Jan Pieter SMP1

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Information about Jan Pieter SMP1

Published on October 3, 2007

Author: Kiska

Source: authorstream.com

Lectures on String Theory:  Music of the Spheres Jan Pieter van der Schaar Lectures on String Theory Pythagoras “Music of the Spheres”:  Pythagoras “Music of the Spheres” 569 – 475 BC, ancient Greece Mathematics, astronomy Pythagoreans Everything related to numbers Positive integers Discovered musical harmonics Planets, cosmic harmony Music of the Spheres String theory: everything is made out of string harmonics Outline of the series:  Outline of the series Why do we need string theory What is string theory Latest developments Quantum mechanics vs. Einstein Quantum mechanics and particle physics General relativity Quantum gravity Goals:  Goals I hope to show that theoretical (string) physicists are not boring Give you a sense of the wonderful, beautiful but strange world described by fundamental theoretical physics Show you the basics, the why, what and how of string theory Get across some of our excitement To have fun R.P. Feynman: “…Poets say science takes away from the beauty of the stars - mere globs of gas atoms…For far more marvelous is the truth than any artists of the past imagined!…What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?” Goals of fundamental physics:  Goals of fundamental physics Find the basic rules of the game (nature) Principle of Science: the test of all knowledge is experiment Source of knowledge: experiment, imagination and guesses Division of labor: experimental and theoretical To see complete nature as different aspects of one set of phenomena and unify our understanding Heat and mechanics Electricity, magnetism and light Special relativity and gravity R.P. Feynman Unification:  Unification Picasso: “A painter should work with as few elements as possible” String Theory The Correspondence Principle:  The Correspondence Principle Most and perhaps all laws of nature are only an approximation, valid up to a certain scale. Even though corrections can be extremely small, in terms of our ideas behind the laws of nature (philosophically) we are completely wrong. So very small effects sometimes require profound changes in our ideas. The large and small:  What is the world made off ? Elementary particles What holds it together ? Forces The large and small Physical laws of motion and forces The Standard Model of elementary particles Quantum mechanics and special relativity Gravity General relativity Quantum Mechanics:  Quantum Mechanics Black body radiation and the photo-electric effect Particles are waves and waves are particles! Light rays become photon bundles (energy quanta) Electron bundles become electron rays (electron waves) Apparent when probing very short distances, typical scale is the size of atoms, 0.00000001 cm M. Planck: “... the whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be” M. Planck A. Einstein Quantum fuzziness:  Quantum fuzziness Heisenberg’s uncertainty principle W. Heisenberg Nothing can sit still, which is what we mean with quantum fuzziness, or the jittery nature of the quantum world Quantum interference and probability:  Quantum interference and probability QM only predicts probabilities Wavelike interference of amplitudes If it can happen, it will happen Identical particles: FERMIONS and BOSONS Half integer and integer SPIN respectively Fermions Bosons W. Pauli Pauli exclusion principle: Probing matter:  Probing matter Accelerate and collide particles Particle/wave duality, wavelength = h/p Distance/energy relation L. De Broglie Moral: to gather the most information about an object, use the smallest possible probe, visible light: 0.00005 cm (cell) Special relativity:  Special relativity Speed of light is the same for all observers! Confirmed experimentally: Michelson-Morley (1887) Consequences: moving clocks run slower and moving sticks are shorter Mass is just a form of energy: E=mc2 Space and time become space-time Apparent at velocities that are a significant fraction of the speed of light A. Einstein H. Minkowski: “Space of itself, and time of itself will sink into mere shadows, and only a kind of union between them shall survive” Special relativity in a nutshell:  Special relativity in a nutshell Quantum field theory:  Quantum field theory Matter and forces are all quantum relativistic fields Particles are lumps (quanta) of the fields, e.g. photons, electrons, gluons and quarks: many-particle theory ! General prediction : anti-matter, matter + anti-matter = force field lumps (e.g. photons) Interactions matter and force fields due to exchange of messenger particles, the lumps of the force field Feynman diagrams P.A.M. Dirac Yang, Mills Feynman Gell-Mann Schwinger ‘t Hooft Veltman Weinberg Dyson, and Many others Feynman diagrams:  Feynman diagrams Calculates the probability that something happens Interactions at space-time points, called vertices Quantum corrections correspond to loops If it can happen, it will happen Because e ~ 1/137 is a small number we can make consecutive approximations using Feynman diagrams = + + e e e e e INFINITE ! e The Standard Model:  The Standard Model Range: Infinite 10-16 cm Infinite 10-13 cm Strength: 10-40 10-3 1 10-100 The Standard Model poster:  The Standard Model poster http://particleadventure.org Beyond the Standard Model:  Beyond the Standard Model Strength of electromagnetic, weak and strong interactions (almost) meet when extrapolated to higher energies Unification interactions ~ 1016 GeV, Grand Unified Theory (GUT) Explaining 21 parameters; masses, charges etc. Dark matter in our universe Inclusion of gravitational interaction Experimental sites:  Experimental sites CERN (Geneve): electron/positron SLAC (San Francisco): electron/positron FERMILAB (Chicago): proton/anti-proton Accelerator scales:  Accelerator scales Today (~25 km): ~10-17 cm or 104 GeV Earth (~40,000 km): ~10-21 cm or 108 GeV Universe: ~1022 km Proton mass ~ 1 GeV, electron mass ~ 0.5 MeV Mega = 106 Giga = 109 1 GeV ~ 10-24 grams TERRA INCOGNITA ! String scale General relativity:  General relativity Equivalence acceleration and gravitational fields Equivalence inertial and gravitational mass Space-time is curved by presence of energy Test objects follow the shortest paths in curved space-time (geodesics) Experiment: Bending of light Shifting of perihelion in orbit Mercury Stage of physics is no longer fixed, rather it has become a treacherous swamp ! J. Wheeler: “Mass grips space by telling it how to curve, space grips mass by telling it how to move” A. Einstein Curved space-time:  Curved space-time Test objects follow shortest paths Positive and negative curvature Singularities are points of infinite curvature; our stage breaks down ! Source is any energy Analogy; the rubber sheet Gravity, particles and QM:  Gravity, particles and QM General relativity is a classical theory describing classical space-time Gravity is weak, but always acts in the same direction (“clumps”) Describes large scale physics very accurately Can be neglected for elementary particles More energy means stronger gravity Planck scale is 10-33 cm, where quantum gravity effects are thought to become important Space-time foam and quantum gravity When large meets small:  When large meets small Space-time singularities (points of infinite curvature) Big Bang Inside black holes Vacuum energy in quantum field theory Particle physics near the Planck length: 10-33 cm or 1018 GeV QFT and GR don’t mix:  QFT and GR don’t mix Gravitational waves, lumps of GR: gravitons “Quantizing” GR gives untamable infinities What does it mean to “quantize” space and time ? Interactions in QFT are point-like We have to be more creative ! Point-like and smeared interactions String theory:  String theory Points replaced by loops of string Q: loops of what ? A: stuff or energy Two-dimensional Feynman diagrams : tubes or pants Gravitons included ; finite quantum corrections ! J. Schwarz M. Green To summarize::  To summarize: Come back next week:  Come back next week String modes and elementary particles Open and closed strings Extra space-time dimensions Supersymmetry Consistent superstring theories Anonymous: “It is all string theory to me”

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