Time Dilation Cosmology 3: Mathematical Proof of the $\sqrt{3}$ Temporal and $\sqrt{2}$ Spatial Acceleration Factors

This is the fifth paper in a series on Time Dilation Cosmology, TDC. TDC is an eternal holographic model of the universe based on time dilation that ties astrophysics to quantum physics and resolves all the conundrums in astrophysics and serves as a model for the unified field. In the author’s previous four TDC papers, it was demonstrated that all gravitationally induced velocities are compensation for the apparent difference in the rates of time, “dRt”, due to mass/energy densities, and, vice-versa, in all force-induced velocities the dRt is compensation for the velocity, so the uniform evolution of the continuum at c is maintained at the invariant 1 s/s rate of time of the universe as a whole. These compensations make it impossible for an event to lag behind or get ahead of the evolving continuum. When the author did the first velocity formula derivations in “General Relativity: Effects in Time as Causation” [1], the author felt the explanations for the appearance of the $\sqrt{2}$ spatial and the $\sqrt{3}$ temporal acceleration factors in the formulas were correct, but poorly explained and incomplete. This paper is a proof of the temporal and spatial acceleration factors used in the time dilation-based velocity formula derivations in the Time Dilation Cosmology model.