Quantum Phenomena
II:
Matter Matters
Second
Handout
Atomic
Structure

Hydrogen atom



Quantum numbers
Electron intrinsic spin
Other atoms



More electrons!
Pauli Exclusion Principle
Periodic Table
2nd Handout
Fundamental Physics

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
April/May 2003
Chris Parkes
The Structure of Matter


Quarks have most of mass
Electrons spatial extent
and determine chemical
properties
Fundamental ?

450BC Empedocles, Aristotle



Democritus “Atoms & space”

1661 Boyle Elements





4 basic elements
Similar philosophies in China /
India
…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
Looking at smaller scales





Naked Eye
Light Microscope
Size of Atom
Size of Proton
Size of quark, electron, neutrino..



Study using Particle Accelerators




Fundamental particles
No constituents
Labs: CERN, Fermilab…
Acelerators: LEP/LHC, Tevatron
Collide particles at high energies
Look at what comes out !
10-4 m
10-6 m
10-10 m
10-15 m
0 (so far..)
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
CERN’s 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
Fermions & Bosons



We introduced spin for electron…but general
particle property
Determines particle properties
Half-integer spin particles – Fermions



Whole-integer spin particles – Bosons





Fermi-Dirac Statistics
Pauli Exclusion principle
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
Fermions: Building blocks of matter
rest mass
electric charge
other charges
+ 2/3 e
colour & weak
in MeV/c2
“up” quark u
300
QUARKS
“down” quark d
300
-1/3 e
colour & weak
electron e-
0.5
-e
weak
LEPTONS
neutrino e
v. small but >0
0
weak
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
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
Bosons: Force Carriers
Force
boson
mass
interaction charge
relative strength
range
mass
10-39

weak charge
10-5
10-18 m
in GeV/c2
Gravity
graviton
?0?
Weak
W+,W-,Z
80/91
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

Strong




Bind electrons to nuclei
Sticks atoms together to make molecules
Gravity


glues quarks to make protons / neutrons
Glues protons / neutrons to make nuclei
Electromagnetism


Forces : some basic
consequences
Holds large lumps of matter together: stars, planets, galaxies
Weak


Radioactive decay
Cross-generational couplings….
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
Particle interactions

Some basic standard model vertices:
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
Dirac Equation, 1930,
relativistic version of
Schrödinger for electrons,
but it seemed to have -ve
energy electrons !
No, positive energy but antimatter!
Anderson discovered in
1931
Electron &
positron
bending in
magnetic
field
Some particles are their
own anti-particles:
Photon, neutral pion
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.”
Bubble Chamber photo,
A very old fashioned
photographic form of
particle detector
A typical modern particle
physics experiment
DELPHI experiment
@ LEP collider
E=mc2
or rather
E2=(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
Particles and their
anti-particles
e , e
ve , ve
Bosons
graviton, graviton
photon, photon
gluon, gluon
u, u
Z 0, Z 0
d,d
W  ,W 
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
A BC


momentum 0  p
B  pC
Energy


pB   pC
m A  mB  mC
mA  EB  EC
mA  pB  mB  pB  mC
2
2
2
2
Energy,momentum conservation – but energy includes rest mass
So particles go off back-to-back
and we must have enough energy to make them
Three generations
And ONLY 3 ! LEP from number of neutrinos
Bosons: graviton, W+,WZ0, 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
Standard Model: one extra –
the Higgs boson (H),
responsible for mass
No gravity
Still to
find…
Higgs
Boson
?Graviton ?
+ anti-particles. all fermions found
Conservation Laws
Tell us which processes can happen
Short-cut for Feynman diagrams
Conserved quantities in a reaction





1.
2.
3.
4.
•
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
Fundamental Particles

Anti-particles have
opposite
properties
e.g. Positron e+ has
Q=+1, Le=-1


Hence, particleantiparticle
combinations have
zero everything!

e.g. composite
particle  0
made of uu , dd
Baryon number is fractional, so that proton & neutron have B=1
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:
and their opposites:
red, green, blue
anti-red,anti-green anti-blue
Hadrons: where quarks hide

Hadrons are the bound states of quarks we
observe


Controlled by strong force, remember leptons don’t feel this
Only colourless states can be made
1.
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 ,+ ,2.
‘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:
Other Hadrons


These last states only contained up, down quarks
Also have strange, charm, top, bottom



We will consider only the strange quark



Can make hadrons with these also
….hence very large number of combinations!
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
(with spin ½)
Kaon mesons are
counterparts of pions with
s rather than d quark
Strange Baryons
 Sigma ,  Lamda,  Xi
(with spin 0)
Quark Jets

Don’t 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
Some Key Points

Forces are due to exchange of the fundamental
force carrying bosons


Know the fundamental particles


Confined in colourless hadrons
Added some more conservation laws



Three generations of quarks and leptons
Don’t observe free quarks


Photon,gluon,W+,W-,Zo (and presumably graviton)
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.
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……
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.
The Big Bang

Evidence for the Big Bang





The evolution of the universe


It is dark at night! See Olbers Paradox
Universe expanding
Cosmic microwave background
Relative abundance of elements in universe
Stages in the formation of the universe
Big Crunch ? http://lhcb.web.cern.ch/lhcb/
Looking at larger scales







Man
1m
Planet Earth
107 m
Solar System
1013 m
Star separation
1017 m
Galaxy size
1021 m
Galaxy separation
in a cluster of Galaxies
Large Scale Structure

1 light-day
10 light-years
100,000 light-years
5 million light-years
50 million light-years
1 billion light-years
Walls, voids etc.. in distribution of galaxies
Solar system
seen from the
outside!
Voyager 1
1977…
Picture, 1990
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

Hubble’s law:

v
Velocity
=
H
Hubble const.
x
d,
distance
H ~ 20 km/s/million light yrs
Age of Universe

Extrapolate back with Hubble’s law
d 1
t 
 1.5 1010 yrs
v H

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
Olber’s “Paradox”: Why is the sky dark
at night ?

If the observable universe is
1.
2.
3.

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)
Resolving Olbers “Paradox”

The universe is not infinitely old

Approx 15 billion years
Sky is dark at night because
1.

The speed of light is finite

We can only see part of the universe
Universe is young –
distant light hasn’t
reached us yet
and also
2.
Expansion causes
doppler shift (red-shift) of
light
So,Big Bang solves Paradox
Stages in the evolution of the Universe
1.
2.
3.
4.
Planck Era
GUT Era
Electroweak Era
Particle Era
Book:
“The first
three
minutes”, by
Steven
Weinberg
5.
6.
7.
8.
Era of Nucleosynthesis
Era of Nuclei
Era of Atoms
Era of Galaxies – Now!
(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

open
string
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.
closed
string
(2) The GUT Era: up to 10-35 seconds

We still don’t know a great deal but have some
better ideas !

Universe full of fundamental particles, antiparticles,
photons, gluons…everything!


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
(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
(4) The Particle Era: up to 10-3 seconds



Temperature now dropped to ~1012K
Contains almost equal amount of particles and
anti-particles

u , u , d , d , e  , e  , e , e

And photons, gluons…
Electroweak Force splits into Electromagnetism
and Weak Interaction.



As we cool further…
Confinement starts:


W+,W-,Z become heavy, get the Higgs boson (not found yet)
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
(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
75/25 % as
measured, good
evidence for big
bang


No stable nuclei with 5
particles, so very few
nuclei above He
formed
Nuclei only, energy too high to bind electrons into
atoms
The other nuclei come from Stars much later
(6) The Era of Nuclei:
3 minutes to 300,000 years

Universe is as hot as centre of sun (107K)

Plasma of light nuclei and electrons and photons
(7) Era of Atoms:
300,000 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!
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
COBE satellite, 1990
BUT not completely uniform
at 10-5 K scale
COBE was first to see
anisotropy, small fluctuations
in temperature.
Latest results WMAP Feb.
2003
Compatible with inflation model
(8) Era of Galaxies:
1 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
(but measurements on galaxy rotation show
particle physics does not give enough matter!
Dark matter ?)

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
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!
“I’d like to thank the Swedish Academy”: five ways you
can win a Nobel prize!
1.
Why is there more matter than anti-matter in the
universe ?
2.
Find the Higgs Boson.
3.
Is there a Cosmological constant ?
4.
What is dark matter ?
5.
Develop a Theory Of Everything !