Quantum Phenomena II: Matter Matters

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Quantum Phenomena IIMatter Matters
2nd Handout
Atomic Structure
Second Handout
Fundamental Physics

• Hydrogen atom
• Quantum numbers
• Electron intrinsic spin
• Other atoms
• More electrons!
• Pauli Exclusion Principle
• Periodic Table

• Particle Physics
• The fundamental particles
• The fundamental forces
• Cosmology
• The big bang
• The evolution of the universe

http//ppewww.ph.gla.ac.uk/parkes/teaching/QP/QP.
html
Chris Parkes
April/May 2003
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The Structure of Matter

• Quarks have most of mass
• Electrons spatial extent and determine chemical
  properties

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Fundamental ?

• 450BC Empedocles, Aristotle
• 4 basic elements
• Similar philosophies in China / India
• Democritus Atoms space
• 1661 Boyle Elements
• Medeleyev lots of them !
• C19 Dalton, elements composed of atoms

• nucleus
• Protons, neutrons.
• Lots more started turning up!
• Quarks
• Standard model

"Young man, if I could remember the names of
these particles, I would have been a botanist!,
Fermi
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Looking at smaller scales

• Naked Eye 10-4 m
• Light Microscope 10-6 m
• Size of Atom 10-10 m
• Size of Proton 10-15 m
• Size of quark, electron, neutrino.. 0 (so far..)
• Fundamental particles
• No constituents
• Study using Particle Accelerators
• Labs CERN, Fermilab
• Acelerators LEP/LHC, Tevatron
• Collide particles at high energies
• Look at what comes out !

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Particle Physics Accelerators

• Collisions are Fixed target or colliding beam
• colliding beam uses all available energy
• And accelerators
• Linacs (straight) or synchotrons (circles)
• Particles are accelerated by electric fields
• Bent by magnetic fields
• Beams made to collide inside detectors
• Can keep particles travelling round and round in
  circle
• But lose energy, radiate photons, when travelling
  in a circle

• CERNs big accelerators
• 27 km long tunnel,100m underground
• French/Swiss Border near Geneva
• 1989 2000 Large Electron Positron collider
  (LEP), colliding beam synchotron
• 2007 onwards Large Hadron Collider (LHC), proton
  collider

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Fermions Bosons

• We introduced spin for electronbut general
  particle property
• Determines particle properties
• Half-integer spin particles Fermions
• Fermi-Dirac Statistics
• Pauli Exclusion principle
• Whole-integer spin particles Bosons
• Bose-Einstein statistics
• No Exclusion principle, as many as you want in
  same state
• Matter is made of the fundamental fermions
• Forces are carried by the fundamental bosons
• Standard Model is theory which contains these
  fundamental particles

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Fermions Building blocks of matter
rest mass electric charge other charges in
MeV/c2 up quark u 300 2/3 e colour
weak down quark d 300 -1/3 e colour
weak electron e- 0.5 - e weak
neutrino e v. small but gt0 0 weak
QUARKS
LEPTONS
The first generation fermions

• This is what everything around us is made of
• But there are more !
• Proton uud Neutron udd electron
• Neutrino given off in Beta decay

All spin ½ particles
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Forces of nature

• Forces mediated by particle exchange

Force acts on particles with that type of charge
e.g. electromagnetism photon exchange between
electrically charged particles
Feynman Diagram
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Bosons Force Carriers
Force boson mass interaction charge relative
strength range in
GeV/c2 Gravity graviton ?0? mass
10-39 ? Weak W,W-,Z
80/91 weak charge 10-5 10-18 m
Electromagnetism Photon (?) 0 charge 10-2
? Strong gluon (g) 0 colour charge 1 10-15
m
The four forces and their carriers

• All particles feel gravity, graviton not
  discovered
• All particles have weak charge feel weak force
• Electric charged feel emag.
• Only quarks feel strong force, confined, colour
  neutral

Spin 1, except graviton spin 2
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Forces some basic consequences

• Strong
• glues quarks to make protons / neutrons
• Glues protons / neutrons to make nuclei
• Electromagnetism
• Bind electrons to nuclei
• Sticks atoms together to make molecules
• Gravity
• Holds large lumps of matter together stars,
  planets, galaxies
• Weak
• Radioactive decay
• Cross-generational couplings.

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Feynman Diagrams

• We already saw one for electron,positron
  annihilation
• Here is neutron decay
• By following sets of rules, we can see if this
  reaction will happen

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Particle interactions

• Some basic standard model vertices

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Anti-matter

• Each particle has an anti-particle
• e.g. electron / positron
• Properties are opposite
• Opposite charge
• (and weak and colour)
• same mass and spin

Electron positron bending in magnetic field
Dirac Equation, 1930, relativistic version of
Schrödinger for electrons, but it seemed to have
-ve energy electrons ! No, positive energy but
anti-matter! Anderson discovered in 1931
Some particles are their own anti-particles Photo
n, neutral pion
Bubble Chamber photo, A very old fashioned
photographic form of particle detector
Dirac This result is too beautiful to be false
it is more important to have beauty in one's
equations than to have them fit experiment.
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A typical modern particle physics experiment
DELPHI experiment _at_ LEP collider
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Emc2or ratherE2(pc)2(mc2)2

• Particle and anti-particle annihilate to pure
  energy
• m is rest mass
• Add K.E. term
• Basis of most modern particle physics accelerator
  expts
• Smash highly energetic particle and anti-particle
  together

1st generation fermions
Bosons
Particles and their anti-particles
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Basic Kinematics

• Apply what you have learnt about relativity
• e.g. particle A decays into particles B C
• Work in rest frame of particle A
• Reaction
• momentum
• Energy

Energy,momentum conservation but energy
includes rest mass
So particles go off back-to-back and we must
have enough energy to make them
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Three generations
And ONLY 3 ! LEP from number of neutrinos
Bosons graviton, W,W- Z0, gluon, photon
II Rabi

• Muon discovered by Street Stevenson 1937 using
  Wilson Cloud chamber
• .
• b quark was found in 1977, Fermilab
• top quark MUCH heavier (40x) found in 1995,
  Fermilab
• W/Z found at CERN 20 years ago

Still to find Higgs Boson ?Graviton ?
Standard Model one extra the Higgs boson (H),
responsible for mass No gravity
anti-particles. all fermions found
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Conservation Laws

• Tell us which processes can happen
• Short-cut for Feynman diagrams
• Conserved quantities in a reaction
• Same before initial state
• As after final state

• Momentum vector, p
• Energy E, relativistic so due to momentum and
  rest mass
• Baryon number B
• Number of quarks remains constant
• Electric Charge Q
• Helpfully, most particles have charge as
  superscript on name
• e.g. ?
• Lepton number, for each generation Le,L?,L?

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Fundamental Particles

• Anti-particles have opposite properties
• e.g. Positron e has
• Q1, Le-1
• Hence, particle-antiparticle combinations have
  zero everything!
• e.g. composite particle
• made of

Baryon number is fractional, so that proton
neutron have B1
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Confinement

• Strong force very strong !
• Quarks bound cannot break free
• No free quarks
• Lower energy to produce new particles than
  separate quarks
• All particles observed have no net colour

Electric charge has one type , and its opposite
- Colour charge comes in three types red,
green, blue and their opposites
anti-red,anti-green anti-blue
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Hadrons where quarks hide

• Hadrons are the bound states of quarks we observe
• Controlled by strong force, remember leptons
  dont feel this
• Only colourless states can be made
• Coloured quark and anti- that same colour quark
• This is called a Meson (integer spin, hence a
  boson)
• Most common mesons are the pions ?0 ,? ,?-
• Mix three colour charges together
• This is called a Baryon (½ integer spin, hence a
  fermion)
• Most common Baryons are proton neutron

These are the basic first generation composite
states
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Other Hadrons

• These last states only contained up, down quarks
• Also have strange, charm, top, bottom
• Can make hadrons with these also
• .hence very large number of combinations!
• We will consider only the strange quark
• Next lightest quark after up,down
• Like a heavy version of the d quark, mass 500
  MeV, Q-1/3
• Strange quark has strangeness -1
• These states are unstable decay into proton,
  neutron, pions

Kaon mesons are counterparts of pions with s
rather than d quark
(with spin ½)
Strange Baryons ? Sigma , ? Lamda, ? Xi
(with spin 0)
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Quark Jets

• Dont observe free quarks
• Quarks form into composite states of two quarks
  (mesons) or three quarks (baryons)
• in particle detectors often see showers of these
  particles jets of mesons and baryons

Jet of particles seen in tracking System of
detector
Jet of mesons Baryons Produced from one
initial high Energy quark Or anti-quark


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Some Key Points

• Forces are due to exchange of the fundamental
  force carrying bosons
• Photon,gluon,W,W-,Zo (and presumably graviton)
• Know the fundamental particles
• Three generations of quarks and leptons
• Dont observe free quarks
• Confined in colourless hadrons
• Added some more conservation laws
• Energy, momentum, electric charge
• Baryon number, lepton number
• Particle interactions can be written as Feynman
  diagrams
• Know the basic vertices, and conservation laws to
  see whether or not a reaction will occur.

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Searching for a Grand Unified Theory

• Electroweak theory well established in SM
• Electromagnetic and weak forces are part of same
  theory
• Unify at high energy
• ?? Unifies with strong force also at high energy
  ??
• then maybe eventually combine gravity also

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Particle Physics Glossary

• Fermion ½ integer spin particle
• Quarks fundamental fermions which come in six
  types up,down,strange,charm,top,bottom
• have fractional electrical charge and colour
  charge
• Leptons fundamental fermions which come in six
  types electron, muon,tau (all with electric
  charge) and electron neutrino, muon neutrino, tau
  neutrino (all neutral)
• Generations quarks and leptons come in three
  generations. Each generation looks like the
  previous but heavier.
• Boson integer spin particle. The fundamental
  bosons are the force carrier particles.
• Electromagnetic force carried by photon,
  interacts with electrically charged particles
• Strong Force carried by gluon, interacts with
  colour charged particles the quarks. Joins
  quarks into hadrons
• Weak Force carried by Z0,W,W-, responsible for
  nuclear Beta decay
• ElectroWeak Theory Electromagnetic and Weak
  Forces are explained by one combined theory.
• Hadron composite particle made of quarks
• Meson type of hadron containing 2 quarks (or
  more precisely one quark, one anti-quark)
• Pions the most common mesons (Kaons are most
  common meson with s quark)
• Baryon type of hadron containing 3 quarks
• Proton,neutron the most common baryons
• Anti-matter particles have anti-matter
  equivalents with same mass,opposite charge these
  behave identically.
• Standard Model very precisely tested theory of
  particle physics, containing electroweak and
  strong forces and fundamental particles.

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The Big Bang

• Evidence for the Big Bang
• It is dark at night! See Olbers Paradox
• Universe expanding
• Cosmic microwave background
• Relative abundance of elements in universe
• The evolution of the universe
• Stages in the formation of the universe
• Big Crunch ? http//lhcb.web.cern.ch/lhcb/

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Looking at larger scales

• Man 1 m
• Planet Earth 107 m
• Solar System 1013 m 1 light-day
• Star separation 1017 m 10 light-years
• Galaxy size 1021 m 100,000 light-years
• Galaxy separation 5 million light-years
• in a cluster of Galaxies 50 million
  light-years
• Large Scale Structure 1 billion light-years
• Walls, voids etc.. in distribution of galaxies

Solar system seen from the outside! Voyager
1 1977 Picture, 1990
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The expanding Universe
Expansion of space, not in space

• Light from other galaxies is red-shifted
• Doppler shift
• Edwin Hubble (1929)
• Whole universe is uniformly expanding
• There is no centre to the universe
• Hubbles law

H 20 km/s/million light yrs
v H x d, Velocity Hubble const.
distance
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Age of Universe

• Extrapolate back with Hubbles law
• Hence universe came into existence with very high
  density, expanded out from there
• Particle and Nuclear physics determined the early
  stages of evolution of the universe

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Olbers Paradox Why is the sky dark at
night ?

• If the observable universe is
• Static (eternal)
• Infinite
• Approximately uniformly filled with stars
• Then sky should be as bright as the surface of a
  star
• A faraway star looks dimmer, but there are more
  stars further away!
• Brightness falls off as 1/r2
• But area at distance r in some angular region,
  rises as r2
• Hence, these cancel and sky should be equally
  bright as sun.
• (e.g. Snowy mountains on a sunny day, equally
  bright in all directions irrespective of
  distance)

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Resolving Olbers Paradox

• The universe is not infinitely old
• Approx 15 billion years
• The speed of light is finite
• We can only see part of the universe

• Sky is dark at night because
• Universe is young distant light hasnt reached
  us yet
• and also
• Expansion causes doppler shift (red-shift) of
  light

So,Big Bang solves Paradox
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Stages in the evolution of the Universe

• Planck Era
• GUT Era
• Electroweak Era
• Particle Era

• Era of Nucleosynthesis
• Era of Nuclei
• Era of Atoms
• Era of Galaxies Now!

Book The first three minutes, by Steven
Weinberg
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(1) Planck Era up to 10-43 seconds

• Mysterious !
• Universe begins at very high temperature
• Maybe gravity unified with the other forces ?
• General Relativity and Quantum mechanics have
  never been successfully combined.
• We need a theory of Quantum Gravity
• Characteristic Planck Time and Planck Length
• Highly Speculative theories include
• M-theory particles are excitations on high
  dimensional membranes. This has taken over
  from(and includes) String Theory, where particles
  are different vibrations of one type of string.

open string
closed string
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(2) The GUT Era up to 10-35 seconds

• We still dont know a great deal but have some
  better ideas !
• Universe full of fundamental particles,
  antiparticles, photons, gluonseverything!
• No composite particles
• Maybe the electroweak and strong forces (separate
  in Standard Model) become united ? (GUT)
• Particle physics experiments give some support
  for converging coupling constants
• Inflation a short period of rapid expansion in
  the universe.
• Universe starts as a rapidly expanding quantum
  bubble
• Analysis of cosmic background radiation of
  universe gives some support for this model

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(3) The Electroweak Era up to 10-10 seconds

• Universe cooling, but still very hot, 1028K
• Again, no composite particles yet.
• Three forces in the universe
• Gravity
• Strong
• Electroweak
• Electromagnetism and weak force are unified in
  Electroweak
• W,W-,Z are massless, like the photons and gluons

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(4) The Particle Era up to 10-3 seconds

• Temperature now dropped to 1012K
• Contains almost equal amount of particles and
  anti-particles
• And photons, gluons
• Electroweak Force splits into Electromagnetism
  and Weak Interaction.
• W,W-,Z become heavy, get the Higgs boson (not
  found yet)
• As we cool further
• Confinement starts
• Quarks, anti-quarks,gluons combine to form
  protons and neutrons
• Antimatter disappears
• Matter/anti-matter cancel out.
• Small excess of matter ? Why ?
• Particle physics experiments are investigating

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(5) Era of Nucleosythensis 0.001seconds to 3
minutes

• Temperature 1012 to 109 K
• The first composite particles, the protons and
  neutrons combine to form light nuclei
• At the End
• 75 (by mass) Hydrogen nuclei p,pn,pnn
• 25 (by mass) Helium nuclei ppn,ppnn
• 0 Lithium
• Nuclei only, energy too high to bind electrons
  into atoms
• The other nuclei come from Stars much later

75/25 as measured, good evidence for big bang
No stable nuclei with 5 particles, so very few
nuclei above He formed
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(6) The Era of Nuclei3 minutes to 300,000 years

• Universe is as hot as centre of sun (107K)
• Plasma of light nuclei and electrons and photons

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(7) Era of Atoms300,000 to 1 billion years

• Universe cools so atoms can be formed (3000K)
• Electrons captured by nuclei
• Universe is transparent photons can fly around
  freely !
• No longer electrons that interact with them
• This is how the microwave background was created
• Most impressive evidence for big bang
• Universe was once very hot!

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Cosmic Microwave Background

• Photons from when atoms formed
• Universe continued to expand and cool
• Expect remnant radiation with 2.7K blackbody
  spectrum with isotropic spectrum
• Discovered Penzias,Wilson 1965

BUT not completely uniform at 10-5 K scale COBE
was first to see anisotropy, small fluctuations
in temperature. Latest results WMAP Feb. 2003
COBE satellite, 1990
Compatible with inflation model
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(8) Era of Galaxies1 billion to 15 billion
years (NOW)

• Gravity plays its role
• Neutral H and He gas attracted
• Small density variations are amplified
• Form gas clouds
• .And eventually stars
• Thermonuclear reactions in stars form heavier
  atoms
• Helium nuclei fusion
• e.g. 12C is lower energy state than 3 x 4He
• Get nuclei up to Iron
• Iron is most stable nuclei (binding energy per
  nuclei)
• Higher nuclei require additional energy input
• Provided in supernova explosions
• So, earth is supernova debris

(but measurements on galaxy rotation show
particle physics does not give enough matter!
Dark matter ?)
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The Future of the Universe ?

• Gravity fights the acceleration of the universe
• Expansion of universe could slow,stop, and then
  contract.
• Big Crunch?
• Amount of visible matter is not enough
• But strong evidence for additional dark matter
• But still not enough!
• Could expand forever, but expansion slower and
  slower
• And if there is a cosmological constant
• An extra term that can give dark energy with
  negative pressure
• Expansion of universe may be accelerating!

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Id like to thank the Swedish Academy five
ways you can win a Nobel prize!

• Why is there more matter than anti-matter in the
  universe ?
• Find the Higgs Boson.
• Is there a Cosmological constant ?
• What is dark matter ?
• Develop a Theory Of Everything !