1Phy107 Lecture 401Wed. May 3, 2006From Last Time…Practice problems available this evening (web site)Exam 4 Friday. In-class review: Wednesday• Quantum field theory is a relativistic quantum theory offields and interactions.• Leptons and quarks make up matter, and exchangeparticles “mediate” the forces• Standard Model: Quarks and leptons are separateparticles, strong and electroweak bosons, Higgs boson.• Lots of particles, lots of interactions, but can beunified to some extent.Phy107 Lecture 402Wed. May 3, 2006Grand Unified Theories: GUTs• Unify particles: quarks & leptons - 3 generations• Unify all the forces: strong force and gravity• Quantize the forces - QFT very successful• Explain all the different masses and strengths• Explain physics at very high energy - big bangPhy107 Lecture 403Wed. May 3, 2006Not all that easyPhy107 Lecture 404Wed. May 3, 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 405Wed. May 3, 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?Phy107 Lecture 406Wed. May 3, 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.2Phy107 Lecture 407Wed. May 3, 2006Some history: Kaluza-Klein• 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 408Wed. May 3, 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 409Wed. May 3, 2006“Compactificaton” 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 4010Wed. May 3, 2006Problems in Kaluza-Klein• The Kaluza-Klein theory cannot be quantized.• When standard methods are applied, the theorygives answers that have no physical meaning.• E.g., infinite values for energies.• Physicists say the theory is not renormalizable.• The problem is that the graviton is qualitativelydifferent than the other field particles.(spin 2 rather than spin 1)Phy107 Lecture 4011Wed. May 3, 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 wavesPhy107 Lecture 4012Wed. May 3, 2006A quantum field theory of gravity• Graviton should be excitation of “gravity field”.• Particle couple to gravity field, excite graviton• Problem is “point-like” interactions in QFTThis doesn’t work for gravitygravitonMassiveparticleMassiveparticleThis w ould work, if particleswere “smeared out”3Phy107 Lecture 4013Wed. May 3, 2006String theory• A string is a fundamental quantum mechanicalobject that has a small but nonzero spatial extent.• Just like a particle has a mass, a string has a‘tension’ that characterizes its behavior.• Quantum mechanical vibrations of the stringcorrespond to the particles we observePhy107 Lecture 4014Wed. May 3, 2006•Strings can vibrate in different waysFor example:Guitar stringDifferent vibration Different sound!•Fundamental stringDifferent vibration Different particles!electron photon gravitonWhat are these strings?We describe them only in terms of a fundamentaltension – as for a rubber bandHow big are they?A particle of energy E has a wavelength E = h c / λ = 1240 eV-nm / λSo can probe down to scales of order λ…. So far we’redown to much less than the size of atomic nucleus…strings could be 1019 times smaller!TPhy107 Lecture 4016Wed. May 3, 2006Types of stringsThere are two basic types ofstrings: open and closedBut the natural interactions ofstrings is via their endpoints -strings join together when theirendpoints touch.Open strings can be come closedstrings.Phy107 Lecture 4017Wed. May 3, 2006String Interactions• Strings interact by joiningand splitting2 strings joinedsplit into 2Phy107 Lecture 4018Wed. May 3, 2006Back to the endsDifferent ‘boundary conditions’for the ends of the strings.Anchored to the sides of the small dimensions (branes)Graviton cannot be anchored -it is an excitation of a closed string(with no ends). Behaves differently4Phy107 Lecture 4019Wed. May 3, 2006Some problems• Strings are collections of points— an infinite number of points• Much more complex behavior than ‘points’.• Theory for a classical relativistic string worked• But quantizing the string leads to a physicaltheory only in 26 dimensions!Phy107 Lecture 4020Wed. May 3, 2006Results of the theory• The first string excitation is a particle withimaginary mass — a tachyon(negative mass squared = negative energy)– Could go backwards in time: seems unlikely!• But the next excitation is a massless spin-2particle satisfying general relativity– The graviton!• So string theory became a theory of gravityPhy107
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