Have been following along as you folks struggle to define and discuss the theory.
Would this 23 page article on special relativity be of any aid to you guys? It has a glossary, examples and lots of charts and graphics that might help the discussion settle upon agreed upon defined terms to further your conjectures.
http://science.howstuffworks.com/science-vs-myth/everyday-myths/relativity.htm
To give you an idea of some of what it covers, here's the last page's summary:
Conclusion
SR deals with contractions and dilations that are not in agreement with our commonsense views of the universe. In fact, they almost appear ludicrous. Yet, there have been several observations that agree with the predictions of SR. So, until the theory is proved wrong or a simpler theory produces the same results, SR will maintain its position as the best theory out there.
Here are five concepts you have discovered in this article:
There is no such thing as an absolute (completely stationary) frame of reference.
The laws of physics apply equally to all frames of reference.
The speed of light is constant in all frames of reference.
There is no simultaneity of events between separate frames of reference.
You are never too old to learn.
As you pursue a better understanding of SR, Do Not fall prey to these errant statements:
Time slows as speed increases. (Only when viewed by another frame of reference)
Objects shorten as speed increases. (Same as above)
SR can't handle acceleration. (Biggest misconception about SR)
Mass increases with speed. (Energy increases, not the rest mass)
Nothing can travel faster than the speed of light. Crossing the speed of light barrier from either a faster or a slower speed is disallowed.
The beauty in the theory of special relativity is that it gives us laws from which we can unite space and time and also energy and mass. Special relativity is definitely a thinking person's playground.