Relativity (1931)/Section 6

Layout 2

←

The Principle of Relativity (in the Restricted Sense)

Relativity
Albert Einstein, illustrated by [[Author:Hermann Struck|Hermann Struck]], translated by Robert William Lawson

The Theorem of the Addition of Velocities employed in Classical Mechanics

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

→

New York: Peter Smith, pages 19–20

Albert EinsteinHermann Struck4371909Relativity — The Theorem of the Addition of Velocities employed in Classical MechanicsRobert William Lawson

VI

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 he 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.