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SCI 224 Astrophysics and Cosmology Part 4

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

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

Forces and messenger particles

Building blocks

Feel Strong Nuclear Force

Heavy particles

Do NOT feel Strong Force

Light particles

Building blocks and

messengers

Feel Strong Nuclear Force

Do NOT feel Strong Force

Family Hierarchy

increasing mass

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)

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

Elementary Particles the building blocks

Strong Interaction and Quarks

Quark confinement the proton disco......

Quark Confinement

Difference between Bosons and Fermions Spin and

behaviour

Energy Levels (Quantized)

Spin 0, 1, 2, 3 . Spin

1/2, 3/2, 5/2, ..

Feynman diagram

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

Weak nuclear force gauge bosons W- and Z0 are

massive!

Corresponding classical potential

Example Klein-Gordon Equation

Waves and the wave vector

Plane waves and the exponential function

Fundamental representation of periodic

function in space and time

wavelength

wave period

Differentiation rules

Application to plane waves in one dimension

Differentiation with respect to coordinate

Application to plane waves in one dimension

Differentiation with respect to coordinate

Differentiation with respect to time

Plane waves in three dimensions

Effect of Laplaces operator

Klein-Gordon Equation

Trial Solution a plane wave

Solution condition

Compare energy-momentum relation for single

particle of mass m

Quantum-correspondence

Static Klein-Gordon field the Coulomb Analogy I

Static Klein-Gordon field the Coulomb Analogy II

g

Static, spherically symmetric KG field due to

single charge g at r0

KG Equation

Static, spherically symmetric KG field due to

single charge g at r0

KG Equation

Solution

m0 Newton or Coulomb potential, m? 0 Yukawa

potential!

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.

Interaction energy between two charges and the

coupling constant

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

Quantum Vacuum is not empty!

Experimental Proof Casimir effect ..

.and Zitterbewegung electron in Hydrogen atom

Debye cloud in a plasma

Virtual Shielding Clouds around Charges

Same effect (vacuum polarization) in Feynman

diagrams

Quantum Electro Dynamics

Quantum Chromo Dynamics

Energy E and the resolution of particle

experiments

Resolution Quantum Wavelength

Charge shielding resolution energy-dependent

charges!

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)

Neutrinos and helicity

Right-handed (not seen)

Left-handed (seen)

Helicity combination of motion (translation)

and rotation (spin)

Standard model is not complete

For instance (some) neutrinos have mass!

Sudbury Neutrino Observatory Observes neutrinos

from 8B

Neutrino oscillations

Observed in 1998 only possible if (some)

neutrinos are massive!

Cosmic-Ray induced Airshowers

Source of atmospheric neutrinos

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Nuclear reactions in the Sun

14

0.1

99.9

86

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Charge shielding resolution energy-dependent

charges!

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!

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

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)

Example Hamiltonian Formulation of Classical

Mechanics

Example Hamiltonian Formulation of Classical

Mechanics

Example particle moving in a potential

Possible symmetries

Translation symmetry Hamiltonian function does

not depend on one of the coordinates, say x

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

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 a Cooling

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

Gravity needs Quantum Physics when these lengths

are (roughly) equal!

This condition defines the Planck Mass and Planck

Energy

Other quantities Planck length, Planck time and

Planck Temperature

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Big Bang List of Events