From Osher Doctorow Ph.D.
The gamma or beta factor of Special Relativity or its inverse is given by: 1) b = sqrt(1 - v^2/c^2) Since 1 = 1^2, this motivates the idea of an ellipse via: 2) (r/ro)^2 = (definition) b^2 = 1 - v^2/c^2 which is the ellipse: 3) r^2/ro^2 + v^2/c^2 = 1 The simplest differential equation which can be derived from this is obtained by setting: 4) v^2 = 1 +/- d(r^2)/dt The positive sign results in the solution: 5) r^2 = exp(k1)exp(-t/ro^2) where k1 is the constant of integration. The negative sign results in the solution: 6) r^2 = exp(k1)exp(t/ro^2) Thus, we obtain either exponential growth/expansion or exponential contraction with time. Since v is more or less unrestricted, r could be related to a macroscopic or microscopic radius or length including a principal radius of the Universe. Interestingly, (6) appears to permit acceleration of the Universe by implicit differentiation, although it doesn't require it. Osher Doctorow Ph.D.