A traveler in a rocket of proper length 2d sets up a coordinate system S' with its origin O' anchored at the exact middle of the rocket and the x' axis along the rocket's length. At time t' = 0 she ignites a flashbulb at O'. (a) Write down the coordinates (x'_F,t'_F )and (x'_B, t'_B ) for the arrival of the light at the front and back of the rocket. (b) Now consider the same experiment as observed from a frame S relative to which the rocket is traveling with speed V (with S and S' in the standard configuration). Use the inverse Lorentz transformation to find the coordinates (x_F,t_F )and (x_B,t_B ) for the arrival of the two signals. Explain clearly in words why the two arrivals are simultaneous in S' but not in S. This phenomenon is called the relativity of simultaneity.