Adding Velocities without Exceeding the Velocity of Light: Wilhelm Wien's Algorithm (1904) and Albert Einstein's Light Postulate (1905)

We propose a likely path to Einstein’s postulate of the constancy of the velocity of light as part of his theory of relativity in 1905. Our principal claim is that the issue of adding velocities played a crucial role in pointing the way to positing a second postulate, for Einstein realized that the principle of relativity is not sufficient to provide the basis for the new theory. We suggest that Wilhelm Wien’s novel algorithm for adding velocities, published in 1904 in Annalen der Physik, stimulated Einstein’s thinking, which led to the light postulate.