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2:03 PM
(Ignore all my self-ranting above. Working on re-deriving special relativity. Right now I suspect there is an invalid simplification being made in the standard equation, because it looks like I might be able to get the equation using polar coordinates by neglecting motion in r. Terrell-Penrose rotation implies there should be some relative acceleration, I'll be re-deriving special relativity a second time once I finish with the first to see what effect the relative acceleration has.)
Using a definition of simultaneity such that relative time is equal to distance divided by c, I get a derivative of t with some interesting properties, (xdx/dt + ydy/Dy + zdz/dt)/(c*distance), which implies that motion directly away and directly towards an observer creates a divergence in observed time equal to change in distance over c. That is, time dilation moving away, time contraction moving towards.
Experimenting with polar coordinates now to see if the standard equation results from considering centripetal force
 
3:10 PM
Hrm. This would be much easier with an assumption of linearity.
 
 
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