How Many Postulates Are Needed for Deriving the Lorentz Transformation

It is generally believed that Einstein derived special relativity from two postulates, the principle of relativity and the constancy of the speed of light, without paying much attention to the results of the Michelson-Morley experiment and Lorentz’s interpretation. In this study, the minimum conditions for deriving the Lorentz transformation are investigated, and one of Einstein’s derivations and one textbook derivation of the Lorentz transformation analyzed. It was found that Einstein’s two postulates are not sufficient for deriving the Lorentz transformation and at least 4 postulates are necessary. In order to obtain the Lorentz transformation, Einstein made several logical mistakes by using same symbols for different quantities and variables. When these symbols are made unequivocal, Einstein’s derivation cannot lead to the Lorentz transformation. Therefore, it is a false assertion that Einstein derived special relativity from only two postulates. This study demonstrates that there are an infinite number of linear and non-linear transformations that are consistent with the principle of relativity and the constancy of the speed of light. Having four postulates for deriving the Lorentz transformation is effectively equivalent to postulating the Lorentz transformation directly.