# A Revision of the Friedmann Cosmology

Discussion in 'A Revision of the Friedmann Cosmology' started by admin, Feb 17, 2018.

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4. The Continuon

4.1 The Hubble Node of the Inflaton in the Instanton

4.2 The Dark Matter - Baryon Matter Intersection

Baryon-Dark Matter Saturation:

ΩDM = 1-ΩBM until Saturation for BM-DM and Dark Energy Separation

ρBM+DM/ρcritical = ΩoY{[n-ΣΠnk-1]/Πnk}/{(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)}3 = MoY{[n-ΣΠnk-1]/Πnk}/{ρcriticalRk(n)3}

Baryon Matter Fraction ΩBM = ΩoY{Nk} = Ωo.Y{[n-ΣΠnk-1]/Πnk}

Dark Matter Fraction ΩDM = ΩoY{[n-ΣΠnk-1]/Πnk}{1-{(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)}3/{(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)}3 = ΩoY{[n-ΣΠnk-1]/Πnk}{(n-ΣΠnk-1+Πnk)3-(n-ΣΠnk-1)3}/{n-ΣΠnk-1}3
= ΩoY{[n-ΣΠnk-1]/Πnk}{(1+Πnk/[n-ΣΠnk-1])3 -1} = ΩBM{(1+Πnk/[n-ΣΠnk-1])3 -1}

Dark Energy Fraction ΩDE = 1- ΩDM - ΩBM = 1 - ΩBM{(1+Πnk/[n-ΣΠnk-1])3}

ΩBM=constant=0.0553575 from Saturation to Intersection with Dark Energy Fraction

ΩoY{[n-ΣΠnk-1]/Πnk} = ρBM+DMRk(n)3/MH = [Nk]3/[Nk+1]3 = {(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)}3 = Rk(n)3/VH = VdS/VAdS
for ρBM+DM = MH/RH3 = ρcritical and for Saturation at Ni = 6.541188... = constant ∀ Ni

(Mo/MH).Y{[n-ΣΠnk-1]/Πnk} = {(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)}3 with a Solution for f(n) in Newton-Raphson Root Iteration and first Approximation x0

xk+1 = xk - f(n)/f'(n) = xk - {(Mo/MH).Y{[n-∑∏nk-1]/Πnk} - (n-∑∏nk-1)/(n-ΣΠnk-1+Πnk)3}/{(Mo/MH).[lnY]Y{[n-ΣΠnk-1]/Πnk} - 3(n-ΣΠnk-1)2/(n-ΣΠnk-1+Πnk)4}

x1 = x0 - {(Mo/MH).Y[n] - (n/n+1)3}/{(Mo/MH).[lnY]Y[n] - 3n2/[n+1]4}
= x0 - {(Mo/MH).Y{N0} - (N0)3/(N0+1)3}/{(Mo/MH).[lnY]Y{N0} - 3(N0)2/1(N0+1)4}
x1 = x0 - {(Mo/MH).Y{[n-1]/n1} - (n-1)3/(n-1+n1)3}/{(Mo/MH).[lnY]Y{[n-1]/n1} - 3(n-1)2/(n-1+n1)4}
= x0 - {(Mo/MH).Y{N1} - (N1)3/(N1+1)3}/{(Mo/MH).[lnY]Y{N1} - 3(N1)2/n1(N1+1)4}
x1 = x0 - {(Mo/MH).Y{[n-1-n1]/n1n2} - (n-1-n1)3/(n-1-n1+n1n2)3}/{(Mo/MH).[lnY]Y{[n-1-n1]/n1n2} - 3(n-1-n1)2/(n-1-n1+n1n2)4}
= x0 - {(Mo/MH).Y{N2} - (N2)3/(N2+1)3}/{(Mo/MH).[lnY]Y{N2} - 3(N1)2/n1n2(N2+1)4}
.......

n = 1.N0 = Ni = 6.541188....⇒ Ni ∀i for ∏nk = n0 = 1
n = n1N1+1 = (234.472)(6.541188...)+1 = 1534.725.... for ∏nk = n0n1 = n1
n = n1n2N2+1+n1 = (234.472x245.813)(6.541172)+1+234.472 = 377,244.12.... for ∏nk = n0n1n2 = n1n2
n = n1n2n3N3+1+n1+n1n2 = (234.472x245.813x257.252)(6.541172)+1+234.472+(234.472x245.813) = 97,044,120.93.... for ∏nk = n0n1n2n3= n1n2n3
......

Baryon-Dark Matter Intersection:

Nk=√2 for n = √2.Πnk + ΣΠnk-1
n0 = 1.√2 + 0 = no
n1 = n1√2 + 1 = 332.593 = n1√2 + 1
n2 = n1n2√2 + 1 + n1 = 81,745.461
n3 = n1n2n3√2 + 1 + n1 +n1n2 = 21,026,479.35

.....

Hypermass Evolution:

Yk{(n-ΣΠnk-1)/Πnk} = 2πΠnk.RHps = Πnk.RH/rps = ΠnkMH*k/mH*k for MH = c2RH/2Go and mH = c2rps/2Go

Hypermass MHyper = mH.Yk{(n-ΣΠnk-1)/Πnk}

.....= Yn = Y([n-1]/n1) = Y([n-1-n1]/n1n2) =.....

k=0 for MHyper = MH = 1.MH = mH.Y{(n)} with n = 1.{ln(2π/nps)/lnY} = n1
= 234.472

k=1 for MHyper = n1.MH = MH* = mH.Y{(n-1)/n1} with n = [1] + n1.{ln(2πn1/nps)/lnY} = [1] + n1n2
= 1 + 234.472x245.812 = 57,637.03

k=2 for MHyper = n1n2.MH = MH** = mH.Y{(n-1-n1)/n1n2} with n = [1 + n1] + n1n2.{ln(2πn1n2/nps)/lnY} = [1 + n1] + n1n2n3
= 235.472 + 234.472x245.812x257.251 = 14,827,185.4

k=3 for MHyper = n1n2n3.MH = MH*** = mH.Y{(n-1-n1-n1n2)/n1n2n3} with n = with n = [1 + n1 + n1n2] + n1n2n3.{ln(2πn1n2n3/nps)/lnY} = [1 + n1 + n1n2] + n1n2n3n4
= 57,871.74 + 234.472x245.812x257.251x268.785 = 3,985,817,947.8

4.3 The Multiversal Hubble Cycles

A measured and observed flat universe in de Sitter (dS) 4D-spacetime with curvature k=0, emerges as the result of a topological mirror symmetry between two Calabi Yau manifolds encompassing the de Sitter spacetime in a multitimed connector dimension.
The resulting multiverse or braneworld so defines a singular universe with varying but interdependent time cyclicities.

Parallel universes synchronise in a quantized protoverse as a function of the original lightpath of the Instanton, following not preceding a common boundary condition, defined as the Inflaton.
The initial conditions of the Inflaton so change as a function of the imposed cyclicity by the boundary conditions of the paired Calabi Yau mirror duality; where the end of a Instanton cycle assumes the new initial conditions for the next cycle of the Instanton in a sequence of Quantum Big Bangs.

The outer boundary of the second Calabi Yau manifold forms an open dS spacetime in 12-dimensional brane space (F-Vafa 'bulk' Omnispace) with negative curvature k=-1 and cancels with its inner boundary as a positively curved k=1 spheroidal AdS spacetime in 11 dimensions to form the observed 4D/10-dimensional zero curvature dS spacetime, encompassed by the first Calabi Yau manifold.

A bounded (sub) 4D/10D dS spacetime then is embedded in a Anti de Sitter (AdS) 11D-spacetime of curvature k=+1 and where 4D dS spacetime is compactified by a 6D Calabi Yau manifold as a 3-torus and parametrized as a 3-sphere or Riemann hypersphere.
The outer boundary of the 6D Calabi Yau manifold then forms a mirror duality with the inner boundary of the 11D Calabi Yau event horizon.

Yn = RHubble/rWeyl = 2πRHubbleWeyl = ωWeyl/Ho = 2πnWeyl = nps/2π = 1.003849x1049

2nd Inflaton/Quantum Big Bang redefines for k=1: RHubble(1) = n1RHubble = c/Ho(1) = (234.472)RHubble = 3.746x1028 m* in 3.957 Trillion Years for critical nk
3rd Inflaton/Quantum Big Bang redefines for k=2: RHubble(2) = n1n2RHubble = c/Ho(2) = (234.472)(245.813)RHubble = 9.208x1030 m* in 972.63 Trillion Years[/size]for critical nk
4th Inflaton/Quantum Big Bang redefines for k=3: RHubble(3) = n1n2n3RHubble = c/Ho(3) = (57,636.27)(257.252)RHubble = 2.369x1033 m* in 250.24 Quadrillion Years for critical nk
5th Inflaton/Quantum Big Bang redefines for k=4: RHubble(4) = n1n2n3n4RHubble = c/Ho(4) = (14,827,044.63)(268.785)RHubble = 6.367x1035 m* in 67.26 Quintillion Years for critical nk
...
(k+1)th Inflaton/Quantum Big Bang redefines for k=k: RHubble(k) = RHubble P nk = c/Ho P nk

...
nk = ln{ωWeylRHubble(k)/c}/lnY = ln{ωWeyl/Ho(k)}/lnY

Last edited: Sep 20, 2018

Messages:
3,142
The [Alpha]-Variation is the dimensional intersection of M-C-space, 10D-C-space forming a holographic image in 12D-F-space.
The chargequantum (e) is defined via the Riemann Analysis of B(n), the supersymmetric wavefunction of the universe:
{B(n) = [2e/hA]exp(-[Alpha]xT(n) Inverse Sorce energy or Magneto charge units (C*)}; where {T(n) =...- 3 - 2 - 1 +0+ 1 + 2 + 3 +...= n(n+1)} and the Feynman-Path-Integral for all particle histories as an alternative formulation to the Schrödinger- Dirac- and Klein-Gordon Equations for the quantum mechanistic probability distribution of quantum states in the particle-wave duality.

The Action Law of (Action=ee*) manifests the lightspeed (c)-independent form of [Alpha] and can then be calibrated via the definition of the (c)-inclusive form in magnetic constant (μo). {[Alpha] = 60πe2/h = e2/(2εohc) = μoce2/(2h) = 1/137.0470731}

A Newton-Raphson iteration for B(n) and the boundary condition {T(n)=i2 in B{-[1/2]+-i(½√3)}, with a first approximation: (e1=(½hA=1.618221145x10-19 C*) converges to: (e=1.606456344x10-19 C*).

Abstract time in F-Space is defined as:

and so allows the definition of Inverse Time as frequency parameter physicalizing this abstraction for time in modular mirror duality made manifest in the string epoch of the Inflaton.
This then defines the GENESIS BOSON as the Particle of creation using the fundamental constants of Creation from the SEps algorithms. Those constants are then used inductively in the future by any sufficiently mentally evolved and cosmically selfaware civilisation to construct selfconsistent and logical measurement systems to rediscover their own nature and origins in a self induction of physical consciousness of their own cocreated Genesis in a perceived timearrow of entropy, flowing apparently from the past to the present to the future.

In practical terms, this engages the measurement and analysis of two fundamental constants, namely the speed of light 'c' and the Planckian quantum constant 'h' to relate the quantum as a micro energy selfstate (eigenvalue) to what is termed the classical physics of macro selfstates exemplified in the theoretical physics of Newton, Maxwell and Einstein in scientific models of reality and encompassing mechanics, electromagnetism and the relativities respectively. The dimensional analysis of 'hc' as a energyxdisplacement parameter suffices to calibrate the unitary mensuration parameters for mass, displacement and time, say in the Terran System International or SI-system of measurements of fundamental quantities, say here the kilogram, the meter and the second respectively. The other elementary units ain the SI-system are derived from the algorithmic masterconstant set and comprise the Kelvin for temperature as kinetic measure of the quantum states, the Ampere and Coulomb for electric current, the mole for molarity , the candela for luminosity with the sterradian an additional geometrized unit for angular measures.

Any arbitrary measurement system of an UO in a defined spacetime can then experimentally determine relationships and corollaries between experimental data and the changes in energy associated with dynamical systems. The UO has a mensuration system SI say and can calibrate its SI-system to any other unitary system like the star-* system of the UO*.

Dimensional Unit Calibration:

[m/s]/[m*/s*] = [c*/c] = [3x108/2.99792458x108] = [1.000692286] for {m/m*} = {1.000692286} {s/s*}​

[Js]/[J*s*] = [h*/h] = [6.66666666..x10-34/6.62607004x10-34] = [1.006126803] for {J/J*} = {1.006126803} {s*/s}​

[m5/s3]/[m5/s3]* = {[m/m*]2}.[c*/c]3 = Go*h*/Goh = 30ch*/30c*h = [c/c*][h*/h] = [0.999308193x1.00612803] = [1.005431984]​
for {m/m*} = [c/c*]2.√[h*/h] = [0.998616864x1.00305872] = [1.001671357]​

for {m}2 = 1.00334349 {m*}2 and m = 1.001671357 m* and m* = 0.998331431 m​

s = {m/m*}.[0.999308193] s* = [1.001671357x0.999308193] s* = 1.000978394 s* and {m/s} = 1.000692286 {m/s}* for {m/s}2 = 1.00138505 {m*/s*}2 as c2

J = {s*/s}[h*/h] J * = [0.999022562x1.006126803] J* = 1.005143377 J* and J* = 0.994882942 J​

kg = {s*/s}.{s/m}2.{m*/s*}2.[h*/h] kg* = {s/s*}{m*/m}2.[h*/h] kg* = [1.000978394x0.996665646x1.006126803] kg* = 1.003753126 kg*​

[H/m]/[H*/m*] = [J/J*][m*/m][C*/C]2.[s/s*]2 = μo*/μo = [120π/c*]/[4πx10-7]​
for C = √{[Js/J*s*][m*s/ms*]} C* =√{[h*/h][c/c*]} C* = √[1.006126803/1.000692286] C* = 1.002711702 C*​

[eV]/[eV*] = [e±J]/[e±J]* = [e±/e±*].[J/J*] for eV = [1.60217662x10-19/1.606456344x10-19].[1.005143377] eV* = 1.00246560 eV*​

[J/K]/[J*/K*] = {J/J*}.{K*/K} = [k*/k] = [1.411721579x10-23/1.380649x10-23] = [1.022505777] for K = [J/J*]/[1.022505777] K* = [1.005143377/1.022505777] K*= 0.983020397 K*​

Conversion Units are:
{s} = 1.000978394 {s*}​
{m} =1.001671357 {m*}​
{kg} = 1.003753126 {kg*}​
{C} = 1.002711702 {C*}​
{J} = 1.005143377 {J*}​
{eV} = 1.00246560 {eV*}​
{K} = 0.98301975 {K*}​

(m*= 0.998331431 m; s*= 0.999022562 s ; kg*=0.99626091 kg) in calibration of the base masterconstants (h/h*, c/c*, [Go]u=(1/30c)) and we note the numerical constancy for the magnetic constant in both mensuration systems: (μo)=4πx10-7 Henry/m (H/m) in (SI) and (μo)=120π/c (H*/m*) in (*).​
We recall that: (c=2.99792458x108 m/s (SI) and c*=3x108 m*/s* (*)).​
The Henry is a derived (SI) unit for magnetic inductance and has base units (Js2/C2=kgm2/C2), which so must give the (C to C*) unitary calibration in (μoo*)=1=0.994598576 C*2/C2, which gives (C*=0.997295631C) and DEFINES the (SI)-Coulombic Charge quantum as: (e=0.997295631e*=1.6021119x10-19 C (SI)).​

The textbooks of SI-physics have (e'=1.60217662x10-19 C (SI)), however and a value which differs from the value demanded by the magnetic constant (μo ) in a factor of (e'/e=1.0000403).
As the electropolic charge quantum appears squared in the [Alpha]-Constant, the [Alpha]-variation so becomes (1.0000807), with the old value of (e') exceeding the new value of (e) in so 4 parts in 100,000 and [Alpha]' greater in magnitude than [Alpha] by 81 parts in a million and in agreement with the Churchill-Webb measurements of 1998, increasing from Alpha = μoc.e2/2h = 1/137.047075 to Alpha' = 1/137.036003.
And I would suspect, that measuring [Alpha] even further back towards the Quantum Big Bang with increasing redshift, would better approximate the 80 parts per million increase in Alpha from say lower deviations at the say 8 parts per million at lower redshifts.

So the '[Alpha]-Dip' indicates that the textbook value for the electropole is fractionally too high; but that the Alpha Finestructure-Constant remains indeed constant, once the variation in the electronic charge quantum is taken into account.
Because the magnetic permeability constants are numerically the same in both the (SI) and the (*) unitary measurement systems; but
εo = 1/120πc = 8.841941283x10-12 (F/m)* and is εo = 8.8541878176x10-12 F/m (SI), the (SI) measurement is too large by a factor of 1.00138505 to correlate correctly wirth the magnetic permeability constant μo to give the Maxwell constant μoo = (120π/c).(1/120πc) = 1/c2.

It is experimentally measured in the (e/me)-ratio of the electron, subject to electric- and magnetic fields and this fits in nicely with my analysis of the electromagnetic mass of the electron.

In particular, the effective mass of the electron: (me=h[Alpha]/(2πRec)=9.29052715x10-31 kg*), also contains a magnetocharged part via (e*=2Rec2) for ([Alpha]=meπe*/(hc)) in the unification of the EMI with the GI by [Go=4πεo]u.
This magnetocharged part, intrinsic to the UFoQR as definition from (μo) and the quantisation of (λps) in (Re), we term 'Electromagnetic Mass':
(meEMR = 2μoe2/(3Ree* = 1.556643x10-32 kg*)) which is subtracted from the effective mass (me), gives me = 9.134865x10-31 kg* or 9.10071x10-31 kg (SI) and in agreement with the SI-textbook value of 9.1093835x10-31 kg (SI) to 95 parts in 100,000, subject to perturbation theory in the factor 2/3 in the electromagnetic mass.

The 'naked' restmass of the electron is about 98.245% of the effective mass, the latter specifying the 'naked' electron to move with a speed of (0.18077c) through an electric potential of (8.5748 keV*).
A detailed analysis of the electron's relativistic mass increase in equality with its energy of magnetic self induction forms the mathematical basis to 'prove' the 'Theory of Quantum Relativity' via a binomial distribution of the (v/c) parameter about the (X+Y=XY=i2=exp[iπ]= -1) FRB or 'Functional Riemann Bound' in a 'Complex Riemann Analysis'.
The '[Alpha]-Dip' is like a double symmetry; the magneto charged part of the electron is hidden and une requires the 'image of the image' to notice the skewing of the experimental data. The [Alpha]-Variation provides the mirroring of the nodes in the boundaries and vice versa and so indicates the intrinsic definition of the [Alpha]-Finestructure-Constant as the manifestation of the interdimensional law of action, leading to a 4-dimensional superconductivity coupled to the vacuum or zero-point-energy.

In the attempt to explain the [Alpha]-Dip, some theoretists have proposed a 'slowing down' of (c).
Recent formulations by populist physicist Paul Davies and in co-authorship with Tamara Davis and Charles Lineweaver from the Department of Astrophysics at the University of New South Wales, Sydney, Australia have followed the wrong avenues for the interpretation of the data however.
In a paper published in ('Nature': 'Black Holes constrain varying constants'; August 8th, 2002), the authors propose a varying light speed to be responsible for the [Alpha]-Dip and discount any possible variation in the electro charge quantum.

Davies' argument that an increase in (e) would alter the evolution of Black Holes in their entropic definitions does not take into account that a productation of the Boltzmann Constant (defining entropy), with (e) forms a fundamental finestructured constant in its own right.

In particular, the universe's wavefunction B(n) is localised in any arbitrary spacetime in 'unfreezing' the M-space 'stuck' in between the (X,Y) coordinates and subsequently in between real and imaginary linearised time parameters. This demands the establishment of a Mean-Alignment-Time or MAT, relative to a 'unfreezing definition' in a specification of the 'naked singularity', oscillating as zero-point about the FRB.

As E*.e= Epsx1/Eps = 1 as fundamental unity in the 11D Membrane-Mirror-Space of modular duality with e* the magneto charge; one can heuristically state that
(Energy E x charge quantum e) in the lower dimensional C-Line-Space C can be expressed as the inversed identity in the form of 1/T.
This then sets E.e=kTe=1 for [ek]=1/T and using an inverse proportion for mass in the lower dimensionality: [e*k*] = 1/T* sets a function f(n) = [ek]/[e*k*] = [T*/T].

This is the case for the Mass-Temperature inverse proportionality for the evolution of Black Holes from micro states to macro states and as in the Hawking Mass-Temperature relation for Black Holes:

{Minimum Planck Oscillator = ½hfPlanck = ½mPlanck.c2 for Tmax=Tps and Tmin=Tss in string modular T-duality for[/indent]
½mPlanck.TPlanck = (1/8π)(4π).mPlanck.TPlanck = Hawking Modulus HM = hc3/4πGok = MBHmin.TBHmax ={c2/4π2}. MBHmax.TBHmin.}.

B(n) is assigned B(np) = {[ek](SI)/[ek](*)}, with {[ek](SI)=constant=(1.60217662x10-19 C)(1.380649x10-23 J/K) = 2.21204355x10-42 CJ/K} and using the old (SI) value with the Alpha-Variation for (e'); using (e±=1.6021119x10-19 C) without the Alpha-Variation gives {[ek](SI)} = 2.21195419x10-42 CJ/K}.

The (*)-constant is a relatively fixed constant as: (e±*k*=2.267869086x10-42 (CJ/K)*) and subsequently B(np) calculates a particular value for n at the asymptote B(n⇒±∞)=0 as:

{[e±k](SI)/[e±k]*} = (2.21204355/2.267869086) = 0.975384145 (0.975344742)= [2e/hA].exp(-[Alpha]x[np2+np]), which yields an unique (np) as a complex solution to the quadratic equation by ln(0.975384145/0.992729803) = {ln(0.982527312)/-Alpha} = 2.415747501 = np2+np for: np2 + np - 2.415747501 = 0
solving as: (np=FRB(-½) ± 1.6327117).
For the unfrozen M-space with Alpha-Variation: {10D-root: np = 1.1327117 (real) & 12D-root: np = -2.1327117 (imaginary)}.
For the unfrozen M-space without Alpha-Variation: {10D-root: np = 1.1344063 (real) & 12D-root: np = -2.1344063 (imaginary)}.

This 'unfreezing' of M-space then allows the singularity algorithm of the cosmogenesis to manifest in what might be called the sex chromosomes of the universal DNA-encoding in terms of frequency or a number count.

A new physical quantity in 'awareness' is defined as the timedifferential of frequency and allows the concept of 'consciousness' to be born from the defining qualities of magneto charges.
Electromagneto-monopolic 'Life' derives as consequence of selfinductions of quantum geometric entities, specified from super membranes, macro-crystallised in electropolic self-capacitances and magnetopolic self-inductances, subsequently becoming subject to mutual cross inductances.
The purpose of the superbranial selfreplication on ever increasing scales, and until modular duality is reached in minmax boundary conditions; is to establish the multiversal nestings of the smallest within the largest - a process which constituted the beginnings of it all in the 'naked singularity' becoming defined as the Genesis BOSON.

The GENESIS Boson then becomes the parametric initialisation of creation in the abstract labelings of:
ENERGY=k.TEMPERATURE=h.FREQUENCY=h/TIME=MASS.c2 and using the SEps-MasterConstant Set: {4; 6; 7; Lo=1/[6x1015]; c2=9x1016; 11; h=1/[15x1032]; A=14x1524; k=1/[15x1618]; 26x6561} in reverse order and with arbitrary symbols as shown becoming associated with those 'master constants'.

Particularly then: ENERGY=hRmaxps with MASS=hRmaxpsc2=0.01183463299 and TEMPERATURE=hRmax/kλps=7.544808988..x1037 and FREQUENCY=Rmaxps=1.59767545..x1048

This becomes the 'Atomic-Mass-Unit' in 12D-F-Space in using one protonucleon mc=Alpha9Lplanck for every one of the 12 monopolar current loops in the Unified Field of Quantum Relativity (UFoQR).
A first Eps-Coefficient in the Expansion Series of the fundamental priciples from the SEps algorithm then crystallizes the 'Counter for matter' in Avogadro's Constant for Molarity:
MASS(20/33)/12mc = Navogadro = 6.02242143x1023 1/mol*

N=npsps/Rmax in REAL Time relative to the Quantum Big Bang to be created following the string epoch and relating to IMAGINARY TIME relative to this selfsame creation in the Cosmogony of the Genesis Boson of the Abba-Baab 11-dimensional supermembrane. This UNREAL Quantum Relative Time then is the Hubble-FREQUENCY Ho=c/Rmax in proportionality to the Source Frequency of the Eps-Gauge Photon fps=c/λps in the expression HoRmax=c=λps.fps

N then becomes the Nulltime for the initialisation of the string/supermembrane-serpent modular duality in the De Broglie phasespeed initialisation, beginning with the Oscillation (or Bounce) of the Planck-Length and specifies the Instantenuity of Now-Cycle-Time nps=Hotps=Ho/tss as the Time Instanton tps=1/fps=fss and the Inflaton Rmax=RHubble=c/Ho with de Broglie Phasespeed Vdebroglie=Rmax.fps=Rmax.c/λps=c/nps as the 'Heartbeat of the Cosmic Mother Black Hole' frequency of the oscillating cosmos in the Cosmology of QR and in the imaginary F-Space Time of NHo generalised in the Real Time n=Hot for any time in the evolving Cosmology and minimised in nps=Hotps.

L(nps,T(nps) = 6π2λps2.σ.T4 = 2.6711043034x1096 Watts*, where σ = Stefan's Constant = 2π5k4/15h3c2 and as a product of the defined 'master constants' k, h, c2, π and 'e'.

L(n,T) = 3HoMo.c2/550n and for Temperature T(nps)
T(nps) = 2.93515511x1036 Kelvin*.

This manifests as a 'false vacuum' and as a temperature gradient, as a causation of the Big Bang Instanton on physical grounds.
The metaphysical ground is the symmetry breaking from the source parity violation described in the birth and necessity of the Graviton to resymmetrize the UFoQR.

But modular string duality defines the Inverse Energy of the wormhole as the quantum of physical consciousness in units of the product of the classical electron diameter and the proportionality between energy and mass in the Maxwell constant c2 = 1/εoμo and the inverse of the product between electric permittivity εo=1/120cπ and magnetic permeability μo=120π/c for 'free space' impedance:
Zo= electric field strength E/magnetic field strength H = √(μoo) = cμo = 1/cεo = 120π}.

Coulomb Electro Charge e = LP.√α.c2 ↔ 2Re.c2 = e* (Star Coulomb Magneto Charge)

e* = 2Rec2 = 2ke2/me = e2/2πεome = αhc/πme with Alpha-Variation (1.6021119x10-19/1.60217662x10-19)2 = 0.99991921...for the calibration
{Reme} = μoe2/4π = (2.8179403267x10-15 m)(9.10938356x10-31 kg) = (10-7)(1.60217662x10-19 C)2 = [2.56696992x10-45].[1.001671358][1.003753127].(0.99991921..) (mkg)*
= [2.56696992x10-45].[1.002711702]2.[0.99991921..] = 2.580701985x10-45 {mkg}* = (2.77777..x10-15 m*)(9.290527148x10-31 kg*) = μoe2/4π for e=1.606456344x10-19 C*
for the quantum mechanical electron and adjusted in the [SI/*] alpha variation [mkg/C2] = Alpha Variation αvar in {Remevar}SI = {αvaroe2/4π}SI = {Reme}* = {μoe2/4π}*.

Decreasing the electronic charge quantum from 1.60217662x10-19 C to 1.602111893x10-19 C so calibrates the SI-unitary measurement system with the star based * unitary mensuration system in the alpha variation in a reduced classical electron radius of Re = 2.77314286x10-15 m for an increased electron effective restmass of me = 9.255788996x10-31 kg
for (Reme) = (μoe2/4π) = 2.566762517x10-45 mkg.

Note that the defined maximum scale for the electron in the Penning Trap is consistent with the defined size of the wormhole radius rps=10-22/2p metres as minimum spacetime configuration of the Instanton. The 'point particular' electron of Quantum ElectroDynamic and its point-like particle fields, so crystallizes naturally from the theory of the string-membrane classes.

xxx

Calculation of the ELECTRONMASS leading to the recurrence of the Fibonacci Roots X=0.618033... and Y=1.618033... as elementary Resonance factors in the UFoQR

The magnetic energy stored in a magnetic field B of volume V and area A=R2 for a (N-turn toroidal) current inductor N.i=BdR/μo for velocity v and selfinduction L=NBA/i is:

Um=½Li²=½(μo.N2R)(BR/μoN)²=½B²V/μo [/sup]
and the Magnetic Energy Density per unit volume is then:

Um/V=½B²/μo.

Similarly, the Electric Energy density per unit volume is:

Ue/V=½εoE² say via the Maxwell equations and Gauss' law.

By the Biot-Savart and Ampere Law:

B=μoq.v./4πr² and εo=1/c²μo for the E=cB foundation for electrodynamic theory.

So for integrating a spherical surface charge distribution dV=4πr².dr from Re to ∞:

Um=∫{μoq²v²/8πr²}dr = μoq²v²/8πRe.

Similarly,

Ue=∫dUe=q²v²/8πεoRe =kq²/2Re=½mec² as per definition of the classical electron radius and for the total electron energy mec² set equal to the electric potential energy. We term me here the EFFECTIVE electronmass and so differ it from an actual 'bare' restmass mo.

We now define the electric electromagnetic mass and the magnetic electromagnetic mass as:

melectric=kq²/2Rec²=Ue/c²=½me and consider the electric electron energy to be half the total energy (akin the virial theorem for PE=2KE, say in the Bohr atom)

PE=(-)ke²/RBohr = e²/4πεoRBohr = 2e²/8πεoRBohr =2KE

mmagneticoe²[v/c]²/8πRe=melectric.(v/c)²=½me.(v/c)² and which must be the KE by Einstein's c²dm=c²(me-mo)

and for the relativistic electronmass m=mo/√(1-B) for B=(v/c)²

Note: (B here is not the magnetic flux density vector B=E/c, measured in Tesla or gauss but a conventional label for the (v/c) ratio in Special Relativity).

But we can see, that should one use the measured electron mass from the Re-definition as the electron's restmass, that mmagnetic + melectric=me{½+½(v/c)²} < me , because of the mass-velocity dependency factor B and the groupvelocities v<c.

So we introduce the relativistic restmass mo and set Constant Amooe²/8πRe for AB=1/√[1-B] -1

from:

c2(m-mo)=μoe²v²/8πRe with m=mo/√(1-[v/c]2)

1=(1+AB2)2(1-B2)=1+B2(2A+A2B2-2AB2-A2B4-1) and so: {A2}B4+{2A-A2}B2+{1-2A}=0

with solution in roots:

B=([A-2]±√[A²+4A])/2A={(½-1/A)±√(¼+1/A)}.

This defines a distribution of B=(v/c)² velocity ratios in mo.AB=μoe²[v/c]²/8πRe

mmagneticoe²[v/c]²/8πRe=mo.AB=½me.(v/c)²

then finestructures mmagnetic in the relation moA=½me and allows correlation between the relativistic and kinetic restmass mo and the effective electron groundmass me (say).

In particular me =2Amo and is moA for A=½ AS the NEW minimisation condition.

In string parameters and with me in *units, the following is found:

moA=30e²c/e*=½me=4.645263574x10-31 kg*

This implies, that for A=1, mo=½me , where me=9.290527155x10-31 kg* from the prequantum algorithmic associations, based on the magnetic constant defining the Classical Electronic Radius.

As B≥0 for all velocities v, bounded as groupspeed (not de Broglie Phasespeed always vdB=(h/mvgroup)(mc2/h)=c2/vgroup >c) in c for which B=1 ; a natural limit is found for the B distribution at A=½ and A=∞

The electron's restmass mo so is binomially distributed for the B quadratic.
Its minimum value is half its effective mass me and as given in:

melectric=kq²/2Rec²=Ue/c²=½me for A=½ and its maximum for A=∞ is the unity v=c for B=1

The X-root is always positive in an interval from 0 to 1 and the Y-root is always negative in the interval from -3 to 0.

For A=½: B=-3/2±3/2 for roots x=0 and y=-3;

for A=¾: B=-5/6±√(19/12) for roots x=0.425 and y=-2.092;

for A=1: B=-½± ½√(5) for roots x=X=0.618033... and y=Y=-1.618033...;

for A=∞: B=½[-]±½[+] for roots x=1[-] and y=0[-];

AB2 = ([1-B2]-1) = 1+½B2-3B4/8+5B6/16 -35B8/128+...-1

Letting B=n, we obtain the Feynman-Summation or Path-Integral for dimensionless cycletime n=Hot=ct/RHubble with Ho=dn/dt in the UFoQR for 1=(1-B2)(1+B2)2 as B4+B2-1=0 for T(n)=n(n+1)=1.

The Binomial Identity gives the limit of A=½ in:

A=1/2 - B2{3/8 - 5B2/16 + 35B4/128 -...} and as the nonrelativistic low velocity approximation of E=mc² as KE=½mov².

But the FRB or Functional-Riemann-Bound in Quantum Relativity (and basic to the pentagonal string/brane symmetries) is defined in the renormalisation of a wavefunction B(n)=(2e/hφ).exp(-alpha.T(n)), exactly about the roots X,Y, which are specified in the electron masses for A=1 in the above.

The unifying condition is the Euler Identity: XY=X+Y = i2 = -1 = cos(π)+isin(π) = ℮

A Derivation of Hyperspace ET-UFO-Craft Acceleration

The Thuban Council releases the mathematical basis for ET-Craft acceleration as a fundamental extension of the Newtonian Forcelaw modulated by Classical Relativity and the Change of photon momentum in Quantum Mechanics.
An intrinsic relationship to the electromagnetic inertia of the classical electron is supplemented to indicate the elementary velocity distribution of the electron as applied in the ET-UFO-Craft propulsion as a parallel energy vector in hyperspace albeit suppressed or 'shadowed' in the Linespace of the lower dimensional 4D-spacetimes.

Quantum-Photon-Energy (Planck): E=hf
Quantum-Photon-Momentum: pphoton = E/c = hf/c = h/l

Mass Energy (Einstein): E=mc2 = moc2/√(1-[v/c]2)
Mass Momentum: pmass = mv = mov/√(1-[v/c]2) = hf.v/c2√(1-[v/c]2)

for the Photon inertia (mass) mo = hf/c2

This is related by the Energy-Momentum Formulation: E2 - Eo2 = p2c2 and from Eo = moc2 and indicating the mass-velocity relationship between a total energy content E=mc2 with its Kinetic Energy and change of momentum.

Newton's Force Law: FNewton = mass (m) x acceleration (a=dv/dt)

FNewton = d{mv}/dt = d{hf.v/c2√(1-[v/c]2)}/dt = {h/c2}{ d(v/√(1-[v/c]2))/dt + v.(df/dt)/√(1-[v/c]2}

Let u = v/√(1-[v/c]2) for du/dt = (du/dv).(dv/dt) = (v2/c2.(dv/dt)/(√(1-[v/c]2)3 + (dv/dt)/(√(1-[v/c]2) = (dv/dt)/(√(1-[v/c]2)3

(df/dt) = (c2/h).d{mo/√(1-[v/c]2)}/dt = mov.(dv/dt)/{h(√(1-[v/c]2)3}

Therefore:

FNewton = d{mv}/dt = d{hf.v/c2√(1-[v/c]2)}/dt = {h/c2}{f.(dv/dt)/(√(1-[v/c]2)3+ v.df/dt/√(1-[v/c]2}

= mo(dv/dt)/(√(1-[v/c]2)3.....................+...................(hv/c2).(df/dt)/(√(1-[v/c]2)

= Classical Relativistic Newton Force + Newtonian Frequency Law Extension

In terms of Energy: Energy=Work=ForcexDisplacement=FNewton.R

For the cosmic boundary parameters the maximum acceleration for a spacetime quantum is (dv/dt)|max = c.fps for the displacement quanta or wavelength lps = c/fps = R|min

R.mo(dv/dt)/(√(1-[v/c]2)3 then becomes supplemented in (R.hv/c2).( mov.(dv/dt)/{h(√(1-[v/c]2)3})/(√(1-[v/c]2)
= (mo.R.v2/c2).(dv/dt)/(1-[v/c]2)2 = (molpsfpsc.v2/c2)/(1-[v/c]2)2 = mov2/(1-[v/c]2)2 = Quantum Frequency-Velocity (Shadow) Energy as basic derivative from the Zero-Point-Field ZPE or Vortex-Potential Energy (VPE).

The form of the 'shadow' energy of the ET-UFO-Craft so assumes a velocity dependent inertial expression which is focused on the factor v2/(1-[v/c]2)2 to become identical at lightspeed c2 and a factor which becomes a multiplier for the original classically observable energy content of the ET-UFO-Craft in the form of E=mc2

In hyperspace, meaning the higher dimensional universe separating the de Broglie superluminal tachyonic phasespeed vdeBroglie from the lightspeed invariance of the lower dimensional universe characterised by the groupspeed vgroup; the 'shadow' energy manifests from the combined Energy equation relating the quantum mechanics to the classical relativistic dynamics:

Energy E = mc2 = hf

E=hf (Planck) iff m=mo=0
This manifests the lower dimensional observational matter-energy expressions

Energy E=mc2 (Einstein) iff f=fss=1/fps for mo = Sfss for the mass-frequency quantisation
This manifests the 'shadow matter' as a change in the mass eigen frequency fss under modular string-membrane duality

moc2/{√(1-[v/c]2)}3..........+.......... mov2/(1-[v/c]2)2 = 2moc2/{√(1-[v/c]2)}3

Lower 10D Anti-deSitter asymptotic .................+.................Higher 11D deSitter asymptotic
hyperbolic open(-) C-String spacetime............................spheroidally closed(+) M-mirror spacetime

moc2/{√(1-[v/c]2)}3..................................+................................ mov2/(1-[v/c]2)2 = 2moc2/{√(1-[v/c]2)}3

Classical Curvature Energy CCE................+...............Quantum Curvature Energy QCE...=...2CCE

as generalised 'Virial' Theorem: 2KE+PE=0 for CCE=QCE

Fcentripetal=mv2/R=GmM/R2=Fgravitational for a circular orbiting mass m about mass M, a distance R apart and so v2=GM/R

with gravitational PEgravitational=-GmM/R2 for ½mv2=GmM/2R and KE=-½PE

Generally QCE/CCE = [v/c]2/√(1-[v/c]2)

for the Perturbation Expansion for U=[v/c]2 as:

U{1-U} = U{1+U/2+3U2/8+5U3/16+35U4/128+63U5/256+...}

U<X for Higher D QCE < Lower D CCE
U=X for Higher D QCE = Lower D CCE
U>X for Higher D QCE > Lower D CCE

Subsequently:

[v/c]2 = (1-[v/c]2)2 for the Quadratic [v/c]4 - 3[v/c]2 +1 = 0 with solutions: [v/c]2 = ½{3 ± √(9-4)}

As [v/c]2 must be less than 1 for all lower dimensional groupspeeds; the real spacetime root is [v/c]2 = ½{3-√(5)} = 1+½{1-√5} = 1 - 0.61803398... = 0.3819660... as the Difference between the Fibonacci root termed the 'Golden Proportion' and Unity 1.

The focal resonance speed of the ET-UFO-Craft so is vUFO-Resonance/c = √{½(3-√5)}c = √0.3819660... = 0.61803398...=½(√5 - 1) = Golden Proportion = 1/Phi = 1/F

CCE=QCE for [v/c]2 = √(1-[v/c]2) and [v/c]4 = 1-[v/c]2 for [v/c]2 = ½{-1 ± √5} = X and |-Y|=1/X

X = √(1-X) for X2 = 1 - X for the particle history (Path Integral) T(n)=n(n+1)=1

and a UFO-spacecraft speed of √(√X2) = 0.78615...c

The ET-UFO-Craft henceforth engages a Resonance Physics of Hyperspace in the Unified Field of Quantum Relativity (UFoQR) and 'attunes' or 'taps' into this unified spacetime matrix at a speed of 0.618033..c or so 185,409.900 kilometres per second.

xxx

Note that Richard Feynman describes alpha in its squareroot, just as is required to define the Planck-Length Oscillation for the Inflaton in relation to the Stoney Units for the electric charge quantum.

Last edited: Sep 20, 2018

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The Inflaton and the Grand Unification Symmetry in a Transformation of Supermembranes

SEWG-------------SEWg---SEW.G---SeW.G---S.EW.G------S.E.W.G
Planck Unification I----------IIB----------HO32------------IIA-----------HE64---------Bosonic Unification

2.1 Graviton Unification in Monopole Class IIB
SEWG ---- SEWg as string transformation from Planck brane to (Grand Unification/GUT) monopole brane

 String-Boson Decoupling Time s* Wavelength (λ=2πl) m* Energy (hc/λ) J* & eV* Modular Wavelength m* Temperature K* Significance 1. Planck-Boson I/SEWG tP=2πrP/c 4.377x10-43 1.313x10-34 1.523 GJ* or 9.482x1027 eV* 7.617x1033 1.079x1032 Outside Hubble Horizon Limit in Protoverse 2. Monopole-Boson IIB/SEWg GI-GUT decoupling tM=2πrM/c 1.537x10-40 4.6110x10-32 4.337 MJ* or 2.700x1025 eV* 2.169x1031 3.072x1029 Outside Hubble Horizon Limit in Protoverse 3. XL-Boson HO32/SEW.G tXL=2πrXL/c 2.202x10-39 6.605x10-31 302.817 kJ* or 1.885x1024 eV* 1.514x1030 2.145x1028 Outside Hubble Horizon Limit in Protoverse 4. ECosmic Bosons IIA/SeW.G SNI decoupling tEC=2πrEC/c 6.717x10-34 2.015x10-25 0.9927 J* or 6.180x1018 eV* 4.964x1024 7.032x1022 Galactic Supercluster Sarkar Mo=RSarkarc2/2Go Scale 5. False Higgs Vacuum tHiggsPE=2πrHiggsPE/c tps.T(nps)/Talgo 1.297x10-32 [max] to 2.8473697...x10-32 [min] 3.891x10-24 0.0514 J* or 3.200x1017 eV* 2.570x1023 3.641x1021 Galactic Supercluster Scale 6. Weyl-Boson HE64/S.EW.G Big Bang-Instanton EMI decoupling tps=2πrps/c 3.333x10-31 1.000x10-22 0.002 J* or 1.245x1016 eV* 1.000x1022 1.417x1020 Galactic Halo(Group) Scale 7. T(n)=Tps Bosonic Unification tBU=nBU/Ho 1.897x10-9 0.56902 Protoverse T(n)4 = {[n+1]2/n3}HoMoc2/(2π2sRH2[550]) = 18.1995{[n+1]2/n3} (K4/V)* 1.757 Protoverse Tps-bosonic TEW4= 18.2[n+1]2/n3 n=HotBU Unitary Modular Geometric Mean Scale 8. Higgs Boson Vacuum Electroweak WNI decoupling tEW=nEW/Ho 0.00274~1/365 4.167x10-18 Quantum Scale 4.799x10-8 J* or 298.785 GeV* 2.400x1017 3.400x1015 Inner Mesonic Ring Quantum Scale
The Coupling of the Supermembranes in Vafa-F-Space of Inflaton Selfdual Monopole IIB

We next reduce the atomic scaling to its intrinsic superstring dimension in deriving the Higgs Bosonic Restmass Induction, corresponding to the Dilaton of M-Theory.

Renormalising the wavefunction B(n) about the FRB=-½ as maximum ordinate gives a probability y2dV for y(0) = √(alpha/2π) for the renormalization.

Alpha/2π being the probability of finding the FRB fluctuation for the interval [-X,X-1] in volume element dV as the uncertainty fluctuation.
This volume element defines the dimensional intersection from C-Space into F-Space via M-Space in the topological mapping of the complex Riemann C-Space about the Riemann pole of the FRB as the Calabi-Yau superstring space in 10 dimensions.

X=½(√5-1) = 0.618033..... and Y = -(X+1) = -½(√5+1) = -1.618033...

-X(X-1) = 0.236067... in analogue to X(X+1) = 1= T(n) and XY = X+Y = -1 = i2 as the complex origin.

But 0.236067..= X3, so defining the 'New Unity' as #3=Alpha and the precursive unity as the Cuberoot of Alpha or as # in the symmetry #:#3 = SNI:EMI = Strong Nuclear Interaction Strength {ElectroMagnetic Interaction Strength}.

The Strong-Interaction-Constant SIC = √Alpha = √e2/2εohc = √(60πe2/h) in standard and in string units, reduces the SNI finestructure constant # by a factor Alpha1/6 ; that is in the sixth root of alpha and so relates the SIC at the post quantisation level as # to the pre-quantum epoch as SIC = √Alpha = #3/2.

The SNI is therefore so 11.7 times weaker at the XL-Boson 'Grand-Unification-Time' SEW.G of heterotic superstring class HO(32), than at the EpsEss time instantenuity S.EW.G of the superstring of the Quantum Big Bang in heterotic class HE(8x8) {this is the stringclass of Visi in the group theories}.
This then is the Bosonic Gauge Coupling between superstrings HO(32) and HE(8x8).

The coupling between superstrings IIA (ECosmic and manifesting the cosmic rays as superstring decay products) and IIB (Magnetic Monopole) derives directly from the B(n), with B(n=0) = Jo = 2e/hA = 0.9927298 1/J* or 6.2705x109 GeV* and representative of the ECosmic stringclass and the super high energy resonances in the cosmic ray spectrum, bounded in the monopolic resonance limit of 2.7x1016 GeV*.

1-Jo = 0.00727021 approximates ρg/c2=4/550=0.007272... approximates Alpha at n = nps.

The Unity of the SNI transforms to [1-X] = X2 and the EMI transforms as the Interaction of Invariance from X to X.
The Weak Nuclear Interaction or WNI as X2 becomes [1+X] = 1/X and the Gravitational Interaction or GI transforms as X3 transforms to [2+X] = 1/X2 by MODULAR SYMMETRY between X and Alpha and the encompassing Unification Unity: [1-X][X][1+X][2+X] = 1.

This Unification Polynomial U(u) = u4+2u3-u2-2u+1 = 0 then has minimum roots (as quartic solutions) at the Phi = X and the Golden Mean Y = -(1+X).

This sets the coupling between SNI and EMI as X; the coupling between EMI and WNI becomes X2 and the coupling between WNI and GI then is again X.
The general Force-Interaction-Ratio so is: SNI:EMI:WNI:GI = SEWG = #:#3:#18:#54.

This is the generalisation for the cubic transform: x→x3 with the Alpha-Unity squaring in the functionality of the WNI and defining G-Alpha as Alpha18 in the Planck-Mass transforming in string bosonic reduction to a basic fundamental nucleonic mass (proton and neutrons as up-down quark conglomerates and sufficient to construct a physical universe of measurement and observation):

mc = mplanck Alpha9 from the electromagnetic string unification with gravitation in the two dimensionless finestructures:

For Gravitational Mass Charge from higher D Magnetic Charge: 1 = 2πG.mplanck2/hc

For Electromagnetic Coulomb Charge as lower D Electric Charge: Alpha = 2πke2/hc

Alpha as the universal masterconstant of creation, then becomes defined via the Riemann Analysis from XY=i2 definition, reflecting in modulation in the statistical renormalisation of the B(n) as the probability distributions in quantum wave mechanics however.U(u) has its maximum at u = -½ = FRB for U(-½)=25/16 = (5/4)2 for the B(n) supersymmetry.

The derivation of the HBRMI draws upon this definition process and sets the coupling angle as arcsin(X/@) for a Unitary 'Force' @=(#fG).cfpsE-Alpha/Alpha and with the electron mass replacing the fundamental nucleonmass mc in the definition of E-Alpha.

A disassociated GI unifies with the WNI in the L-Boson and is supersymmetric to an intrinsic unification between the SNI and the EMI as the X-Boson for the duality fGfS = 1 in modular definition of a characteristic GI-mass #fG as the disassociated elementary gauge field interaction.

The transformation of the 5 superstring classes proceeds in utilizing the self-duality of superstring IIB as the first energy transformation of the Inflaton in the Planck string class I transmutating into the monopole string class IIB.

The transformation of the 5 superstring classes proceeds in utilizing the self-duality of superstring IIB as the first energy transformation of the Inflaton in the Planck string class I transmutating into the monopole string class IIB.

The quantization of mass m so indicates the coupling of the Planck Law in the frequency parameter to the Einstein law in the mass parameter.
The postulative basis of M-Theory utilizes the coupling of two energy-momentum eigenstates in the form of the modular duality between so termed 'vibratory' (high energy and short wavelengths) and 'winding' (low energy and long wavelengths) selfstates.

The 'vibratory' selfstate is denoted in: Eps=Eprimary sourcesink = hfps = mpsc2 and the 'winding' and coupled selfstate is denoted by: Ess = Eecondary sinksource = hfss = mssc2

The F-Space Unitary symmetry condition becomes: fpsfss = rpsrss = (λps/2π)(2πλss) = 1

The coupling constants between the two eigenstates are so: EpsEss = h2 and Eps/Ess = fps2 = 1/fss2

The Supermembrane EpsEss then denotes the coupled superstrings in their 'vibratory' high energy and 'winded' low energy selfstates.

The coupling constant for the vibratory high energy describes a MAXIMISED frequency differential over time in df/dt|max = fps2 and the coupling constant for the winded low energy describes its MINIMISED reciprocal in df/dt|min = fss2.

F-Theory also crystallizes the following string formulations from the EpsEss superbrane parameters.

Electromagnetic Finestructure: αe = 2πke2/hc = e2/2ε0hc

Gravitational Finestructure (Electron): αg = 2πGome2/hc = {me/mPlanck}2

Gravitational Finestructure (Primordial Nucleon): αn = 2πGomc2/hc

Gravitational Finestructure (Planck Boson): αPlanck = 2πGomPlanck2/hc

1/Eps = e* = 2Rec2 = √{4αhce2/2πGome2} = 2e√α[mP/me = 2e√{αeg}
= {2e2/me}√(k/Go) = 2e2/Gome = e2/2πεome

for Go = 1/k = 4πεo for the cosmological unification of the finestructures.

Eps = 1/Ess = 1/e* = ge}/2e = Gome/2e2

Here e* is defined as the inverse of the sourcesink vibratory superstring energy quantum Eps=E* and becomes a New Physical Measurement Unit is the StarCoulomb (C*) and as the physical measurement unit for 'Physical Consciousness'.

Re is the 'classical electron radius' coupling the 'point electron' of Quantum- Electro-Dynamics (QED) to Quantum Field Theory (QFT) and given in the electric potential energy of Coulomb's Law in: mec2 = ke2/Re;
and for the electronic restmass me.
Alpha α is the electromagnetic finestructure coupling constant α = 2πke2/hc for the electric charge quantum e, Planck's constant h and lightspeed constant c.
Go is the Newtonian gravitational constant as applicable in the Planck-Mass mP = √(hc/2πGo).

As the StarCoulomb unit describes the inverse sourcesink string energy as an elementary energy transformation from the string parametrization into the realm of classical QFT and QED, this transformation allows the reassignment of the StarCoulomb (C*) as the measurement of physical space itself.

The following derivations lead to a simplified string formalism as boundary- and initial conditions in a de Sitter cosmology encompassing the classical Minkowski-Friedmann spacetimes holographically and fractally in the Schwarzschild metrics.

The magnetic field intensity B is classically described in the Biot-Savart Law:
B =μoqv/4πr2 = μoi/4πr = μoqω/4πr = μoNef/2r
for a charge count q=Ne; angular velocity ω=v/r=2πf; current i = dq/dt and the current element i.dl = dq.(dl/dt) = vdq.

The Maxwell constant then can be written as an (approximating) finestructure:
μoεo = 1/c2 = (120π/c)(1/120πc) to crystallise the 'free space impedance' Zo = √(μoo) = 120π~377 Ohm (Ω).

This vacuum resistance Zo so defines a 'Unified Action Law' in a coupling of the electric permittivity component (εo) of inertial mass and the magnetic permeability component (μo) of gravitational mass in the Equivalence Principle of General Relativity.
A unified selfstate of the preinertial (string- or brane) cosmology so is obtained from the finestructures for the electric- and gravitational interactions coupling a so defined electropolic mass to magnetopolic mass respectively.

The Planck-Mass is given from Unity 1 = 2πGmP2/hc and the Planck-Charge derives from Alpha=2πke2/hc and where k=1/4πεo in the electromagnetic finestructure describing the probability interaction between matter and light (as about 1/137).

The important aspect of alpha relates to the inertia coupling of Planck-Charge to Planck-Mass as all inertial masses are associated with Coulombic charges as inertial electropoles; whilst the stringed form of the Planck-Mass remains massless as gravitational mass. It is the acceleration of electropoles coupled to inertial mass, which produces electromagnetic radiation (EMR); whilst the analogy of accelerating magnetopoles coupled to gravitational mass and emitting electromagnetic monopolic radiation (EMMR) remains hitherto undefined in the standard models of both cosmology and particle physics.

But the coupling between electropoles and magnetopoles occurs as dimensional intersection, say between a flat Minkowskian spacetime in 4D and a curved de Sitter spacetime in 5D (and which becomes topologically extended in 6-dimensional Calabi-Yau tori and 7-dimensional Joyce manifolds in M-Theory).

The formal coupling results in the 'bounce' of the Planck-Length in the pre-Big Bang scenario, and which manifests in the de Broglie inflaton-instanton

The Planck-Length LP = √(hG/2πc3) 'oscillates' in its Planck-Energy mP = h/λPc = h/2πcLP to give √Alpha).LP = e/c2 in the coupling of 'Stoney units' suppressing Planck's constant 'h' to the 'Planck units' suppressing charge quantum 'e'.
Subsequently, the Planck-Length is 'displaced' in a factor of about 11.7 = 1/√Alpha = √(h/60π)/e and using the Maxwellian finestructures and the unity condition kG=1 for a dimensionless string coupling Go = 4πεo, describing the 'Action Law' for the Vacuum Impedance as Action=Charge2, say via dimensional analysis:

Zo = √([Js2/C2m]/[C2/Jm]) = [Js]/[C2] = [Action/Charge2] in Ohms [Ω = V/I = Js/C2] and proportional to [h/e2] as the 'higher dimensional source' for the manifesting superconductivity of the lower dimensions in the Quantum Hall Effect (~e2/h), the conductance quantum (2e2/h) and the Josephson frequencies (~2e/h) in Ohms [Ω].

This derivation so indicates an electromagnetic cosmology based on string parameters as preceding the introduction of inertial mass (in the quantum Big Bang) and defines an intrinsic curvature within the higher dimensional (de Sitter) universe based on gravitational mass equivalents and their superconductive monopolic current flows.

A massless, but monopolically electromagnetic de Sitter universe would exhibit intrinsic curvature in gravitational mass equivalence in its property of closure under an encompassing static Schwarzschild metric and a Gravitational String-Constant Go = 1/k = 1/30c (as given in the Maxwellian finestructures in the string space).
In other words, the Big Bang manifested inertial parameters and the matter content for a subsequent cosmoevolution in the transformation of gravitational 'curvature energy', here called gravita as precursor for inertia into inertial mass seedlings; both however describable in Black Hole physics and the Schwarzschild metrics.

The Gravitational Finestructure so derives in replacing the Planck-Mass mP by a protonucleonic mass:

mc = √(hc/2πGo).f(alpha) = f(Alpha).mP and where f(Alpha) = Alpha9.
The Gravitational finestructure, here named Omega, is further described in a fivefolded supersymmetry of the string hierarchies, the latter as indicated in the following below in excerpt.

This pentagonal supersymmetry can be expressed in a number of ways, say in a one-to-one mapping of the Alpha finestructure constant as invariant X from the Euler Identity:

X+Y = XY = -1= i2 = exp(iπ).

One can write a Unification Polynomial: (1-X)(X)(1+X)(2+X) = 1 or X4+2X3-X2-2X+1 = 0
to find the coupling ratios: f(S)¦f(E)¦f(W)¦f(G) = #¦#3¦#18¦#54 from the proportionality
#¦#3¦{[(#3)2]}3¦({[(#3)2]}3)3 = Cuberoot(Alpha):Alpha:Cuberoot(Omega):Omega.

The Unification polynomial then sets the ratios in the inversion properties under modular duality:

(1)[Strong short]¦(X)[Electromagnetic long]¦(X2)[Weak short]¦(X3)[Gravitational long]
as 1¦X¦X2¦X3 = (1-X)¦(X)¦(1+X)¦(2+X).

Unity 1 maps as (1-X) transforming as f(S) in the equality (1-X) = X2; X maps as invariant of f(E) in the equality (X) = (X); X2 maps as (1+X) transforming as f(W) in the equality (1+X) = 1/X; and X3 maps as (2+X) transforming as f(G) in the equality (2+X) = 1/X2 = 1/(1-X).

The mathematical pentagonal supersymmetry from the above then indicates the physicalised T-duality of M-theory in the principle of mirror-symmetry and which manifests in the reflection properties of the heterotic string classes HO(32) and HE(64), described further in the following.

Defining f(S) = # = 1/f(G) and f(E) = #2.f(S) then describes a symmetry breaking between the 'strong S' f(S) interaction and the 'electromagnetic E' f(E) interaction under the unification couplings.
This couples under modular duality to f(S).f(G) = 1 = #55 in a factor #-53 = f(S)/f(G) = {f(S)}2 of the 'broken' symmetry between the longrange- and the shortrange interactions.

SEWG = 1 = Strong-Electromagnetic-Weak-Gravitational as the unified supersymmetric identity then decouples in the manifestation of string-classes in the de Broglie 'matter wave' epoch termed inflation and preceding the Big Bang, the latter manifesting at Weyl-Time as a string-transformed Planck-Time as the heterotic HE(64) class.

As SEWG indicates the Planck-String (class I, which is both openended and closed), the first transformation becomes the suppression of the nuclear interactions sEwG and describing the selfdual monopole (stringclass IIB, which is loop-closed in Dirichlet brane attachement across dimensions say Kaluza-Klein R5 to Minkowski R4 or Membrane-Space R11 to String Space R10).

The monopole class so 'unifies' E with G via the gravitational finestructure assuming not a Weylian fermionic nucleon, but the bosonic monopole from the kGo = 1 initial-boundary condition GmM2 = ke2 for mM = ke = 30[ec] = mP√Alpha.

The Planck-Monopole coupling so becomes mP/mM = mP/30[ec] = 1/√Alpha
with f(S) = f(E)/#2 modulating f(G) = #2/f(E)=1/# ↔ f(G){f(S)/f(G)} = # in the symmetry breaking f(S)/f(G) = 1/#53 between short (nuclear asymptotic) and long (inverse square).

The shortrange coupling becomes f(S)/f(W) = #/#18 = 1/#17 = Cuberoot(Alpha)/Alpha6
and the longrange coupling is Alpha/Omega = 1/Alpha17 = #3/#54 = 1/#51 = 1/(#17)3.

The strong nuclear interaction coupling parameter so becomes about 0.2 as the cuberoot of alpha and as measured in the standard model of particle physics.

The monopole quasimass [ec] describes a monopolic sourcecurrent ef, manifesting for a displacement λ=c/f. This is of course the GUT unification energy of the Dirac Monopole at precisely [c3] eV or 2.7x1016 GeV and the upper limit for the Cosmic Ray spectra as the physical manifestation for the string classes: {I, IIB, HO(32), IIA and HE(64) in order of modular duality transmutation}.

The transformation of the Monopole string into the XL-Boson string decouples Gravity from sEwG in sEw.G in the heterotic superstring class HO(32). As this heterotic class is modular dual to the other heterotic class HE(64), it is here, that the protonucleon mass is defined in the modular duality of the heterosis in: Omega = Alpha18 = 2πGomc2/hc = (mc/mP)2.

The HO(32) string bifurcates into a quarkian X-part and a leptonic L-part, so rendering the bosonic scalar spin as fermionic halfspin in the continuation of the 'breaking' of the supersymmetry of the Planckian unification. Its heterosis with the Weyl-string then decouples the strong interaction at Weyl-Time for a Weyl-Mass mW, meaning at the timeinstanton of the end of inflation or the Big Bang in sEw.G becoming s.Ew.G.

The X-Boson then transforms into a fermionic protonucleon triquark-component (of energy ~ 10-27 kg or 560 MeV) and the L-Boson transforms into the proto-muon (of energy about 111 MeV).

The last 'electroweak' decoupling then occurs at the Fermi-Expectation Energy about 1/365 seconds after the Big Bang at a temperature of about 3.4x1015 K and at a 'Higgs Boson' energy of about 298 GeV.

A Bosonic decoupling preceeded the electroweak decoupling about 2 nanoseconds into the cosmogenesis at the Weyl-temperature of so TWeyl = Tmax = EWeyl/k = 1.4x1020 K as the maximum Black Hole temperature maximised in the Hawking MT modulus and the Hawking-Gibbons formulation: McriticalTmin = ½MPlanckTPlanck = (hc/2πGo)(c2/2k) = hc3/4πkGo for Tmin = 1.4x10-29 K and Boltzmann constant k.

The Hawking Radiation formula results in the scaling of the Hawking MT modulus by the factor of the 'Unified Field' spanning a displacement scale of 8π radians or 1440° in the displacement of 4λps.

The XL-Boson mass is given in the quark-component: mX = #3mW/[ec] = Alpha.mW/mP = #3{mW/mP}~1.9x1015 GeV; and the lepton-component: mL = Omega.[ec]/#2 = #52[ec/mW] ~ 111 MeV.

A reformulation of the rotational dynamics associated with the monopolic naturally superconductive currentflow and the fractalisation of the static Schwarzschild solution follows. in a reinterpretation of the Biot-Savart Law.

All inertial objects are massless as 'Strominger branes' or extremal boundary Black Hole equivalents and as such obey the static and basic Schwarzschild metric as gravita template for inertia.

This also crystallises the Sarkar Black Hole boundary as the 100 Mpc limit (RSarkar = (Mo/Mcritical.RHubble) = 0.028.RHubble~237 Million lightyears) for the cosmological principle, describing large scale homogeneity and isotropy, in the supercluster scale as the direct 'descendants' of Daughter Black Holes from the Universal Mother Black Hole describing the Hubble Horizon as the de Sitter envelope for the Friedmann cosmology (see linked website references on de Sitter cosmology) for the oscillatory universe bounded in the Hubble nodes as a standing waveform.

The Biot-Savart Law: B = μoqv/4πr2 = μoi/4πr = μoNef/2r = μoNeω/4πr for angular velocity ω=v/r transforms into B = constant(e/c3)gxω

in using acentripetal = v2/r = rω2 for g = GM/r2 = (2GM/c2)(c2/2r2) = (RSc2/2R2) for a Schwarzschild solution RS = 2GM/c2.

B = constant(eω/rc)(v/c)2 = μoNeω/4πr yields constant = μoNc/4π = (120πN/4π) = 30N with e = mM/30c for
30N(eω/c3)(GM/R2) = 30N(mM/30c)ω(2GM/c2)/(2cR2) = NmM(ω/2c2R)(RS/R) = {M}ω/2c2R.

Subsequently, B = Mw/2c2R = NmM(RS/R){ω/2c2R} to give a manifesting mass M finestructured in
M = NmM(RS/R) for N = 2n in the superconductive 'Cooper-Pairings' for a charge count q = Ne = 2ne.

But any mass M has a Schwarzschild radius RS for N = (M/mM){R/RS} = (M/mM){Rc2/2GM} = {Rc2/2GmM} = {R/RM} for a monopolic Schwarzschild radius RM = 2GmM/c2 = 2G(30ec)/c2 = 60ec/30c3 = 2e/c2 = 2LP√Alpha = 2OLP.

Any mass M is quantised in the Monopole mass mM = mP√Alpha in its Schwarzschild metric and where the characterising monopolic Schwarzschild radius represents the minimum metric displacement scale as the Oscillation of the Planck-Length in the form 2LP√Alpha~LP/5.85.

This relates directly to the manifestation of the magnetopole in the lower dimensions, say in Minkowski spacetime in the coupling of inertia to Coulombic charges, that is the electropole and resulting in the creation of the mass-associated electromagnetic fields bounded in the c-invariance.
From the Planck-Length Oscillation or 'LP-bounce': OLP = LP√Alpha = e/c2 in the higher (collapsed or enfolded) string dimensions, the electropole e = OLP.c2 maps the magnetopole e*= 2Re.c2 as 'inverse source energy' EWeyl = hfWeyl and as function of the classical electron radius Re = ke2/mec2 = RCompton.Alpha = RBohr1.Alpha2 = Alpha3/4πRRydberg = 1010{2πRW/360} = {e*/2e}.OLP.

The resulting reflection-mirror space of the M-Membrane space (in 11D) so manifests the 'higher D' magnetocharge 'e*' AS INERTIAL MASS in the monopolic current [ec], that is the electropolic Coulomb charge 'e'.
This M-space becomes then mathematically formulated in the gauge symmetry of the algebraic Lie group E8 and which generates the inertial parameters of the classical Big Bang in the Weylian limits and as the final Planck-String transformation.

The string-parametric Biot-Savart law then relates the angular momentum of any inertial object of mass M with angular velocity ω in selfinducing a magnetic flux intensity given by B = Mω/2Rc2 and where the magnetic flux relates inversely to a displacement R from the center of rotation and as a leading term approximation for applicable perturbation series.

This descriptor of a string based cosmology so relates the inherent pentagonal supersymmetry in the cosmogenesis to the definition of the Euler identity in its finestructure X+Y = XY = i2 = -1, and a resulting quadratic with roots the Golden Mean and the Golden Ratio of the ancient omniscience of harmonics, inclusive of the five Platonic solids mapping the five superstring classes. Foundations and applications of superstring theory are also indicated and serve as reference for the above.

The quantization of mass m so indicates the coupling of the Planck Law in the frequency parameter to the Einstein law in the mass parameter.
The postulative basis of M-Theory utilizes the coupling of two energy-momentum eigenstates in the form of the modular duality between so termed 'vibratory' (high energy and short wavelengths) and 'winding' (low energy and long wavelengths) selfstates.

The 'vibratory' selfstate is denoted in: Eps = Eprimary sourcesink = hfps = mpsc2 and the 'winding' and coupled selfstate is denoted by: Ess = Esecondary sinksource = hfss = mssc2

The F-Space Unitary symmetry condition becomes: fpsfss = rpsrss = (λps/2π)(2πλss) = 1

The coupling constants between the two eigenstates are so: EpsEss = h2 and Eps/Ess = fps2 = 1/fss2

The Supermembrane EpsEss then denotes the coupled superstrings in their 'vibratory' high energy and 'winded' low energy selfstates.

The coupling constant for the vibratory high energy describes a MAXIMISED frequency differential over time in df/dt|max = fps2 and the coupling constant for the winded low energy describes its MINIMISED reciprocal in df/dt|min = fss2.

F-Theory also crystallizes the following string formulations from the EpsEss superbrane parameters.

1/Eps = e*= 2Rec2 = √{4αhce2/2πGome2} = 2e√α{mP/me} = 2ke2/me = αhc/πme

Here e* is defined as the inverse of the sourcesink vibratory superstring energy quantum Eps = E* and becomes a New Physical Measurement Unit is the StarCoulomb (C*) and as the physical measurement unit for 'Physical Consciousness'.

Re is the 'classical electron radius' coupling the 'point electron' of Quantum- Electro-Dynamics (QED) to Quantum Field Theory (QFT) and given in the electric potential energy of Coulomb's Law in: mec2 = ke2/Re; and for the electronic restmass me.

Alpha α is the electromagnetic finestructure coupling constant a =2πke2/hc for the electric charge quantum e, Planck's constant h and lightspeed constant c.
Go is the Newtonian gravitational constant as applicable in the Planck-Mass mP = √(hc/2πGo).

As the StarCoulomb unit describes the inverse sourcesink string energy as an elementary energy transformation from the string parametrization into the realm of classical QFT and QED, this transformation allows the reassignment of the StarCoulomb (C*) as the measurement of physical space itself.

2.2 Quark-Lepton Unification in XL-Boson Class HO(32)
SEWg --- SEW.G

2.3 Cosmic Ray Unification in XL-Boson Class IA
SEW.G --- SeW.G

The Elementary Cosmic Ray Spectrum

The elementary Cosmic Ray Spectrum derives from the transformation of the Planck-String-Boson at the birth of the universe.

The following tabulation relates those transformation in energy and the modular duality between the distance parameters of the macrocosm of classical spacetime geometry and the microcosm of the quantum realm.

 String-Boson Wavelength (λ) m Energy (hc/λ) J & eV Modular Wavelength m Significance 1. Planck-Boson 1.2x10-34 m 1.6 GJ or 9.9x1027 eV 8.0x1033 m Outside Hubble Horizon Limit 2. Monopole-Boson 4.6x10-32 m 4.3 MJ or 2.7x1025 eV 2.2x1031 m Outside Hubble Horizon Limit 3. XL-Boson 6.6x10-31 m 303 kJ or 1.9x1024 eV 1.5x1030 m Outside Hubble Horizon Limit 4. X-K-Boson transit (+) 8.8x10-28 m 227 J or 1.6x1021 eV 1.1x1027 m 2πRHubble11D 5. X-K-Boson transit (-) 1.0x10-27 m 201 J or 1.2x1021 eV 1.0x1027 m 2πRHubbleHorizonLimit 6. CosmicRayToe 1.9x10-27 m 106 J or 6.6x1020 eV 5.3x1026 m 2πRHubble10D 7. CosmicRayAnkle 2.0x10-25 m 1.0 J or 6.2x1018 eV 5.0x1024 m Galactic Supercluster Scale 8. CosmicRayKnee (+) 1.0x10-22 m 0.002 J or 1.24x1016 eV 1.0x1022 m Galactic Halo(Group) Scale 9. CosmicRayKnee (-) 6.3x10-22 m 0.3 mJ or 2.0x1015 eV 1.6x1021 m Galactic Disc(Halo) Scale 10.CosmicRay 1.4x10-20 m 0.002 mJ or 1.4x1013 eV 7.1x1019 m Galactic Core Scale
Lower Cosmic Ray energies then become defined in standard physics, such as supernovae, neutron stars and related phenomena, engaging electron accelerations and synchrotron radiation.

7. represents the ECosmic-Boson aka superstring class IIA as a D-brane attached open string dual to the (selfdual) monopole string class IIB and where the D-Brane or Dirichlet-Coupling in both cases becomes the 'intermediary' heterotic (closed loop) superstring HO(32).
It is the HO(32) superstring, which as a bosonic full-quantum spin superstring bifurcates into the subsequently emerging quark-lepton families as the K-L-Boson split into Proto-DiNeutronic Ylemic NeutronMatter.
The Ylem then manifests the massless Higgs Bosonic precursor as a scalar 'Neutron-Boson' (10), which then becomes massinductive under utility of the Equivalence Principle of General Relativity, relating gravitational mass to inertial mass.

It are supersymmetric double neutrons which bifurcate into the observed mass content in the universe and not a decoupling matter-antimatter symmetry.
The primordial neutron beta-decay so manifests the nucleon-lepton distinction in the decoupling of the strongweak nuclear interaction, mediated by the electromagnetic alpha-interaction hitherto unified with the omega-gravitational interaction. This primordial ylem radioactivity manifests the bosonic string class IIB as a monopolic masscurrent as a D-brane interaction in modular duality to the transformation of the selfdual magnetic monopole to the bi-dual electromagnetic cosmic rays at the ECosmic energy level.
The monopole class is chiral (selfdual) and the Ecosmic class is nonchiral (bi-dual); from this derives the nonparity of the spacial symmetry aka the CP-Violation of the weak nuclear interaction, related to neutrinoflux as monopolic superconductive currentflows.

As the heterotic classes are all 'closed looped', the elementary particles of the standard models emerge from the HE(64) class coupled to the HO(32) class in the inflationary string epoch.

8. depicts the Weyl-Boson of the Big Bang Planck-singularity of the Weyl-Geodesic of relativistic spacetime as the final 'octonionised' string class HE(8x8).

9. modulates the experimentally well measured 'knee' energy for Cosmic Rays as the distribution flux of high-energy protons as the primary particle in the 2π-factor. The wormhole radius is 10-22 m/2π for a Halo-(DarkMatter)-Radius of 2πx1022 metres.

10. is the massless ancestor of the Higgs-template and defined through the Weyl-String-Eigenenergy E* = kT* = hf*= m*c2 = 1/e* = 1/2Re c2.
The scale of (10) emerges from the holographic principle as 2π2R*3.f*2 = e* for R*=h/(2πm'c)=1.41188..x10-20 m for a Compton Energy of E' = m'c2 = 2.2545..x10-6 J or 14.03 TeV, which serendipitously is the maxium energy regime for which the LHC is designed.

The Experimental Evidence for the Superstrings is observed indeed every day in the laboratories of the astrophysics around the globe.

Last edited: Apr 3, 2018

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The X-Boson is modular dual to the L-Boson in the string class transformation from the Planck brane to the monopole brane to the X/L-brane to the Cosmic String brane to the Weyl brane.
For the X-Boson, the coupling can be written as: : #.(mps/mPlanck)f(G) and for the L-Boson it is written as: #54.(mPlanck/mps)f(S) to indicate the inherent modular duality.
As alpha=#3 specifies the emmr-matter-emr interaction probability; EMI/SNI=#3/#=#2 breaks the unified symmetry via the WNI and defines #f(G) as a unitary mass.

A 'mixing angle' θps is defined via constant X ⇒ {ℵ}3 ⇒ alpha α as X = ϖ(n). sin θps for a unitary force action ϖ(n) acting on the inflaton acceleration cfps modulated from the inflaton source hyper-acceleration of the de Broglie matter wave for phase speed RHfps in RHfps2=1.43790791x1087 (m/s2)* in the displacement lightpath for the nodal Hubble constant Ho = dn/dt = c/RH defining the frequency ratio
nps = λps/RH = 2πrps/RH =fps/Ho as the linearization of the wormhole from its closed Planck brane form as string class I into its trasformation as open string class HE(8x8) then manifesting as the Compton-de Broglie wavelengths in the emr-matter-emmr interactions.

The Hubble law so modulates the inflaton as the instanton in a dimensionless cycle time parameter n in a timerate change constant as the nodal Hubble constant H(n)|min = Ho = 58.04 km/Mpc/s and in inverse proportion to its maximum as the wormhole frequency fps, becoming the maximum node for H(n) in the associated mulktiverse cosmology, which defines this multiverse as parallel in timespace, but as holofractally nested in spacetime. It is then a quantum tunneling of the entire universe upon the completion of interwoven cycles defining the nodal oscillations in particular nodal 'walls of time' defined in the lightpath, which become the medium for this quantum tunneling of spacetime itself.

The inflaton angle θps so is maximised at 90° at X = ϖ(n). sin θps for θps = 38.17270761° for a unitary force ϖ(n)=1 and for the X/L bosonic coupling for a GUT scale characterising SEW.G for the decouupling of he gravitational interaction from the unified energy field described by the Standard Model.
Now the Planck string for a Planck time of tP=2πrP/c = 4.377x10-43 is connected to the X/L string via the monopole string at the unified SEWG level in the selfduality of the GUT-monopole at [ec.c2]uimd = 2.7x1016 GeV* and at a brane inflaton time of tM=2πrM/c=1.537x10-40 s* and for which SEWG transformed into sEwG to indicate the unified nature between the longrange EMI and GI in a coupling of the electromagnetic and gravitational fine structures here termed alpha and g-alpha respectively.

The X/L boson time is tXL=2πrXL/c=2.202x10-39 and string class HO(32) decouples gravity in replacing f(G)/mPlanck by the monopole mass #2/[ec]uimd modular dual to f(S)mPlanck
to account for the SNI/EMI breaking of the native super-symmetry SEWG and to transform the Planck brane energy scale into the X/L brane energy scale.

mXB = alpha.mps/[ec]uimd = #3.mps/[ec]uimd = 3.364554269x10-12 kg* = 1.884955575x1015 GeV* unifying SEW in the monopolar electron boson energy mec|max = αmps

mLB = alpha18.[ec]uimd/#2.mps =#52.[ec]uimd/#2.mps = 1.982105788x10-28 kg* = 111.0453587 MeV* unifying EWG at the bosonic muon energy

Last edited: Apr 4, 2018