VI. The Theorem of the Addition of Velocities Employed in Classical Mechanics

Relativity: The Special and General TheoryAlbert Einstein

Let us suppose our old friend the railway carriage to be travelling along the rails with a constant velocity vv, and that a man traverses the length of the carriage in the direction of travel with a velocity ww. How quickly or, in other words, with what velocity WW 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 vv equal numerically to the velocity of the carriage. As a consequence of his walking, however, he traverses an additional distance ww relative to the carriage, and hence also relative to the embankment, in this second, the distance ww being numerically equal to the velocity with which he is walking. Thus in total be covers the distance W=v+wW=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.

VII. The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity

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