THE THEOREM OF THE
ADDITION OF VELOCITIES
EMPLOYED IN CLASSICAL MECHANICS


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