LECTURE II

Modern Physics

Atomic Particles

Atoms are made of protons, neutrons and electrons

99.999999999999% of the atom is empty space Electrons have locations

described by probability functions

Nuclei have protons and neutrons

nucleus

mp = 1836 me

Leptons

An electron is the most common example of a lepton – particles which appear pointlike

Neutrinos are also leptons There are 3 generations of leptons, each has

a massive particle and an associated neutrino Each lepton also has an anti-lepton (for

example the electron and positron) Heavier leptons decay into lighter leptons

plus neutrinos (but lepton number must be conserved in these decays)

Types of Leptons

Lepton Charge

Mass (GeV/c2)

Electron neutrino

0 0

Electron -1 0.000511

Muon neutrino

0 0

Muon -1 0.106

Tau neutrino

0 0

Tau -1 175

Quarks

Experiments have shown that protons and neutrons are made of smaller particles

We call them “quarks”, a phrase coined by Murray Gellman after James Joyce’s “three quarks for Muster Mark”

Every quark has an anti-quark

Modern picture of atom

Types of Quarks

Flavor Charge Mass (GeV/c2)

Up 2/3 0.003

Down -1/3 0.006

Charm 2/3 1.3

Strange -1/3 0.1

Top 2/3 175

Bottom -1/3 4.3

Quarks come in three generations

All normal matter is made of the lightest 2 quarks

Combining Quarks

Particles made of quarks are called hadrons

3 quarks can combine to make a baryon (examples are protons and neutrons)

A quark and an anti-quark can combine to make a meson (examples are pions and kaons)

proton

meson

Fractional quark electromagnetic charges add to integers in all hadrons

Color charges

Each quark has a color charge and each anti-quark has an anti-color charge

Particles made of quarks are color neutral, either R+B+G or color + anti-color

Quarks are continually changing their colors – they are not one color

Gluon exchange Quarks exchange gluons within a nucleon

movie

Atomic Forces

Electrons are bound to nucleus by Coulomb (electromagnetic) force

Protons in nucleus are held together by residual strong nuclear force

Neutrons can beta-decay into protons by weak nuclear force, emitting an electron and an anti-neutrino

F = k q1 q2

r2

n = p + e +

Protons and neutrons are made up of quarks bound together by gluons.

Like charges repel, so why does the positive charge within a proton not cause the proton toexplode?

The (Coulomb) repulsion isdefeated by a new force:The STRONG force.

Fundamental Forces

Gravity and the electromagnetic forces both have infinite range but gravity is 1036 times weaker at a given distance

The strong and weak forces are both short range forces (<10-14 m)

The weak force is 108 times weaker than the strong force within a nucleus

Force Carriers

The Uncertainty Principle Classical physics

Measurement uncertainty is due to limitations of the measurement apparatus

There is no limit in principle to how accurate a measurement can be made

Quantum Mechanics There is a fundamental limit to the accuracy of a

measurement determined by the Heisenburg uncertainty principle

If a measurement of position is made with precision x and a simultaneous measurement of linear momentum is made with precision p, then the product of the two uncertainties can never be less than h/2

xx p

The Uncertainty Principle

Virtual particles: created due to the UP

E t

xx p

Force Carriers

Each force has a particle which carries the force and is unaffected by it

Photons carry the electromagnetic force between charged particles

Gluons carry the strong force between color charged quarks

Force Carriers

Separating two quarks creates more quarks as energy from the color-force field increases until it is enough to form 2 new quarks

Weak force is carried by W and Z particles; heavier quarks and leptons decay into lighter ones by changing flavor

Forces are mediated by particles

Photons mediate electric and magnetic forces. (Faraday and Ampère demonstrated that electric and magnetic forces were different manifestations of the same “electromagnetic” force.)

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ee

Forces are mediated by particles

Gluons mediate the strong force.

q

q

q

q

g

There is also the weak force

It is responsible for the process by which two protons “fuse” together in the core of the sun.

It is “carried” by the W and Z particles.

Neutrons transform to protons via beta decay. It is a result of the weakforce.

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Gravity is the only other force.

It so weak as to be negligible in particle physics experiments.

Einstein’s “General Theory of Relativity” superseded Newton’s Theory of Gravity in 1915.

An “ultimate” theory should explain how gravitons mediate gravity…….?

Unifying Forces

Weak and electromagnetic forces have been unified into the “electroweak” force They have equal strength at 10-18 m Weak force is so much weaker at larger distances

because the W and Z particles are massive and the photon is massless

Attempts to unify the strong force with the electroweak force are called “Grand Unified Theories”

There is no accepted GUT at present

Gravity

Gravity may be carried by the graviton – it has not yet been detected

Gravity is not relevant on the sub-atomic scale because it is so weak

Scientists are trying to find a “Theory of Everything” which can connect General Relativity (the current theory of gravity) to the other 3 forces

There is no accepted Theory of Everything (TOE) at present

Electric Magnetic

ElectromagneticWeak

StrongElectroweak

Gravity

Theory of Everything?

Standard Model

Ampere, Faraday, Maxwell

Glashow, Salam, Weinberg

The Standard Model

The weak and electromagnetic forces were unified by Glashow, Weinberg &Salam. Electroweak force

GWS also explained how to incorporateQCD, the model of the strong force.

Their model defines the laws for all known interactions except gravity.

Force Summary

Spin

Spin is a purely quantum mechanical property which can be measured and which must be conserved in particle interactions

Particles with half-integer spin are “fermions” Particles with integer spin are “bosons”

* Graviton has spin 2

Quantum numbers

Electric charge (fractional for quarks, integer for everything else)

Spin (half-integer or integer) Color charge (overall neutral in particles) Flavor (type of quark) Lepton family number (electron, muon or tau) Fermions obey the Pauli exclusion principle –

no 2 fermions in the same atom can have identical quantum numbers

Bosons do not obey the Pauli principle

Standard Model

6 quarks (and 6 anti-quarks) 6 leptons (and 6 anti-leptons) 4 forces Force carriers (, W+, W-, Zo, 8 gluons, graviton)

Some questions

Do free quarks exist? Did they ever? Why do we observe matter and almost no antimatter if

we believe there is a symmetry between the two in the universe?

Why can't the Standard Model predict a particle's mass? Are quarks and leptons actually fundamental, or made

up of even more fundamental particles? Why are there exactly three generations of quarks and

leptons? How does gravity fit into all of this?