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JoAnne Hewett

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Courtesy: Y.K. Kim Primitive Thinker

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What is the world made of? What holds the world together? Where did we come from? Courtesy: Y.K. Kim

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Evolved Thinker Courtesy: Y.K. Kim

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Evolved Thinker Courtesy: Y.K. Kim What is the world made of? What holds the world together? Where did we come from?

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Evolved Thinker Courtesy: Y.K. Kim 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? 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? Top Questions in Particle Physics:

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Extra dimensions is real science.

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What is a dimension?

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What is a dimension? Traveling by car 1-dimensional space Republican City, NE

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What is a dimension? Traveling by car 1-dimensional space 2-dimensional space Republican City, NE San Francisco city grid

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What is a dimension? Traveling by car 1-dimensional space 2-dimensional space 3-dimensional space Republican City, NE San Francisco city grid Lombard Street

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What is a dimension? A more abstract view 1-dimensional space 2-dimensional space 3-dimensional space P=x P=(x, y) P=(x, y, z) x x x y y z

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Cartesian coordinates Points in 3-dimensional space are represented mathematically by their Cartesian coordinates x, y, z Rene Descartes 1596-1650

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Cartesian coordinates Points in 3-dimensional space are represented mathematically by their Cartesian coordinates x, y, z Rene Descartes 1596-1650

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Cartesian coordinates Points in 3-dimensional space are represented mathematically by their Cartesian coordinates x, y, z Rene Descartes 1596-1650

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Cartesian coordinates geometric shapes can be described by algebraic equations x 2 + y 2 = 1 x 2 + y 2 + z 2 =1 x 2 + y 2 + z 2 + w 2 =1 sphere circle hypersphere

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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

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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

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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

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Nude Descending a Staircase 1912, Marcel Duchamp Science influences art

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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

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A fifth dimension? Finnish physicist Nordstrom showed in 1914 that gravity and electromagnetism could be unified in a single theory with 5 dimensions However, this theory incorporated Nordstrom’s theory of gravity – in competition with Einstein’s at the time - and was largely ignored Gunnar Nordstrom 1881-1923

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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 “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” Theodor Kaluza 1885-1954

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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

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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…

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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 “Klein’s paper is beautiful and impressive” Oskar Klein 1894-1977

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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 James Clerk Maxwell 1831-1879 The strength of a force changes with energy. We believe the forces will unify at higher energies. Schematic representation

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Unification of the forces Unification of Weak and Electromagnetic forces has been demonstrated Electroweak force! Energy Currently Probing this Energy

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Unification of the forces Unification of Weak and Electromagnetic forces has been demonstrated Electroweak force! Energy Currently Probing this Energy

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Unification of the forces Energy Currently Probing this Energy Two BIG questions: 1. When does gravity unify? 2. What breaks the Electroweak force?

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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:

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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

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String theory predicts extra dimensions of space String theory predicts there are 6 or 7 extra dimensions of space!

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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

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New generation of extra dimension ideas! Lisa Randall Harvard Raman Sundrum Johns Hopkins Gia Dvali New York Univ. Nima Arkani-Hamed Princeton Savas Dimopoulos Stanford

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New generation of extra dimension ideas! Nima Arkani-Hamed Harvard

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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!

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Extra dimensions are difficult to visualize: I 3-dimensional shadow of a rotating hypercube 2-dimensional shadow of a rotating cube One picture: shadows of higher dimensional objects

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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

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Every point in spacetime has curled up extra dimensions associated with it One extra dimension is a circle

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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

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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

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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

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Particles in extra dimensions This famous formula is incomplete For a particle in motion with momentum p in 3 spatial dimensions: E 2 = (p x c) 2 + (p y c) 2 + (p z c) 2 +(mc 2 ) 2

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Kaluza-Klein particles Imagine a particle moving in a single extra dimension of size R It has momentum from this motion Quantum Mechanics says this momentum comes in steps: it has to be a multiple of 1/R p extra = n = 0, 1, 2, … “Particle in a Box” R n R

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Kaluza-Klein tower of particles E 2 = (p x c) 2 + (p y c) 2 + (p z c) 2 + (p extra c) 2 + (mc 2 ) 2 In 4 dimensions, looks like a mass! Recall p extra = n/R

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Kaluza-Klein tower of particles E 2 = (p x c) 2 + (p y c) 2 + (p z c) 2 + (p extra c) 2 + (mc 2 ) 2 In 4 dimensions, looks like a mass! Recall p extra = n/R Small radiusLarge radius Tower of massive particles

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Kaluza-Klein tower of particles E 2 = (p x c) 2 + (p y c) 2 + (p z c) 2 + (p extra c) 2 + (mc 2 ) 2 In 4 dimensions, looks like a mass! Recall p extra = n/R Small radiusLarge radius Small radius gives well separated Kaluza-Klein particles Large radius gives finely separated Kaluza- Klein particles Tower of massive particles

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An artist’s rendition of Kaluza-Klein particles Dawn Meson The possibility of additional dimensions captivates everyone’s imagination!

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The observation of a Kaluza-Klein tower of particles is experimental evidence for extra dimensions

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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

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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? …

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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?

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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!

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Information is gathered even if the animal is extinct!

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Likewise, information is gathered on extra dimensions, even if we can’t see them directly

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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

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Modifications of Newtonian gravity Newton discovered Force gravity = G Newton Mass apple Mass earth r2r2 Sir Isaac Newton 1642-1727

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Modifications of Newtonian gravity Newton discovered Force gravity = G Newton Mass apple Mass earth r2r2 r = distance between apple and earth Sir Isaac Newton 1642-1727 A constant

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Modifications of Newtonian gravity Newton discovered Force gravity = G Newton Mass apple Mass earth r2r2 Sir Isaac Newton 1642-1727

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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 F ~ Distances r < R F ~ 1 r2r2 1 r4r4 r r

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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

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Modifications of Newtonian gravity Compared to Klein’s prediction of 0.000000000000000000000000000001 centimeters 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! Present limit

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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

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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!

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High energy colliders: Powerful microscopes. They make high energy particle beams that allow us to see small things E ~ 1/x seen by high energy beam (better resolution) seen by low energy beam (worse resolution)

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High energy colliders: Time machines. They make particles last seen in the earliest moments of the universe Energy Particles annihilate each other and create energy particle beam energy particle beam energy

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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

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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!!!!!

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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

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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

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Finding extra dimensions at colliders: I Braneworld scenario I: Extra dimensions are flat Kaluza-Klein particles are gravitons Produce gravitons in the lab They escape to the other dimensions We don’t see them! gravitons escape Very tricky experiment!

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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

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Finding extra dimensions at colliders: II Braneworld scenario II: Extra dimensions are curved Kaluza-Klein particles are gravitons Produce gravitons in the lab Gravitons decay to ordinary particles which we see Number of particles produced Energy

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Finding extra dimensions at colliders: II Braneworld scenario II: Extra dimensions are curved Kaluza-Klein particles are gravitons Produce gravitons in the lab Gravitons decay to ordinary particles which we see Number of particles produced Energy

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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

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Example: Production of graviton Kaluza- Klein particles in flat extra dimensions Production rate for graviton particles 10 4 10 5 10 6 with 7 Extra Dimensions

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Example: Production of graviton Kaluza- Klein particles in flat extra dimensions Production rate for graviton particles 10 4 10 5 10 6 with 7 Extra Dimensions 6

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Example: Production of graviton Kaluza- Klein particles in flat extra dimensions Production rate for graviton particles 10 4 10 5 10 6 with 7 Extra Dimensions 6 5 4 3 2 Size of Measurement error

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Prepared By A.K.M. Moinul Haque Meaze Center for High Energy Physics Kyungpook National University Daegu 702-701 Korea 2003-09-30 For the class of Respected.

Prepared By A.K.M. Moinul Haque Meaze Center for High Energy Physics Kyungpook National University Daegu 702-701 Korea 2003-09-30 For the class of Respected.

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