0. The Principia of the Encoding
MATHIMATIA=IAMTHATIAM=YAHWHEY=95
1. The MetaMathematics of Divisibility
Consider the maximum conditions
of a system as being the inverse of the minimum conditions. This in
a nutshell is Modular Duality as discussed in QR.
Allow this LINEAR scale from
minimum to maximum to RECIRCULARISE itself, so reflecting the initialising
process of something NOT describable in 'measurable' terms to THEN become measurable.
This is the Mathematics of 0=1=∞=Infinity as some
metaphysical ultimate Identity, which 'bounds' all of the
mensuration physics in principles of mathematics.
The major principle here is that DIVISION DOES NOT EXIST.
So one cannot divide 0 nor 1 nor ∞=Infinity.
Then the Identities 0=0 and 1=1 and ∞=∞ form
the SELFINTERACTION of the UNDIVIDED system.
The link to DIVISION and partitioning of the UNITY in THREE (Circular
closure symbolised by cipher '0' ; its unfolding symbolised
by cipher '1' and its multiplication symbolised by cipher '8' as 'two circles' moebian-connected
in inventing 3D from 2D and 1D and 0D*) then are the ASYMPTOTES or LIMITS of the ratios 0/0=1/1=∞/∞.
{That is 3D-Volume as locus of a surface-point around a centre is contained
within a 2-Sphere, whose 2D-Surface-Area is the locus
of a circle as a 1-Sphere, rotated about the centre generating the sphere say. Defining
this centre as midway between two endpoints then defines the 0-Sphere as 1D-Line from the 0D-Centre}.
This LIMIT must be 1, because only IF it is 1 do the Identities 0=0 and
1=1 and ∞=∞ hold true in the mapped system
of the MetaMathematics or OmniMathematics becoming Mathematics, where only the Division of 1/1=1
is allowed by definition.
One could then define 0/0=1=1/1=∞/∞; 0/1=0 and
0/∞=02 for 0=∞.02 in 1/∞=0
and 1/0=∞
and ∞/0=∞2 for 1/0=∞.
Those definitions of OmniMathematics then become the limits of Mathematics
by MetaMathematics.
The Division-Transformation dij=(0,1,∞) then
can be expressed in the square matrix:
A
=
x
y
z
w
Next Steps
A = x
y z w Next Steps
1 Infinity Infinity^2]
[ 0 1 Infinity ] = D with Determinant detD, where
[0^2 0 1 ]
detD=1(1^2-0.Infinity)-Infinity(0.1-0^2.Infinity)+Infinity^2(0.0-1.0^2)=1^3-1.0.Infinity-Infinity.0.1+(Infinity.0)^2
=1^
3-2.1^2+1^2=0
Thus matrix D is singular and has no inverse, all cofactors being also
0.
Matrix D is however symmetric in its transpose (exchanging rows i with
columns j) for detD^
T=0.
2. The MetaPhysics of the Boundary Parameters in QR
Call the maximum scale of the 'unfolding' the maximum Hubble-Radius R
max
in some bounding dimensionality
D
max.
The definition in QR is R
max=c/Ho=lps.fps/Ho for specified superstring parameters
c=lps.fps and Ho under an
INVARIANCE condition symbolised by constant c, also rendering H
o=constant
as boundary condition for a subsequent
change in the 'finestructure' of the invariant 'c', (say as yet undefined
'velocity').
The Inverse Minimum is 1/R
max, which under Modular
Duality also describes the same mensuration unit as the
maximum, say if R
max=1.596..x10^26 metres, then the modular dual would be
Rmin=6.265..x10^-27 metres.
This arbitrary scale 'as distance' definition is the 'unfolding' of a
cicular multidimensional continuum, with the
'cutting of the circle' representing an arbitrary 'point' on the 'circle's'
perimeter, where the 'cut' is made.
The two generated 'endpoints' of the 'unfolded' circle now become the
R
max and Rmin boundary conditions
in linearity.
Now introduce a parameter of linearisation, called TIME to 'change' any
one of the endpoints under Modular Duality.
This then becomes the 'Oscillation' of the Boundary Conditions and allows
new degrees of freedom to 'be born'.
We define the degrees of freedom as translational in 3D following the
linearisation of the circular as rotational
in 3D (following the 3D generation from 2D from 1D from 0D).
Thus the QR-cosmology becomes 6D-Rotational enfolded in 3D-Translational.
The 'oscillation' of the boundary conditions now allow a 9D-Vibrational
cosmology, embedded in a 6D-rotational
universe encompassed by a 3D-translational one.
Specifically the invariant 'c' can now become a 'velocity' as the ratio
of displacement/TIME and the TIME can become
'differentiable' and bounded by H
o.
The QR-definition is dn/dt=Ho where n=TIME as dimensionless ratio between
the minimum/maximum conditions.
Then TIME could become defined in R
min/Rmax=1/Rmax^2 dimensionless
(under Modular Duality); but this describes
a 6-dimensional cosmology without the oscillation degrees requiring a
9D-continuum.
It is thus the 'finestructuring' of the invariant 'c' as a velocity product
of wavelengthxfrequency, which introduces the
dimensional extension for the QR cosmology from 6 dimensions to 9 embedded
in 3.
The QR definition for TIME then introduces the QUANTUM OSCILLATION as
the the 6D-R
min
mapped onto the 9D-lps
and using the definition for invariant c in superbrane parameters (it
is called heterotic supermembrane HE(8x8)).
Subsequently: DIMENSIONLESS QUANTUM-TIME TIME=
lps/Rmax=nps=c/(fps.Rmax)=Rmax.Ho/(fps.Rmax)=Ho/fps.
TIME as the Connector-Dimensionality, then maps the Minimum/Maximum Scale/Displacement
ratio in inverse proportion
unto the Maximum/Minimum Frequency ratio under Modular Duality in Invariant
c=
lps.fps=Rmax.Ho.
This describes a 9-dimensional quantum cosmology in Quantum Relativity
for a specified boundary condition given in a
particular superstring E
psEss=(Class
HE(8x8)), with ss defining the Modular Duality to ps (say as primary sourcesink and
secondary sinksource).
The modular dual to
lps=10^-22/2p metres, thus is lss=2p.10^22
metres in relating the microquantum to the macroquantum.
Now there is not one, but five classes of superstrings under modular
duality bounded above in the Planck-Scale and below
by the ps-ss-scale.
Henceforth, the minimum/maximum scenario given in the 9D-Identity: c=
lps.fps=Rmax.Ho requires extension in dimensionality
to encompass R
min=6.265..x10^-27 metres and Rmax=1.596..x10^26 metres
in the ps-ss modular duality.
We use the Time-Connector Dimensions of LINEARITY to CLOSE the 9D-universum
in 12 Dimensions and introduce the Degrees
of Freedom for Quantisation as the Principle of Holography under Modular
Duality.
The 4th dimension so becomes REAL in connecting LineSpace of 3D to HyperSpace
of 6D in translation encompassing rotation
and in say rendering a 3D-Volume mathematically equivalent to a 5D-Volume
under transformation/projections of a 3D-Surface
being the inside-out 5D-Surface under 4D-HyperTime.
A 4D-Volume universe described in toroidal parameter 2
p^2,
then dimensionally reduces to a 3D-Surface 6p^2
in HyperTime and
the information contained within a 5D-HyperVolume and be described as
the 4D-Surface mapping from HyperSpace to LineSpace.
In terms of mathematical physics, this becomes the modelling of the information
contained within a 'Black Holed' Volume in 3D being
mapped onto its Surface-Area in 2D as the 'Event Horizon', bounded necessarily
in the scaled maxima of the parameters.
Because the 'inside' area is TIME-Connected to the 'outside' area, the
time-connector dimensions alsoconnect the freedom degrees
described as tranalation, rotation, oscillation and quantisation.
The 7th dimension connects 6D-HyperSpace to 9D-QuantumSpace in 7D-QuantumTime
and the 10th dimension connects
9D-QuantumSpace to 12D-OmniSpace in 10D-OmniTime.
But 4D-HyperTime of Rotation is congruent with 7D-QuantumTime of Vibration
is congruent with 10D-OmniTime of Quantisation.
This then must close the continuum in 1D-LineTime as the 13D-Time of
reconnecting the quantising freedom degrees in the
simple 3D-Envelope of 4D-SpaceTime.
This rigorously defines OmniSpace dimensions 10,11 and 12 as becoming
the Boundary Dimensions for our 9D-Space-Extension
for the oscillations and the rotations superposed onto the translational
freedom degrees.
The entire continuum defined in maximum/minium parameters under modular
duality then superposes the Time-Dimensions
onto the Space-Dimensions and allows a nesting within nesting (or fractalisation)
of the evolvement of the intial conditions
under the freedom degrees.
Thus an archetypical minimum/maximum 'seedling' is defined in 9D-QuantumSpace
and specified in the R
max (Hubble-Radius)
parameter.
Superposing the linearised Time-Parameter of 4D-SpaceTime of Special
Relativity then results in a 10D universe defined in
Riemann's HyperSphere as the 'cosmic envelope' of translation.
A 4D-HyperSpaceTime of Rotation then is congruent with the 4D-Seedling
of Translation and also congruent with a
4D-QuantumSpaceTime of Oscillation, rendering the 'conifolded/enfolded/collapsed'
dimensions of the HyperQuantisation
as a 6D-Calabi-Yau 'Conifoldment' of Toroidal Topology.
This can be described in a 10D-superstring theory of five classes in
the metrics of General Relativity OR this can be
greatly simplified in mathematical concept in extension to the 12D-OmniSpaceTime
of demetricated Quantum Relativity.
QR uses the described dimensional congruency in mapping the congruent
volume-dimensions, area-dimensions and
line-dimensions onto the 10D-'seedling' of the Riemann-Einstein-Poincare-Hypersphere
which equates the 4D toroidal volume
as a 3D surface, then becoming the 2D 'event horizon' of say a Bekenstein-Hawking
Black Hole and the basic Schwarzschild
Solution of the basic Einstein Tensor/Metric in General Relativity.
This requires the Hubble-Radius to be considered demetricated as a macroquantum
and unity; which is the case as the
maximum boundary condition in 10D, now described as the 4D-Hypersphere
of maximum volume 2
p^2.Rmax^3. and
maximum surface area 6
p^2.R^2.
This Volume in 4D then is also a HyperVolume in 7D, a QuantumVolume in
10D and an OmniVolume in 13D, with the latter
being a LineVolume of OmniPhysics in 1D, which MANIFESTS as the Volume
of 4D SpaceTime, thus closing the continuum.
3. The Physics of the Boundary Parameters in QR
The 10D Universe in OmniSpace so represents a demetricated equivalent
and macroquantum for the 4D SpaceTime of the
standard cosmology of Riemann-Einstein metrics and Minkowskian 4D-SpaceTime.
The 'inside-out' topology of the differential geometry in OmniSpace is
simply the higher-D mapping of the 0D-1D-2D-3D
geometry of say a dimensionless mathematical point generating displacement
in equidistant extension to define a 1D-diameter,
about which a 2D area can then become self-generated in rotation.
Repeating the rotation in 2D then generates the 3D volume in an exact
copying of the Translation-Rotation-Vibration-Quantisation of
degrees of freedom previously discussed.
The completion of a 9D continuum in 'space', then introduces an extension
in oscillation by quantising the generating dimensional
parameters in 'time'; a process which recircularises a 12D-continuum
in 3D.
The physical 4D-SpaceTime of measurement and observation is so a multidimensional
universe of boundary conditions,
the latter which manifest as 'elementary particles' of gauge and interaction;
all however seeded on the minimum/maximum
conditions of the cosmogenesis.
Conservation Laws in regards to the parameters based on the dimensionless
definition of NOW-TIME become applied and relate
the concepts of interaction in terms of the laws of nature and the mathematical
equations describing them.
Those laws are a consequence of the initiatory OmniMathematical definition
process; say in the definition of what numbers are
in their generation from the Trinity of the 0=1=Infinity.
Certain algorithms then generate 'invariants' like 'c' and other 'fundamental
constants' from the same OmniMathematics,
which selfgenerates and extends itself under application of fundamental
principles derived from the selfiterative process itself.
The most important constants defining the nestings of the minimum/maximum
conditions are the dimensionless constants of
the 'finestructures' and combinations of 'invariants' to result in dimensionless
'master constants'such as the electromagnetic
finestructure constant Alpha and its gravitational interaction partner
G-Alpha resulting in the Planck-Mass under Unitisation.
Alpha=60
p.e^2/h or e^2/(2eohc) and G-Alpha=2p.G.mPlanck^2/hc=1 defines mPlanck=Sqrt{hc/(2pG}=Sqrt{Macg.hc/2p}.
Subsequently the Planck-Mass must define a Planck-Length r
Planck (via E=mc^2=hf=hc/l and l=2pr
for
r
Planck=h/(2p.mPlanck.c)=Sqrt{Gh/(2pc^3)}=Sqrt{h/(2p.Macg.c^3)}.
So this Planck-Length must define the upper limit for the said superstring
classes in 10D being superbranes in 11D and being
supervolumars in 12D as the OmniSpaceTime.
This in standard physics becomes the Planck-Boson (or superstring class
I) with associated Plamck-Scale-Parameters, derived
from the dimensionless unification of the finestructures relating electromagnetic
interactions to the gravitational ones via the
MacGamma (
Macg)
as the inversion proportionality parameter for the Modular Duality between Coulombic Charge quantum 'e'
and the elementary particle masses limited by the Planck-Mass.
We can now define the LIMIT for the displacement scale under 9D-oscillation
freedom degrees as the oscillation of the
Planck-Length itself, using its definition in constants c, h,
Macg and p.
QR derives this as a dimensionless unification in the MacGamma proportionality,
which relates the proportionality constant
for the Planck-Length Oscillation as being the SqauareRoot of the electromagnetic
Alpha and thus relating chargequantum 'e'
directly to the Planck-Length and subsequently to the Planck-Mass and
the Planck-Scale as the upper limit for the cosmogenesis.
The formulation becomes: Planck-Length-Oscillation=PLO=r
Planck.Sqrt(Alpha)=[e/c^2] dimensionless.
In terms of physical measurement then, the Planck-Length reduces by a
factor of about 11.7 in its oscillation about the upper
boundary linearly defined in the Planck-Length and a value given as about
1.78x10^-
36 metres.
This corresponds to an increase in the Planck-Mass by the same factor
to about 1.98x10^-
7 kilograms and which must represent the
maximum mass for a microquantum Black Hole particle equivalent.
The Modular Duality of 4D is bounded in R
max=1.596..x10^26 metres without the PLO and mirrors itself in the wavelength
l
ps=10^-22 metres to describe a linearly TIMELESS universe situated
in dimensionless NOW-TIME.
The Modular Duality of 7D is also bounded in R
max,
but without the oscillation freedom degrees, the modular mirror is at
R
min=6.265..10^-27 metres, that is in between the 10D-mirror and the
Planck-Length-Mirror.
The Modular Duality of 10D then closes the superbrane realm in positioning
the modular mirror for R
max at the Planck-Length
r
Planck=2.08x10^-35 metres.
One so finds the following Modular Duality Pairings, which allow the
oscillated nestings or 'phase-jumps' between the 'mirrors'.
13D-Minimum=PLO=1.78x10^-
36 metres...............13D-Maximum=1/PLO=5.62x10^35 metres (13D/0D OmniSpace)
10D-Minimum=r
Planck=2.08x10^-35 metres............10D-Maximum=1/rPlanck=4.81x10^34
metres (12/3-D OmniQuantumSpace)
7D-Minimum=R
min=6.265x10^-27 metres................7D-Maximum=Rmax=1.596x10^26
metres (11/2-D OmniHyperSpace)
4D-Minimum=r
ps=lps/2p=1.59x10^-23 metres.........4D-Maximum=2p.lss=6.28.x10^22
metres (10/1-D OmniLineSpace)
1D-Minimum=1D-Maximum=Quantisation of r
ps via rPlanck in Re to
reconstruct OmniSpace as 0D/13D of the original 9D 'space'
of timelessness.
This minimum/maximum scaling parameter is known as the Classical Electron-Radius
R
e=Macg.e^2/(me.c^2)=2.77x10^-15 metres,
with m
e the effective electronmass.
In terms of superbrane parameters it is defined independent from the
electronmass as: R
e=10^10.lps/360, that is as a direct
proportionality to the lower bounding superstring realm.
The quantum angular momentum h/2
p of circularity is linearised in superbrane scale rps=lps/2p=(360/2p).Re/10^10 , that is
precisely 10 Billion superbrane perimeters fit into 1 ElectronRadius,
scaled as a Radian.
Then the independence of the angular displacement from the scale of the
radius sets 360 degrees = 2
p = Unity in OmniSpace,
manifesting as the classical electron scale in the 4D SpaceTime.
The quantum geometry of QR's cosmology is now evident.
There is a macroquantum realm bounded in R
max,
which transmutes the 10D-Maximum to the 7D-Maximum and compensates
in a microquantum 1D-Maximum defined in R
e
as the mapping for the 4D-Maximum (known as the Sarkar Scale for the
entire cosmic architecture and supercluster gravitational limit).
Then all 'elementary particles' become macroquantised superstrings bounded
in size by R
e,
the Re-scale
of quantum physics
then becoming the modular building block for the Sarkar bound of the
superclusters as macroquantised supersuperstrings of
electronic radii, also describing the atomic nuclei.
The R
max of the macrocosmos
then forms the envelope for the superclusters, mapped as the electron configured atoms of
chemistry.
A corresponding transmutation of the 7D-Minimum to the 10D-Minimum defines
a mass-limit of so 3.35x10^-
16 kilograms or
1.88x10^
20 electronvolt.
This is acknowledged universally as the HECR=High-EnergyCosmicRay limit
NOT explicable by the standard models of
cosmology.
In QR the HECR-events are a natural manifestation of the superbrane monopole
spectra bounded in R
min above from below
and superstring class IIB as upper limit for the Magnetic Monopole of
energy 2.7x10^
25 electronvolt from above.
The superbrane epoch ends at the Instanton for Time and the Inflaton
for Space at the ps-ss parameters, encompassing the
five superstring classes and beginning with the Planck-Boson.
So both the 7D-Minimum and the 7D-Maximum of Modular Duality describe
the QR-Cosmology fully supported by experiment.
The 4D-Maximum describes the 'Sarkar Black Hole' as the 'Seedling' M
o=Sqrt{E}.mPlanck.mc/me,
where E is a spacequanta
counter related to the definition of R
max=c/Ho,
and mc is a
nucleonic protomass derived from a superbrane class (HO(32)).
The Sarkar-Radius R
Sarkar=GoMo/c^2=Lambda(nps).Rmax/adeBroglie describes a Black
Hole Maximum as macroquantised
supersuperstring and the supercluster scale for gravitational interaction,
after which the universe can be said to obey the
cosmological principle of homogenous distribution of energy parameters.
Lambda is the Einstein acceleration/quintessence as a function of cycletime
n at the instanton, when a de Broglie matter
wave hyperaccelerated the 4D-cosmos to manifest the 7D-maximum as R
max and Go=1/Macg as
the superbraned
gravitational constant equal to 4
peo=4p/c^2mo for electric permittivity eo and
magnetic permeability mo.
The 7D-Maximum describes the 'Infinity' Black Hole of critical density
(M
critical) for an overall Euclidean flat cosmos from
the Einstein Field Equations of General Relativity.
The Ratio M
o/Mcritical
describes Omega, the ratio of actual 'seeded' and critical density for the flat universe.
It also is twice the deceleration parameter, which renders the Sarkar-Radius
proportional to the Schwarzschild Radius in
a factor of 2, i.e. 2R
Sarkar=4.478..x10^24 metres and 2RSarkar/Rmax=Omega=2qo
(deceleration parameter)=0.0281...
We can now fully describe the cosmic evolution of the universe with the
introduction of the Black Body Planck-Radiator
spectrum provided by mass-seedling Mo as a function of the Luminosity
in terms of the Surface Area 6
p^2.R(n)^3, with R(n) the
demetricated scalefactor of General Relativity given in the Schwarzschild
evolution of the univerrse as a Black Hole bounded
in R
max.
In 10D, this demetricated scalefactor derives from the definition of
the natural exponent 'e' as
Limit[
n->Infinity]{1+1/n}^n=1+1/1!+1/2!+1/3!+...+1/n!
and is related to the Euler Harmonic of summing 1/R from 1 to Infinity (n)
and then subtracting the natural logarithm (ln(n)) from this sum as Euler's
Constant (~0.5772).
The QR demetricated scale factor of curvature R
c in General Relativity is R(n)=Rmax(n/(n+1)).
This describes the asymptotic approach of the universe's expansion from
the ps-ss parametrisation of General Relativity to R
max
and in terms of the Black Body Luminosity Spectrum.
In terms of mass-seedling M
o then, the universe will have a finite temperature after an infinite (linear) time elapse, bounded
by Rmax.
This temperature can be calculated through the following formulation:
6
p^2.R(n)^2.s.T^4=3HoMoc^2/(550n),which for n=1 and Stefan's Constant s becomes T(1)~Fourth Root
(18.4x4)~2.929 degrees Kelvin.
This, amongst many other things, indicates, that the asymptotic evolution
of the 10D universe is encompassed in a 11D-envelope
which oscillates between nodal values of integral n for the macroquantisation
of R
max and
as defined in the inflaton of lps/2p to
R
max in 'timeinstantenuity'.
As the present 10D-temperature can be calculated as 2.747..Kelvin*, which
is reduced in a 11D-temperature of 2.680..Kelvin* for a
11D-Volume 7.56 times greater than the 10D-Volume (and defining the Dark
Matter in the baryon-seed critical seed ratio)) the Omnispace
intersects itself with 11D M-Space the boundary surface between the 'inner'
10D C-Space and the 'outer' 12D F-Space.
{We term OmniSpace as the dimensionalities C=Child, M=Mother, F=Father
after M-Theory nomenclature}.
The major c
