Quantum Quantum Phenomena Phenomena

II:II:Matter Matter MattersMatters

Chris Parkes April/May 2003

Hydrogen atomHydrogen atom Quantum numbers Electron intrinsic spin

Other atomsOther atoms More electrons! Pauli Exclusion Principle Periodic Table

Particle PhysicsParticle Physics The fundamental particles The fundamental forces

CosmologyCosmology The big bang The evolution of the

universe

Fundamental PhysicsAtomic Structure2nd Handout

Second Handout

http://ppewww.ph.gla.ac.uk/~parkes/teaching/QP/QP.html

The Structure of MatterThe Structure of Matter

Quarks have most of massQuarks have most of mass Electrons spatial extent and Electrons spatial extent and

determine chemical propertiesdetermine chemical properties

Fundamental ?Fundamental ? 450BC Empedocles, Aristotle450BC Empedocles, Aristotle

4 basic elements Similar philosophies in China / India

Democritus “Atoms & space”Democritus “Atoms & space”

1661 Boyle Elements1661 Boyle Elements …Medeleyev lots of them !

C19 Dalton, elements composed of atomsC19 Dalton, elements composed of atoms

nucleusnucleus Protons, neutrons….Protons, neutrons….

Lots more started turning up!Lots more started turning up! QuarksQuarks

Standard modelStandard model

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

Looking at smaller scales Looking at smaller scales

Naked EyeNaked Eye 1010-4-4 m m Light MicroscopeLight Microscope 1010-6-6 m m Size of Atom Size of Atom 1010-10-10 m m Size of ProtonSize of Proton 1010-15-15 m m Size of quark, electron, neutrino..Size of quark, electron, neutrino.. 0 (so far..)0 (so far..)

Fundamental particles No constituents

Study using Study using Particle AcceleratorsParticle Accelerators Labs: CERN, Fermilab… Acelerators: LEP/LHC, Tevatron

Collide particles at high energiesCollide particles at high energies Look at what comes out !Look at what comes out !

•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

Particle Physics AcceleratorsParticle Physics Accelerators

Fermions & BosonsFermions & Bosons

We introduced spin for electron…but general We introduced spin for electron…but general particle propertyparticle property

Determines particle propertiesDetermines particle properties Half-integer spin particles – Half-integer spin particles – FermionsFermions

Fermi-Dirac Statistics Pauli Exclusion principle

Whole-integer spin particles – Whole-integer spin particles – BosonsBosons Bose-Einstein statistics No Exclusion principle, as many as you want in same state

Matter is made of the fundamental fermionsMatter is made of the fundamental fermions Forces are carried by the fundamental bosonsForces are carried by the fundamental bosons

Standard ModelStandard Model is theory which contains these is theory which contains these fundamental particlesfundamental particles

Fermions: Building blocks of matterFermions: Building blocks of matter

This is what everything around us is made ofThis is what everything around us is made of But there are more !

Proton: uudProton: uud Neutron: uddNeutron: udd electronelectron Neutrino given off in Beta decayNeutrino given off in Beta decay

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 >0 0 weak

QUARKS

LEPTONS

The first generation fermionsThe first generation fermions

All spin ½ particles

Forces of natureForces of nature

Forces mediated by particle exchangeForces mediated by particle exchange

e.g. electromagnetism :

photon exchange between electrically charged particles

Force acts on particles with that type of “charge”

Feynman Diagram

Bosons: Force CarriersBosons: Force Carriers

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

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 mThe four forces and their carriersThe four forces and their carriers

Spin 1, except graviton spin 2

Forces : some basic Forces : some basic consequencesconsequences

Strong Strong glues quarks to make protons / neutrons Glues protons / neutrons to make nuclei

ElectromagnetismElectromagnetism Bind electrons to nuclei Sticks atoms together to make molecules

GravityGravity Holds large lumps of matter together: stars, planets, galaxies

Weak Weak Radioactive decay Cross-generational couplings….

Feynman DiagramsFeynman Diagrams

We already saw one forWe already saw one for electron,positron electron,positron annihilationannihilation

Here is neutron decayHere is neutron decay

By following sets of rules, we can see if this By following sets of rules, we can see if this reaction will happenreaction will happen

                                                         

                                                                                        

Particle interactionsParticle interactions

Some basic standard model vertices:Some basic standard model vertices:

Anti-matterAnti-matter

Each particle has an anti-particleEach particle has an anti-particle e.g. electron / positron

Properties are oppositeProperties are opposite Opposite charge (and weak and colour) same mass and spin

Bubble Chamber photo,

A very old fashioned photographic form of particle detector

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:

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.”

A typical modern particle A typical modern particle physics experimentphysics experiment

DELPHI experiment @ LEP collider

Particle and anti-particle Particle and anti-particle annihilate to pure energyannihilate to pure energy

m is rest massm is rest mass Add K.E. termAdd K.E. term Basis of most modern particle Basis of most modern particle

physics accelerator exptsphysics accelerator expts Smash highly energetic particle and

anti-particle together

E=mcE=mc22

or ratheror ratherEE22=(pc)=(pc)22+(mc+(mc22))22

dd

uu

vv

ee

ee

,

,

,

,

WW

ZZ

gluongluon

photonphoton

gravitongraviton

,

,

,

,

,

00

Particles and their anti-particles

1st generation fermions Bosons

Basic KinematicsBasic Kinematics

Apply what you have learnt about relativityApply what you have learnt about relativity e.g. particle A decays into particles B & Ce.g. particle A decays into particles B & C

Work in rest frame of particle A

ReactionReaction

momentum momentum

EnergyEnergy

2222

0

CBBBA

CBA

CB

mpmpm

EEm

pp

CBA

CBA

CB

mmm

pp

So particles go off back-to-back

and we must have enough energy to make them

Energy,momentum conservation – but energy includes rest mass

II Rabi

Three generationsThree generations

•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

And ONLY 3 ! LEP from number of neutrinos

Bosons: graviton, W+,W- Z0, gluon, photon

+ anti-particles. all fermions found

Standard Model: one extra –the Higgs boson (H), responsible for mass

No gravity

Still to find…

Higgs Boson

?Graviton ?

Conservation LawsConservation Laws

Tell us which processes can happenTell us which processes can happen Short-cut for Feynman diagramsShort-cut for Feynman diagrams Conserved quantities in a reactionConserved quantities in a reaction

Same before – initial state As after – final state

1. Momentum vector, p2. Energy E, relativistic so due to momentum and rest mass3. Baryon number B

• Number of quarks remains constant4. Electric Charge Q

• Helpfully, most particles have charge as superscript on name• e.g. +

• Lepton number, for each generation: Le,L,L

Fundamental ParticlesFundamental Particles

Anti-particles have Anti-particles have opposite opposite propertiesproperties

e.g. Positron e+ has

Q=+1, Le=-1

Hence, particle-Hence, particle-antiparticle antiparticle combinations have combinations have zero everything!zero everything!

e.g. composite particle

made of dduu ,

0

Baryon number is fractional, so that proton & neutron have B=1

ConfinementConfinement Strong force very strong !Strong force very strong ! Quarks bound cannot break freeQuarks bound cannot break free

No free quarks Lower energy to produce new particles than separate quarksLower energy to produce new particles than separate quarks All particles observed have no net colourAll 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

Hadrons: where quarks hideHadrons: where quarks hide Hadrons are the bound states of quarks we Hadrons are the bound states of quarks we

observeobserve Controlled by strong force, remember leptons don’t feel this

Only colourless states can be madeOnly colourless states can be made1. 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 HadronsOther Hadrons These last states only contained up, down quarksThese last states only contained up, down quarks Also have strange, charm, top, bottomAlso have strange, charm, top, bottom

Can make hadrons with these also ….hence very large number of combinations!

We will consider only the strange quarkWe 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 =-1Strange 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

Strange Baryons

Sigma , Lamda, Xi

(with spin ½)

(with spin 0)

Quark JetsQuark Jets

Don’t observe free quarksDon’t observe free quarks

Quarks form into composite Quarks form into composite states of two quarks states of two quarks (mesons) or three quarks (mesons) or three quarks (baryons)(baryons)

in particle detectors often in particle detectors often see showers of these see showers of these particles – particles – jetsjets of mesons of mesons and baryonsand baryons

Jet of mesons &BaryonsProduced from one initial high Energy quarkOr anti-quark

Jet of particles seen in trackingSystem of detector

Some Key PointsSome Key Points

Forces are due to exchange of the fundamental Forces are due to exchange of the fundamental force carrying bosonsforce carrying bosons

Photon,gluon,W+,W-,Zo (and presumably graviton)

Know the fundamental particlesKnow the fundamental particles Three generations of quarks and leptons

Don’t observe free quarksDon’t observe free quarks Confined in colourless hadrons

Added some more conservation lawsAdded some more conservation laws Energy, momentum, electric charge Baryon number, lepton number

Particle interactions can be written as Feynman Particle interactions can be written as Feynman diagramsdiagrams

Know the basic vertices, and conservation laws to see whether or not a reaction will occur.

Searching for a Grand Unified Searching for a Grand Unified TheoryTheory

Electroweak theory well established in SMElectroweak 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 ???? Unifies with strong force also at high energy ?? …………then maybe eventually combine gravity also……then maybe eventually combine gravity also……

Particle Physics GlossaryParticle 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 BangThe Big Bang

Evidence for the Big BangEvidence 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 universeThe evolution of the universe Stages in the formation of the universe

Big Crunch ? http://lhcb.web.cern.ch/lhcb/Big Crunch ? http://lhcb.web.cern.ch/lhcb/

Looking at larger scales Looking at larger scales

ManMan 1 m1 m Planet EarthPlanet Earth 101077 m m Solar System Solar System 10101313 m m1 light-day1 light-day Star separationStar separation 10101717 m m10 light-years10 light-years Galaxy sizeGalaxy size 10102121 m m100,000 light-years100,000 light-years Galaxy separation Galaxy separation 5 million light-years5 million light-years

in a cluster of Galaxies in a cluster of Galaxies 50 million light-years50 million light-years Large Scale StructureLarge Scale Structure 1 billion light-years1 billion light-years

Walls, voids etc.. in distribution of galaxiesSolar system seen from the outside!

Voyager 1

1977…

Picture, 1990

The expanding UniverseThe expanding Universe

Light from other galaxies is red-shiftedLight from other galaxies is red-shifted Doppler shift Edwin Hubble (1929)

Whole universe is uniformly expandingWhole universe is uniformly expanding There is There is no centreno centre to the universe to the universe

Hubble’s law:Hubble’s law:

v = H x d,

Velocity Hubble const. distance

H ~ 20 km/s/million light yrs

Expansion of space, not in space

Age of UniverseAge of Universe

Extrapolate back with Hubble’s lawExtrapolate back with Hubble’s law

Hence universe came into existence with very Hence universe came into existence with very high density, expanded out from therehigh density, expanded out from there

Particle and Nuclear physics determined the early Particle and Nuclear physics determined the early stages of evolution of the universestages of evolution of the universe

yrsHv

dt 10105.1

1

Olber’s “Paradox”: Why is the sky dark Olber’s “Paradox”: Why is the sky dark at night ?at night ?

If the observable universe isIf the observable universe is1. Static (eternal)

2. Infinite

3. Approximately uniformly filled with stars

Then sky should be Then sky should be as bright as the surface of a staras 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”Resolving Olbers “Paradox”

The universe is not infinitely oldThe universe is not infinitely old Approx 15 billion years

The speed of light is finiteThe speed of light is finite We can only see part of the universe

Sky is dark at night because

1. 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 UniverseStages in the evolution of the Universe1.1. Planck EraPlanck Era

2.2. GUT EraGUT Era

3.3. Electroweak EraElectroweak Era

4.4. Particle EraParticle Era

5.5. Era of Nucleosynthesis Era of Nucleosynthesis 6.6. Era of NucleiEra of Nuclei7.7. Era of AtomsEra of Atoms8.8. Era of Galaxies – Now!Era of Galaxies – Now!

Book:

“The first three minutes”, by Steven Weinberg

(1) Planck Era: up to 10(1) Planck Era: up to 10-43-43 seconds seconds

Mysterious !Mysterious ! Universe begins at very high temperatureUniverse begins at very high temperature Maybe gravity unified with the other forces ?Maybe gravity unified with the other forces ? General Relativity and Quantum mechanics have General Relativity and Quantum mechanics have

never been successfully combined.never been successfully combined. We need a theory of Quantum GravityWe 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

(2) The GUT Era: up to 10(2) The GUT Era: up to 10-35-35 seconds seconds

We still don’t know a great deal but have some We still don’t know a great deal but have some better ideas !better ideas !

Universe full of fundamental particles, antiparticles, Universe full of fundamental particles, antiparticles, photons, gluons…everything!photons, gluons…everything!

No composite particles

Maybe the electroweak and strong forces (separate Maybe the electroweak and strong forces (separate in Standard Model) become united ? (in Standard Model) become united ? (GUTGUT))

Particle physics experiments give some support for converging coupling constants

InflationInflation: a short period of rapid expansion in the : a short period of rapid expansion in the universe. 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 103) The Electroweak Era: up to 10-10-10 seconds seconds

Universe cooling, but still very hot, 10Universe cooling, but still very hot, 102828KK Again, no composite particles yet.Again, no composite particles yet. Three forces in the universeThree forces in the universe

Gravity Strong Electroweak

Electromagnetism and weak force are unified in Electromagnetism and weak force are unified in ElectroweakElectroweak

W+,W-,Z are massless, like the photons and gluons

(4) The Particle Era: up to 10(4) The Particle Era: up to 10-3-3 seconds seconds Temperature now dropped to ~10Temperature now dropped to ~101212KK Contains almost equal amount of particles and Contains almost equal amount of particles and

anti-particlesanti-particles And photons, gluons…

ElectroweakElectroweak Force splits into Force splits into ElectromagnetismElectromagnetism and and WeakWeak Interaction. Interaction.

W+,W-,Z become heavy, get the Higgs boson (not found yet)

As we cool further…As we cool further… Confinement starts:Confinement starts:

Quarks, anti-quarks,gluons combine to form protons and neutrons

Antimatter disappearsAntimatter disappears Matter/anti-matter cancel out. Small excess of matter ? Why ?

Particle physics experiments are investigating

eeeedduu ,,,,,,,

(5) Era of Nucleosythensis: (5) Era of Nucleosythensis: 0.001seconds to 3 minutes0.001seconds to 3 minutes

Temperature 10Temperature 101212 to 10 to 1099 K K The first composite particles, the protons and The first composite particles, the protons and

neutrons combine to form light nuclei:neutrons combine to form light nuclei: At the End:At the End:

75% (by mass) Hydrogen nuclei p,pn,pnn 25% (by mass) Helium nuclei ppn,ppnn ~0% Lithium

Nuclei onlyNuclei only, energy too high to bind electrons , energy too high to bind electrons into atomsinto atoms

The other nuclei come from Stars The other nuclei come from Stars muchmuch later later

75/25 % as measured, good evidence for big bang

No stable nuclei with 5 particles, so very few nuclei above He formed

(6) The Era of Nuclei:(6) The Era of Nuclei:3 minutes to 300,000 years3 minutes to 300,000 years

Universe is as hot as centre of sun (10Universe is as hot as centre of sun (1077K)K)

PlasmaPlasma of light nuclei and electrons and photons of light nuclei and electrons and photons

(7) Era of Atoms:(7) Era of Atoms:300,000 to 1 billion years300,000 to 1 billion years

Universe cools so atoms can be formed (3000K)Universe cools so atoms can be formed (3000K) Electrons captured by nucleiElectrons captured by nuclei

Universe is transparent – photons can fly around freely !Universe is transparent – photons can fly around freely ! No longer electrons that interact with them

This is how the This is how the microwave backgroundmicrowave background was created was created Most impressive evidence for big bang Universe was once very hot!

Cosmic Microwave BackgroundCosmic Microwave Background

Photons from when atoms formedPhotons from when atoms formed Universe continued to expand and coolUniverse continued to expand and cool Expect remnant radiation with 2.7K blackbody Expect remnant radiation with 2.7K blackbody

spectrum with isotropic spectrumspectrum 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:(8) Era of Galaxies:1 billion to 15 billion years (NOW)1 billion to 15 billion years (NOW)

Gravity plays its roleGravity plays its role Neutral H and He gas attractedNeutral H and He gas attracted

Small density variations are amplified Form gas cloudsForm gas clouds …….And eventually stars .And eventually stars

Thermonuclear reactions in stars form heavier Thermonuclear reactions in stars form heavier atomsatoms

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 ?)

The Future of the Universe ?The Future of the Universe ?

Gravity fights the acceleration of the universeGravity fights the acceleration of the universe Expansion of universe could slow,stop, and then Expansion of universe could slow,stop, and then

contract.contract. Big Crunch?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 Could expand forever, but expansion slower and slower…slower…

And if there is a cosmological constant…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 I’d like to thank the Swedish Academy”: five ways Academy”: five ways youyou can can

win a Nobel prize!win a Nobel prize!

1.1. Why is there more matter than anti-matter in the Why is there more matter than anti-matter in the universe ?universe ?

2.2. Find the Higgs Boson.Find the Higgs Boson.

3.3. Is there a Cosmological constant ?Is there a Cosmological constant ?

4.4. What is dark matter ?What is dark matter ?

5.5. Develop a Theory Of Everything !Develop a Theory Of Everything !