1Phy107 Lecture 401Wed. May 3, 2006Final Exam• Monday, May 8: 2:45 - 4:45 pm2241 Chamberlin• Note sheet: two double-sided pages• Cumulative exam-covers all material, 40 questions– 11 questions from exam 1 material– 12 questions from exam 2 material– 11 questions from exam 3 material– 6 questions from post-exam 3 materialStudy Hint: download blank hour exams from web siteand take them closed-book, with note sheet only.In-class review: Friday, May 5 in classPhy107 Lecture 402Wed. 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 403Wed. 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 405Wed. 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 406Wed. May 3, 2006String Interactions• Strings interact by joiningand splitting2 strings joinedsplit into 22Phy107 Lecture 407Wed. 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 differentlyPhy107 Lecture 408Wed. 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 409Wed. 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 Lecture 4010Wed. May 3, 2006SuperstringsImposing supersymmetry on strings gets rid ofthe tachyon - it is no longer a solution.And the number of dimensionsrequired for consistency dropsfrom 26 to 10!Fundamental object is now a‘superstring’Phy107 Lecture 4011Wed. May 3, 2006Extra dimensions in string theory• Superstring theory has a 10 dimensional spacetime,• How do we get from 10 dimensions down to 4?• Introduce some of the ideas from Kalaza-Klein theory– Roll up the extra dimensionsinto some very tiny space of their own.– Kaluza-Klein compactification.• Add some of the advantages of Kaluza-Klein theoryPhy107 Lecture 4012Wed. May 3, 2006Compactification• Roll up the extra 6dimensions in consistentway.• The exact way to rollthese up determines theways in which the stringscan vibrate– How many ‘handles’– Size of each handle– # & location of branes– # of flux lines wrappedIn particular compactifications, most of the matter and forceparticles we know about can be found.3Phy107 Lecture 4013Wed. May 3, 2006Vibrating stringsPhy107 Lecture 4014Wed. May 3, 2006Energy scalesForce Symbol Strength RangeStrong nuclear as 1/3 10-15 mWeak nuclear aW 1/30 10-16 mElectromagnetic aEM 7x10-3 InfinityPhy107 Lecture 4015Wed. May 3, 2006Particle physics and the universe• These extremely high energies and masseshave a lot to say about the large-scalestructure of the universe.• The details of the Higgs field, forceunifications, and maybe even string theoryare directly responsible for the physics ofthe early universe.• How can this be?Phy107 Lecture 4016Wed. May 3, 2006The universe is expandingHubble’s great discoveryPhy107 Lecture 4017Wed. May 3, 2006Alvy's mother: He's been depressed.All of a sudden, he can't do anything.Doctor: Why are you depressed, Alvy?Alvy's mother: Tell Dr. Flicker.(To the doctor) It's something he read.Doctor: Something he read, huh?Alvy: The universe is expanding...Well, the universe is everything,and if it's expanding, some day itwill break apart and that will be the end of everything.Alvy's mother: What is that your business?(To the doctor) He stopped doing his homework.Alvy: What's the point?Alvy's mother: What has the universe got to do with it? You're here inBrooklyn. Brooklyn is not expanding.Phy107 Lecture 4018Wed. May 3, 2006“Brooklyn is not expanding!”• The expansion of the universe is anexpansion of space itself.– Not an explosion with pieces flying out fromsome center• The universe is not expanding into anything.– It is creating new space between the galaxies asit grows.• Each galaxy is at rest with the Hubble flow– and “sees” the other galaxies moving away withan apparent speed that increases with distance4Phy107 Lecture 4019Wed. May 3, 2006In the beginning…• Just after bigbang, theuniverse was– Very dense– Very hot– Very high energy• Forces unified?• String theory?Phy107 Lecture 4020Wed. May 3, 2006Phy107 Lecture 4021Wed. May 3, 2006Phy107 Lecture 4022Wed. May 3, 2006Cosmic Microwave Background• While preparing a sensitive hornantenna for radio astronomyexperiments, Penzias and Wilsonhad a constant low level noisedisrupting their reception.• They could find no malfunction.• The ‘static’ was present ofantennae direction.• The frequency spectrum matched toa temperature 2.7!KelvinPenzias and WilsonThey had stumbled onto the mostconclusive evidence to date supportingthe Big Bang Theory.Phy107 Lecture 4023Wed. May 3, 2006Phy107 Lecture 4024Wed. May 3, 2006WMAP: WMAP: present temperature resolution.5Phy107 Lecture 4025Wed. May 3, 2006Geometry of the UniverseGeometry of the Universe.Phy107 Lecture 4026Wed. May 3, 2006Actual angular size of microwave background anisotropy predicted.Travel of microwave signal through curved space time
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