A. Devise a procedure for synchronizing clocks at two ends of a train by means of light signals, and show that an observer who regards the train as moving will NOT consider them synchronized. One possibility: Every minute, clock-1 on one end sends a light signal to clock-2 on the other end of the train. Clock-2 sets its time to 0s at the instant it receives the light from clock-1, then waits 30s and sends a return signal. When clock-1 receives the return signal, it will be late by some amount T. T is the transit time for the light to travel both directions, so clock-2 sets itself back by T/2. Then they are synchronized. This technique is used extensively by any two systems separated in space that need accuractely synchronized clocks.
B. Does the postulate of relativity require gravity, as well as light, to have a finite velocity of propagation? Explain. Yes, one corallary of the two postulates are that no signal or mass can travel faster than the speed of light, thus the velocity of gravitation must be less than or equal to the speed of light.
D. In the example of the spaceship with mirrors, state the observable fact on which both observers agree. The observers see both return flashes simultaneously. See 1st sentence pg 103.