Addition of Velocities
Law of Propagation of Light and Relativity Principle
Section Six, Section Seven
Einstein states the Theorem of the addition of velocities in Section Six. Let us apply this theorem to the light emitted by you on the embankment, as seen by you and by Einstein on the carriage traveling with velocity v into the same direction as the light.
When Einstein talks about the velocity of light, he has not only kinematical or mechanical laws in mind but also the electromagnetism in general (one of the major fields of physics); he intends to include all these fields into the sphere of the principle of relativity. Thus Einstein concludes as follows:
But this result comes into conflict with the principle of relativity set forth in Section 5. For, like every other general law of nature, the law of the transmission of light in vacuo must, according to the principle of relativity, be the same for the railway cariage as reference-body as when the rails are the body of reference. (pp. 22-23)
Where did we go wrong? Einstein predicts his answer:
As a result of an analysis of the physical conceptions of time and space, it became evident that in reality there is not he least incompatibility between the principle of relativity and the law of propagation of light, and that by systematically holding fast to both these laws a logically rigid theory could be arrived at. This theory has been called the special theory of relativity ... (pp. 23-24)
Last modified, April 18, 2002. (c) Soshichi Uchii
suchii@bun.kyoto-u.ac.jp
