SR, Spring '10

Homework 11, covers Mermin Chapter 13 (and the return of the zombie question that won't die part 2 1/2)

(a) What is the point of this chapter?

(b) What question does it raise that you'd like to discuss further?

2. This is the zombie question. It's really the same question as before, but let me take yet another stab at formulating it in a way that will encourage you to approach it in a way that will actually allow you to do it. So... Alice and her friend Charlie live on a train station platform -- Alice all the way on the left, and Charlie all the way on the right, a distance X away (as measured, of course, by Alice and Charlie). Alice and Charlie have previously synchronized their watches (in their own rest frame of course). And they have previously arranged that, when their watches both read "t=0", Charlie will push the "start" button on a time-bomb which is set to explode a time T after the "start" button is pushed. So in a coordinate system in which Alice is located at x=0 and Charlie and the bomb are located at x=X, the space and time coordinates of the bomb's explosion are X and T.

Now assume that Bob is riding past on a train moving to the right at speed v. It happens that his watch reads "t'=0" just as he passes Alice at the left end of the platform. And we should assume that he uses a coordinate system which assigns position x'=0 to himself. Now the question is: what temporal and spatial coordinates (i.e., what values of t' and x') will Bob assign to the explosion of the bomb? I'll pose here a series of questions which should allow you to step through this systematically to the answer:

(a) According to Bob, what does Charlie's watch read at t'=0 -- i.e., at the moment Bob and Alice are next to each other?

(b) Since Charlie's watch reads "t = T" when the bomb actually explodes, how much time does Charlie's watch tick off between Bob's passing Alice (i.e., t'=0) and the explosion of the bomb?

(c) Since (according to Bob) Charlie's watch is running slow this whole time, how much time actually elapses between t'=0 and the explosion of the bomb?

This should be the time T' that we were looking for. Now let's figure out how to get X'.

(d) According to Bob, how far away is the Bomb at t'=0 (i.e., when Bob and Alice are next to each other)?

(e) According to Bob, how fast is the Bomb moving toward him?

(f) According to Bob, how much time elapses before the bomb explodes?

(g) So, according to Bob, how far to his right is it when it explodes?

This should be the position X' that we were looking for.