Poetry of Physics and the Physics of Poetry

The Special Theory of Relativity 127

The Special Theory of Relativity 121

the front and the rear of the train when the train is in the position

represented by the dashed lines. The train has a length L and velocity v.

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.

Fig. 14.1

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.

lightning

instruct us, then the velocity of the signals arriving from the front and
the rear of the train to the stationary observer, Dr. B would not have
been the same. The velocity of the light from the lightning striking the
rear of the train would have traveled towards the stationary observer
with the velocity c + v while the signal from the front of the train would
have traveled with the velocity c – v as Fig. 14.1 indicates. The distance
from the rear of the train to the stationary observer when the lightning
strikes is L(1 + v/c)/2 whereas the distance to the front of the train is
L(1 – v/c)/2. This means that if the velocities had added in the
Newtonian sense, they would have arrived at exactly the same time. We
must, therefore, attribute the different sense of time possessed by our two
observers to be due the constancy of the velocity of light.

Fig. 14.1

The result of the constancy of the velocity of light will also affect the
spatial perceptions of the two observers moving with a constant velocity
with respect to each other. The difference in the spatial perception of our
two observers manifests itself in terms of the Lorentz-Fitzgerald
contraction. Let us consider a stick, which, at rest, has the length Lo,