1. Exam II Median Score: 78

2. Today: Continue Einstein’s Special Relativity Short intro to General Relativity Monday: What is Quantum Mechanics? (15 minutes) Last Clicker Competition!

3. A spaceship carrying an alien flies past an observer The observer sees the left turn signal blink once per second. The alien sees his turn signal blink… A)Once per second B)Less than once per second C)More than once per second D)Wong, aliens never use their turn signal Time dilation Which is the proper time?

4. A spaceship carrying an alien flies past an observer The observer sees the left turn signal blink once per second. The time between blinks is a “proper time” to the A)Alien B)Observer C)Both D)Neither, the alien is turning right Time dilation dt = ° dt 0 So dt observer = ° dt alien dt alien = (1/ ° ) dt observer

5. A spaceship carrying an alien flies past an observer The space craft is 5 meters long To the observer, the length is… A)5 meters B)Less than 5 meters C)More than 5 meters D)Wong, flying saucers are round Length contraction Which is the proper length?

6. 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 long pole fit in barn?

7. 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 barn What happens when barn doors close? Solution: Doors open and close at different times “Simultaneity” depends on frame of reference

8. 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

9. E = ° m 0 c 2 How can photons (particles of light) travel at the speed of light? °  infinity but m=0

10. 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?

11. 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) isBruno PontecorvokaonStanislav Mikheyev Alexei Smirnov Lincoln WolfensteinMikheyev– Smirnov–Wolfenstein effect Wikipedia

12. If a particle travels at a speed of.5c, ¯ is about A 3 x 10 8 m/s B 1.5 x 10 8 m/s C 0.5 D 1.00005 E.998

13. A 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… Ais exactly 3 seconds Bis about 3 seconds because the ball does not travel fast Cgreater than 3 seconds Dless than 3 seconds Edepends on the average speed of the ball

14. A 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… Aexactly 5 feet Bless than 5 feet Cgreater than 5 feet Ddepends on the distance to the space ship Edepends on the average speed of the ball

15. Which curve best represents the shape of the Lorentz factor, ° ? A B C D E

16. Muons created 15 km up in the Earth’s atmosphere take 50 ¹ sec to reach the Earth’s surface. Some muons reach the surface because… A in their frame, they take less than 50 ¹ sec B in their frame, they take greater than than 50 ¹ sec C in their frame they travel less than 15 km D (A) and (C) E (B) and (C)

17. 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

18. General Relativity Result: Clocks run faster at higher elevations dt’ = (1/f) dt (time between click ticks decreases) where f=1+gh/c 2 g= 9.8 m/s 2 h = increase in height Example:h= 10 meters givesf = 1+ 10 -15 Tiny, but it has been measured!

19. 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)