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33-115 Exam II Fall 2009

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Score

Exam II Median Score: 78

Today:Continue Einstein’s Special Relativity

Short intro to General Relativity

Monday:What is Quantum Mechanics? (15 minutes)Last Clicker Competition!

A spaceship carrying an alien flies past an observerThe observer sees the left turn signal blink once per second.

The alien sees his turn signal blink…

A) Once per secondB) Less than once per secondC) More than once per secondD) Wong, aliens never use their turn signal

Time dilation

Which is the proper time?

A spaceship carrying an alien flies past an observerThe observer sees the left turn signal blink once per second.

The time between blinks is a “proper time” to the

A) AlienB) ObserverC) BothD) Neither, the alien is turning right

Time dilation dt = ° dt0

So dtobserver=° dtalien

dtalien = (1/° ) dtobserver

A spaceship carrying an alien flies past an observerThe space craft is 5 meters long

To the observer, the length is…

A) 5 metersB) Less than 5 metersC) More than 5 metersD) Wong, flying saucers are round

Length contraction

Which is the proper length?

Pole Vaulter Paradox

Doors open, pole longer than barn

Pole length contracts as vaulter runs very fast forward

Doors are shut while vaulter runs through barn

Doors open and vault runs out

Does longpole fit in barn?

The View from the Pole Vaulter

Doors open, pole longer than barn

Barn contracts and moves towards Pole Vaulter

The Paradox: Pole doesn’t fit in barnWhat happens when barn doors close?

Solution: Doors open and close at different times“Simultaneity” depends on frame of reference

The Twin Paradox: Part 1)• Sue and Jane are identical twins.• Sue gets on a rocket ship which travels very fast• During the trip, which one ages the slowest?

Part 2) (The Real Paradox)• Sue’s rocket returns to earth.• Which twin is the youngest?• Sue is younger!• Full answer involves treatment of acceleration• Not just a constant velocity problem

Each thinks the other is aging slower

E = ° m0c2

How can photons (particles of light) travel at the speed of light?

° infinity

but m=0

Neutrinos

• Elementary particle

• Most of sun’s energy release is neutrino energy

• We thought they were massless until ~2000

• How could we make that mistake?

• Could photons have a small mass?

A practical method for investigating neutrino oscillations was first suggested by Bruno Pontecorvo in 1957 using an analogy with the neutral kaon system; over the subsequent 10 years he developed the mathematical formalism and the modern formulation of vacuum oscillations. In 1985 Stanislav Mikheyev and Alexei Smirnov (expanding on 1978 work by Lincoln Wolfenstein) noted that flavor oscillations can be modified when neutrinos propagate through matter. This so-called Mikheyev–Smirnov–Wolfenstein effect (MSW effect) is

Wikipedia

1 If a particle travels at a speed of .5c,¯ is about

A 3 x 10 8 m/sB 1.5 x 10 8 m/sC 0.5D 1.00005E .998

2A boy throws a ball 5 feet straight up and catches it when it comes down a time 3 seconds later. To an observer moving upwards in fast space ship, the time interval is…

A is exactly 3 secondsB is about 3 seconds because the ball does

not travel fastC greater than 3 secondsD less than 3 secondsE depends on the average speed of the ball

3A boy throws a ball five feet straight up and catches it when it comes down a time 3 seconds later. To an observer moving upwards in fast space ship, the went up…

A exactly 5 feetB less than 5 feetC greater than 5 feetD depends on the distance to the space shipE depends on the average speed of the ball

4 Which curve best represents the shape of the Lorentz factor, ° ?

A

B

C

DE

5Muons created 15 km up in the Earth’s atmosphere take 50¹sec to reach the Earth’s surface. Some muons reach the surface because…

A in their frame, they take less than 50¹secB in their frame, they take greater than than 50¹secC in their frame they travel less than 15 kmD (A) and (C)E (B) and (C)

General Relativity(Gravity and acceleration)

Einstein’s Equivalence Principle

Standing inside a box (elevator?), you can’t tell the difference between accelerating and being in a gravitational field

Which leads him to conclude that

• Time is effected by gravity

• Gravity is a warping of space and time

General Relativity Result:

Clocks run faster at higher elevations

dt’ = (1/f) dt (time between click ticks decreases)

where f=1+gh/c2

g= 9.8 m/s2

h = increase in height

Example: h= 10 metersgives f = 1+ 10-15

Tiny, but it has been measured!

Is General Relativity Relevant to Anyone?

• Astrophysics• Studies of the universe

• Big bang• Black holes• Dark matter• Dark energy

• Global Position Systems• Special Relativity fast satellites have slow clocks

loose 7.3 microseconds/day• General Relativity far above Earth clocks speed up

gain 45 microseconds/day• Net error 38 microseconds/day (needs to be corrected)