September 16, 2015
Einstein, History of Science, Special Theory of Relativity
The general consensus in literature concerning Einstein’s 1905 paper on special relativity, is that he independently derived the Lorentz transformations using a kinematic method. That is he was apparently unaware of the latter work of Lorentz and others while composing the paper. Here it is demonstrated that the derivation is mathematically inconsistent. There are several errors in the development and the main one is the inconsistent steps of requiring a partial derivative to be zero at one point, but necessarily finite at the last step. This derivative can only equal zero if the relative velocity between the frames goes to zero. It is also shown that the scheme of following a light beam reflecting between two moving mirrors (the kinematic method) cannot correctly arrive at the transformations. A study of many textbooks on relativity will reveal that this derivation is almost never used to introduce the Lorentz transformations. Only one source was found that discussed this particular method; and it was in an appendix.