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AntonioLao · Quote #24 (**permalink**) 04-15-2005, 12:52 PM

Quote:

Originally Posted by battybat

My problem is that to get a complete picture of what's happening I need to be working in an expanding frame of reference

Try using an Archimedean spiral whose general polar equation is given by

$r=a\theta^{\frac{1}{n}}$

when n=-2, it's called lituus spiral; n=-1, hyperbolic spiral; n=1, Archimedes' spiral; n=2, Fermat's spiral. Look more about it at http://mathworld.wolfram.com/ArchimedeanSpiral.html

I am also trying to use the spiral to justify my own Lorentz invariance expression given by

$\mathbf{a}\cdot\mathbf{r}=c^2$

a is generalized acceleration, r is the metric, c is the speed of light.