A rocket ship of length L (in the rocket's frame) leaves the earth at speed v. A light signal is sent after it which arrives at the rocket's tail at t'=0 and t=0 according to earth clocks. My question is: Why is it that the total time (according to earth) for the signal to get to the head and back can be found by multiplying the rocket's time to get back by gamma, but the time to reach the head (according to earth) can't be found by multiplying the rocket's time to reach head by gamma? I know it has to do with how you can multiply time by gamma only if the two events happen at the same place (same place in the proper frame? Is the Proper frame *defined* to be the frame in which the two events happen at the same place?), and that you can multiply distance by gamma only when the two events happen at the same time (in the proper frame? Which is *defined* to be the frame in which they happen at the same time)? So in the rocket problem we are allowed to multiply the length of the Rocket by gamma to get the length of the rocket according to earth people because it's possible for the earth people to find a ruler such that the ends of the ruler can touch the ends of the rocket at the same time? When we want to know the distance, the two events are the left end of the ruler on the left end of the rocket, and the right end of the ruler on the right end of the rocket? When we want to know the time, the two events are the light being at the tip of the rocket's tail before reaching the head and after coming back? Can you give me an example of a rocket problem with a light signal in which to find the *length* of the rocket according to earth people I *can't* take the length of the rocket according to the rocket and multiply it by gamma, but in which to find the *time* according to earth people that it takes for the light signal to get from the tail to the head I *can* multiply the time that it takes in the rocket's frame for the light to go from the tail to the head by gamma? I want to know a problem as similar to your rocket problem as possible where I can do the above.