RelativityChallenge - Revealing Einstein's 1912 Mistake (c) 2005

Revisiting Einstein's 1912 Derivation

Einstein creates the Special Relativity transformation equations in Section 9 of his 1912 manuscript. He begins with equations for two spheres:

He then states that these equations are equivalent to each other, which is expressed mathematically as:

We will call this statement P.

Einstein then mathematically concludes that the above expression produces

We will call this statement Q.

Confirming the Math Rule Violation

In Einstein's 1912 derivation, P implies Q, such that any solution for P is also a solution for Q, regardless of the value of lambda. Therefore Q can be used as a replacement for P as long as P would have been TRUE. Such an implication does not enable us to pick any combination of x, y, z, and t, but instead we are constrained to only those values that form a sphere. Using Q as a replacement for P for all combinations of x, y, z, t, represents a mathematical error.

While implication does not allow us to use Q for all combinations of x, y, z, t, and lambda, we need to determine if equivalence will. Although Einstein determines that statement Q is an identity, it does not remove the requirement that P must be equivalent to Q for all values of x, y, z, t, and lambda. This includes the case where lambda is 0. In such cases, Q can be TRUE while P is FALSE, indicating that the statements are not equivalent. Using Q as a replacement for P represents a mathematical error because the two statements are not equivalent.

Q does not mathematically follow from P for all values of x, y, z, t, and lambda. Thus, the remainder of Einstein's 1912 derivation is invalidated because Q is incorrectly used to replace P.

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