126 The Poetry of Physics and The Physics of Poetry
The observer, Dr. A, sitting precisely in the middle of the train sees the
two flashes of lightning hit the train at exactly the same time. He is
sitting exactly in the middle of the train and, therefore, the times for the
transit of the signals of the lightning hitting the two ends of the train to
his eyes are the same, namely L/2c. He concludes that the two flashes of
lightning struck the train at exactly the same time.
The train travels a distance of vL/2c in the time it takes the light from
the lightning flashes hitting the train to travel into Dr. A’s eyes. The train
at this moment is represented by the solid lines. An observer, Dr. B, is
stationed at rest beside the railroad track so that he is exactly opposite the
moving observer, Dr. A, precisely at the moment when the light from the
lightning striking the ends of the train enters Dr. A’s eyes. Will the
stationary observer, Dr. B, also report that the two bolts of lightning
struck the train at the same time? In order to determine this, let us
consider how Dr. B will perceive the two events under consideration.
When the lightning actually struck the train, the train was farther down
the tracks by the amount vL/2c, as illustrated in Fig. 14.1. This is the
distance between the position of the dashed train when the lightning
strikes and the position of the solid train when Dr. A sees the two bolts of
lightning at the same time. Note that at the moment the lightning struck
the train, the stationary observer, Dr. B, was actually closer to the front
of the train than to the rear of the train. Because of the fact that the
velocity of light is a constant, the light from the two bolts of lightning
striking the front and the rear of the train travels towards our stationary
observer, Dr. B, at the same speed, c, even though the front of the train is
moving away from him and the rear of the train is moving towards him.
Because of the constancy of the velocity of light and the fact that the
stationary observer is closer to the front of the train when the lightning
strikes, he will see the lightning strike the front of the train before it hits
the rear of the train. He will conclude that the lightning struck the front
of the train before it hit the rear of the train. The stationary observer, Dr.
B, has a completely different sense of time from that of the moving
observer, Dr. A. The two events, which the moving observer, Dr. A
reported to be simultaneous, occur at different times in the frame of
reference of the stationary observer, Dr. B.
The discrepancy in the timing of the two events by our two observers
is due to the fact that the velocity of light is a constant in both frames of
reference. If the velocity of light added with the velocity of the train, as
our intuition would have us believe or as Newtonian physics would