Here's a quick review of the 15 minute discussion we had about relativity.
The speed of light is the same for all observers.
As the speed of a "moving" frame increases relative to a "stationary" frame, all the lengths in the moving frame appear to contract according to observers in the stationary frame. (The reverse is also true.)
As the speed of a "moving" frame increases relative to a "stationary" frame, all the clocks in the moving frame appear to run slower according to observers in the stationary frame. (The reverse is also true.)
Events that are simultaneous in one frame of reference are not simultaneous in another frame that is moving with respect to the first.
So now you're ready for the puzzle ...
A command ship is located exactly midway between two scout ships, A and B. All three ships are moving in formation with the same velocity, relative to a "stationary" observer, C. The commander sends an isotropic broadcast signal (an electromagnetic wave) to the front and the back scout ships instructing them to increase their speed. In the spaceship frame of reference, the two scout ships receive the signals and increase their speeds simultaneously, thereby maintaining the same distance of separation. However, the stationary observer C does not see this. Answer the following:
According to C, does the distance between the scout ships increase, decrease or stay the same?
According to C, which ship received the signal first, or was it at the same time? (Think about the first statement!)
(Another hint: Be sure that your two answers are consistent with one another.)
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