We started with a review of wave properties so that we could remind ourselves
We also learned that there are different ways to view or look at 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.
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 EXCLUSIVEŤ YOU DONT HEAR A NOTE WITH ONE SNAP. YOU DONíT 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= x2- x1
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
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.
How describe motion
1) Establish a coordinate system
2-dimensional coordinate system (obviously need three coordinate for the most general description)
2) Establish time as a parameter.
3) Define relevant quanties
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.
Galilean transformation for a 1-d boost.
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)
Energy mass relation
What would happen if we allowed our transformations to depend on position.
1900-1930 Special and General Relativity and QM
1897 Thomson discovers the
1932 Chadwick discovers the neutron
1930 Dirac combines QM and Special Relativity
What is spin ????????
† It contains the normal notion of spinning classical objects
Study there interactions: