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Space and the Hunt for Hidden Dimensions

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Space and the Hunt for Hidden Dimensions Powered By Docstoc
					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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