Physical Mathematics

Inconsistency in the Development of the Lorentz Factor in Section 3 of ‘On the Electrodynamics of Moving Bodies’

Abstract

Masahiko Makanae

In 1905, Albert Einstein published his paper ‘On the Electrodynamics of Moving Bodies’, which is referred as the special theory of relativity. In Section 3 of this work, he developed a factor for describing a moving system in terms of a reference stationary system known as the Lorentz factor. In the climax of the development of Lorentz factor in this section, Einstein provided the series of equations that contains the mutual terms c, v, t, and x’. Clearly, ‘c’ corresponds to the velocity of light, ‘v’ is the velocity of the moving system, and ‘t’ is the time passage in the reference stationary system. However, regarding x’, the meaning is not clear as a mutual term. Besides, the values of x', which should have identical values, differ for the various equations. Thus, there is an inconsistency as regarding the usage of x' in the development of the Lorentz factor in Section 3 of ‘On the electrodynamics of moving bodies’. This issue should be discussed not only from the viewpoint of mathematics, but also from the viewpoint of formal logic, which is a practical tool for the study of any science.