October 8, 2013

A marble rolling about in a bowl – not suitable for a local description? Rationale for just 3-dimensions?

Is a 3-surface model description of local motion, even though Ricci tensor (contraction of Riemannian 4-curvature tensor) is zero? Might not  a 3-surface (3-space), together with MTC Modified Time Construct Δ2V3L for example, change in rate of Hubble expansion of 3-volume, suffice to describe not only how a 3-volume evolves, but also describe local motion in such 3-surface? Might it be somewhat like ( product space?) so-called neo-Newtonian space and time model, but instead using change in rate of Hubble expansion  ΔH  as cosmic time tc ?

Would an equation with stress tensor and 3-curvature suffice? Radio signal delay and curvilinear null geodesics in 3-dimension gravitational field, would still seem suitable. Still limit of finite velocity of light, with increasing inertia, and hence mass. Could one dispense with light cone; hence no space-like and time-like description? Yet still 3-dimensional shortest null geodesic. Could one still have a 3-dimensional black hole description? Although possible deformation of 3-surface, still gravity wave description seem more  feasible in 4-dimension? However smoothness of manifold favors 3 dimensions. Overall then isn’t a 3-surface description simpler and more realistic for a gravitation description? That is, although 4-surface model might be useful, don’t we live in an evolving 3-surface; with curvature only for near compact objects?

The latter being consistent with mathematical statement that the number of ways in which to smooth a manifold is greatest in 3 or fewer dimensions. Entropic flavor?

Also non-abelian for 3-dimensions (rather than just 2-D) description would seem consistent with MSM Modified Set Generality: alleged ongoing maximizing of cardinality of set for all stages and for all scales of System?

Is our 3-volume regional volume Vyoung or old? The LSS (large scale streaming) of our small cluster (Local Group) is ~630 km/sec, and change in rate of Hubble parameter ΔH is undetected (i.e. linear) out to at least redshift z~ .3-.4  i.e. ~5 billion years? But if always exponentially changing, then never any detectable non-linear change? Likewise for similar duration in future, since far out on equiangular spiral curve, with always alleged exponential decline of change in Hubble parameter. So considering these two factors, there would seem to be a very slow deceleration of expansion, but still a quite high large scale peculiar velocity, a tangent vector to equiangular spiral modified global trajectory in SRM model.

Therefore the duration of our 3-manifold (3-volume) would seem to eventually be extremely long (trillion+ years?). Hence we would to seem to be in a very early stage of our ‘universe’, which then likely has a very atypical appearance. Perhaps only hard GRBs (gamma ray bursts from BH jetting, if such colliding (merging?) beams’ accelerator process continues for entire age of ‘universe, even if extreme?) and red dwarfs (fission stars?) detectable for such far future long quiescent stages for our 3-manifold and System? If long persistence for red dwarf fission stars, then terrestrial life would also seem persistent, and unending, even for extremely long duration 3-manifold.  TMM


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