Introduction to Quantum Relativity and the Quantum Geometry

by William MacArthur


Well let's take the first part - Imagine a line segment, and call it a
1-sphere. Now, it has no surface, because a surface is necessarily 2D.
Yet the surface has been defined by the length of the segment.. You'll
see why in a moment.

Introduce a second dimension and spin the segment around its centre, and
it traces out a circle. Now call the circle a 2-sphere. It has a
surface! Namely the perimeter, but it it has no volume, because a volume
is necessarily 3D. However, the circle defines the volume even so,
because if we introduce a third dimension and spin the circle around a
diameter, we get a ball!

Now the ball is a 3-sphere, right? It has a surface, and a volume, and
the volume defines - something else, but it isn't there yet because the
something else is 4D. Now spin the ball around - um - well, you have to
stop trying to visualise now because you actually spin the ball around
a planar section, but in such a way that it is orthogonal to all 3
visible dimensions, and you get a 4-sphere, only now there's a fourth
dimension to this thing, which I think is called a hypersphere (Tony?).

Now the fun thing is that you can actually start even lower than the
line segment, at a point, and call it a 0-sphere, and a "rotation" here
has to take the form of a double translation along a line to produce the
1-sphere, but we will call it an 0D rotation. Of course there is no
surface, no volume, nothing at all, except position. Its "rotation"
produces a 1-sphere (line segment ) that has position and magnitude.

Spin the 1-sphere around it 0D centre (the position) and you get the
2-sphere with position, magnitude and a surface. Now spin that around
its 1D axis and you get a 3-sphere with position, magnitude, a surface
and a volume. Now spin the 3-sphere around a suitable orthogonal 2D
section and it makes a 4-sphere, which has position, magnitude, surface,
volume and...... duration? See how we produce ever higher hyperspheres
we get more and more basic properties?

And so it goes on. As an aid to visualising, let's go the other way and
slice a 4-sphere with a 3D volume (don't try to visualise this or you'll
go mad) and you get a 3-sphere. Slice a 3-sphere with a 2D plane
surface and you get a 2-sphere or plane circle. Slice a 2-sphere with a
1D line and you get a 1-sphere, and lastly slice this with a point to
get the 0-sphere.

Tony is using brane terminology, but basically this is the operation
he's talking about I think The rest is a bit more abstract still and
rather mathematical. The speed of light is c and it is constant.
Furthermore, light as the one entity that actually moves at this rate is
a wave with frequency and wavelength, but also mass-energy (it's all
kinetic - there is no *rest* mass energy, so no inertia, and that's why
it can never accelerate, decelerate, or even exist unless it's buzzing
along at c.)

So - we have a constant manifest in real terms as a wave with a
frequency (inverse time) a wavelength (a space function), and a
mass-energy, and they are all inextricably entwined. The mass m is
E/c^
2. The energy is E = hn, and the frequency n is 1/t, where t is a
time parameter yet to be determined.. The constant speed c is
nl
where
l is the wavelength, and you can use simple algebra to get the other
dependencies.

So, this is a self consistent simultaneous set of equations in six
dimensions (but two are constant so you can set it up as 4D) that can be
represented using matrix algebra. You can describe such a system as a
matrix, and all matrices have certain powerful mathematical properties.
Things like discriminants, and very powerfully, an "eigenvalue" which is
unique to the matrix. If two matrices have the same eigenvalue, then
they are merely variants of the same system.

OK, now, setting this system up as a matrix, we can compute the
eigenvector and eigenvalue for the matrix, (don't ask me how - I'm a
conceptual physicist who visualises stuff, not a mathematician, so I
leave the donkey work to the mathos) and it turns out to be a function
of photon mass with the physical dimension of time.

That is, the eigenvalue which is a characteristic constant of the system
is fixed, and we can give it a name. Tony calls it an instanton, which
can also be regarded as a quantum of time for that system (obviously
though different photon energies will give different eigenvalues and so
the instanton is a variable when we consider all possible frequencies.)

Note though that the evolution of the system is such that you can take
time as the initial parameter on which everything else is going to
depend. From it we have a frequency, and from frequency we have
wavelength (i.e. space) and lastly we have energy (mass) from the Plank
energy equation expressed relativistically, E = h
n = mc^2.

Now - say we shrink our system to the smallest possible length and time
that makes any physical sense, namely the Planck scale. You now have an
instanton that is absolutely the very foundation of quantisable
spacetime. It is a true time quantum from which EVERYTHING else derives.

I think Jim would be very pleased with this outcome as he sees
absolutely EVERYTHING as being built from Planck actions, a notion with
which I personally agree wholeheartedly. And you should be pleased
because it strongly vindicates your concept of a primal clock underlying
all reality (incidentally, in loop quantum gravity, these "instantons"
are ticked out by spin vectors that serve to generate space, so again
your early intuitions seem to be vindicated).....

Even though Tony's terminology is a bit obscure - and I for one am not
into brane theory at all yet, so I have to do a double take with most of
his stuff - it's mathy and I'm no motho - when I said it makes sense,
it's because I can *see* it clearly in my mind's eye. It certainly does
seem to be the way things work..........


Postulates of Quantum Relativity:

1. Set of Postulates of SR (verbatim): Principle of Relativity
2. Set of Postulates of GR (verbatim): Principle of Equivalence
3. Set of Postulates of QR (A,B,C,...): Principle of Quantization

A: Modular Duality between vibratory and winded Energy Eigenstates or
EE's, allows the description of high frequency/small radius EE's
as physically equivalent to low frequency/big radius EE's
The EE's are themselves defined in the Planck-Scale of the various
mensuration parameters as given in postulates 1. and 2.

Description:

The Operator E=f/R+wR describes vibratory mode f and winding mode w as being

as being invariant under simultaneous exchange of f & w and R & 1/R.

f=3 and w=2 for R=10 -> E=3/10+2.10=20+3/10 is IDENTICAL to

f=2 and w=3 for R=1/10-> E=2.10+3/10=20+3/10

 

In Point-Particle Quantum Mechanics, displacement and momentum are related

by Heisenberg's Constant and Fourier Transform.

 

EigenState [x> of position on the circle radius R is defined in [x>=Sf .exp[ixp]]p>

where p=f/R and [p> is a momentum eigenstate as the uniform vibration state of

the string with phase factor h/4p<=Et for t~1/E~R.

x is periodic with period T=2pR as position x on a circle radius R.

 

EigenState [X> of position on the circle radius 1/R is defined in [X>=Sw.exp[iXP]]P>

where P=wR and [P> is a momentum eigenstate as the uniform winding state of

the string with phase factor h/4p<=Et for t~1/E~1/R.

X is periodic with period T=2p/R as position X on a circle radius 1/R.

 

Two wavepackets x and X then evolve in time in proportionality of their respective

radii to the time required to complete a revolution of the circles and as given in the

Heisenberg Relation.

This serves as a technical description for 'displacement' in modular duality.

B: Modular Duality is defined in the threshold of the GR postulates
as the 'quantumsmeared' singularity of the Planck-Scale (1. & 2.)

E=f/R+wR/LP^2, with LP=Sqrt(Gh/2pc^3)=Planck-Length remains invariant

under exchange of f & w, as well as R & LP^2/R.



C: The fundamental constants, which define the Planck-Scale are al-
gorithmically obtainable in considering a demetricated senario, in
which space and time are undefined and subject to definition by a
Machian Observer doing the defining.

The derivation of the Electromagnetic Electronmass below indicates this.

A detailed analysis is found in the Algorithmic Gravity Paper.



D: The engagement of the Machian Observer then results in the Planck
Scale and under postulates B and A reattains the sets of the pos-
tulates as given in 1. and 2.

This is described in the 'Machian Momentum' for the Universe Paper.



E: The algorithm defining the fundamental constants is based on the
premise of a mathematical supersymmetry, thus becoming realised
as physical reality, defined in postulate A.

The Cosmic Wavefunction is the following Differential Equation:

dB/dT + aB(n) = 0; a being the Electromagnetic Finestructure as the

probability of light-matter interaction (~1/137).

This has a solution: B(n) = Bo.exp[-a.T(n)];

Bo=2e/hA from QR boundary conditions defining:

T(n)=n(n+1) as the Feynman Path-Summation of particular histories

under the pentagonal supersymmetry given in the identity:

XY=X+Y=-1=i^2=exp[ip] and lim [n->X]{T(n)}=1

This allows the Normalisation of the [Y]^2 wavefunction to sum

to unity in B(n)=(2e/hA).exp[-a.n(n+1)] with Functional Riemann Bound

FRB=-1/2, centred on the interval [Y,...-1,...-X,...-1/2,...(X-1),...0,...X].

Interval [Y,-1] sets F-Space; interval [-1,0] sets M-Space with uncertainty

interval [-X,(X-1)] and interval [0,n) sets the C-Space, encompassing OmniSpace.

n<0 is imaginary as real reflection of real n>0 of the C-Space, metrically defined

at the coordinate n=0 mapping n=nps, which is the instanton tps=fss=1/fps.

Cycletime n is defined in GR as dimensionless TauTime in curvature radius

Rc=c.dt/dt for the pathlength of x=ct and become dn/dt=Ho, n=Hot in QR,

with Ho the nodal HubbleConstant defined in c=HoRmax=lps.fps.

 

The Feynman Path so sums both negative and positive integers

as: -n......-3...-2...-1...0...1...2...3......n =T(n) in absolute value to double the

infinities as the entropy reversal of lightpath x=c.t=(-c)(-t) in the Moebius

Property of the 4 worlds as outlined in the Machian Momentum Paper.

Cantor Cardinality Aleph-Null is thus Unitised in Aleph-All, counting infinities

as if they were integers of the Feynman Path.

This allows the Feynman interpretation of Quantum Mechanics as alternative

to the formulations of Schroedinger (fermions 1/2spin) and Klein-Gordon (bosons)

as timeindependent and timedependent (free particle form inconsistent with SR

in Schroedinger in 1st order t & 2nd order x), formulations respectively.

 

The units of B(n) are 1/J, that is Inverse Energy, with A^2 an algorithmic constant

defining Current-Squared and 2e/h the Josephson Constant in Amperes/Joules.

B(n) as the universal cosmic wavefunction describes the universe as a potentially

infinite collection of 'frozen' wormhole- eigenstates at n=0.

The timeinstanton 'unfreezes' one such eigenstate and activates the protoverse as

discussed in the Machian Momentum Paper.

This then allows the 'Mappings' of the C-Space 'real time n>0' from the F-Space of the

'imaginary time n<-1' under utility of the M-Space interval as 'mirror-space'.

QR unifies electromagnetic and gravitational finestructures in F-Space using the Planck-

Length-Oscillation LPSqrt(a)=e/c^2 from the subtimespace.

This yields the decisive mapping for the B(n):

Coulomb Charge e = LP.Sqrt(a).c^2 <-->2Re.c^2 = e* (StarCoulomb Charge)

But the StarCoulomb is Inverse Energy by definition of the vibratory part of the

modular dual heterotic supermembrane HE(8x8)=EpsEss.

........................,...Eps=hfps=hc/lps=(me/2e).Sqrt[2pGo/ahc]=me/{2emPSqrt(a)}=1/e*.

mP is the Planck-Mass and Go is the initiatory Gravitational Constant, defined in

the FineStructure-Relation, which defines the Planck-Length-Oscillation in the

unification of electromagnetic interactions with those of gravitational permittivity:

Go=4peo=1/30c with dimensionless c-ether constant [c]unified.

This defines the MacArthur-Gamma as: "LightMass-Constant" LMC=Macg=30[c]unified.

 

Thus Quantum Relativity is defined in the charge mappings between the OmniSpace

dimensions; F maps magnetocharges e* onto electrocharges e under agency of the

11D-Witten Mirror, which is a Onesided Surface moebian connecting 10D to 12D.

The all encompassing source energy quantum is the Eps-Gauge Boson, which manifests

as the Gauge mediator for the four elemental interactions, suppressing the weak inter-

action in a primary triplicity however to allow the Higgs Restmass Induction mechanism

to proceed in the defining qualities of the Unified Field of Quantum Relativity (UFoQR).

The details are discussed in the aformentioned papers and the archives of the QR website

and its links.

 

The paper below introduces some of those details.

 

CALCULATION OF THE ELECTRONMASS

The Main Idea is that the Electronmass is made up of two parts.

One part is the 'naked electronrestmass' and the other an additional part (a magneto-charged part also called electromagnetic mass).

Together this gives a dynamic effective electronmass, which derives naturally from the other integerbased fundamental constants.

There are three such constants given by an algorithmic program, which relate directly to Energy concepts.

1. Einstein-Constant as: (9,10,16)=> 9x10^16=c^2.

2. Planck-Constant as: (15,10,32) => 1/(15x10^32)=h.

3. Boltzmann Constant as: (15,16,18) => 1/(15x16^18)=k.

They are all dimensionless in pre-quantum algorithm space (prePlanck-Phase).

In a transitionphase, relating to the 'Quantum Big Bang', a boundary between a 'quantum realm' and classical physics became established in a quantum tunneling of a 'false vacuum'.

This is described in de Broglie phase-inflation.

This phase inflation defines a closed curvature topologically equivalent to an open curvature and specifies modular duality between maximum/minimum conditions.

The dimensionless number constants became physically manifested and related to many other derived parameters relating to energy in the order of Temperature, Radiation and Mass; that is in the order of Boltzmann, Planck and Einstein.

One such relationship finestructures Maxwell's: 1/c^2=moeo.

Another relationship defines the electronic radius as a quantum macroboundary in terms of the magnetic constant mo.

Another relationship sets the linearisation of a circular quantum continuum in direct relation to a prequantumscale, that is the supermembrane epoch from Planck-Time to Wormholetime.

The wormholetime derives from finestructuring the Action-Constant.

This formulation involves the electronic radius as a number constant.

From that electronic radius, the electronmass is implied as:

meo.c^2=e^2/[4peo.(electronic radius Re)].

Equality of dynamic electromagnetic mass in magnetic selfinduction to the relativistic mass increase, then leads to a finestructure for the effective electronmass (above) as a distribution and as set out below.

There are a number of parameters and fundamental constants which are given by the pentagonal supersymmetry between four dimensionally nested worlds.

The lightconstant 'c' becomes dimensionless in: c^2=9x10^16 for example, giving a 'cosmic standard' system where c=300,000 km*/sec* precisely.

Calibration to the SI-system differs often less than 1%.

The electronmass was not amongst the elementaries however, because all restmasses are set to 0 in the first world (here termed Omnispace of dimensions 10-11-12-(13=1)).

So we must derive the electronmass from the other given elementals.

It proceeds something like this.

One first finestructures the Maxwell-Constant into electric and magnetic parts and then applies the OmnispaceLaw {ACTION=CHARGE^2} to find dimensionless (superconductive) expressions for electric permittivity eo and magnetic permeability mo.

This ACTION LAW maximises/minimises the Lagrangian in Omnispace, especially the boundary condition of the Planck-Length-Oscillation, which maps the ForceCharges between Omnispace and Linespace.

Linespace connects Omnispace in dimension 1=13, which then also becomes a mirrored Timedimension in 1-2-3-4 D. Hyperspace is world #3 mapping 4-5-6-7 and Quantumspace maps this as 7-8-9-10 into Omnispace as world #4).

There are two equal expressions for the Planck-Length Oscillation; allowing mappings from the creation world into the first manifestation.

Planck-Length-Oscillation: (e/c^2)=Planck-Length.SqrtAlpha.

This allows mapping of MagnetoCharges (e*) from 13D as Coulombic charges (e) as 1D (say).

Since Magnetocharge is defined as Inverse SourceEnergy in the form:

e*=Classical Electronic Diameter.c^2 in units (m^3/s^2) or as [Volume.Angular Acceleration] and also as:

E[ps]=hf[ps]=h/f[ss]=1/e*,

we find modular duality in supersymmetric associations between magnetocharges and electrocharges.

In particular, the vibrating Supermembrane (in 11D) E[ps=primary sourcesink] is modular dual to the E[ss=secondary sinksource] and so relates the inversion properties of Maximum Radius to Minimum Radius.

This is the backbone of M-Theory, which labels our supermembrane EpsEss as the heterosis between the HE-Superstring (8x8) in 10 dimensions with a Bosonic superstring in 26 dimensions.

In particular, you now find the mapping:

(e=Planck-Length-Oscillation.c^2) <=>(e*=Classical Electronic Diameter.c^2) for electropole e and magnetopole e*.

The overall symmetry, crucial for deriving the electronmass is found in the Cosmic Wavefunction:

B(n)=(2e/hA).exp(-Alpha.T(n)),

where A is an algorithmic constant relating to (Current^2); Alpha is the Electromagnetic Finestructure Constant related to the Gravitational Finestructure Constant in direct scaleproportion as:

ALPHA(GR)=ALPHA(EMR)^18;

and T(n)=n(n+1) is the Feynmann Summation, the Path-Integral over all possible particular histories, summing all absolute integers in a Cantor Cardinality of Aleph-Null becoming Aleph-All, the counting of infinities as integers differing in 1).

The crucial point here is, that this wavefunction defines an infinite number of 'frozen' spacetimes, which upon a process of 'thawing' (we could call it a spiritual awakening) can ACTIVATE themselves in (coming alive); but redefining themselves as eventuating 'Baby Universes'.

Renormalising those frozen wormholes/potential universes, then defines a Functional-Riemann-Bound in the Complex Plane at imaginary cycletime n=Hot (Ho a nodal Hubble Constant at 58 Hubble Units).

The statistical mean is at [n=-1/2] for the squared wavefunction as a density distribution.

This [FRB=-1/2] then relates to many fields in pure number theory, such as the Riemann Hypothesis of the Zeta Function and the Euler Harmonic.

B(n) is also a disguised form of Stirling's Formula as function of Alpha.

But we now have expressions for the magnetic constant, which relate to the propagation of the unified field in the form of 12 selfintersecting monopolic current-'knots'/junctions, giving rise to all particle families,

bosonic and fermionic in the application of a colourtrinity, triplets of unification (Red-Green-Blue=White in Radiation) and (Yellow-Cyan-Magenta=Black in Paint/Mass).

Complementary triplets/doublets/singlets then define the unitary symmetries, such as 8 gluonic intermediate mesonic states in {RC=MG=BY} and the permutation octet (WWW,WWB,WBW,BWW,BBW,BWB,WBB,BBB).

In particular there are exactly 10^10/180 l[ps] wavelengths in the Classical Electron-Diameter, the latter

which is found modular dual in the expression: c=l[ps]f[ps]=1/l[ss].f[ss].

This links Gravitational Radiation to Electromagnetic Radiation as Lagrangian Boundary Condition.

Because of this quantisation of the wormholeradius r[ps]=l[ps]/2p; we can directly relate the unified fieldpropagation (which is 4l[ps] or 8p radians) to the magnetic constant linking the linearisation of the worm-holeperimeter to the fourfoldedness of the angular multivalued expression.

Define the electronrestmass as equality between the relativistic massincrease and its dynamic magnetic selfinduction.

You have: c^2.(m-me)=mo.e^2.v^2/(8pRe), where me is the electronmass; e the electropolecharge; v the electron velocity; mo the magnetic constant and Re the Classical Electronic Radius.

Now set: Constant A=mo.e^2/(8pRe.me) and let Constant B=(v/c).

This leads to the quadratic: B^2=([A-2]/2A)+-[A^2+4A]^1/2/2A.

This defines a distribution of B^2=(v/c)^2 relativistic velocity ratios in me.A=mo.e^2/8pRe.

Using our definitions, we find: me.A=30e^2.c/e*=4.645263574x10^-31 kg*.

This implies, that for A=1, me=me/2, where me=9.290527155x10^-31 kg* from the prequantum algorithmic associations, based on the magnetic constant defining the Classical Electronic Radius.

Here me is the EFFECTIVE ELECTRONMASS and includes a MAGNETOCHARGED PART; added to the 'Naked Electronmass meo'.

As B^2>=0 for all velocities v, bounded as groupspeed (not de Broglie Phasespeed always >c) in c for which B^2=1; a natural limit is found for the B^2 distribution at A=1/2 and A=Infinity.

For A=1/2: B^2=-3/2(+-)3/2 for roots x=0 and y=-3;

for A=3/4: B^2=-5/6(+-)(19/12)^1/2 for roots x=0.425 and y=-2.092;

for A=1: B^2=-1/2(+-) Sqrt(5)/2 for roots x=X and y=Y;

for A=Infinity: B^2=(1/2)[-](+-)(1/2)[+] for roots x=1[-] and y=0[-];

Letting B^2=n, we obtain the Feynman-Summation and the Binomial Identity gives the limit of A=1/2 in:

A=1/2 - B^2{3/8 - 5B^2/16 + 35B^4/126 -...}.

But the FRB is defined in the renormalisation of B(n) exactly about the roots X,Y and so the model of the 'heavenly boundary conditions' is proved, (relative to the composer).

The unifying condition is: XY=X+Y=i^2=-1=exp(ip).

One can now introduce the magnetocharge to derive the 'naked electronmass' by perturbation and the

REDUCED CHARGE.

Let me*=me-meo for me*=2me.e^2/3Re.e*=1.556642765x10^-32 kg* {EQ.*}

as a first approximation and introduce the unitvolume V in: me*=mo.e^2.V/(4pRe^2.c^2).

"Cubing the Sphere" in the ratio of an inscribed (or circumscribed) sphere of unitradius and bounded by a cube of side 2-units then sets the unitvolume in an octagonised coordinate system.

V so becomes 4p/3 in the ratio 4p/(3.8)=p/6 and we have {EQ.*}.

Using perturbation techniques, one then approximates the 'naked electronmass' from its magnetocharged and effective progenitor.

A complication arises because of the higher dimensional independence of the Alpha-Finestructure Constant from electric permittivity.

The creation world form for Alpha=60p.e^2/h as a direct reflection of the ACTION LAW (h*=ee*).

This results in a measured Alpha-Dip for certain cosmological redshift intervals (10D-11D intersections of electromagnetic parameters) and other factors discussed in the 'Gravitational Constant' File, found on this site.

There is a possibility that Euler's Constant explicitly defines the electropolecharge and hence Alpha, but this is a work in the wings.

But any empirical measurements of the 'Naked Electronmass' engage the Charge/Mass ratio [e/m] and are thus subject to further finetuning.

Tony Sirebard


The Machian Momentum for the Universe

We consider the universe to be a Quantum Universe; that is we sum all fermionic spin-states (N) as Intrinsic Angular Momenta to become the Intrisic Spin Angular Momentum for the Universe as a quantised protoverse.

This total momentum we considered mirrored in a dimensional 11-DWittenMirror reflecting 12D-OmniSpace onto 10D-OmniSpace in a complexified within-without topology of a doublesided surface becoming onesided.

The modular duality of superbrane theory will prove useful in application in that regard.

This rather naturally engages the Heisenbergian Uncertainty Principle in the form of the fermionic (or halfspin) intrinsic angular momentm given in h/4p as the limit for measurement regarding dynamical systems.

We engage the absolute polarity cancellation, say as x=v.t=(-v)(-t) in this doubling process in engaging the 4world scenario of George Ryazanov and described in our context in the following analysis.

1. Moments of Inertia and the nested curvatures of dimension mappings

The Moment of Inertia of a solid sphere mass M and radius R is (2/5).MR^2 and that of a spherical shell of the same dimensions is (2/3).MR^2 as determined by integration across the geometries.

We consider the universe to be the Hypersphere of Riemann of 4D-Volume [2p^2Rmax^3], which is also a 3D-surface of toroidal derivative, i.e. a KleinBottle as Moebian extension in 2D.

This kind of topology incorporates naturally our doubling of a onsided surface via a dimensional twist of a doublesided surface.

This we term the Francom-Moebius Adjacency about a Wolford-Centre or mathematical point singularity.

As precisely 8 spheres radius (a) fit into a sphere radius (2a) and volume (4p/3)(8a^3)=

(32p/3)(a^3); we define the curvature factor (3p/2) to relate toroidal volume [(2p^2)a^3] to spherical volume [(4p/3)a^3].

Considering now the topology of such a torus, defined in radii a and 2a; we can observe a positive spherical curvature encompassing a negative hyperbolic curvature in a 3D perspective, the latter which we expand into 4D as the hypersphere of Riemann.

The encompassment or enveloping of a lower surface dimension by a volume dimension is however twosided.

We must consider the mapping of volumes onto both the inner and outer surfaces in the same dimensional sense.

Whilst the inner volume of the earth, say is mapped onto the inner manifold comprising the earth's surface; the outer volume of the earth (the outer space) is mapped onto the outer manifold as the encompassing volume and as given in the 4D hypersphere, which is a 3D surface.

This consideration then allows us to extend the 3D/4D scenario in the application of conifolded or enfolded higher dimensional geometries.

Especially, there exist toroidal derivatives in 6D, which are called Calabi-Yau manifolds and their extensions into 7D are termed Joycian shaped topologies.

We so invoke here the nomenclature of superbrane theory, without its mathematical formalism.

In our analysis of the Machian observer, we shall find the principle behind higher dimensional M-Theory of the superbranes.

The underlying principle is the Principle of Quantum Relativity (QR) as a natural extension for the Principle of General Relativity (GR), itself a natural consequence for the Principle of Special Relativity (SR).

We rename M-Theory in 11 dimensions as FMC-Theory of Quantum Relativity in 12 dimensions for this purpose.

The elementary precept of modular duality in M-Theory shall also be the defining foundation for QR.

We then consider 3D-surfaces as 4D-volumes to conifold 6D-Calabi-Yau shapes and 7D-Joyce manifolds in the connector dimensions of their enfolding.

This process renders the Minkowski-Riemann spacetime metric as a scalerelative enfolding of space within time, thus leading to the 'sharing of dimensions' and any object moving through time with maximum speed 'c', requiring to be necessarily at rest relative to its scale relative spacial dimensions.

Any motion of the object relative to the space dimensions, would decompose the Minkowski 4-vector and reduce the speed c via the formalisms of Special Relativity and its postulates.

For simplicity, we define the 12 dimensions as a simple superpositioning of four worlds superimposed upon one another, say as:

LineSpace (1-2-3)HyperSpace(4-5-6)QuantumSpace(7-8-9)OmniSpace(10-11-12)(13=1-2-3)..

Each of the four worlds is the Riemann hypersphere with 3 spacial dimensions and a connector time dimension, which forms however a spacial dimension for the adjacent superimposed world.

So LineSpace connects to HyperSpace via a convenient, but ultimately imaginary timedimension and as say expressed in the Minkowsi 4-vector.

We could also extend our 4 worlds in ascribing Translation to LineSpace, Rotation to Hyperspace, Vibration to QuantumSpace and Quantization to OmniSpace, the decisive constant being the speed of light in 'free space', denoted as 'c'.

2. The Machian observer and the principles of relativity and the Weyl nullification

The rotational frames of references of HyperSpace will become elucidated in the Machian observer.

Consider the rotation of a dynamical system about its axis of rotation, say a solid circular disk radius R with angular velocity w=v/R=2pf; f the frequency of rotation and v the tangential velocity linked to angular centripetal acceleration ac =v^2/R.

The postulates of SR lead to Time-Dilation and Lorentz-Contraction and invoke the notion of no absolute motion being measurable between two oberservers moving uniformely or at rest with respect to one another.

This and the invariance of 'c', irrespective as to the dynamical motion of the observer, forms the Principle of Special Relativity.

The Principle of General Relativity states, that a dynamical system of SR, that is in uniform motion of an inertial frame of reference and which is experiencing a gravitational field; is indistinguishable from a non-inertial system subject to accelerations, which is not experiencing such a gravitational field. This is known as the Principle of Equivalence.

Our rotating disk above so experiences both inertial and non-inertial frames of references, so applying both SR and GR in the one dynamical system.

In particular the radius vector must remain invariant, being normal to the central force, causing the centripetal acceleration.

The tangent vector experiences Lorentz-Contraction relative to a Bird's Eye Observer (BEO), which remains stationary relative to the rotating frame of reference (FOR).

Using SR and allowing an observer to rotate with the FOR must produce the invariance of 'c'.

Now any 'observation point' for the corotating FOR must be somewhere on the disk, resolved in the radius vector and the tangent vector.

We 'shrink' the radius vector using GR until we encounter the Weyl-Limit.

The Riemann Tensor of GR's field equations consists of two parts; the Weyl-Tidal-Tensor and the Ricci-Density-Tensor with the g-metric.

The Weyl-Tensor preserves volume, but deforms the volume, whilst the Ricci-Tensor reduces volume in accelerating the particles comprising the warping surface inwards.

But our radius vector must remain invariant and when the limit for measurement is reached in the 'point-limit', then there can be no deformation by the Weyl-Tensor, because this would violate the invariance of the radius vector.

Subsequently, the Weyl-Curvature must be 0 and the 'point limit' must be a dewarped singularity, which we now rename as the wormhole perimeter lps=rps/2p as the metrically defined geodesic.

As mensuration limit, no further Lorentz-Contraction below the wormhole perimeter is possible.

This is a consequence of QR in the modular duality definitions for heterotic superstring HE(8x8), which we rename here as the Supermembrane EpsEss.

3. Quantum Relativity definitions for the Mach observer

The Identity coupling the macrorealm to the microrealm is given in the inverse properties of SourceBoson Eps and SinkBoson Ess, the subscripts denoting ps=primary sourcesink and ss=secondary sinksource.

QR defines the following:......Energy:..........E = moc^2 = hf

.........................................................................................E=hf iff mo=0

.........................................................................................E=mo iff f=fss=1/fps=lps/c

All elementary particles/wavelets thus carry an intrinsic EigenFrequency or Lightequivalent fss=1/fps=tps, which is the TimeInstanton, the beginning of the universe as described by GR and the metricated scenarios of mensuration, observation and scalerelative measurements.

This gives the inverse proportionality for lightspeed 'c' to the coupling between the vibratory Eps of high frequency/small radius source-part, modular dual to the winded Ess of low frequency/big radius sink-part.

Gravitational Radiation is the modular inverse of Electromagnetic Radiation, differing in the scale-independent and algorithmically QR-derived supersonstant c^2.

A derived minimum/maximum coupling relates the frequency of the 11D-oscillating universe with nodally fixed Hubble Constant Ho=58.04 (km/Mpc.s) and maximum curvature radius Rmax=c/Ho to the wormhole in the constancy for c in: c = Ho.Rmax = fps.lps

Also, the dimensionless TauTime(t) in GR, applied to the curvature Rc=c.dt/dt, becomes the cycletime n in our descriptions as dn/dt=Ho, n=Ho.t.

The wormhole perimeter is directly quantised in terms of the classical electron radius Re=e^2/(4peo.mec^2), which is proportional to the Compton Radius of quantum-atomic-structure in RCompton=Re/Alpha.

Alpha is the electromagnetic finestructure given as Alpha=e^2/2eohc and as Alpha=60pe^2/h in QR, and denotes the interaction probability between matter and light.

(QR derives a superconductive form for the Action Law: Action = Charge^2, electrical conductance quantum,

Quantum Hall effect and Josephson Constant).

There are exactly 10^10 lps/360 wormholeperimeters in one Re; relating to the finestructure of Planck's Constant h as: h=lps/[8p.Rec^3] in dimensionless Action-Units (relating to the monopole superstring class IIB).

{The 360 count is not arbitrary, because the QR derivation for transcendental p, engages trigonometric series which lead to the cipher 180 as a limit in Archimedean polygon approximations, also related to QR definitions for magnetic permeability and electric permittivity}.

The nodal and 11D oscillating universe grows under agency of 'c' in electromagnetic parameters, encompassing the asymptotically expanding, but decelerating 10D hyperbolically curved 4D-volumed hypersphere as its inner surface mapping in say the 5D-Anti DeSitter hyperspace.

The volume as 4D-information becomes the 3D-surface of the inner LineSpace mapping the 5D-surface of the outer HyperSpace.

The volume is nested between the surfaces of two worlds, an ekpyrotic universe of LineSpace blending with the Hyperspace, encompassed in the cyclicity of the 10th dimension , reflecting off the M-Space of the Witten-Mirror.

Thus the connector-time dimensions are 4-7-10-13=1 and the four worlds are defined in perfect supersymmetry.

Maxwell's equations are introduced to the magnetic monopole(as selfdual superstring class IIB) and 12 magnetopolic junction points within a fourfolded propagation of the wormhole toroidal spacequantum define the Unified Field of Quantum Relativity (UFoQR).

And yet, this fourfoldedness is just the one world of our Machian Observer.

The singularity is no more; it has become the selfrelative BEO at the centre of rotation as the Machian Observer.

It is irrelevant if the BEO rotates with the Perimeter FOR or is stationary relative to it.

As Machian BEO, shehe is located literally at the centre of the universe, with everything else rotating or moving relatively to himher.

The uniform motion of SR implies invariance of c, should the perimeter FOR rotate with the FOR.

It is only at the now demetricated singularity, that this corotation becomes arbitrary.

Demetricating the field equations of GR blends QuantumTheory with Classical Mechanics, culminating in General Relativity, itself emerged from Special Relativity and the physics of Newton and Galileo.

The nullification of the Weyl-Tensor hence dewarps Minkowskian spacetime into the Schwarzschild solutions for the overall cosmic evolution, from the wormhole singularity as limit for the g-metric onto the Sarkar-architecture of the fractal universe in 236.5 million lightyears, then onwards towards the asymptotic boundary defined by the Spherical Standing Wave defined by the Hubble-Oscillation and c-invariance.

Meanwhile so the oscillating cosmos has returned in its cyclicity to intersect the dimensions 2.2 Billion years ago, superposing its blueshift onto the cosmological redshift and giving the 'appearance' of an accelerating cosmic expansion, linked to a 'dip' in the Alpha-Electromagnetic Finestructure Constant to about 80 parts per million in a redshift interval from 1.08 to 1.84, mapped again around an Arpian present cycle value of 0.2505.

But the finite cosmos is enfolded within the infinite one, creating space and time as it moves ever onwards under invariance of 'c'.

4. The Mach momentum for the universe

Let us now calculate the Machian Momentum for the Universe and the intrinsic angular momentum for it as a Quantum Universe, a Protouniverse or monosong.

The geometry can be modelled on a prolate ellipsoid with major axis invariance under rotation.

The focalpoints would remain mathematical singularities as the 0-brane of Quantum Relativity.

Any minor axis rotation would merge the focus points in a pointcircle and the 1-brane of QR would define an oblate ellipsoid of phaseshifted multiverses; integrated as angular function of the complex OmniSpace as the Omniverse.

As there is no gravitational field outside the enfolded protouniverse, uniform motion of the protoverse in inertial frames is not equivalent to accelerated motion in noninertial frames by the postulates of GR.

Subsequently, rotating the protouniverse in the nongravitational undefined spacetime without does not cause centripetal forces balanced by centrifugal (coriolis) forces within the enfolded and metrically defined spacetimes.

The Machian and Einsteinian postulates of 'Relativity of Inertia' hence becomes the BEO -frame within the protoverse as referring to the centre of rotation as the Machian observer, a reference previously known as 'relative to the fixed stars'.

It is only in that FOR, that the BEO becomes independent from any other coexisting relative rotational systems in the measurement of the invariance of light, say as in the Sagnac Effect.

The monosongs become tunes, melodies and a symphony of the supermembranes as particle/wavelets of the UFoQR.

 

The Total Momentum for the Universe is given in:..................(2/3)M.Rmax^2.w = N.h/4p

We consider the Universe's mass M to be the surface mapping of 10D onto the inside of the 11D-manifold and use the moment of inertia of a spherical shell. (This is the 2-brane/2-sphere of LineSpace).

We incorporate all fermionic particles, including the (anti)neutrinos, whose number is given in the baryon/photon ratio (Eta h) and a number which increases N by a factor of about 10^9.

QR calculates, for a present cycletime np=1.1324.., the following parameters:

Deceleration Parameter qo=0.014015 for Sarkar-Architecture at cosmological redshift z=7.477 or 236.5 Mly.

Critical Density rc=3Ho^2/8pG=Rmax.c^2/2GVmax ....(rc=Ho^2/4p^2.G for 11D-curvature)

Mo=1.81371262x10^51 kg*

M8=6.47061227x10^52 kg*

Rmax=1.59767545x10^26 m*; R10D(n)=Rmax(1 - n/(n+1)) m*; R11D(n)=n.Rmax m*

No=1.8275x10^78

N8=6.5197x10^79

h10D=3.64x10^-10

h11D=4.82x10^-11

 

w = 2pf = 2p /T = 3Nh/{8phMRmax^2} = 3.06x10^-50 1/s for the asymptotic 10D-massparametric universe

(T=Period)................................................................= 5.08x10^-50 1/s for the oscillating 11D-electromagnetic universe

The QR definition for time sets the natural limit for this in the minimum/maximum ratio of lps/Rmax=nps.

The Timeinstanton tps=fss=3.333..x10^-31 s thus relates nps=1/lssRmax=6.26x10^-49; mapping the 'real' time tps onto the 'imaginary' time Ho.tps=1.17x10^-66 s/s.

This analysis has lead us into the realms of the poets and dreamers.

Leonardo de Vinci's 'Vitruvian Man' has literally become the Machian Observer, encompassing the entire universe as 'Cosmic Man', the Adam Kadmon of Lurianic-Hebrew Kabbalah or the Purusha of Hindu cosmology.

Molecules are mapped as star systems from the 'inner space' and biovital cells become the galaxies of 'outer space'.

Every sentient being is mapped holographically as a neuron in all other 'immortalised' non-telomere depleted 'neuronal brains'.

The monosongs become tunes, melodies and a symphony of the supermembranes as particle/wavelets of the UFoQR.

 

Anthony Paul Bermanseder, BSc.

From: "Tony Bermanseder/Sirebard" <pacificap@hotmail.com>

RESOLUTION OF NEWTON'S GRAVITATIONAL CONSTANT MEASUREMENTS

The speed of light 'c' has been measured to an accuracy of 8

decimal places and Planck's Constant 'h' is known with an error not

exceeding one part per million.

This is not so for Newton's Gravitational Constant 'Big G'.

The National Bureau of Standards (NBS) in Gaithersburg, Maryland, US

began measuring 'G' in the 1930's to establish the Luther-Towler-

Number LTN=6.67259x10^-11 G-units (m^3/kg.s^2].

So it stood until 1994, when the renowned PTB in Braunschweig,

Germany's Standards Laboratory measured G much higher, differing in

the 3rd decimal place.

Then New Zealand's Measurements Standard Laboratory published a

value significantly below the LTN and the University of Wuppertal

derived a value in between the NZ one and the LTN.

Notwithstanding the ever improving technological advances and

measuring techniques; using torsion pendulums, tungsten cylinders

or suspended or accelerating testmasses; 'Big G' has proven to be

intractable to conformity.

One of the latest measurements are 6.67327x10^-11 G-units and

6.6742(10)x10^-11 G-units and values by no means definitive.

What is going on?

Shifting heavy objects in the vicinity of the test apparatus seems

to influence the atomic structure of the testmasses, irrespective

of the isolated environment created for the testing conditions.

The following treatise shall resolve the conundrum and illustrate

the unruly behaviour of 'G' as a consequence of the initial boundary

conditions for the universe's subsequent evolvement.

It shall indicate that even a 'massless' universe would contain a

diminished G-component as the electric permittivity of a massless

macroquantised (Hawking) BlackHole and that the present dilemma

derives from a finestructure of the nucleonic constituents, which,

by definition, must comprise the testmasses.

A precise measurement so would rely on an unambiguous calculation

for two neutronic restmasses, a condition which we shall show to be

unachievable, because of the nature and interrelationship between

the parameters of inertial mass and those of electromagnetic charges.

1. Boundary Conditions for G and a First Approximation

2. G-Modification through the Hawking Modulus (hm).

3. A BlackHole-Nucleon connection.

4. The Precision Measurement of G.

1.BOUNDARY CONDITIONS FOR G AND A FIRST APPROXIMATION

The Mother of all Boundary Conditions must be the statement of:

"No Boundary conditions apply!"

So we consider a NullTime and a NullSpace in an undefined, say

Platonic-Penrosian 'Space' of mathematical abstraction.

This is like a 'thought' or an 'idea'; how can IT become real or

even manifest as a physical and quantifiable universe?

In hindsight one knows how to answer this.

An idea is born from observations; mental energy is linked to passion

and the emotions, breeding the inventiveness to engage in a course

of experimentation and to bring the idea (say a lightbulb, follo-

wing the observation of a lightning strike) into physical manifes-

tation.

But how can one apply foresight, when no observational reference

frame exists in the NullState of the NAKED SINGULARITY or the

GENESIS BOSON?

This then is the 'Boundary Condition' for the NullState, nothing

exists and everything requires to become invented.

The Everything is the Nothing and so one can model this state on

the 'idea' of an infinite selfrepeating computer loop, representing

the Father of all algorithms.

This can only be one thing, namely a mathematical representation

of the Nothing, say in the numeral 0 representing circular clo-

sure, which linearises in the cipher 1.

Angular multivalued Complex Infinity is linearised in negative and

positive polarity of a Doubled-Infinity.

The hindsight then defines the closed circular NullState continuum

as a closed looped superstring class I of the Planck-Scale, also

containing the openended members of that same family.

But that wasn't the beginning program of the primary algorithm, but

this is a secondary algorithm, which can be stated as:

"ADD THE END TO THE BEGINNING AND START WITH THE OLD END"!

This specifies the methodology of RECIRCULARISING the linearised

dimensions of the binary dyad (0,1) into the root-reductive decimal

monad (1,2,3,4,5,6,7,8,9,0) (or some other number system).

Here then we define: 10=1+0=1*; 11=1+1=2*; 12=1+2=3* and so on until

26=2+6=8** and 27=2+7=9** give a kind of closure in the doubled (or

squared) application of the algorithm, reflecting the 'Doubling of

Infinity'.

The hindsight then one day discovers, that there exists a mathe-

matical entity, called the 26-dimensional Bosonic Superstring,

which folds up the Ricci-Metric in Calabi-Yau manifolds in 6- and

in Joyce manifolds in 7 circularised dimensions.

A heterosis of 26-dimensional counterclockwise rotating vibration

patterns becomes 'married' to such states of frequency, rotating in

10 dimensions in a clockwise manner.

A DEFINITION of TIME then became effected, once the first algorith-

mic definitions had reset themselves in the pattern:

CIRCULARISED - LINEARISED - RECIRCULARISED - ENERGY=FALSE VACUUM

- QUANTUM TUNNELLING OF TEMPERATURE WELL = QUANTUM BIG BANG.

Curling up the 16-dimensional anticlockwise patterns in special

toroidal geometries, then would allow a definition of Heterotic

classes of superbranes (HE(8x8) and HO(32)), one of whom would

become the sought after MINIMUM condition for the Naked Singularity

to manifest itself in its escape from the infinity-loop.

The primary algorithm results from the application of 10 elementary

principles/antiprinciples which defined the algorithm as itself.

And because this algorithm engages a fivefolded symmetry, there would

be five classes of 10-dimensional superstrings, upon whom the second

algorithm could then act.

The ten principalities are:

1.Identity/Antiidentity

2.Expansion/Contraction

3.Order/Disorder or Entropy or Chaos

4.Symmetry/Asymmetry or Distortion or Nonparity

5.Divergence or Infinity/Convergence or Limit

6.Inversion or Reciprocity/Constancy or Invariance

7.Reflection/Absorption

8.Relativity/No Antiprinciple

9.Quantisation/No Antiprinciple

10.New Identity/No New AntiIdentity, because of the

application of the other 9 principalities to effect

the transformation of One Self into Two Selves,yet

as the One Unity of One extended Self.

The purpose for the establishment of the first algorithmic program

is its cosmogenetic selfreproduction.

Adding Self/Infinity to Self/Infinity still gives Self/Infinity,

but somehow, the second Self is different (more), than the first

Self.

The first algorithm becomes the mapping of two integral number

series onto each other, complementing each other in a filling in

the gaps, created by one of the sequences as a one-to-one corres-

pondence (like even and odd numbers for example, together forming

the set of integers).

But this one-to-one correspondence resulted in the following data:

(266561); (151618); (141524); (151032); 11; (091016); (061015); 7; 6

and 4 with a natural limit of 12, set and generated by the princi-

palities as boundary condition for the selfiterative programming.

The secondary algorithm then utilised the initiatory number constant

E and generated the continuation, which would allow the Temperature

Gradient or Energy-Wall to manifest in the linearisation of the

physical parameters defined by the permutations of the code from the

first algorithm.

The secondary code became (with initialising counter E): BEGIN;

ABCDEFG(H=ABCD) with E=(266561); F=(136656); G=(673665); STOP GENE-

RATION because 5+6=11=2* is rootreductive; CONTINUE D=(465612);

C=(256124); B=(361242); A=(312423); STOP GENERATION because no mo-

nadic archetype can yield Z(Z+A)BCXY=312423 from its precursor

ABCXYZ=(1-Z)24233, ending in rootreduction (1-Z)=1-3=-2=-11=-2*;

END of 2nd algorithm.

The first algorithm applied the Ordering Principality to DEFINE

TIMESPACE and the ordering of the constants as given.

Constant#1=E became the Number of Spacequanta defining the compac-

tified 16 dimensions of the superbrane scenario upon initialisation

of the second algorithm.

All principalities are engaged and the ORDER of the Constant appli-

cation uniquely sets the physical parameters manifest in the order

specified;(i.e. Temperature before Radiation before Restmass, etc.)

Constant#2 defined ENERGY=(Constant#2).TEMPERATURE.

Constant#3 defined ENERGY in terms of ELECTROMAGNETIC CHARGES and

in a Universal wavefunction, normalised about the pentagonal sym-

metry of the first algorithm.

Hindsight would discover that a local application of this wave-

function would result in summation of integer states or probabi-

lities, which upon normalisation and the 'squaring' of the state

would reproduce the Unity of the original wavefunction in the

pentagonal symmetry.

These would be known as the wave equations of quantum mechanics.

In particular one summation: T(n)=n(n+1) would, upon unitising;

define the universal wavefunction explicitely in a Feynman-Path-

Summation and allow the following identity to engage the timespace

evolution of certain parameters, including the linking of Constant#3

to Constant#6.

This would achieve a synthesis known as Gravitational Constant 'G'.

The all encompassing Identity is: XY=X+Y=-1=i^2=exp(ip) for the

generating waveequation: B(n)=[2e/hA].exp(-Alpha.T(n)).

Here A^2=Constant#3 and the roots X and -Y form the Bounds for the

NullTime definition in both real-positive and imaginary-negative

linearised time parameters about the normalised Mean of B(n) for

n=0 becoming reflective in n=-1/2.

C-Space is n-real from n=0 and F-Space is n-imaginary from n=-1

towards the negative integral count.

In between in the interval [-1,0], is the M-Space further symmetrised

about the Functional-Riemann-Bound: FRB=-1/2 and as the Point of

Origin.

Three orthogonal axes so define 3D-Space, about which a 6D-Twistor-

Space indicates two further degrees of freedom, each of the arbitrary

up-down, left-right and in-out linear axes setting the NullTimeSpace

as defined by B(n) allowing a clockwise or anticlockwise chirality

in the compactification of the circularised Linespace.

This extended definition for 3D-LineSpace into 6D-HyperSpace sub-

sequently transforms into 9D-QuantumSpace in introducing the degree

of stretching/contacting by the application of Principality #2,

following the Identity/Antiidentity initiation.

All principalities are engaged in their defined Order, indicating

that 9D-QuantumSpace manifests the identity of an expanding and

ordered and selfcontained continuum within the symmetry principality.

9D-QuantumSpace then diverges/converges in the setting of certain

boundary conditions, which must incorporate the principles of

inversion and of reflection with their antiprinciples.

Henceforth, 9D-QuantumSpace sets a limiting condition, which

hindsight would define in all manners of temporal parameters.

The relativity principle then allows the perception of being located

at either of two observation points, namely the principalled or

antiprincipalled vantage point, given in the kaleidoscope of all the

combined principalities.

Thus, a 10D-OmniSpace is created, which reflects/absorbs itself

under engagement of inversion/invariance, becomes relative and

subject to the 9th principality of the quantisation.

This defines OmniSpace to quantise itself in 3D-Linespace, following

the definition of the root-reductive decimal monad, so birthing the

New Identity as Antiidentity to itself in the completion of the self-

iterative and selfrelative programming of the first algorithm.

OmniSpace hence requires to be 12-dimensional in the construction

of the mastercode, becoming physically implemented in the Universal

Cosmic Wavefunction B(n).

The interval [-X,X-1] specifies the maximum for B(n) as a probabi-

lity interval with B(-1/2)=[2e/hA].exp(Alpha/4) and a standard de-

viation about the first moment by the multiplier (Alpha/2p)^1/2.

Hindsight would discover this as the Schwinger numbers to extend the

QED-Feynman diagrams to account for multiple particle interactions

as permutational possibilities in perturbation dynamics.

Constant#4 defines ENERGY=(Constant#4)FREQUENCY.

Constant#5=11 defines the Identity-Relation between Constant#4

and Constant#6 in Equality by DimensionCounter 11.

Constant#6 defines ENERGY=RESTMASS(Constant#6) as the Parity-Mirror.

Hindsight would define: (1) hf = moc^2 [Eq.#1]

(2) Energy=hf iff mo=0

(3) Energy=moc^2 iff fo=flimit=fss

Hence all restmass carrying entities must possess a minimum eigen-

frequency to exist and this existence relies upon the definition of

TIME as the Inverse of some frequency: TIMEINSTANTENUITY=1/fps;

where fps is the MAXIMUM FREQUENCY modular dual to the MINIMUM

FREQUENCY defined in fss.

A direct consequence for 'G' derives from this in the Schwarzschild-

Solution applied to the HE(8x8) Supermembrane.

Hindsight would discover a best fit for the observed and experi-

mentally measured physical parameters, as given by that superstring.

The Coupling Constants between the vibratory (MAXIMUM) part of that

supermembrane (Eps for Energy of primary source) and the winded or

(MINIMIM) part (Ess for Energy of secondary sink) are:

EpsEss=h^2; Eps/Ess=fps^2 with lps.lss=fps.fss=1.

A direct consequence is the Hawking Black Hole for a minimum

temperature condition from the inverse proportionality between

Mass and Temperature for the BlackHole spectra.

Wavelength lps=WormholePerimeter=2p.rps and rps is modular dual

to rss in (2p)lss=2GoM(Hawking)/c^2 in the Schwarzschild solution.

This is the manifestation of the mathematical modular duality for

the B(n) definition in: X=1/-Y=1/(1+X).

We shall use the expression:

2M(Hawking)=(2plss.c^2/Go [Eq.#2]

in our resolution of the 'G' dilemma.

Preempting the discussion somewhat; a massless universe would be

characterised by an diminished G<=>Go and the Hawking Black Hole would

be defined in terms of its Force-Charges.

Constant#7 defines a transformation from the Radiative EnergyState

into the Restmassive one given above and the integers 7, 6 and 4 are

dimension counters, limited by the counter 12 as the holographic

image for the summed lower dimensionalities, i.e in 4+6=10 & 4+7=11.

We return to foresight and find ourselves equipped with a new

possible definition for TIME as: MINIMUM/MAXIMUM=CYCLETIME (n).

Algorithm #2 has defined the limiting boundary for a potential

expansion of 10D into 11D in spacequanta counter E=Constant#1.

Quantum Geometry, applied to the concept of representing a 4D-Volume

as a 3D-Surface defines the Riemannian Hypersphere with a toroidal

volume (2(p)^2.R^3), R taking the linearised form of the MINIMUM

condition as lps to define a spacequantum in the potential mani-

festation of monopolic space, hindsight would term 'The Vacuum'.

This Vortex-PE or VPE is still contained in the NAKED SINGULARITY

of the GENESIS BOSON, whose eigendefinition in terms of physical

parameters can now proceed.

Those quantities are necessarily BELOW the MINIMUM condition,

manifesting as the last and most physically applicable form of

the superbrane families in the EpsEss=HE(8x8) heterosis.

And so a subcontinuum, a dimensional divide becomes established to

allow the 10D-universe, manifesting as a 3D-Surface, to expand into

the 11D-universe as a 4D-Volume.

The 10D-Universe must be hyperbolic, hindsight measurements would

detect and hindsight would also conclude, that the overall universe

would be Euclidean flat and of zero curvature.

Eventually, hindsight would understand, that the closed geometry of

11D-M-space mirrors the open geometry of 10D-C-space onto itself as

a mapping into the holographic image of the 12D-F-space.

So just like one can observe both open and closed curvatures in the

multiconnectedness of a 2D doughnut/torus; the inner hole curving

hyperbolically encompassed in a spherical envelope, so is the uni-

verse multiple-connected within its own unity.

But the superbrane scenario maps the MINIMUM onto itself and becomes

the MAXIMUM, the dimensional expansion of C-Space into the M-space in

the duality perception of being located at the Point of origin as

the Big Bang Singularity or as the Event Horizon Singularity at the

wavefront of the selfsame expansion.

The vibrating Eps becomes the MINIMUM SCALE and the winding Ess the

MAXIMUM SCALE in that subcontinuum.

Defining the toroidal volume generator as a consequence of the

integral H-count: H=[2p.rmax/lps]^3, then define rmax as a 10D/11D

boundary.

Hindsight would calculate: rmax=1.59767545x10^26 metre-units.

Hindsight would also discover that a dimensional DIM-factor would

assume the value 7.56 at the time of its discovery; implying that

so 7.56 10D-universes would 'fit' into the 11D-universe at that time,

defining a discrepancy of matter in the cosmological calculations.

We shall find that the baryonic matter is just 2.803% of the

critical density at the Big Bang; an inertial mass seed, which would

grow to 3.68% at the time of discovery, adding to a kind of 'shadow'

or 'dark' matter amounting to 27.8% of the necessary total for

Euclidean closure.

This is a function of the deceleration parameter, which as a scale

ratio defines not only the architectural scale (Gravitationally

bounding Sarkar Constant centred in the supercluster interval from

236.1-472.2 Million lightyears), but also the Black Hole spectrum

bounded by the critical density.

So Foresight defines TIME=lps/rmax=6.259093473x10^-49 = nps, the

cycletime at timeinstantenuity, after the second algorithm had

implemented the cosmic interaction of the dimensionalities, which

hindsight would term de Broglien hyperinflation, proceeding with a

phasespeed of rmax.fps and a phase acceleration of rmax.fps^2.

And here the 'False Vacuum' develops to energise the process.

TEMPERATURE=ENERGY/k=h.FREQUENCY/k=h/(k.TIME)=h.rmax/(lps.k) and this

calculates as 7.544809x10^37 Temperature-Units at Genesis Boson Time,

which is the superbrane epoch.

RESTMASS becomes: h.rmax/(lps.c^2)=0.011834633 (leading to a defi-

nition of Avogadro's Constant upon application of Unified Field

parameters, which span 8p radians of the 4-folded lps-wavelength

(of quadrupled 3D-LineSpace as Line-Hyper-Quantum-OmniSpace) and

integrating as the toroidal spacequantum in its sinusoidal pro-

pagation in: (p/4)[S]{sin(3x/2)-cos(3x/4)}^2.dx and the VPE-

sourcesink-quantum in: VPE-Quantum=(4p.hfps/lps^3)=2.51327..x10^64

as energy desity in (Energy/Volume)-units.

Since 12 magnetopolic current 'knots' specify this field, the

vacuum is energised by the magnetopolic energy.

This energy is given as [c^3] unified F-space units and manifests in

the lower dimensions as the Current/Linespace quantum [ec] or as

exactly 27x10^24 eV, which is a monopolemass of [ec=4.82x10^-11] kg-

units.

The VPE of the vacuum so becomes defined in wormhole parameters for

the Naked Singularity putting 'some clothes' on.

In terms of TEMPERATURE however, the nps cycletime is lower than

the Genesis Boson Time in 2.93516x10^36 Temperature-units.

The 'False Vacuum' so induces the tunneling of the higher tempera-

ture to its lower value.

This becomes the decisive parametrisation for the mechanism and

dynamics of the tunneling matter wave inflation.

The de Broglie phaseacceleration calculates as: 1.437908x10^87

(m/s^2) units and the Temperature-Field of the universe as a 'Black

Body' gives the Quintessence or Einstein-Lambda as the Schwarzschild

expression: GoMo/lps^2=2.015x10^85 (m/s^2) units, with Mo a Mass-

Seedling from the first algorithm defined as a function of E:

Mass-Seedling: Mo= [E]^1/2.mc.mP/me=1.813713x10^51 kg-units [Eq.#3]

mc is the nucleonic prototype; mP is the Planck-Mass and me is the

effective electronmass.

mc and me derive from the couplings between the superbrane classes,

one of which gives the scalerelation between the electromagnetic

and the gravitational interactions as: [AlphaGR]=[AlphaEMR]^18.

mc derives from that and me is a consequence of the definition,

linking wormhole perimeter lps to the classical electronic radius Re

(and hence the effective electronmass).

There are exactly 10^10/360 lps wavelengths in one electronic radius

as a consequence of linearising rps=lps/2p into lps over a 2p or

360 'degree' count.

The 360-degree count is not arbitrary, because the dimensionless

unification for the electric permittivity (eo=1/(120p.c) with

the magnetic permeability (mo=120p/c) specifies a halfrotation in

the geometric definition of the number (p) as a trigonometric expan-

sion and sets 180 as that limit.

Now the deceleration parameter, aptly so called in 'reducing' the

de Broglie Phase acceleration to the instanton of the classical

and metricased cosmic expansion of the quintessence calculates as:

qo=GoMo/c^2.rmax=0.01401506=Mo/2Mcritical=Omega/2 [Eq.#4]

The critical Mass for closure for all definitions produced by the

first algorithm is given in considering the universe as a 11D-Mother

Black Hole (F-M-C-Space=Father-Mother-Child-Space).

Then using the linearised time definition from cycletime n=Ho.t and

the Nodal Hubble-Definition: Ho=c/rmax, we get the critical Volume

as 2(p)^2.rmax^3 and the critical density as Ho^2/4(p)^2.Go.

Using the spherical 3D-volume would give the critical density as

3Ho^2/8(p)Go, which differs in the Feigenbaum-Chaos-Delta=(3p/2)

as dimensional unifier for the curvatures.

Mcritical so becomes explicitely defined as the MassTotal for the

universe and as 6.446x10^52 kg-units.

If we set the instanton time as tps=fss (modular), then this gives

the MINIMUM SCALAR HIGGS FIELD POTENTIAL from INFLATION MA-

XIMUM into the superbrane epoch as tinflationlimit=3.946x10^-32 seconds*.

The instanton relates as fss as 3.333.x10^-31 seconds*.

TIME as linear expression for the multivalued circular singularity

spectrum 'BEGINS' at TIMEINSTANTENUITY=tps=fss(modular).

But 'G' was not defined in the first algorithm, so where did it

derive from?

We begin with the Gravitational Finestructure being a scaled version

of the Electromagnetic Finestructure Alpha, with a generalised for-

mulation: Dimensionless Constant =(Constant).(Charge^2)/hc,

ForceCharge taking either the form of Coulombic Charge e or of

Restmass Charge m.

We now relate the Forcefields in the identity [ke^2]u=[Gm^2]u,

subscript u denoting unification; and where 'Coulomb-Charge' e

becomes defined (say in a Newton-Raphson Iteration) in the

wavefunction B(n).

The primordial algorithm specifies A=h/(2e) as the manifestation of

supermembrane class IIA and that in modular duality to the neigh-

bouring EpsEss heterotic supermembrane.

This relates to superconductive states in the Josephson Constant and

the Quantum Hall Effect, both derivative from the F-Space ACTION-LAW

of ACTION=CHARGE^2, which was applied before.

Generally, all mass definitions are defined in terms of the ma-

gnetic monopole, manifesting as class IIB.

Hence all mass is rendered magneto-monopolic at this stage of the

definition process.

The following expressions for the magnetocharge e* (measured in the

StarCoulomb C'*) are applied in the mapping of magnetopole charge

[e*] in F-space onto the electropole charge [e] in C-space.

This transition relates to the superbrane epoch before timeinstan-

tenuity.

(a) 2p.Go.mc^2/hc=Alpha^18 =(60p.e^2/h)^18 [Eq.#5]

(b) Eps=hfps=Ess.fps^2=[(2p.Go.me^2/(4Alpha.hc.e^2)]^1/2=1/e*

(c) (2e).(Re) = (e*).(lPlanck^1/2)

(d) Eo=e.Sqrt(E/Alpha)=1.886461127x10^38 C* (ChargeSeed)

(e) Mo/mc=1.813713x10^51/9.924724572x10^-28

=1.827469354x10^78 (No of SeedNucleons)

Mcritical/mc=6.519663x10^79 (No of Nucleons)

(f) OlPlanck=(e/c^2)=lPlanck.Alpha^1/2

The last expression is the Planck-Length-Oscillation, unifying

Gravitation with Electromagnetism.

For unitary consistency in C-space the dimensionless nature of the

Force-Charges must become linked to the monopolic spectrum and that

is achieved in the mapping of e* onto e.

The C-Space relation 2Re.c^2 maps the F-Space relation OlPlanck.c^2

and the unitary symmetry is the relation between the electric

permittivity and gravitation in the identity:

Go = (4p.eo) = 1/30c (dimensionless) [Eq.#6]

via unitary unity: [metre/Farad=Jm/C^2]=[kg^2/Nm^2].

The C'* =[m^3/s^2] =[Volume.Angular Acceleration] and

crystallises in the diameter of the electronic spacial extent.

This manifests the energy of F-space in magnetopolic equivalence to

the electropolic size of an atomic nucleus in 3 dimensions.

We note the independence of the primordial Energy from the

restmass.

Substituting k=1/(4p.eo)=1/Go into the electric constant from

the Maxwell Constant gives the 1/30c numeracy, independent from

the [kg] unit.

The generation of the masterconstants demands the establishment of a

cosmic-standardised unitary system (*) and the only constant shared

between both the (*) and the SI-system is the magnetic permeability

constant.

This is decisive in determining the lower dimensional 'dip' in the

Alpha-Constant, which remains invariant in the higher dimensional

settings, (where Alpha is independent of c and eo).

But now the Charge-Mass relation, as manifesting in C-space, is

indicated.

We set the Constant=Go.mc^2 = G(n)X^n.Mi.Y^(n/2).Mj.Y^(n/2) for any

cycletime n and a measurement G(n).

The partitioning of masses does not change the productation, since

(XY)^n remains unity for all values of cycletime n.

This is an addition in the form of the baryonic mass seed given in

Mo/Mcritical however and a First Approximation for G(n) becomes:

G(n) = Go.X^n [1 + Mo.Y^(n/2)/Mcritical] [Eq.#7]

For an universe devoid of any mass, we have m=0 and G(n)=Go.X^n,

the following identity needing to be be satisfied:

Mo/Mcritical = 2.MHawking/[Mo.(hm)^2] with Mo=hFo/c^2 by [Eq.#1].

But this is only the case for the Hawking Modulus [hm]=1, a con-

dition leading to [Eq.#2].

This would mean however, that no distribution for nucleonic states

exists, and that the mc-protonucleon only manifests in its restmass

equivalent or photonic-bosonic (or supersymmetric) state.

For a calibration: 1.000692265[m^3/kg.s^2]*=[m^3/kg.s^2](SI),

G(npresent)=6.684953x10^-11 [Nm^2/kg^2], is a first approximation.

This is the upper bound for G and will, under utility of the Hawking

Modulus, be substantially reduced.

 

2.G-MODIFICATION THROUGH THE HAWKING MODULUS

We recall the Hawking Modulus (hm) and relabel the Hawking Mass

under consideration of it specifying a minimum Temperature Con-

dition under application of the modular duality coupling constants:

Tmax=Tps=Eps/k; Tmin=Tss=Ess/k;

lps.lss=fps.fss=1=fps.lps/c=c.fss.lss

Then (hm)^2 = 2MHawkingMax.Mcritical/Mo^2 [Eq.#8]

For (hm)=1: 2MHawkingMax=Mo^2/Mcritical=2p.lss.c^2/Go [Eq.#2]

and as the Schwarzschild solution for rss=l/rps=2p/lps=2p.lss

But if (hm) is not equal to 1, we require an alternative method

to determine MHawkingMax, using its defined relationship to Tmin.

The superbrane epoch defines the Zero-Point-Vacuum-Oscillator as:

EPlanck/2 = h.fPlanck/2=mPlanck.c^2/2=[hc/(2p.Go)]1/2.c^2/2 and

the Planck-Temperature is: TPlanck=[hc^5/(2p.Gok^2)]^1/2.

We use a generalised Mass-Temperature Product MBlackHole.TBlackHole

and initialise it in the value of superbrane class I, which is the

Planck Boson.

MBlackHole.TBlackHole=mPlanck.TPlanck/2=hc^3/(4p.Go.k)

Then, at the instanton tps=fss, this becomes:

hc^3/(4p.Go.k) = mps.Tps = lps.c^2/(4p.Go).Tmax, with Tmax=hfps/k

Hence h.lps.fps.c^2/(4p.Go.k)=hc^3/(4p.Go.k) as required for the

maximum Temperature and minimum Mass condition of inverse propor-

tionality.

For the minimum Temperature and maximum Mass condition, the mo-

dulation of the electromagnetic spectrum for the propagation of

information at lightspeed 'c' must become redefined in the Hawking

Constant (HC) however.

Particularly, hc^3/(4p.Go.k)=(HC).mss.Tss=(HC).2p.lss.fss.c^2.h/k,

which is (HC).p.ch/(Go.k), defining (HC) explicitely for all Black

Holes in the generalised proportionality.

HAWKING CONSTANT (HC) = c^2/(4p^2) (dimensionless)

This is reflected in the modular duality of Gravitational Radiation

(GR) being modulated in the inverse lightspeed 1/c to that of

Electromagnetic Radiation (EMR) and as a consequence of the modular

duality between the two fundamental interactions reciprocating each

other in the mappings of 12D-magnetocharges onto 3D-electrocharges

via the medium of the vaccum and the VPE.

For EMR: l.f = c modular dual to l.f =1/c for GR, the unifier

being the dimensionless form of Constant#6=(091016), defined as the

integer square-triplet (9,10,16)=9x10^16 by the first algorithm of

the cosmogenesis.

The BlackHole Mass-Temperature Relation for dimensionless c^2 so is:

Mass(BlackHole).Temperature(BlackHole)=(HC).MHawkingMax.Tmin

=h.c^3/(4p.Go.k) [Eq.#9]

The Hawking Mass so must be:

2MHawkingMax=(4p^2.hc/(4p.Gok)/Tmin=60p.c^3/lps (dimensionless)

= 60p(eV-Monopole-Mass)/(primary source wavelength).

We note the relationship to the F-Space in Alpha=60p.e^2/h ,

which independent from the electric permittivity and constant 'c',

nevertheless defines the critical masstotal for the universe as

being of monopolic origin.

A particular finestructure for Heisenberg's Constant derives the

numerical value for the wormhole perimeter independent of experiment

and as a direct consequence of the primary algorithmic definitions

given so far.

(a) Planck-Length-Oscillation: OlPlanck=[e/c^2]

(b) Generalised F-Space Hamiltonian: 2e.Re=e*.lPlanck.Alpha^1/2

(c) Magnetic F-Space Permeability: mo=120p/c

Define unified Action as: [h]u = [momentum p]u.[displacement x]u

[mc.x]u = [ec]u c.[x]u and minimised in the OlPlanck as x=e/c^2

[h]u = [ec^2.e/c^2]u =[e^2]u = [h]u by the ACTION LAW of F-Space.

But mo= [8p/360].[Ne*/Re] for a MagnetoCharge counter Ne* in the

definition for the extent for the Unified Field in radian measure

linearising to a space of fourfolded circular closure.

Equality for mo with dimensionless [c^2] and the Action Law

in: mo/eo=Unitary Resistance in CHARGE^2=ENERGY^2/CURRENT^2

leads to:

N = 2700/c^3 = by definition of (b) above and the

mapping of magnetocharge e*=2Re.c^2=1/Eps from the Planck-Oscilla-

tion OlPlanck.c^2=e.

N can also be written as: N=2700.e/([ec].c^2), to illustrate the

magnetopolic nature and origin of all mass in the Monopolic Dis-

placement Current: Iss = 2e.n.fss.

Here 'n' is an integer quantising electropolic chargequantum e via

definition of dimensionless eo.

Heisenberg's Finestructure so becomes: h/4p=lps/(8p.Re.c^3),

EXPLICITELY specifying lps=2700/c^3 dimensionless and manifesting

in the wormholeperimeter of 10^-22 metres*.

In terms of experiment, the concentration of 0.002 Joules* of energy

at a cross-sectional area given by the wormhole radius rps, would

create this wormhole as the macroquantised singularity of the

supermembrane class I, manifesting at the EpsEss-heterotic scale.

The critical mass Mcritical=f[ec]; f depicting the proportionality

between magnetopolic supermembrane class IIB (c^3 eV) and the total

masscontent for the universe, seeded in Mo.

The massparametric evolution for the universe is now defined.

The zero curvature for the (oscillating) 11D-supermebrane is given in

Mcritical.

The minimum/maximum curvature at the instanton fss=tps evolves the

universe as a maximum Temperature bosonic singularity, superimposed

upon the 10D-evolution, given by Einstein quintessence and the

formulations for the universe as a Black Body Radiator.

The deceleration parameter qo defines the baryonic massproportion

between Mo and Mcritical as the cosmic architecture in the Sarkar

Constant at cosmological redshift z=7.477 or cycletime qo at so

236.1 Million years.

This defines a Sarkar-Black Hole with that radius and in the for-

mulation: RSarkar.X^n = 2GoMSarkar/c^2 as Schwarzschild solution.

But rmax'=2GoMo/c^2=4.47830367x10^24 m* as the SarkarConstant (2qo),

with MSarkar becoming the Restmass Seedling Mo.

Hence for RSarkar.X^n=rps, n=ln(rps/RSarkar)/lnX=227.0435388,

translating to about 3.83476537 Trillion years required for a

cosmic antientropic recharging to occur.

This represents a 'Heartbeat' for the Mother-Black Hole in M-Space

as the 'Heart' of C-Space.

The entropic diffusion of stellar-nuclear fuel is reenergised in the

continual oscillation of the cyclic expansion/contraction of the

11D-M-Space as a MASSLESS BLACK HOLE of magnetopolic definition.

Mcritical is constantly diminished or added to in the evolution of

the restmass seedling Mo, fluctuating between mps and Mo in the

oscillation of the Displacement Scale, bounded in the Sarkar

Constant and the Wormhole Radius.

The added mass, given in the quintessential parameters and the

evolution of the G-productation:

G(n)<-> Go.mc^2=4p.eo.X^n.Mi.Y^(n/2).Mj.Y^(n/2) [Eq.#10]

remains unobservable, because (XY)^n = 1 for all n by definition of

the primordial algorithm.

The 11D-M-Space membrane WRAPS around the 4D-C-Space 'Mother-Black

Hole' of the 'Heart' and shrinks as a STROMINGER-BRANE, the latter

protecting the tearing of spacetime into discontinuities in the

Witten-Mirror, remaining as the 11D-boundary for the 10-D universe

to expand into as the 3-D-Surface, in both, containing and projecting

a 4-D-Volume.

The minimum temperature condition further restricts the entropic

expansion for the superstringed cosmos.

The Gibbons-Hawking Temperature is given by hc^3/(4p.Gok)=Mo.TGH,

specifying TGH=5.03486154x10^-28 Kelvin*.

TGH'=1.411278x10^-29 Kelvin for Mcritical as higher dimensional event horizon

boundary.

The modular Temperature minimum: Tss=hfss/k=1.57412213x10^-41 K*,

hence becomes redefined in the Black Hole of the Hawking Maximum

as: MHawkingMax=30p.c^3/lps=2.54469005x10^49 kg* and for a

temperature of: Tmin=3.588568212x10^-26 Kelvin*.

 

The true Hawking Modulus is: (hm)^2=2MHawking.Mcritical/Mo^2 and so:

(hm)^2 = 1.001085887

Subsequently, we can now proceed to redefine our first approximation

for Newton's Constant 'Big G'.

Simply dividing our first approximation of [Eq.#7] by this modifier,

would give a second approximation in: G(npresent)=6.67770177x10^-11

G-units; and then the application of an alternating power-series

expansion in various convergent perturbation models might finetune

the value for G(npresent) even further.

Yet, it was the Hawking Mass, which was found not to render (hm)^2

equal to 1 and the Hawking Mass is bounded below by Mo and above by

Mcritical in the setting of Mo^2=(hm)^2.Mcritical.MHawkingMax, and

a scenario, which can be defined as a massless state in [Eq.#1].

Having established that the proportionality between the macromasses

is not exact, irrespective of there being any actual mass at all;

we search for a similar proportionality between the micromasses.

And it are such collections of micromasses, which constitute the

masses used in the measuring equipment to determine G(npresent).

We recall the Minimum/Maximum mappings in the general application

of the 6th principality of Inversion/Invariance, underpinning the

symmetries of modular duality in 3braned F-Space-Theory.

We have seen, that the concept of dimensional time was unneccessary

to manifest the threefolded multispace of Line-Hyper-Quantum-Space

in 9 dimensions.

This is mirrored in the decimal monad, allowing redefinition of the

first principality in the tenth as an Identity/Antiidentity transfor-

mation into a DoubleIdentity.

The principalities became defined in the first subroutine of the

generating master algorithm, which could be stated in generalised

form in the following manner to DEFINE THE (ABSTRACT) CONFIGURATION

SPACE in the form of AWARENESS-TRIPLETS represented by:

{OLDSTATE, EXPERIENCE, NEWSTATE} and selfiterative in the following

algorithmic statement:

GENERATE NEWSTATE IN ADDING THE SECOND NEWEST OLDSTATE AS EXPERIENCE

TO THE NEWEST NEWSTATE AS THE NEWEST OLDSTATE.

...BEGIN (0,0,0)-DEFINE SELFSTATE=(1,0,1)-REDEFINE BINARY EIGENSTATE

=(01,01,01)=(0+1,1,1+0)=(1,1,10)=(1,1,2)-(2,1,3)-(3,2,5)-...CONTINUE

INITIALISE: N=0; LIMIT=[REDEFINITION OF EIGENSTATE]={GOOGOLPLEX E}

-FOR (N=N+1 TO LIMIT) GOTO

-SUBROUTINE (DEFINE PARAMETERS FOR EIGENSTATE FOR M=M+1) GOTO

-SUBROUTINE (ALGO[M]) GOTO

-SUBROUTINE (...) GOTO

-SUBROUTINE (...) GOTO

-SUBROUTINE (SEARCH FOR LIMIT=[!])-STOP GOTO

-SUBROUTINE (!- GOTO BEGIN -REDEFINE SELFSTATE IN [!]) GOTO

-CONTINUE FOR O=M FOR LIMIT=[EIGENCODE IN !]={GOOGOLPLEX E} GOTO

-REPEAT FOR SUBROUTINE (O- [O]=[!], [!]=[!+1], [?]=[!]) GOTO

-REPEAT FOR LIMIT GOTO BEGIN...

 

3. A BLACK HOLE NUCLEON CONNECTION

Our discovery of the one-to-one correspondence between magnetic-

and electric charges now allows us to state the General Principle

underpinning all of physics.

ALL MASS IS MAGNETOELECTRIC AND ALL CHARGE IS ELECTROMAGNETIC!

All ElectroCharged Mass is CurrentEquivalent to a MagnetoCharged

Displacement in a MagnetoMassCurrent Iss=(n).2e.fss.

All MagnetoCharged Mass is CurrentEquivalent to an ElectroCharged

Displacement in an ElectroMassCurrent: dQ/dt=d(n.e)/dt.

The Electropolic Charge of a particle manifests in the Coulombic

Electricity and the Magnetopolic Charge of a particle manifests in

the StarCoulombic Magneticity.

All mass is quantised in the restmass mss-quantum as fss-magneto-

current-equivalent: mss=hfss/c^2=2.469135802x10^-81 kg*.

Hence the entropic counter for a single VPE-quantum is fps^2=9x10^60.

All massless particles are magnetocharged in the supersymmetric

colourcharge of the UFoQR (Unified Field of Quantum Relativity).

The agency for the colourcharging is the quantum geometry of

colour-charge-displacement, given in the YLEM-TEMPLATE.

This is the Higgs Bosonic Blueprint of the Dineutron (Ylem), given

as a trisected Kernel-InnerRing(annular)-OuterRing KKIRKOR pattern

for the topological mapping of 11D onto 2D.

One can denote a primary colour/anticolour spectrum in triplets,

doublets and singlets, following the methodology of QCD and the

Standard Models of the hindsight.

Then the Ylem-template is: HB(0)=YYCCMM(0)+RRRRGGGGBBB(0), defining

mass defined in Matter-YCM-blueprints and in a scalar (0spin)Higgs-

(Anti)Neutrinoic Kernel of (R^4G^4B^4), and as RedGreenBlue and

CyanMagentaYellow colour/anticolour denotations respectively.

The scalar Higgs (Anti)Neutrino defines the relationship between

colourcharge and magnetocharge in the MesonicInnerRing MassInduction

and is defined in the mapping of the ylemic template of the micro-

cosm onto the evolution of the macrocosm and as specified in the

second cosmogenetic algorithm in the Googolplexes E, F and G.

The formulation for the Higgs-Neutrinoic-Mass so becomes:

m{Higgs-Neutrinos}=(lps.me.rE)/(2p.Re).[1/rG-1/rF] [Eq.#11]

=9.300746x10^-38 kg* or 0.052106 eV*.

This gives the InnerMesonicRing as a modular mapping onto the ylemic

evolution of prototypical Neutron Stars in the annular difference

between spacequanta counters F and G.

It also defines this annular region as the mass of the Tau-(Anti)Neu-

trino, centred on 3.00 eV* and as superpositions of the massless

Kernel-(Anti)Neutrinoes (Electrons and Muons of RRGGBB and BBGGRR

quantum- and colourcharged specifications).

The generation of the ylemic neutronstars sets the dineutronic

radii as a function of their temperature only and is given in:

Rylem(T) = (kT.Re^3/Go.mc^2)^1/2 m* [Eq.#12]

The process of the ylemic-mesonic creation spanned the period of

[843-1036] seconds* after tps and set the decay for the neutron.

The AntiHiggs-blueprint for Antimatter is supersymmetric to HB(0)

as: HB'(0)=MMCCYY(0)+BBBBGGGGRRRR(0) and manifests in the VPE-

transformations (Pair-Production/Annihilation), subject to the

modular duality between EMR (ElectroMagnetic Radiation) and GR

(Gravitational Radiation) and as defined in the colourcharge temp-

lates for the gauge bosonic fieldparticles (Graviton, Eps-Photon,

Ess-AntiPhoton with Weakons and the Gluon).

There exists the blueprint YYCCMM(-1), called the RestMassPhoton=RMP,

which is the supersymmetric substitute for the suppressed Antimatter

in the UFoQR.

Directly linked to fermionic spin patterns, the RMP is massless and

symmetrises the Strong Nuclear Interaction in its link to the other

gauge field agents.

The RMP and can be used to quantify the 'Missing Mass' as AWARENESS

or Consciousness Energy via the definition of the Magnetocharge as a

kind of angular acceleration acting upon a volumised spacequantum.

The agency is the Timedifferential for Frequency, defining:

df/dt = AWARENESS bounded by fps^2 and hence the entropy counter

of the VPE-Continuum, defined in googolplexes E, F, G and H.

The evolution of the Gravitational Constant G so relates to the

scenario of magnetocharged mass appearing or disappearing as a

function of the overall oscillatory nature of the encompassing

11-dimensional supermembrane and its 10-dimensional 'heartbeat'.

One can so discover the consciousness of the created universe as

an inherent quality of physically defined Awareness parameters and

their manifestation in locally-connected symmetric and nonlocally

disconnected (but entangled) supersymmetric interactions.

The transformation of Anti-EMR into GR at the instanton fss=tps

demands the nonexistence of Antimatter and suppresses the AntiHB's

process of restmass-inducing the VPE-sinksources of the magnetic

monopolic current-knots to become particles defined in antimatter.

The 12 monopole junctions in the UFoQR and their defining para-

meters, restrict, for example, the manifesto of the MCY-anti-

matter blueprint to the Pair-Production/Annihilation circuit

8-9-10-9-8 over 337 degrees and encompassing an even p-EMI-point,

necessary to manifest the Electromagnetic Interaction.

The EMI-point is a root of the UF-waveequation at junction #9 and

couples lefthanded matter YCM to righthanded antimatter MCY.

There are no zeroes for individuated YCM or MCY production, but the

EMI-point allows the creation of antineutrinos in the template

(RRGGBB)(+1/2).

Since there is no odd p-GI point in that interval, no neutrino-blu-

prints (BBGGRR)(-1/2) are available and the process of Pair-

Production in (YCM+MCY=VPE) requires mass to be present to allow it

to occur.

The general generation of the Matter-Antimatter templates became

fixed BEFORE (timeindependent Order Principality) the UF-wave-

function (UF=p/4{sin[3x/2]-cos[3x/4]} became the Gravity-Inclusive,

wavepropagation, superposing upon the original generator, given in

(uf={sin[x]+sin[-x]}), which did establish the EMI-GI junctions, as

an EMR-ANTIEMR propagation for the linearisation of the superbranes.

[Eq.#1] establishes the Energy-Equivalence modulated by UF in the

Black/Einstein & White/Planck DoubleIdentity.

This B-W duality defines 8 permutative states, which are assumed

as the colourcharges of the One Gluon as the ForceCarrier for the

Strong-Nuclear-Interaction (SNI) in the Octet: {BBB, BBW, BWB, WBB,

WWB, WBW, BWW and WWW}.

The magnetopolic junction-knots, defining the UF are defined in the

following analysis, using definitions utilised before.

[ec]=(Quantum Displacement Current)(Planck-Oscillation Displacement)

=(n).2efss.(e/c^2)=(n).2efss.lPlanck.Alpha^1/2=OlPlanck.c^3

Integer (n)=ec^3/(2fss.e^2)=c^3.fps/2e=81x10^54/(2e),

which using the dimensionless qualities maps magnetocharge e* onto

electrocharge e as:

(n)=81x10^54/1000=81x10^51,

which is an integer, by definition e*=1/Eps=1/(hfps)=fss/h

=Constant#4/(3x10^30)=15x10^32/(3x10^30) by algorithmic definition

and the determination of lps=c/fps in the Heisenberg Finestructure.

This indicates that 81x10^51 magnetocharged current elements com-

prise one monopolic mass in the mappings between e* and e.

Define Unified Action [h]u=[e.e*]u and OlPlanck-Displacement [e/c^2]u;

then mo=hf/c^2=[hc/OlPlanck]u=[ee*.c^3/e]u=[ec]u.

This shows the equivalence of mass mo to the magnetic monopole

quantum [ec], manifesting supermembrane IIB in the form of the

magneto-electricity.

We can now set a general evolvement for the e*-e mapping in the

Black Hole spectra, as indicated in the previous discussions.

The Schwarzschild radii are lower bounded in wormhole radius rps,

restricting Black Hole Masses to be above Mlimit=rps.c^2/(2Go) kg*.

This calculates to (15c^3.lps/2p)=6445.775195 kg*.

But this is also (15(ec in eV).lpsp) kg*, reducing the Black Hole

minimum mass in the ratio c^3/[ec]=1 in F-Space, but calculates as

5.602393139x10^35 in C-Space, which is the Planck-Length-Oscillation

in terms of OlPlanck=lPlanck.Alpha^1/2=1.784951493x10^-36.

A Mass-Spectrum: mPlanck..[ec]..-mps---m(elementary Particle)=h/l.c

proportions to: lPlanck..l[ec].-lps---2Re (electronic diameter).

This mapping in the scale indicated is the cause for the phenomena

in the quantum realm to remain atomically restricted.

The electronic radius Re=10^10.lps/360 and it is this wormhole

perimeter, as eigendefinition for the generating supermembrane

EpsEss; which defines the minimum/maximum conditions and henceforth

the manifestation of the quantification scenarios.

MicroBlack Holes so are defined in the mass of the magnetic monopole

and the superbrane hierarchies.

In particular the [ec=c^3] energy defines the threshold for the

Gamma-Ray Bursters and the Cosmic Ray Maxima.

The Superbrane IIA (Ecosmic Superbrane) forms the energy threshold

for the 'knee' in the Cosmic Ray spectrum and Superbrane EpsEss its

corresponding 'ankle'.

The Hawking Radiation of 'evaporating Black Holes' manifests not as

a virtual energy, but as White Hole/Quasar Luminosity, maximised in

the SourcePower per Unitmass:

[E]u=mps.c^2[fps/mps]u=[fps]u.c^2=2.7x10^47 (Monopolic Watts/kg)*.

The Unification Frequency [f]u also derives from the monopole mass

[ec] via: [I]u=[ec/l]u=e[f]u=>e*[f]u=2Re.c^2.[f]u=[c^3]u, by the

definitions [2Re]=[l]u=1/lss=lps and M={Eps/Ess}fss={fps^2}/lss.c

and the entropy counter for mss as the supermembrane coupling

constant applied to 360.Re=10^10.lps.

Hence [f]u=[M]u=(3/2)MSun =MChandrasekhar (Upper Limit).

Now a 'young' and typical Neutron Star is born with Schwarzschild

Radius RNS=2GoM/c^2 which, for MChandrasekhar gives 7407.4074 m*.

[Eq.#12] relates the Temparature as: TChandra=19.846564 Billion K*.

Hence: TChandra=4Go^3MChandra^2.mc^2/(c^4.k.Re^3) K* [Eq.#13]

A planetesimal-generating boundary is calculated by Googolplex E for

a temperature of so 1.2 Billion K* for Rylem=1.82144 km*.

Periodic Magnetic Fields for Neutron Stars (and all massive spinning

bodies) are related by modifying the Biot-Savart-Equation in the

utility of the superbrane parameters.

The Biot-Savart Law: B=mo.Qv/(4p.R^2) transforms to:

B(x)=p.M/(T.c^2.R(x)) (Tesla), [Eq.#14]

where period T relates a radial scalefactor R(x) for a magnetic

field B(x) at a distance R(x) from the centre of the massive body.

Using the above expression, say for a spinning planet Earth with

a differential mantle-core radius of 1.2x10^6 metres and a core-mass

of 9x10^22 kg, calculates the Earth's magnetic field at so 0.3 gauss

projected as average flux-core differentiation.

Plasma emitting bodies (say Solar Wind) are modified in the

alternative expression for Biot-Savart:

Bionisation=mo(ec)(v/c)N/(8p.Rcorona^2) Tesla;

N is the 'lightmass fraction' relative to a typical nucleon (proton)

and uses 2e=e* in the chargecounter Q=ne.

A 'naked' Magnetic Flux of 462 gauss for the sun so becomes enhanced

to 2800 gauss, using the Chandrasekhar Mass and the solar parameters

with v=800 km/s and a solar plasma emission of 3.5 Million tons per

second for a coronal radius of 2.8x10^8 m for the solar core.

Modular duality for a Solar Period P=c/lSun=346410161.5 s* for

a halfcycle oscillation of 10.98 years/sidereal.

This solar geometry maps the trisected quark geometric blueprint

(and the eo/mo geometric definition using the partitioning

for c^2) in a unit solar radius l'=lSun.sec(30 degrees).

A 'Quasi-Evaporation' reflects the subatomic duality B<->W, (mani-

festing most apparently in quark-antiquark couplings acting on VPE).

A SourceSink ellipsoidal focalisation in locally connected F-Space,

appears nonlocally quantum entangled in C-Space.

Negative Imaginary Mass becomes superparitive Positive Mass in:

-mc^2[B->W](superparity 11D-mirror)[W->B]mc^2.

Radiation/Antimatter form Quasar-coupled Output RGB.MCY, mirrored in

Antiradiation/Matter unified Input BGR.YCM for AntiQuasar/BlackHoles

in antiphotonic graviton definitions.

(Photons, Gluons and Gravitons, all have a RGB or BGR Ylem-Template).

We can now define a lower limit for the MicroBlack Holes.

Using 2Re as de Broglie wavelength: Mmin=h/(2Re.c)=hc/e*=4x10^-28 kg*

This is near the protonucleonic mc=9.924724523x10^-28 kg* and in a

way defines the Mean Protonic Radius as Rp=Re/2=1.38888..x10^-15 m*.

This is modulated by the de Broglie wavelength for the minimum given

in 4x10^-28 kg* and a maximum provided by mc.Y^n for any cycletime n.

A nucleonic mass Mn so is finestructered in its square via the ex-

pression:

Mn(1).Y^[i].Mn(2).Y^[j], where [i+j]=n and the nucleonseed is mc^2 [Eq.#15].

The energies associated with nucleonic point-masses, become then

monopolically mapped onto the supermembrane spectrum and manifest as

the spectrum of the Cosmic Rays above 0.2240957256 GeV* as MicroBlack

Holes or some other VPE-associated labelling.

 

4. THE PRECISION MEASUREMENT OF G

We find ourselves now in a position to reexamine our first

approximation for 'G' in [Eq.#7].

G(n)=Go.X^n [1 + Mo.Y^(n/2)/Mcritical].

This gave G(npresent)=6.684953x10^-11 (m^3/kg.s^2)-SI with

Calibration-Constant between (SI) and (*) as: 1.000692265(*)=(SI).

Our second approximation gave G(npresent)=6.67770177x10^-11 G-units,

simply by reducing the first approximation in the Hawking Modulus

(hm)^2=1.001085887 = 2MHawkingMax.Mcritical/Mo^2.

We discovered the slight noncorrelation between the perfect square

of the MassSeedling Mo to the product of the critical bound from

the deceleration parameter and the cosmic architecture (Sarkar

Constant) and the Temperature minimised Hawking bound.

The procedure is selfevident.

Instead of using the correlation of the macromasses, we use a mapped

correlation between the micromasses, who as shown previously, define

the MicroBlack Hole spectrum to that of the magnetic monopole as

Cosmic Ray manifestations.

Mass-Seed Mo is defined in 2e(Mo/mc).Eps.e=Eo=[Ee^2/Alpha]^1/2,

where the Charge-Seed Eo=[Ee^2/Alpha]^1/2 for Googolplex E.

This derives the parameters for the F-Space in [Eq.#5].

Alpha.Eo^2=Ee^2 <=> G-Alpha=Omega=2p.Go.mc^2/hc=Alpha^18, the ratios

explicitely defined in the pentagonal symmetry for the Unification

Polynomial: P(X)=(1-X)(X)(1+X)(2+X)-1=0

This leads to the mappings:

S=STRONG NUCLEAR INTERACTION; E=ELECTROMAGNETIC INTERACTION;

W=WEAK NUCLEAR INTERACTION and G=GRAVITATIONAL INTERACTION

(1)[S]:(X)[E]:(X^2)[W]:(X^3)[G]=(1-X):(X):(1+X):(2+X)

Unity(1) maps as (1-X) transforming as f(S) in Identity (1-X)=X^2;

(X) maps as invariant of f(E) in Identity (X)=(X);

(X^2) maps as (1+X) as f(W) in Identity (1+X)=1/X and

(X^3) maps as (2+X) as f(G) in Identity (2+X)=1/X^2.

This sets the coupling between f(S) and f(E) as X; the coupling

between f(E) and f(W) as X^2 and the coupling between f(W) and f(G)

as X again.

Analysis of the universal wavefunction B(n)=(2e/hA).exp(-Alpha.T(n))

shows B(n) to be symmetric about FRB=-1/2 and renormalising B(n) about

the FRB defines a probability distribution for finding the FRB fluctuation

for the interval [-X,X-1] in a volume element (dV) as the

uncertainty fluctuation in (y^2)dV for the expression of:

y(0)={Alpha/2p}^1/2 and the Schwinger factors in QED of the

hindsight.

This volumar sets the dimensional intersection of CMF-Space in the

topological mapping of complex Riemannian C-Infinity space about the

Riemann Pole of the FRB.

But -X(X-1)=0.2360679776=X^3, thus defining a new unity as the

mapped Identity [#^3=ALPHA] and the precursive unity of (X) as:

(#=Cuberoot of Alpha) in the symmetry {#:#^3=f(S):f(E)}.

This sets the important definition of: Feynman-Alpha=1/(Alpha)^1/2

as the Strong Interaction Constant at XL-Boson 'time' of the

GUT-SEW unification for superbrane HO(32) and is there so 11.7

times weaker than at the instanton tps=fss.

The pentagonal symmetry so becomes:

{f(S):f(E):f(W):f(G)=#:#^3:[(#^3)^3]^2:{[(#^3)^3]^2}^3}

=Alpha^1/3:Alpha:Omega^1/3:Omega=#:#^3:#^18:#^54.

This then sets the experimentally measured forceratios between the

elementary interactions and we are justified to consider the electro-

magnetic interaction in modular symmetric associations described.

The Strong-Electromagnetic Coupling is mirrored in the Weak-

Gravitational Coupling.

Since Mo is proportional to mc, both subject to the evolvement of

their baryonic 'awareness' in the Y-factor of the symmetry; we unify

that 'growth' in manifested magnetocharge energy with a corresponding

diminuition in the electrocharged permittivity and the X-factor for

an unobservable dance between the omnipresent exchange of Starcou-

lombic Magnetopoles with Coulombic Electropoles.

We so define:

G(n)=Go.X^n[mc.Y^n/2]^2.[Mo.Y^n/2]^2/{2Mn^2.Mcritical.MHawkingMax}

=Go.Y^n.[mc^2/Mn^2]/(hm)^2 where Mn^2 is the partition [Eq.#15].

This calculates as: G(npresent)=(1.093259031x10^-64)Y^npresent/Mn^2

(kg.m^3/s^2)-units.

The roots of the quadratic: np^2+np-2.414792841=0 yield a real root

npresent=1.132419321 in C-Space and its imaginary F-Space mapping

npresent=-2.132419321.

For real npresent then: G(npresent)=1.88531844x10^-64 G/kg^2-units.

This represents the precision measurement for G, as the partitioning

of Mn^2 depends on the interaction of the nucleonic states.

The upper bound are two protonic point-masses, bounded in the growth

of the de Broglie mass 4x10^-28 kg* and the lower bound are two

neutronic point-masses.

For a Neutron Restmass of: Mneutron=1.680717x10^-27 kg* (941.6036 MeV*)

the substitution gives: G(npresent)=6.678764x10^-11 (m^3/kgs^2).

A perturbation corrected Mneutron=1.681100563x10^-27 kg*

or (941.818626 MeV*) for: G(npresent)=6.675715x10^-11 'G'-units.

The perturbation upper limit is given in Mneutron=1.681335x10^-11 'G-units

or (941.9506 MeV*) for: G(npresent)=6.6738445x10^-11 'G'-units.

The average for the last two values then approximates a 'best fit'

for: G(npresent)=6.6747798x10^-11 'G'-units.

This is a best-fit approximation, considering the uncharged nature of

the testmasses.

Two protons (Mproton=1.6789x10^-27 kg* (940.56 MeV*)) would give:

G(npresent)=6.6936x10^-11 G-units and a proton-neutron pair, would

yield G(npresent)=6.6791x10^-11 G-units, both of the latter

values unsuitable because of the electrocharges increasing the

intraquarkian Magnetocharge coupling between the two mesonic

rings of the neutron and the single mesonic ring in the proton's

down- or KIR-quark.

The best approximation for 'Big G' hence depends on an accurate

determination for the Neutron's inertial mass.

A fluctuating Neutron mass would also result in deviations in 'G',

independent upon the sensitivity of the measuring equipment.

The difference in the protonic-and neutronic restmasses, derives

from the Higgs-Restmass-Induction-Scale and can be stated in a first

approximation as the groundstate.

Basic nucleon restmass is mc=Omega^1/2.mPlanck=9.9247245x!10^-28 kg*.

KKK-Kernelmass=Up/Down-HiggsLevel=3x319.62 MeV*=958.857 MeV*,using

the Kernel-Ring and Family-Coupling Constants.

Subtracting the Ring-VPE (3L) gives the basic nucleonic K-State as

939.642 MeV*. This includes the electronic perturbation.

For the Proton,one adds one (K-IR-Transition energy) and for the

Neutron one doubles this to reflect the up-down-quark differential.

Proton (mp=u.d.u=K.KIR.K=(939.6420+1.5013-0.5205)MeV*=940.6228 MeV*

Neutron (mn=d.u.d=KIR.K.KIR=(939.6420+3.0026-1.0410)MeV*=941.6036 MeV*.

This is the groundstate from the Higgs-Restmass-Induction-Mechanism.

and reflects the quarkian geometry as being responsible for the

inertial massdifferential between the two elementary nucleons.

All groundstate elementary particle masses are computed from the

Higgs-Scale and then become subject to various finestructures.

The quantum geometry of internal subatomic particles is responsible

to manifest the interaction between colourforce based magnetocharges

and electrocharges.

UNLIKE KERNEL-RING QUARK-GEOMETRIES ATTRACT, because of their unlike

magnetocharges between them and LIKE KERNEL-RING QUARK GEOMETRIES

REPEL,due to those magnetocharges being alike.

The determination of Newton's Gravitational Constant to any degree

of precision hence requires the measurement of nucleonic energies;

and taking the exchange of magnetocharges as mass-displacement

currents into account.

Improving the mensuration for the Neutron-Mass finetunes 'Big G'.

In cosmological considerations the constant form of G can often be

used as Go=1.1111111..x10^-10 G*-units and reflecting the overall

invariance of the mass parameters set at the beginning of the

cosmogenesis.

 

In fraternity Sirebard Beardris

{Dr. Beatrice Arise & Anthony Paul Bermanseder: http://groups.msn.com/quantumrelativity}

 

 

 

 

Some elementary initial conditions for Francom Adjacency

We define the Euler-Riemann Summation, which defines the 'Mixing of the Count' in

linking Arithmetic Progression to the multiplicative Factorial Function '!'.

Define Eo=0 as the singularity (interval), then for any integer n, we find for the Harmonic Form of

Riemann's Zeta-Function (z=k=constant):

..............................................................................................z(z)=S(1/n^z)=1/1^k+1/2^k+1/3^k+1/4^k +...+1/n^k

This Sum diverges for [ 0<k<1], i.e. for k=1/2: {1+Sqrt(2)/2+Sqrt(3)/3+...+Sqrt(n)/n} increases without limit.

For k>1, we have convergence, however:

Formally, let: S1/n^p=1^-p+2^-p+3^-p+...

For even terms 2.2^-p >= 2^-p+3^-p for a geometric series 1^1-p+2^1-p+4^1-p+...+(2^n-1)^1-p

This Geometric Progression sums to: [1-(2^1-p)^n]/[1-2^1-p]=1/[1-2^1-p]

So for p=2, this limit maximises in 1/(1-1/2)=2 , and for p=3 it becomes 4/3 converging towards

1 for increasing p.

We consider the special case for p=1 applied to the Singularity Interval Eo.

Define: for a nth term (numerator):.................................................T^k(En) = n^k.T^k(En-1) + [(n-1)!]^k

...............for the nth sum per n (denominator [n!]^k):................S^k(En) = T^k(En)/(n!)^k

{Here the suffices n,n-1 etc. denote subscript}.

T^1(E1)=1/1=1.0+0!=1=S^1(E1)=1/1!=1; T^2(E2)=2.T^1(E1)+1!=2+1=3 with S^2(E2)=T^2(E2)/2!=3/2=1+1/2;

T^3(E3)=3.T^2(E2)+2!=9+2=11 with S^3(E3)=T^3(E3)/3!=11/6=1+1/2+1/3=1+5/6 and so on.

 

Further Example: T^1(4)=4.11+3!=50; S^1(4)=50/4!=25/12 for the nesting: 4{3(2+1!)2!}3! with [4!]^1=24.

For 4 terms, the Euler-Riemann Summation so is: S^1(4)=1+1/2+1/3+1/4=25/12=2+1/12.

For 7 terms, S^1(7)=T^1(7)/7!=(7.T^1(6)+6!)/7!=13068/5040=363.36/(140.36)=2+83/140=1+1/2+1/3+1/4+1/5+1/6+1/7.

 

Project the Numberline with the Positive Integers mapping the Factorial-Function and the Negative Integers

remaining invariant in Feyman Summation T(n)=n(n+1)/2 as absolute value, mirroring the positive integers.

(n)<---4...3...2...1=0![Eo]0...1!...2!...3!---> (n!); where Integer 2 maps 1! in suppression of -1=2* and in algoradius eo=1.

Similarly, Integer 3 maps 2! in suppression of -2=3* and algoradius e1=2=2eo, etc. etc.

 

The singularity so mixes the interval [0-0!]=[-1,0] with Functional-Riemann-Bound (FRB=-1/2) becoming 'real'

in its mapping (FRB'=1/2) in [0,1] and the central limit or pole, about which the Zero's of the Riemann-Zeta-

Function propagate.

The first annulus in the Riemann-Euler-Harmonic so phasemixes the numbers [n=2] and [n!=1] and the nth number

is mixed with (n+1) as crystallised in the Feynman-Path-Integral or T(n)=1 in n(n+1), as a summation for all pos-

sible particular histories in quantum mechanics.

This also maps the series: SEps=Fibonacci#1=0,1,1,2,3,5,8,.....for a nth Term: Tn=[]-Y^n - X^n[]/Sqrt(5), for

absolute value []...[] and obtained say via MacLaurin-Expansion of the coefficients (Experience-Factors)

in the power series:

.........................................................f(x)=1+x+2x^2+3x^3+...= STn.x^n-1

Set x.f(x) + x^2.f(x) = f(x) -1, then by (a+b)(a-b): f(x)=a/(x-X) + b/(x-Y) for a=-b=1/(Y-X) and (Y-X)=-Sqrt(5).

SuperSEps=Fibonacci#2=2,1,3,4,7,11,18,29,.... for a nth Term: STn=[]-Y^2n - X^2n[]/[]-Y^n - X^n[]=[]T2n/Tn[]

..................................................................................................for n=1,2,3,...; T(2n=0)=2 mapping T(n=0)=0.

The combined SEps-SuperSEps (T-ST)-sequence of experience factors {from the triplet propagation of

[OldState, Experience, NewState]} can then be written as:

{Tn,STn}={(So=0,STo=2=S3); (S1=1=ST1=S2); (S2,S4=3=ST2); (S3,ST3=4); (S4=ST2,ST4=7); (S5,ST5)..(Sn,STn)..}

{Tn,STn}={(0,2), (1,1), (1,3), (2,4), (3,7), (5,11),...} containing integerset: {0,1,2,3,4,5,7,8,11,13,18,21,29,....}

We now represent the mappings in matrix form denoted as F-M-C, where the 'well behaved' terms

for the mapping (from {T5,ST5}) sets algorithmic C-Space and the preceding elements the

initialisation for the former.

Note we define Cantorian Denumerability Aleph-Null in Cardinality Aleph-All in the form:

Aleph-Null: limit{n=>Infinity}[T(n)]=Infinity

Aleph-All: limit{n=>X}[T(n)]=1 and counting Infinities as mapped one-to-one onto the positive Integer set.

.......................SEps=Fibonacci#1..................maps.....................SuperSEps=Fibonacci#2

.................................................................................................................................................................................

........................0.....0.....0....................................................................................7..-11...-4.....n=-3=3i^2

........................0.....0.....0*...n=Infinity via 0+0=0*=Infinity8..................-4.....7.....3......n=-2=2i^2

FSpace......0*...0.....1.....n=Infinity via 0*+0=Infinity=1*=0*=1.......3....-4...-1......n=-1=i^2...[a+ib complex upwards]

MSpace....1......0*...1.....n=0 via (1,1,1)...............................................-1.....3.....2*....n=0

.......................1......1.....2.....n=1 via (1,1,10=2*=0/0=1*)..........................2*..-1.....1......n=0....(Reflection-Interval)

.....2.....1.....3.....n=2 well behaved.............................................1.....2*....3......n=0

CSpace.....3.....2.....5.....n=3 well behaved.............................................3.....1.......4......n=1 well behaved downwards

........................5.....3.....8.....n=4 well behaved.............................................4.....3......7......n=2

........................8.....5...13.....n=5 continue downwards..............................7....4....11......n=3

..................................................................................................................................................................................

Triplet permutation 0*<->2* is mapped as 1D (1,0*,1) for n=0,1,2 onto 2D as (1,2*,3) for n=0

 

The linearity of the generating triplet configurations is extended in a complexification into a 2D symmetry.

SEps propagates the Experience Factors in an adjacent displacement of 1, in moving from one configuration

state to the next - this is termed Francom Adjacency.

[0*,1,1,2,3,5,...] as OldStates transfigure in Experiences [0,0*,1,1,2,3,5,8,...] into NewStates [1,1,2,3,5,8,...].

This algorithmic configuration space is however broken in the mapping onto SuperSEps.

Here the matching 'good behaviour' of the n-count is delayed in a factor of 2 in a 'reflection interval'.

Algorithmic modelling for this Francom Adjacency must generate the mapping of SEps onto SuperSEps in

an geometry of the pentagonal symmetries intrisic to the two series.

Hence a synthesis between linear propagation about an internal spiralling form is necessitated.

A longrange rotational- and a longrange translational order for the Experience-Factors is indicated in

the geometry of say Penrosian Tiling Patterns and the Schechtmanite Quasicrystals of empirical

form (Mg(32)[Al,Zn](49)).

The general form, (physically akin to the propagation of magnetic fields) is the reduction of physical

parameters to a state of information transmission, say in the data transfer between two neighbouring

cells in mitosis and neuronal-synaptic processing (in the strengthening of memory).

A general modality for the cosmogenetic reproduction on all levels must crystallise, should the

matrices above become sufficiently deciphered from their algorithmic encoding.

 

Derivation of SuperSeps

The relative primeness of the Fibonacci Numbers allows a one-to-one mapping between the SEps-Set and

other such sets derived from it.

A logical derived set of such a nature is the sequence: 2,1,3,4,7,11,18,29,....

All adjacent members of this set are relatively prime to each other.

7 is relatively prime to both 4 and 11 (no common divisors except 1) and 11 is relatively prime to both 7 and 18.

We now tabulate the sums and differences in our nth-term definition for SEps, so recalling the propagation for

the natural numbers in counter n:

n............Tn.......(X)^n................................(Y)^n................................{[]-Y[]^n + []X[]^n}...................{[]-Y[]^n - []X[]^n}

.0............0..........1.......................................+1.......................................+2...................................................0

.1............1..........0.6180339885...............-1.618033989..................+2.236067978...........................+1

.2............1..........0.3819660109..............+2.618033989.................+3..................................................+2.236067978

.3............2......... 0.2360679772...............-4.236067979.................+4.472135956............................+4

.4............3..........0.1458980335..............+6.854101970................+7...................................................+6.708203937

.5............5..........0.0901699436.............-11.09016995..................+11.18033989............................+11

.6............8..........0.0557280899..............17.94427193...................+18...............................................+17.88854384

.7..........13..........0.0344418537.............-29.03444189..................+29.06888374............................+29

.8..........21..........0.0212862362............+46.97871382..................+47...............................................+46.95742758

.9..........34..........0.0131556175............ -76.01315572..................+76.02631134...........................+76

10.........55..........0.0081306187..........+122.9918696..................+123............................................+122.983739

............................................................................................................................................................................................................

20....6765..........0.0000661070......+15126.99998..................+15127.......................................+15126.99991

............................................................................................................................................................................................................

We see that for increasing n, the absolute magnitude for Y converges to an integral value in the Sum {+},

but only for even n.

For odd n, the difference Sum {-} gives a specific integer for specific n.

The product of the two sums is:........{+}.{-} = []-Y[]^2n - []X[]^2n=Sqrt(5).T2n .

The sum of the two sums is:...............{+}+{-}= 2[]-Y[]^n , with STn ={+}+{-} - Tn.Sqrt(5) = [](-Y)^n +(X)^n[]

Multiplying each term as: Sqrt(5).({+}+{-}), we can form the alternating series:

(0+2.Sqrt(5)), (5+1.Sqrt(5)), (5+3.Sqrt(5)), (10+4.Sqrt(5)), (15+7.Sqrt(5)), .....as the alternating form of

SuperSEps, given in the term:

..................................................................[5.Tn + Sqrt(5).T'n],

But for even n, we have: T'n ={+} and for odd n, we have T'n ={-}; then by (a-b)(a+b)=a^2-b^2 :

STn.Sqrt(5).Tn={+}.{-}=Sqrt(5).T2n & STn=T2n/Tn = []-Y^2n - X^2n[]/[]-Y^n - X^n[] (quod erat demonstrandum).

The significance of this result is that STn, T2n and Tn are all integers.

We so have a primary extension for SEps with elements 1, 2 and 3 duplicated and resulting in the mappings

as previously specified.

The Null-Initialisation (OSj, EXj, NSj) as the Fibonacci-Triplet (An-1, An, An+1) then reflects STn about n=0*

to define the complex number set as negative STn's mapped in a 0=>1=>Infinity correspondence to Tn.

This is the mathematical mapping of Cantorian Enumerability as previously indicated.

pacificap@hotmail.com................................................................................................................................Tony Bermanseder


Love from the DragonHeart!

As a mathematical physicist, I also study ancient scrolls and the signature can be evaluated on a number of levels; from childishly naive to profoundly esoteric---Tony Whynot, Unicorn of SophiaGnosis !

ARMAGEDDON=DRAGONMADE=ANDROMEDAG=MARRY7=GODNAMEDRA=82 =666+1=1+2+3+...34+35+36+1=1+2.2+3.3+5.5+7.7+11.11+13.13+17.17

<http://au.msnusers.com/quantumrelativity>