RelativityChallenge - Root Cause of 1905 Mistake (c) 2005

The Time Function

Although Einstein creates a time function (or "Funktion"), as noted in Section 3 of his manuscript, he incorrectly treats it as an equation in the remainder of his derivation.

Equations and Functions

The problem occurs because Einstein wrote the function informally, in much the same way he would write an equation. Notice the difference between the equation:

and the formal function definition

Functions must be invoked before they are used. They can be explicitly or implicitly invoked. In computer science, functions are typically explicitly invoked due to the specific way in which instructions are communicated to the computer. In other disciplines, however, functions are often implicitly invoked and treated as equations. Generally, this does not result in a problem unless one or more of the invoking arguments is complex.

Analysis of Einstein's Function Invocation

In order to illustrate the problem, the function must be explicitly invoked. By presenting the derivation in this manner, it will be easy to show that Einstein actually uses two time equations, one as the stand-alone equation and another that is used to produce the X-axis transformation equation.

Discussion

By invoking the function explicitly, we show that Einstein implicitly invoked the function twice, once to produce the stand-alone time equation and once as used to create the X-axis transformation equation.

Einstein implicitly performed the function invocation by replacing t with x'/(V-v) in creating the X-axis transformation. However, he does not use the same complex argument when producing the stand-alone time equation. The result is an invalid system of equations that is discovered and validated using the "if a=bc then b=a/c" math rule.

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