1Phy107 Lecture 391Mon. May 1, 2006From last time…• Quantum field theory is a relativistic quantumtheory of fields and interactions.• Fermions make up matter, and bosonsmediate the forces by particle exchange.• Lots of particles, lots of interactions, but canbe unified to some extent.• Standard Model: Quarks and leptons areseparate particles, strong and electroweakbosons, Higgs boson.Phy107 Lecture 392Mon. May 1, 2006Beyond the standard model?• Standard model has been enormously successful.• Consistent picture of particles and theirinteractions.• Predictive power with unusual accuracy.• Questions:– Why 3 generations?– What determines all themass values and interaction strengths?– Can we relate the quarks and leptons and the forces?Phy107 Lecture 393Mon. May 1, 2006What does the SM say?• We can calculate how interactions would work atenergies like those of the big bang.– The results don’t make sense.• Astrophysics observations indicate that there ismore mass in the galaxy and universe than we cansee: Dark Matter– No standard model particle could explain this.• All the standard model interactions create electronsand positrons or quarks and antiquarks in pairs.– However, everything around us is made of quarks andelectrons. Where did the positrons and antiquarks go?None of these things can be explained by the SM!Phy107 Lecture 394Mon. May 1, 2006Grand Unified Theories• What do we really need to unify particle physics?• Maxwell unified the electric and magneticinteractions into electromagnetic (EM)• The standard model unified the EM and weakinteractions into the electroweak interaction• Start with the strong force.• What kind of theory is needed to unify this?Phy107 Lecture 395Mon. May 1, 2006Unifications: now and the futurePhy107 Lecture 396Mon. May 1, 2006What GUTs might do• Flavor changing interactions in quarks(e.g. changing a top quark to a bottom quark byemitting a W+) suggest that quarks can be viewedas different ‘orientations’ of the same object.• Have found the same thing for leptons.• But maybe there should be a lepto-quark field?– Quarks could turn into leptons, leptons into quarks– All matter particles would be different ‘orientations’ ofthe same fundamental object.• If we unify leptons and quarks then weak andstrong forces may be shown to be two aspects ofone force.2Phy107 Lecture 397Mon. May 1, 2006Not all that easyPhy107 Lecture 398Mon. May 1, 2006More Unifications?Phy107 Lecture 399Mon. May 1, 2006The price of unification• When the SM unified EM and weak interactions, weended with more force-carrying bosons (e.g. the Zo)• This is because our fundamental ‘particle’ increasedin complexity– e.g. from an electron to an electron-neutrino pair• If our ‘particle’ now encompasses both leptons andquarks, the interaction also becomes more complex.• In one particular GUT, we get 24 exchange bosons(W+,W-,Z0, photon, 8 gluons, and 12 new ones)Phy107 Lecture 3910Mon. May 1, 2006Supersymmetry:‘solution’ to a different problem• Matter (fermions) and forces (bosons) behave differently.• Half integer spin (1/2) are fermions and integer spin (1) arebosons• Quantum version of “rotation”,which is connected to rotational symmetry transformations• Space-time symmetries can be uniquely extended withsupersymmetries that connect fermions and bosonsFermions BosonsPhy107 Lecture 3911Mon. May 1, 2006Checklist for a theory of everything• Unify all the forces: strong force - gravity• Quantize the forces - QFT very successful• Unify the particles: quarks lepton - 3 generations• Explain all the different masses and strengths• Explain dark matter• Explain why universe is mostly mater• Explain physics at very high energy - big bangPhy107 Lecture 3912Mon. May 1, 2006Gravity• Haven’t talked recently about gravity.• Gravity not particularly relevant at the scale ofparticle physics, because the particles are notmassive enough to interact gravitationally.• But shouldn’t we be able to explain gravity inframework as particles and interactions?• Can’t we unify both quantum mechanics andgravity into a theory of everything?3Phy107 Lecture 3913Mon. May 1, 2006Einstein’s gravityGeneral Relativity is a classical theory.• Einstein was a classical guy,even though he receivedNobel for photoelectric effect,general theory of relativityhas nothing to do withquantum mechanics.• General relativity has to dowith curved space-time, andmotion of objects in thatcurved space time.Phy107 Lecture 3914Mon. May 1, 2006A. Gravity is so weak.B. Gravity is only attractive.C. Gravity has infinite range.D. Mass and weight aredifferent.Gravity QuestionWhat fundamental property of gravity makes it sohard to fit in with the other forces?Gravity is only attractive.How can you have a masscharge?Opposite charges attract.If you have two objectswith a plus and minusmass charge then a thirdobject should be repelledby one and attracted tothe other.Phy107 Lecture 3915Mon. May 1, 2006Kaluza-Klein: EM & gravity• Connect electromagnetism and gravityin a classical relativistic theory.• Kaluza and Klein found a theory in fivedimensions (four space & one time)with one interaction(5-dimensional gravity).• When one of the dimensions was‘compactified’,two interactions resulted:gravity and electromagnetism.• What appears to us as two distinctinteractions originate from only one.Kaluza & Klein, 1920Phy107 Lecture 3916Mon. May 1, 2006Extra dimensions?• How can there be extra dimensions?• Can imagine more physical dimensions,but we do not see them• We would be unaware of them if they were verysmall, e.g. very strongly curved a la GRThe 2nd dimension was curved so much we do not notice it.Phy107 Lecture 3917Mon. May 1, 2006Compactificaton in Kaluza-Klein• The process of ‘rolling up’ the extra dimensionto leave four space-time dimensions…• …made the 5-dimensionalgeometrical gravitational interactionappear as two different interactions in 4D:Another unification!Electromagnetism — GravityPhy107 Lecture 3918Mon. May 1, 2006QFT and GR don’t mix• GR leads to gravitational waves.• These are classical waves that should appear asparticles in a quantum field theory.• But “quantizing” GR gives untamable infinities• Interactions in QFT are point-likePoint-like and smeared interactionsGravity waves4Phy107 Lecture 3919Mon. May 1, 2006Still in Progress• The Kaluza-Klein theory cannot
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