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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In Episode 17, we take an advanced look at Einstein’s derivation of the SRT transformation equations given in Section 3 of his 1905 paper to generate the equations and analyze the problem in creating his Tau equation. In the the past, I have reviewed Einstein’s derivation from an algebraic perspective. While that perspective remains valid, a precise analysis and re-examination requires that Einstein’s derivation be reviewed from a functions perspective. While the material in this Episode will be most comfortable to those with an understanding of namespaces, overloaded variables, and functions, it should be appropriate to all viewers interested in increasing their understanding of Special Relativity.
This video assumes some familiarity with functions, which might be considered an Advanced topic for some viewers/listeners. If you are not familiar with the behavior of functions, I encourage you to first watch Episode 8.
In this Episode, I present Part 1 of a 2 part series that I delivered at this year’s AAAS/NPA conference held at the University of New Mexico. This presentation looks at the impact of bi-directional movement in generating the equations associated with moving systems. It establishes the foundational equations that are used by the leading models (e.g., Einstein, Lorentz, Michelson-Morley) as well as by the model of Complete and Incomplete Coordinate Systems. This presentation also uses the math associated with an Incomplete Coordinate System to graphically explain key mathematical elements that are found in Einstein’s 1905 paper.
In Episode 4, I introduce the concept of a Coordinate System along with two specific variants; a Complete Coordinate System and an Incomplete Coordinate System. I explain what these systems are and how they are different from what Einstein proposed in his theory.
[podcast]http://www.relativitychallenge.com/media/RelativityChallenge.Com-Episode4.mp3[/podcast]
I delivered a presentation at a conference held at the University of Connecticut in May 2007. This presentation is a more polished version of the material covered in Episode #2 of the podcast. It presents, in mathematical terms, the problem in Einstein’s 1905 derivation, points out the root cause, and briefly introduces the Model of Complete and Incomplete Coordinate Systems. Two versions are available for download; one as the stand-alone version and a second with audio annotation.
Presentation in PowerPoint Format
Storrs Conference Presentation (video – wmv format)
In episode 2, I take a look at the steps Einstein used to create his equations. Specifically, we look at the rules of math (e.g., algebra) to help identify a problem in Einstein’s derivation. This podcast was originally aired in April 2007.
[podcast]http://www.relativitychallenge.com/media/RelativityChallenge.Com-Episode2.mp3[/podcast]
