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New Revolutions in Particle Physics: Standard Model | Lecture 5

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studied 2 different theories a riverbed quantum electrodynamics quantum chromodynamics both of them are gage theories do reflect just about all of nature as we know it in 1 way or another if his controlled by gage theories of different kinds and so I want to tell you gage theories now I'm not going to get in there and in depth with gage symmetry was going to tell you what gage but gage theory In more or less the minimal mathematical the the 1st and simplest gage theory is Maxwell Maxwell's theory of light of Maxwell's theory of electromagnetism what's not worry about what the word gage means what we may go through it later but not now but Our what it is is a theory on fields which have all of the properties of the electromagnetic field electromagnetic field has 6 component 3 components of electric field 3 components Our magnetic field you can represent 0 6 components in terms of it for vector call the vector potential just write it down for you with so I'm not gonna play role today anyway but just tell you there's a 4 vector that's generally called a friend of hers In indexed knew has 4 components a 0 At the time component of it and the 3 space components and a 1 2 and 3 REX y and z detail so it contains 83 vector and 84th component the significance of meanwhile is that it's the electrostatic potential it's a thing hose gradient is the electric force so for example the electric force Army charged particle just gotten by multiplying the electric charge by the gradient derivative S X derivative of a naught respect acts just electrostatic potential measured both foreigners in particle physics of course is that measure vaults of volts per unit charged to make measured in terms our in whatever way you measure electrostatic potential bus ameliorate nor phrenologist 1st of all i'll and of course this is the electric field this is electric field has 3 components the river respect XYO gradients gradient of AT and the gradient just called electric fields of electric field is determined by the gradient of a knot and the magnetic field is determined by also derivatives also derivatives of vector potential and fact magnetic field is the curl of the vector potential sold 1 of 2 ways you could study elected dynamics either in terms of the electric and magnetic fields of which there are 6 or are in terms of the vector potential of which there are 4 but their equivalent descriptions of electrodynamics amount we will go into Maxwell's equations but let me just remind you that Maxwell's equations give rise to electromagnetic waves electromagnetic waves is a wave of electric and magnetic field the typical electromagnetic wave has a directions that moves such as represented by a narrow and has a polarization from the sale of the polarization means you have to think about electric and magnetic fields of electron electric and magnetic fields of oscillators you've Obama way to use electric field for example the whole thing moves with the speed of light but any given instead electric field might look like that and the magnetic field is always perpendicular to the electric field stranded draws surrendering drawing its demands electric field is in the horizontal plane and always perpendicular to good George perpendicular like cell inappropriate units electric and magnetic field equal to each other and perpendicular this would be up Filene's polarized electromagnetic waves the plane polarized electromagnetic wave the direction of polarization which of course is always perpendicular to the direction of motion the direction of polarization is determined by electric field of electric field terms is a director polarization Mets electromagnetism and allots electromagnetic waves and much else the other thing of course about electromagnetic waves Is there source is the sources Our charges currents looks particularly focused on resources of the electric field the sources of the electric field are electric charge and to just throw picture put that the level of pictures off every electric charge creates an electric field the electric field linings never end except by cover charges a positive convention the convention is a positive electric charge puts out a electric field which is radially outward falls off as as 1 of our squared you could imagine that number of electric field lines coming out of a charge is fixed proportional to the charge and therefore a number of electric field lines passing through any sphere is the same amount for the say that mathematically In the growth of the electric field over sphere it is the same were you go far you go that gasses lower but does as long as they take else's lawyer has a very strong consequences if you don't have any of the charges in the system but they just a plus charge then you can get and rulers of electrical lines are only in on charges then there's no way to get rid of a charge no way to get rid of a charge to try to get rid of the charge I either the electric field has suddenly disappear everywhere that would violate the rules Of the speed of light but you can send a signal that the speed of light so instead if you said that weighty moved outward of missing electric field that also would make sense not unless they were charges at the end points of the electric field so all this would really be as this would not be the elimination of the charge it would just be taking charge and sending it out as a shell shell charge going out the charge would not have disappeared so it's a consequence of deep consequence of these structure the mathematical structure delta's laws that electric charge is considered that is former essence other gage theories as a gage theory Maxwell
like fields so use word Maxwell like because not all truly Maxwell's electromagnetic uh field Maxwell like fields consisting of electric light and magnetic like fields if they LIFE gage field is weakly coupled I'll tell you what that means later but basically means that if the interactions between the parts of the electromagnetic fuel weak enough that they don't interact with each other seriously then be motion I each field is exactly the same as a lightweight polarization they will move down the axis with the speed of light on unless something else something in the dynamics changes that Our naively at least it's in every way symbolic of electromagnetic field the only difference is also has sources every gage field has sources analogous to electric charge but it may not be electric charges might be something else let me give you an example which is a month physical example on physical not because it's inconsistent but because it just happens not to to be true it from Reno there is another quantity in nature called the barrier number it's simply the number of quarks disturb conserved quantity and Yukon of imagine that bounty on numbers the shortest of rebellion number is not elected job well because protons and neutrons habit so it is not electric charge but we'd quantities the authority only gage if it water that would mean that they would be forced to each between protons neutrons protons protons neutrons neutrons that would be analogous to the long forces between charges said they would have nothing to do with electric charge it would have only could do with barrier sofa example to objects with the same barrier number would repel each other a proton and neutron would repel each other because they have the same area a proton and a proton repelled on the other hand Proton meant that Proton having opposite barrier number would attract only Robin assignment is that there is no such gage field coupled tool the barrier barrier number does not come with a feel like there's that surrounds it and no longer range force associated with it so number was not an example colors example then the color forces of quantum chromodynamics also on all before I do that were known to other points to appoint the other point of course is this is a completely classical description of an electromagnetic wave the corresponding quantum mechanical description is in terms of quanta but because we think of Qantas particles our at least that's the about the only mental picture that we have to describe his duties a discreet little objects the discreet blue objects which drawing them of course it is always misleading but let me draw photon is far from the point level photon has a position more was the speed of light but also has a little fled associated with it and that the flag Our is is polarization I won't try to draw flag another words it has they have a point there which is the points this way this way of somewhere between that indicates the polarization Of the electromagnetic wave all of which it is a quantum that's a complicated state think you get Seoul photons come With polarization and that polarization in principle could be rotated Yukon rotated by sending it to a quarter wave played there and any number of ways raised on and that's photons as the photon theory director magnetism and in a quantum theory 1 can think of the call field was roughly speaking a field set up by the emission and absorption of photon emission absorption of these OK so that's that's electorate dynamics of Cutchogue electrons a charge probe Honda charge so for and interactive this way with the gage field another aspect of gage two-year-old Avery mentioned it that there's always conservation laws associated with them namely conservation of the forces of the conservation laws In both quantum mechanics in classical mechanics are always associated with symmetries symmetries of some sort or another always behind conservation laws are conservation of electric charge we've talked about that and I showed you how or if you will study the quantum mechanics of electrons in terms of charged particles in general a wave field describing those particles could be a lecture armed and symmetry associated with the concentration of charge is just the multiplication the field by effort so that was the simplest example of a gage theory gage charge mainly electric charge and a symmetry that goes along with the concentration of that charge those things go together OK whoa how probably just very quickly remind you work in quantum chromodynamics In quantum chromodynamics for more complicated structure you don't have Maxwell like fields but for label them Maxwell like fields are labeled by indices of quantum Quellette continued call them there is no universal symbol they teach field of quantum chromodynamics sometimes it's called Golgi's sometimes it's called a sometimes called being sometimes called CE unrecorded AP but in order to distinguish it from the electromagnetic field we give it some indices Heidi in Jake it's a matrix now it's a matrix and then matrix transforms under a group the group was U so just remind you very very quickly that we started thinking about us you 3 not by thinking about global arms this course will be the glue on field but by thinking about quarks Salk work was an object which we called Q kill could stand for the quantum field of a quirk ended has index the index it's not opt bound index not the charm strange index will come of that it is the color index rate renal blow I takes 3 values and be symmetry operation is not multiplying by the I figure but multiplying by a Terry special unitary matrix J but Askew prime i.e. Balazs
symmetry operation which is a kind of rotation in a and a kind three-dimensional complex based on confuse it with ordinary three-dimensional space of the symmetry operation and 1 would say that accused think of them as
particles if you like Ecuador's former representation of S U 3 which is called the fundamental representations call the fundamental representation has 3 entries red green and blue sometimes call the defining representation at the smallest nontrivial representation and just has just to be thought of as as a 3 component that were want to 3 and unitary matrices before I make a makers OK we've got through that the other thing I told you use that is works for that particles in general are represented by the complex conjugate fields fields which are simply complex conjugate of the original warms the relation of mathematical relation between particle an entire article for the wave functions of particles by particles that relationship is complex conjugation wicket ask how In that particles transformed well we simply realized if you want to transformed the complex 100 years old you should use the complex conduit matrix if you multiply Q. by you get to prime than you must multiply Q star by you start to get Q Prime Star the matrices you call a representation of the group the set matrices you
start are a distinct and different representation group language would use is that quarks and hit work are described by three-dimensional three-dimensional representation and we could call a three-star meaning complex conjugate it's usually indicated by a ball are 2 different representations of to 3 but the permanent 8 9 actual well sorry USB Amaterasu Zorana you is that the number generators a gap because these matrices are assumed to be special unitary may look at gets interesting Basque what we're kind of theory would you make if you insist that they be special and I'll tell you another time maybe later but not now OK now was a AIJ AIJ has 2 industries and the waiter think about it is that 1 of those In his mathematically got the same group theory structure Assange symmetry structure as having a quark J and and dike or are you another words this is an object was indices transformed 1 next as the three-dimensional representation and the other index as the 3 bar another way to think about it is it has all of the properties with respect to the symmetry now with respect the or physical properties but with respect to the way transforms it transforms if if it were a quark nearby quirks in the top of each other if not Spain just its color as if a war of quark work with 1 special rule namely the trace of the AIG parishes the seemed like a single at that you could make the piece which has no transformation property under group at all that Duke killed and forget about that's why there at 8 AIG reasons that not so AIJ it is like a thing with a quarterly intact work index but because it has a quirky work index 8 also transforms when you under the S U 3 transformation in that sense it's different than the photo the photon was completely electrically neutral its field the Photon Field does not get a phase when you rotate electron wave function like charms guilty I made a Times electrons positrons goatee of minus are a favorite punch positrons photons do nothing but because they don't have electric charge but the gone so they do will have color know what kind of color they have they have the color of a particle and name that particle say worker particle that article shouldn't have any color but they don't because you could have a red particle and a blue and particles a red that would make a things which was not really neutral which Norway about color so glum will have cholera and they have color in what is called the adjoint representation which is representation of the BAT generators OK now but what about what about the interaction between courts incidentally I there are many other gage theories of interest they're all pretty similar to each other the group might not be as you 3 might be astute to it might be as you for MIPS you can might be anything and objects of the group might not be called quarks nevertheless body fundamental objects of the Group analogs of quarks might be called something else they might have a different our but they would be objects which had a single index they're the entire objects would also have a single index above the complex conjugate analog of the blue ones which are called gage bows gage goes on Maxwell like fields always have 1 index of particle type another index of the impact particle price so that means called for talking about S U Win that means how many generators altogether well in times His and squared minus 1 for trace of and squared minus 1 distinct gone now what is their quotas connections between or more generous more generally particles which transformed like Quark quarks perhaps in more general rate what's the connection between them and the gage bosons explained that to you before this remind you again our if you have a court labeled by I I could be red green or blow and other core labeled by J. Everybody quirk could become the GAO's quirk if a gage blows on his myriad what kind of gage Bozo well has surgery for the way they think about it it is just think about these lines running through the diagram I Iran's right to rule that i and j also runs right through except when Jay's pointing downward it should be thought of as an IBM that particle and so I would become a J by meetings quanta a quantum of the feel of a JI RIJ um I think by Jay JI doesn't matter a march by maybe will 1 of the IGA and I particle becomes a jade
particle that is 1 of the basic interactions of quantum grow along gage theories and general of gage theories and general fundamental objects analogous to quirks gage analogous throughout blue ones and they roll of about emission and absorption that you have the fault lines and never Lewis an index for a mill at reasons something new if a glue on itself as the properties of a quark and antiquark so let's say this is i.e. J. kind of glue well I gave kind of glue on can also be made of low on I would do it the ICJ glue 1 could become the on case glue Warren IGA let's say red green blue 1 could become the red Warren as long as the indices makes sense that followed by Katie I so this would be a a interaction in which a glut of Type II J. became the water type by K and ones they are warned of type KJ who worked at K. J the order of iron Katie matters the KJ is not the same as J. but firm by that introduces something absolutely knew which is not in electrodynamics namely that the glow on themselves are charged particles and therefore exert forces on each other they exert forces in a way that photons do not exert forces on each other but the dynamics of ones is much much more complicated than the dynamics of 4 times West time where I told you was that 1 of these are not going to let the mathematics of this fully understood even now but enough set 1 of the important effects it is if you have a source of color and a bit of color With field lines coming out of it again those CO lines and not allowed to end but the effect let's opposes quirky is manned by Corporal field lines have to come into it so fuel lines have through be continuous so for more men Mel be affected that the field lines interact with each other in a way that they don't electrodynamics and the effect is very simple the fuel lines get hold in bundles which of course flocks to the result of which Is that you're not a how far apart cocoa quirks no never escape from each other because the energy stored in stone piece of glue who just increases linearly with distance between that's such a summit command but also a summary of gage theory torso summary very very quick summary of gage theory Maxwell like fields sources Dallas's Mickey show you have conservation and cemeteries symmetries having to do with the conservation laws but more than that the symmetries telling you how the particles interact with each other In terms of emission and absorption there is 1 or other things in a gage theory and that's that coupling constant the coupling constant is analog of the charge of electron the charge of electron let's talk about what the charge of electrons means there is of course the coefficient in a fine diagram when you emit a photon from a charged particle amplitude leprechaun mechanical amplitude that is the electric charge but if you want to think about it the operationally you Bucanan emerge an electric charge slamming into of a totally and cathode cathode of Capra great when slams into a tickets accelerated and the question is what it is the probability that an
electron which is stopped suddenly emits a folk did is the square of the electric charge the square freely square of electric charge parties each bars things but there but basically the square of the electric charge suitable units are is the probability for emitting a photon that's worked in quantum mechanics and field theory that is what the meaning of electric charges some measure of the problem the square of electric charges the probability white because probabilities role we squares ramp workers but that's the yeah that's a fundamental significance of electric charge and electric charge dimensionless numbers just the probability that when you stop electron you photons so to dimensionless number on that's a small dimensionless number in the talk with appropriate set of definitions be squalor of electric charge really what tends the commenter things is not quite the square of electric charges square of electric charge provided by some for pie for Kaiser always floating around in their eyes call the fine structure constant and the fine structure constant which is pretty much the probability of a photon emission is a number of about 1 per cent are close to being 1 over 37 famous number 1 over 137 the 137 there was no particular significance which just numerically about what do a fine structure constant call a 1 per cent it says is a 1 per cent probability of Emilio photon so that picture that when electron hits a cathode ray tube sends out a spray of photons that's not right what is right it is that a 137 followed storms hit the capital capital breakthrough on the average 1 of them will give off a afloat and that's since electromagnetism is all week 4 a week process the probability of mission is weak well I'm that and that's that quick summary of gage theory what I want to do is give you up a very very briefly mountains a rundown on some numbers in orders of magnitude in various parts of particle atomic physics and then go on to the weak interaction memories giving you in rundown about numbers is to show you how different the weak interactions quantum chromodynamics is the fury of the strong interactions with the strong interactions with the word before quantum chromodynamics was invented for the interactions between some nuclear particles between Haiti drawn between protons neutrons mayors arms and all the things which are made of quirks and we want so it's fear strong interactions column and there are electromagnetic interactions and also weak interactions so I want to spend the time with numbers to show you what with the terminology came from why 1 is called week 1 was called strong y electromagnetism sort of in the middle between 2 of them but doughnuts much of where her review Hupper numbers on 1st oil in terms of Unix energy distance and time do not have to be thought of as different units they're all related with each of the 1st of all time in distance really should not be distinguished in any and sensible set of units that useful for fundamental physics are we could set the speed of light equal to 1 and if we don't have we fix the speed of light equal to 1 time and distance have the same units are we can we can use we're Turks on the air as far as energy goes we could also choose to set Planck's constant equal the 1 that's a useful thing to do Inquirer Canucks all awful lot of equations get simpler if you were a fusillade particle the 1 will get a lot simpler adjusted to buyers but there are 4 to consider age 1 remind you was a Camacho between energy E equals each frequency right original age Borel make them all the same thing on the units of age well we set age bar equaled 1 so units in which age bar recalled 1 managers eagled the frequency for what a frequency 1 over time number of oscillations per 2nd so that means that energy and time
have inverse units to each other you don't need to have a separate unit for parliament and to any time you have a unit of energy is defined also a unit of Time course unit of energy is inverse a unit of Time so bt energies correspond to small time intervals and the orchestra what's what's right and connections or end since energy and Colleen are connected to each other and time and space have the same units whimsy is equal to 1 then kind space have units which adjust In the 1st units units of energy so for example is a unit of energy 1 electron use electron volts before 1 electron volt cannot be thought of as a unit of distant but the inverse 1 in numerous electron volts marriage was over an electron inverse electron volt it a unit of distance and just I have an idea of what is it's about 10th of minus severance leaders 1 electron voters about 10 to the minus 7 meters so electron is a fairly small distance but on the scale of fundamental physics it's not small distanced and my 7 meters or and minus 10 meters young research all I'm atomic diameter the family and we can write atomic diameter our 1 Adam is atomic diameter that's about 10 to the minus end news and so you can convert that electron volts electron volts the shortest and 80 years of about a thousand electron volts kill electron immersed kill electron Voltaire's upon diameter but OK another fact just converting distance of Reno the distance size of atom than we know the time that it takes like the Gore cross it right Servio transit time quantity transit time find that takes transit time the time for light to cross comic diameter arose that that's about to enter a minus 18 seconds and use the fact that like those at about 10 30 meters per 2nd order of magnitude and the
minus 18 seconds is some numbers that I just apparent but different time scale the time scale for like the across a different times and by Adam I don't mean the nucleus the whole at another time scale it is the time scale take for a electron store orbit and that they might think why isn't that just about transit time transit times about 10 to the minus 18 7 the reason is because electromagnetic forces are fairly weak because they are fairly weak before Sunday and the ultimate reason that they're week is because the fine structure constant alpha which East square for time that's a small number of about 1 over 137 another way this it it the the electromagnetic force on an electron this week because of that the acceleration of the electrons not too big and the orbit is fairly large the week of the forest object the larger the orbit is going to be our sorry this the electron moves were meant to say lot of electrons move and because the electron moves slowly by comparison with the speed of light how much slower about 1 per cent well about this much slower the electron moves around with only about 1 % the speed of light and that means the what do orbital but that's about tent Have a minus our bigger that times bigger the 16 seconds when other quantities sometimes of interest is the Dick Cheney time for an how long does it take for it and excited Adam what's a hydrogen atoms with its electron 1 orbital up from the ground state 1 up from the ground state how long does it take to decay that that is small doubly small with 2 powers of alpha or that the powers of Alpha 1st of all the acceleration of the China is small member charges in May 8 radiation when they're accelerated the acceleration is small because the forces small so 1st of all the acceleration small field electron more there with relatively small acceleration our compared to what it could have been powerful figure was around a small acceleration but on top of that just like the X the electron plowing the cathode ray too is another factor Alfred when the electron accelerated in the probability that a mix of photon saw as electron goes around here 1st of all it's moving with a slow acceleration and 2nd of all even that acceleration is not very efficient in producing photons just because the fine structure constant small the net result is that these kinds scale order of magnitude decay time how long it takes for an add-on to decay take time is about and then I was 2nd tantalum minus 9 seconds much longer than the orbital time or the transit time so that the main thing is is a variety of different scales and their old related by the fine structure a related by powers of the fine structure constant fine structure constant being a small number there are fairly large ratios between different time scales transit orbital and decay time I now let's come to Hayes runs a Johns are like Adams Adams made up of quarks with this very much the same kind of question is 1st of all we could ask whether these hadronic diameter the hadronic diameter of a typical hate could be a proton neutron on or more or less the same take advantage on the hadronic Obama there is a lot smaller than electron Oregon it's a lot smaller sucked into the minus 10 meters it's about 5 orders of magnitude smaller and minus 15 cm that's also more less leader of the diameter of a nucleus nucleus of course being a few protons and neutrons is bigger meters sorry meters paid on Obama is about into a minus 15 meters 5 orders of magnitude smaller Adam the reason is because prices still reasons 2 reasons why not 1 of them has to do with the fact that the constituents a heavier and heavier things was too close the video center the other has to do with something else but about 5 hours American troops more the transit time of the transit time is just got from the size straightforwardly Chad transit turned this is not an independent thing system of the measure of the size of the things just their number tend minus 20 30 seconds so that's a typical time-scale for half all hours for like the across Abidjan of it but now we can also talk about orbital motion of quirks How long does it take for a quarter swirling around the way functional swing around the interior of the idea of a proton and then answer is about 10 to the minus 20 seconds while about the decay time of a typical Hey John than the typical fund excited state of a drop of vibrating he drama oscillating Hey John how long does it take for the Katie and the answer it is about man talking about particular kinds of decays a decay where you hit a proton slot oscillating and been a mix of pirated froze the case analyzed torrent of about 10 to the minus 23rd 2nd different than this hierarchy of scales here what is a conclusion that conclusion is analog of the fine structure constant is much bigger closed who 1 play drop another words the emission probability aquatic what they did stop and a fictitious cathode ray quirky cathode ray 2 court flying off the probability for it to admit a cool 1 would be about 1 that's what these things indicated here the hierarchy here is entirely due to the fine structure constant the lack of a hierarchy here can only mean the corresponding quantities in quantum chromodynamics must be closed the 1 by now it's been measured in many ways it is much closer toward a much larger than we the corresponding quantity for Electra 1 of those seen it that is up it is about as fast as it
could be lowered the about presses it could be nothing slowing down this is why the strong interactions a called strike now the facts about the numbers you would known before 1 former dynamics and was understood but there was no hierarchies scales and that's why I was called strong interactions we now trace it the properties I'll be charge or fine structure constant incidentally a quantum chromodynamics analogous quantities not really 1 minutes about a 5th but much bigger than the 1 over 130 7th year to that that was just some numbers In some facts about the area most it will have to His go out but got out choosing me that's about . tools I had a of heat how may be right now and her to referred to was up for QEB but I think if you were writing a paper with both of them my called or procure it's never seemed to think he I think I don't think I've ever seen all it's just call for sometimes over unshielded 1 called the bear the issue called renormalize Balfour Dokic well that brings us to the weak interaction was the weak interactions called week primarily because the data did 8 times associated with them are very long them much longer than the decay times associated with them With even pay Johns and there even even tend to be longer and the Cape Times associated with Adams so there are prophecies in nature decay prophecies nature in which particles elementary or otherwise dictated by weak interactions where they kind scale in other words the half-life of these decays is far longer than any scale that can be accounted for babies numbers white so an example there's some examples Bell for lifetime our neutron neutron is ahead run the head effort decays neutron goes to electron proton plus and by neutrino and the lifetime tho that is about 12 minutes that's absurdly long now particle physics scales pardon the reason is easy but it hardly accounts for the year the extraordinary stability of the neutron path of the reason is neutron is only a little bit bigger then the combined masses of electrons protons and neutrons neutrino just as they are going about their pocket calculator pocket the best of the neutron it is 900 and 40 immunity buying 40 about 9 40 the mess of photons about 939 I think the actual difference between them is about 1 and a half and unity but then as electron which has amassed about half an MTV altogether out of this 940 almost a thousand DVD a difference of masks Of the Croat probably amount available masks left over this kind . 1 per cent last if the neutron was slightly later than the sum of businesses it could not decay at all just energy conservation would not allow it remember messes energy it would not have enough energy to became and still leave over some energy for kinetic energy of these particles so if the new trial was exactly the same as the sum of the energy of the electron proton neutrinos some of the massive and it wouldn't be able to carry or if you gave it a man's playing Hang a bit above that it would be able the decay but it would take a very long time decay would be very slow so part of the slowness of the long lifetime of the neutron is attributable to the fact that the very little energy on available for the place but given that that's hardly the bulk of the story 12 minutes is so absurdly long along with the something much much more than that going on another example Lee De Keyser derided another example Of this is called a week for obvious reasons it's called weak decay another example it is 8 charged on but say a pine minus choice for decays tool and electron like China's negative charge and nearby by neutrino some area train that's another possible to charge goes to an electron and neutrino a positively charged pion could become a positron and neutrino the lifetime that I believe is about chain seconds longer than these comic pick 8 times and a comic decay times are very very long by comparison with the particle physics to Tecate times now with of course there is a decay of the charge clients these particles as another decay involving new ones with company 1 soon enough similar to electrons the the point is not the particles of the decay until but 2 things 1st of all they are also decay very slowly nanoseconds but there's plenty of energy available for these decays these decays and not suppressed by the fact that the energies of the initial and all the masses of the initial and final states a very close to each other so there's something else going on Our in weak interactions where the we whatever we can to taxes on the something that makes them proceeded very very slowly and weekly we come to next is weak interactions
are be primarily oldest example of which is the decay of the neutron the beta decay of the neutron called because electrons originally called better away that's and this is called the beta decay of and fact quite similar quite similar physics goes in the both of them so To understand what's going on and we need to understand about some more particles protocols or we have country yet electron Buzz go back quick From what went to let me just make a table on the different kinds of quarks horizontally or a carmaker a sequence TO which will be red blue and green these are colors of quarks Apple no along here let me list up quarter down quarks charmed quark strange quirk top court and course each 1 of these boxes filled there are red blue and green up quirks of put X there next year the next year the next year was here so forth but these axes represent all the possible quirks that exist now quantum chromodynamics has to do with symmetries which connect red to green Kabul has to do with a unitary transformations which makes up the colors of quarks they do not those symmetries do not Mix horizontally and ASU 2 S U 3 symmetry of color cemetery Maine rotate an upgrade quark until up blow Corcoran up green quark and the nature of the symmetry is that active vertically makes up things this way this way and also at the same time will make the difference down quirks the different colors of bank works saying symmetry will mix different colors of charmed quarks a strange quirks and so forth so the colors symmetry act vertically mixes up the different rose here at the yes the unitary matrices mix-up red green and blue from III might have been better to put young rose with columns on the columns of rose on but not it's good it's good that good but right the weak interactions are associated with symmetries which act horizontally in this picture they mix up with them they mix and the same time that they mix up with their own mix charm with strain and they mixed topped with religious remind you that up Kansas saying properties apart for its mass St. properties of the charm quark Our top quark the bank works of some of the strange quark some bottom quarks ops have charged 2 3rd downs have charged minus to near here I'm sure these are cemeteries which makes the fuel like up on this will down at at the same time charm this with strangers and partners with Bob mixes these up symmetries or symmetries what there were due Carol speculate on what group might be involved as you tool fears act on things on public we simply have 3 redouble its here and never there don't take opted genre the top simply actor up-and-down horizontally among pairs of thing from group SU tool and it is a gage symmetry another words it is also comes together with forces were gage bows armed with interactions and with gage interaction gage field get to those sure enough but we left about something from this table here it's kind of Abbas if there was a 4th color memories of what role here is not usually identified as a color and the reason is because the particles do not interact with the blue ones but nevertheless it is not the role here another in which there are particles which a film India and a certain sense there when machines and there are also double these particles were also Dr Blix and also get mixed up under this S U 2 symmetry which moved things horizontally where are they were those particles bill at times so sent the 4th color could be thought of as let time number but what other let tons electrons Our are 1st of all in the 1st column he added are analogous to the upward analogous to the downed there is the electronic electron was a laptop but it's quite its price is the neutrino but they let different neutrinos is not only 1 of neutrino this is called the electron neutrino what comes in next column new on the new 1 in every respect except from Mass the same of electron just as in every respect except for masks the charm quark is like a court strange caucus like a bank or and together with it because it it's only neutrino New on neutrino and finally the last 1 is called Howell and Newsome tell all of the charged times and neutrinos of course as you might guess from name are electrically neutral the electrons new ones and powers have charged minus 1 that put they are put under the column here not because the charges is seen as the charge but because the difference between the charges of the 2 is the same as the chair difference up here What's the difference between the charge of an opera about two-thirds mind this minus 1 3rd of the difference between this common this column is plus 1 Nunavut charge the difference between this column in this column is also 1 unit of charge 1 sorry 0 minus negative 1 show as you go from here you'll decreased charged by 1 unit as you go horizontally now to adhere break for 5 minutes with a brick farmers and then I will tell you about W. bows on W. bows on par with gage arms of the weak interaction that's drive
mountains your maker microscopic Deitch theory of the weak interactions are as I said the weak interactions are based on a gage theory which mixes opted down neutrino electronic and so forth and so rather than to get into mathematics for the moment the mathematics of the group as U 2 which will combat to rule let's I think a little more a brain we've seen in various situations the gage bows arms typically have the quantum numbers or orally quantum properties of a particle and they have that particles in the case Of these In the case of a quantum Cuomo dynamical interactions yet it a quarter meant that work so that's where we have was so forth early the removing trace so we could we could start by saying let's look at the possibilities gage bows on which have the properties she did it at the back of a particle and get that article but it let's not distinguish between whether we're talking about our quirks red quotes book look screen quotes a lot pardons let's just say a particle from this column with an aunt particle of this column and the simplicity let's just focus on the lap times you see in a moment that you get the same thing if you are focused on quirks but would focus on the lack funds and talk about objects that we could make it work a lap time and direct sun but 1st of all we could have some simple things electron positron that I don't really literally mean electron within electrons and positrons electrons and positrons have no work charger all so let's drop that for will come back tho it drop things which have properties of electrons and by electron neutrinos Olympic penetrate house but more interesting for the moment is the combination of electron entice neutrino so what is the charge of an object which has video evidence saying conserved quantities saying properties as an electron with a stock on top of the neutrino well let's just focus on each charge its electric charge its electric charge is minus 1 neutrinos neutral electric electron has negative charge so whatever this object is it has negative electric charge let's give name and let's call it a gage bows on what's assume a beverages also a gage bows on gage goes on means that behaves like Max will feel the wholesale but it has negative charge code W W that's the traditional name for it W minus why minus because it has negative electric charge we could I was there was this 1 with this 1 we could have taken up and down quark with AIDS and die upcourt downcourt what happens if they work with quote on strategy again my yes same is this bank quark with a cork were also on my charge so if you like you could also imagine that the W minus has the same properties as a downcourt and buy up quite another word it's 1 from the 2nd column and in Taiwan from the 1st column that's a property has let's call W week in fact I think W was originally a notation for four-week negatively charged W bars on and of course also positively charged roars on W. bars which is like and died down with an up or like positron plus with neutrino because of the neutrino would be a W plus that's oppose the pattern is pretty similar to quantum chromodynamics the W boson ions are like either photons on 1 knee and were like glue ones which means that they would be objects which could be emitted from the lap times they would be objects which would allow a lap time of 1 kind with a letter the 1 kind become lap time of another kind by emitting a W bars on pursuing find some examples our are in electron Kerry made a W minus to become a neutrino electron becomes neutrino commissioner of bubble miners see the action these gage bows arms is to do the same kind of transition that these symmetry is ultimately going to be a match dude the mix electron neutrino very much the same way that colors got mixed by mingle you could follow the lines if you like and say the electrons and they intend to train or here can be imagined to be W miners bows on think pattern let's just by saying that W. minuses e-mail but that's all you can do with a W minus you can also have a down quarter they torn up Court word W minus that also works and sacked the W minus is an object which can be emitted in a transition from let's see from the you right column on the left column arrange down commit commemorate up work by emitting a W blue found work could
become a little work I'm hitting W. likewise for green button will further the strange quark not restrict what we got a strange quark could become a charmed quark the other 1 strange quirk John toward again W. Myers so this no symmetry idea of the new cemetery or attract horizontally and only horizontally between neighboring parity introduces the possibility of gage both arms which caused transitions between electron neutrino downcourt cannot Court Strange control course no W plus a W miners are impact particles of each other the meaning of that is that you could put these diagrams but W. miners found W. here but when you flip it becomes a W plus sort W. plus can be absorbed by an electron plus a unit of charge might charged to become a neutrino so a whole family of different answers these are codified by this 1 vertex here we turned upside down neutrino goes you know you don't have to be things before and Brown that's the basic no element of the weak interactions actually do not look the In all 3 cases thought this could be the last we levels of the means to me part I need to talk to us my but we haven't seen any reason well take that that's right but work comes down to a in is an empirical fact it's the empirical fact that the symmetry of the weak interaction act simultaneously on all of these double went up goes toward Obama charm has the lowest Ranger Powell has to go top pastoral bottom end of electrons have to mix with whichever simultaneously the implication of that the implication of that from a practical point of view is simply saying cemetery which acts it's the same age both arms which Yukon legend series in which quite mathematically consistent to emerge in a theory with different W. type bows ions would've been been emitted by up court John corks court or even whether minor it's a fact of nature a factor nature that's nature's simpler than might have been that the same day Devos arms cost transitions between 80 Raul a former role you know I mean a for Travis OK well 1st of all Adderley water processes we explained Kennedy Kennedy of my father and what they saw as it you can say yes yes yes yes you go what Barrows Inacomp look certainly foot Larrosa yeah absolutely absolutely and also flip lines up and down in various ways for example another way you could flip the lines you could take this up quirky havoc instead of going out since 7 upcourt going out and aunt tie-up court comes in whenever you flip a line from past the future of future to pass your also change from particle that are not as his travels there really is a large yes let's they there Brazil that's great to hear that is not literally a stranger just the rollover tells you that whatever these W. bows on Va there associated with transitions from 1 column for the other but I am sorry strange Fred but chanted neutrino strange to Chalmers a wrong who settles a mirror charm does not mean if you follow the lines Our draft at the point where light turns around it has to be thought of as a name that particles right or if your life you can always think of as strange can't die charm coming in and making a W just keep in mind review flipped from the past the future awkward W. bows arm will be Kato with really bad down it would take to a stranger chart that really can happen we will alone from my father and there and then holiday about changing if traders were some of this process is a good come from sorts let's think about the other's processes let's start just for fun let's start with the decay of the pie minus whether pie might apply minors as a quirk and and court with altogether negative charge so let's see Court Kanabec awkward negative charge had better be there is a prime minus that's equal to a quarks and in died of course down and and I are now what can down and back up do see refined down the entire period ready at that the end up become W minus but as a possible transition that is allowed by the physics of
W bars on Saudi is W minors but a W minus can do something else W. minus here it is the saying here is W plus W. plus upstairs here started W miners now and has put the neutrino downstairs and banditry and read this as saying but W minus goes to watch electron and banditry no of W miners control to electron by neutrino and areas you might Midas ordinary electron so that's the basic underlying process that governs the beta decay of the negatively charged ions into into an electron and thereby neutrino now which is they neutrino isn't there were 3 distinct intend train its electronic banditry in Albania electron intended trees but they can also enjoy all the various possibilities but any place you so an electronic you could put a new 1 place and as long as you carry along the new 1 neutrino so I'm not process is you want to and that new on the train it the master plan is that as French also plan to hire a of all of a sudden I changed directions if time as Atlanta's number encounters operate I become a computer scientist and made daily do right now as Bremer who we are good a came through very easily yacht that is essentially a fireman Byram describing the of pie minus 2 your as it happens fervor technical reasons having to do with some complications and find diagrams of interesting to us as it happens the primary the primary means most probable most probable decay of upon minus Mr. the new 1 banditry known not for the trees that's a technical point of no no special interest tours just happens to be that he is the man behind the times he she can we do to wobble things can happen both things and not not chemical equilibrium were an empty space where empty space except somebody made a pie might a pie 9 this was created how a pie minus might be created by some nuclei on coming together and creating by strong interaction by strong interactions of pie minus might be created now that Landis's is going along and say Wait a minute I indicate fire likened to a neutrino and knew then of course the train on the new 1 have enough energy kinetic energy the fly off and they won't come back together again because departed on a life of it on the other hand it is truly a few of the cake you want and need banditry fire the toward each other it would be a certain probability that they would make upon my so Oh yes to permit it both ways but still a good and will eventually led to the finish possible 3 of the supply love as you fire as your friend not kind to plot now e as far from them uptight diary horny get astute tool that will be happier for you to get the basic ideas of you to act now Cuba my we're doing something a little bit funny because we have S 2 has had generators is weak some engaged on branches have some of volatility W. plus W. must be another 1 working around and that other 1 must be associated somehow or something like Our electron aided by electron and neutrino antineutrino come just like Dow work from there is a 3rd gage on working around and it does play a big role in the weak interactions but it didn't play a big role historically and their weak interactions with just be costs for reasons will come through on historically it was W bows which was the 1st to be jacked up here was the latest suspected of course surface the start of a history the history of the of these forces goes back to back goes back to the radioactivity alpha beta and gamma decay alpha decay was what mission on 2 protons and 2 neutrons from nucleus as a strong interaction part of the theory drums nuclear beta decay that workers this 1 right here weak interactions gamma decay our time is of the historic rate at the same time are in the same experiment at later version of the book says some committed to locate bombs yacht energy cut its with you never worried about energy conservation and intermediate states there's a half the energy of the intermediate state doesn't match the energies Of the initial and final state it just means that the intermediate state only last for a very short time energy time uncertainty principle you could violate the energies of finding diagram for short periods of time so don't worry about conservation of energy between here and the way that you have to worry about his initial energy in the final hour picture oratory about pie on has energy are over boats a mezzo suppose upon his arrest the rest of the time is roughly about a 140 and I was the energy of the art of these new ones in the neutrino will 1st of all it's the rest energy of the new ones and the neutrino an arrest energy the rest mass of the mass of the neutrino mess of the new 1 I think is about a hundred and 180 have get exactly and this military nose for practical purposes
0 too small to be important here so there's more energy to start with energy India and these were masses of 2 final particle was that really can't happen now it just means that the particles will go often carry some kinetic energy so the difference between the energy on this side and the sums of the masses on this side is just a kinetic energy of the outgoing particles of balance the momentum also has to be conserved and that means if the pie on was rests to begin with the momentum of the new 1 and momentum of these neutrino have to be equal Per back-to-back saying flew the With neutron Karen narrow neutron work 2 but as a symbol of 1st let's do what you want to carry the new 1 is also something to carry so let's 2nd a new 1 morning along Know what can you want do them you want can become a neutrino new 71 an e-mail but WO or Trevor W. W. miners right cover bubbly minors and the neutrino but now 1 of the things a W minus can do 0 is it can become an electron Anthony and neutrino so this W. miners can become an electron and and in neutrino of the electron variety can this happen the only thing that would press yes it can happen now we can happen this is the way the new 1 Katie's our Demulen decays because it is sufficiently much heavier electrons much heavier than electron about 200 times heavier electron neutrinos are practically mess Lewis so the energy balances you have about a hundred media half of the year and the rest goes off kinetic energy so that's an example of a what's called a purely let tonic process no courts in the law it is a lot to me death Wanda Trina 1 intended electron so that happens and that's the primary the primary decay only decay of the new 1 so the new 1 an unstable particle because of this but the reason you want is unstable and not electron just me 1 happens to be heavy enough to be able to keep of electron electron not heavy enough to to make a new 1 hour sensitive accident of masses the same is true of the talents and wait talkin also the Cato funds but the fact that the new decay and notice the components of the same basic components of the saying transition from 1 column to another followed by W and then the W makes another transition from 1 column for the other all if you like a decade from 1 column for the other about these are the decay of neutron decay of the neutron insists that the stated purpose of sorry to say it effectively increase the massive electrons so that it can now goes the change in attitude of absolutely your butt that's exactly right OK with Medtronic 8 so the China's I have may better switch the vertical vertical vertical my attention back vertical no trial is 3 quarks toned down quarks and up quite right my dear our mind for 3rd plus 2 courage reminders to various sets a neutron electrically neutral rich neutrons coming in OK now what is possible 1st of all we can have up Quark become and e-mail some sort of W but that'll give us 3 down quarks 3 down corpses of find thing is nothing wrong with 3 down quirks except that the massive Three down quarks on the other end of a particle with 3 down quarks is always 2 heavy for the neutron became so that our what about 1 of the down quarks downcourt Kim W become an off-court is again and W minus downcourt emits a W minus becomes an up quirk and now we have To what quirks of Bellport up of down was I called as a proton W course W. does work the W always in it the 2nd decay decays to an electron linear by neutrino electron and by neutrino so rats CEO of at the beta decay of these new trial could dictate until a new 1 and neutrino can not enough energy New on till heavy so that they wouldn't be enough energy left over for the new 1 but other than that if it were not for that could happen familiar say it is if you could some more energy and neutron albedo did he get a shot of the and the trial excited excited enough it can indicate to a proton and neutrino and banditry new 1 but not somehow providing that extra energy I neutron will only decay proton electron that trainer OK now let's come to where are we I think would finish for tonight to cushion should remember we have a parcel and the puzzle is why is it that the weak interactions gives such slow decay rate and I can think of what namely the coupling constant tho they catalog of video of the fine structure constant could be read beat illicitly small so the probability of admitting these W. bows arms would be very very small and is not the the reason the fine structure constant for the weak interactions is about the same as for electromagnetism was not the the reason the reason something else will come from something else next time shall we say if sheer lie the grungy lower grungy and invariant undergoes operation that's exactly what I want start writing bunches of Lagrangian views the shorthand right that's what it means for more please visit us at
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Titel New Revolutions in Particle Physics: Standard Model | Lecture 5
Serientitel Lecture Collection | Particle Physics: Standard Model
Teil 5
Anzahl der Teile 10
Autor Susskind, Leonard
Lizenz CC-Namensnennung 3.0 Deutschland:
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DOI 10.5446/15084
Herausgeber Stanford University
Erscheinungsjahr 2010
Sprache Englisch

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Fachgebiet Physik
Abstract (February 8, 2010) Professor Leonard Susskind discusses gauge theories.

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