So imagine two lightning bolts hit the ground, simultaneously to a stationary observer. There is also a person on a train traveling to the right at a constant velocity. I know that if he started in the midpoint, he would see the light from the right first because he is shortening the distance. I know the equation for calculating the time difference is $t'_2-t'_1= \gamma[-\frac{V}{c^2}(x_2-x_1)]$.
However, I am very confused because the time difference only depends on the positions of the lightning strikes and the velocity of the train. But if the train was to the left of the leftmost lightning strike, the left light would reach him first which is the opposite of what happens when he is between them. I am confused because this doesn't change the equation at all. Obviously changing x' should change this equation, but I don't know why or how.
