**Title**

Communicating Special Relativity Theory’s Mathematical Inconsistencies

**Summary**

This paper reveals Einstein’s mathematical mistakes in his 1905 paper, his 1912 paper, and his Relativity book. While the material contained in this paper is accurate, I have found more effective ways of communicating my findings. Please see Episode 17 in the Podcast section, for example.

**Abstract**

**Einstein’s Special Relativity Theory is believed to be mathematically consistent. Here we find subtle and difficult to detect mathematical mistakes in each of Einstein’s derivations. In his 1912 paper, the mistake is traced to the misuse of set algebra instead of statement algebra. Specifically, he uses the “=” relation on the Real set instead of the “=” relation on the Binary set, incorrectly establishing the equivalence of equations. Because the two “=” relations operate on different sets, they cannot be used interchangeably. In his 1905 paper, he begins the derivation of the transformations with the equation ξ=cτ. Mathematically, his final transformation equations fail the internal validity check because the stand-alone equation he derives for τ does not always equal τ=ξ/c. This mistake is traced to the mistreatment of the time function, which is the result of the partial differential equation, as an equation rather than as a function.**

**Status**

- Created: February 2005
- Last Revised: August 2005
- Publication Status: Accepted for publication by Galilean Electrodynamics