April 17, 2014

Eratosthenes unbound?

Just as Eratosthenes of Alexandria measured the circumference of the earth (but not it’s easily measured tilt, from summer to winter solstice and horizon intercept, divided by 2), might we now measure the circumference, radius, surface area, and volume of alleged divergent System S≡{UT}, but for just 1 UT for current spherical shell MGS (Modified Global Simultaneity) stage?

More specifically, for cosine equiangular φ (angle between radial vector and tangent vector) for φ=45 degrees for example, together with adjacent radial side, and 13.8 byrs hypotenuse, one would have .7 =cos 45= radius/hypotenuse (13.8). That is, 13.8 x .7 = 9.66 Byrs for modified global radial time proxy (for ‘distance’). In comparison, the smallest radial extent for MGS stage, for a set of 3-volumes, would still be positive definite. Then circumference of MGS spherical shell is 2πr, with surface area of 4πr2. And 3-volume of such stage of System would be 4/3πr3. So for current MGS stage, the radial extent of System would be much less than our current 13.8 byrs modified global trajectory for our 3-volume manifold. Thus from an overall perspective, the System (i.e. radius of MGS spherical shell) would have a smaller size than an assumed radial Big Bang explosiveness; the latter rather has a modified global trajectory distance proxy of 13.8 byrs. Nevertheless, MGS and Hubble expansion for our changing 3-volume, are both interdependent modified global variables; that is, they change together.
In principle, instead of utilizing a time proxy, one could integrate the velocity over 13.8 byrs to give total distance of arc length to rm minimum stage. Or what might the average velocity be? As an approximation, could one discard most all binned velocities, and consider only an assumed extremely high finite velocity for near and at rm minimum stage? One has 1010 cm/s for light velocity. Then for example for ~90 greater orders of magnitude, one would have 1 google velocity, 10100 cm/s. Or ~1082 light years distance for over 1 second for near rm minimum, since ~1018 cm/lyr.  Nature’s warp engine?

But then the corresponding very early Hubble expansion would be enormous. Was the energy density i.e. temperature, so great that subsequent (~10-2-102 sec. later?) nuclear-synthesis energy density level was sustainable, even at such extreme increased 3-volume size? Like for modified global velocity vector, could one discard all Hubble parameter (i.e. Hubble expansion) bins, except a guess as to the earliest (highest) value for near rm minimum? Might such early extremely rapid expansion be consistent with later widely distributed clustering of dark mass, rather than an artificial assumed randomness, and subsequent early gravitational effect? If minimal 3-volume scale were ~10-29cm (~4 orders >Planck scale?), then 29 orders of magnitude for up to 1 cm scale; cubing for volume, gives 87 orders of change for 3-volume. Consistent with steeper portion of an exponential curve? Might this give one a sense (for illustrative purposes only), that possibly most expansion (and also modified global velocity tangent vector effect) came very early on – at the first bin  i.e. first light? Or is integrative accumulative effect of rest of bins significant? That is, velocity would dominate for the first bin, while duration would dominate for all other bins; likewise for expansion. tmm

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