SCI 224 Astrophysics and Cosmology Part 4

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SCI 224 Astrophysics and CosmologyPart 4

• Bram Achterberg
• http//www.astro.uu.nl/achterb/SCI224

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The Micro-Cosmos

• Why bother?
• The Early Universe can only be understood
  using the
• physics of Fundamental Particles and
  Forces
• New ideas for solving the problems of
  Standard
• Big Bang Cosmology use ideas and concepts
• from Particle Physics!

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Fundamental Forces of Nature
Force Relative strength Role in Nature
Range Strong Nuclear 1
stable nuclei, 10-13
cm Force
nuclear fusion in stars Electromagnetism
1/137 light, radio waves
infinite
and
(bio)chemistry Weak Nuclear 10-4
radio activity,
10-15 cm Force
decay of the neutron Gravity 1
0-38 Existence of planets, infinite

stars and galaxies
Evolution
of the Universe
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Forces and messenger particles
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Building blocks
Feel Strong Nuclear Force
Heavy particles
Do NOT feel Strong Force
Light particles
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Building blocks and
messengers
Feel Strong Nuclear Force
Do NOT feel Strong Force
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Family Hierarchy
increasing mass
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Elementary Particles the messengers (Gauge
Bosons)
Force Associated Gauge Bosons Strong
Nuclear Force 8 mass-less gluons, indirect
experimental evidence Weak Nuclear Force 3
Vector Bosons W, W- and Z0
discovered experimentally in
1983 at CERN, mass 10-25 kg Electromagnetic
Force 1 mass-less photon Gravity 1 mass-less
graviton (hypothetical)
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Forces and Charges
Force Charge effect on Quarks/Leptons
Strong colour
colour change / no Electromagnetic electric
charge yes / e-, ? and ? Weak
weak charge flavour
change
(within
family) Gravity mass (energy) yes
/ yes
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Elementary Particles the building blocks
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Strong Interaction and Quarks
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Quark confinement the proton disco......
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Quark Confinement
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Difference between Bosons and Fermions Spin and
behaviour
Energy Levels (Quantized)
Spin 0, 1, 2, 3. Spin
1/2, 3/2, 5/2,..
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Feynman diagram
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Gauge boson mass and the range of a force
Electromagnetism mass-less photons Gravity
mass-less gravitons Classically
both forces have a 1/r potential
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Weak nuclear force gauge bosons W- and Z0 are
massive!
Corresponding classical potential
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Example Klein-Gordon Equation
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Waves and the wave vector
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Plane waves and the exponential function
Fundamental representation of periodic
function in space and time
wavelength
wave period
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Differentiation rules
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Application to plane waves in one dimension
Differentiation with respect to coordinate
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Application to plane waves in one dimension
Differentiation with respect to coordinate
Differentiation with respect to time
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Plane waves in three dimensions
Effect of Laplaces operator
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Klein-Gordon Equation
Trial Solution a plane wave
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Solution condition
Compare energy-momentum relation for single
particle of mass m
Quantum-correspondence
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Static Klein-Gordon field theCoulomb Analogy I
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Static Klein-Gordon field theCoulomb Analogy II
g
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Static, spherically symmetric KG field due to
single charge g at r0
KG Equation
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Static, spherically symmetric KG field due to
single charge g at r0
KG Equation
Solution
m0 Newton or Coulomb potential, m? 0 Yukawa
potential!
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Summary

• We have learned that
• The building blocks of matter are quarks and
  leptons,
• all of them fermions with spin ½
• Forces are mediated by gauge bosons which act as
• messenger particles, and have spin 1
• (except for the hypothetical graviton with spin
  2 )
• The range of a force depends on the mass of the
• gauge boson infinite range (1/r potential)
  means
• mass m 0, finite range (? ? 1/m) for m?0.

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Interaction energy between two charges and the
coupling constant
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Virtual processes
One of Heisenbergs Uncertainty Relations
Consequence you can borrow an amount of
energy ?E, Creating it spontaneously, if you
return it within a time
This leads to Virtual Processes which are
unobservable individually
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Quantum Vacuum is not empty!
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Experimental Proof Casimir effect..
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.and Zitterbewegung electron in Hydrogen atom
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Debye cloud in a plasma
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Virtual Shielding Clouds around Charges
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Same effect (vacuum polarization) in Feynman
diagrams
Quantum Electro Dynamics
Quantum Chromo Dynamics
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Energy E and the resolution of particle
experiments
Resolution Quantum Wavelength
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Charge shielding resolution energy-dependent
charges!
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Summary

• In quantum field theory charges are
• energy-dependent
• This effect is due to vacuum polarization
• the effect of a shielding cloud of virtial
  particles
• The effect of this shielding is
• - weakening of electric charges with distance
  for
• electromagnetism
• - strengthening of colour charges for
  the
• strong nuclear force.

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The Standard Model

• Main Features
• The fundamental entities are point-particles
• (quarks, leptons and Gauge Bosons)
• All neutrinos are massless
• Fermions and Bosons are truly separate entities
• Electromagnetism and the Weak Nuclear Force
• are part of the same fundamental interaction.
• (Glashow-Weinberg-Salam electro-weak theory)

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Neutrinos and helicity
Right-handed (not seen)
Left-handed (seen)
Helicity combination of motion (translation)
and rotation (spin)
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Standard model is not complete
For instance (some) neutrinos have mass!
Sudbury Neutrino Observatory Observes neutrinos
from 8B
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Neutrino oscillations
Observed in 1998 only possible if (some)
neutrinos are massive!
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Cosmic-Ray induced Airshowers
Source of atmospheric neutrinos
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Nuclear reactions in the Sun
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0.1
99.9
86
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Charge shielding resolution energy-dependent
charges!
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New Physics beyond the Standard Model

• Grand Unified Theories theories that include
  the
• Strong Nuclear Force in a common description
• Super-symmetric Theories theories that connect
• fermions and bosons
• (doubles the number of fundamental particles!)
• Strings and branes theories that use extended
• objects rather than point particles as the
• fundamental entities
• EXTRA DIMENSIONS!

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Unity in Forces

• General Ideas
• Strong, Weak and Electromagnetic Forces stem
  from
• one underlying theory (Grand Unified Theory
  GUT)
• At high energy, the symmetry is between forces is
• manifestly realized, at low energy it is
  hidden
• Electromagnetic/Weak symmetry breaking
• 4. Electro-weak/Strong symmetry breaking

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The Analogy with the Physics of Crystals
CRYSTAL GUTs SYMMETRY
Rotational Invariance Forces
indistinguishable, (high temperature) in fluid
state Electron, neutrino and quark
indistinguishable SPONTANEOUS
Crystallization Forces and particles SYMM.
BREAKING three distinguishable become
distinguishable (critical temperature)
crystal axes HIDDEN SYMMETRY Three
fundamental Three distinguishable (low
temperature) axes of space, forces,
three sound speeds three kinds of leptons
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Symmetry and conserved quantities in Physics

• Physical systems can have symmetries such as
• External symmetries such as invariance under
• rotations of coordinates
• Internal symmetries such as the invariance
  under
• replacement of fields by a set of equivalent
  fields
• ( field rotations)

• Symmetries always lead to conserved quantities
• (conservation laws)

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Example Hamiltonian Formulation of Classical
Mechanics
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Example Hamiltonian Formulation of Classical
Mechanics
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Example particle moving in a potential
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Possible symmetries
Translation symmetry Hamiltonian function does
not depend on one of the coordinates, say x
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Possible symmetries
Translation symmetry Hamiltonian function does
not depend on one of the coordinates, say x
Time-shift symmetry Hamiltonian function does
not depend on time
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Example of a internal symmetry
For strong interaction physics the up- and
down Quarks are almost indistinguishable
Mass proton (uud) mass neutron (udd) 1 GeV/c2
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Consequence Phase Transitions in aCooling
Universe
GUT Phase Transition
Electro-Weak Phase Transition
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What about Gravity?
Relativity Fundamental Radius for mass
M is the
Schwarzschild radius
Quantum Physics Fundamental length for mass M is
the Compton
Wavelength
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Gravity needs Quantum Physics when these lengths
are (roughly) equal!
This condition defines the Planck Mass and Planck
Energy
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Other quantities Planck length, Planck time and
Planck Temperature
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Big Bang List of Events