Einstein made mathematical errors in each of his derivations including his original 1905 paper, his 1912 paper, and Appendix 1 of his Relativity book. These mistakes invalidate his theoretical conclusions.
I state that there are mathematical rules and definitions that exist independent of physics; Equivalence, Implication and the rule that if a=bc then b=a/c. I further state that these rules can be used to assess the validity of Einstein’s derivations.
In Section 3 of his 1905 paper, he begins to create his equations using an equation in the form a=bc. Mathematically, if a=bc then b=a/c. Einstein’s final equations must adhere to this mathematical rule, and we find that generally they do not.
In Appendix 1 of his Relativity book and in his 1912 paper, he begins with equations in the form a-b=0 and c-d=0. He then concludes that a-b=c-d using a technique called a Generalized Multiplier. In this case, Einstein incorrectly replaces the mathematical statement “a-b=0 is equivalent to c-d=0” with the statement “a-b=c-d”. Mathematically, the two statements are not equivalent and his replacement is in error.
See the Papers section for the mathematical proofs behind these findings.
