Final Exam Monday, May 8: 2:45-4:45 pm 2241 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 material String theory A string is a fundamental quantum mechanical object 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 string correspond to the particles we observe In-class review: Friday, May 5 in class Study Hint: download blank hour exams from web site and take them closed-book, with note sheet only. Phy107 Lecture 40 1 Phy107 Lecture 40 2 Strings can vibrate in different ways Different vibration Fundamental string Different vibration For example: Guitar string Different sound! Different particles! electron photon graviton Phy107 Lecture 40 3 What are these strings? We describe them only in terms of a fundamental tension as for a rubber band How big are they? T A particle of energy E has a wavelength E = h c / λ = 1240 ev-nm / λ So can probe down to scales of order λ. So far we re down to much less than the size of atomic nucleus strings could be 10 19 times smaller! Types of strings There are two basic types of strings: open and closed But the natural interactions of strings is via their endpoints - strings join together when their endpoints touch. Open strings can be come closed strings. String Interactions Strings interact by joining and splitting 2 strings joined split into 2 Phy107 Lecture 40 5 Phy107 Lecture 40 6 1
Back to the ends Different 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 differently Some 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 physical theory only in 26 dimensions! Phy107 Lecture 40 7 Phy107 Lecture 40 8 Results of the theory Superstrings The first string excitation is a particle with imaginary mass a tachyon (negative mass squared = negative energy) Could go backwards in time: seems unlikely! But the next excitation is a massless spin-2 particle satisfying general relativity The graviton! So string theory became a theory of gravity Imposing supersymmetry on strings gets rid of the tachyon - it is no longer a solution. And the number of dimensions required for consistency drops from 26 to 10! Fundamental object is now a superstring Phy107 Lecture 40 9 Phy107 Lecture 40 10 Extra 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 dimensions into some very tiny space of their own. Kaluza-Klein compactification. Add some of the advantages of Kaluza-Klein theory Roll up the extra 6 dimensions in consistent way. The exact way to roll these up determines the ways in which the strings can vibrate How many handles Size of each handle # & location of branes # of flux lines wrapped Compactification In particular compactifications, most of the matter and force particles we know about can be found. Phy107 Lecture 40 11 Phy107 Lecture 40 12 2
Vibrating strings Energy scales Force Symbol Strength Range Strong nuclear a s 1/3 10-15 m Weak nuclear a W 1/30 10-16 m Electromagnetic a EM 7x10-3 Infinity Phy107 Lecture 40 13 Phy107 Lecture 40 14 Particle physics and the universe The universe is expanding These extremely high energies and masses have a lot to say about the large-scale structure of the universe. The details of the Higgs field, force unifications, and maybe even string theory are directly responsible for the physics of the early universe. How can this be? Phy107 Lecture 40 15 Hubble s great discovery Phy107 Lecture 40 16 Brooklyn is not expanding! Alvy'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 it will 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 in Brooklyn. Brooklyn is not expanding. The expansion of the universe is an expansion of space itself. Not an explosion with pieces flying out from some center The universe is not expanding into anything. It is creating new space between the galaxies as it grows. Each galaxy is at rest with the Hubble flow and sees the other galaxies moving away with an apparent speed that increases with distance Phy107 Lecture 40 17 Phy107 Lecture 40 18 3
Just after big bang, the universe was Very dense Very hot Very high energy Forces unified? String theory? In the beginning Phy107 Lecture 40 19 Phy107 Lecture 40 20 Cosmic Microwave Background While preparing a sensitive horn antenna for radio astronomy experiments, Penzias and Wilson had a constant low level noise disrupting their reception. They could find no malfunction. The static was present of antennae direction. Penzias and Wilson The frequency spectrum matched to a temperature 2.7 Kelvin They had stumbled onto the most conclusive evidence to date supporting the Big Bang Theory. Phy107 Lecture 40 21 Phy107 Lecture 40 22 WMAP: present temperature resolution. Phy107 Lecture 40 23 Phy107 Lecture 40 24 4
Geometry of the Universe. Phy107 Lecture 40 25 Actual angular size of microwave background anisotropy predicted. Travel of microwave signal through curved space time distorts signal to measured values -> WMAP can determine curvature of universe Phy107 Lecture 40 26 Fluctuations in the CMBR Wilkinson Microwave Anisotropy Probe (WMAP) measure fluctuations in the CMB temperature at 0.1 angular resolution. Hot and cold spots : regions of high and low density at the time of recombination. The dominant angular scale is sensitive to the geometry of the universe. They conclude that the universe is flat. Ω total = 1.02+/-0.02 Problems with the Big Bang Horizon Problem Microwave background measurements: show that the temperature is the same in all directions. But regions of the sky separated by more than a few degrees could have never been in contact with each other and could not have come into thermal equilibrium. Flatness Problem If Ω 1, it rapidly moves away from Ω = 1 as universe expands. If Ω is close to unity now, it had to be within 10-28 of unity (0.999999999999999999999999999) near the beginning of time. Only if Ω is precisely = 1 would it remain = 1. What mechanism could fine-tune the universe to this degree? Phy107 Lecture 40 27 Phy107 Lecture 40 28 Inflation 1979: Alan Guth proposed an inflationary universe to solve the horizon problem and to explain the apparent flatness of the universe. From ~10-35 - 10-33 s, universe doubled in size every 10-35 s, expanding by a factor of 10 28, giving Ω = 1. Proposed: Inflation powered by a time-dependent vacuum energy transformed itself into all the matter and energy in the universe today. Inflation Phy107 Lecture 40 29 Phy107 Lecture 40 30 5
Inflationary rapid expansion of the size scale of the universe can excite gravity waves. Interaction of these with matter particles distorts cosmic microwave background radiation Produces anisotropy we see today. Phy107 Lecture 40 31 Gravity-wave excitations during inflation and damping sets size scale for microwave background anisotropy Phy107 Lecture 40 32 Phy107 Lecture 40 33 Phy107 Lecture 40 34 What caused inflation/big bang? Unknown Some extremely rapid expansion in the early universe. Dark matter / energy Inflation leaves its imprint on later universe NOVA Elegant Universe clip: http://www.pbs.org/wgbh/nova/elegant/media2/3014_qd_06.html Phy107 Lecture 40 35 6