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JoAnne Hewett Primitive Thinker Courtesy: Y.K. Kim What is the world made of? What holds the world together? Where did we come from? Courtesy: Y.K. Kim Evolved Thinker Courtesy: Y.K. Kim What is the world made of? What holds the world together? Where did we come from? Evolved Thinker Courtesy: Y.K. Kim Top Questions in Particle Physics: 1. Are there undiscovered principles of nature: New symmetries, new physical laws? 2. How can we solve the mystery of dark energy? 3. Are there extra dimensions of space? 4. Do all the forces become one? 5. Why are there so many kinds of particles? 6. What is dark matter? Evolved Thinker How can we make it in the laboratory? 7. What are neutrinos telling us? 8. How did the universe come to be? 9. What happened to the antimatter? Courtesy: Y.K. Kim Extra dimensions is real science. What is a dimension? What is a dimension? Traveling by car • 1-dimensional space Republican City, NE What is a dimension? Traveling by car • 1-dimensional space Republican City, NE • 2-dimensional space San Francisco city grid What is a dimension? Traveling by car • 1-dimensional space Republican City, NE • 2-dimensional space San Francisco city grid • 3-dimensional space Lombard Street What is a dimension? A more abstract view P=x • 1-dimensional space x y P=(x, y) • 2-dimensional space x y P=(x, y, z) • 3-dimensional space x z Cartesian coordinates Rene Descartes 1596-1650 Points in 3-dimensional space are represented mathematically by their Cartesian coordinates x, y, z Cartesian coordinates Rene Descartes 1596-1650 Points in 3-dimensional space are represented mathematically by their Cartesian coordinates x, y, z Cartesian coordinates Rene Descartes 1596-1650 Points in 3-dimensional space are represented mathematically by their Cartesian coordinates x, y, z Cartesian coordinates geometric shapes can be described by algebraic equations x 2 + y2 = 1 circle x2 + y2 + z2 =1 sphere x2 + y2 + z2 + w2 =1 hypersphere Time is the fourth dimension Time: 1. Required by relativity to be a dimension 2. Required, along with three spatial dimensions, to specify the location of an event Albert Einstein 1879-1955 Time is the fourth dimension Time: 1. Required by relativity to be a dimension 2. Required, along with three spatial dimensions, to specify the location of an event Four dimensional spacetime •Spacetime is four dimensional: x, y, z, and t •Universal constant “c”, which relates measurements of space to measurements of time •c = 670,615,200 miles per hour Hermann Minkowski 1864-1909 Science influences art Nude Descending a Staircase 1912, Marcel Duchamp A fifth dimension? • Finnish physicist Nordstrom showed in 1914 that gravity and electromagnetism could be unified in a single theory with 5 dimensions Gunnar Nordstrom 1881-1923 A fifth dimension? • Finnish physicist Nordstrom showed in 1914 that gravity and electromagnetism could be unified in a single theory with 5 dimensions Gunnar Nordstrom 1881-1923 • However, this theory incorporated Nordstrom‟s theory of gravity – in competition with Einstein‟s at the time - and was largely ignored A fifth dimension? • Polish mathematician Kaluza showed in 1919 that gravity and electromagnetism could be unified in a single theory with 5 dimensions – using Einstein‟s theory of gravity Theodor Kaluza 1885-1954 “The idea of achieving a unified theory by means of five-dimensional world would never have dawned on me…At first glance I like your idea tremendously” A fifth dimension? • Nordstrom, Kaluza, and Einstein all assumed the fifth dimension was not real • After all, we don‟t see it • So it must be a mathematical trick A fifth dimension? • Nordstrom, Kaluza, and Einstein all assumed the fifth dimension was not real • After all, we don‟t see it • So it must be a mathematical trick • Worth recalling that in 1905 some skeptical scientists didn‟t believe in the atom because we couldn‟t see it… The fifth dimension • Swedish physicist Klein proposed in 1926 that the fifth dimension was real, but too tiny to be observed • Computed it had a size of 0.000000000000000000000000000001 centimeters to unify gravity with electromagnetism Oskar Klein 1894-1977 “Klein‟s paper is beautiful and impressive” Unification of the forces In the 1860‟s Maxwell unified the electric and magnetic forces into a single force: electromagnetism Today: we aspire to unify all the known forces Schematic representation James Clerk Maxwell 1831-1879 The strength of a force changes with energy. We believe the forces will unify at higher energies. Unification of the forces Currently Probing this Energy Unification of Weak and Electromagnetic forces has been demonstrated Electroweak force! Energy Unification of the forces Currently Probing this Energy Unification of Weak and Electromagnetic forces has been demonstrated Electroweak force! Energy Unification of the forces Currently Probing this Energy Two BIG questions: 1. When does gravity unify? 2. What breaks the Electroweak force? Energy A theory of gravity: String theory • All elementary particles of nature are different vibrations of microscopic loops of string electron 10-15 cm 10-33 cm String theory reconciles quantum mechanics with gravity and can reproduce all known elementary particles IF: A theory of gravity: String theory • All elementary particles of nature are different vibrations of microscopic loops of string electron 10-15 cm 10-33 cm String theory reconciles quantum mechanics with gravity and can reproduce all known elementary particles IF: there are extra dimensions of space String theory predicts extra dimensions of space String theory predicts there are 6 or 7 extra dimensions of space! Radical idea: Large extra dimensions • Why is the strength of gravity 100,000,000,000,000,000,000,000,000,000,000,000,000 times weaker than the other forces? • Perhaps gravity is strong, but only appears to be weak to us. It moves through the entire higher dimensional spacetime, and spreads out, spending very little time in our 3 spatial + 1 time dimensional universe. • Given this hypothesis, extra dimensions could be as big as 0.0001 centimeters! • Could be responsible for breaking the Electroweak force New generation of extra dimension ideas! Lisa Randall Harvard Savas Dimopoulos Stanford Raman Sundrum Johns Hopkins Nima Arkani-Hamed Gia Dvali Princeton New York Univ. New generation of extra dimension ideas! Nima Arkani-Hamed Harvard What are extra dimensions good for? • Can unify the forces • Can explain why gravity is weak • Can break the electroweak force • Can explain Dark Matter (the mysterious matter which comprises 25% of the universe) • Can explain Dark Energy (the mysterious entity which comprises 70% of the universe) • Can explain fermion and neutrino masses …… Extra dimensions can answer lots of questions! Extra dimensions are difficult to visualize: I •One picture: shadows of higher dimensional objects 2-dimensional shadow of a rotating cube 3-dimensional shadow of a rotating hypercube Extra dimensions are difficult to visualize: II • Another picture: extra dimensions are too small for us to observe they are „curled up‟ and compact The tightrope walker only sees one dimension: back & forth. The ants see two dimensions: back & forth and around the circle Every point in spacetime has curled up extra dimensions associated with it One extra dimension is a circle Every point in spacetime has curled up extra dimensions associated with it One extra dimension is a circle Two extra dimensions can be represented by a sphere Every point in spacetime has curled up extra dimensions associated with it One extra dimension is a circle Two extra dimensions can be represented by a sphere Six extra dimensions can be represented by a Calabi-Yau space Extra dimensions are difficult to visualize: III • Yet another picture: the Braneworld scenario • We are trapped on a 3-dimensional spatial membrane and cannot move in the extra dimensions • Gravity spreads out and moves in the extra space • The extra dimensions can be either very small or very large Particles in extra dimensions • This famous formula is incomplete • For a particle in motion with momentum p in 3 spatial dimensions: E2 = (pxc)2 + (pyc)2 + (pzc)2 +(mc2)2 Kaluza-Klein particles • Imagine a particle moving in a single extra dimension of size R R • It has momentum from this motion • Quantum Mechanics says this momentum comes in steps: it has to be a multiple of 1/R • pextra = n = 0, 1, 2, … n R • “Particle in a Box” Kaluza-Klein tower of particles E2 = (pxc)2 + (pyc)2 + (pzc)2 + (pextrac)2 + (mc2)2 Recall pextra = n/R In 4 dimensions, looks like a mass! Kaluza-Klein tower of particles E2 = (pxc)2 + (pyc)2 + (pzc)2 + (pextrac)2 + (mc2)2 Recall pextra = n/R In 4 dimensions, looks like a mass! Tower of massive particles Small radius Large radius Kaluza-Klein tower of particles E2 = (pxc)2 + (pyc)2 + (pzc)2 + (pextrac)2 + (mc2)2 Recall pextra = n/R In 4 dimensions, looks like a mass! Tower of massive particles Small radius Large gives well radius gives separated finely Kaluza-Klein separated particles Kaluza- Klein particles Small radius Large radius An artist‟s rendition of Kaluza-Klein particles The possibility of additional dimensions captivates everyone‟s imagination! Dawn Meson • The observation of a Kaluza-Klein tower of particles is experimental evidence for extra dimensions • The observation of a Kaluza-Klein tower is experimental evidence for extra dimensions • Measurement of the properties of the Kaluza-Klein particles reveals the properties of the extra dimensions Once observed: Things we will want to know • How many extra dimensions are there? • How big are they? • What is their shape? • What particles feel their presence? • Do we live on a membrane? • … Once observed: Things we will want to know • How many extra dimensions are there? • How big are they? • What is their shape? • What particles feel their presence? • Do we live on a membrane? • … • Can we park in extra dimensions? • When doing laundry, is that where all the socks go? Footprints of extra dimensions Skilled animal trackers can determine: •type of animal •size of animal •speed of animal travel •if animal is injured •… Without direct observation of animal! Information is gathered even if the animal is extinct! Information is gathered even if the animal is extinct! Likewise, information is gathered on extra dimensions, even if we can‟t see them directly Searches for extra dimensions Three ways we hope to see extra dimensions: 1. Modifications of gravity at short distances 1. Effects of Kaluza-Klein particles on astrophysical/cosmological processes 1. Observation of Kaluza-Klein particles in high energy accelerators Modifications of Newtonian gravity Newton discovered Massapple Massearth Forcegravity = GNewton r2 Sir Isaac Newton 1642-1727 Modifications of Newtonian gravity Newton discovered Massapple Massearth Forcegravity = GNewton r2 A constant r = distance between apple and earth Sir Isaac Newton 1642-1727 Modifications of Newtonian gravity Newton discovered Massapple Massearth Forcegravity = GNewton r2 Sir Isaac Newton 1642-1727 Modifications of Newtonian gravity • Newtonian inverse-squared law of gravity is modified with extra dimensions • Example: 2 extra dimensions of size R • Distances r > R 1 F~ r r2 • Distances r < R 1 F~ r4 r Modifications of Newtonian gravity • Several experiments (Colorado, Stanford, Washington) • Apparatus is small (1 foot tall)! • Torsion wheels of tiny differing masses spin about each other test gravity at small distances Current best limit on size of extra dimensions: R < 0.0160 centimeters Adelberger etal Modifications of Newtonian gravity • Compared to Klein‟s prediction of 0.000000000000000000000000000001 centimeters Present limit This constraint is not very small ! • We currently have fairly poor limits on the size of extra dimensions from this technique • Extra dimensions could be BIG! Finding extra dimensions in the stars • When stars burn up their fuel, they explode • This is called a supernova • It expels particles and releases energy • Kaluza-Klein particles would be ejected into extra dimensions This does not agree with our standard model of supernova explosion Sets a constraint of R < 0.00000005 centimeters for 2 extra dimensions Finding extra dimensions in the stars • When stars burn up their fuel, they explode • This is called a supernova • It expels particles and releases energy • Kaluza-Klein particles would be ejected into extra dimensions This does not agree with our standard model of supernova explosion Sets a constraint of R < 0.00000005 centimeters for 2 extra dimensions Should recall our standard model of supernova explosion has many assumptions! High energy colliders: Powerful microscopes. They make high energy particle beams that allow us to see small things E ~ 1/x seen by seen by low energy beam high energy beam (worse resolution) (better resolution) High energy colliders: Time machines. They make particles last seen in the earliest moments of the universe particle beam particle beam Energy energy energy Particles annihilate each other and create energy The Large Hadron Collider High energy proton-proton collider: •Will explore energy regions factor of 7-10 above current accelerators •Begins operation in Geneva Switzerland in 2009 The Large Hadron Collider High Energy proton-proton collider: •Will explore energy regions factor of 7-10 above current accelerators •Begins operation in Geneva Switzerland in 2009 WE ARE ALL TERRIBLY EXCITED!!!!! LHC detectors • Two LARGE detectors to probe high energy interactions • SLAC is a member of one of the collaborations – ATLAS: 1500 Collaborators, Detector weighs 7000 tons, Claim it can float http://atlaseye-webpub.web.cern.ch/atlaseye-webpub/web-sites/pages/UX15_webcams.htm A proposed collider: longer version of SLAC‟s accelerator • collides electrons and positrons • 30 kilometers (20 miles) long • same energy as the LHC • we would like to build it in the US Finding extra dimensions at colliders: I Braneworld scenario I: Extra dimensions are flat • Kaluza-Klein particles are gravitons • Produce gravitons in the lab gravitons • They escape to the other escape dimensions • We don‟t see them! Very tricky experiment! Finding extra dimensions at colliders: I Looking for particles we can‟t see • We know total energy of collision • We measure energy of particles we see • Check to see if they match up! • If not missing energy We search for missing energy Simulation of graviton production with missing energy Finding extra dimensions at colliders: II Braneworld scenario II: Extra dimensions are curved Number of particles produced • Kaluza-Klein particles are gravitons • Produce gravitons in the lab • Gravitons decay to ordinary particles which we see Energy Finding extra dimensions at colliders: II Braneworld scenario II: Extra dimensions are curved Number of particles produced • Kaluza-Klein particles are gravitons • Produce gravitons in the lab • Gravitons decay to ordinary particles which we see Energy These searches at the LHC WILL set a limit of: R < 0.0005 centimeters for 2 extra dimensions R < 0.0000000000001 centimeters for 6 extra dimensions Still much bigger than Klein‟s prediction of 0.000000000000000000000000000001 centimeters Example: Production of graviton Kaluza- Klein particles in flat extra dimensions Production rate for graviton particles with 7 Extra 106 Dimensions 105 104 Example: Production of graviton Kaluza- Klein particles in flat extra dimensions Production rate for graviton particles with 7 Extra 106 6 Dimensions 105 104 Example: Production of graviton Kaluza- Klein particles in flat extra dimensions Production rate for graviton particles with Size of Measurement 7 error Extra 106 6 Dimensions 5 4 105 3 2 104

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Space, hidden dimensions, string theory, superstring theory, einstein, Black Holes, quantum physics, general relativity, Quantum Field theory, Mathematical Physics, extra dimensions, particle physics, Quark Soup, gauge theories, quark-gluon plasma, heavy quarks, astronomy and astrophysics, dark energy

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posted: | 2/23/2010 |

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