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DARK AND LUMINOUS MATTER
================
Notes: We consider "matter" as a metalanguage shortcut
pointing to particular aspects of Gravity- and its
equivalent Inertia Field.
Capitalized "SPACE" denotes symbolic, mathematical
constructs, in order to distinguish them from the
homonymous "space" of the perception.
================
Galactic mechanics posits some unobserved Dark Matter (DM),
of mass exceeding the observed by ratio 0.96/0.04 .
On the other hand, the General Relativity models the Cosmos
as curved 4d SPACE embedded in 10d.
Several reasons argue for confining the DM within the 10d
embedding "inside" of the cosmos:
1.Restricting cosmology to curved hypersurface (4d) and
neglecting its embedding "inside" (10d) seems "superficial",
as would be a geology restricted to the 2d Earth surface
and neglecting its embedding 3d inside.
2.The 4D relativistic hypersurface is quite well explored
and known, so that, if the DM were contained therein, it
would long since have been observed.
3.Our electro-magnetic detectors cannot pass the boundary
of the 4D hypersurface, which would account for DM being
"dark", or as yet unobservable.
4.The compactness (ratio of embedded, to embedding volume)
is very low, which makes it qualitatively compatible with
the requested ratio of 0.04/0.96.
Quantitative verification reposes upon the following
considerations:
1.Models don't tell what happens in the transcendental
"World Out There", but are abstract constructs justified
exclusively by their capacity to coordinate observable
events. Thus, physical models don't explain "reality",
but coordinate particular, pertinent event domains.
Our objective is to examine our postulated Split of matter
into dark and luminous as equivalent to the embedding and
embedded spaces of the General Relativity, in the light of
the commonly accepted Standard Model's timetable of the Big
Bang. We shall start therefore by positioning the GR and
our Split postulate within this timetable.
2.On the one hand the GR deals with such material constructs
as galaxies and, on the other hand, matter can split only
after or while being created. Consequently, the GR space
structuration and our Split postulate acquire sense and
adequacy at the beginning of the hadron epoch (10^-6 sec
after the Big Bang), when started to form such baryons as
protons and neutrons, which compose most of our matter.
.
3.Prior to the GR structuration, cosmos may be modeled as a
sphere and the structuration - as transformation of
its 2d embedded surface and embedding 3d volume, respectively
into 4d and 10d GR structures. This sphere contained the
"raw material" of baryons, to wit, quarks and gluons which
were distributed between its surface and volume according
to its compactness and it seems reasonable to suppose that
this distribution has been conserved by the transformation
to the GR.
4.Consequently, calling
Ts=time of Split
Th=10^-6 sec start of the hadron epoch
Ve - average speed of cosmos expansion during 0-Th
Rs=Ts*Ve cosmos radius at Ts
Ss=4 pi Rs^2 surface of cosmos sphere at Ts
Vs=(4 pi Rs^3)/3 volume of cosmos sphere at Ts
Ks=Ss/Vs=3/Rs compactness postulated=0.04/0.96
we have 3 variables, Ks, Ve, Ts of which we have
to fix two and calculate the third. Ks=0.04/0.96
is fixed by our Split postulate, so we have to
decide which of Ve, Ts to fix and which to calculate.
It seems preferable to fix Ts=Th=10^-6 and to
calculate Ve (giving 0.24C). Fixing Ts=Th
is conform with the sense of Standard Model's
timetable and Ve smaller than C could be a finding
restoring the timetable to causality, distorted by
fanciful periods of the Inflation Epoch assuming
Ve greater than C.
The surface of a sphere of radius Rs: Ss=4*pi*Rs^2
The enclosed volume: Vs=(4*pi*Rs^3)/3
Compactness:
Ks = Ss/Vs = 3/Rs = 0.04/0.96 (Split postulate)
thus Rs = 3*0.96/0.04 = 72m = 0.072km
Cosmos has expanded at Ve during 0 - Ts=10^-6:
thus
Ve=Rs/Ts= 0.072/10^-6=72000km/sec=0.24C
