Let us suppose our old friend the railway carriage to be travelling along the rails with a constant velocity v, and that a man traverses the length of the carriage in the direction of travel with a velocity w.  How quickly or, in other words, with what velocity W does the man advance relative to the embankment during the process ?  The only possible answer seems to result from the following consideration:  If the man were to stand still for a second, he would advance relative to the embankment through a distance v equal numerically to the velocity of the carriage.  As a consequence of his walking, however, he traverses an additional distance w relative to the carriage, and hence also relative to the embankment, in this second, the distance w being numerically equal to the velocity with which he is walking.  Thus in total be covers the distance W=v+w relative to the embankment in the second considered.  We shall see later that this result, which expresses the theorem of the addition of velocities employed in classical mechanics, cannot be maintained ; in other words, the law that we have just written down does not hold in reality.  For the time being, however, we shall assume its correctness.

The apparent incompatibility of the
law of propagation of light with the
principle of relativity

There is hardly a simpler law in physics than that according to which light is propagated in empty space.  Every child at school knows, or believes he knows, that this propagation takes place in straight lines with a velocity c= 300,000 km./sec.  At all events we know with great exactness that this velocity is the same for all colours, because if this were not the case, the minimum of emission would not be observed simultaneously for different colours during the eclipse of a fixed star by its dark neighbour.  By means of similar considerations based on observa- tions of double stars, the Dutch astronomer De Sitter was also able to show that the velocity of propagation of light cannot depend on the velocity of motion of the body emitting the light.  The assumption that this velocity of propagation is dependent on the direction “in space” is in itself improbable.

In short, let us assume that the simple law of the constancy of the velocity of light c (in vacuum) is justifiably believed by the child at school.  Who would imagine that this simple law has plunged the conscientiously thoughtful physicist into the greatest intellectual difficulties?  Let us consider how these difficulties arise.