Lecture 3

We started with a review of wave properties so that we could remind ourselves

- Waves can be spread out
- Waves can interfere
- Waves can go around corners

We also learned that there are different ways to view or look at waves

- Tuning fork waves

This wave is only a pure note if is played for a very long time. So we must strike the fork an let it ring. This means that it is spread out in time.

- Snaps

Short duration, localized waves.

**ANY WAVE CAN BE
PRODUCED BY COORDINATING A SERIES OF SNAPS**

**ANY WAVE CAN BE
PRODUCED BY COORDINATING A SERIES OF TUNING FORKS**

**BOTH ARE MUTUALLY
EXCLUSIVE****è YOU DONT HEAR A NOTE
WITH ONE SNAP. YOU DON’T HEAR A SNAP WITH ONE TUNING FORK.**

Certain real quantities now must follow this same type of relationship.

Uncertainty principle of QM

Δx Δp > h
position, momentum Δx= x_{2}-
x_{1}

ΔE Δt > h time energy

An event that is associated with a specific time cannont simultaneously be expected to be a single energy. If you try to define very precisely when an atom emits light your result will be an unclear determination of the lights energy. If you try to localize an electron then you loose track of its velocity.

QM must absorb these features into its formulation and it does.

$$**************************************************

So Maxwell had succeeded in writing down a complete set of relationships between

- +, -, N, S electric and magnetic charges
- E, B electric and magnetic fields

Eq.

Charges produce fields

Moving electric/magnetic charge produce Magnetic/Electric fields

Change electric/magnetic produce Magnetic/Electric

Combine these results and you predict waves moving at speed c.

If you are on a train the air moves with you in the train car. The speed of sound will be the nominal value for the people on the train but will appear faster or slower to and observer outside the train.

RELATIVITY

How describe motion

1) Establish a coordinate system

2-dimensional coordinate system (obviously need three coordinate for the most general description)

coordinates x,y,z

2) Establish time as a parameter.

3) Define relevant quanties

· Position

· Velocity

· Acceleration

ASIDE: We discussed our first classical model in terms of BBs. One additional feature of very small objects is that their motion might perhaps be simplified.

What difference might exist in the way that a BB vs a basketball might move ?

How does motion change based on observers location ?

1) Move to a new location

2) Observe from a moving location

**Transformations relate one observer to the next.**

· Translations

· Rotations

· Boosts

Galilean transformation for a 1-d boost.

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** **

This is the transformation on which we based our idea that light should move at different speeds depending on reference frame.

Einstein said what if it is a law of nature that the speed of light is constant in all reference frames ?

We are going to be asked to BREAK something to do this. We will need to give up some fundamental intuitive ideas to incorporate this principle. Galilean relativity becomes a valid transformation only when objects are moving slowly.

_{}

Try it for speed c.

Time dilation (Muon lifetime)

Length Contraction

Energy mass relation

Twin paradox

What would happen if we allowed our transformations to depend on position.

1900-1930 Special and General Relativity and QM

1897 Thomson discovers the
electron

1911

1932 Chadwick discovers the neutron

1930 Dirac combines QM and Special
Relativity

- Anti
particles
- Spin

What is spin ????????

It contains the normal notion of spinning classical objects

- Angular
momentum
- Rotating
charge has magnetic effect

**Defines Fermions and Bosons**- Fermions never overlap
- Bosons can pileup

Study there interactions:

- neutron decays to a proton, electron and an anti-electron neutrino

_{}

- pi-plus decays to mu-plus and a muon neutrino

_{}

- positive muon decays to a muon antineutrino, a positron and an electron neutrino

_{}

- K
zero decays to a
^{ }pi-minus and pi-plus via the weak interaction

_{}

- lambda zero decays to a proton and a pi-minus via the weak interaction

_{}

- a sigma plus decays to a proton and a pi-zero via the weak interaction

_{}

- electron positron annihilation to two photons

_{}

- xi-zero decays to a lambda zero and a pi-zero

_{}

- positive kaon decays to three pions

_{}

- sigma-zero decays to lambda zero and a photon

_{}

- omega minus decays to xi-zero and a negative pion

_{}

- positive kaon interacts with a proton to produce a neutral kaon and a delta++

_{}

- antiproton interacts with a proton to produce a neutron and an antineutron

_{}

- omega-minus decays to xi-zero, an electron and an electron antineutrino

_{}

atoms

Nucleus