seat of a 4th in the a Pierre and another are square so artery for us to right this is kept gap Burrell cancel square but what I said the 1st laws while Mark Cuban and energy now force forces were what are the 4 picked so when you bring particles really close together squeeze them by whatever means either accelerator accelerates them the very high energies of we get very close together for put another box squeeze the no boxes gold particles but that relativistic but somehow or another when the particles could that close together Beyond the Forest Lawn is quite different Coolong for are before OK now want they ask the following question yacht where they were fears it's an attractive for right and it is much more potent at small distances than it is at large distances while of a 4th is a much much bigger In 1 of ours where the world is for what is because of relativistic be met short right right right exactly exactly solved Veracruz pocket now wants I ask at what links scale on other is the gravitational force approximately the same order of magnitude as the electromagnetic force that tools but on this the electric charge the electrons electric charges of pure number it happens to be fairly small let's forget it but not not ridiculously small it's a fairly small number of something like a pimp or something like that are natural natural units on cell offer the 1st round we did just that electric charge of an electron equal told 1 for simplicity and then we could ask and what only scale is be forced the gravitational force between a pair of particles the same as electromagnetic force but say a pair of electrons because I've ever happen and ordinary scales electric forces are vastly larger than electric grab gravitational forces electric as you bring them closer together because the gravitational forces increased like 1 or 2 before eventually the gravitational force will cause the year of our of electrostatic force and at small distances will become even more important even so let's see where that happens find out where that happens we should set yes equal to ease quartered all over are square foot simpler city for the moment let's just say the electric charge equal the 1 that's not be quota warned about a some about its more than 1 she they did GRT free we went so that's simplified 1 he which is not too long he squares really something like that can accepted that approximately right now like a real offer this and what scaled these 2 kinds of forces become equal to each other does multiply by 4th this becomes ah squared hiya now take the square root of word that idea for me Dot yeah for guarantee or square our article in the state so there is a stake shame the number is not ready for it around you that major policy honesty squared onto a 4th is 1 of our squared Syria's page Haji each bargee overseen so is girl is equal art farce weird it was a or
are part of the 4th here right and then there was a 1 of our squared he so around squared here and there it there are now that what you get up that a robot but From what I really didn't really get H. bar oversee H pharmacy square Jirak right which is the square root Our H. bars square GE oversee squared no squares said that joint correct must be gantlet chart no not electric charges that mention worsened will always sector a 2nd with 2nd armed young and I think there I think I lost somebody mentioned this is energy reaI This is let's let's were so in terms of energy terms of energy and I wanna said that equal to East aired or are but this is not dimensionally assist intifada ancient works so I need some I need some H. bars and there now he it 4 well I want the chance to be dimensionless happened an auto value when dimensionless units at about 10 the coastal 1 were so we have to put some corrects Mrs. units of energy right effect so it so we have 1 or more are 1 or are aII if I put in this is not correct is not correct not Peninsula consistent if I put H. bar here and this would be momentum proposed see there it is now eventually consistent H follow on has units of energy and now this electric charge here is dimensionless and that's the 1 which is owned which is about 10 close 1 OK so I made a mistake by state I should have our areas is lost its garden 8 Baker much of the figures right now now it OK now multiplied by our Scott Q we get our squared up here now we have see their steep fuel down here and they will and H. bar and I get are now is equal to the square root of G H bar was secure if a guy like that right where ever wake as a pork loin part of the farm plane is the place where big cause of the growth of energy with squeezing I would diminishing wavelength because of that the gravitational force increases and becomes comparable or even bigger few factors can bigger the new electromagnetic force at the plant quite so they also so the electromagnetic for the week force be strong force and the gravitational force all growth also become more or less comparable somewhere near the park scale this is what the B this is thought to be something important if is as important as its then the puzzle becomes not Hawaii is the 1 clean so small Hawaii is the plant a so large why is the that 719 such a big number is wine that an is so small and natural units How does it happen that that F which controls the massive energy scales of all week electromagnetic all the ordinary interaction in particular controls a massive W quirks electron why is it so small 1 number love which is not some 15 orders of magnitude smaller than that any fundamentally scales for as we can tell just that 1 number which is very small ones that 1 numbers explained why it is so small all the ministers will be elementary particles that we know about follow all the others for all we know could be up at the plant massive the natural scale they had no reason to be light they 1 their masses did not have to be proportional symmetry breaking scale so that that's kind of where we are puzzled about like this AFP is so so small now whoa whoa go more deeply into this next quarter it's not only that it's more it's also very fine between him and how to about calculate capped calculates category buttock but any any ordinary calculation of death will give a huge number at White the come up to be proportional fundamental scalar must unless there's some credible conspiracy that yet you calculated also can a lot Street leaders think it's right that he was not hopeful to him exist but he we are more it is that of day week what are the pure follow the want you
wouldn't want 25 55th bear because that would break the symmetry between them what's Fireman's Yucaipa 5 6 there but John there should reach box now that the work it Bob absolutely OK so that's another right once you know all these numbers you could predict something about scattering the pigs bows arms to Higgs bombs on of our is brought to a halt most of the new bank Beyond fight of the 4th becomes was called renormalize ball which is a bad thing Yuri so we can talk about 185 4th that a review of the matter at hand a a a a bag of false all their actions or would presume to remove his corporate cards example sofa directions between warm worst give you the opposite effect from what happens of electrodynamics of interaction between flocks lines pulls together into a Indian sort cable and the upshot that year running electric charge what are the things become in my orders you have to calculate them but fortunately for us all of the coupling constants equates more so the higher-order cross terms of more than but the age of 5 what the position that the mom up from right if for more please
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Titel New Revolutions in Particle Physics: Standard Model | Lecture 10
Serientitel Lecture Collection | Particle Physics: Standard Model
Teil 10
Anzahl der Teile 10
Autor Susskind, Leonard
Lizenz CC-Namensnennung 3.0 Deutschland:
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DOI 10.5446/15088
Herausgeber Stanford University
Erscheinungsjahr 2010
Sprache Englisch

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

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