Revisiting Einstein's 1905 Derivation
Einstein creates the Special Relativity transformation equations in Section 3 of his 1905 manuscript. Midway through the section, he begins to derive the transformation equation using an equation in the form a=bc.
Einstein completes his derivations at the end of Section 3, giving us his final transformation equations.
Confirming the Math Rule Violation
The mathematical rule states that "if a=bc then b=a/c". However, we find that in general with Einstein's equations, a/c does not equal b. In following Einstein's computation in Section 3 of his 1905 paper, we mathematically find that:
Here we further find that generally:
or
This represents a math error that must be corrected. This mistake invalidates the remainder of Einstein's 1905 derivation.
(Note, modern convention uses c instead of V. Also note that modern convention uses x', y', z', and t' instead of Greek variables.)
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