RelativityChallenge.Com

“I live 20 miles per hour from the University.” Is that statement confusing?  It should be.  In Episode 20, we take a look at Rates and Functions, and discuss how they have been mistreated for the past century.  More importantly, we’ll take a look at how key concepts and mathematics can get confused if we don’t say the right thing.  For example, would you feel confused if I had began with “I live 20 miles from the University.”?  This Episode is a replay of a presentation that I delivered the Pacific Region AAAS conference at San Francisco State University in August 2009.

This Episode summarizes and synthesizes a lot of the material we’ve looked at over the past 9 videos.  New visitors will find that it serves as a good introduction to the material on the site.

The following specific points are covered in this video:

• A brief history of moving systems equations and SRT
• A look at the mathematical and conceptual mistakes we’re still making today
• Revisiting the improved results to the Michelson-Morley and Ives-Stillwell equations
• Implications on position-based navigation systems

In addition to the video, a PDF version of the presentation is available for download.
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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 and a set of rules that the scientific community already accepts. This approach has the advantage of being readily verifiable by the greater scientific community.

Specifically, there are two main problems associated with Einstein’s SRT derivation.  As indicated in Episode 20, wavelength is commonly misstated as a measure (e.g., meters) when, in fact, it should be correctly stated as a rate (e.g., meters per cycle).  This is a significant conceptual and mathematical problem in Einstein’s work.

Readers familiar with namespaces and overloaded variables, and their relationship withfunctions, will find the second problem accurately addressed in Episode 17 of the Podcast Series – A Look at Einstein’s 1905 Derivation (Video).  Simply stated, Einstein mistreats the Tau function as if it were an equation. Readers without this background will find the algebra-based approach given in the Storrs Conference Presentation (Video), easier to follow. Interestingly, Einstein and Lorentz drop a Beta term in each of their respective derivations.  This point is also discussed briefly in Episode 17 of the Podcast series.

Identification of the problem in Einstein’s 1905 derivation is best performed using the formal tools and techniques of Computer Science. I have found that this discipline offers a superior method of explaining how functions work and provides a specific notation that makes it easy to view the problem.

Begin by considering the following pseudo-code:
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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.
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