# A Revision of the Friedmann Cosmology

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

1. ### adminWell-Known MemberStaff Member

Messages:
3,047
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: Mar 14, 2018
2. ### adminWell-Known MemberStaff Member

Messages:
3,047
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/eomo and the inverse of the product between electric permittivity eo=1/120cp and magnetic permeability mo=120p/c for 'free space' impedance:
Zo= electric field strength E/magnetic field strength H = √(mo/eo) = cmo = 1/ceo = 120p}.

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

e* = 2Rec2 = 2ke2/me = e2/2peome = ahc/pme
for the calibration {Reme} = (2.8179403267x10-15 m)(9.10938356x10-31 kg) = [2.566969656x10-45].[1.001671358][1.003753127].(1.00543065) (mkg)* = 2.580701985x10-45 {mkg}* = (2.77777..x10-15 m*)(9.290527148x10-31 kg*) for an adjusted classical electron radius Re = 2.83324358x10-15 m for the quantum mechanical electron.
The electron has no known substructure.[1][75] and it is assumed to be a point particle with a point charge and no spatial extent.[9] In classical physics, the angular momentum and magnetic moment of an object depend upon its physical dimensions. Hence, the concept of a dimensionless electron possessing these properties contrasts to experimental observations in Penning traps which point to finite non-zero radius of the electron. A possible explanation of this paradoxical situation is given below in the "Virtual particles" subsection by taking into consideration the Foldy-Wouthuysen transformation.

The issue of the radius of the electron is a challenging problem of the modern theoretical physics. The admission of the hypothesis of a finite radius of the electron is incompatible to the premises of the theory of relativity. On the other hand, a point-like electron (zero radius) generates serious mathematical difficulties due to the self-energy of the electron tending to infinity.[76] These aspects have been analyzed in detail by Dmitri Ivanenko and Arseny Sokolov.

Observation of a single electron in a Penning trap shows the upper limit of the particle's radius is 10−22 meters.[77] Also an upper bound of electron radius of 10−18 meters[78] can be derived using the uncertainty relation in energy.

There is also a physical constant called the "classical electron radius", with the much larger value of 2.8179×10−15 m, greater than the radius of the proton. However, the terminology comes from a simplistic calculation that ignores the effects of quantum mechanics; in reality, the so-called classical electron radius has little to do with the true fundamental structure of the electron.[79][note 5]
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.

Richard Feynman, one of the originators and early developers of the theory of quantum electrodynamics (QED), referred to the fine-structure constant in these terms:

There is a most profound and beautiful question associated with the observed coupling constant, e – the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!

— Richard Feynman, Richard P. Feynman (1985). QED: The Strange Theory of Light and Matter. Princeton University Press. p. 129. ISBN 0-691-08388-6.
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.

3. ### adminWell-Known MemberStaff Member

Messages:
3,047
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:

N=Minimum Radius/Maximum Radius = λps/RHubble =λps/Rmax = nps

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)

This leads to the quadratic (in B2):

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: Mar 14, 2018
4. ### adminWell-Known MemberStaff Member

Messages:
3,047
The Self-interaction of the Electron as a function of its Quantum Mechanical Mass
Electromagnetic Mass in the Compton constant, Quantum Geometry and the Yukawa Potential

http://www.feynmanlectures.caltech.edu/II_28.html

Abstract:
Despite the experimental success of the quantum theory and the extension of classical physics in quantum field theory and relativity in special and general application; a synthesis between the classical approach based on Euclidean and Riemannian geometries with that of 'modern' theoretical physics based on statistical energy and frequency distributions remains to be a field of active research for the global theoretical and experimental physics community.
In this paper a particular attempt for unification shall be indicated in the proposal of a third kind of relativity in a geometric form of quantum relativity, which utilizes the string modular duality of a higher dimensional energy spectrum based on a physics of wormholes directly related to a cosmogony preceding the cosmologies of the thermodynamic universe from inflaton to instanton.
In this way, the quantum theory of the microcosm of the outer and inner atom becomes subject to conformal transformations to and from the instanton of a quantum big bang or qbb and therefore enabling a description of the macrocosm of general relativity in terms of the modular T-duality of 11-dimensional superbrane theory.

Using the linked Feynman lecture at caltech as a background for the quantum relative approach; this paper shall focus on the way the classical electron with a stipulated electromagnetic mass as a function of its spacial extent exposes the difficulty encountered by quantum field theories to model nature as mathematical points without spacial extent.

In particular, a classical size of the proton can be found in an approximation ½Re.X = Rp and where the factor X represents the symmetry equilibrium for a B=(v/c} velocity ratio distribution for the effective electron restmass me proportional to the spacial extent of the electron.
For the symmetry equilibrium, the electric potential energy and the magnetic action energy are related for a electron velocity of ve = 0.78615138.c and a reduced classical electron radius given by
rec = λps{X/4α2π2} = 4.140931406x10-22 m* and where rps = λps/2π represents the limiting boundary or minimum size of the electron at the quantum big bang instanton.
For the proton then, its 'charge distribution' radius becomes averaged as Rproton = 0.85838052x10-15 m* as a reduced classical electron radius and for a speed for the self-interactive or quantum relativistic electron of 2.96026005x10-13 c. This quantum relativistic speed reaches its v/c = 1- limit at the instanton boundary and defines a minimum quantum relativistic speed for the electron at ve = 1.50506548x10-18 c for its electrostatic potential, where Ue=∫{q²/8πεor²}dr = q²/8πεoRe = ½mec2 for a classical velocity of ve=0 in a non-interacting magnetic field B=0.
2Ue = mec2 so implies a halving of the classical electron radius to obtain the electron mass me = 2Ue/c2 and infers an oscillating nature for the electron size to allow a synergy between classical physics and of quantum mechanics.

The Heisenberg Uncertainty principle relating energy with time and displacement with momentum in the expression ΔE.Δt = Δx.Δp ≥ h/4π applied to the quantum mechanical scale of de Broglie wave matter λdB = h/mv and the Compton mass-photon interaction Δx = rcompton = h/2πcm shows a natural limit for the measurement of position in Δp = Δmv ≥ h/4πΔx = ½mc.

When Δp exceeds mc , then ΔE exceeds mc in the Energy-Momentum relation E2 = (pc)2 + (mc2)2 and we can apply this natural limitation on measurement to the position of the electrostatic electron mass in
a variabel classical electron radius as rec = αh/2πcm = αrcompton = {μoe2c/2h}.{h/2πcmec} = μoe2/4πmec and rendering the Compton mass-photon interaction modified in the electromagnetic finestructure constant α to relate the inverse proportionality between the electron's restmass to its spacial extent in:

meRe = constant = αh/2πc = mecrec [Eq.1]

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 self-induction L=NBA/i is:
Um=½Li²=½(μo.N2R)(BR/μoN)²=½B²V/μo 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=½εo say via the Maxwell equations and Gauss' law. So for integrating a spherical surface charge distribution dV=4πr².dr from Re to ∞:

Ue=∫{q²/8πεor²}dr = q²/8πεoRe = ½mec2

2Ue = mec2 so implies a halving of the classical electron radius to obtain the electron mass me = 2Ue/c2 and infers an oscillating nature for the electron size to allow a synergy between classical physics and of quantum mechanics.
The Heisenberg Uncertainty principle relating energy with time and displacement with momentum in the expression ΔE.Δt = Δx.Δp ≥ h/4π applied to the quantum mechanical scale of de Broglie wave matter λdB = h/mv and the Compton mass-photon interaction Δx = rcompton = h/2πcm shows a natural limit for the measurement of position in Δp = Δmv ≥ h/4πΔx = ½mc.

When Δp exceeds mc , then ΔE exceeds mc in the Energy-Momentum relation E2 = (pc)2 + (mc2)2 and we can apply this natural limitation on measurement to the position of the electrostatic electron mass in
a variabel classical electron radius as rec = αh/2πcm = αrcompton = {μoe2c/2h}.{h/2πcmec} = μoe2/4πmec and rendering the Compton mass-photon interaction modified in the electromagnetic finestructure constant α to relate the inverse proportionality between the electron's restmass to its spacial extent in:

meRe = constant = αh/2πc = mecrec [Eq.1]

In particular, a classical size of the proton can be found in an approximation ½Re.X = Rp and where the factor X represents the symmetry equilibrium for a B=(v/c} velocity ratio distribution for the effective electron restmass me proportional to the spacial extent of the electron.
For the symmetry equilibrium, the electric potential energy and the magnetic action energy are related for a electron velocity of ve = 0.78615138.c and a reduced classical electron radius given by
rec = λps{X/4α2π2} = 4.140931406x10-22 m* and where rps = λps/2π represents the limiting boundary or minimum size of the electron at the quantum big bang instanton.
For the proton then, its 'charge distribution' radius becomes averaged as Rproton = 0.85838052x10-15 m* as a reduced classical electron radius and for a speed for the self-interactive or quantum relativistic electron of 2.96026005x10-13 c. This quantum relativistic speed reaches its v/c = 1- limit at the instanton boundary and defines a minimum quantum relativistic speed for the electron at ve = 1.50506548x10-18 c for its electrostatic potential, where Ue=∫{q²/8πεor²}dr = q²/8πεoRe = ½mec2 for a classical velocity of ve=0 in a non-interacting magnetic field B=0.

Considering the surface charge distribution of the electron's electric potential to also exhibit a self-interactive term applying to a spacial distribution of the electron mass in its quantum relativistic volume, then this part can be defined as the self-interaction of a purely electromagnetic part of the electron's electrodynamic energy.

Then for a constant charge density in the electron's volume; ρ=3q/(4πr3) and q=4πρr3/3 with dq/dr = 4πρr2dr

The electrostatic potential for this charge distribution V(r) = q/4πεor
then contains an energy dU = qdq/(4πεor) for U(r) =∫{16π2ρ2r5/12πεor} dr = (4πρ2/3εo)∫r4dr = ⅗.e²/4πεoRe = ⅗.μoe²c2/4πRe = ⅗.mec2 for a electron restmass me=2Ue/c2 reduced by 40%.

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 = ½mev2

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 electron mass and so differing it from an actual 'bare' restmass mo.
The 'bare' restmass mo of the electron can be said to be somewhat unphysical, as the electron cannot be at rest relative to its environment and as a consequence of its quantum nature as an effect of the Planck oscillator EPo = ½hfo , which in this paper will be associated with a Weyl frequency self state fo = fweyl = fps and applicable to the so termed Quantum Big Bang or qbb.

We shall so show that the 'bare' electron mass mo can be modified to an initial ground state for the electron at an energy

f{alpha α} = {4π2α2 - 8π2α3 + 1 - α }/{4π2α3 + α}
[Eq.1]
δps = δqbb = {1 - α}/α - {4π2α2}/{4π2α2+1}

and descriptive for an electron moving with speed ve = 0.17 c in an electric potential of eV.

In the SI measurement system Planck's constant h = 6.62607004x10-34 Js and the speed of light is c = 2.99792458x10-8 m/s and the electron charge is e=1.60217662x10-19 C for a bare electron mass of 9.10938356x10-31 kg.
In a mensuration system in which c would be precisely 3x108 (m/s)*; the following conversions between the SI-system and the *-system are applied in this paper.

Furthermore, there exists one fundamental constant in the magnetic permeability constant uo = 4πx10-7 H/m which becomes numerically equal in the Maxwell constant μo = 1/εoc2 in an applied fine structure μoo = {120π/c}.{1/120πc} = 1/c2 (s/m)2; (s/m)2*. Subsequently in the calculation of alpha, the speed conversion must be incorporated for unitary consistency.
Alpha remains constant for a cosmology descriptive of a non-accelerating cosmology; but will result in a change in the electric charge quantum in a cosmology, which measures an accelerated spacial expansion, which can however be the result of a self-intersection of the light path for particular cosmological redshift intervals in an oscillating cosmology.
Here a particular alpha variation reduces the SI-measurement for the square of the charge quantum e in a factor of (1.6021119x10-19/1.60217662x10-19)2 = 0.99991921...for the calibration

Alpha α = μoce2/2h = 2π.(2.99792458)(1.6021119)2x10-37/(6.62607004x10-34) = 60πe2/h = 7.2967696x10-3 = 1/137.047072

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*}​

Applying this alpha to the bare electron mass calculates its effective restmass in [Eq.1] as: me = (9.10938356x10-31)( 1.003695584) kg = 9.14304805x10-31 kg {9.17736306x10-31 kg*}
}now define the electric electromagnetic mass and the magnetic electromagnetic mass as:

melectric = kq²/2Rec² = kq²/e*= q²/8πεoRe c2 = 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/Re = e²/4πεoRe = 2e²/8πεoRe = 2KE and where for a single hydrogen electron:
RBohr = h2/πmee2μoc2 = Re2 = RCompton/α = hα/2πmec for a electromagetic fine structure constant alpha = α = e2/2εohc = μoce2/2h

mmagnetic = μoe²[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 electron mass m=mo/√(1-B2)=moγ = for B2=(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 group velocities v<c.

So we introduce the relativistic restmass mo = hf/c2 and set Constant Amooe²/8πRe for AB2=1/√[1-B2] -1
from: c2(m-mo)=μoe²v²/8πRe = moc2(1/√[1-B2] - 1) = mov2A with m=mo/√(1-[v/c]2)

This leads to the quadratic (in B2): 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:

B2=([A-2]±√[A²+4A])/2A={(½-1/A)±√(¼+1/A)} and A = {-1 ± 1/√(1-B2)}/B2 solving the quadratic (2AB2+2-A)2 = A2 + 4A

This defines a distribution of B2=(v/c)² and B=v/c velocity ratios in mo.AB2oe²[v/c]2/8πRe

mmagneticoe²[v/c]²/8πRe=mo.AB2=½me.(v/c)²

then fine structures 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 pre-quantum algorithmic associations, based on the magnetic constant defining the Classical Electronic Radius.
As B≥0 for all velocities v, bounded as group speed (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:
A = μoe²/8πmoRe = ½me/mo for a distributed rest-mass mo = me/2A

melectric = kq²/2Rec² = μoe2/8πRe = Ue/c² = ½me for A=½ and its maximum for A=∞ is the unity v=c for B=1

The classical rest-mass mo of the electron and as a function of its velocity from v=0 to v=c so is itself distributed in its magnetic mass potential about its effective restmass meoe2/4πRec2 and as a function of the classical electron radius.
Its minimum condition is defined by the electric potential energy in mo=½me for a value of A=½ with effective restmass me being the restmass for a stationary electron v=0 without magnetic inertia component.
For v=c; the mass of the electron assumes a purely relativistic magnetic monopolic value for which mo=0 and the effective restmass me assumes the minimum rest energy for the electron at A=1 and generalised as me=2Amo.
The classical restmass mo=hf/c2 so decreases from its maximum value as mo=me to mo=0 as a function of the velocity distribution and in the extension of the classical force to incorporate the restmass differential d(mo) = hd(f)/c2 by FNewton = Fa + Fα = F-acceleration + F-alpha as the sum of the classical Newtonian linear momentum change and the quantum mechanical angular acceleration momentum change in the self-interaction for the electron.

The extension of Newton's Law in relativistic momentum and energy leads to:

dprel/dt = d(moγv)/dt = mod(γv)/dt + γvd(mo)/dt = mod(γv)/dt + {γvh/c2}df/dt = moγ3.dv/dt + {γvh/c2}df/dt = Fa + Fα.

The Self-interaction of the Electron as a function of its quantum mechanical mass

The product me.Re = Compton constant = hα/2πc = α.lplanck.mplanck
A changing electron size re changes the electron restmass mo in proportionality re ∝ 1/mo and where mo= mec = me as the electromagnetic quantum mass for re= Re = Rcompton/α.
The boundary relativistic electron mass so becomes the Compton wormhole mass of the Quantum Big Bang α.mps=α.hfps/c2

The classical electron's acceleration a=Fa/m from its relativistic force Frel =d(prel)/dt for a constant restmass mo a is supplemented by a quantum acceleration α from its quantum mechanical Compton mass mecompton = mec = hα/2πcre and where the classical restmass mo changes as mecc2 = (hvre/c2).γ.(df/dt).

The frequency differential over time is maximized in {df/dt}|max = {(fps - fss)/fss} = fps2 - 1 as the maximum entropy frequency permutation eigenstate fps2 = 9x1060 for its minimum state fss2 = 1/fps2 by modular string T-duality fps.fss = 1 of super-membrane EpsEss and wormhole frequency fWeyl = fps.
In units of angular acceleration, df/dt so relates Planck's constant h and the Planck action in dE/dt = hdf/dt and the Heisenberg Uncertainty principle in dE.dt = h.df.dt in this string T-duality of the frequency selfstates fps|max and fss|min. and for the mass eigen frequency quantum fss = mssc2/h by brane coupling constants Eps.Ess = h2 and Eps/Ess = fps2 .

(1) Energy E=hf=mc2 (The Combined Planck-Einstein Law)
(2) E=hf iff m=0 (The Planck Quantum Law E=hf for light speed invariance c=λf)
(3) E=mc2 iff f=fo=fss (The Einstein Law E=mc2 for the light speed upper limit)

(1) Whenever there is mass (M=Minertial=Mgravitational) occupying space; this mass can be assigned either as a photonic mass {by the Energy-Momentum relation of Special Relativity: E2=Eo2+(pc)2} by the photonic momentum p=h/λ=hf/c} OR a 'rest mass' mo=m/√[1-(v/c)2] for 'rest energy' Eo=moc2.

The 'total' energy for the occupied space so contains a 'variable' mass in the 'combined' law; but allows particularisation for electromagnetic radiation (always moving at the Maxwell light speed constant c in Planck's Law and for the 'Newtonian' mass M in the Einstein Law.

(2) If M=0, then the Einstein Law is suppressed in favour of the Planck Law and the space contained energy E is photonic, i.e. electromagnetic, always dynamically described by the constancy of light speed c.

(3) If M>0, then there exists a mass-eigen frequency fss=fo=Ess/h=mssc2/h, which quantizes all mass agglomerations m=Σmss in the mass quantum mss=Ess/c2.

Letting rec be the oscillating classical electron radius rec from its maximum value Re = μoe2/4πme = αh/2πcme to its minimum qbb value rpsps/2π from the de Broglie wave matter wavelength λe = h/mec = c/fe = hc/Ee = hc/mec2 ; the eletron's energy for its quantum mechanical self-interaction part can be stated as:

h∑f frequency energy states = hfe = mecc2 = (hvrec/c2).γ.(df/dt) = {vγ}{rec.hfps2/c2} = {vγ}{hrecps2} for the maximum frequency summation at rec=rps

for v/√(1-[v/c]2) = mecc2λps2/hrec = αcλps2/2πrec2 using mecrec = constant = hα/2πc = meRe
and v2/{1-[v/c]2} = {αcλps2/2πrec2}2 = Ø2 solving for v2{1+Ø2/c2} = Ø2 with (v/c}2 = Ø2/(c22) = 1/{1+[c/Ø]2}

The quantum relativistic mechanical electron's velocity distribution for a variable classical electron radius Re in the proportional Compton restmass mec and rec generalised in the wave matter constancy of de Broglie for the quantum relativistic part of restmass mo=hf/c2 and a purely self-interacting electromagnetic monoplic part as electromagnetic monopolar radiation (emmr) so is:

Juju's Electron Equation: 31|31 applied for the maximum integrated quantum energy state: {melectric + mmagnetic + memmr}c2 = Eweyl = hfweyl = Eqbb = mpsc2 = 1/e*

{vec/c}2 = 1/{1 + 4π2rec42λps4} [Eq.7]

This formulation sets an upper and lower bound for velectron in the electron radius in the interval: 〈 Re|max ......... Rec|min = λps/2π = rps = rWeyl = rwormhole = rqbb

For 〈 Re.me = hα/2πc 〉|max , the maximised classical electron radius Re minimises the speed of the electron in:
me=hα/2πcRe = ke2/Rec2 = μoe2/4πRe for {ve/c} = 1/√{1+Re4/4π2α2rps4} = 1/√{1+(2π.1010/360)4/4π2α2} = 1.50506548x10-18
and as the speed of the quantum mechanical electron at rest in the classical frame vec = 1.50506548x10-18 c = 0.45151964 (nano metres per second)*.

The inversion speed of light is vec = 1/c =3.3333... nano metres per second* in modular brane duality to define an impedance 'bubble' characterising astrophysical 'Hill spheres' for orbital equilibrium conditions for satellites and moons in a Radius of Hill Impedance/Hubble Time as RHI=Ho/c as inversion displacement, which for a Universal Age of 19.12 Gy as Hubble time for a nodal Hubble constant oscillating between fps and Ho=c/RH = 58.04 (km/Mpc.s)* for RH=1.59767545x1026 m* and becomes RHI = 19.12 Gy/c = 2.011229x109 m* and encompassing a 'planetary bubbe radius' to approximately 5% to both the neighbouring planets Venus and Mars.

This represents a magnetic mass mm = μoe2(vec/c)2/4πRe = me(vec/c)2 = (2.265221x10-36)me = 2.1045107x10-66 kg* for the alpha-energy Eαω = mmc2 = hfαω= 1.8940596x10-49 J* for a total frequency integral of fαω = 2.84108945x10-16 = ∑fss = ∑mssc2/h = fαω/fss = 8.52326834x1014 frequency self states and mss=hfss/c2 by the time instanton fpsfss=1.
The classical electron restmass mo=me so is reduced to the magnetic mass mm in the factor {ve/c}2.

{melectric + mmagnetic}c2 = me{1+{vec/c}2}c2 = mtotalc2

---------------------------------------​

For 〈 Rec.mec = hα/2πc 〉|min ,
{v/c} = 1/√{1+1/4π2α2} = 0.04579881 in units * as conformal mapping of the wormhole radius of the electron onto its classical representation in the proportion 1010 = 360Re/2πrps in a correlation between circular measure in linearized radians and angular degrees.

This represents a magnetic mass mm = μoe2(vec/c)2/4πrec = Reme(vec/c)2/Rec = mec(vec/c)2 = (2.09753100x10-3)mec = 3.4011525x10-25 kg and a magnetic mass manifesting at the atomic scale at 3.06100x10-8 J* or 190.5433 GeV* for a wavelength of λm = h/mmc = 6.53382x10-18 m* for a total electron mass mec/√{1-(vec/c)2 } = αmps = 1.621502875x10-22 kg* as the Weyl mass having replaced the classical relativistic electron restmass mo by the quantum dynamic Compton restmass mec.
αmps{vec/c}2 = mm and so the Compton encompassing mass mec is reduced to the magnetic mass in the factor {vec/c}2 characterising the mass-radius relationship for all electrons.

{melectric + mmagnetic}c2 = mec{1+{vec/c}2}c2 = mtotalc2

-----------------------------------

The speed of the quantum mechanical electron of mass mec= αmps kg*, so is maximised in its minimum radius of the wormhole as 0.045799 c or 13,739,643.01 (m/s)* and limits the classical relativistic electron speed in:
mec/√{1-(vec/c)2 } = αmps = 1.621502875x10-22 kg* = me/√{1-(ve/c)2} for {ve/c}2 = 1 - {me/αmps}2

Classical electron mass/quantum mechanical electron mass = √{1-[ve/c]2}/√{1-[vec/c]2} = me/mec
ve|max = √{1 - (5.72957797x10-9)2} c = √{1 - 3.28280637x10-17} c ~ {1 - 1.64140319x10-17} c = c-

and as the self-energy Eec=mecc2 = αmpsc2 = αEps = α/e* J* for the Weyl electron of the quantum big bang (qbb) or instanton following the inflaton of the string epoch.

This energy manifests in the 'physical consciousness awareness quantum' αω=df/dt in the maximised frequency entropy state in a brane volumar
Vbrane.(df/dt)|max = 2π2Rrmp3.fps2 = e* =1/Eps = 2Rec2 in a restmass photonic or 'dark matter' radius Rrmp = ∛{e*/2π2fps2} = 1.411884763x10-20 m* for the nuclear electron at

mfermi = h/2πcRrmp= 2.50500365x10-23 kg* or 14.034015 TeV*. (This is near the maximum energy potential of the Large Hadron Collider or LHC in Geneva, Switzerland).

For the Compton electron e*/α = 2Rec2/α = 2Rcomptonc2 ; Rrmp = ∛{e*/2απ2fps2} = 7.279292496x10-20 m* for the Compton electron at an energy of
mcompton = h/2πcRrmp= 4.85868164x10-24 kg* or 2.722024 TeV*

For the Bohr electron e*/α2 = 2Rec22 = 2Rbohrc2 ; Rrmp = ∛{e*/2α2π2fps2} = 3.75300456x10-19 m* for the atomic Bohr electron at an energy of
mcompton = h/2πcRrmp= 9.4238534x10-25 kg* or 527.9613 GeV*

The classical electromagnetic rest-mass memr=me becomes quantum mechanical in the string-brane sourcesink energy E*-Gauge photon quantum of the Quantum Big Bang Weylian wormhole.

E* = Eps = hfps = hc/λps = mpsc2 = (me/2e).√[2πGo/αhc] = {me/mP}/{2e√α} = 1/2Rec2 = 1/e*

Monopolic charge quantum e*/c2 = 2Re ⇐ supermembrane displacement transformation ⇒ √α.lplanck = e/c2 as Electropolic charge quantum

me = 2e√α.mplanck/2Rec2 = lplanck√α.√α.mplanck/Re = α.lplanck.mplanck/Re
= {e/c2}{√(2πke2/hc}{√(hc/2πGo)}/Re ={√(Goh/2πc3)}{2πke2/hc}{√(hc/2πGo)}/Re = {h/2πc}{2πke2/hc}/Re
= {ke2/c2}/Re = {μoe2}/4πRe

The product me.Re = Compton constant = hα/2πc = α.lplanck.mplanck
A changing electron size re changes the electron restmass mo in proportionality re ∝ 1/mo and where mo= me for re= Re = Rcompton/α = Rbohr2
The boundary relativistic electron mass so becomes the Compton wormhole mass of the Quantum Big Bang α.mps= α.hfps/c2

For the wormhole limit re = rps = λps/2π = Re |minimum in unified string Planck-Stoney units
me = αmps = αhfps/c2 = αh/cλps = α/e*c2 = α/2Rec4 = hα/2πcrps = {60πhe2/2πhcrps} = 30e2/crps = 1.62150288x10-22 kg = meγ = me/√{1 - [v/c]2}
for velectron = c-; [v/c]2 = 1-3.2828...x10-17 for v={1-½(3.2828x10-17)} c ~ c

The pre-Big Bang 'bounce' of many models in cosmology can be found in a direct link to the Planck-Stoney scale of the 'Grand-Unification-Theories'.
In particular it can be shown, that the Squareroot of Alpha, the electromagnetic fine structure constant, multiplied by the Planck-length results in a Stoney-transformation factor
LP√α = e/c2 in a unitary coupling between the quantum gravitational and electromagnetic fine structures and so couples the unitary measurement of displacement in the Planck-Length oscillation equal to Coulombic charge quantum 'e' divided by the square of the speed of light 'c2' in a proportionality of Displacement = ChargexMass/Energy.
This couples the electric Coulomb charge quantum to the magnetic monopole quantum e* as the inverse of the 10-dimensional superstring sourcesink energy Eps to the 10-dimensional superstring sinksource energy Ess as the 11-dimensional super-membrane EpsEss.

{Gok=1 for Go=4πεo and representing a conformal mapping of the Planck length onto the scale of the 'classical electron' in superposing the lower dimensional inertia coupled electric charge quantum 'e' onto a higher dimensional quantum gravitational-D-brane magnetopole coupled magnetic charge quantum 'e*' = 2Re.c2 = 1/hfps = 1/EWeyl wormhole by the application of the mirror/T duality of the super membrane EpsEss of heterotic string class HE(8x8)}.

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) = ℮

The classical approach described in the Feynman lecture derives the momentum of a moving electron in deriving the volume element for electromagnetic momentum p=melectromagnetic.v.=memr.v with the component of the electron's motion v parallel gsinθ and a relativistic velocity vrel=vγ=v/√{1-[v/c]2} modifying prel=pγ

Electromagnetic Mass - Distribution for the Rest Energy of the Electrodynamic Electron

 A B2 x root y root velocity v velocity vec = 1/{1 + 4π2rec4/α2λps4} rec /Re rec Um/c2 = ½me(v/c)2 mo δ=½{1+∪) ∪=(mo/me-1)/B2 mo=Δm =me-mo ½hfe/c2 memr = mo Δme=me-mo =mo=½hfe/c2 Minimum Planck Oscillator Symmetry 205,068.8 ½±½ 2.26522x10-36 1 0 mec=me mm=xme 1.5051x10-18 c ∞ Re 0.42265 ½ 3/2±3/2 0.0 -3 mec=½me 0 c 1.5051x10-18 c ∞ Re 0.0 1me ½{1+(1-1)/B2}= ½+0 = ½ 0me memr = me μoe2/4πRe 0me ½hfe=0mec2 1me||0me ----½||½---- 2.09753x10-3 0.0458 c 0.0458 c 5.72958x10-9 ¾ Mean: ½{½+1} -⅚±√(19/12) 0.42497 -2.09164 mec=⅔me 0.6519 c 0.6519 c 1.32316x10-9 ½mo [½-δ]me(v/c)2 = ⅙me ⅔me ½{1+(⅔-1)/B2}= ½(1-⅓(c/v)2)=0.1078177 ⅓me memr = ⅔me μoe2/6πRe ⅓me ½hfe=⅓mec2 ⅔me||⅓me ----½||½---- 1 -½±½√(5) 0.61803 -1.61803 mec=me 0.7862 c 0.7862 c 1.08775x10-9 ½mo [½-δ]me(v/c)2 = ¼me ½me ½{1+(½-1)/B2}= ½(1-⅓(c/v)2)=0.0954915 ½me memr = ½me μoe2/8πRe ½me ½hfe=½mec2 ½me||½me ----½||½---- 2 0±½√(3) 0.86603 -0.86603 mec=¼me 0.9306 c 7.69397x10-10 ½mo [½-δ]me(v/c)2 = [3/8]me ¼me ½{1+(¼-1)/B2}= ½(1-¾(c/v)2)=0.0669873 ¾me memr = ¼me μoe2/16πRe ¾me ½hfe=¾mec2 ¼me||¾me ----½||½---- 3 ⅙±√(7/12) 0.93043 -0.59710 0.9646 c 6.41523x10-10 ½mo [½-δ]me(v/c)2 = [7/12]me ⅙me ½{1+(⅙-1)/B2}= ½(1-⅚(c/v)2)=0.0521780 ⅚me memr = ⅙me μoe2/24πRe ⅚me ½hfe=⅚mec2 ⅙me||⅚me ----½||½---- 4 ¼±√(½) 0.95711 -0.45711 0.9783 c ½mo [½-δ]me(v/c)2 = [7/16]me ⅛me ½{1+(⅛-1)/B2}= ½(1-⅞(c/v)2)=0.0428932 ⅞me memr = ⅛me μoe2/32πRe ⅞me ½hfe=⅞mec2 ⅛me||⅞me ----½||½---- 205,068.8 ½±½ 1- 0- 1.5051x10-18 c 1.7048x1032 ½±½ 1- 0- 0.04579881 c rps/Re= 5.7295797x10-9 ∞ ½-±½+ 1- 0- c ½mo [½-δ]me(v/c)2 = ½me 0me ½{1+(0-1)/B2}= ½(1-1(c/v)2) = 0 1me memr = 0me 0 1me ½hfe=mec2 0me||1me ----½||½----

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=∞: B2-±½+ for roots x=1- and y=0-; for v=c with Um = (½v2oe2/8πRe = (½v2oe2/4πRe = ½mec2 = mmagneticc2 = melectricc2 and mo = 0me

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

The Binomial Identity gives the limit of A=½ in: A=½ - B2{3/8 - 5B2/16 + 35B4/128 -...} and as the non-relativistic low velocity approximation of E=mc² as KE=½mov².

Letting B2=n, we obtain the Feynman-Summation or Path-Integral for dimensionless cycle time 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 Wave Matter of de Broglie: λdeBroglie = h/p

The Wave matter of de Broglie from the Energy-Momentum Relation is applied in a (a) nonrelativistic, a (b) relativistic and a (c) superluminal form​
in the matter wavelength: λdeBroglie = h/p = hc/pc for (pc) = √{E2 - Eo2}= moc2.√{[v/c]2/(1-[v/c]2)}​

(a) Example:
A pellet of 10g moves at 10 m/s for a de Broglie wavelength vdB = h/mv = h/0.1 = 6.7x10-33 m*​
This matter wavelength requires diffraction interference pattern of the order of λdB to be observable and subject to measurement​

(b) Example:
An electron, moving at 80% of light speed 'c' requires relativistic development​

Eo = moc2 with E = mc2 = moc2/√{1-[v/c]2}, a 66.66% increase in the electron's energy describing the Kinetic Energy E - Eo = {m - mo}c2
for a relativistic momentum p = moc.√{[0.8]2/(1-[0.8]2)} = (1.333..) moc = h/λdeBroglie and for a relativistic de Broglie wavelength, 60% smaller, than for the non-relativistic electron in​
λdeBroglie = h/1.333..moc < h/0.8moc =λdeBroglie (1.83x10-12 m relativistic and 3.05x10-12 m* non-relativistic for an electron 'restmass' of 9.11x10-31 kg* and measurable in diffraction interference patterns with apertures comparable to this wave matter scale).​

(c) The de Broglie matter wave speed in its 'group integrated' form derives from the postulates of Special Relativity and is defined in the invariance of light speed 'c' as a classical upper boundary for the acceleration of any mass M.​
In its 'phase-individuated' form, the de Broglie matter wave is 'hyper accelerated' or tachyonic, the de Broglie wave speed being lower bounded by light speed 'c'​

vphase = wavelength.frequency = (h/mvgroup)(mc2/h) = c2/vgroup > c for all vgroup < c​

m = Energy/c2 = hf/c2 = hc/λdeBrogliec2 = h/λdeBrogliec = mdeBroglie = [Action as Charge2]mod/c(Planck-Length Oscillation)​
= [e2]mod/clPlanck√alpha = [e2c2/ce]mod = [ec]modular

as monopole mass of GUT-string IIB and as string displacement current mass equivalent for the classical electron displacement 2Re = e*/c2 = [ec]modular as Wormhole minimum spacetime configuration for the Big Bang Instanton of Big Bang wormhole energy quantum Eps=hfps=mpsc2=kTps as a function of e*=1/Eps of Heterotic superstring class HE 8x8 and relating the Classical Electron Diameter {2Re} as Monopole Mass [ec]mod in Curvature Radius rpsps/2π = Gomps/c2.​

The factor 2Go/c2 multiplied by the factor 4π becomes Einstein's Constant k = 8πGo/c2 = 3.102776531x10-26 m/kg describing how spacetime curvature relates to the mass embedded in that spacetime in the theory of General Relativity.​

The selfduality of the superstring IIB aka the Magnetic Monopole selfstate in GUT Unification 2Re/30[ec]mod = 2Rec2/30[ec3]mod = e*/30[ec3]modκ for a proportionality constant {κ*}=2Re/30k[ec]mod = 2Re.c2/8πe = e*/8πe =1.2384..x1020 kg*/m* in string units for Star Charge in Star Colomb C*/Electro Charge in Coulomb C unified.​

The monopolar Grand Unification (SEWG gravitational decoupling SEW.G) has a Planck string energy reduced at the IIB string level of​
e*=[ec3]modular for mpsc2c/[ec]modular = [c3]modular = 2.7x1025 electron volt or 4.3362x106 J for a monopole mass [ec]modular = mmonopole = 4.818x10-11 kg* .​

Mass M = n.mss = Σmss = n.{h/2πrdeBrogliec} .[Ess.e*]mod = n.mps.[Ess.{9x1060}.2π2Rrmp3]mod = n.mps.[Ess.{2Re.c2}]mod = n.[Eps.Ess]mod.[2Re]mod
for λdeBroglieps=h/mpsc and [Eps.e*]mod =1​

{2Rec2} = 4GoMHyper for the classical electron radius Re=ke2/mec2 and describes its Hyper-Mass MHyper-electron = Rec2/2Go = ke2/2Gome = 1.125x1012 kg* for an effective electron mass of me = ke2/2Go(1.125x1012) =9.290527148x10-31 kg* in string units and where k=1/4πεo = 9x109 (Nm2/C2)*.​

The curvature radius for the electron mass me = relectronc2/2Go then becomes relectron = 2Gome/c2 = 2.293957...x10-57 m* in string-membrane inflaton space as 1.44133588x10-34 rps in the wormhole instanton space.​

Re/rinflaton-electron = MHyper-electron/me = 1.2109108..x1042 = ½(EMI/GI) = ½(e2/Go2me2) =½ {e/Gome}2 = ½(2.421821677x1042 ) for the classical electron radius Re halved from the classical electron diameter 2Re from the definition for the modulated supermembrane coupled in EpsEss=h2 and Eps/Ess=fps2=1/fss2.​

Mass M = n.mss = Σmss = n.{mps} .[Ess.e*]mod = n.{mps}[{hfss}{fps/fss}.2π2Rrmp3]mod = n.mps.[Eps.e*/fss2]mod = n.mps/|fss2|mod

The classical approach described in the Feynman lecture derives the momentum of a moving electron in deriving the volume element for electromagnetic momentum p=melectromagnetic.v.=memr.v with the component of the electron's motion v parallel gsinθ and a relativistic velocity vrel=vγ=v/√{1-[v/c]2} modifying prel=pγ

For magnetic field B = vxE/c2 = v.E.sinθ/c2 the momentum density εoExB = εov.E2sinθ/c2 electric energy density Ue=½εoE2 and E=q/(4πεor2) and dV = 2πr2.sinθ.dθ.dr for the spacetime interval from some minimum boundary a to ∞ and with ∫1/r2 dr = |-1/r|[∞,a] = 0- + 1/a = 1/a for a=Re for the waved particle electron

p = ∫εov(Esinθ/c)2 dV = prel = {2πεovγ/c2}{q2/16π2εo2}∫r-2.{sin3 θ.dθ}.dr = {vγq2/8πεoc2}∫r-2.{sin3 θ.dθ}.dr
= {vγq2/8π.a.εoc2}∫sin3 θ.dθ = {vγq2/8π.a.εoc2}∫{1-cos2θ}sinθ.dθ
= {vγq2/8π.a.εoc2}|⅓cos3θ -cosθ|[π,0] = {vγq2/8π.a.εoc2} |-⅓+1-⅓+1| = vγq2/6π.a.εoc2 = μovγe2/6π.Re
prel = μovγe2/6π.Re for memr = μoγe2/6π.Re = {4/3}½me = ⅔me > ½me

The electromagnetic mass must however be exactly Ue/c2 by the postulates of Relativity and so the classical derivation must be modified in the particle nature of the electron in its associated quantum mechanical nature.

Using memr = mo = me/2A = μoγe2/6π.Re = {4/3}½me = ⅔me defines A=¾ in the (v/c)2 distribution and for a velocity:

B2={v/c}2 = -⅚±√(19/12) for roots x=0.425 and y=-2.092; with velectron = 0.65189908 c in Um = (½v2oe2/4πRe = ½mev2

{4/3}.Ue/c2 = {4/3}γe2/8π.εoRe c2 = {4/3}½me = {4/3}.Um/c2 = {4/3}.μoγe2/8π.Re = {4/3}γke2/e* = {4/3}γke2.hf* = (1-⅓)me for ⅓me=hf/c2 and f=⅓mec2/h as the frequency supplement from the alpha force of the self-interacting electron moving with velocity 0.6518991 c with apparent restmass ⅔me.

The classical electromagnetic mass memr becomes quantum mechanical in the string-brane sourcesink energy E*-Gauge photon quantum of the Quantum Big Bang Weylian wormhole. In particular setting the classical electron radius at Re = 2/3c2 = 7.407407...x10-18 m* (7.3950476435...x10-18 m) from 2Rec2 = 4/3 normalizes the {4/3} factor from the classical derivation of the electromagnetic mass for the electron.

E* = Eps = hfps = hc/λps = mpsc2 = (me/2e).√[2πGo/αhc] = {me/mP}/{2e√α} = 1/2Rec2 = 1/e*

The pre-Big Bang 'bounce' of many models in cosmology can be found in a direct link to the Planck-Stoney scale of the 'Grand-Unification-Theories'.
In particular it can be shown, that the Squareroot of Alpha, the electromagnetic fine structure constant, multiplied by the Planck-length results in a Stoney-transformation factor
LP√α = e/c2 in a unitary coupling between the quantum gravitational and electromagnetic fine structures and so couples the unitary measurement of displacement in the Planck-Length oscillation equal to Coulombic charge quantum 'e' divided by the square of the speed of light 'c2' in a proportionality of Displacement = ChargexMass/Energy.
This couples the electric Coulomb charge quantum to the magnetic monopole quantum e* as the inverse of the 10-dimensional superstring sourcesink energy Eps to the 10-dimensional superstring sinksource energy Ess as the 11-dimensional super-membrane EpsEss.

{Gok=1 for Go=4πεo and representing a conformal mapping of the Planck length onto the scale of the 'classical electron' in superposing the lower dimensional inertia coupled electric charge quantum 'e' onto a higher dimensional quantum gravitational-D-brane magnetopole coupled magnetic charge quantum 'e*' = 2Re.c2 = 1/hfps = 1/EWeyl wormhole by the application of the mirror/T duality of the super membrane EpsEss of heterotic string class HE(8x8)}.

The corresponding energy level for this wavelength of Re is 2.7x10-8 Joules* or 168.0718 GeV* (167.6584 GeV) for a mass of 3x10-25 kg* (2.988783x10-8 kg).

Expressing the electromagnetic mass in a series perturbation expansion in decreasing the classical electron size so sets a minimum size for the electron at the Weyl boundary or 'Planck-Stoney Bounce' limit at Re in x/c2 = λps/2π for x = rpsc2 = 2GoMHubble = Wormhole Radius of the Instanton of the quantum gravitational Big Bang creation event.

Modular duality Eps= hfps=1/e* = Energy primary sourcesink quantum as the Weyl wormhole energy then transforms the electron's self- energy in a decomposition or fine structure of the classical electron radius and as 'spacetime awareness' or 'physical consciousness'.
Spacetime awareness |df/dt| acting on a volume of space in a holographic Weyl Bound conformally maps and integrates the quantum gravitational wormhole of wavelength λps=10-22 m* onto the the classical electron radius as: Rwormhole/Relectron = 360/(2π.1010).

This can be defined as a form of angular acceleration |alphaomega = αω| = |df/dt|e = e*/V* = λps/hc.V* acting on space time volumars or multi-dimensional branes in particle-wave interactions of elementary particles-wavicles. It is so the space occupied and containing dynamical interactions, which render the synthesis of classical physics with quantum mechanics possible; the underpinning nature for those interactions being based on the quantum geometry of the conformal transformations from and to the higher dimensional and closed Anti de Sitter (AdS) spacetimes intersecting the lower dimensional and open de Sitter (dS) spacetimes.

memr = μoγe2/6π.Re = {4/3}.Ue/c2 = {4/3}γe2/8π.εoRe c2 = {4/3}½me = {4/3}.Um/c2 = {4/3}.μoγe2/8π.Re = {4/3}γke2/e* = {4/3}γke2.hf*

Multiplying the electromagnetic mass memr by the extent of the Unified Field of Quantum Relativity (UFoQR) divided by the magneto charge quantum e*=1/Eps=2Rec2 gives
8πmemr/e* = 8πμoγe2/6π.e*.Re = {4/3}μoγe2/2(Rec)2= {2/3}μoγe2/(Rec)2 = 3.113285515x10-32 kg*.
The restmass of the electron then can be calculated as a velocity distribution bounded by the speed of light in subtracting the electromagnetic mass from the bounding effective magnetic restmass me with m0 = ½me/A = memr.

{A=½}: mo = me = 9.290527148x10-31 kg* or 9.255788996x10-31 kg
{A=0.50803597}: mo = (0.98418228)me = 9.143572233x10-31 kg* or 9.10938356x10-31 kg
{A=¾}: mo = ⅔me =(0.66666666)me = 6.19368415x10-31 kg* or 6.17052538x10-31 kg
{A=1}: mo = ½me = 4.645263574x10-31 kg* or 4.627894498x10-31 kg

{A=1.58889830}: mo = (0.31468345)me for me{(1- (8π/e*)(0.31468345)} = me - 1.46954915x10-32 kg* = me - Δmemr = 9.143572233x10-31 kg* or 9.10938356x10-31 kg
{A=1}: mo = ½me = memr for me {(1- (8π/e*)(½)} = me - 2.33496415x10-32 kg* = me - Δmemr = 9.05703073x10-31 kg* or 9.02316566x10-31 kg
{A=¾}: mo = ⅔me = memr for me {(1- (8π/e*)(⅔)} = me - 3.1132855x10-32 kg* = me - Δmemr = 8.979190597x10-31 kg* or 8.94561656x10-31 kg
{A=⅔}: mo = ¾me = memr for me {(1- (8π/e*)(¾)} = me - 3.5024462x10-32 kg* = me - Δmemr = 8.94028253x10-31 kg* or 8.90685399x10-31 kg
{A=½}: mo = me = memr = for me{(1 - (8π/e*)} = me - 4.66992829x10-32 kg* = me - Δmemr = 8.82353432x10-31 kg*or 8.79054231x10-31 kg
{A=⅓}: mo = (1.5)me = memr for me {(1- (8π/e*)(1.5)} = me - 7.00489244x10-32 kg* = me - Δmemr = 8.59003791x10-31 kg* or 8.55791896x10-31 kg

The electromagnetic mass must however be exactly Ue/c2 by the postulates of Relativity and so the classical derivation must be modified in the particle nature of the electron in its associated quantum mechanical nature.
A Self-Interaction for the electron in the jerk or time derivative of acceleration d3x/dt3 is naturally found in the definition of the classical size of the electron in the wormhole quantization.
The self-interaction of the electron then can be considered as a deformation of the size of the electron using both the classical scale of the particular and the quantum mechanical form in the nature of its intrinsic quantum spin in the form of an angular acceleration given as the time derivative of frequency df/dt.

The extension of Newton's Law in relativistic momentum and energy leads to dprel/dt = d(moγv)/dt = mod(γv)/dt + γvd(mo)/dt = mod(γv)/dt + {γvh/c2}df/dt = moγ3.dv/dt + {γvh/c2}df/dt.
It then is the dynamical interaction of the electron with spacetime itself, that changes the classical volume of the electron as a function of df/dt in the membrane space of 2Rec2=Volume x Angular radially independent acceleration.

Using this electron self-interaction as a conformal mapping from the Quantum Big Bang 'singularity' from the electric charge in brane bulk space as a magnetic charge onto the classical spacetime of Minkowski and from the Planck parameters onto the atomic-nuclear diameters in 2Rec2 = e* from the Planck length conformally maps the Planck scale onto the classical electron scale as the classical electron radius and as defined in the alpha electromagnetic fine structure and the related mass-charge definition for the eigen energy of the electron in mec2=ke2/Re.

The pre-Big Bang 'bounce' of many models in cosmology can be found in a direct link to the Planck-Stoney scale of the 'Grand-Unification-Theories'. In particular it can be shown, that the Squareroot of Alpha, the electromagnetic fine structure constant, multiplied by the Planck-length results in a Stoney-transformation factor LP√α = e/c2 in a unitary coupling between the quantum gravitational and electromagnetic fine structures {Gok=1 for Go=4πεo and representing a conformal mapping of the Planck length onto the scale of the 'classical electron' in superposing the lower dimensional inertia coupled electric charge quantum 'e' onto a higher dimensional quantum gravitational-D-brane magnetopole coupled magnetic charge quantum 'e*' = 2Re.c2 = 1/hfps = 1/EWeyl wormhole by the application of the mirror/T duality of the super membrane EpsEss of heterotic string class HE(8x8)}.

Also in a model of quantum relativity (QR), there is a quantization of exactly 1010 wormhole 'singularity-bounce' radii defining the radian-trigonometric Pi ratio as Rwormhole/Relectron = 360/2π.1010 or 1010 = {360/2π}{Re/rwormhole} as a characteristic number of microtubules in a conformal mapping from the classical electron space onto the 'consciousness' space of the neuron-cell intermediate between the Hubble scale of 1026 m and the Planck scale of 10-35 m as geometric mean of 10-4 to 10-5 metres.

It is so the geometry of the architecture of the microtubules and the nature of their construction utilizing the pentagonal quasi-crystalline pattern in its application for maximising the compression of information in the Fibonacci geometrical pattern-sequencing. This then results in the conformal mapping of this geometry as a quantum geometry and defining physical consciousness as a conformal mapping of the quantum of spacetime in the form of Weylian 'Quantum Big Bang' wormholes of the cosmogenesis.
The 4/3 factor from the classically derived electromagnetic mass appears in the quantum geometry of the subatomic particles, namely in the different quark content for the positively charged proton and the electrically overall neutral neutron, both displaying an internal charge distribution however.

For the Proton, one adds one (K-IR-Transition energy) and subtracts the electron-mass for the d-quark level and for the Neutron one doubles this to reflect the up-down-quark differential.
An electron perturbation subtracts one 2-2/3=4/3 electron energy as the difference between 2 leptonic rings from the proton's 2 up-quarks and 2-1/3=5/3 electron energy from the neutron' singular up-quark to relate the trisected nucleonic quark geometric template. This is revisited below.

Proton mp=u.d.u=K.KIR.K=(939.776+1.5013-0.5205-0.1735) MeV* = 940.5833 MeV* (938.270 MeV).
Neutron mn=d.u.d=KIR.K.KIR=(939.776+3.0026-1.0410+0.1735) MeV* = 941.9111 MeV* (939.594 MeV).

This is the groundstate from the Higgs-Restmass-Induction-Mechanismand reflects the quarkian geometry as being responsible for the inertial mass differential between the two elementary nucleons. All groundstate elementary particle masses are computed from the Higgs-Scale and then become subject to various fine structures.

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.

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*}​

The electron has no known substructure.[1][75] and it is assumed to be a point particle with a point charge and no spatial extent.[9] In classical physics, the angular momentum and magnetic moment of an object depend upon its physical dimensions. Hence, the concept of a dimensionless electron possessing these properties contrasts to experimental observations in Penning traps which point to finite non-zero radius of the electron. A possible explanation of this paradoxical situation is given below in the "Virtual particles" subsection by taking into consideration the Foldy-Wouthuysen transformation.​

The issue of the radius of the electron is a challenging problem of the modern theoretical physics. The admission of the hypothesis of a finite radius of the electron is incompatible to the premises of the theory of relativity. On the other hand, a point-like electron (zero radius) generates serious mathematical difficulties due to the self-energy of the electron tending to infinity.[76] These aspects have been analyzed in detail by Dmitri Ivanenko and Arseny Sokolov.​

Observation of a single electron in a Penning trap shows the upper limit of the particle's radius is 10−22 meters.[77] Also an upper bound of electron radius of 10−18 meters[78] can be derived using the uncertainty relation in energy.​

There is also a physical constant called the "classical electron radius", with the much larger value of 2.8179×10−15 m, greater than the radius of the proton. However, the terminology comes from a simplistic calculation that ignores the effects of quantum mechanics; in reality, the so-called classical electron radius has little to do with the true fundamental structure of the electron.[79][note 5]

Note that the defined maximum scale for the electron in the Penning Trap is consistent with the defined size of the wormhole radius rps=10-22/2π metres as minimum spacetime configuration of the Instanton. The 'point particular' electron of Quantum ElectroDynamics and its point-like particle fields, so crystallizes naturally from the theory of the string-membrane classes. The classical electron radius Re has much to do with the quantum mechanical electron addressed by Richard Feynman in the linked lecture.

From the Feynman Lecture:
There is, however, one fundamental objection to this theory and to all the other theories we have described. All particles we know obey the laws of quantum mechanics, so a quantum-mechanical modification of electrodynamics has to be made. Light behaves like photons. It isn’t 100 percent like the Maxwell theory. So the electrodynamic theory has to be changed. We have already mentioned that it might be a waste of time to work so hard to straighten out the classical theory, because it could turn out that in quantum electrodynamics the difficulties will disappear or may be resolved in some other fashion. But the difficulties do not disappear in quantum electrodynamics. That is one of the reasons that people have spent so much effort trying to straighten out the classical difficulties, hoping that if they could straighten out the classical difficulty and then make the quantum modifications, everything would be straightened out. The Maxwell theory still has the difficulties after the quantum mechanics modifications are made.

The quantum effects do make some changes—the formula for the mass is modified, and Planck’s constant h/2π appears—but the answer still comes out infinite unless you cut off an integration somehow—just as we had to stop the classical integrals at r=a. And the answers depend on how you stop the integrals. We cannot, unfortunately, demonstrate for you here that the difficulties are really basically the same, because we have developed so little of the theory of quantum mechanics and even less of quantum electrodynamics. So you must just take our word that the quantized theory of Maxwell’s electrodynamics gives an infinite mass for a point electron.​

It turns out, however, that nobody has ever succeeded in making a self-consistent quantum theory out of any of the modified theories. Born and Infeld’s ideas have never been satisfactorily made into a quantum theory. The theories with the advanced and retarded waves of Dirac, or of Wheeler and Feynman, have never been made into a satisfactory quantum theory. The theory of Bopp has never been made into a satisfactory quantum theory. So today, there is no known solution to this problem. We do not know how to make a consistent theory—including the quantum mechanics—which does not produce an infinity for the self-energy of an electron, or any point charge. And at the same time, there is no satisfactory theory that describes a non-point charge. It’s an unsolved problem.​

In case you are deciding to rush off to make a theory in which the action of an electron on itself is completely removed, so that electromagnetic mass is no longer meaningful, and then to make a quantum theory of it, you should be warned that you are certain to be in trouble. There is definite experimental evidence of the existence of electromagnetic inertia—there is evidence that some of the mass of charged particles is electromagnetic in origin.​

It used to be said in the older books that since Nature will obviously not present us with two particles—one neutral and the other charged, but otherwise the same—we will never be able to tell how much of the mass is electromagnetic and how much is mechanical. But it turns out that Nature has been kind enough to present us with just such objects, so that by comparing the observed mass of the charged one with the observed mass of the neutral one, we can tell whether there is any electromagnetic mass. For example, there are the neutrons and protons. They interact with tremendous forces—the nuclear forces—whose origin is unknown. However, as we have already described, the nuclear forces have one remarkable property. So far as they are concerned, the neutron and proton are exactly the same.​

The nuclear forces between neutron and neutron, neutron and proton, and proton and proton are all identical as far as we can tell. Only the little electromagnetic forces are different; electrically the proton and neutron are as different as night and day. This is just what we wanted. There are two particles, identical from the point of view of the strong interactions, but different electrically. And they have a small difference in mass. The mass difference between the proton and the neutron—expressed as the difference in the rest-energy mc2 in units of MeV—is about 1.3 MeV, which is about 2.6 times the electron mass. The classical theory would then predict a radius of about ½ to ⅓ the classical electron radius, or about 10-13 cm. Of course, one should really use the quantum theory, but by some strange accident, all the constants—2π’s and h/2π’s, etc.—come out so that the quantum theory gives roughly the same radius as the classical theory.​

The only trouble is that the sign is wrong! The neutron is heavier than the proton.​

Nature has also given us several other pairs—or triplets—of particles which appear to be exactly the same except for their electrical charge. They interact with protons and neutrons, through the so-called “strong” interactions of the nuclear forces. In such interactions, the particles of a given kind—say the π-mesons—behave in every way like one object except for their electrical charge. In Table 28–1 we give a list of such particles, together with their measured masses. The charged π-mesons—positive or negative—have a mass of 136.9 MeV, but the neutral πo-meson is 4.6 MeV lighter. We believe that this mass difference is electromagnetic; it would correspond to a particle radius of 3 to 4x10-14 cm. You will see from the table that the mass differences of the other particles are usually of the same general size.​

Now the size of these particles can be determined by other methods, for instance by the diameters they appear to have in high-energy collisions. So the electromagnetic mass seems to be in general agreement with electromagnetic theory, if we stop our integrals of the field energy at the same radius obtained by these other methods. That’s why we believe that the differences do represent electromagnetic mass.
You are no doubt worried about the different signs of the mass differences in the table. It is easy to see why the charged ones should be heavier than the neutral ones. But what about those pairs like the proton and the neutron, where the measured mass comes out the other way? Well, it turns out that these particles are complicated, and the computation of the electromagnetic mass must be more elaborate for them. For instance, although the neutron has no net charge, it does have a charge distribution inside it—it is only the net charge that is zero. In fact, we believe that the neutron looks—at least sometimes—like a proton with a negative π-meson in a “cloud” around it, as shown in Fig. 28–5. Although the neutron is “neutral,” because its total charge is zero, there are still electromagnetic energies (for example, it has a magnetic moment), so it’s not easy to tell the sign of the electromagnetic mass difference without a detailed theory of the internal structure.​

The negatively charged pion cloud of Feynman and Yukawa can be substituted by the inner negatively charged mesonic Inner Ring in the quantum geometry of the quarks based on colour charged or chromodynamic double charged kernels surrounded by an Inner Mesonic and an outer Leptonic Ring wave structure asymptotically confined by a magneto charged region known as the classical radius of the electron. The rings are oppositely charged to the kernel quarks. They however remain coupled in the kernel trisection say as the protons udu=K.KIR.K=K(K+IR)K or the neutron's dud=KIR.K.KIR=(IR+K)K(K+IR) except when they experience the electro-weak decays.

There actually exist three uds-quark states which decay differently via strong, electromagnetic and weak decay rates in the uds (Sigmao Resonance); usd (Sigmao) and the sud (Lambdao) in increasing stability.
This quantum geometry then indicates the behaviour of the triple-uds decay from first principles, whereas the contemporary standard model does not, considering the u-d-s quark eigenstates to be quantum geometrically undifferentiated.
The nuclear interactions, both strong and weak are confined in a ' Magnetic Asymptotic Confinement Limit coinciding with the Classical Electron Radius Re=ke²/mec² and in a scale of so 3 Fermi or 2.8x10-15 meters. At a distance further away from this scale, the nuclear interaction strength vanishes rapidly.

Subtracting the Ring-VPE (3L) gives the basic nucleonic K-State as 939.776 MeV*. This excludes the electronic perturbation of the IR-OR oscillation.

For the Proton, one adds one (K-IR-Transition energy) and subtracts the electron-mass for the d-quark level and for the Neutron one doubles this to reflect the up-down-quark differential.
An electron perturbation subtracts one 2-2/3=4/3 electron energy as the difference between 2 leptonic rings from the proton's 2 up-quarks and 2-1/3=5/3 electron energy from the neutron' singular up-quark to relate the trisected nucleonic quark geometric template.

Proton mp=u.d.u=K.KIR.K=(939.776+1.5013-0.5205-0.1735) MeV* = 940.5833 MeV* (938.270 MeV).
Neutron mn=d.u.d=KIR.K.KIR=(939.776+3.0026-1.0410+0.1735) MeV* = 941.9111 MeV* (939.594 MeV).

This is the groundstate from the Higgs-Restmass-Induction-Mechanismand reflects the quarkian geometry as being responsible for the inertial mass differential between the two elementary nucleons. All groundstate elementary particle masses are computed from the Higgs-Scale and then become subject to various fine structures.

{1} Matter interacts with antimatter based Neutrinos in Majorana-Dirac Electron Capture

An Electron in the inner atomic nucleus is captured by a proton to create a neutron accompanied by an electron neutrino. This requires a u-quark of the proton to transform into a d-quark of the neutron. As the d-quark is a KIR quark of inner mesonic ring of electro charge [+2/3] coupled to the MIR of electro charge [-1], a W- weakon must be engaged to couple to a left handed proton via the nonparity of the weak nuclear interaction. However in electron capture a left handed electron neutrino is emitted, requiring the interaction of a W+ weakon as the kernel gauge for any such right handed antimatter weak decay.
So should the interacting electron initiate electron capture then a W- becomes the bosonic partner for the interaction; but if it is the interacting proton, then a W+ should become the weak interaction agent to neutralize its positive electric charge with the negative electric charge of the interacting electron.
The interaction of matter and anti-matter in the form of the weak interaction bosons and their associated anti-neutrinos and neutrinos can however be shown to result from a basic kernel-ring interaction of the anti-neutrinos and neutrinos as both Majorana particles and as Dirac particles.
Majorana particles are their own anti-particles allowing identification of right handed anti-neutrinos as left handed neutrinos in the base templated or massless self-state.
Dirac particles distinguish right handed anti-neutrinos from left handed neutrinos due their mass and inertia in their native oscillation potential.

For a left handed proton u[-½]d[+½]u[-½] and a left handed electron e-[-½], the W- consisting of a right handed electron and a right handed anti-neutrino initiates the KIR-Oscillation from the Anti-Neutrino-Gluon kernel of the up quark in coupling it to the OR part of the W-. The colourless Graviphoton rendering the 'virtuality' of the W- as physically real in neutralizing the bosonic weakon spin, which 'flips' the right handed anti-neutrino into a left handed neutrino observed.

Proton p+[-½] + Electron e-[-½] ⇒ p+[-½] + OR-[-½]* + ({Electron e-[+½] + Antiνelectron[+½]}W- + Graviphoton[-1])
⇒ d[+½]u[-½]{u[-½] + IR-[0]}*{KIR-Oscillation (OR-IR)o[-½]+W-[+1]+GP[-1]} ⇒ d[+½]u[-½]d[-½] + {(OR-IR)o[0] + Antiνelectron[+½]+GP[-1]} ⇒ no[-½] + νelectron[-½]
with the KIR-Oscillation transferring the interacting left handed electron charge -1 without spin in the OR-IR-K for the IR-K up-down quark transformation {+2/3-1=-1/3} and neutralizing the weakon associated intrinsic right handed electron spin as +½-½=0 for the remaining OR-IR transition.
The neutron is cyclically delinearised from spin selfstate d[+½]u[-½]d[-½] into the triplet configuration YCM=CMY=MYC as d[-½]u[+½]d[-½].

A Magneto axis symmetric Proton K(KIR)K transforms into Magneto axis symmetric Neutron KIR(K)KIR as one of the proton's end Kernel up-quarks 'captures' the Weakonic VPE scalar OR- Electron Outer Ring in the Unified Field of Quantum Relativity.

It is in fact a W-, that interacts, but coupling to the left handed electron instead of the left handed proton, the latter requiring some coupling to the W+ weakon in the quantum field to materialize the electron neutrino from the W+ template in a direct fashion and not as the Majorana-Dirac 'flip' initiated by the W- from before.
It is the W+ intrinsic positron which is 'flipped' to 'free' the materialising neutrino from the W+ weakon base state.
But as the resultant Outer Ring - Inner Ring remnant {(OR-IR)+[0]} is positively charged and not charge neutral as was the case for the previous W- weakon interaction; the W+ weakon from the proton is suppressed in electron capture in favour of the W- weakon from the electron.

Proton p+[-½] + Electron e-[-½] ⇒ p+[-½] + IR-[-½] + ({Positron e+[-½] + νelectron[-½]}W+ + Graviphoton[+1])
⇒ d[+½]u[-½]{u[-½] + IR-[0]}*{KIR-Oscillation (OR
-IR)o[-½]+e+[+½]+velectron[-½]} ⇒ d[+½]u[-½]d[-½] + {(OR-IR)+[0]} +νelectron[-½]
⇒ no[+½]+νelectron[-½] + {(OR-IR)+[0]}

The W- then supplies the required KIR for the up-quark to down-quark transmutation with the gauge spin neutralizer of the left handed Graviphoton [-1] flipping the right handed electron anti-neutrino constituent of the W- into its anti-particular form of a left handed electron neutrino as a Majorana self-state transforming into a Dirac self-state.

Electron capture so displays the Majorana nature of the two base neutrinos of the electron-positron and muon-antimuon definition in their massless gauge nature when engaged in the direct interaction or 'tapping' of the UFoQR in the Vortex-Potential-Energy or VPE/ZPE in R2G2B2[+½]+B2G2R2[-½] = BY2B[0]=GM2G[0]=RC2R[0] = VPE[0].
Anti-Neutrino template R2G2B2[+½] = W2[+½] = B2G2R2[-½] as Neutrino template in E=hf radiative 'White'-eigen energy and being indifferentiated between the particle and anti-particular energy eigen state under the application of the spin symmetry of the 'flipping' 'white' Graviphoton.
The Dirac nature of the base neutrinos then can be said to apply to all (anti)neutrinos carrying mass in their oscillation potential and properties exhibited in their wave mechanical dynamics manifested in the Anti-Neutrino template R2G2B2[+½] being the anti-state for the Neutrino template B2G2R2[-½] and without or following the Graviphoton 'flip'.

{2} Matter interacts with matter based Anti-Neutrinos via superposed VPE-Weakon Action

Protons transform into neutrons with antimatter positrons and where the interacting anti-neutrino as constituent part of the W- weakon induces Pair-Production for weakon's electron in tapping the VPE to manifest a like spinning positron to neutralize the boson spin of the Graviphoton. The spin of the Graviphoton so cancels the spin of the Pair-Production VPE as well as the spin of the weakon boson in a superposition of the VPE and the weak interaction.

A up quark of the proton then changes into a down quark for the produced neutron in a double transition from the Outer Ring of the weakon's electron transiting to the Inner Ring and the original anti-neutrino transits from the Inner Ring onto the Gluon-Neutrino kernel K as the decay products of a free neutron. The right handed spin quantum of the anti-neutrino cancels the left handed quantum spin of the weakon's electron base which was flipped by the Graviphoton for the MIR oscillation between the up quark and the down quark transformation.

{Mass produced photons (by acceleration of inertia coupled electro charges), have no magneto charge and so form their own anti-particles; whilst gauge or 'virtual' photons carry cyclic and anticyclic colour charges as consequence of the matter-antimatter asymmetry}.

Proton p+[-½] + Antiνelectron[+½] ⇒ p+[-½] + {Antiνelectron[+½] + (Electron e-[+½]}W- + Positron e+[+½]VPEo[+1] + Graviphoton[-1]
⇒ p+[-½] + {Electron e-[-½] + Antiνelectron[+½]} + Positron e+[+½] ⇒ {p+[-½]+IR-[0]+Ko[-½+½]} + e+[+½] ⇒ no[-½] + e+[+½]

{3} Matter interacts with antimatter based Neutrinos via Unified Weakon Action {OR-+Antiν=W-;ν+Anti-OR+=W+}

Neutrons transform into protons with muons, the latter decaying into electrons and anti-neutrinos and neutrinos, so reducing the elementary matter-neutrino interaction to basic neutron beta-minus-decay with the leptonic coupling between the 'resonance electron' as a basic muon coupled to its neutrino. A neutron's down quark transforming into a up quark in disassociating the mesonic Inner Ring part of the down quark from its up quark kernel part to become the leptonic Outer Ring part of the manifesting muon. The interacting muon neutrino couples with the anti-neutrino of the weakon template as its own anti particle transferring its mass to the muon and changing its self-state from mass defined Diracness to massless Majorananess in the process.

Neutron no[-½] + νmuon[-½] ⇒ no[-½] + νmuon[-½] + ({Antiνmuon[+½] + (Muon μ-[+½]}W- +GP[-1])
⇒ d[-½]u[+½]d[-½] + *{KIROR-Oscillation (OR-IR-K)[+½] +Antiνmuon[+½]+νmuon[-½] + GP[-1]}
⇒ d[-½]u[+½]u[-½] + IR-[0] + {OR-[+½]+GP[-1]} +{R2G2B2[-½]+B2G2R2[+½]} ⇒ p+[-½] + μ-[-½] + VPE[0]
⇒ p+[-½] + μ-[-½] +VPE[0] ⇒ p+[-½] + *{KIROR-Oscillation (OR-IR-K)[-½]}({e-[+½] + Antiνelectron[+½]}W- + GP[-1])
⇒ p+[-½] + νmuon[-½] + e-[-½] + Antiνelectron[+½]

In the muon beta decay, the KIROR oscillation transfers the spin of the interacting muon as the spin of its self-state neutrino and enabling the constituents of the matter weakon W- to manifest with the right handed electron part flipping to manifest the left handed electron of the beta decay.

mνHiggs=meλw.rE/(2πrMRe){1/rG-1/rF} ~ 9.3x10-38 kg or 0.052 eV for a scalar blueprint AntiνHiggs = R4G4B4[0] with anti-state νHiggs = B4G4R4[0]
and coupling as the Tauon (Anti) Neutrino as
Antiνtauon = R2G2B2[+½] + R4G4B4[0] = R6G6B6[+½] = Antiνelectron + AntiνHiggs and
νtauon = B2G2R2[-½] + B4G4R4[0] = B6G6R6[-½] = νelectron + νHiggs

For a differential equation for Potential Energy: ∇2∅ - {μr}2 = 0

2∅ - {r/Re}2 = 0 = (1/r).∂2/∂r2{r∅} - {r/Re}2.∅
2/∂r2{r∅} = {r/Re}2.(r∅) for a solution
r∅ = constant.exp[-r/Re] for the Yukawa Potential with μ = 1/Re = 4πεomec2/e2 = 4πmeoe2

∅ = constant.(1/r).exp[-r/Re] ⇒ mec2 = (μoe2c2/4πR).exp[-R/Re] for R/Re = exp[-R/Re]

f(R/Re) = R/Re - exp[-R/Re] = f(x) = x - exp[-x] = 0 with derivative f'(R/Re) = f'(x) = 1 + exp(-x)
and xk+1 = xk - f(x)/f'(x) for a Newton-Raphson solution xo =½ for

x1 = ½ - (-0.10653066)/(1.6065307) = 0.56631100;
x2 = 0.56631100 - (-0.00130508243)/(1.56761552) = 0.56714353
x3 = 0.56714353 - (0.00000037547)/(1.56714316) = 0.56714330... for R = 0.5671433 Re

For the potential energy of the electron with effective mass me = μoe2/4πR, the Yukawa potential for the nucleus reduces the classical electron radius to 0.5671433 Re, which is approximates the radius of the proton as ½Re.

From the Feynman Lecture:
This function is called the Yukawa potential. For an attractive force, K is a negative number whose magnitude must be adjusted to fit the experimentally observed strength of the forces.
The Yukawa potential of the nuclear forces dies off more rapidly than 1/r by the exponential factor. The potential—and therefore the force—falls to zero much more rapidly than 1/r for distances beyond 1/μ, as shown in Fig. 28–6. The “range” of nuclear forces is much less than the “range” of electrostatic forces. It is found experimentally that the nuclear forces do not extend beyond about 10−13 cm, so μ]≈1015 m−1.​

Fig. 28–6.The Yukawa potential e−μr/r, compared with the Coulomb potential 1/r.

Last edited: Mar 24, 2018
5. ### adminWell-Known MemberStaff Member

Messages:
3,047
The monopolar self-interaction of the quantum relativistic classical electron

Electromagnetic Mass in the Compton constant, Quantum Relativistic Geometry and the Yukawa Potential

http://www.feynmanlectures.caltech.edu/II_28.html

Abstract:
Despite the experimental success of the quantum theory and the extension of classical physics in quantum field theory and relativity in special and general application; a synthesis between the classical approach based on Euclidean and Riemann geometries with that of 'modern' theoretical physics based on statistical energy and frequency distributions remains to be a field of active research for the global theoretical and experimental physics community.
In this paper a particular attempt for unification shall be indicated in the proposal of a third kind of relativity in a geometric form of quantum relativity, which utilizes the string modular duality of a higher dimensional energy spectrum based on a physics of wormholes directly related to a cosmogony preceding the cosmologies of the thermodynamic universe from inflaton to instanton.
In this way, the quantum theory of the microcosm of the outer and inner atom becomes subject to conformal transformations to and from the instanton of a quantum big bang or qbb and therefore enabling a description of the macrocosm of general relativity in terms of the modular T-duality of 11-dimensional supermembrane theory and so incorporating quantum gravity as a geometrical effect of energy transformations at the wormhole scale.

Using the linked Feynman lecture at caltech as a background for the quantum relative approach; this paper shall focus on the way the classical electron with a stipulated electromagnetic mass as a function of its spacial extent exposes the difficulty encountered by quantum field theories to model nature as mathematical point-particles without spacial extent.

In particular, a classical size for the proton can be found in an approximation ½Re.X = Rp for a classical electron radius Re and where the factor X represents the symmetry equilibrium for a ß = (v/c} = f(A) velocity ratio distribution for the effective electron rest mass me proportional to the spacial extent of the electron and evolving real solutions for the electron parameters from a quasi-complex space solution for its rest mass meo.
Using the ß2 distribution in a unitary interval, then bounded in a function of the electromagnetic fine structure constant alpha; the SI-CODATA value for the rest mass of the electron is derived from first inflaton-based principles in the minimum energy Planck-Oscillator Eo=½hfo in a conformal mapping of the M-Sigma relation applied to the Black Hole Mass to Galactic Bulge ratio for the alpha bound. The M-Sigma ratio so can be considered as a scaling proportion between the interior of a Black Hole mapped holographically and radius-conformally as the internal monopolar volume of the electron as a basic premise of the quantum gravitational approach in quantum relativity and in scaling the Schwarzschild solution onto the electron.

A unification condition in a conformal mapping of the alpha fine-structure α onto X described by X ⇔ α in ℵ(Transformation) = {ℵ}3 : X → α{#}3 → # → #3 → (#2)3 → {(#2)3}3 is applied in this context to indicate the relative interaction strengths of the elementary gauge interactions in proportionality: SNI:EMI:WNI:GI = SEWG = #:#3:#18:#54.

For the symmetry equilibrium, the electric potential energy and the magnetic action energy are related for a electron velocity of veX = 0.78615138.c and an effective mass energy of mef = γme = mecf = 1.503238892x10-30 kg*. This mass-velocity relationship is supplemented by the Compton constant as: meRe = Compton constant = αh/2πc = lplanck.α.mplanck = mecrec , which proportionalises the quantum relativistic size of the electron with its mass.
Subsequently then for an electron speed veX and for rec = αh/2πmecf = 5.150283117x10-7 m* as a largely increased self-relative classical electron radius given by the Compton constant, we calculate a negligible monopolar velocity component in (vps/c)2 = 1/{1+rec4/([2πα]2rps4)} = 1.916797918x10-69 and characteristic for any substantial velocity for the electron.

The analysis then defines a maximum velocity for the electron with a corresponding quantum relative minimum mass in the form of the electron (anti)neutrino in
ve|max = (1 - 3.282806345x10-17) c and m(νe)=m(ντ)2 = 0.00297104794 eV* (0.002963740541 eV) respectively. At this energy then, no coupling between the electron and its antineutrino would be possible and the W- weakon could not exist.
Subsequently, we shall indicate the effect of the Compton constant and of the quantum relativistic monopolar electron to calculate all of the neutrino masses from first principles in setting mν = mneutrino = me.(rneutrino)/Re and where rv naturally applies at the limit of the electron's dynamical self-interaction as indicated, that is the electron's quantum relativistic mass approaches that of the instanton of the qbb.
This leads to: mνElectronc2 = mvTauon2)c2 = mνMuon2Higgs2)c2 = μo{Monopole GUT masses ec}2rps/4πRe2 and where vHiggs is a scalar (anti)neutrino for the mass induction of the (anti)neutrinos in tandem with the mass induction of the scalar Higgs boson in the weak Goldstone interaction.

For the electrostatic electron the ß distribution at A=½, the Compton constant gives mecrec = meRe for ß2 = 0 and at A=1, the Compton constant gives mecrec = ½me.2Re for ß2 = X and as the mean for a unitary interval is ½, the electron radius transforms into the protonic radius containing monopolic charge as internal charge distribution in Rp = ½XRe and proportional to the effective electron restmass me proportional to the spacial extent of the electron.

For the proton then, its 'charge distribution' radius becomes averaged as Rproton = 0.85838052x10-15 m* as a reduced classical electron radius and for a speed of the self-interactive or quantum relativistic electron of vps = 1.576125021x10-17 c. This monopolic quantum relativistic speed reaches its quantum relativistic {v/c = 1-} limit and its maximum QR monopolar speed of 0.0458 c at the instanton boundary and defines a minimum quantum monopolar relativistic speed for the electron at vpse = 1.50506548x10-18 c for its electrostatic potential, where Ue=∫{q²/8πεor²}dr = q²/8πεoRe = ½mec2 for a classical velocity of ve=0 in a non-interacting magnetic field B=0.
2Ue = mec2 so implies a halving of the classical electron radius to obtain the electron mass me = 2Ue/c2 and infers an oscillating nature for the electron size to allow a synergy between classical physics and that of quantum mechanics.

The local geometry related to the Compton radius h/2πm is shown to manifest in a linearization of the Weyl wormhole wavelength λps = λweyl of the qbb in the photon-mass interaction as a quantum gravitational limit proportional to the mass of the electron in rweyl = λweyl/2π = 2GoMc/c2 = h/2πcmps for a curvature mass Mc = hc/4πGomps conformally transforming Mc = 6445.79 kg* into 2.22..x10-20 kg* quantum gravitationally and in a corresponding increase of a sub Planck length linearisation of rcplanck = 2Gomps/c2 = 5.4860785x10-47 m* (star units calibrated to the SI mensuration system) to the wormhole scale of the quantum big bang as a quantum geometric curvature effect.
The qbb results from a Planck scale conformal transformation of fundamental parameters in the inflaton, descriptive of energy transformations between five classes of superstrings culminating in the Weyl-Eps wormhole as the final superstring class of heterotic symmetry 8x8 to manifest the super membrane EpsEss as the wormhole of the 'singularity creation', which is a derivative from a monopolar Planck-Stoney cosmogenesis.

Recircularising the Compton radius into a Compton wavelength in a {photon - gauge photon} interaction labeled as electromagnetic monopolar radiation or {emr - emmr}, then is shown to define the quantum energy of the vacuum per unit volume as a horn toroidal space-time volumar in Vortex-PE = VPEps = ZPEweyl = 4πEpsps3 and completing the encompassing energy spectrum in integrating the electric-, magnetic- and monopolic field properties in {½melectric + ½mmagnetic(v/c)2 + δmmonopolic}c2 = mc2.

The self-interaction of the electron in energy, so crystallizes its monopolar superbrane origin in the addition of a quantum self-relative magnetic energy acting as a 'hidden' electromagnetic monopolar field in the volume of spacetime occupied by the electron as a conformal transformation from the inflaton epoch. A Planck-Stoney 'bounce' of the electronic charge quantum established the interaction potential between charge and mass energy to break an inherent super-symmetry to transform string class I into string class IIB in modular conformal self-duality of the monopole super-membrane. Following this initial transformation relating displacement to electric charge in the magneto charge of the monopole; a heterosis between string classes HO(32) and HE(64) enabled the bosonic superstring to bifurcate into fermionic parts in a quark-lepton hierarchy from the HO(32) superstring to the HE(64) superstring of the instanton of the qbb and who is called the Weyl or wormhole boson Eps in this paper.

We shall also indicate the reason for the measured variation of the fine structure constant by Webb, Carswell and associates; who have measured a variation in alpha dependent on direction.
This variation in alpha is found in the birth of the universe as a 'bounce' or oscillation of the Planck length as a minimum physical displacement and becomes related to the presence of the the factor γ3 in the manifestation of relativistic force as the time rate of change of relativistic momentum prel.
Furthermore, the mass-charge ratio {e/meo} relation of the electron implies that a precision measurement in either the rest mass moe or the charge quantum e, would affect this ratio and this paper shall show how the electromagnetic mass distribution of the electron crystallizes an effective mass me from its restmass resulting in meoγ = meγ2 related to the coupling ratio between the electromagnetic (EMI) and the strong nuclear interaction (SNI), both as a function of alpha and for an asymptotic (not running) SNI constant defined from first principles in an interaction transformation between all of the four fundamental interactions.

Since {1-ß2} describes the ß2 distribution of relativistic velocity in the unitary interval from A=0 to A=1, setting the quantum relativistic mass ratio [moe/me]2 = {1-ß2} equal to a cosmological M-Sigma ratio conformally transformed from the Planck scale, naturally defines a potential oscillatory upper boundary for any displacement in the unit interval of A. An increase or decrease in the 'bare' electron mass, here denoted as moe can then result in a directional measurement variation due to the fluctuating uncertainty in the position of the electron in the unitary interval mirroring the natural absence or presence of an external magnetic field to either decrease or increase the monopolar part of the electron mass in its partitioning: melectric + mmagnetic + δmmonopolic = mec{½+½[v/c]²} + δpsmec = mec with mec2√{1 + v2γ2/c2} = mec2γ = mecc2 for m = mec from the energy-momentum relation E2 = Eo2 + p2c2 of classical and quantum theory.
The cosmic or universal value of alpha so remains constant in all cosmological time frames; with the fluctuation found to depend on a constant #=∛α in a strong interaction constant as a function of alpha.

The Electromagnetic Mass Energy and the [v/c]2 Velocity Ratio Distribution

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 self-induction L=NBA/i is:
Um=½Li²=½(μo.N2R)(BR/μoN)²=½B²V/μo 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=½εo say via the Maxwell equations and Gauss' law. So for integrating a spherical surface charge distribution dV=4πr².dr from Re to ∞:

Ue=∫{q²/8πεor²}dr = q²/8πεoRe = ½mec2

2Ue = mec2 so implies a halving of the classical electron radius to obtain the electron mass me = 2Ue/c2 and infers an oscillating nature for the electron size to allow a synergy between classical physics and of quantum mechanics.
The Heisenberg uncertainty principle relating energy with time and displacement with momentum in the expression ΔE.Δt = Δx.Δp ≥ h/4π applied to the quantum mechanical scale of de Broglie wave matter λdB = h/mv and the Compton mass-photon interaction Δx = rcompton = h/2πcm shows a natural limit for the measurement of position in Δp = Δmv ≥ h/4πΔx = ½mc.

When Δp exceeds mc , then ΔE exceeds mc in the Energy-Momentum relation E2 = (pc)2 + (mc2)2 and we can apply this natural limitation on measurement to the position of the electrostatic electron mass in
a variablel classical electron radius as rec = αh/2πcm = αrcompton = {μoe2c/2h}.{h/2πcmec} = μoe2/4πmec and rendering the Compton mass-photon interaction modified in the electromagnetic finestructure constant α to relate the inverse proportionality between the electron's restmass to its spacial extent in:

meRe = Compton constant = αh/2πc = lplanck.α.mplanck = mecrec ................................................................[Eq.1]

In particular, a classical size for the proton can be found in an approximation ½Re.X = Rp and where the factor X represents the symmetry equilibrium for a B=(v/c} velocity ratio distribution for the effective electron restmass me proportional to the spacial extent of the electron.
For the symmetry equilibrium, the electric potential energy and the magnetic action energy are related for a electron velocity of ve = 0.78615138.c and an effective mass energy of mef = γme = mecf = 1.503238892x10-30 kg* for rec = αh/2πmecf = 5.150283117x10-7 m* as a largely increased classical electron radius given by the Compton constant for a negligible monopolar velocity component in (vps/c)2 = 1/{1+rec4/([2πα]2rps4)} = 1.916797918x10-69 for any substantial velocity for the electron.

For the proton then, its 'charge distribution' radius becomes averaged as Rproton = 0.85838052x10-15 m* as a reduced classical electron radius and for a speed for the self-interactive or quantum relativistic electron of 2.96026005x10-13 c. This quantum relativistic speed reaches its v/c = 1- limit at the instanton boundary and defines a minimum quantum relativistic speed for the electron at ve = 1.50506548x10-18 c for its electrostatic potential, where Ue=∫{q²/8πεor²}dr = q²/8πεoRe = ½mec2 for a classical velocity of ve=0 in a non-interacting magnetic field B=0.

Considering the surface charge distribution of the electron's electric potential to also exhibit a self-interactive term applying to a spacial distribution of the electron mass in its quantum relativistic volume, then this part can be defined as the self-interaction of a purely electromagnetic part of the electron's electro-dynamic energy.

Then for a constant charge density in the electron's volume; ρ=3q/(4πr3) and q=4πρr3/3 with dq/dr = 4πρr2dr

The electrostatic potential for this charge distribution V(r) = q/4πεor
then contains an energy dU = qdq/(4πεor) for U(r) =∫{16π2ρ2r5/12πεor} dr = (4πρ2/3εo)∫r4dr = ⅗.e²/4πεoRe = ⅗.μoe2c2/4πRe = ⅗.mec2 for an electron restmass me = 2Ue/c2 reduced by 40%.
In the linked Feynman lecture; the discrepancy between the electron radius and its electromagnetic mass is found in a factor of U(r) = ¾.mec2 for Ue = μoe2c2/6πRe = ½(1+⅓)mec2 = ⅔mec2 and here reduced by 33⅓%.
Then a question about the cause and origin of the discrepancy in the electrodynamic properties of the electron can be asked. As it seems that the total mass of the electron is somehow distributed between the electric and the magnetic field properties to which should be added a self-interaction effect o account for the differences.

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 ß and the group velocities v<c. To account for the 'missing' mass we simply introduce a 'missing' mass term δme and call it the monopolic self-interaction mass of the electron to write:
melectric + mlmagnetic + δmmonopolic = mec{½+½[v/c]²} + δpsmec = mec with mec2√{1 + v2γ2/c2} = mec2γ = mecc2 for m = mec from the energy-momentum relation E2 = Eo2 + p2c2 of classical and quantum theory.
The aim is to redefine δps = 1/2γ2 in ß2 to relate the mass discrepancy to the monopolic nature of the electron.

δps = ½{1 - {v/c]2} = 1/2γ2 for γ = √(1 - [v/c]2) = √(1 - ß2) .................................................................................. [Eq.2]

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 = ½mev2
mmagnetic = μoe²[v/c]²/8πRe = mec.Aß2 = ½me.(v/c)²

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 electron mass and so differing it from an actual 'bare' restmass mo.

melectric = kq²/2Rec² = kq²/e*= q²/8πεoRe c2 = 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/Re = e²/4πεoRe = 2e²/8πεoRe = 2KE and where for a single hydrogen electron:
RBohr = h2/πmee2μoc2 = Re2 = RCompton/α = hα/2πmec for a electromagnetic fine structure constant alpha = α = e2/2εohc = μoce2/2h

mmagnetic = μoe²[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 electron mass m=mo/√(1-ß2)=moγ = for ß2=(v/c)2

So we introduce a quantum relativistic (QR) monopolar restmass mec = hf/c2, which will be the effective minimum restmass for the electron as twice the restmass of the electron at rest in the electrostasis without interaction from an externally applied field in Maxwell's equations and as a function of the Compton constant.

It is then a monopolar or self-interaction of the electron which effectively doubles its restmass as a magnetic field applied internally and as a charge distribution for a quantum geometric electron in its nature as a 7-dimensional Calabi-Yau manifold or Riemann 3-sphere volumar quantizing 11-dimensional spacetime into Weylian wormholes as compactified horn toroidal Dirichlet branes attached in modular string dualities to a hyperbolic open de Sitter (dS) spacetime, but in mirror duality from a closed spheroidal Anti de Sitter spacetime (AdS) to cancel the curved spacetimes in the Vortex-Potential-Energy per unit volume or wormhole VPE of the Weylian spacetime quanta defined for a monopolar group velocity vps and the Compton parameters in:

Vortex-PE/V = VPEEps = ZPEweyl = 4πEpsps3 = 16π3λpsα2Eps{[c/vps]2 -1}/rec4 = Eps/Vps ................................................[Eq.3]
Vps = (2πrps).(πrps2) = 2π2rps3

The Extension of Newton's Law in Relativistic Momentum and Energy and the Magnetopolar Self-Interaction of the Electron

Newton's law for force, mass and acceleration F = ma can be written in relativistic form as the change of the linear momentum over time and with an associated 'hidden' form of angular momentum change and acceleration in the change of restmass as photonic energy and mass equivalent over time itself:

dprel/dt = d(moγv)/dt = mod(γv)/dt + γvd(mo)/dt =
mod(γv)/dt + {γvh/c2}df/dt = moγ3.dv/dt + {γvh/c2}df/dt = Fa + Fα for γ = 1/√{1 - [v/c]2 } ........................... [Eq.4]

The product me.Re = Compton constant = hα/2πc = α.lplanck.mplanck
A changing electron size re changes the electron restmass mo in proportionality re ∝ 1/mo and where mo= mec = me as the electromagnetic relativistic quantum mass for re = Re = Rcompton/α.
The boundary relativistic electron mass so becomes the Compton wormhole mass of the Quantum Big Bang α.mps = α.hfps/c2

The classical electron's acceleration a = Fa/m from its relativistic force Frel = d(prel)/dt for a constant restmass mo a is supplemented by a quantum acceleration α from its quantum mechanical Compton mass
mecompton = mec = hα/2πcre and where the classical restmass mo changes as mecc2 = (hvre/c2).γ.(df/dt).

The frequency differential over time is maximized in {df/dt}|max = {(fps - fss)/fss} = fps2 - 1 as the maximum entropy frequency permutation eigenstate fps2 = 9x1060 for its minimum state fss2 = 1/fps2 by modular string T-duality fps.fss = 1 of super-membrane EpsEss and wormhole frequency fWeyl = fps.
In units of angular acceleration, df/dt so relates Planck's constant h and the Planck action in dE/dt = hdf/dt and the Heisenberg Uncertainty principle in dE.dt = h.df.dt in this string T-duality of the frequency self-states fps|max and fss|min. and for the mass eigen frequency quantum fss = mssc2/h by brane coupling constants Eps.Ess = h2 and Eps/Ess = fps2 .

(1) Energy E = hf = mc2 (The Combined Planck-Einstein Law)
(2) E = hf iff m = 0 (The Planck Quantum Law E=hf for light speed invariance c=λf)
(3) E = mc2 iff f = fo = fss (The Einstein Law E = mc2 for the light speed upper limit)

(1) Whenever there is mass (M = Minertial = Mgravitational) occupying space; this mass can be assigned either as a photonic mass {by the Energy-Momentum relation of Special Relativity:
E2 = Eo2 + (pc)2} and by the photonic momentum p = h/λ = hf/c} or as a 'rest mass' m o= m/√[1-(v/c)2] for 'rest energy' Eo = moc2.

The 'total' energy for the occupied space so contains a 'variable' mass in the 'combined' law; but allows particularisation for electromagnetic radiation (always moving at the Maxwell light speed constant c in Planck's Law and for the 'Newtonian' mass M in the Einstein Law.

(2) If M=0, then the Einstein Law is suppressed in favour of the Planck Law and the space contained energy E is photonic, i.e. electromagnetic, always dynamically described by the constancy of light speed c.

(3) If M>0, then there exists a mass-eigen frequency fss = fo = Ess/h = mssc2/h, which quantizes all mass agglomerations m = Σmss in the mass quantum mss = Ess/c2.

Letting rec be the oscillating classical electron radius rec from its maximum value Re = μoe2/4πme = αh/2πcme to its minimum qbb value rpsps/2π from the de Broglie wave matter wavelength
λe = h/mec = c/fe = hc/Ee = hc/mec2 ; the electron's energy for its quantum mechanical self-interaction part assigns the photon - mass interaction in the Compton constant in its linearized nature of the QR electron and can be stated as:

h∑f frequency energy states = hfe = mecc2 = (hvrec/c2).γ.(df/dt) = {vγ}{rec.hfps2/c2} = {vγ}{hrecps2} for the maximum frequency summation at rec = rps

for v/√(1-[v/c]2) = mecc2λps2/hrec = αcλps2/2πrec2 using mecrec = constant = hα/2πc = meRe
and v2/{1-[v/c]2} = {αcλps2/2πrec2}2 = Ø2 solving for v2{1+Ø2/c2} = Ø2 with (v/c}2 = Ø2/(c22) = 1/{1+[c/Ø]2}

The quantum relativistic mechanical electron's velocity distribution for a variable classical electron radius Re in the proportional Compton restmass mec and rec generalised in the wave matter constancy of de Broglie for the quantum relativistic part of restmass mo = hf/c2 and a purely self-interacting electromagnetic monopolic part as electromagnetic monopolar radiation (emmr) so is:

"Juju's Electron Equation 31|31:" [/size] applied for the maximum integrated quantum energy state: {melectric + mmagnetic + memmr}c2 = Eweyl = hfweyl = Eqbb = mpsc2 = 1/e*

{vps/c}2 = 1/{1 + 4π2rec42λps4} = 1/{1 + rec4/4π2α2rps4} ............................................................................................ [Eq.5]

δps = ½{1 - {v/c]2} = 1/2γ2 for γ = √(1 - [v/c]2) = √(1 - ß2) ................................................................................................... [Eq.2]

This sets the proportionality between monopolar emmr and electromagnetic emr in the constancy of light speed c:
v2/(1-2δps) = c2 = vps2/{1 + rec4/4π2α2rps4} for the monopolar δps and letting vps = xc as a fractional monopolar velocity colinear with v:

For δps → 0+ as v → c- , ½- of the electron's mass will be magnetic in the external magnetic field B supplementing the remaining half of the electrostasis with a decreasing monopolar compenent as a function of the monopolar velocity of the electron vps.

For δps → ½+ as v → 0 , ½ of the electron's mass will be monopolic in the internal magnetic field in lieu of the absence of an external magnetic field B=0, with the remaining half being the energy of the electrostasis.

δps = ½{1 - [v/xc]2/(1 + [rec4/4π2α2rps4])} ....................................................................... [Eq.6]

Then the upper limit for rec = rps and the qbb wormhole boundary is: δps = ½{1 - [v/xc]2/(1 + 1/4π2α2)} = ½{1 - [v/xc]2(4π2α2)} showing that as [v/c] → 1- ; δps → 0 for ½ of the electron's mass being from the electric field and the other half being from the external magnetic field for increasing velocity v decreasing the monopolic part.

vps|max = xc = 2παc/√(4π2α2+1) = 0.045798805 c as the maximised monopolar magnetic speed for the electron and decreasing to its minimum speed
vps|min = c/√(1 + 4π2(1010/360)42) ≈ α{129,600x10-20/2π) c = 1.50506540x10-18 c for the classical electron radius scale given by Re and the internal velocity of the electron in electrostasis.

The lower limit for rec = Re = 1010λps/360 (from the Planck-Stoney-QR Unification) becomes:
δps = ½{1 - [v/vps]2/(1 + [4π22][1010/360]4} = ½ -½[v/vps]2/(1 + 4.41457863x1035), showing that as [v] → 0+ ; δps → ½ for ½ of the electron's mass being monopolic.

The wave nature of the electron changes the Compton radius to its Compton wavelength however and the derivation of [Eq.5] results in a recircularization of parameters to give a statistical root-mean-square velocity for the QR electron.

(hvλps/c2).γ.(df/dt) = hvλps.fps2.γ/c2 = hfps = mpsc2

(v/√(1-[v/c]2) = c and v2/{1-[v/c]2} = c2 solving for v2 = c2 - v2 and v2 =½c2 for an averaged Compton emr-emmr speed of

vλc = c/√2 ............................................................................................................................................................................... [Eq.7]

This formulation sets an upper and lower bound for velectron in the electron radius in the interval: 〈 Re|max ......... Rec|min = λps/2π = rps = rWeyl = rwormhole = rqbb

The speed of the quantum mechanical electron of mass mec= αmps kg*, so is maximised in its minimum radius of the wormhole as 0.045799 c or 13,739,643.01 (m/s)* and limits the classical relativistic electron speed in:

mec/√{1-(vec/c)2 } = αmps = 1.621502875x10-22 kg* for {ve/c}2 = 1 - {me/αmps}2[/left]

ve|max = √{1 - (5.72957797x10-9)2} c = √{1 - 3.28280637x10-17} c ~ {1 - 1.64140319x10-17} c = c-

and as the self-energy Eec=mecc2 = αmpsc2 = αEps = α/e* J* for the Weyl electron of the quantum big bang (qbb) or instanton following the inflaton of the string epoch.

This energy of self-interaction represents the original Zero-Point or VPE energy of the matrix of spacetime in the miniumum Planck oscillator |½Eo| = |h/4π| = ½Eplanck which manifests the quantization for the parameters describing dynamical interaction within it.
As such a VPE-Volumar brane the conformal transformation of the Planck oscillator into the Weyl oscillator can be used to define the concept of a 'physical consciousness awareness quantum' αω=df/dt in the maximised frequency entropy state in a brane volumar and as per [Eq.3]. Here a 4-dimensional Riemann sphere with volume V4(r) = ½π2r4 manifests as a 3-dimensional surface: dV4/dr = 2π2r3 and so as the encompassing 'mother black hole' solution for the inner horizon of an open de Sitter holographic cosmology bounded by that inner black hole surface as a one-sided 11-dimensional hyper-surface, whose outside uses the mirror modular duality of string physics to define the outer horizon as a Möbian connected topology of closed Anti de Sitter space-time as a quasi 12th dimension, which can be labeled as a Vafa's 'father white hole', quantum entangling the inner- and outer horizons of the Witten manifold mirror in the membrane modular duality.

This allows a number of predictions for particular energy levels to be made.
For the maximised volumar brane at the Weyl energy and for the maximized frerquency permutation state.
Vbrane.(df/dt)|max = 2π2Rrmp3.fps2 = e* =1/Eps = 2Rec2 in a restmass photonic or 'dark matter' radius Rrmp = ∛{e*/2π2fps2} = 1.411884763x10-20 m* for the nuclear electron at mfermi = h/2πcRrmp= 2.50500365x10-23 kg* or 14.034015 TeV*. This is near the maximum energy potential of the Large Hadron Collider or LHC in Geneva, Switzerland and a form of the 'dark matter' particle should make an appearance at 14 Tev.

For the Compton electron e*/α = 2Rec2/α = 2Rcomptonc2 ; Rrmp = ∛{e*/2απ2fps2} = 7.279292496x10-20 m* for the Compton electron at an energy of
mcompton = h/2πcRrmp= 4.85868164x10-24 kg* or 2.722024 TeV*

For the Bohr electron e*/α2 = 2Rec22 = 2Rbohrc2 ; Rrmp = ∛{e*/2α2π2fps2} = 3.75300456x10-19 m* for the atomic Bohr electron at an energy of
mcompton = h/2πcRrmp= 9.4238534x10-25 kg* or 527.9613 GeV*

The classical electromagnetic rest-mass memr=me becomes quantum mechanical in the string-brane sourcesink energy E*-Gauge photon quantum of the Quantum Big Bang Weylian wormhole.

E* = Eps = hfps = hc/λps = mpsc2 = (me/2e).√[2πGo/αhc] = {me/mP}/{2e√α} = 1/2Rec2 = 1/e*

Monopolic charge quantum e*/c2 = 2Re ⇐ supermembrane displacement transformation ⇒ √α.lplanck = e/c2 as electropolic charge quantum

me = 2e√α.mplanck/2Rec2 = lplanck√α.√α.mplanck/Re = α.lplanck.mplanck/Re
= {e/c2}{√(2πke2/hc}{√(hc/2πGo)}/Re ={√(Goh/2πc3)}{2πke2/hc}{√(hc/2πGo)}/Re = {h/2πc}{2πke2/hc}/Re
= {ke2/c2}/Re = {μoe2}/4πRe

The product me.Re = Compton constant = hα/2πc = α.lplanck.mplanck
A changing electron size re changes the electron restmass mo in proportionality re ∝ 1/mo and where mo= me for re= Re = Rcompton/α = Rbohr2
The boundary relativistic electron mass so becomes the Compton wormhole mass of the Quantum Big Bang α.mps= α.hfps/c2

For the wormhole limit re = rps = λps/2π = Re |minimum in unified string Planck-Stoney units
me = αmps = αhfps/c2 = αh/cλps = α/e*c2 = α/2Rec4 = hα/2πcrps = {60πhe2/2πhcrps} = 30e2/crps = 1.62150288x10-22 kg = meγ = me/√{1 - [v/c]2}
for velectron = c-; [v/c]2 = 1-3.2828...x10-17 for v={1-½(3.2828x10-17)} c ~ c

Frequency permutation states in the monopolic velocity distribution

As the maximum frequency permutation state from the alpha-part of the relativistic force expression [Eq.4] is always applied to the monopolar velocity vps ; df/dt|max = fps2 = 1/fss2 = cfpsps = cfps/2πrps for an angular frequency ωps= 2πfps as Compton frequency; the maximum monopolar velocity ratio {vps/c}2 applied to the mass m = mec will be proportional to that maximised frequency state.
The de Broglie group velocity vdB = h/mecλdB = h/2πmecrdB linearized so is recircularized in the monopolar velocity vps in the Compton constant mec.rdB = h/2πvps and with vps assuming c in the relativistic limit of the Compton radius.

For 〈 Rec.mec = rps.mec = hα/2πc 〉|min , the minimised classical electron radius rps maximises the monopolar speed of the electron in:
{vps/c} = 1/√{1+1/4π2α2} = 0.04579881 as a conformal mapping of the wormhole radius of the electron onto its classical representation in the proportion 1010 = 360Re/2πrps in a correlation between circular measure in linearized radians and angular degrees. This is in correspondence to the wave nature expressed in the Compton and de Broglie wavelengths and of the particle nature from the Compton and de Broglie radii in an encompassing electromagnetic and electromagnetic monopolar emr-emmr interaction.

This monopolar ß represents a magnetic mass mmm = μoe2(vps/c)2/4πrps = Reme(vps/c)2/rps = mec(vps/c)2 = (2.09753100x10-3)mec = 3.4011525x10-25 kg for the alpha-energy Eαω = mmmc2 = hfαω= 3.051037256x10-8 J* for a total frequency integral of fαω = 4.59160179x1025 = ∑fss = ∑mssc2/h = fαω/fss = 1.377480544x1056 frequency self states and mass quantum mss eigen inertia states by mss = hfss/c2 by the time instanton fpsfss = 1 = Eps.e* as universal and natural self-identity for the supermembrane EpsEss.consisting of a high energy vibratory part Eps and a low energy winding part Ess in a mirror duality coupling.

This is a magnetic mass manifesting at the atomic scale at 3.06100x10-8 J* or 190.5433 GeV* for a wavelength of λmm = h/mmc = 6.53382x10-18 m* for a total electron mass mec/√{1-(vec/c)2 } = αmps = 1.621502875x10-22 kg* as the Weyl mass having replaced the classical relativistic electron restmass mo by the quantum dynamic Compton restmass mec as a function of the effective classical electron mass me.
αmps{vps/c}2 = mmm and so the Compton encompassing mass mec is reduced to the magnetic mass in the factor {vps/c}2 characterising the mass-radius relationship for all electrons.

For 〈 Re.me = hα/2πc 〉|max , the maximised classical electron radius Re minimises the monopolar speed of the electron in:
me=hα/2πcRe = ke2/Rec2 = μoe2/4πRe for {vps/c} = 1/√{1+Re4/4π2α2rps4} = 1/√{1+(2π.1010/360)4/4π2α2} = 1.50506548x10-18
and as the speed of the quantum relativistic mechanical electron at rest in the classical frame vps = 1.50506548x10-18 c = 0.45151964 (nanometres per second)*.

The inversion speed of light is vps = 1/c =3.3333... nanometres per second* in modular brane duality to define an impedance 'bubble' characterizing astrophysical 'Hill spheres' for orbital equilibrium conditions for satellites and moons in a Radius of Hill Impedance/Hubble Time as RHI = Ho/c as inversion displacement, which for a Universal Age of 19.12 Gy as Hubble time for a nodal Hubble constant oscillating between fps and Ho=c/RH = 58.04 (km/Mpc.s)* for RH = 1.59767545x1026 m* and becomes RHI = 19.12 Gy/c = 2.011229x109 m* and encompassing a 'planetary bubble radius' to approximately 5% to both the neighbouring planets Venus and Mars.

This represents a magneto-monopolic mass mmm = μoe2(vps/c)2/4πRe = me(vps/c)2 = (2.265221x10-36)me = 2.1045107x10-66 kg* for the alpha-energy Eαω = mmmc2 = hfαω= 1.8940596x10-49 J* for a total frequency integral of fαω = 2.84108945x10-16 = ∑fss = ∑mssc2/h = fαω/fss = 8.52326834x1014 frequency self states for the mass-frequency coupling mss = hfss/c2 .
The classical electron restmass mo = me so is reduced to the magneto-monopolar mass mmm in the factor {vps/c}2.

The Mass Distribution for the Quantum Relative Classical Electron

We set Constant A in Amec = μoe2/8πcRe for Aß2 = 1/√[1 - ß2] - 1
from: c2(m - mec) = μoe2v2/8πRe = mecc2(1/√[1-ß2] - 1) = mecv2A with a total QR monopolar mass m = mec/√(1-[v/c]2)

This leads to a quadratic in ß2: 1 = (1 + Aß2)2(1-ß2) = 1 + ß2(2A+A2ß2-2Aß2-A2ß4 - 1) and so: {A24+{2A-A22+{1-2A} = 0
with solution in roots:

ß2 = ([A-2] ± √[A²+4A])/2A = {(½-1/A)±√(¼+1/A)} ................................................................. [Eq.8]
and A = -{1 ± 1/√(1-ß2)}/ß2 solving (4 roots) the quadratic (2Aß2+2-A)2 = A2 + 4A

This defines a distribution of ß2 = (v/c)² and ß = v/c velocity ratios in mec.Aß2 = μoe²[v/c]2/8πRe

The electromagnetic mass mec in the relation mecA = ½me is then the monopolic quantum relativistic restmass and allows correlation by the Compton constant and between its internal magnetopolar self-interaction with its external magnetic relativistic and kinetic effective electron ground state mass me respectively.
In particular me = 2Amec and is mec for A=½ as the new minimisation condition. In string parameters and with me in *units, meA=30e²c/e*=½me=4.645263574x10-31 kg*
In terms of the superstring quantum physics, the expression [ec]unified = 4.81936903x10-11 kg* or [ec3]u = 2.7x1016 GeV* as the Grand-Unification (GUT) energy scale of the magnetic monopole, which represents the first superstring class transformation from the Planck-string class I of closure to the self dual opening of class IIB, as the magnetic monopole of the inflaton epoch.

E* = Eweyl = Eps = hfps = hc/λps = mpsc2 = (me/2e).√[2πGo/αhc] = {me/mP}/{2e√α} = 1/2Rec2 = 1/e* .................................................... [Eq.9]

Monopolar charge quantum e*/c2 = 2Re ⇐ super-membrane displacement transformation ⇒ √α.lplanck = e/c2 as Electropolar charge quantum

This implies, that for A=1, mec = ½me , where me = 9.290527155x10-31 kg* from particular algorithmic associations of the QR cosmogony and is related to the fine structure of the magnetic permeability constant μo = 120π/c = 1/εoc2, defining the classical electronic radius.
As ß≥0 for all velocities v, bounded as group speed in c for which ß2=ß=1, (and not de Broglie phase speed: vdB = (h/mvgroup)(mc2/h) = c2/vgroup >c); a natural limit for the ß distribution is found at A = ½ and A = ∞.

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

μoe²/8πmeRe = ½me for a distributed rest-mass mec/Re = me/rec in A and melectric = kq²/2Rec² = μoe2/8πRe = Ue/c² = ½me for A=½ and its maximum for A=∞ is the unity v=c for B=1

The classical rest-mass mo of the electron and as a function of its velocity from v=0 to v=c so is itself distributed in its magnetic mass potential about its effective restmass meoe2/4πRec2 and as a function of the classical electron radius.
Its minimum condition is defined by the electric potential energy in mo=½me for a value of A=½ with effective restmass me being the restmass for a stationary electron v=0 without magnetic inertia component.
For v=c, the mass of the electron incorporates a purely relativistic and quantum relative self-interacting magnetic monopolic value for which mo=0 and the effective restmass me assumes the minimum rest energy for the electron at A=1 and generalised as me=2Amo.

The classical restmass mo=hf/c2 so decreases from its maximum value as mo=me to mo=0 as a function of the velocity distribution and in the extension of the classical force to incorporate the restmass differential d(mo) = hd(f)/c2 by FNewton = Fa + Fα = F-acceleration + F-alpha as the sum of the classical Newtonian linear momentum change and the quantum mechanical angular acceleration momentum change in the self-interaction for the electron. [Eq.4]

Electromagnetic Mass Distribution for the Quantum Relativistic Electrodynamic Electron

 A=μoe2/ 8πmecRe as |Eps*| ß2 = 1-{meo/me}2 = 1-{meoRe/mecrec}2 ß2 ⇒ (iß)2 for A < ½ x root y root meo kg*/ meo kg meo = me√(1-ß2) = me/γ ß2 ⇒ (iß)2 for A < ½ v/c (vps/c)2 = 1/{1+rec4/4π2α2rps4} for magnetopolar.velocity.in c (m/s)* rec = Re/γ = √(1-ß2) Re rec /Re = me/mec in m* self-relative-QR-re 0 0 ± 0 1/0+ -1/0+ [1/0+]me i/0+ algorithmic metaphysicality inflaton spacetime as complex vps = ic = ci [∝] Re 1-½√2 = 0.292893218 -2.914213562 ±1.914213562 -1 = i2 x-root is complex 1+½√2 = -4.82842714 y-root is complex 0 0 i 1 c 1 0 0 Re (2/0+)Re {1-½√2}+O(10-17) = 0.292893218+ -{1±1/√[1-ß2]} /ß2 ~-1{1±1+½ß2}/ß2 ßcompleximage2 = -2.914213561....... ± 1.91421356200.. -0.999999999..... {i.me/αmps}2 = -1+3.282806345x10-17 -4.82842714+ 0+ 0+ i- vps= 2παc/√{1+4π2α2} =0.045798805 ic 13,739,641.79 [m/s]* rec=rps=180Re/(π1010) 1.591549431x10-23 5.729577953x10-9 Re 349,065,850.6 Re Alb = 0.487459961 ßlb2 = -1.55145054 ± 1.517053242 -0.034397297 -3.068503782 9.129344446x10-31 9.095208981x10-31 0.185i 1.558679858x10-18 ic 4.676039573x10-10 2.729585632x10-15 0.982650855 Re 1.018 Re A1 = 0.488459961. ß12 = -1.547250706 ± 1.515668402 -0.031582303 -3.062919108 9.142642017x10-31 9.108456831x10-31 0.177i 1.554149091x10-18 ic 4.662447273x10-10 2.733561478x10-15 0.984082159 Re 1.016 Re A3l = 0.488500361 ß3l2 = -1.547081394 ± 1.515612547 -0.031468847 -3.062693941 9.143177565x10-31 9.108990376x10-31 0.177i 1.55396695x10-18 ic 4.661900851x10-10 2.733721674x10-15 0.984139803 Re 1.016 Re ASI = complex 0.488502266 [e/m]= 1.758820024 x10-11 C/kg with αvar A-root complex=real ßSI2 = -1.54707341 ± 1.515609914 -0.031463495 -3.062683324 9.14320282x10-31 9.109015537x10-31 δmeo =- 9.5x10-8 uncertainty solution complex - real 0.177i 1.553958288x10-18 ic 4.661874865x10-10 2.733729293x10-15 0.984142545 Re 1.016 Re ASI = complex 0.488502361 [e/m]= 1.758820024 x10-11 C/kg with αvar min ßSI2 = -1.547073013 ± 1.515609783 -0.03146323 -3.062682796 9.143204074x10-31 9.109016786x10-31 0.177i 1.016 Re A3u = 0.488540761 ß3u2 = -1.54691211 ± 1.5155567 -0.03135541 -3.06246881 9.143712983x10-31 9.109523792x10-31 0.177i 1.016 Re A5l = 0.489123658 ß5l2 = -1.54447277 ± 1.514751719 -0.029721051 -3.059224489 9.151423661x10-31 9.117205639x10-31 0.172i 1.015 Re A5u = 0.489164058 ß5u2 = -1.544303917 ± 1.514695982 -0.029607935 -3.058999899 9.151957085x10-31 9.117737069x10-31 0.172i 1.015 Re ½ -3/2 ± 3/2 0.0 -3 meo = me 9.290527148x10-31 9.255789006x10-31 0 1.5050654x10-18 c 2.7777777...x10-15 = 1.00 Re Re 0.50078795 ßrealimage2 = -1.496853158 ± 1.498950686 0.002097530539 0.00209752801 -2.995803844 9.280778463x10-31 9.246076772x10-31 0.0458 1.508228953x10-18 c 4.524686858x10-10 2.774863014x10-15 0.998950685 Re 1.001576 Re A4l = 0.511459239 ß4l2 = -1.455190021 ± 1.484988222 0.029798201 -2.940178243 9.151059822x10-31 9.1163843161x10-31 0.173 1.551286282x10-18 c 2.73608263x10-15 = 0.98498975 Re 1.015 Re A4u = 0.511499639 ß4u2 = -1.455035593 ± 1.484936225 0.029900632 -2.939971818 9.15057674x10-31 9.116361885x10-31 0.173 1.55145488x10-18 c 2.73593396x10-15 = 0.98493623 Re 1.015 Re A2 = 0.511540039 ß22 = -1.45488119 ± 1.484884234 0.030003044 -2.939765424 9.150093721x10-31 9.115880672x10-31 0.1732.86 1.55161873x10-18 c 2.7357895x10-15 = 0.98488423 Re 1.015 Re A6l = 0.512082536 ß6l2 = -1.452810201 ± 1.484186714 0.031376513 -2.936996915 9.143613382x10-31 9.109424564x10-31 0.177 1.553818818x10-18 c 2.73385198x10-15 = 0.98418671 Re 1.016 Re ASI = real 0.512116936 [e/m]= 1.758820024 x10-11 C/kg with αvar max ßSI2 = -1.452679026 ± 1.484142522 0.031463496 -2.936821548 [1.02/1.02]me√(1-x) 9.14320282x10-31 9.109015537x10-31 0.177 1.553958371x10-18 c 2.73372922x10-15 = 0.98414252 Re 1.016 Re A6u = 0.512122936 ß6u2 = -1.452656072 ± 1.484134815 0.031478742 -2.936790887 9.143130852x10-31 9.108943838x10-31 0.177 1.553982826x10-18 c 2.73370771x10-15 = 0.98413478 Re 1.016 Re Aub = 0.512540039 ßub2 = -1.451067085 ± 1.483599368 0.032532283 -2.934666453 9.138156632x10-31 9.103988218x10-31 0.180 1.555675057x10-18 c 2.73222047x10-15 = 0.98359937 Re 1.017 Re ¾ Mean: ½{½+1} ∑surface charge -⅚ ± √(19/12) 0.424972405 -2.09164 [3/2]⅔me√(1-x) 7.045060062x10-31 7.018717929x10-31 0.652 2.617379438x10-18 c vps = 7.852138314x10-9 2.10640483x10-15 = 0.75830574 Re 3Re/2 ⅚ ∑Volume charge -7/10 ± √(29/20) 0.504159457 -1.904159458 [5/3]⅗me√(1-x) 6.542012566x10-31 6.517551374x10-31 0.710 3.035381866x10-18 c vps = 9.106145598x10-10 1.9559985x10-15 = 0.70415946 Re 5Re/3 1 -½ ± ½√(5) 0.618033988 -1.618033988 [2]½me√(1-x) 5.741861551x10-31 5.720392198x10-31 0.786 3.94031237x10-18 c vps = 1.182093711x10-9 1.71676108x10-15 = 0.61803399 Re 2 Re 1+½√2 = 1.707106781 -0.085786437 ±0.914213562 0.828427125 x-root is real -1 = i2 y-root is complex [3.41/3.41]me√(1-x) 3.848262343x10-31 3.833873334x10-31 0.910 8.77216401x10-18 c 2.631649203x10-9 1.150593228x10-15 0.414213562 Re =( √2 - 1) Re 3.414213562 Re = (2+√2) Re 2 0 ± ½√(3) 0.866025403 -0.866025403 [4]⅙me√(1-x) 3.400568951x10-31 3.387853908x10-31 0.931 1.123396092x10-17 c 3.370188275x10-9 1.01673724x10-15 = 0.36602540 Re 4 Re 2.47213603 0.095491515 ± 0.809016986 0.904508501 -0.7135255471 [4.94/4.94]me√(1-x) 2.870930718x10-31 2.860196042x10-31 0.951 1.576125021x10-17 c 4.728375064x10-9 Rproton = 0.85838052x10-15 = 0.309016987 Re 4.94427206 Re 3 ⅙ ± √(7/12) 0.930429282 -0.597195949 [6]⅙me√(1-x) 2.450493743x10-31 2.44133112x10-31 0.965 2.163360455x10-17 c 6.490081364x10-9 7.32673935x10-16 = 0.26376262 Re 6 Re 4 ¼ ± √(½) 0.957106781 -0.457106781 [8]⅛me√(1-x) 1.924131173x10-31 1.916936668x10-31 0.978 3.50886558x10-17 c 1.052659674x10-8 5.75296616x10-16 = 0.20710678 Re 8 Re 174,532,925.3 -{1±1/√[1-ß2]} /ß2 ~-1{1±1+½ß2}/ß2 0.499999..4 ± 0.500000..5 ~ ½- ± ½+ 0.999999999..... {me/αmps}2 = 1-3.282806345x10-17 -0.000000..1 [#/#]me√(1-x) 5.323079946x10-39 5.303176457x10-39 minimum mass (electron-neutrino) 0.00297104794 eV* mνe =mvτ2 = 0. 002982..eV* 0.999 qbb boundary of physicality 0.045798805 c 13,739,641.79 rec = rps =(me/αmps)Re 1.59154943x10-23 = 5.7296x10-9 Re 349,065,850.6 Re ∞ ½- ± ½+ 1- 0- [∞-]0+me√(1-x)=me meo=0+ 1- algorithmic metaphysicality inflaton spacetime as complex vps = ic = ci [∞] Re

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=∞: ß2-±½+ for roots x=1- and y=0-; for v=c with Um = (½v2oe2/8πRe = (½v2oe2/4πRe = ½mec2 = mmagneticc2 = melectricc2 and mo = 0me
2 = ([1-ß2]-1) = 1+½ß2-3ß4/8+5ß6/16 -35ß8/128+...-1​

The Binomial Identity gives the limit of A=½ in: A=½ - ß2{3/8 - 5ß2/16 + 35ß4/128 -...} and as the non-relativistic low velocity approximation of E=mc² as KE=½mov².

Letting ß2=n, we obtain the Feynman-Summation or Path-Integral for dimensionless cycle time n = Hot = ct/RHubble with Ho=dn/dt in the UFoQR for 1 = (1-ß2)(1+ß2)2 as ß42-1=0 for T(n) = n(n+1 )= 1.

The bare restmass of the electron in the Coulombic charge quantum and the mensuration calibration in the alpha finestructure

We shall also indicate the reason for the measured variation of the fine structure constant by Webb, Carswell and associates; who have measured a variation in alpha dependent on direction.
This variation in alpha is found in the presence of the the factor γ3 in the manifestation of relativistic force as the time rate of change of relativistic momentum prel. Furthermore, the mass-charge ratio {e/meo} relation of the electron implies that a precision measurement in either the restmass moe or the charge quantum e, would affect this ratio and this paper shall show how the electromagnetic mass distribution of the electron crystallizes an effective mass me from its restmass resulting in meoγ = meγ2 related to the coupling ratio between the electromagnetic (EMI) and the strong nuclear interaction (SNI), both as a function of alpha and for an asymptotic (not running) SNI constant defined from first principles in an interaction transformation between all of the four fundamental interactions.

Since {1 - ß2} describes the ß2 distribution of relativistic velocity in the unitary interval from A=0 to A=1, letting {1 - ß2} = {√α}3 = 6.232974608...x10-4, naturally defines a potential oscillatory upper boundary for any displacement in the unit interval of A. An increase or decrease in the 'bare' electronmass, here denoted as moe can then result in a directional measurement variation due to the fluctuating uncertainty in the position of the electron in the unitary interval mirroring the natural absence or presence of an external magnetic field to either decrease or increase the monopolar part of the electron mass in its partitioning: melectric + mmagnetic + δmmonopolic = mec{½+½[v/c]²} + δpsmec = mec with mec2√{1 + v2γ2/c2} = mec2γ = mecc2 for m = mec from the energy-momentum relation E2 = Eo2 + p2c2 of classical and quantum theory.
The cosmic or universal value of alpha so remains constant in all cosmological time frames; with the fluctuation found to depend on a asymptotically constant strong interaction constant as a function of alpha.

In the SI measurement system Planck's constant h = 6.62607004x10-34 Js and the speed of light is c = 2.99792458x10-8 m/s and the electron charge is e=1.60217662x10-19 C for a bare electron mass of 9.10938356x10-31 kg.
In a mensuration system in which c would be precisely 3x108 (m/s)*; the following conversions between the SI-system and the *-system are applied in this paper.

Furthermore, there exists one fundamental constant in the magnetic permeability constant uo = 4πx10-7 H/m which becomes numerically equal in the Maxwell constant μo = 1/εoc2 in an applied fine structure μoo = {120π/c}.{1/120πc} = 1/c2 (s/m)2; (s/m)2*. Subsequently in the calculation of alpha, the speed conversion must be incorporated for unitary consistency.
Alpha remains constant for a cosmology descriptive of a non-accelerating cosmology; but will result in a change in the electric charge quantum in a cosmology, which measures an accelerated spacial expansion, which can however be the result of a self-intersection of the light path for particular cosmological redshift intervals in an oscillating cosmology.
Here a particular alpha variation reduces the SI-measurement for the square of the charge quantum e in a factor of (1.6021119x10-19/1.60217662x10-19)2 = 0.99991921...for a calibrated:

alpha variation αvar = 1 - (1.6021119x10-19/1.60217662x10-19)2 = 1 - 0.9999192 = 8.08x10-5.................................[Eq.10]

Alpha α = μoce2/2h = 2π.(2.99792458)(1.6021119)2x10-37/(6.62607004x10-34) = 60πe2/h = 7.2967696x10-3 = 1/137.047072

 {s} = 1.00098 {s*} = 0.999023 {s} {m} = 1.00167 {m*} = 0.998331 {m} {kg} = 1.00375 {kg*] = 0.996261 {kg} {C} = 1.00271 {C*} = 0.997296 {C} {J} = 1.00514 {J*} = 0.994883 {J} {eV} = 1.00247 {eV*} = 0.99754 {eV} {K} 0.98302 {K*} = 1.01727 {K}

From the unification polynomial U(x) = x4 + 2x3 - x2 - 2x + 1 = 0 and derivative U'(x) = 4x3 + 6x2 - 2x - 2 with minimum roots at x1 = X and x2 = -(X+1) = Y and maximum root at x3 = ½ we form the the factor distribution (1-X)(X)(1+X)(2+X) = 0 and form a unification proportionality:

SNI:EMI:WNI:GI = [Strong Nuclear Interaction #]:[Electromagnetic Interaction #3]:[Weak Interaction #18]:[Gravitational Interaction #54] under the Grand Unification transformation of X ⇔alpha α

X ⇔ α in ℵ(Transformation) = {ℵ}3 : X → α{#}3 → # → #3 → (#2)3 → {(#2)3}3 ......................................................................................... [Eq.11]

This redefeines the Interaction proportion as: SNI:EMI:WNI:GI = [#]:[#3]:[#18]:[#54] = [1-X]:[X]:[1+X]:[2+X] for the X Alpha Unification, which is of course indicated in the unitary interval from A = 0 to A =1 in the ß2 distribution for the electron mass.

 SNI:EMI [1-X]:[X] X X #:#3 #-2 α-⅔ 1/∛α2 Invariant Upper Bound X-Boson SNI:WNI [1-X]:[1+X] [2X-1] X3 #:#18 #-17 α-⅓(17) 1/∛α17 SNI:GI [1-X]:[2+X] [1-X]2 X4 #:#54 #-53 α-⅓(53) 1/∛α53 EMI:WNI [X]:[1+X] [1-X] X2 #3:#18 #-15 α-5 1/∛α15 EMI:GI [X]:[2+X] [2X-1] X3 #3:#54 #-51 α-17 1/∛α51 WNI:GI [1+X]:[2+X] X #18:#54 #-36 α-12 1/∛α36 Invariant Lower Bound L-Boson

For the unitary interval at A=½ the Compton constant defines me.Re, but at A=1, the constancy becomes ½me.2Re and at the average value at A=¾ it is ⅔me.⅓Re.
This crystallizes the multiplying (4/3) factor calculated from the integration of the volume element to calculate the electromagnetic mass in the Feynman lecture and revisited further on in this paper. if the electrostatic potential energy is proportional to half the electronmass is changed by a factor of (4/3), then the full electron mass will be modified to ⅔ of its value.
Using the ß2 velocity distribution, one can see this (4/3) factor in the electromagnetic mass calculation to be the average between the two A-values as ½(½+1) = ¾ for a corrected electron mass of ⅔me. for a surface distribution for the electron.

The problem with the electromagnetic mass so becomes an apparent 'missing mass' in its distribution between the electric- and magnetic external fields and the magnetopolar self-interaction fields as indicated in the discussions before.
In the diagram above the mass of the electron is distributed as mec in the unitary interval applied to the Compton constant and where exactly half of it can be considered imaginary or complex from A=0 to A=½. The mass of the electron at A=0 is however simply half of its effective mass me, whch is realised at the half way point at A=½ as the new origin of the electron's electrostatic energy without velocity in the absence of an external magnetic field. We have seen however, that the electrostatic electron carries a minimum eigen-velocity and so magnetopolar self-energy, calculated as vps = 1.50506548x10-18 c and manifesting not as a dynamic external motion, but as fαω = 2.84108945x10-16 = ∑fss = ∑mssc2/h = fαω/fss = 8.52326834x1014 mass- or frequency self-states.

But how can the bare electron mass be obtained from first principles? This bare electron restmass must be less, than the effective mass me at A=½ and more than half of me at the absolute 0 state of A=0.
We know that it is ⅓me that would be this discrepancy on the mathematical grounds and so one might relate the Compton constant in the ⅓Re to set the ⅓me interval as being centred on A=½ for two bounds A1 and A2 in the 'complex' region where ß2 is negative and where ß2 is positive respectively. To approximate the two bounds, we shall define the sought interval for the bare electron mass meo as a function of alpha and as a function of the classical electron radius.

The monopolar energy is defined in the Weyl energy of the qbb and in Eps = 1/e* = 1/2Rec2 and using the modular string duality we use the magneto charge quantum not as inverse energy Eweyl, but as energy to set m*= E*/c2 = 2Re* and so the unification factor for the electron mass mec at A=1. As can be seen in the diagram, the alpha variation becomes a delta energy added to the magneto charge quantum to finetune the electron restmass interval.

The elementary interaction ratios can be applied to the quantum nature of the electron in the form of the original superstring transforms (discussed further later in this paper) and apply here in the EMI/SNI = αto set the electron's interaction relative to the SNI and a decreasing size of the electron centred at the Re scale decreasing towards the nuclear centre with increasing speed in the 'real interval'.
As we require me as the average in the surface charge interval from A=½ to A=1 we define the sought bounding interval for the bare electron mass as ⅓α+ ⅓α = ⅔α.
The lower bound for meo so is Alb = ½ - ⅓α= 0.487459961.... and the upper bound becomes Aub = ½ + ⅓α= 0.512540039... for a total A-interval of Alb + Aub = 0.0025080078... = 2(0.012540039).

We so can define me(meo2 ) = me/ √(1 - ß2) = meo/ (1 - ß2) for any meo in the interval defined in the ß2 distribution and [Eq.8] with the effective restmass me = 9.290527148x10-31 kg* in * units.

ßlb2 (0.487459961..) = -1.55145054.. + 1.517053242.. = -0.034397297.. (equilibrium in x-root) for meo = me√(1 - i2ß2) = 9.129344446x10-31 kg* for 9.095208981x10-31 kg.

ßo2 (0.5000000000) = -1.50000000.. + 1.5000000000.. = 0.000000000.. (complex in x-root) for meo = me√(1 - 0) = 9.290527148x10-31 kg* for 9.255789006x10-31 kg.

ßub2 (0.512540039..) = -1.451067085.. + 1.483599368.. = 0.032532283.. (real in x-root) for meo = me√(1 - ß2) = 9.138156632x10-31 kg* for 9.103988218x10-31 kg.

So we know that the bare electron mass will be near 0.982651 of the real me in the complex region of the unitary interval.
To correlate the complex solution for meo with the real solution for meo, we are required to shorten the interval Aub - Alb in a symmetry for the electron mass. This will result in a complex solution in the complementary x-root. We can ignore the y-roots for ß2, as they are all negative in view of the x-root always being negative in the described interval.

A reasonable approach is to remain in the described interval and next utilize the Compton cosntant in the form of the magneto charge quantum as the inverse of the Weyl wormhole energy, also noting the scale of magnitude of the 1/e* = 1/2Rec2 being of the same order as alpha as α/Eweyl = αe* = 3.648381483 or e*= 0.274094144 α.
Additionally a conformal mapping of the minimum Planck energy as a Planck oscillator Eo = ½hfo at the Planck energy of superstring class I onto the heterotic superstring HE(8x8) in the qbb energy quantum Eps = Eweyl associates and couples the unitary interval to the displacement bounce of the inflaton. We denote the Eps energy quantum as |Eps| in its unified modular self state where Eps.e* = 1 = E*e*
As ß2 = (1 - {me/mec}2) and (1 - {meo/me}2) as a distribution of mass ratios, it can be linked to the Compton constant in me/mec = rec/Re in an inverse proportionality and so the unitary interval and the electron's mass and spacial extent distribution.

We set the interval A2 = Aub - ½|Eps| = 0.512540039...- 0.001 = 0.511540039... and the conjugate interval as A1 = Alb + ½|Eps| = 0.487459961... + 0.001 = 0.488459961...

ß12 (0.488459961..) = -1.547250706.. + 1.515668402.. = -0.031582303.. (complex in x-root) for meo = me√(1 - i2ß2) = 9.142642017x10-31 kg* for 9.108456831x10-31 kg.

ß22 (0.511540039..) = -1.45488119.. + 1.484884234.. = 0.030003044..(real in x-root) for meo = me√(1 - ß2) = 9.150093721x10-31 kg* for 9.115880672x10-31 kg.

For the final interval fine structure we apply the alpha variation, also noting that the excess of the original upper and lower bounds are very near the fractional divergent parts.
{Aub - ½} + {½ - Alb} = 2(0.012540039) = 0.025080078 = 2(⅓α) = 1/40 + 0.000080078... = ½|Eps|(25) + 0.000080078... = ½|Eps|(25) + [~]αvar in 7.22x10-7 parts.
Aub - A4l = A3u - Alb = 0.0010808...) = 0.001 + 0.0000080078 = ½|Eps| + [~]αvar .

Aub = ½ + ⅓α= 0.512540039...= 0.51254 + 0.000000039.. and Alb = 0.487459961.. = 1 - 0.5124 - 0.00000039..

The alpha variation αvar = 1 - (1.6021119x10-19/1.60217662x10-19)2 = 1 - 0.9999192 = 8.08x10-5 by [Eq.10]

A3l = A1 + ½αvar = 0.488459961.. + 0.0000404.. = 0.488500361.. and its image is A4u = A2 - ½αvar = 0.511540039... - 0.0000404.. = 0.511499639..
A3u = A1 + αvar = 0.488459961.. + 0.0000808.. = 0.488540761.. and its image is A4l = A2 - αvar = 0.511540039... - 0.0000808.. = 0.511459239..

ß3l2 (0.488500361..) = -1.547081394.. + 1.515612547.. = -0.031468846.. (complex in x-root) for meo = me√(1 - i2ß2) = 9.143177565x10-31 kg* for 9.108990376x10-31 kg.
ß3u2 (0.488540761..) = -1.54691211.. + 1.5155567.. = -0.03135541.. (complex in x-root) for meo = me√(1 - i2ß2) = 9.143712983x10-31 kg* for 9.109523792x10-31 kg.
ß4u2 (0.511499639..) = -1.455035593.. + 1.484936225.. = 0.029900632..(real in x-root) for meo = me√(1 - ß2) = 9.15057674x10-31 kg* for 9.116361885x10-31 kg.
ß4l2 (0.511459239..) = -1.455190021.. + 1.484988222.. = 0.029798201..(real in x-root) for meo = me√(1 - ß2) = 9.151059822x10-31 kg* for 9.1163843161x10-31 kg.

The bare electron mass meo should be found in the interval defined by the alpha variation applied both to the square and the singular value for the charge quantum e, but weighted towards the square of e as in the definition of the alpha finestructure constant with {e/meo = 1.606456344x10-19 C*/9.143202823x10-31 kg* = 1.756995196x1011 C*/kg* } and {e/meo = 1.602111894x10-19 C/9.10901554x10-31 kg = 1.758820024x1011 C/kg } minimised in the alpha variation maximum.

There is a deviation in the symmetry between the complex solution and the real solution for the bare electron mass and this deviation mirrors the original bounce of the Planck length at the cosmogenesis of the inflaton. We recall the super membrane displacement transformation of [Eq.9]:

Monopolar charge quantum e*/c2 = 2Re ⇐ super-membrane displacement transformation ⇒ √α.lplanck = e/c2 as Electropolar charge quantum

We so apply this bounce of the original definition for the minimum displacement to our described interval in adjusting the alpha variation interval using [Eq.11]:
X ⇔ α in ℵ(Transformation) = {ℵ}3 : X → α{#}3 → # → #3 → (#2)3 → {(#2)3}3 by the factor (√α)3 and so setting the cosmogenetic displacement bounce of the qbb as being proportional to our lower and upper bounded A valued interval for the ß2 distribution.

⅔α ∝ (√α)3 in ⅔α ≈ 1/40 + αvar = {⅔α-⅚}(√α)3 ....................................................................................................................... [Eq.12]
for proportionality constant {⅔α-⅚} = 1/{1/40 - 1.477074222x10-4} = 1/{1/40 - 1.828.αvar}

For (√α)3 = 6.232974608x10-4 then:

A5l = A3l + 6.232974608x10-4 = 0.488500361..+ 6.232974608x10-4 = 0.489123658..
A5u = A3u + 6.232974608x10-4 = 0.488540761..+ 6.232974608x10-4 = 0.489164058..
A6u = A4u + 6.232974608x10-4 = 0.511499639..+ 6.232974608x10-4 = 0.512122936..
A6l = A4l + 6.232974608x10-4 = 0.511459239..+ 6.232974608x10-4 = 0.512082536..
for the ß2 solutions:
ß5l2 (0.489123658..) = -1.54447277.. + 1.514751719.. = -0.029721051.. (complex in x-root) for meo = me√(1 - i2ß2) = 9.151423661x10-31 kg* for 9.117205639x10-31 kg.
ß5u2 (0.489164058..) = -1.544303917.. + 1.514695982.. = -0.029607935.. (complex in x-root) for meo = me√(1 - i2ß2) = 9.151957085x10-31 kg* for 9.117737069x10-31 kg.
ß6u2 (0.512122936..) = -1.452656072.. + 1.484134815.. = 0.031478742..(real in x-root) for meo = me√(1 - ß2) = 9.143130852x10-31 kg* for 9.108943838x10-31 kg.
ß6l2 (0.512082536..) = -1.452810201.. + 1.484186714.. = 0.031376512..(real in x-root) for meo = me√(1 - ß2) = 9.143613382x10-31 kg* for 9.109424564x10-31 kg.

The real solution for the bare electron mass so converges at A = 0.512082536.. = 1 -0.487917464 to its complex mirror solution at A = 0.488540761.. = 1 - 0.511459239.. for a ΔA = (√α)3 = 6.232974608x10-4 to indicate the nature of the electron mass as a function of the cosmogenesis from definiton to inflaton to instanton to continuon.

The M-Sigma conformal mapping onto {meo/me}2 in the ß2 distribution

As the ß2 distribution is bounded in {Aub - Alb = ⅔α} as a sub-unitary interval in a smaller sub-interval of ½αvar ; the SI-CODATA value for the restmass of the electron is derived from first inflaton-based principles in a conformal mapping of the M-Sigma relation applied to the Black Hole Mass to Galactic Bulge ratio for the alpha bound.

 Minimum Planck Oscillator ½|Eo|⇔ |Eps|* = 1/|e*| ½|Eps| ¾|Eps| 1|Eps| 5/4|Eps| 3/2|Eps| Value in energy (Joules; Joules*) 1/1000 1/666⅔ 1/500 1/400 1/333⅓ Value as modulated to A-interval as M-Sigma 1x10-3 1.5x10-3 2x10-3 2.5x10-3 3x10-3 |Eps|*/|e*| to reunitize-renormalize E*e*=1 2x10-6 3x10-6 4x10-6 5x10-6 6x10-6 ⅔-value in partition interval ⅔me.⅓Re for mean A=¾ 1/2 3/4 1 5/4 3/2 Fraction of Renormalization effect 1/3 1/2 2/3 5/6 1 Value of Δ(½αvar} in A6lb - A6ub and in A3ub - A3lb 2x10-6 complex minimum 3x10-6 4x10-6 5x10-6 6x10-6 real maximum
The ½avar sub-interval so is adjusted by 6x10-6 from A6ub - Δ(½αvar} = ASI for ßSI2 for meoSI for the real solution

The Planck-Stoney Bounce in conformal supermembrane cosmology

The pre-Big Bang 'bounce' of many models in cosmology can be found in a direct link to the Planck-Stoney scale of the 'Grand-Unification-Theories'.
In particular it can be shown, that the Squareroot of Alpha, the electromagnetic fine structure constant, multiplied by the Planck-length results in a Stoney-transformation factor
LP√α = e/c2 in a unitary coupling between the quantum gravitational and electromagnetic fine structures and so couples the unitary measurement of displacement in the Planck-Length oscillation equal to Coulombic charge quantum 'e' divided by the square of the speed of light 'c2' in a proportionality of Displacement = ChargexMass/Energy.
This couples the electric Coulomb charge quantum to the magnetic monopole quantum e* as the inverse of the 10-dimensional superstring sourcesink energy Eps to the 10-dimensional superstring sinksource energy Ess as the 11-dimensional super-membrane EpsEss.

{Gok=1 for Go=4πεo and representing a conformal mapping of the Planck length onto the scale of the 'classical electron' in superposing the lower dimensional inertia coupled electric charge quantum 'e' onto a higher dimensional quantum gravitational-D-brane magnetopole coupled magnetic charge quantum 'e*' = 2Re.c2 = 1/hfps = 1/EWeyl wormhole by the application of the mirror/T duality of the super membrane EpsEss of heterotic string class HE(8x8)}.

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) = ℮

The charge radius for the proton and neutrinos in quantum relativity

It is the unitary interval between A=½ and A=1 which so determines the quantum nature for the quantum mechanics in the relativistic ß distribution.

In particular for A=½ and for ß2 = x = 0, the Compton constant defines the required electron restmass of electrostasis as ½mec2 = e2c²/8πεoRe} for an effective elecetron size of Re, whilst for A=1 the mec2 = e2c²/4πεoRe for a doubling of this radius to 2Re for ß2 = x = X.

In the Feynman lecture the discrepance for the electron mass in the electromagnetic mass multiplier of 4/3 is discussed.
Its solution resides in the unitary interval for A, as the arithmetic mean of: ½{½+1} = 4/3 as the present internal magnetic charge distribution of the electron, namely as a trisection of the colour charge in 3x⅓=1 negative fraction charges in the quantum geometry of the electron indicated below in this paper.

The classical size for the proton so is likewise approximated at the mean value of its own colour charge distribution, now consisting of a trisected quark-gluon-anti-neutrino kernel of 3x⅔=2 positive fraction charges, which are 'hugged' by a trisected 'Inner Mesonic Ring' (d-quark-KIR) as a contracted 'Outer Leptonic Ring' (s-quark-KOR) for the manifestation of the electron-muon-tauon lepton family of the standard model.

For the electrostatic electron the ß distribution at A=½, the Compton constant gives mecrec = meRe for ß2 = 0 and at A=1, the Compton constant gives mecrec = ½me.2Re for ß2 = X and as the mean for a unitary interval is ½, the electron radius transforms into the protonic radius containing monopolic charge as internal charge distribution in Rp = ½XRe and where the factor X represents the symmetry equilibrium for a ß = (v/c} velocity ratio distribution for the effective electron restmass me proportional to the spacial extent of the electron.

For the proton then, its 'charge distribution' radius becomes averaged as Rproton = 0.85838052x10-15 m* as a reduced classical electron radius and for a speed for the self-interactive or quantum relativistic electron of 2.96026005x10-13 c. This quantum relativistic speed reaches its v/c = 1- limit at the instanton boundary and defines a minimum quantum relativistic speed for the electron at ve = 1.50506548x10-18 c for its electrostatic potential, where Ue=∫{q²/8πεor²}dr = q²/8πεoRe = ½mec2 for a classical velocity of ve=0 in a non-interacting magnetic field B=0.
2Ue = mec2 so implies a halving of the classical electron radius to obtain the electron mass me = 2Ue/c2 and infers an oscillating nature for the electron size to allow a synergy between classical physics and that of quantum mechanics.

A mapping of the atomic nucleus onto the thermodynamic universe of the hyperspheres

Consider the universe's thermodynamic expansion to proceed at an initializing time (and practically at lightspeed for the lightpath x=ct describing the hypersphere radii) to from a single spacetime quantum with a quantized toroidal volume 2π²rweyl and where rweyl=rps is the characteristic wormhole radius for this basic building unit for a quantized universe (say in string parameters given in the Planck scale and its transformations).
At a time tG, say so 18.85 minutes later, the count of space time quanta can be said to be 9.677x10102 for a universal 'total hypersphere radius' of about rG=3.391558005x1011 meters and for a G-Hypersphere volume of so 7.69x1035 cubic meters from N{2π2.rps3} =Volume = 2π2.RHk3.
{This radius is about 2.3 Astronomical Units (AU's) and about the distance of the Asteroid Belt from the star Sol in a typical (our) solar system.}
This modelling of a mapping of the quantum micro-scale onto the cosmological macro-scale should now indicate the mapping of the wormhole scale onto the scale of
the sun itself.
rweyl/Rsun=Re/rE for Rsun=rweyl.rE/Re=1,971,030 meters. This gives an 'inner' solar core of diameter about 3.94x105 meters.

As the classical electron radius is quantized in the wormhole radius in the formulation Re=1010rweyl/360, rendering a finestructure for Planck's Constant as a 'superstring parametric': h=2πrweyl/2Rec3; the 'outer' solar scale becomes Rsun[o]=360.Rsun=7.092x108 meters as the observed radius for the solar disk.

19 seconds later; a F-Hypersphere radius is about rF=3.451077503x1011 meters for a F-count of so 1.02x10103 spacetime quanta for the thermodynamically expanding universe from the instanton.
We also define an E-Hypersphere radius at rE=3.435971077x1014 meters and an E-count of so 10112 to circumscribe this 'solar system' in so 230 AU.
We so have 4 hypersphere volumes, based on the singularity-unit and magnified via spacetime quantization in the hyperspheres defined in counters G, F and E. We
consider these counters as somehow fundamental to the universe's expansion, serving as boundary conditions in some manner.
As counters, those googol-numbers can be said to be defined algorithmically and independent on mensuration physics of any kind.

Should we consider the universe to follow some kind of architectural blueprint; then we might attempt to use our counters to be isomorphic (same form or shape) in a one-to-one mapping between the macro-cosmos and the micro-cosmos.
So we define a quantum geometry for the nucleus in the simplest atom, say Hydrogen. The hydrogenic nucleus is a single proton of quark-structure udu and which we assign a quantum geometric template of Kernel-Inner Ring-Outer Ring (K-IR-OR), say in a simple model of concentricity.
We set the up-quarks (u) to become the 'smeared out core' in say a tripartition uuu so allowing a substructure for the down-quark (d) to be u+Inner Ring.
A down-quark so is a unitary ring coupled to a kernel-quark. The proton's quark-content so can be rewritten and without loss of any of the properties associated with the quantum conservation laws; as proton ⇒ udu ⇒ uuu+IR = KKK+IR. We may now label the Inner Ring as Mesonic and the Outer Ring as Leptonic.

The Outer Ring is so definitive for the strange quark in quantum geometric terms: s=u+OR.
A neutron's quark content so becomes neutron=dud=KIR.K.KIR with a 'hyperon resonance' in the lambda=sud=KOR.K.KIR and so allowing the neutron's beta decay to proceed in disassociation from a nucleus (where protons and neutrons bind in meson exchange); i.e. in the form of 'free neutrons'.
The neutron decays in the oscillation potential between the mesonic inner ring and the leptonic outer ring as the 'ground-energy' eigenstate.

There actually exist three uds-quark states which decay differently via strong, electromagnetic and weak decay rates in the uds (Sigmao Resonance); usd (Sigmao) and the sud (Lambdao) in increasing stability.
This quantum geometry then indicates the behaviour of the triple-uds decay from first principles, whereas the contemporary standard model does not, considering the u-d-s quark eigenstates to be quantum geometrically undifferentiated.
The nuclear interactions, both strong and weak are confined in a ' Magnetic Asymptotic Confinement Limit, coinciding with the Classical Electron Radius Re=ke²/mec² and in a scale of so 3 Fermi or 2.8x10-15 meters. At a distance further away from this scale, the nuclear interaction strength vanishes rapidly.
The wavenature of the nucleus is given in the Compton-Radius Rcompton = h/2πmc with m the mass of the nucleus, say a proton; the latter so having a scale reduced from Re by some partitioning of the classical electron size.

As the Planck Oscillator Eo=½hfo f the Zero-Point-Energy or ZPE as Vortex-Potential-Energy or VPE defines its ground state at half its effective energy of Ek=hfk, and as a conformal mapping from the string energy scale of the inflaton onto the qbb scale of the instanton in the Eweyl = Eps=/e*=1/2Rec2|mod gauge boson; we define a subatomic scale at half of Re as rmean =½Re.

The wave-matter (after de Broglie generalising wavespeed vdB from c in Rcomptonc) then relates the classical electron radius as the 'confinement limit' to the Compton scale in the electromagnetic finestructure constant in Re=Alpha.Rcompton.
The extension to the Hydrogen-Atom is obtained in the expression Re=Alpha².Rbohr1 for the first Bohr-Radius as the 'ground energy' of so 13.7 eV at a scale of so 10-10 metres (Angstroems).

These 'facts of measurements' of the standard models now allow our quantum geometric correspondences to assume cosmological significance in their isomorphic
mapping. We denote the Outer Ring as the classical electron radius and introduce the Inner Ring as a mesonic scale contained within the geometry of the proton and all other elementary baryonic- and hadronic particles.
Firstly, we define a mean macro-mesonic radius as: rM=½(rF+rG) =3.421317754x1011 meters and set the macro-leptonic radius to rE=3.435971077x1014 meters.
Secondly, we map the macro-scale onto the micro-scale, say in the simple proportionality relation for the micro-mesonic scale Rmean = Re.rM/rE = 2.765931439x10-18 meters.
So reducing the apparent measured 'size' of a halving of Re in a factor about about 1000 gives the scale of the sub-nuclear mesonic interaction, say the strong interaction coupling by pions.

The Higgsian Scalar-Neutrino

The (anti)neutrinos are part of the electron mass in a decoupling process between the kernel and the rings. Neutrino mass is so not cosmologically significant and
cannot be utilized in 'missing mass' models'.
We may define the kernel-scale as that of the singular spacetime-quantum unit itself, namely as the wormhole radius rweyl = rps =10-22/2π meters.
Before the decoupling between kernel and rings, the kernel-energy can be said to be strong-weakly coupled or unified to encompass the gauge-gluon of the strong
interaction and the gauge-weakon of the weak interaction defined in a coupling between the leptonic Outer Ring and the Kernel and bypassing the mesonic Inner Ring.

So for matter, a W-Minus ( weakon) must consist of a coupled lepton part, yet linking to the strong interaction via the kernel part. If now the colour-charge of the gluon transmutates into a 'neutrino-colour-charge'; then this decoupling will not only define the mechanics for the strong-weak nuclear unification coupling; but also the
energy transformation of the gauge-colour charge into the gauge-lepton charge.
There are precisely 8 gluonic transitive energy permutation eigenstates between a 'radiative-additive' Planck energy in W(hite)=E=hf and an 'inertial-subtractive'
Einstein energy in B(lack)=E=mc2, which describe the baryonic- and hyperonic 'quark-sectors' in: mc2=BBB, BBW, WBB, BWB, WBW, BWW, WWB and WWW=hf.
The permutations are cyclic and not linearly commutative. For mesons (quark-antiquark eigenstates), the permutations are BB, BW, WB and WW in the SU(2) and
SU(3) Unitary Symmetries.

So generally, we may state, that the gluon is unfied with a weakon before decoupling; this decoupling 'materialising' energy in the form of mass, namely the mass of
the measured 'weak-interaction-bosons' of the standard model (W- for charged matter; W+for charged antimatter and Zo for neutral mass-currents say).
Experiment shows, that a W- decays into spin-aligned electron-antineutrino or muon-antineutrino or tauon-antineutrino pairings under the conservation laws for
momentum and energy.
So, using our quantum geometry, we realise, that the weakly decoupled electron must represent the Outer Ring, and just as shown in the analysis of QED ( QuantumElectro-Dynamics). Then it can be inferred, that the Electron's Anti-neutrino represents a transformed and materialised gluon via its colour charge, now decoupled from the kernel.
Then the Outer Ring contracts (say along its magnetoaxis defining its asymptotic confinement); in effect 'shrinking the electron' in its inertial and charge- properties to its experimentally measured 'point-particle-size'. Here we define this process as a mapping between the electronic wavelength 2πRe and the wormhole perimeter
λweyl=2πrweyl.

But in this process of the 'shrinking' classical electron radius towards the gluonic kernel (say); the mesonic ring will be encountered and it is there, that any mass inductions should occur to differentiate a massless lepton gauge-eigenstate from that manifested by the weakon precursors.
{Note: Here the W- inducing a lefthanded neutron to decay weakly into a lefthanded proton, a lefthanded electron and a righthanded antineutrino. Only lefthanded
particles decay weakly in CP-parity-symmetry violation, effected by neutrino-gauge definitions from first principles}.
This so defines a neutrino-oscillation potential at the Inner Ring-Boundary. Using our proportions and assigning any neutrino-masses mν as part of the electronmass
me, gives the following proportionality as the mass eigenvalue of the Tau-(Anti)Neutrino as Higgsian Mass Induction in the Weak Nuclear Interaction at the Mesonic
Inner Ring Boundary within the subatomic quantum geometry utilized as the dynamic interaction space:

mHiggs/Tauon = meλweyl.rE/(2πrMRe) = meλweyl.rE/(2πrMRe)~ 5.345878435-36 kg* or 2.994971267 eV*............................................[Eq.13]

So we have derived, from first principles, a (anti)neutrinomass eigenstate energy level of 3 eV as the appropriate energy level for any (anti)neutrino matter interaction within the subatomic dynamics of the nuclear interaction.
This confirms the Mainz, Germany Result as the upper limit for neutrino masses resulting from ordinary Beta-Decay and indicates the importance of the primordial
beta-decay for the cosmogenesis and the isomorphic scale mappings stated above.
The hypersphere intersection of the G- and F-count of the thermodynamic expansion of the mass-parametric universe so induces a neutrino-mass of 3 eV* at the
2.765931439x10-18 meter marker.
The more precise G-F differential in terms of eigenenergy is 0.052 eV as the mass-eigenvalue for the Higgs-(Anti)neutrino (which is scalar of 0-spin and constituent of the so called Higgs Boson as the kernel-Eigenstate). This has been experimentally verified in the Super-Kamiokande (Japan) neutrino experiments published in 1998 and in subsequent neutrino experiments around the globe, say Sudbury, KamLAND, Dubna, MinibooNE and MINOS.
Recalling the Cosmic scale radii for the initial manifestation of the primordial 'Free Neutron (Beta-Minus) Decay', we rewrite the Neutrino-Mass-Induction formula:

rE = 3.435971077x1014 meters and an E-count of (26x6561) = 1.00x10112 spacetime quanta:
mνHiggs-E = mνelectron = me.rps{rE/rE}/Re = 5.323079952x10-39 kg* or 0.00298219866 eV* as Weak Interaction Higgs Mass induction.

But in this limiting case the supermembrane modular duality of the instanton identity Eps.e* = 1 applied to the Compton constant will define the limiting neutrino mass for the electron as a modular neutrino mass per displacement quantum defined in the Compton constant and for a modulation displacement factor {Re2/rps}:

|mνHiggs-E = mνelectron|modular = me.rps{Re2/rps}/Re = alpha.h/2πc = 2.580701988x10-45 (kg/m)*..................[Eq.14]

rF = 3.451077503x1011 metres for the F-count of (13x6656) = 1.02x10103 spacetime quanta:
mνHiggs-F = mνmuon=me.rps{rE/rF}/Re = 5.299779196x10-36 kg* or 2.969144661 eV* as Weak Interaction Higgs Mass induction.

rG = 3.39155805x1011 metres for the G-count of (67x3665) = 9.68x10102 spacetime quanta:
mνHiggs-G = mνtauon = me.rps{rE/rG}/Re = 5.392786657x10-36 kg* or 3.021251097 eV* as Weak Interaction Higgs Mass Induction.

The mass difference for the Muon-Tau-(Anti)Neutrino Oscillation, then defines the Mesonic Inner Ring Higgs Induction:............[Eq.15]
mνHiggs = me.rps{rE/rG - rE/rF}/Re = 9.3007461x10-38 kg* or 0.05210643614 eV* as the Basic Cosmic (Anti)Neutrino Mass.

This Higgs-Neutrino-Induction is 'twinned' meaning that this energy can be related to the energy of so termed 'slow- or thermal neutrons' in a coupled energy of so
twice 0.0253 eV for a thermal equilibrium at so 20° Celsius and a rms-standard-speed of so 2200 m/s from the Maxwell statistical distributions for the kinematics.
The (anti)neutrino energy at the RE nexus for RE = rps∛(26x6561) m* and for mνHiggs-E = mνelectron = μoe2c2.rps/4πRe2c2 = 30e2λps/2πcRe2 or μo{Monopole GUT masses ec}2rps/4πRe2c2 = 2.982198661x10-3 eV* and for:

mνElectronc2 = mvTauon2)c2 = mνMuon2Higgs2)c2 = μo{Monopole GUT masses ec}2rps/4πRe2. ...............................................[Eq.16]

This can also be written as mνHiggs-E=mνelectron=mνTauon2 to define the 'squared' Higgs (Anti)Neutrino eigenstate from its templated form of the quantum geometry in the Unified Field of Quantum Relativity (UFoQR).
Subsequently, the Muon (Anti)Neutrino Higgs Induction mass becomes defined in the difference between the masses of the Tau-(Anti)Neutrino and the Higgs
(Anti)Neutrino.

mνTauon = B4G4R4[0]+B2G2R2[-½]=B6G6R6[-½] = √(mνelectron)=√(0.002982)=0.0546... eV*
mνHiggs= B4G4R4[0] = meλps.rE{1/rG-1/rF}/(2πRe) ~ 9.301x10-38 kg* or 0.0521... eV*
mνMuon = B2G2R2[-½] = √(mνTauon2 - mνHiggs2) = √(0.00298-0.00271) = √(0.00027) = 0.0164... eV*
mνElectron = B2G2R2[-½] = (mνTauon)2= (0.054607...)2=0.002982... eV*

This energy self state for the Electron (Anti)Neutrino then is made manifest in the Higgs Mass Induction at the Mesonic Inner Ring or IR as the squared mass differential between two (anti)neutrino self states as:

(mν3 + mν2).(mν3 - mν2) = mν32 - mν22 = 0.002981...eV*2 to reflect the 'squared' energy self state of the scalar Higgs (Anti)Neutrino as compared to the singlet energy eigen state of the base (anti)neutrinos for the 3 leptonic families of electron-positron and the muon-antimuon and the tauon-antitauon.
The Electron-(Anti)Neutrino is massless as base-neutrinoic weakon eigenstate and inducted at RE at 0.00298 eV*.
The Muon-(Anti)Neutrino is also massless as base-neutrinoic weakon eigenstate and inducted at the Mesonic Ring F-Boundary at 2.969 eV* with an effective Higgsian mass induction of 0.0164 eV*.
All (anti)neutrinos gain mass energy however when they become decoupled from their host weakon; either a W- for matter or a W+ for antimatter. So as constituents of the weakon gauge for the weak interaction the electron- and muon (anti)neutrinos are their own antiparticles and so manifest their majorana qualities in the weak interaction. Once emitted into the energy-momentum spacetime however, the monopolic nature from their self-dual GUT/IIB monopole mass [ec]uimd or their energy [ec3=2.7x1016 GeV*]unifiedinmodularduality manifests in their masses. The premise of the older Standard Model for a massless (anti)neutrino so remains valiid for them in respect to their majorana -coupling their lepton partners as the weakon agents in their quantum geometric templates; but is modified for 'free' (anti)neutrinos as Dirac particles.

The Tauon-(Anti)Neutrino is not massless with inertial eigenstate inducted at the Mesonic Ring G-Boundary at 3.021 eV* and meaned at 3.00 eV* as √(0.05212+0.01642) = 0.0546 eV* as the square root value of the ground state of the Higgs inertia induction. The neutrino flavour mechanism, based on the Electron (Anti)Neutrino so becomes identical in the Weakon Tauon-Electron-Neutrino oscillation to the Scalar Muon-Higgs-Neutrino oscillation.

The weakon kernel-eigenstates are 'squared' or doubled (2x2=2+2) in comparison with the gluonic-eigenstate (one can denote the colourcharges as (R²G²B²)[½] and as (RGB)[1] respectively say and with the [] bracket denoting gauge-spin and RGB meaning colours Red-Green-Blue).
The scalar Higgs-Anti(Neutrino) becomes then defined in: (R4G4B4)[0] and the Tauon Anti(Neutrino) in (R6G6B6)[½].
The twinned neutrino state so becomes apparent in a coupling of the scalar Higgs-Neutrino with a massless base neutrino in a (R6G6B6)[0+½]) mass-induction template.

The Higgs-Neutrino is bosonic and so not subject to the Pauli Exclusion Principle; but quantized in the form of the FG-differential of the 0.0521 Higgs-Restmass Induction.
Subsequently all experimentally observed neutrino-oscillations should show a stepwise energy induction in units of the Higgs-neutrino mass of 0.0521 eV.
This was the case in the Super-Kamiokande experiments; and which was interpreted as a mass-differential between the muonic and tauonic neutrinoic forms.

mνHiggs + mνelectron = mνHiggs + (mνTauon)2 for the 'squared' ground state of a massless base (anti)neutrino for a perturbation Higgsian (anti)neutrino in (mνTauon)2 = (mνHiggs + Δ)2 = mνElectron for the quadratic mνHiggs2 + 2mνHiggsΔ+ Δ2 = 0.002982 from (mνHiggs + Δ) = √(mνelectron)
and for a Δ = √(mνelectron) - mνHiggs = mνTauon - mνHiggs = 0.0546 eV - 0.0521 eV = 0.0025 eV.

mνHiggs + Δ = 0.0521 + 0.0025 = (mνHiggs) + (mνelectron) - 0.00048 = mνtauon = 0.0521+0.00298 - 0.00048 + ... = 0.0546 eV* as a perturbation expression for the 'squared' scalar Higgs (Anti)Neutrino.

(mνMuon - mνElectron){(mνMuon + mνElectron) - (mνMuon - mνElectron)} = 2mνElectron(mνMuon - mνElectron) as the squared mass difference:
mνMuon2 - mνElectron2 = 2mνElectron(mνMuon - mνElectron) + (mνMuon - mνElectron)2
and for mνMuon2 = mνElectron - mνHiggs2 = (0.002982 - 0.00271 = 0.00027) for √(0.00027) = mνMuon = 0.01643 = 5.51 mνElectron .

{mνMuon2 - mνElectron2} - mνMuon2 + 2mνMuonmνElectron - mνElectron2 = 2mνMuonmνElectron - 2mνElectron2 = 2mνElectron{mνMuon - mνElectron }
= 2mνElectron2{mνMuon/mνElectron - 1} = 8.892x10-6{11.02-1} = 8.910x10-5, approximating the KamLAND 2005 neutrino mass induction value of 7.997..x10-5 eV2 obtained for a ratio of 11mνElectron = 2mνMuon.

For 3 (anti)neutrinos then, the cosmological summation lower and upper bounds for (anti)neutrino oscillations are:
0 + mνelectron-muon + mνelectron-tauon + mνmuon-tauon = 3(0.002982) = 0.00895 eV* or 0.00893 eV [SI] and 3(0.0030+0.0546) = 3(0.0576) = 0.1728 eV* or 0.1724 eV [SI] respectively.
Inclusion of the scalar Higgs (anti)neutrino as a fourth (anti)neutrino inertial self state extends this upper boundary by 0.0521 eV* and 0.0520 eV to 0.2249 eV* or 0.2243 eV [SI].

∑mν = mνElectron + mνMuon + mνHiggs+ mνTauon = 0.002982..+ 0.0164..+ 0.0521..+ 0.0546.. = 0.1261 eV* or 0.1258 eV.

In terms of the Higgs Mass Induction and so their inertial states, the Neutrinos are their own antiparticles and so Majorana defined; but in terms of their basic magneto charged nature within the Unified Filed of Quantum Relativity, the Neutrinos are different from their AntiNeutrino antiparticles in their Dirac definition of R2G2B2[+1] for the AntiNeutrinos and in B2G2R2[-1] for the Neutrinos.

 {s} = 1.00098 {s*} = 0.999023 {s} {m} = 1.00167 {m*} = 0.998331 {m} {kg} = 1.00375 {kg*] = 0.996261 {kg} {C} = 1.00271 {C*} = 0.997296 {C} {J} = 1.00514 {J*} = 0.994883 {J} {eV} = 1.00247 {eV*} = 0.99754 {eV} {K} 0.98302 {K*} = 1.01727 {K}

The Wave Matter of de Broglie: λdeBroglie = h/p

The Wave matter of de Broglie from the Energy-Momentum Relation is applied in a (a) nonrelativistic, a (b) relativistic and a (c) superluminal form​
in the matter wavelength: λdeBroglie = h/p = hc/pc for (pc) = √{E2 - Eo2}= moc2.√{[v/c]2/(1-[v/c]2)}​

(a) Example:
A pellet of 10g moves at 10 m/s for a de Broglie wavelength vdB = h/mv = h/0.1 = 6.7x10-33 m*​
This matter wavelength requires diffraction interference pattern of the order of λdB to be observable and subject to measurement​

(b) Example:
An electron, moving at 80% of light speed 'c' requires relativistic development​

Eo = moc2 with E = mc2 = moc2/√{1-[v/c]2}, a 66.66% increase in the electron's energy describing the Kinetic Energy E - Eo = {m - mo}c2
for a relativistic momentum p = moc.√{[0.8]2/(1-[0.8]2)} = (1.333..) moc = h/λdeBroglie and for a relativistic de Broglie wavelength, 60% smaller, than for the non-relativistic electron in​
λdeBroglie = h/1.333..moc < h/0.8moc =λdeBroglie (1.83x10-12 m relativistic and 3.05x10-12 m* non-relativistic for an electron 'restmass' of 9.11x10-31 kg* and measurable in diffraction interference patterns with apertures comparable to this wave matter scale).​

(c) The de Broglie matter wave speed in its 'group integrated' form derives from the postulates of Special Relativity and is defined in the invariance of light speed 'c' as a classical upper boundary for the acceleration of any mass M.​
In its 'phase-individuated' form, the de Broglie matter wave is 'hyper accelerated' or tachyonic, the de Broglie wave speed being lower bounded by light speed 'c'​

vphase = wavelength.frequency = (h/mvgroup)(mc2/h) = c2/vgroup > c for all vgroup < c​

m = Energy/c2 = hf/c2 = hc/λdeBrogliec2 = h/λdeBrogliec = mdeBroglie = [Action as Charge2]mod/c(Planck-Length Oscillation)​
= [e2]mod/clPlanck√alpha = [e2c2/ce]mod = [ec]modular

as monopole mass of GUT-string IIB and as string displacement current mass equivalent for the classical electron displacement 2Re = e*/c2 = [ec]modular as Wormhole minimum spacetime configuration for the Big Bang Instanton of Big Bang wormhole energy quantum Eps=hfps=mpsc2=kTps as a function of e*=1/Eps of Heterotic superstring class HE 8x8 and relating the Classical Electron Diameter {2Re} as Monopole Mass [ec]mod in Curvature Radius rpsps/2π = Gomps/c2.​

The factor 2Go/c2 multiplied by the factor 4π becomes Einstein's Constant k = 8πGo/c2 = 3.102776531x10-26 m/kg describing how spacetime curvature relates to the mass embedded in that spacetime in the theory of General Relativity.​

The selfduality of the superstring IIB aka the Magnetic Monopole selfstate in GUT Unification 2Re/30[ec]mod = 2Rec2/30[ec3]mod = e*/30[ec3]modκ for a proportionality constant {κ*}=2Re/30k[ec]mod = 2Re.c2/8πe = e*/8πe =1.2384..x1020 kg*/m* in string units for Star Charge in Star Colomb C*/Electro Charge in Coulomb C unified.​

The monopolar Grand Unification (SEWG gravitational decoupling SEW.G) has a Planck string energy reduced at the IIB string level of​
e*=[ec3]modular for mpsc2c/[ec]modular = [c3]modular = 2.7x1025 electron volt or 4.3362x106 J for a monopole mass [ec]modular = mmonopole = 4.818x10-11 kg* .​

Mass M = n.mss = Σmss = n.{h/2πrdeBrogliec} .[Ess.e*]mod = n.mps.[Ess.{9x1060}.2π2Rrmp3]mod = n.mps.[Ess.{2Re.c2}]mod = n.[Eps.Ess]mod.[2Re]mod
for λdeBroglieps=h/mpsc and [Eps.e*]mod =1​

{2Rec2} = 4GoMHyper for the classical electron radius Re=ke2/mec2 and describes its Hyper-Mass MHyper-electron = Rec2/2Go = ke2/2Gome = 1.125x1012 kg* for an effective electron mass of me = ke2/2Go(1.125x1012) =9.290527148x10-31 kg* in string units and where k=1/4πεo = 9x109 (Nm2/C2)*.​

The curvature radius for the electron mass me = relectronc2/2Go then becomes relectron = 2Gome/c2 = 2.293957...x10-57 m* in string-membrane inflaton space as 1.44133588x10-34 rps in the wormhole instanton space.​

Re/rinflaton-electron = MHyper-electron/me = 1.2109108..x1042 = ½(EMI/GI) = ½(e2/Go2me2) =½ {e/Gome}2 = ½(2.421821677x1042 ) for the classical electron radius Re halved from the classical electron diameter 2Re from the definition for the modulated supermembrane coupled in EpsEss=h2 and Eps/Ess=fps2=1/fss2.​

Mass M = n.mss = Σmss = n.{mps} .[Ess.e*]mod = n.{mps}[{hfss}{fps/fss}.2π2Rrmp3]mod = n.mps.[Eps.e*/fss2]mod = n.mps/|fss2|mod

The classical approach described in the Feynman lecture derives the momentum of a moving electron in deriving the volume element for electromagnetic momentum p=melectromagnetic.v.=memr.v with the component of the electron's motion v parallel gsinθ and a relativistic velocity vrel=vγ=v/√{1-[v/c]2} modifying prel=pγ

For magnetic field B = vxE/c2 = v.E.sinθ/c2 the momentum density εoExB = εov.E2sinθ/c2 electric energy density Ue=½εoE2 and E=q/(4πεor2) and dV = 2πr2.sinθ.dθ.dr for the spacetime interval from some minimum boundary a to ∞ and with ∫1/r2 dr = |-1/r|[∞,a] = 0- + 1/a = 1/a for a=Re for the waved particle electron

p = ∫εov(Esinθ/c)2 dV = prel = {2πεovγ/c2}{q2/16π2εo2}∫r-2.{sin3 θ.dθ}.dr = {vγq2/8πεoc2}∫r-2.{sin3 θ.dθ}.dr
= {vγq2/8π.a.εoc2}∫sin3 θ.dθ = {vγq2/8π.a.εoc2}∫{1-cos2θ}sinθ.dθ
= {vγq2/8π.a.εoc2}|⅓cos3θ -cosθ|[π,0] = {vγq2/8π.a.εoc2} |-⅓+1-⅓+1| = vγq2/6π.a.εoc2 = μovγe2/6π.Re
prel = μovγe2/6π.Re for memr = μoγe2/6π.Re = {4/3}½me = ⅔me > ½me

The electromagnetic mass must however be exactly Ue/c2 by the postulates of Relativity and so the classical derivation must be modified in the particle nature of the electron in its associated quantum mechanical nature.

Using memr = mo = me/2A = μoγe2/6π.Re = {4/3}½me = ⅔me defines A=¾ in the (v/c)2 distribution and for a velocity:

B2={v/c}2 = -⅚±√(19/12) for roots x=0.425 and y=-2.092; with velectron = 0.65189908 c in Um = (½v2oe2/4πRe = ½mev2

{4/3}.Ue/c2 = {4/3}γe2/8π.εoRe c2 = {4/3}½me = {4/3}.Um/c2 = {4/3}.μoγe2/8π.Re = {4/3}γke2/e* = {4/3}γke2.hf* = (1-⅓)me for ⅓me=hf/c2 and f=⅓mec2/h as the frequency supplement from the alpha force of the self-interacting electron moving with velocity 0.6518991 c with apparent restmass ⅔me.

The classical electromagnetic mass memr becomes quantum mechanical in the string-brane sourcesink energy E*-Gauge photon quantum of the Quantum Big Bang Weylian wormhole. In particular setting the classical electron radius at Re = 2/3c2 = 7.407407...x10-18 m* (7.3950476435...x10-18 m) from 2Rec2 = 4/3 normalizes the {4/3} factor from the classical derivation of the electromagnetic mass for the electron.

E* = Eps = hfps = hc/λps = mpsc2 = (me/2e).√[2πGo/αhc] = {me/mP}/{2e√α} = 1/2Rec2 = 1/e*......................[Eq.17]

The pre-Big Bang 'bounce' of many models in cosmology can be found in a direct link to the Planck-Stoney scale of the 'Grand-Unification-Theories'.
In particular it can be shown, that the Squareroot of Alpha, the electromagnetic fine structure constant, multiplied by the Planck-length results in a Stoney-transformation factor
LP√α = e/c2 in a unitary coupling between the quantum gravitational and electromagnetic fine structures and so couples the unitary measurement of displacement in the Planck-Length oscillation equal to Coulombic charge quantum 'e' divided by the square of the speed of light 'c2' in a proportionality of Displacement = ChargexMass/Energy.
This couples the electric Coulomb charge quantum to the magnetic monopole quantum e* as the inverse of the 10-dimensional superstring sourcesink energy Eps to the 10-dimensional superstring sinksource energy Ess as the 11-dimensional super-membrane EpsEss.

{Gok=1 for Go=4πεo and representing a conformal mapping of the Planck length onto the scale of the 'classical electron' in superposing the lower dimensional inertia coupled electric charge quantum 'e' onto a higher dimensional quantum gravitational-D-brane magnetopole coupled magnetic charge quantum 'e*' = 2Re.c2 = 1/hfps = 1/EWeyl wormhole by the application of the mirror/T duality of the super membrane EpsEss of heterotic string class HE(8x8)}.

The corresponding energy level for this wavelength of Re is 2.7x10-8 Joules* or 168.0718 GeV* (167.6584 GeV) for a mass of 3x10-25 kg* (2.988783x10-8 kg).

Expressing the electromagnetic mass in a series perturbation expansion in decreasing the classical electron size so sets a minimum size for the electron at the Weyl boundary or 'Planck-Stoney Bounce' limit at Re in x/c2 = λps/2π for x = rpsc2 = 2GoMHubble = Wormhole Radius of the Instanton of the quantum gravitational Big Bang creation event.

Modular duality Eps= hfps=1/e* = Energy primary sourcesink quantum as the Weyl wormhole energy then transforms the electron's self- energy in a decomposition or fine structure of the classical electron radius and as 'spacetime awareness' or 'physical consciousness'.
Spacetime awareness |df/dt| acting on a volume of space in a holographic Weyl Bound conformally maps and integrates the quantum gravitational wormhole of wavelength λps=10-22 m* onto the the classical electron radius as: Rwormhole/Relectron = 360/(2π.1010).

This can be defined as a form of angular acceleration |alphaomega = αω| = |df/dt|e = e*/V* = λps/hc.V* acting on space time volumars or multi-dimensional branes in particle-wave interactions of elementary particles-wavicles. It is so the space occupied and containing dynamical interactions, which render the synthesis of classical physics with quantum mechanics possible; the underpinning nature for those interactions being based on the quantum geometry of the conformal transformations from and to the higher dimensional and closed Anti de Sitter (AdS) spacetimes intersecting the lower dimensional and open de Sitter (dS) spacetimes.

memr = μoγe2/6π.Re = {4/3}.Ue/c2 = {4/3}γe2/8π.εoRe c2 = {4/3}½me = {4/3}.Um/c2 = {4/3}.μoγe2/8π.Re = {4/3}γke2/e* = {4/3}γke2.hf*

As the electromagnetic mass must however be exactly Ue/c2 by the postulates of Relativity and so the classical derivation must be modified in the particle nature of the electron in its associated quantum mechanical nature.
A Self-Interaction for the electron in the jerk or time derivative of acceleration d3x/dt3 is naturally found in the definition of the classical size of the electron in the wormhole quantization.
The self-interaction of the electron then can be considered as a deformation of the size of the electron using both the classical scale of the particular and the quantum mechanical form in the nature of its intrinsic quantum spin in the form of an angular acceleration given as the time derivative of frequency df/dt.

The extension of Newton's Law in relativistic momentum and energy leads to dprel/dt = d(moγv)/dt = mod(γv)/dt + γvd(mo)/dt = mod(γv)/dt + {γvh/c2}df/dt = moγ3.dv/dt + {γvh/c2}df/dt.
It then is the dynamical interaction of the electron with spacetime itself, that changes the classical volume of the electron as a function of df/dt in the membrane space of 2Rec2=Volume x Angular radially independent acceleration.

Using this electron self-interaction as a conformal mapping from the Quantum Big Bang 'singularity' from the electric charge in brane bulk space as a magnetic charge onto the classical spacetime of Minkowski and from the Planck parameters onto the atomic-nuclear diameters in 2Rec2 = e* from the Planck length conformally maps the Planck scale onto the classical electron scale as the classical electron radius and as defined in the alpha electromagnetic fine structure and the related mass-charge definition for the eigen energy of the electron in mec2=ke2/Re.

The pre-Big Bang 'bounce' of many models in cosmology can be found in a direct link to the Planck-Stoney scale of the 'Grand-Unification-Theories'. In particular it can be shown, that the Squareroot of Alpha, the electromagnetic fine structure constant, multiplied by the Planck-length results in a Stoney-transformation factor LP√α = e/c2 in a unitary coupling between the quantum gravitational and electromagnetic fine structures {Gok=1 for Go=4πεo and representing a conformal mapping of the Planck length onto the scale of the 'classical electron' in superposing the lower dimensional inertia coupled electric charge quantum 'e' onto a higher dimensional quantum gravitational-D-brane magnetopole coupled magnetic charge quantum 'e*' = 2Re.c2 = 1/hfps = 1/EWeyl wormhole by the application of the mirror/T duality of the super membrane EpsEss of heterotic string class HE(8x8)}.

Also in a model of quantum relativity (QR), there is a quantization of exactly 1010 wormhole 'singularity-bounce' radii defining the radian-trigonometric Pi ratio as Rwormhole/Relectron = 360/2π.1010 or 1010 = {360/2π}{Re/rwormhole} as a characteristic number of microtubules in a conformal mapping from the classical electron space onto the 'consciousness' space of the neuron-cell intermediate between the Hubble scale of 1026 m and the Planck scale of 10-35 m as geometric mean of 10-4 to 10-5 metres.

It is so the geometry of the architecture of the microtubules and the nature of their construction utilizing the pentagonal quasi-crystalline pattern in its application for maximising the compression of information in the Fibonacci geometrical pattern-sequencing. This then results in the conformal mapping of this geometry as a quantum geometry and defining physical consciousness as a conformal mapping of the quantum of spacetime in the form of Weylian 'Quantum Big Bang' wormholes of the cosmogenesis.
The 4/3 factor from the classically derived electromagnetic mass appears in the quantum geometry of the subatomic particles, namely in the different quark content for the positively charged proton and the electrically overall neutral neutron, both displaying an internal charge distribution however.

For the Proton, one adds one (K-IR-Transition energy) and subtracts the electron-mass for the d-quark level and for the Neutron one doubles this to reflect the up-down-quark differential.
An electron perturbation subtracts one 2-2/3=4/3 electron energy as the difference between 2 leptonic rings from the proton's 2 up-quarks and 2-1/3=5/3 electron energy from the neutron' singular up-quark to relate the trisected nucleonic quark geometric template. This is revisited below.

Proton mp=u.d.u=K.KIR.K=(939.776+1.5013-0.5205-0.1735) MeV* = 940.5833 MeV* (938.270 MeV).
Neutron mn=d.u.d=KIR.K.KIR=(939.776+3.0026-1.0410+0.1735) MeV* = 941.9111 MeV* (939.594 MeV).

This is the groundstate from the Higgs-Restmass-Induction-Mechanismand reflects the quarkian geometry as being responsible for the inertial mass differential between the two elementary nucleons. All groundstate elementary particle masses are computed from the Higgs-Scale and then become subject to various fine structures.

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) = (2.818054177x10-15 m)(9.109015537x10-31 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 = 2.773142866x10-15 m for an increased electron effective restmass of me = 9.255789006x10-31 kg or for (Reme) = (μoe2/4π) = 2.566762525x10-45 mkg.

The electron has no known substructure.[1][75] and it is assumed to be a point particle with a point charge and no spatial extent.[9] In classical physics, the angular momentum and magnetic moment of an object depend upon its physical dimensions. Hence, the concept of a dimensionless electron possessing these properties contrasts to experimental observations in Penning traps which point to finite non-zero radius of the electron. A possible explanation of this paradoxical situation is given below in the "Virtual particles" subsection by taking into consideration the Foldy-Wouthuysen transformation.​

The issue of the radius of the electron is a challenging problem of the modern theoretical physics. The admission of the hypothesis of a finite radius of the electron is incompatible to the premises of the theory of relativity. On the other hand, a point-like electron (zero radius) generates serious mathematical difficulties due to the self-energy of the electron tending to infinity.[76] These aspects have been analyzed in detail by Dmitri Ivanenko and Arseny Sokolov.​

Observation of a single electron in a Penning trap shows the upper limit of the particle's radius is 10−22 meters.[77] Also an upper bound of electron radius of 10−18 meters[78] can be derived using the uncertainty relation in energy.​

There is also a physical constant called the "classical electron radius", with the much larger value of 2.8179×10−15 m, greater than the radius of the proton. However, the terminology comes from a simplistic calculation that ignores the effects of quantum mechanics; in reality, the so-called classical electron radius has little to do with the true fundamental structure of the electron.[79][note 5]

Note that the defined maximum scale for the electron in the Penning Trap is consistent with the defined size of the wormhole radius rps=10-22/2π metres as minimum spacetime configuration of the Instanton. The 'point particular' electron of Quantum ElectroDynamics and its point-like particle fields, so crystallizes naturally from the theory of the string-membrane classes. The classical electron radius Re has much to do with the quantum mechanical electron addressed by Richard Feynman in the linked lecture.

From the Feynman Lecture:
There is, however, one fundamental objection to this theory and to all the other theories we have described. All particles we know obey the laws of quantum mechanics, so a quantum-mechanical modification of electrodynamics has to be made. Light behaves like photons. It isn’t 100 percent like the Maxwell theory. So the electrodynamic theory has to be changed. We have already mentioned that it might be a waste of time to work so hard to straighten out the classical theory, because it could turn out that in quantum electrodynamics the difficulties will disappear or may be resolved in some other fashion. But the difficulties do not disappear in quantum electrodynamics. That is one of the reasons that people have spent so much effort trying to straighten out the classical difficulties, hoping that if they could straighten out the classical difficulty and then make the quantum modifications, everything would be straightened out. The Maxwell theory still has the difficulties after the quantum mechanics modifications are made.

The quantum effects do make some changes—the formula for the mass is modified, and Planck’s constant h/2π appears—but the answer still comes out infinite unless you cut off an integration somehow—just as we had to stop the classical integrals at r=a. And the answers depend on how you stop the integrals. We cannot, unfortunately, demonstrate for you here that the difficulties are really basically the same, because we have developed so little of the theory of quantum mechanics and even less of quantum electrodynamics. So you must just take our word that the quantized theory of Maxwell’s electrodynamics gives an infinite mass for a point electron.​

It turns out, however, that nobody has ever succeeded in making a self-consistent quantum theory out of any of the modified theories. Born and Infeld’s ideas have never been satisfactorily made into a quantum theory. The theories with the advanced and retarded waves of Dirac, or of Wheeler and Feynman, have never been made into a satisfactory quantum theory. The theory of Bopp has never been made into a satisfactory quantum theory. So today, there is no known solution to this problem. We do not know how to make a consistent theory—including the quantum mechanics—which does not produce an infinity for the self-energy of an electron, or any point charge. And at the same time, there is no satisfactory theory that describes a non-point charge. It’s an unsolved problem.​

In case you are deciding to rush off to make a theory in which the action of an electron on itself is completely removed, so that electromagnetic mass is no longer meaningful, and then to make a quantum theory of it, you should be warned that you are certain to be in trouble. There is definite experimental evidence of the existence of electromagnetic inertia—there is evidence that some of the mass of charged particles is electromagnetic in origin.​

It used to be said in the older books that since Nature will obviously not present us with two particles—one neutral and the other charged, but otherwise the same—we will never be able to tell how much of the mass is electromagnetic and how much is mechanical. But it turns out that Nature has been kind enough to present us with just such objects, so that by comparing the observed mass of the charged one with the observed mass of the neutral one, we can tell whether there is any electromagnetic mass. For example, there are the neutrons and protons. They interact with tremendous forces—the nuclear forces—whose origin is unknown. However, as we have already described, the nuclear forces have one remarkable property. So far as they are concerned, the neutron and proton are exactly the same.​

The nuclear forces between neutron and neutron, neutron and proton, and proton and proton are all identical as far as we can tell. Only the little electromagnetic forces are different; electrically the proton and neutron are as different as night and day. This is just what we wanted. There are two particles, identical from the point of view of the strong interactions, but different electrically. And they have a small difference in mass. The mass difference between the proton and the neutron—expressed as the difference in the rest-energy mc2 in units of MeV—is about 1.3 MeV, which is about 2.6 times the electron mass. The classical theory would then predict a radius of about ½ to ⅓ the classical electron radius, or about 10-13 cm. Of course, one should really use the quantum theory, but by some strange accident, all the constants—2π’s and h/2π’s, etc.—come out so that the quantum theory gives roughly the same radius as the classical theory.​

The only trouble is that the sign is wrong! The neutron is heavier than the proton.​

Nature has also given us several other pairs—or triplets—of particles which appear to be exactly the same except for their electrical charge. They interact with protons and neutrons, through the so-called “strong” interactions of the nuclear forces. In such interactions, the particles of a given kind—say the π-mesons—behave in every way like one object except for their electrical charge. In Table 28–1 we give a list of such particles, together with their measured masses. The charged π-mesons—positive or negative—have a mass of 136.9 MeV, but the neutral πo-meson is 4.6 MeV lighter. We believe that this mass difference is electromagnetic; it would correspond to a particle radius of 3 to 4x10-14 cm. You will see from the table that the mass differences of the other particles are usually of the same general size.​

Now the size of these particles can be determined by other methods, for instance by the diameters they appear to have in high-energy collisions. So the electromagnetic mass seems to be in general agreement with electromagnetic theory, if we stop our integrals of the field energy at the same radius obtained by these other methods. That’s why we believe that the differences do represent electromagnetic mass.
You are no doubt worried about the different signs of the mass differences in the table. It is easy to see why the charged ones should be heavier than the neutral ones. But what about those pairs like the proton and the neutron, where the measured mass comes out the other way? Well, it turns out that these particles are complicated, and the computation of the electromagnetic mass must be more elaborate for them. For instance, although the neutron has no net charge, it does have a charge distribution inside it—it is only the net charge that is zero. In fact, we believe that the neutron looks—at least sometimes—like a proton with a negative π-meson in a “cloud” around it, as shown in Fig. 28–5. Although the neutron is “neutral,” because its total charge is zero, there are still electromagnetic energies (for example, it has a magnetic moment), so it’s not easy to tell the sign of the electromagnetic mass difference without a detailed theory of the internal structure.​

The negatively charged pion cloud of Feynman and Yukawa can be substituted by the inner negatively charged mesonic Inner Ring in the quantum geometry of the quarks based on colour charged or chromodynamic double charged kernels surrounded by an Inner Mesonic and an outer Leptonic Ring wave structure asymptotically confined by a magneto charged region known as the classical radius of the electron. The rings are oppositely charged to the kernel quarks. They however remain coupled in the kernel trisection say as the protons udu=K.KIR.K=K(K+IR)K or the neutron's dud=KIR.K.KIR=(IR+K)K(K+IR) except when they experience the electro-weak decays.

There actually exist three uds-quark states which decay differently via strong, electromagnetic and weak decay rates in the uds (Sigmao Resonance); usd (Sigmao) and the sud (Lambdao) in increasing stability.
This quantum geometry then indicates the behaviour of the triple-uds decay from first principles, whereas the contemporary standard model does not, considering the u-d-s quark eigenstates to be quantum geometrically undifferentiated.
The nuclear interactions, both strong and weak are confined in a ' Magnetic Asymptotic Confinement Limit coinciding with the Classical Electron Radius Re=ke²/mec² and in a scale of so 3 Fermi or 2.8x10-15 meters. At a distance further away from this scale, the nuclear interaction strength vanishes rapidly.

Subtracting the Ring-VPE (3L) gives the basic nucleonic K-State as 939.776 MeV*. This excludes the electronic perturbation of the IR-OR oscillation.

For the Proton, one adds one (K-IR-Transition energy) and subtracts the electron-mass for the d-quark level and for the Neutron one doubles this to reflect the up-down-quark differential.
An electron perturbation subtracts one 2-2/3=4/3 electron energy as the difference between 2 leptonic rings from the proton's 2 up-quarks and 2-1/3=5/3 electron energy from the neutron' singular up-quark to relate the trisected nucleonic quark geometric template.

Proton mp=u.d.u=K.KIR.K=(939.776+1.5013-0.5205-0.1735) MeV* = 940.5833 MeV* (938.270 MeV).
Neutron mn=d.u.d=KIR.K.KIR=(939.776+3.0026-1.0410+0.1735) MeV* = 941.9111 MeV* (939.594 MeV).

This is the groundstate from the Higgs-Restmass-Induction-Mechanismand reflects the quarkian geometry as being responsible for the inertial mass differential between the two elementary nucleons. All groundstate elementary particle masses are computed from the Higgs-Scale and then become subject to various fine structures.

{1} Matter interacts with antimatter based Neutrinos in Majorana-Dirac Electron Capture

An Electron in the inner atomic nucleus is captured by a proton to create a neutron accompanied by an electron neutrino. This requires a u-quark of the proton to transform into a d-quark of the neutron. As the d-quark is a KIR quark of inner mesonic ring of electro charge [+2/3] coupled to the MIR of electro charge [-1], a W- weakon must be engaged to couple to a left handed proton via the nonparity of the weak nuclear interaction. However in electron capture a left handed electron neutrino is emitted, requiring the interaction of a W+ weakon as the kernel gauge for any such right handed antimatter weak decay.
So should the interacting electron initiate electron capture then a W- becomes the bosonic partner for the interaction; but if it is the interacting proton, then a W+ should become the weak interaction agent to neutralize its positive electric charge with the negative electric charge of the interacting electron.
The interaction of matter and anti-matter in the form of the weak interaction bosons and their associated anti-neutrinos and neutrinos can however be shown to result from a basic kernel-ring interaction of the anti-neutrinos and neutrinos as both Majorana particles and as Dirac particles.
Majorana particles are their own anti-particles allowing identification of right handed anti-neutrinos as left handed neutrinos in the base templated or massless self-state.
Dirac particles distinguish right handed anti-neutrinos from left handed neutrinos due their mass and inertia in their native oscillation potential.

For a left handed proton u[-½]d[+½]u[-½] and a left handed electron e-[-½], the W- consisting of a right handed electron and a right handed anti-neutrino initiates the KIR-Oscillation from the Anti-Neutrino-Gluon kernel of the up quark in coupling it to the OR part of the W-. The colourless Graviphoton rendering the 'virtuality' of the W- as physically real in neutralizing the bosonic weakon spin, which 'flips' the right handed anti-neutrino into a left handed neutrino observed.

Proton p+[-½] + Electron e-[-½] ⇒ p+[-½] + OR-[-½]* + ({Electron e-[+½] + Antiνelectron[+½]}W- + Graviphoton[-1])
⇒ d[+½]u[-½]{u[-½] + IR-[0]}*{KIR-Oscillation (OR-IR)o[-½]+W-[+1]+GP[-1]} ⇒ d[+½]u[-½]d[-½] + {(OR-IR)o[0] + Antiνelectron[+½]+GP[-1]} ⇒ no[-½] + νelectron[-½]
with the KIR-Oscillation transferring the interacting left handed electron charge -1 without spin in the OR-IR-K for the IR-K up-down quark transformation {+2/3-1=-1/3} and neutralizing the weakon associated intrinsic right handed electron spin as +½-½=0 for the remaining OR-IR transition.
The neutron is cyclically delinearised from spin selfstate d[+½]u[-½]d[-½] into the triplet configuration YCM=CMY=MYC as d[-½]u[+½]d[-½].

A Magneto axis symmetric Proton K(KIR)K transforms into Magneto axis symmetric Neutron KIR(K)KIR as one of the proton's end Kernel up-quarks 'captures' the Weakonic VPE scalar OR- Electron Outer Ring in the Unified Field of Quantum Relativity.

It is in fact a W-, that interacts, but coupling to the left handed electron instead of the left handed proton, the latter requiring some coupling to the W+ weakon in the quantum field to materialize the electron neutrino from the W+ template in a direct fashion and not as the Majorana-Dirac 'flip' initiated by the W- from before.
It is the W+ intrinsic positron which is 'flipped' to 'free' the materialising neutrino from the W+ weakon base state.
But as the resultant Outer Ring - Inner Ring remnant {(OR-IR)+[0]} is positively charged and not charge neutral as was the case for the previous W- weakon interaction; the W+ weakon from the proton is suppressed in electron capture in favour of the W- weakon from the electron.

Proton p+[-½] + Electron e-[-½] ⇒ p+[-½] + IR-[-½] + ({Positron e+[-½] + νelectron[-½]}W+ + Graviphoton[+1])
⇒ d[+½]u[-½]{u[-½] + IR-[0]}*{KIR-Oscillation (OR
-IR)o[-½]+e+[+½]+velectron[-½]} ⇒ d[+½]u[-½]d[-½] + {(OR-IR)+[0]} +νelectron[-½]
⇒ no[+½]+νelectron[-½] + {(OR-IR)+[0]}

The W- then supplies the required KIR for the up-quark to down-quark transmutation with the gauge spin neutralizer of the left handed Graviphoton [-1] flipping the right handed electron anti-neutrino constituent of the W- into its anti-particular form of a left handed electron neutrino as a Majorana self-state transforming into a Dirac self-state.

Electron capture so displays the Majorana nature of the two base neutrinos of the electron-positron and muon-antimuon definition in their massless gauge nature when engaged in the direct interaction or 'tapping' of the UFoQR in the Vortex-Potential-Energy or VPE/ZPE in R2G2B2[+½]+B2G2R2[-½] = BY2B[0]=GM2G[0]=RC2R[0] = VPE[0].
Anti-Neutrino template R2G2B2[+½] = W2[+½] = B2G2R2[-½] as Neutrino template in E=hf radiative 'White'-eigen energy and being indifferentiated between the particle and anti-particular energy eigen state under the application of the spin symmetry of the 'flipping' 'white' Graviphoton.
The Dirac nature of the base neutrinos then can be said to apply to all (anti)neutrinos carrying mass in their oscillation potential and properties exhibited in their wave mechanical dynamics manifested in the Anti-Neutrino template R2G2B2[+½] being the anti-state for the Neutrino template B2G2R2[-½] and without or following the Graviphoton 'flip'.

{2} Matter interacts with matter based Anti-Neutrinos via superposed VPE-Weakon Action

Protons transform into neutrons with antimatter positrons and where the interacting anti-neutrino as constituent part of the W- weakon induces Pair-Production for weakon's electron in tapping the VPE to manifest a like spinning positron to neutralize the boson spin of the Graviphoton. The spin of the Graviphoton so cancels the spin of the Pair-Production VPE as well as the spin of the weakon boson in a superposition of the VPE and the weak interaction.

A up quark of the proton then changes into a down quark for the produced neutron in a double transition from the Outer Ring of the weakon's electron transiting to the Inner Ring and the original anti-neutrino transits from the Inner Ring onto the Gluon-Neutrino kernel K as the decay products of a free neutron. The right handed spin quantum of the anti-neutrino cancels the left handed quantum spin of the weakon's electron base which was flipped by the Graviphoton for the MIR oscillation between the up quark and the down quark transformation.

{Mass produced photons (by acceleration of inertia coupled electro charges), have no magneto charge and so form their own anti-particles; whilst gauge or 'virtual' photons carry cyclic and anticyclic colour charges as consequence of the matter-antimatter asymmetry}.

Proton p+[-½] + Antiνelectron[+½] ⇒ p+[-½] + {Antiνelectron[+½] + (Electron e-[+½]}W- + Positron e+[+½]VPEo[+1] + Graviphoton[-1]
⇒ p+[-½] + {Electron e-[-½] + Antiνelectron[+½]} + Positron e+[+½] ⇒ {p+[-½]+IR-[0]+Ko[-½+½]} + e+[+½] ⇒ no[-½] + e+[+½]

{3} Matter interacts with antimatter based Neutrinos via Unified Weakon Action {OR-+Antiν=W-;ν+Anti-OR+=W+}

Neutrons transform into protons with muons, the latter decaying into electrons and anti-neutrinos and neutrinos, so reducing the elementary matter-neutrino interaction to basic neutron beta-minus-decay with the leptonic coupling between the 'resonance electron' as a basic muon coupled to its neutrino. A neutron's down quark transforming into a up quark in disassociating the mesonic Inner Ring part of the down quark from its up quark kernel part to become the leptonic Outer Ring part of the manifesting muon. The interacting muon neutrino couples with the anti-neutrino of the weakon template as its own anti particle transferring its mass to the muon and changing its self-state from mass defined Diracness to massless Majorananess in the process.

Neutron no[-½] + νmuon[-½] ⇒ no[-½] + νmuon[-½] + ({Antiνmuon[+½] + (Muon μ-[+½]}W- +GP[-1])
⇒ d[-½]u[+½]d[-½] + *{KIROR-Oscillation (OR-IR-K)[+½] +Antiνmuon[+½]+νmuon[-½] + GP[-1]}
⇒ d[-½]u[+½]u[-½] + IR-[0] + {OR-[+½]+GP[-1]} +{R2G2B2[-½]+B2G2R2[+½]} ⇒ p+[-½] + μ-[-½] + VPE[0]
⇒ p+[-½] + μ-[-½] +VPE[0] ⇒ p+[-½] + *{KIROR-Oscillation (OR-IR-K)[-½]}({e-[+½] + Antiνelectron[+½]}W- + GP[-1])
⇒ p+[-½] + νmuon[-½] + e-[-½] + Antiνelectron[+½]

In the muon beta decay, the KIROR oscillation transfers the spin of the interacting muon as the spin of its self-state neutrino and enabling the constituents of the matter weakon W- to manifest with the right handed electron part flipping to manifest the left handed electron of the beta decay.

mνHiggs=meλw.rE/(2πrMRe){1/rG-1/rF} ~ 9.3x10-38 kg or 0.052 eV for a scalar blueprint AntiνHiggs = R4G4B4[0] with anti-state νHiggs = B4G4R4[0]
and coupling as the Tauon (Anti) Neutrino as
Antiνtauon = R2G2B2[+½] + R4G4B4[0] = R6G6B6[+½] = Antiνelectron + AntiνHiggs and
νtauon = B2G2R2[-½] + B4G4R4[0] = B6G6R6[-½] = νelectron + νHiggs

For a differential equation for Potential Energy: ∇2∅ - {μr}2 = 0

2∅ - {r/Re}2 = 0 = (1/r).∂2/∂r2{r∅} - {r/Re}2.∅
2/∂r2{r∅} = {r/Re}2.(r∅) for a solution
r∅ = constant.exp[-r/Re] for the Yukawa Potential with μ = 1/Re = 4πεomec2/e2 = 4πmeoe2

∅ = constant.(1/r).exp[-r/Re] ⇒ mec2 = (μoe2c2/4πR).exp[-R/Re] for R/Re = exp[-R/Re]

f(R/Re) = R/Re - exp[-R/Re] = f(x) = x - exp[-x] = 0 with derivative f'(R/Re) = f'(x) = 1 + exp(-x)
and xk+1 = xk - f(x)/f'(x) for a Newton-Raphson solution xo =½ for

x1 = ½ - (-0.10653066)/(1.6065307) = 0.56631100;
x2 = 0.56631100 - (-0.00130508243)/(1.56761552) = 0.56714353
x3 = 0.56714353 - (0.00000037547)/(1.56714316) = 0.56714330... for R = 0.5671433 Re

For the potential energy of the electron with effective mass me = μoe2/4πR, the Yukawa potential for the nucleus reduces the classical electron radius to 0.5671433 Re, which is approximates the radius of the proton as ½Re.

From the Feynman Lecture:
This function is called the Yukawa potential. For an attractive force, K is a negative number whose magnitude must be adjusted to fit the experimentally observed strength of the forces.
The Yukawa potential of the nuclear forces dies off more rapidly than 1/r by the exponential factor. The potential—and therefore the force—falls to zero much more rapidly than 1/r for distances beyond 1/μ, as shown in Fig. 28–6. The “range” of nuclear forces is much less than the “range” of electrostatic forces. It is found experimentally that the nuclear forces do not extend beyond about 10−13 cm, so μ]≈1015 m−1.​

Fig. 28–6.The Yukawa potential e−μr/r, compared with the Coulomb potential 1/r.

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

Graviton Unification in a Coupling of the Supermembranes in Selfdual 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 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 transformation 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 multiverse 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

xxxcontinue

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.
This probability then crystallizes in Juju's equation for the monopolar electron velocity:

{vps/c}2 = 1/{1 + 4π2rec42λps4} = 1/{1 + rec4/4π2α2rps4} ............................................................................................ [Eq.5]

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 Heterosis 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*.

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.

Typical decay rates for the nested fundamental interactions then follow the order in the lightpath lp = ctk:
tSNI = Re/c = 2.777..x10-15 m*/3x108 m*/s* = 0.925925...10-24 s* ~ Order (10-23 s*)
tEMI = tSNI/α = 10-23 s*/(7.30x10-3) = 1.37x10-21 s* ~ Order (10-21 s*)
tWNI =tSNI6 = 10-23 s*/(1.51x10-13) = 6.62x10-11 s* ~ Order (10-10 s*)
tGI = tSNI18 = 10-23 s*/(3.44x10-39) = 2.91x1015 s* ~ Order (1015 s* ~ 92 million years characterising the half lives of transuranium elements like Plutonium Pu-244 at 79x106 y)

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 = 2πGo.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.

F-theory is a branch of string theory developed by Cumrun Vafa.[1] The new vacua described by F-theory were discovered by Vafa and allowed string theorists to construct new realistic vacua — in the form of F-theory compactified on elliptically fibered Calabi–Yau four-folds. The letter "F" supposedly stands for "Father".[2]

F-theory is formally a 12-dimensional theory, but the only way to obtain an acceptable background is to compactify this theory on a two-torus. By doing so, one obtains type IIB superstring theory in 10 dimensions. The SL(2,Z) S-duality symmetry of the resulting type IIB string theory is manifest because it arises as the group of large diffeomorphisms of the two-dimensional torus

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 = μoe2c/2h = 60πe2/h .......... (Planck-Stoney-QR units *)

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 proto-nucleonic 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 in the form of an energy dependent 'running coupling constant' and which takes a value of αZ = 0.1184 at the energy level of the Zo weakon at about 92 GeV.

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.

It is this lepton component which necessitates the existence of the muon (and the tauon and their neutrino partners as constituents of the weak interaction gauge bosons) as a 'heavy electron', as the quantum geometry defines the muon mass in a decoupling of the L1 energy level given in a diquark hierarchy and based on a quantum geometry of the quantum relativity:

 particle most symmetric quantum geometry basic.symbol.energy.partition for groundstates gk (+Δ) energy values energy * MeV* energy SI MeV particle name p+ u.d.u=KKIRK mK+[L2}-[e-]-⅓[e-] 939.776+1.5013-0.5205-0.1735 940.5833 938.270 charged proton no d.u.d=KIRKKIR mK+2[L2]-2[e-]-⅔[e-] 939.776+3.0026-1.0410+0.1735 941.9111 939.594 neutral neutron μ± OR* in 1st OR oscillation mL - L1 - Δ n[Ls : 98.19-111.05] 111.04536-(4.90355+Δ) 106.142-Δ 105.658375 charged muon τ± OR** in 2nd OR oscillation LM - mL + Ls + Lud + Δ 1822.45-111.05+53.31+16.02+Δ =1711.4+69.33+Δ 1780.73+Δ 1776.86 charged tauon πo u.ubar; d.dbar mgud - Lud + Δ 150.5767-16.0153+Δ 134.56+Δ 134.9776 neutral pion groundstate π± u.dbar; ubar.d mgud - Lud + L1 + e- 150.5767-16.0153+4.90355+~e- 139.98545 139.5702 charged pion λo d.s.u mno+ mπo + gL2 - L1 + Δ 941.911+134.56+46.103-4.904+Δ 1118.3 1115.683 neutral lambda

For the Proton, one adds one (K-IR-Transition energy) and subtracts the electron-mass for the d-quark level and for the Neutron one doubles this to reflect the up-down-quark differential.
An electron perturbation subtracts one 2-2/3=4/3 electron energy as the difference between 2 leptonic rings from the proton's 2 up-quarks and subtracts 2-1/3=5/3 electron energy from the neutron's singular up-quark to relate the trisected nucleonic quark geometric template.

The X-Boson's mass is: ([Alpha α]xmps/[ec]) modulated in (SNI/EMI=∛{Alpha}/[Alpha]), the intrisic unified Interaction-Strength and as the L-Boson's mass in: ([Omega]x([ec])/(mps.∛(α2).

Ten DIQUARK quark-mass-levels crystallise, including a VPE-level for the K-IR transition and a VPE-level for the IR-OR transition:

 Quark Level Kernel-Energy in MeV* K-Mean(x½) in MeV* Ring-Energy in MeV* IR-OR.Mean.in.MeV* Comment VPE-Level [K-IR] 26.4959-29.9663 gL1 = 14.11554 2.8181-3.1872 L2 = 1.501325 K-IR VPE VPE-Level [IR-OR] 86.5383-97.8729 gL2 = 46.1028 9.2042-10.410 L1 = 4.90355 IR-OR VPE Ground-OR electron level UP/DOWN-Level u=K; d=K+IR 282.5655-319.619 gud = 150.5767 30.062-33.999 Lud = 16.0153 K-KIR basis STRANGE-Level s=K+OR 923.1410-1,044.05 gs = 491.7990 98.185-111.05 muon energy Ls = 52.30875 KIR-KOR basis 1st (K)-OR-Muon level CHARM-Level c=u.ubar.u; U=uu 3,015.08-3,409.98 gcU = 1,606.266 320.68-362.69 LcU = 170.843 singlet apparent BEAUTY-Level b=u.dbar/ubar.d 9,847.55-11,137.34 gb = 5,246.223 1,047.4-1,184.6 Lb = 558.0 doublet apparent MAGIC-Level M=u.sbar/ubar.s 32,163.1-36,375.7 gM = 17,134.71 3,420.9-3,868.9 LM = 1,822.45 max Tauon energy doublet suppressed 2nd K-OR-Tauon level DAINTY-Level D=dd=d.dbar 105,048-118,807 gD= 55,963.7 11,173-12,636 LD = 5,952.25 triplet suppressed TRUTH-Level t=d.sbar/dbar.s 343,098-388,036 gt = 182,783.3 36,492-41,271 Lt = 19,440.75 triplet apparent SUPER-Level S=ss=s.sbar 1,120,592-1,267,366 gS = 596,906.8 119,186-134,797 LS = 63,495.75 triplet suppressed
The K-Means define individual materialising families of elementary particles;

the (UP/DOWN-Mean) sets the (PION-FAMILY: πo, π+, π-);
the (STRANGE-Mean) specifies the (KAON-FAMILY: Ko, K+, K-);
the (CHARM-Mean) defines the (J/PSI=J/Ψ-Charmonium-FAMILY);
the (BEAUTY-Mean) sets the (UPSILON=Υ-Bottonium-FAMILY);
the (MAGIC-Mean) specifies the (EPSILON=Ε-FAMILY);
the (DAINTY-Mean) bases the (OMICRON-Ο-FAMILY);
the (TRUTH-Mean) sets the (KOPPA=Κ-Topomium-FAMILY) and
the (SUPER-Mean) defines the final quark state in the (HIGGS/CHI=H/Χ-FAMILY).

The VPE-Means are indicators for average effective quarkmasses found in particular interactions.
Kernel-K-mixing of the wavefunctions gives K(+)=60.218 MeV* and K(-)=31.987 MeV* and the IROR-Ring-Mixing gives (L(+)=6.405 MeV* and L(-)=3.402 MeV*) for a (L-K-Mean of 1.50133 MeV*) and a (L-IROR-Mean of 4.90355 MeV*); the Electropole ([e-]=0.52049 MeV* and 3x(0.17350 MeV* for e±/3) as the effective electronmass and as determined from the electronic radius and the magnetocharge in the UFoQR.

The restmasses for the elementary particles can now be constructed, using the basic nucleonic restmass (mc=9.9247245x10-28 kg*=(√(OmegaxmP) for np as 1.71175286x10-27 kg* or 958.99 MeV* and setting
(mc) as the basic maximum (UP/DOWN-K-mass=mass(KERNEL CORE)=3xmass(KKK)=3x319.6637 MeV*=958.991 MeV*);
Subtracting the (Ring VPE 3xL(+)=19.215 MeV*, one gets the basic nucleonic K-state for the atomic nucleus (made from protons and neutrons) in: {m(n0;p+)=939.776 MeV*}.

A best approximation for 'Big G' hence depends on an accurate determination for the neutron's inertial mass, only fixed as the base nucleon minimum mass at the birth of the universe. A fluctuating Neutron mass would also result in deviations in 'G' independent upon the sensitivity of the measuring equipment. The inducted mass difference in the protonic-and neutronic restmasses, derives from the Higgs-Restmass-Scale and can be stated in a first approximation as the groundstate.

Basic nucleon restmass is mc=√Omega.mP=9.9247245x10-28 kg* or 958.99 MeV*.

(Here Omega is a gauge string factor coupling in the fundamental force interactions as:
Cuberoot(Alpha):Alpha:Cuberoot(Omega):Omega and for Omega=G-alpha.)
KKK-Kernelmass=Up/Down-HiggsLevel=3x319.66 MeV*= 958.99 MeV*, using the Kernel-Ring and Family-Coupling Constants.

Subtracting the Ring-VPE (3L) gives the basic nucleonic K-State as 939.776 MeV*. This excludes the electronic perturbation of the IR-OR oscillation.

For the Proton, one adds one (K-IR-Transition energy) and subtracts the electron-mass for the d-quark level and for the Neutron one doubles this to reflect the up-down-quark differential.
An electron perturbation subtracts one 2-2/3=4/3 electron energy as the difference between 2 leptonic rings from the proton's 2 up-quarks and 2-1/3=5/3 electron energy from the neutron' singular up-quark to relate the trisected nucleonic quark geometric template.

Proton mp=u.d.u=K.KIR.K=(939.776+1.5013-0.5205-0.1735) MeV* = 940.5833 MeV* (938.270 MeV).
Neutron mn=d.u.d=KIR.K.KIR=(939.776+3.0026-1.0410+0.1735) MeV* = 941.9111 MeV* (939.594 MeV).

This is the groundstate from the Higgs-Restmass-Induction-Mechanism and reflects the quarkian geometry as being responsible for the inertial mass differential between the two elementary nucleons. All ground state elementary particle masses are computed from the Higgs-Scale and then become subject to various finestructures. Overall, the measured gravitational constant 'G' can be said to be decreasing over time.

The HB discussed below is said of having been measured in the decay of W's, Z's and Tau Leptons, as well as the bottom- and top-quark systems described in the table and the text addressing K-KIR-KOR transitions. The K means core for kernel and the IR means InnerRing and the OR mean OuterRing. The Rings are derivatives from the L-Boson of the HO(32 string class) and the Kernels are the products of the decay of the X-Boson from the same brane source.

So the Tau-decay relates to 'Rings' which are charmed and strange and bottomised and topped, say. They are higher energy manifestations of the basic nucleons of the proton and the neutrons and basic mesons and hyperons.

The energy resonances of the Z-boson (uncharged) represents an 'average' or statistical mean value of the 'Top-Quark' and the Upper-Limit for the Higgs Boson is a similar 'Super-Quark' 'average' and as the weak interaction unification energy.

A previous postulated energy for the Higgs Boson of so 110 GeV is the Omicron-resonance, as inferred from the table above.
Now the most fundamental way to generate the Higgs Boson as a 'weak interaction' gauge is through the coupling of two equal mass, but oppositely charged W-bosons (of whom the Zo is the uncharged counterpart).

We have seen, that the W-mass is a summation of all the other quark-masses as kernel-means from the strangeness upwards to the truth-quark level.
So simply doubling the 80.593 GeV* and 80.395 GeV mass of the weak-interaction gauge boson must represent the basic form of the Higgs Boson and that is 161.186 GeV* or 160.790 GeV as a function of the electro-weak coupling.

From Electro-Weak Unification parameters: {1eV = 1.0024656 eV*} with T(nEW=4.67x10-21) =3.40x1015 K*
MW± = ΣKernel-Mean = mup-down+mstrange+mcharm+mmagic+mdainty+mbottom = 0.151+0.492+1.606+5.246+17.135+55.964 = 80.594 GeV*
MZo = 91.39165 GeV* or 91.167 GeV
M = 298.453 GeV* or 297.717 GeV
√2.Fermi Constant G = √2.GF = √2{πα/(√2.MW2[1-MW2/MZ2])} = (1/Higgs-Vacuum-Expectation HVE)2 = 1.5873x10-5 GeV-2* for HVE=251.00 GeV* or 250.38 GeV

As the Charmonium quark state is defined by the coupling of a double-up-diquark U=uu to an anti-up-quark as c=Uu(bar) and so as a quark molecule as the quark singlet state of 3 interacting quarks; whilst the diquark doublet of bottom-magic {b=[ud]bar and m=[us]bar} and the diquark triplet of dainty-top-super {D=[dd]bar and t=[ds]bar and S=[ss]bar} form double quarks; the Kernel-Mean of the Charmonium energy level is added to the HVE and the Difference-VPE levels for the K-IR - IR-OR transitions are subtracted for the quark-antiquark coupling.

MW- + MW+ + MZo = 252.578 GeV* = HVE + mcharm - (mK(-) - mL(-)) = (251.00 + 1.6063 - [0.031987-0.003402]) = 252.578 GeV* or 251.957 GeV
300.031 GeV* - M = mcharm - (mK(-) - mL(-)) = MW- + MW+ + MZo - HEV = 1.578 GeV*
mcharm = MW- + MW+ + MZo + (mK(-) - mL(-)) - HEV = 1.6063 GeV* or 1.6023 GeV.

Quantum Relativity describes the creation of the Higgs Boson from even more fundamental templates of the so called 'gauges'. The Higgs Boson is massless but consists of two classical electron rings and a massless doubled neutrino kernel, and then emerges in the magnetocharge induction as mass carrying gauges.

The Higgs Boson resonance, found by ATLAS and CMS is a diquark resonance.

The 'make-up' of the Higgs Boson can be highlighted in a discovery of a 160 GeV Higgs Boson energy, and incorporating the lower energy between 92 GeV and to the upper dainty level at 130 GeV as part of the diquark triplet of the associated topomium energy level.

In particular, as the bottomium doublet minimum is at 5,246.223 MeV* and the topomium triplet minimum is at 55,963.7 MeV* in terms of their characteristic Kernel-Means, their doubled sum indicates a particle-decay excess at the recently publisized ~125 GeV energy level in 2x(5.2462+55.9637) GeV* = 122.420 GeV* (or 122.119 GeV SI).
These are the two means from ATLAS {116-130 GeV as 123 GeV} and CMS {115-127 GeV as 121 GeV} respectively.

http://press.web.cern.ch/press/PressReleases/Releases2011/PR25.11E.html

Then extending the minimum energy levels, like as in the case to calculate the charged weakon gauge field agent energy in the charm and the VPE perturbations as per the table given, specifies the 125 GeV energy level in the Perturbation Integral/Summation:

2x{55.964+5.246+1.606+0.492+0.151+0.046+0.014} GeV* = 127.02 GeV*, which become about 126.73 GeV SI as an UPPER LIMIT for this 'Higgs Boson' at the Dainty quark resonance level from the UFoQR (Unified Field of Quantum Relativity).
Using the 3 Diquark energy levels U,D and S yield 2x{55.964+5.246+1.606} GeV* = 125.63 GeV* and 125.32 GeV SI.

Some data/discovery about the Higgs Boson aka the 'God-Particle' states, that there seems to be a 'resonance-blip' at an energy of about 160 GeV and as just one of say 5 Higgs Bosons for a 'minimal supersymmetry'.
One, the lowest form of the Higgs Boson is said to be about 110 GeV in the Standard Model. There is also a convergence of the HB to an energy level of so 120 GeV from some other models.
But according to QR, the Higgs Boson, is that is not a particular particle, but relates to all particles in its 'scalar nature' as a restmass inducer.

It is natural, that an extended form of the Higgs Boson can show a blip at the 160 GeV mark and due to its nature as a 'polarity' neutraliser (a scalar particle has no charge and no spin, but can be made up of two opposite electric charges and say two opposing chiralities of spin orientations.)

The Top-Super Diquark Resonance of CERN - December 15th, 2015

As can be calculated from the table entries below; a Top-Super Diquark Resonance is predicted as a (ds)bar(ss)=(ds)barS or a (ds)(ss)bar=(ds)Sbar diquark complex averaged at (182.783+596.907)GeV=779.690 GeV.

In the diquark triplet {dd; ds; ss}={Dainty; Top; Super} a Super-Superbar resonance at 1.1938 TeV can also be inferred with the Super-Dainty resonance at 652.9 GeV and the Top-Dainty resonance at 238.747 GeV 'suppressed' by the Higgs Boson summation as indicated below. Supersymmetric partners become unnecessary in the Standard Model, extended into the diquark hierarchies.

Next we interpret this scalar (or sterile) Double-Higgs (anti)neutrino as a majoron and lose the distinction between antineutrino and neutrino eigenstates.

We can only do this in the case of the Zo decay pattern, which engage the boson spin of the Zo as a superposition of two antineutrinos for the matter case and the superposition of two neutrinos in the antimatter case from first principles.

So the Zo is a Majorana particle, which merges the templates of two antineutrinos say and spin induces the Higgs-Antineutrino.
And where does this occur? It occurs at the Mesonic-Inner-Ring Boundary previously determined at the 2.776x10-18 meter marker.
This marker so specifies the Zo Boson energy level explicitely as an upper boundary relative to the displacement scale set for the kernel at the wormhole radius rps=lps/2π and the classical electron radius as the limit for the nuclear interaction scale at 3 fermis in: RcomptonxAlpha.

So the particle masses of the standard model in QED and QCD become Compton-Masses, which are Higgs-mass-induced at the Mesonic-Inner-Ring (MIR) marker at RMIR=2.776x10-18 meters.

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.

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

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.

References:

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.191101
Indications of a Spatial Variation of the Fine Structure Constant
J. K. Webb, J. A. King, M. T. Murphy, V. V. Flambaum, R. F. Carswell, and M. B. Bainbridge
Phys. Rev. Lett. 107, 191101 – Published 31 October 2011

[/b][/COLOR][/CENTER][/b][/COLOR][/CENTER][/b][/COLOR][/CENTER]

Last edited: Apr 5, 2018
6. ### adminWell-Known MemberStaff Member

Messages:
3,047
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
7. ### adminWell-Known MemberStaff Member

Messages:
3,047
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