Mathematical Analysis And Mistake Identification
Many scientist critical of Special Relativity have challenged Einstein's theory on the grounds of logical inconsistencies (e.g., challenges to the twin paradox or time dilation). While they offer compelling arguments, they have not found definitive evidence resulting in a crisis that the scientific community must respond to.
My challenge to the validity of Einstein's equations is based on mathematics, which greatly simplifies my argument. This foundation in mathematics establishes a set of rules that the scientific community already accepts. This approach has the advantage of being readily verifiable by the greater scientific community.
Readers familiar with namespaces and overloaded variables, and their relationship with functions, will find the problem accurately addressed in Episode 17 of the Podcast Series – A Look at Einstein’s 1905 Derivation. Other readers will find the algebra-based approach given in the Storrs Conference Presentation, and summarized below, easier to follow.
Here we summarize Einstein's Xi derivation as given in his 1905 paper. As illustrated in the following figure, Einstein begins with one math statement and then performs three algebraic substitutions
Since Einstein's derivation consists of three substitutions, mathematically, each highlighted equation must produce the same result on the right-hand side when given the same input values. (Note: His final multiplication of each transformation equation by sqrt(1-v^2/c^2) is not shown, since by that time the problem has already occurred.)
As shown above, each equation does not produce the same result on the right-hand side when given the same input value, representing a mathematical problem in Einstein's derivation. This problem is discussed in detail in Episode 2 of the RelativityChallenge.Com Podcast and in the Storrs Conference presentation. In addition, Episode 8 of the Podcast explains the root cause as the mistreatment of Tau as an equation rather than as a function.
With the problem identified, the inconsistencies in each of Einstein's derivations can be confirmed by analyzing them using accepted mathematical rules.
Click on the Diagram for more information
Approach
The following links are provided for those unable to click on the diagram above.
- Mathematical Analysis and Problem Identification
- Define Success Criteria
- 1905 Manuscript Analysis
- 1912 Manuscript Analysis
- Relativity Book Analysis
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