Special Relativity, Spring '10

Homework 6, covers Mermin Chapter 7 (and everything previous)

2. Alice and Bob get bored with messing around near the traintracks and decide to have a new kind of adventure. Alice decides to fly on a spaceship to alpha centauri, which is (let's say) 6 light years (i.e., 6 c-yrs) away. Bob stays on earth. Alice's ship flies at a speed of 3/5 c with respect to the earth and alpha centauri (which are at rest with respect to each other). Every year, starting precisely one year after her departure (according to her on-board clocks), Alice sends a little flash of light back toward Bob. (Maybe it's a radio transmission telling him how she's doing... all that matters for our purposes is that it travels at the speed of light.) That's the setup; now the questions:

(a) Draw a space-time diagram showing world lines for Alice, Bob, alpha centauri, and all of the light flashes that Alice sends home.

(b) In Bob's frame, how long after Alice's departure does she actually send the first flash back toward home?

(c) When does Bob actually receive that flash?

(d) How much time elapses between receipt of subsequent flashes?

(e) Assuming Alice stops sending the flashes after she arrives at alpha centauri, how many total flashes does she send?

(f) When (according to his own clocks) does Bob receive the last flash?

(g) What is the story that Alice will tell about why she only sent the number of flashes you said in part (e)?

3. This one doesn't have too much to do with Chapter 7, but seems like a good "review exercise" to work through. (It's basically the same as #2 from last week's homework, but with one small modification.) So back to Alice and Bob on the train and tracks respectively. The length of Alice's train is L, and there are previously-synchronized clocks at the front and back. (Both of those statements are "according to Alice".) She's at the back of the train, and when the clock there reads "t=0" she throws a ball at speed u (slower than c) toward the front of the train. The clock at the front of the train is designed to record its reading when the ball hits it. Obviously, this happens after a time L/u, and so that's what the clock reads when the ball gets there. (Blah blah blah with the steel bolts and whatnot!) Now the assignment is: tell the whole story from Bob's point of view. In particular, explain in gory mathematical detail how Bob will explain that final clock reading.