I'm struggling with an introductory example of special relativity. We haven't done the math yet so I would like an explanation based only on the fact that the speed of light is the same in every inertial frame.
An airplane travels east with a certain speed. There is a "clock" at both ends of the airplane. If there is a flash in the middle of the airplane and we're in the airplane's inertial frame, both clocks will register the flash at the same time, say 3.
But if we are an observer standing on the ground, in our inertial frame the light will reach the clock at the end of the airplane faster than the clock in the front. So the clock in the back may reads 3 when the clock in the front only reads 1, for example.
Question: Let's say the airplane has a speed v. The light's speed as it travels in the inertial frame of the observer towards the back will c+v, and the speed as it travels towards the front will be c-v. Let's say the distance from the middle to the back and front respectively is L. Then the time it takes for the light to travel from the middle to the back is L/(c+v) and to the front L/(c-v).
Shouldn't these be the same? If not, why can we say that the clocks will read 3 when the light hits them, no matter what frame is used? This is the argument the book uses to say that the clock must be less than 3, i.e. 1, in the front when the light hits the clock in the back in the observer's inertial frame.