Friday, April 18, 2008

Went over problems 14 in problem sheet.

Went over Giancoli problems in relativity. Students did well on them.

Showed graphs of mass vs speed and speed vs time for a constant force (both Newtonian and Relativistic).

Introduced General Relativity.
Sprang from the mind of Einstein in 1916 paper.
General, because it handles acceleration, whereas the special theory of relativity only dealt with the special case of reference frames moving with respect to each other at constant velocity.

Life on Flat World skit.
We live on a sphere so it is possible to head off in opposite directions and meet.
Happens also in space. Satellite above Earth sends off two probes in opposite directions. They meet because they both orbit the Earth. Newton attributes this to gravity. Einstein said space itself is curved.

Mass tells space how to curve, space tells objects how to move. If you have a rubber sheet with nothing on it, it is flat. If you place objects on the sheet, it will sag. Objects moving on the sheet are affected by the sags and tend to be deflected towards the depressions.

Kindergarten view of General Relativity:
1. Light has energy
2. Energy and mass are connected (E = mc^2)
3. Mass is affected by gravity.
4. Light is affected by gravity.
5. Show thick light beam. If no mass, the beam is straight. If there is mass, the beam is bent. A runner around the track on an inside lane has an advantage because the path is shorter. The inner part of the light beam travels a shorter distance. But...since the speed of light is the same for all observers, the clock for the inner beam ticks more slowly (less ticks). Clocks run slow near sources of gravity!!

Note the difference between clocks in special relativity and those in general relativity. In special relativity, as you go by, I see your clock ticking slow. You are at rest in your rest frame and see me going by. You see my clock as ticking slow. We each see each others clock as ticking slow.

In general relativity, I am in the attic and you in the cellar. I see your clock ticking slow, you see my clock ticking fast. We each see our own clocks ticking correctly but see the differences in the other person's clock.

A black hole is a strong source of gravity. As you approach the black hole, I see your clock running slow, you see my clock running fast. You look back and see the entire future of the universe.

For homework, please look at Hewitt Relativity.