How Many Postulates Are Needed to Derive 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. Some researchers even assert that one postulate, i.e. the principle of relativity, is enough to derive a Lorentz-type transformation. The present study investigates how many postulates are needed to derive the Lorentz transformation without covertly adding more postulates. We found that at least four postulates are necessary to derive the Lorentz transformation when applying only mathematical and logical rules in derivation. They are 1) the principle of relativity; 2) the constancy of the speed of light; 3) motion has no impact on the length or spatial distance in the directions perpendicular to its velocity; 4) the coefficient of the spatial coordinate term such as _x_ (or _x’_) term equals that of the velocity-time term _vt_ (or _v’t’_) on the right-hand side of the Lorentz spatial transformation equations. Without the third and the fourth postulates as constraints, an infinite number of space and time transformations satisfy the constancy of the speed of light and the principle of relativity. The well-known Voigt transformation is one of them. The Lorentz transformation that satisfies the principle of relativity is a sufficient condition for the constancy of the speed of light, but not a necessary condition. Therefore, it cannot be logically derived from the constancy of the speed of light and the principle of relativity. All derivations using Einstein’s two postulates or the principle of relativity alone involve covertly adding more postulates or/and making mathematical and logical mistakes. Since the Lorentz transformation is a sufficient condition for the constancy of the speed of light while the latter and the principle of relativity are not sufficient conditions for the former, it is more logically appropriate to postulate the Lorentz transformation rather than the constancy of the speed of light as the primary principle of the theory of relativity.