Mathematical Issue in Section 2 of 'On the Electrodynamics of Moving Bodies'

Abstract

In Albert Einstein’s first published work, ‘On the Electrodynamics of Moving Bodies’, he introduced a set of equations, namely $t_B−t_A=\frac{γ_{AB}}{c−v}$ and $t′_A−t_B=\frac{γ_{AB}}{c+v}$ which have the form ‘time=distance/velocity’, as a part of the conclusion of Section 2. In these equations, Einstein implied that an event in a moving system viewed from within that moving system differs from the same event viewed from a reference stationary system. This perspective became the fundamental basis of the special theory of relativity (STR).

However, considering Sections 1 and 2 of Einstein’s paper using practical examples and numerical values, we find that an inconsistency is caused by using ‘relative speed’ as ‘velocity’ in the universal equation ‘time=distance/ velocity’. In the conventional mathematics, only ‘mobile speed’ is admitted as ‘velocity’ in ‘time=distance/velocity’. This is a pure mathematical issue that should be solved if we continue to use the STR, under the premise that Sections 1 and 2 of ‘On the Electrodynamics of Moving Bodies’ are correct.