The Monopolar Quantum Relativistic Electron

An extension of the standard model and quantum field theory

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

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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 ½R_{e}.X = R_{p}for a classical electron radius R_{e}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 m_{e}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 m_{eo}.

Using the ß^{2}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 E_{o}=½hf_{o}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 v_{eX}= 0.78615138.c and an effective mass energy of m_{ef}= γm_{e}= m_{ecf}= 1.503238892x10^{-30}kg*. This mass-velocity relationship is supplemented by the Compton constant as: m_{e}R_{e}= Compton constant = αh/2πc = l_{planck}.α.m_{planck}= m_{ec}r_{ec}, which proportionalises the quantum relativistic size of the electron with its mass.

The Compton constant ensures Lorentz invariance across all reference frames in cancelling the length contraction with the relativistic mass increase in the product of the proper length l_{o}and the proper rest mass m_{o}as l_{o}.m_{o}=l_{o}γ.m_{o}/y in special relativity (SR) in the self-relative reference frame of the monopolar electron.

Subsequently then for an electron speed v_{eX}and for r_{ec}= αh/2πcm_{ecf}= 1.71676104x10^{-15}m* as a decreased self-relative classical electron radius given by the Compton constant, we calculate a relatively negligible monopolar velocity component in (v_{ps}/c)^{2}= 1/{1+r_{ec}^{4}/([2πα]^{2}r_{ps}^{4})} = 1.55261006x10^{-35}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 v_{e}|_{max}= (1 - 3.282806345x10^{-17}) c and m(ν_{e})=m(ν_{τ})^{2}= 0.00297104794 eV* (0.002963740541 eV) respectively. At this energy then, no coupling between the electron and its anti-neutrino 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 m_{ν}= m_{neutrino}= m_{e}.(r_{neutrino})/R_{e}and where r_{v}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: m_{νElectron}c^{2}= m_{v}(ν_{Tauon}^{2})c^{2}= m_{ν}(ν_{Muon}^{2}+ν_{Higgs}^{2})c^{2}= μ_{o}{Monopole GUT masses ec}^{2}r_{ps}/4πR_{e}^{2 }and where v_{Higgs}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 givesmfor_{ec}r_{ec}= m_{e}R_{e }ßand at A=1, the Compton constant gives^{2}= 0mfor_{ec}r_{ec}= ½m_{e}.2R_{e}ßand as the mean for a unitary interval is ½, the electron radius transforms into the protonic radius containing monopolar charge as internal charge distribution in^{2}= XRand proportional to the effective electron rest mass m_{p}= ½XR_{e }_{e}proportional to the spacial extent of the electron.

For the proton then, its 'charge distribution' radius becomes averaged as R_{proton}= 0.85838052x10^{-15}m* as a reduced classical electron radius and for a speed of the self-interactive or quantum relativistic electron of v_{ps}= 1.576125021x10^{-17}c. This monopolar 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 v_{pse}= 1.50506548x10^{-18 }c for its electrostatic potential, where U_{e}=∫{q²/8πε_{o}r²}dr = q²/8πε_{o}R_{e }= ½m_{e}c^{2}for a classical velocity of v_{e}=0 in a non-interacting magnetic field B=0.

2U_{e}= m_{e}c^{2}so implies a halving of the classical electron radius to obtain the electron mass m_{e}= 2U_{e}/c^{2}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 linearisation of the Weyl wormhole wavelength λ_{ps}= λ_{weyl}of the qbb in the photon-mass interaction as a quantum gravitational limit proportional to the mass of the electron in r_{weyl }= λ_{weyl}/2π = 2G_{o}M_{c}/c^{2}= h/2πcm_{ps}for a curvature mass M_{c}= hc/4πG_{o}m_{ps }conformally transforming M_{c}= 6445.79 kg* into 2.22..x10^{-20}kg* quantum gravitationally and in a corresponding increase of a sub Planck length linearisation of r_{cplanck}= 2G_{o}m_{ps}/c^{2}= 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-E_{ps}wormhole as the final superstring class of heterotic symmetry 8x8 to manifest the super membrane E_{ps}E_{ss}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 = VPE_{ps}= ZPE_{weyl}= 4πE_{ps}/λ_{ps}^{3}and completing the encompassing energy spectrum in integrating the electric-, magnetic- and monopolar field properties in {½m_{electric}+ ½m_{magnetic}(v/c)^{2}+ δm_{monopolic}}c^{2}= mc^{2}.

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 E_{ps}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 γ^{3}in the manifestation of relativistic force as the time rate of change of relativistic momentum p_{rel}.

Furthermore, the mass-charge ratio {e/m_{eo}} relation of the electron implies that a precision measurement in either the rest mass m_{oe}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 m_{e}from its rest mass resulting in m_{eo}γ = m_{e}'γ^{2}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-ß^{2}} describes the ß^{2}distribution of relativistic velocity in the unitary interval from A=0 to A=1, setting the quantum relativistic mass ratio [m_{oe}/m_{e}]^{2}= {1-ß^{2}} 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 m_{oe}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: m_{electric}+ m_{magnetic }+ δm_{monopolar}= m_{ec}{½+½[v/c]²} + δ_{ps}m_{ec}= m_{ec }with m_{e}c^{2}√{1 + v^{2}γ^{2}/c^{2}} = m_{e}c^{2}γ = m_{ec}c^{2}for m = m_{ec}from the energy-momentum relation E^{2}= E_{o}^{2}+ p^{2}c^{2}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.

At the core of physical consciousness lies quantum consciousness; but there it is called self-interaction of a particle or dynamical system in motion relative to its charge distribution.

We shall indicate, that it is indeed the charge distribution within such a system and quantized in the fundamental nature of the electron and the proton as the base constituent of atomic hydrogen and so matter; that defines an internal monopolar charge distribuition as a quantum geometric formation minimised in the classical size of the electron and the energy scale explored at that displacement scale.

Finally we describe the particles of the Standard Model and including a quantum geometric explanation for the CP violation of the weak interaction, from their genesis in the inflaton and a grand unification symmetry in a transformation of supermembranes and cosmic strings appearing today in a spectrum of cosmic rays:

SEWG------------------------SEWg--------SEW.G---------SeW.G--------S.EW.G-------------S.E.W.G

Planck Unification I----------IIB----------HO32------------IIA-----------HE64---------Bosonic Unification

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=R^{2}for a (N-turn toroidal) current inductor N.i=BdR/μ_{o}for velocity v and self-induction L=NBA/i is:

U_{m}=½Li^{2}=½(μ_{o}.N^{2}R)(BR/μ_{o}N)^{2}=½B^{2}V/μ_{o}and the Magnetic Energy Density per unit volume is then:

U_{m}/V=½B^{2}/μ_{o}

Similarly, the Electric Energy density per unit volume is:

Usay via the Maxwell equations and Gauss' law. So for integrating a spherical surface charge distribution dV=4πr_{e}/V=½ε_{o}E^{2}^{2}.dr from R_{e}to ∞:

U_{e}=∫{q^{2}/8πε_{o}r^{2}}dr = q^{2}/8πε_{o}R_{e }= ½m_{e}c^{2}

2U_{e}= m_{e}c^{2}so implies a halving of the classical electron radius to obtain the electron mass m_{e}= 2U_{e}/c^{2}and infers an oscillating nature for the electron size to allow a synergy between classical physics and of quantum mechanics.

As Enrico Fermi stated in 1922; changing the rest mass of the electron invokes the ratio ß^{2}=v^{2}/c^{2}in an attempt to solve the riddle of electromagnetic mass and the factor of 4/3 differentiating between the electron's relativistic momentum and its relativistic energy.:

"1. It's known that simple electrodynamic considerations^{[1]}lead to the value(4/3)U/cfor the electromagnetic mass of a spherical electricity-distribution of electrostatic energy^{2}U, whencdenotes the speed of light. On the other hand, it's known that relativistic considerations for the mass of a system containing the energyUgive the valueU/c. Thus we stand before a contradiction between the two views, whose solution seems not unimportant to me, especially with respect to the great importance of the electromagnetic mass for general physics, as the foundation of the electron theory of matter.^{2}Especially we will prove: The difference between the two values stems from the fact, that in ordinary electrodynamic theory of electromagnetic mass (though not explicitly) a relativistically forbidden concept of rigid bodies is applied. Contrary to that, the relativistically most natural and most appropriate concept of rigid bodies leads to the valueU/cfor the electromagnetic mass.^{2}We additionally notice, that relativistic dynamics of the electron was studied by M. Born,^{[2]}though from the standpoint only partially different from the ordinary electrodynamic one, so that the value(4/3)U/cfor the Electron's mass was found of course.^{2}In this paper, Hamilton's principle will serve as a basis, being most useful for the treatment of a problem subjected to very complicated conditions - conditions of a different nature than those considered in ordinary mechanics, because our system must contract in the direction of motion according to relativity theory. However, we notice that although this contraction is of order of magnitudev, it changes the most important terms of electromagnetic mass,^{2}/c^{2}i.e, the rest mass."

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 λ_{dB}= h/mv and the Compton mass-photon interaction Δx = r_{compton}= 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 E^{2}= (pc)^{2}+ (mc^{2})^{2}and we can apply this natural limitation on measurement to the position of the electrostatic electron mass in a variable classical electron radius as r_{ec}= αh/2πcm = αr_{compton}= {μ_{o}e^{2}c/2h}.{h/2πcm_{ec}} = μ_{o}e^{2}/4πm_{ec}and rendering the Compton mass-photon interaction modified in the electromagnetic fine structure constant α to relate the inverse proportionality between the electron's rest mass to its spacial extent in:

m..............................................................................................................................._{e}R_{e}= Compton constant = αh/2πc = l_{planck}.α.m_{planck}= m_{ec}r_{ec}[Eq.1]

The Compton constant ensures Lorentz invariance across all reference frames in cancelling the length contraction with the relativistic mass increase in the product of the proper length l_{o}and the proper rest mass m_{o}as l_{o}.m_{o}=l_{o}γ.m_{o}/y in special relativity (SR) in the self-relative reference frame of the monopolar electron.

In particular, a classical size for the proton can be found in an approximation ½R_{e}.X = R_{p}and where the factor X represents the symmetry equilibrium for a B=(v/c} velocity ratio distribution for the effective electron rest mass m_{e}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 v_{e}= 0.78615138.c and an effective mass energy of m_{ef}= γm_{e}= m_{ecf}= 1.503238892x10^{-30}kg* for r_{ec}= αh/2πm_{ecf}= 5.150283117x10^{-7}m* as a largely increased classical electron radius given by the Compton constant for a negligible monopolar velocity component in (v_{ps}/c)^{2}= 1/{1+r_{ec}^{4}/([2πα]^{2}r_{ps}^{4})} = 1.916797918x10^{-69}for any substantial velocity for the electron.

For the proton then, its 'charge distribution' radius becomes averaged as R_{proton}= 0.85838052x10^{-15}m* as a reduced classical electron radius and for a speed for the self-interactive or monopolar 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 v_{e}= 1.50506548x10^{-18 }c for its electrostatic potential, where U_{e}=∫{q²/8πε_{o}r²}dr = q²/8πε_{o}R_{e }= ½m_{e}c^{2}for a classical velocity of v_{e}=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/(4πr^{3}) and q=4πρr^{3}/3 with dq/dr = 4πρr^{2}dr

The electrostatic potential for this charge distribution V(r) = q/4πε_{o}r

then contains an energy dU = qdq/(4πε_{o}r) for U(r) =∫{16π^{2}ρ^{2}r^{5}/12πε_{o}r} dr = (4πρ^{2}/3ε_{o})∫r^{4}dr = ⅗.e²/4πε_{o}R_{e }= ⅗.μ_{o}e^{2}c^{2}/4πR_{e}= ⅗.m_{e}c^{2}for an electron rest mass m_{e }= 2U_{e}/c^{2}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.m_{e}c^{2}for U_{e}= μ_{o}e^{2}c^{2}/6πR_{e }= ½(1+⅓)m_{e}c^{2}= ⅔m_{e}c^{2}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 to account for the differences.

But we can see, that should one use the measured electron mass from the R_{e}-definition as the electron's rest mass, that m_{magnetic}+ m_{electric }= m_{e}{½+½(v/c)²} < m_{e }, 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', potential or inherent mass term δm_{e}and call it the monopolar self-interaction mass of the electron to write:

m_{electric}+ m_{magnetic }+ δm_{monopolic}= m_{ec}{½+½[v/c]²} + δ_{ps}m_{ec}= m_{ec }with m_{e}c^{2}√{1 + v^{2}γ^{2}/c^{2}} = m_{e}c^{2}γ = m_{ec}c^{2}for m = m_{ec}from the energy-momentum relation E^{2}= E_{o}^{2}+ p^{2}c^{2}of classical and quantum theory.

The aim is to redefine δ_{ps}= 1/2γ^{2}in ß^{2}to relate the mass discrepancy to the monopolar nature of the quantum relativistic electron.

δ................................................................................................................................._{ps}= ½{1 - {v/c]^{2}} = 1/2γ^{2}for γ = 1/√(1 - [v/c]^{2}) = 1/√(1 - ß^{2})[Eq.2]

By the Biot-Savart and Ampere Law:

B=μ_{o}q.v./4πr² and ε_{o}=1/c²μ_{o}for the E=cB foundation for electrodynamic theory. So for integrating a spherical surface charge distribution dV=4πr².dr from R_{e}to ∞:

U_{m}=∫{μ_{o}q²v²/8πr²}dr = μ_{o}q²v²/8πR_{e }= ½m_{e}v^{2}

m_{magnetic }= μ_{o}e²[v/c]²/8πR_{e }= m_{ec}.Aß^{2 }= ½m_{e}.(v/c)^{2}for a constant A = (μ_{o}e²/8πR_{e})/m_{ec }= m_{e}/2m_{ec}for R_{e}m_{e}= μ_{o}e²/4π = αh/2πc

Similarly, U_{e}=∫dU_{e}=q²v²/8πε_{o}R_{e}=kq²/2R_{e}=½m_{e}c² as per definition of the classical electron radius and for the total electron energy m_{e}c² set equal to the electric potential energy.

We term m_{e}here the effective electron mass and so differing it from an actual 'bare' rest mass m_{o}.

m_{electric }= kq²/2R_{e}c² = kq²/e*= q²/8πε_{o}R_{e }c^{2}= U_{e}/c² = ½m_{e}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/R_{e}= e²/4πε_{o}R_{e}= 2e²/8πε_{o}R_{e}= 2KE and where for a single hydrogen electron:

R_{Bohr}= h^{2}/πm_{e}e^{2}μ_{o}c^{2}= R_{e}/α^{2}= R_{Compton}/α = hα/2πm_{e}c for a electromagnetic fine structure constant alpha = α = e^{2}/2ε_{o}hc = μ_{o}ce^{2}/2h

m_{magnetic }= μ_{o}e²[v/c]²/8πR_{e }= m_{electric}.(v/c)² = ½m_{e}.(v/c)² and which must be the KE by Einstein's c²dm=c²(m_{e}-m_{o})

and for the relativistic electron mass m=m_{o}/√(1-ß^{2})=m_{o}γ = for ß^{2}=(v/c)^{2}

So we introduce a quantum relativistic (QR) monopolar rest mass m_{ec}with a Compton-de Broglie momentum m_{ec}.c = h/λ_{e }= hf_{e}/c^{2}and consider there to be a frequency dependent photonic part in this rest mass and a part, which we have labeled as having an electromagnetic monopolar radiative or emmr origin.

The effective minimum rest mass for the electron in electrostasis in the absence of an external magnetic field in Maxwell's equations and as a function of the Compton constant then also harbours an internal emmr magnetic field as the sought after self-interaction of the electron.

We shall find that the ß^{2}distribution for the electron velocity defines a natural mirror boundary for an actual electron speed at 0, which so enables a complex electron velocity to decrease towards this complex boundary from a complex electron space and to then increase from this boundary as a real observed part.

We shall find that the classical electrostatic electron in the absence of its monopolar component can be considered to move with a speed of 0.177379525 c through an electrostatic potential of 8.25368811 keV*.

It is then a monopolar or self-interaction of the electron which effectively doubles its rest mass as a magnetic field applied internally and as a charge distribution for a quantum geometric electron and naturally contains the classical factor of (4/3) as a mean value in the ß^{2}distribution.

The volume occupied by the monopolar magnetic charge distribution relates to quantum chromodynamics and its gluon-colour magnetopolar charges in representing quantized higher dimensional spacetime which can be considered as 'collapsed' in its nature as a 7-dimensional Calabi-Yau manifold, but manifesting as a Riemann 3-sphere or 2-Torus (horn-toroidal) volumar quantizing 11-dimensional spacetime into Weylian wormholes in a mirror 12-dimensional Vafa spacetime.

This spacetime then compactifies the higher dimensional spacetime as a 3-dimensional surface, where a 11-dimensional surface manifold manifests in 3-D spacetime through open ended strings or Dirichlet branes attached in modular string dualities to a hyperbolic open de Sitter (dS) spacetime, but is in mirror duality from a closed spheroidal Anti de Sitter spacetime (AdS) to cancel the curved spacetimes in the Vortex-Potential-Energy or Zero-Point-Energy (ZPE) per unit volume or wormhole VPE of the Weylian spacetime quanta defined for a monopolar group velocity v_{ps}and the Compton parameters in:

Vortex-PE/V = VPE...................................................................................................._{Eps}= ZPE_{weyl}= 4πE_{ps}/λ_{ps}^{3}= 2α^{2}E_{ps}{[c/v_{ps}]^{2}-1}/r_{ec}^{3}= E_{ps}/V_{ps}[Eq.3]

V_{ps}= (2πr_{ps}).(πr_{ps}^{2}) = 2π^{2}r_{ps}^{3}

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 rest mass as photonic energy and mass equivalent over time itself:

dp..................................................................................................._{rel}/dt = d(m_{o}γv)/dt = m_{o}d(γv)/dt + γvd(m_{o})/dt =

m_{o}d(γv)/dt + {γvh/c^{2}}df/dt = m_{o}γ^{3}.dv/dt + {γvh/c^{2}}df/dt = F_{a}+ F_{α}for γ = 1/√{1 - [v/c]^{2}}[Eq.4]

The product m_{e}.R_{e}= Compton constant = hα/2πc = α.l_{planck}.m_{planck}

A changing electron size r_{e}changes the electron rest mass m_{o}in proportionality r_{e}∝ 1/m_{o}and where m_{o}= m_{ec}= m_{e}as the electromagnetic relativistic quantum mass for r_{e }= R_{e}= R_{compton}/α.

The boundary relativistic electron mass so becomes the Compton wormhole mass of the Quantum Big Bang α.m_{ps }= α.hf_{ps}/c^{2}

The classical electron's acceleration a = F_{a}/m from its relativistic force F_{rel}= d(p_{rel})/dt for a constant rest mass m_{o}is then supplemented by a quantum acceleration α from its quantum mechanical Compton mass

m_{ecompton}= m_{ec}= hα/2πcr_{e}and where the classical rest mass m_{o}changes as m_{ec}c^{2}= (hvr_{e}/c^{2}).γ.(df/dt).

The frequency differential over time is maximized in {df/dt}|_{max}= {(f_{ps}- f_{ss})/f_{ss}} = f_{ps}^{2}- 1 as the maximum entropy frequency permutation eigenstate f_{ps}^{2}= 9x10^{60}for its minimum state f_{ss}^{2}= 1/f_{ps}^{2}by modular string T-duality f_{ps.}f_{ss}= 1 of super-membrane E_{ps}E_{ss}and wormhole frequency f_{Weyl}= f_{ps}.

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 f_{ps}|_{max}and f_{ss}|_{min}and for the mass-eigen frequency quantum f_{ss}= m_{ss}c^{2}/h by brane coupling constants E_{ps}.E_{ss}= h^{2}and E_{ps}/E_{ss}= f_{ps}^{2}.

(1) Energy E = hf = mc^{2}(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 = mc^{2}iff f = f_{o }= f_{ss}(The Einstein Law E = mc^{2}for the light speed upper limit)

(1) Whenever there is mass (M = M_{inertial }= M_{gravitational}) occupying space; this mass can be assigned either as a photonic mass {by the Energy-Momentum relation of Special Relativity:

E^{2 }= E_{o}^{2 }+ (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 a 'rest energy' E_{o }= m_{o}c^{2}.

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 f_{ss }= f_{o }= E_{ss}/h = m_{ss}c^{2}/h, which quantizes all mass agglomerations m = Σm_{ss}in the mass quantum m_{ss }= E_{ss}/c^{2}.

Letting r_{ec}be the oscillating classical electron radius r_{ec}from its maximum value R_{e}= μ_{o}e^{2}/4πm_{e}= αh/2πcm_{e}to its minimum qbb value r_{ps}=λ_{ps}/2π from the de Broglie wave matter wavelength

λ_{e}= h/m_{e}c = c/f_{e}= hc/E_{e}= hc/m_{e}c^{2}; 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 = hf_{e}= m_{ec}c^{2}= (hvr_{ec}/c^{2}).γ.(df/dt) = {vγ}{r_{ec}.hf_{ps}^{2}/c^{2}} = {vγ}{hr_{ec}/λ_{ps}^{2}} for the maximum frequency summation at r_{ec }= r_{ps}

for v/√(1-[v/c]^{2}) = m_{ec}c^{2}λ_{ps}^{2}/hr_{ec}= αcλ_{ps}^{2}/2πr_{ec}^{2}using m_{ec}r_{ec}= constant = hα/2πc = m_{e}R_{e}and v^{2}/{1-[v/c]^{2}} = {αcλ_{ps}^{2}/2πr_{ec}^{2}}^{2 }= Ø^{2}solving for v^{2}{1+Ø^{2}/c^{2}} = Ø^{2 }with (v/c}^{2}= Ø^{2}/(c^{2}+Ø^{2}) = 1/{1+[c/Ø]^{2}}

The quantum relativistic mechanical electron's velocity distribution for a variable classical electron radius R_{e}in the proportional Compton rest mass m_{ec}and r_{ec}generalised in the wave matter constancy of de Broglie for the quantum relativistic part of rest mass m_{o }= hf/c^{2}and a purely self-interacting electromagnetic monopolic part as electromagnetic monopolar radiation (emmr) so is:

"Juju's Electron Equation 31|31:" applied for the maximum integrated quantum energy state: {m_{electric}+ m_{magnetic}+ m_{emmr}}c^{2}= E_{weyl}= hf_{weyl }= E_{qbb}= m_{ps}c^{2}= 1/e*

{v.................................................................................................................................................................._{ps}/c}^{2}= 1/{1 + 4π^{2}r_{ec}^{4}/α^{2}λ_{ps}^{4}} = 1/{1 + r_{ec}^{4}/4π^{2}α^{2}r_{ps}^{4}}[Eq.5]

δ........................................................................................................................................................_{ps}= ½{1 - {v/c]^{2}} = 1/2γ^{2}for γ = 1/√(1 - [v/c]^{2}) = 1/√(1 - ß^{2})[Eq.2]

This sets the proportionality between monopolar emmr and electromagnetic emr in the constancy of light speed c:

v^{2}/(1-2δ_{ps}) = c^{2}= v_{ps}^{2}/{1 + r_{ec}^{4}/4π^{2}α^{2}r_{ps}^{4}} for the monopolar δ_{ps }and letting v_{ps}= xc as a fractional monopolar velocity colinear with v:

For δ_{ps}→ 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.

For v=½ c; v_{ps}= 2.006753867x10^{-18}c and r_{ec}= 0.866025403 R_{e}for δ_{ps}=½{1-0.25} = 0.375

For v= 0.651899075 c; v_{ps}= 3.035381866x10^{-18}c and r_{ec}= 0.758305739 R_{e}for δ_{ps}=½{1-0.315985704} = 0.34200715

For δ_{ps}→ 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 component δ_{ps}as a function of the monopolar velocity of the electron v_{ps}.

δ..........................................................._{ps}= ½{1 - [v/v_{ps}]^{2}{4π^{2}α^{2}r_{ps}^{4}/(4π^{2}α^{2}r_{ps}^{4}+ r_{ec}^{4})} = ½{1 - [v/v_{ps}]^{2}{1/(1 + [r_{ec}/r_{ps}]^{4}/4π^{2}α^{2})}}[Eq.6]

Then the upper limit for r_{ec}= r_{ps}and the qbb wormhole boundary is: δ_{ps}= ½{1 - [c^{-}/v_{ps}|_{max}]^{2}(4π^{2}α^{2})/(1+4π^{2}α^{2})} = ½{1 - 1^{-}} = 0^{+}for v_{ps}|_{max}^{2 }= (4π^{2}α^{2}c^{2})/(1+4π^{2}α^{2}) showing that as [v/c] → 1^{-}; δ_{ps}→ 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 relativistic velocity v increasing the monopolar part in v_{ps }to its maximum at the wormhole qbb scale.

v_{ps}|_{max}= xc = 2παc/√(4π^{2}α^{2}+1) = 0.045798805 c as the maximised monopolar magnetic speed for the electron and decreasing to its minimum speed

v_{ps}|_{min}= c/√(1 + 4π^{2}(10^{10}/360)^{4}/α^{2}) c = 1.50506540x10^{-18}c for the classical electron radius scale given by R_{e }and the internal velocity of the electron in electrostasis.

The lower limit for r_{ec}= R_{e}= 10^{10}λ_{ps}/360 (from the Planck-Stoney-QR Unification) becomes:

δ_{ps}= ½{1 - [v/v_{ps}|_{min}]^{2}(4π^{2}α^{2})/(4π^{2}α^{2}+ [2π.10^{10}/360]^{4})} = ½{1 - [v/v_{ps}|_{min}]^{2}(1/(1+ 4π^{2}.10^{40}/α^{2}.360^{4})}

= ½ - ½[v]^{2}(2.265221852x10^{-36})/(4.5151962x10^{-10}) = ½ - (2.508442326x10^{-27})v^{2}, showing that as [v] → 0^{+}; δ_{ps}→ ½ for ½ of the electron's mass being monopolar.

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.

(hvλ_{ps}/c^{2}).γ.(df/dt) = hvλ_{ps}.f_{ps}^{2}.γ/c^{2}= hf_{ps}= m_{ps}c^{2}

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

v............................................................................................................................................................................................................................................_{λc}= c/√2[Eq.7]

This formulation sets an upper and lower bound for v_{electron}in the electron radius in the interval: 〈 R_{e}|_{max }....... R_{ec}|_{min }= λ_{ps}/2π = r_{ps}= r_{Weyl}= r_{wormhole}= r_{qbb }〉

The speed of the quantum mechanical electron of mass m_{ec}= αm_{ps}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:

m_{ec}/√{1-(v_{ec}/c)^{2 }} = αm_{ps}= 1.621502875x10^{-22 }kg* for {v_{e}/c}^{2}= 1 - {m_{e}/αm_{ps}}^{2}

v_{e}|_{max}= √{1 - (5.72957797x10^{-9})^{2}} c = √{1 - 3.28280637x10^{-17}} c ~ {1 - 1.64140319x10^{-17}} c = c^{-}

and as the self-energy E_{ec}=m_{ec}c^{2}= αm_{ps}c^{2}= αE_{ps}= 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 |½E_{o}| = |h/4π| = ½E_{planck}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 V_{4}(r) = ½π^{2}r^{4}manifests as a 3-dimensional surface: dV_{4}/dr = 2π^{2}r^{3}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.

V_{brane}.(df/dt)|_{max}= 2π^{2}R_{rmp}^{3}.f_{ps}^{2}= e* =1/E_{ps}= 2R_{e}c^{2 }in a restmass photonic or 'dark matter' radius R_{rmp }= ∛{e*/2π^{2}f_{ps}^{2}} = 1.411884763x10^{-20}m* for the nuclear electron at m_{fermi}= h/2πcR_{rmp}= 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 = 2R_{e}c^{2}/α = 2R_{compton}c^{2}; R_{rmp }= ∛{e*/2απ^{2}f_{ps}^{2}} = 7.279292496x10^{-20}m* for the Compton electron at an energy of

m_{compton}= h/2πcR_{rmp}= 4.85868164x10^{-24}kg* or 2.722024 TeV*

For the Bohr electron e*/α^{2}= 2R_{e}c^{2}/α^{2}= 2R_{bohr}c^{2}; R_{rmp }= ∛{e*/2α^{2}π^{2}f_{ps}^{2}} = 3.75300456x10^{-19}m* for the atomic Bohr electron at an energy of

m_{compton}= h/2πcR_{rmp}= 9.4238534x10^{-25}kg* or 527.9613 GeV*

The classical electromagnetic rest-mass m_{emr}=m_{e}becomes quantum mechanical in the string-brane sourcesink energy E*-Gauge photon quantum of the Quantum Big Bang Weylian wormhole.

E* = E_{ps }= hf_{ps }= hc/λ_{ps }= m_{ps}c^{2}= (m_{e}/2e).√[2πG_{o}/αhc] = {m_{e}/m_{Planck}}/{2e√α} = 1/2R_{e}c^{2 }= 1/e*

Monopolar charge quantum e*/c^{2}= 2R_{e}⇐ supermembrane displacement transformation ⇒ √α.l_{planck}= e/c^{2}as electropolar charge quantum

m_{e}= 2e√α.m_{planck}/2R_{e}c^{2}= l_{planck}√α.√α.m_{planck}/R_{e }= α.l_{planck}.m_{planck}/R_{e}

= {e/c^{2}}{√(2πke^{2}/hc}{√(hc/2πG_{o})}/R_{e}={√(G_{o}h/2πc^{3})}{2πke^{2}/hc}{√(hc/2πG_{o})}/R_{e}= {h/2πc}{2πke^{2}/hc}/R_{e}

= {ke^{2}/c^{2}}/R_{e}= {μ_{o}e^{2}}/4πR_{e}

The product m_{e}.R_{e}= Compton constant = hα/2πc = α.l_{planck}.m_{planck}

A changing electron size r_{e}changes the electron restmass m_{o}in proportionality r_{e}∝ 1/m_{o}and where m_{o}= m_{e}for r_{e}= R_{e}= R_{compton}/α = R_{bohr}/α^{2}

The boundary relativistic electron mass so becomes the Compton wormhole mass of the Quantum Big Bang α.m_{ps}= α.hf_{ps}/c^{2}

For the wormhole limit r_{e}= r_{ps }= λ_{ps}/2π = R_{e }|_{minimum }in unified string Planck-Stoney units

m_{e}= αm_{ps}= αhf_{ps}/c^{2}= αh/cλ_{ps}= α/e*c^{2}= α/2R_{e}c^{4}= hα/2πcr_{ps}= {60πhe^{2}/2πhcr_{ps}} = 30e^{2}/cr_{ps}= 1.62150288x10^{-22}kg* = m_{e}γ = m_{e}/√{1 - [v/c]^{2}}

for v_{electron}= c^{-}; [v/c]^{2 }= 1-3.2828...x10^{-17}for v = {1-½(3.2828x10^{-17})} c ~ c

The Compton constant so relates the pre-spacetime formulation in the Planck-Stoney oscillation to the post-qbb cosmic evolution of the lightpath x=ct as:

√α.l_{planck}√α.m_{planck}= αh/2πc = √α.r_{planck}√α.M_{curvature}= √α.m_{ps}√α.r_{ps}= α.m_{ps}.r_{ps}= m_{ec}.r_{ec}= m_{e}R_{e}showing the limiting electron masses m_{e}and αm_{ps}to be attained precisely at the wormhole mass m_{ps}as the modulation with the shrinking classical electron radius R_{e}to the wormhole radius r_{ps}as the linearization of the Compton wavelength of the wormhole event horizon λ_{ps}=2πr_{ps}.

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 v_{ps }; df/dt|_{max}= f_{ps}^{2}= 1/f_{ss}^{2}= cf_{ps}/λ_{ps}= cf_{ps}/2πr_{ps}for an angular frequency ω_{ps}= 2πf_{ps}as Compton frequency; the maximum monopolar velocity ratio {v_{ps}/c}^{2}applied to the mass m = m_{ec}will be proportional to that maximised frequency state.

The de Broglie group velocity v_{dB}= h/m_{ec}λ_{dB}= h/2πm_{ec}r_{dB}linearized so is recircularized in the monopolar velocity v_{ps}in the Compton constant m_{ec}.r_{dB}= h/2πv_{ps}and with v_{ps}assuming c in the relativistic limit of the Compton radius.

For 〈 R_{ec}.m_{ec}= r_{ps}.m_{ec}= hα/2πc 〉|_{min }, the minimised classical electron radius r_{ps}maximises the monopolar speed of the electron in:

{v_{ps}/c} = 1/√{1+1/4π^{2}α^{2}} = 0.04579881 as a conformal mapping of the wormhole radius of the electron onto its classical representation in the proportion 10^{10}= 360R_{e}/2πr_{ps}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 m_{mm }= μ_{o}e^{2}(v_{ps}/c)^{2}/4πr_{ps}= R_{e}m_{e}(v_{ps}/c)^{2}/r_{ps}= m_{ec}(v_{ps}/c)^{2}= (2.09753100x10^{-3})m_{ec}= 3.4011525x10^{-25}kg for the alpha-energy E_{αω}= m_{mm}c^{2 }= hf_{αω}= 3.051037256x10^{-8}J* for a total frequency integral of f_{αω}= 4.59160179x10^{25}= ∑f_{ss}= ∑m_{ss}c^{2}/h = f_{αω}/f_{ss}= 1.377480544x10^{56}frequency self states and mass quantum m_{ss}eigen inertia states by m_{ss }= hf_{ss}/c^{2}by the time instanton f_{ps}f_{ss }= 1 = E_{ps}.e* as universal and natural self-identity for the supermembrane E_{ps}E_{ss}, consisting of a high energy vibratory part E_{ps}and a low energy winding part E_{ss}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 λ_{mm}= h/m_{m}c = 6.53382x10^{-18}m* for a total electron mass m_{ec}/√{1-(v_{ec}/c)^{2 }} = αm_{ps}= 1.621502875x10^{-22}kg* as the Weyl mass having replaced the classical relativistic electron restmass m_{o}by the quantum dynamic Compton restmass m_{ec }as a function of the effective classical electron mass m_{e}.

αm_{ps}{v_{ps}/c}^{2}= m_{mm}and so the Compton encompassing mass m_{ec}is reduced to the magnetic mass in the factor {v_{ps}/c}^{2}characterising the mass-radius relationship for all electrons.

For 〈 R_{e}.m_{e}= hα/2πc 〉|_{max }, the maximised classical electron radius R_{e}minimises the monopolar speed of the electron in:

m_{e}=hα/2πcR_{e}= ke^{2}/R_{e}c^{2}= μ_{o}e^{2}/4πR_{e}for {v_{ps}/c} = 1/√{1+R_{e}^{4}/4π^{2}α^{2}r_{ps}^{4}} = 1/√{1+(2π.10^{10}/360)^{4}/4π^{2}α^{2}} = 1.50506548x10^{-18}

and as the speed of the quantum relativistic mechanical electron at rest in the classical frame v_{ps}= 1.50506548x10^{-18}c = 0.45151964 (nanometres per second)*.

The inversion speed of light is v_{ps}= 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 R_{HI }= H_{o}/c as inversion displacement, which for a Universal Age of 19.12 Gy as Hubble time for a nodal Hubble constant oscillating between f_{ps}and H_{o}=c/R_{H}= 58.04 (km/Mpc.s)* for R_{H }= 1.59767545x10^{26}m* and becomes R_{HI}= 19.12 Gy/c = 2.011229x10^{9}m* and encompassing a 'planetary bubble radius' to approximately 5% to both the neighbouring planets Venus and Mars.

This represents a magneto-monopolar mass m_{mm}= μ_{o}e^{2}(v_{ps}/c)^{2}/4πR_{e}= m_{e}(v_{ps}/c)^{2}= (2.265221x10^{-36})m_{e}= 2.1045107x10^{-66}kg* for the alpha-energy E_{αω}= m_{mm}c^{2 }= hf_{αω}= 1.8940596x10^{-49}J* for a total frequency integral of f_{αω}= 2.84108945x10^{-16}= ∑f_{ss}= ∑m_{ss}c^{2}/h = f_{αω}/f_{ss}= 8.52326834x10^{14}frequency self states for the mass-frequency coupling m_{ss }= hf_{ss}/c^{2 }.

The classical electron restmass m_{o }= m_{e}so is reduced to the magneto-monopolar mass m_{mm}in the factor {v_{ps}/c}^{2}.

The Mass Distribution for the Quantum Relativistic Classical Electron

We set Constant A in Am_{ec }= μ_{o}e^{2}/8πcR_{e}for Aß^{2 }= 1/√[1 - ß^{2}] - 1

from: c^{2}(m - m_{ec}) = μ_{o}e^{2}v^{2}/8πR_{e}= m_{ec}c^{2}(1/√[1-ß^{2}] - 1) = m_{ec}v^{2}A with a total QR monopolar mass m = m_{ec}/√(1-[v/c]^{2})

This leads to a quadratic in ß^{2}: 1 = (1 + Aß^{2})^{2}(1-ß^{2}) = 1 + ß^{2}(2A+A^{2}ß^{2}-2Aß^{2}-A^{2}ß^{4 }- 1) and so: {A^{2}}ß^{4}+{2A-A^{2}}ß^{2}+{1-2A} = 0

with solution in roots:

ß[ ...................................................................................................................................................................................................^{2 }= ([A-2] ± √[A²+4A])/2A = {(½-1/A)±√(¼+1/A)}[Eq.8]

and A = -{1 ± 1/√(1-ß^{2})}/ß^{2 }solving (in 4 roots) the quadratic (2Aß^{2}+2-A)^{2}= A^{2}+ 4A

This defines a distribution of ß^{2 }= (v/c)² and ß = v/c velocity ratios in m_{ec}.Aß^{2 }= μ_{o}e²[v/c]^{2}/8πR_{e}

The electromagnetic mass m_{ec}in the relation m_{ec}A = ½m_{e}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 m_{e}respectively.

In particular m_{e}= 2Am_{ec }and is m_{ec}for A=½ as the new minimisation condition. In string parameters and with m_{e}in *units,m_{e}A=30e^{2}c/e*=½m_{e}=4.645263574x10^{-31 }kg*

In terms of the superstring quantum physical theory, the expression [ec]_{unified}= 4.81936903x10^{-11}kg* or [ec^{3}]_{u}= 2.7x10^{16}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* = E......................................................._{weyl}= E_{ps }= hf_{ps }= hc/λ_{ps }= m_{ps}c^{2}= (m_{e}/2e).√[2πG_{o}/αhc] = {m_{e}/m_{P}}/{2e√α} = 1/2R_{e}c^{2 }= 1/e*[Eq.9]

Monopolar charge quantum e*/c^{2}= 2R_{e}⇐ super-membrane displacement transformation ⇒ √α.l_{planck}= e/c^{2}as Electropolar charge quantum

This implies, that for A=1, m_{ec }= ½m_{e }, wheremfrom particular algorithmic associations of the QR cosmogony and is related to the fine structure of the magnetic permeability constant μ_{e }= 9.290527155x10^{-31 }kg*_{o}= 120π/c = 1/ε_{o}c^{2}, defining the classical electronic radius.

As ß≥0 for all velocities v, bounded as group speed in c for which ß^{2}=ß=1, (and not de Broglie phase speed:v); a natural limit for the ß distribution is found at A = ½ and A = ∞._{dB }= (h/mv_{group})(mc^{2}/h) = c^{2}/v_{group}>c

The electron's restmass m_{ec}so is binominally distributed for the ß quadratic. Its minimum value is half its effective mass m_{e}and as given in:

μ_{o}e²/8πm_{e}R_{e}= ½m_{e}for a distributed rest-mass m_{ec}/R_{e}= m_{e}/r_{ec }in A and m_{electric }= kq²/2R_{e}c² = μ_{o}e^{2}/8πR_{e}= U_{e}/c² = ½m_{e}for A=½ and its maximum for A=∞ is the unity v=c for ß=1

The classical rest-mass m_{o}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 m_{e}=μ_{o}e^{2}/4πR_{e}c^{2}and as a function of the classical electron radius R_{e}.

Its minimum condition is defined by the electric potential energy in m_{o}=½m_{e}for a value of A=½ with effective restmass m_{e}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 m_{o}=0 and the effective restmass m_{e}assumes the minimum rest energy for the electron at A=1 and generalised as m_{e}=2Am_{o}.

The classical restmass m_{o}=hf/c^{2}so decreases from its maximum value as m_{o}=m_{e}to m_{o}=0 as a function of the velocity distribution and in the extension of the classical force to incorporate the restmass differential d(m_{o}) = hd(f)/c^{2}by F_{Newton}= F_{a}+ F_{α}= 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=μ_{o}e^{2}/

8πm_{ec}R_{e }

=ke^{2}/

2m_{ec}R_{e}c^{2}

=ke^{2}/m_{ec}e*

=ke^{2}|E_{ps}*|/m_{ec}

ß^{2 }= 1-{m_{eo}/m_{e}}^{2}

= 1-{m_{eo}R_{e}/m_{ec}r_{ec}}^{2}

ß^{2 }⇒ (iß)^{2 }

for A < ½x rooty root

self-relative-QR-m_{eo}

m/_{eo }kg*m_{eo }kg

m_{eo}= m_{e}√(1-ß^{2})

= m_{e}/γ

ß^{2 }⇒ (iß)^{2 }

for A < ½

v/c

(v_{ps}/c)^{2}= 1/{1+r_{ec}^{4}/4π^{2}α^{2}r_{ps}^{4}}

for magnetopolar.velocity.in

c (m/s)*

r_{ec}= R_{e}/γ = √(1-ß^{2}) R_{e}

r_{ec}/R_{e }= m_{e}/m_{ec}in m*

self-relative-QR-r_{e}00 ± 01/0^{+}-1/0^{+}[1/0^{+}]m_{e}i/0^{+}

algorithmic metaphysicality

inflaton spacetime as complex v_{ps}= ic = ci[∝] R_{e}

1-½√2 =

0.292893218

-2.914213562

±1.914213562

-1 = i^{2}

x-root is complex

1+½√2 =

-4.82842714

y-root is complex

0

0i

1 c

1

0

0 R_{e}(2/0^{+})R_{e}

{1-½√2}+O(10^{-17})

= 0.292893218^{+}

-{1±1/√[1-ß^{2}]} /ß^{2}

~-1{1±1+½ß^{2}}/ß^{2}

ß_{compleximage}^{2}= -2.914213561.......

± 1.91421356200..

-0.999999999.....

{i.m_{e}/αm_{ps}}^{2 }=

-1+3.282806345x10^{-17}

-4.82842714^{+}

0^{+}

0^{+}i ^{-}

v_{ps}= 2παc/√{1+4π^{2}α^{2}}

=0.045798805 ic

13,739,641.79 [m/s]*

r_{ec}=r_{ps}=180R_{e}/(π10^{10})

1.591549431x10^{-23}

5.729577953x10^{-9}R_{e}349,065,850.6 R _{e}

A_{lb}=

0.487459961

ß_{lb}^{2}=

-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 R_{e}1.018 R _{e}

A_{1}=

0.488459961.

ß_{1}^{2}=

-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 R_{e}1.016 R _{e}

A_{3l}=

0.488500361

ß_{3l}^{2}=

-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 R_{e}1.016 R _{e}

A_{SI}= complex

0.488502266

[e/m]=

1.758820024

x10^{-11}C/kg

with α_{var}

A-root

complex=real

ß_{SI}^{2}=

-1.54707341

± 1.515609914-0.031463495-3.062683324

9.14320282x10^{-31}

9.109015537x10^{-31}

δm_{eo}=- 9.5x10^{-8}

uncertainty solution

complex - real0.177i

1.553958288x10^{-18}ic

4.661874865x10^{-10}

2.733729293x10^{-15}

0.984142545 R_{e}1.016 R_{e}

A_{SI}= complex

0.488502361

[e/m]=

1.758820024

x10^{-11}C/kg

with α_{var }

min

ß_{SI}^{2}=

-1.547073013

± 1.515609783-0.03146323-3.062682796

9.143204074x10^{-31}

9.109016786x10^{-31}0.177i

1.553957936x10^{-18}ic

4.661873808x10^{-10}

2.733729603x10^{-15}

0.984142657 R_{e}1.016 R_{e}A_{3u}=

0.488540761

ß_{3u}^{2}=

-1.54691211

± 1.5155567-0.03135541 -3.06246881 9.143712983x10 ^{-31}9.109523792x10^{-31}0.177i

1.553784965x10^{-18}ic

4.661354894x10^{-10}

2.733881762x10^{-15}

0.984197434 R_{e}1.016 R _{e}A_{5l }=

0.489123658

ß_{5l}^{2}=

-1.54447277

± 1.514751719-0.029721051 -3.059224489 9.151423661x10 ^{-31}9.117205639x10^{-31}0.172i

1.551167736x10^{-18}ic

4.653503207x10^{-10}

2.73618718x10^{-15}

0.985027384 R_{e}1.015 R _{e}A_{5u}=

0.489164058

ß-1.544303917_{5u}^{2}=

± 1.514695982-0.029607935 -3.058999899 9.151957085x10 ^{-31}9.117737069x10^{-31}0.172i

1.550986921x10^{-18}ic

4.652960762x10^{-10}

2.736346668x10^{-15}

0.9850848 R_{e}1.015 R _{e}½-3/2 ± 3/20.0-3

m_{eo}= m_{e}= m_{ec}

9.290527148x10^{-31}9.255789006x10^{-31}0

1.5050654x10^{-18 }c

2.7777777...x10^{-15}

= 1.00 R_{e}R_{e}0.50078795 ß _{realimage}^{2}= -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 R_{e}1.001576 R _{e}A_{4l}=

0.511459239

ß-1.455190021_{4l}^{2}=

± 1.4849882220.029798201 -2.940178243 9.151059822x10 ^{-31}9.1163843161x10^{-31}0.173

1.551286282x10^{-18}c

2.73608263x10^{-15 }

= 0.98498975 R_{e}1.015 R _{e}A_{4u}=

0.511499639

ß_{4u}^{2}=

-1.455035593

± 1.4849362250.029900632 -2.939971818 9.15057674x10 ^{-31}9.116361885x10^{-31}0.173

1.55145488x10^{-18}c

2.73593396x10^{-15}

= 0.98493623 R_{e}1.015 R _{e}A_{2}=

0.511540039

ß_{2}^{2}=

-1.45488119

± 1.4848842340.030003044 -2.939765424 9.150093721x10 ^{-31}9.115880672x10^{-31}0.1732.86

1.55161873x10^{-18}c

2.7357895x10^{-15}

= 0.98488423 R_{e}1.015 R _{e}

A=_{6l}

0.512082536

ß_{6l}^{2}=

-1.452810201

± 1.4841867140.031376513 -2.936996915

9.143613382x10^{-31}9.109424564x10^{-31}0.177

1.553818818x10^{-18}c

2.73385198x10^{-15}

= 0.98418671 R_{e}1.016 R _{e}

A_{SI}= real

0.512116936

[e/m]=

1.758820024

x10^{-11}C/kg

with α_{var}max

ß_{SI}^{2}=

-1.452679026

± 1.4841425220.031463496-2.936821548

[1.02/1.02]m_{e}√(1-x)

9.14320282x10^{-31}

9.109015537x10^{-31}0.177

1.553958371x10^{-18}c

2.73372922x10^{-15}

= 0.98414252 R_{e}1.016 R_{e}

A_{6u}=

0.512122936

ß_{6u}^{2}=

-1.452656072

± 1.4841348150.031478742 -2.936790887

9.143130852x10^{-31}9.108943838x10^{-31}0.177

1.553982826x10^{-18}c

2.73370771x10^{-15}

= 0.98413478 R_{e}1.016 R _{e}

A_{ub}=

0.512540039

ß_{ub}^{2}=

-1.451067085

± 1.4835993680.032532283 -2.934666453

9.138156632x10^{-31}9.103988218x10^{-31}0.180

1.555675057x10^{-18}c

2.73222047x10^{-15}

= 0.98359937 R_{e}1.017 R _{e}

4(⅔√3-1)

0.618802153

-1.116025404

±1.366025404

-¼(1+2√3)±½√(4+2√3)¼

-2.4820500808

-(¾+√3)

[1.24/1.24]m_{e}√(1-x)

8.045832525x10^{-31}

8.015748411x10^{-31}0.500 2.006753867x10 ^{-18}c

v_{ps}= 6.020261601x10^{-9}

2.405626121x10^{-15}

= 0.866025403 R_{e}1.238 R _{e}

¾

Mean: ½{½+1}

∑surface charge-⅚ ± √(19/12) 0.424972405 -2.09164

[3/2]⅔m_{e}√(1-x)

7.045060062x10^{-31}

7.018717929x10^{-31}0.652

2.617379438x10^{-18}c

v_{ps}= 7.852138314x10^{-9}

2.10640483x10^{-15}

= 0.75830574 R_{e}3R _{e}/2

⅚

∑Volume charge-7/10 ± √(29/20) 0.504159457 -1.904159458

[5/3]⅗m_{e}√(1-x)

6.542012566x10^{-31}

6.517551374x10^{-31}0.710

3.035381866x10^{-18}c

v_{ps}= 9.106145598x10^{-10}

1.9559985x10^{-15}

= 0.70415946 R_{e}5R _{e}/31-½ ± ½√(5)0.618033988-1.618033988

[2]½m_{e}√(1-x)

5.741861551x10^{-31}

5.720392198x10^{-31}0.786

3.94031237x10^{-18}c

v_{ps}= 1.182093711x10^{-9}

1.71676108x10^{-15}

= 0.61803399 R_{e}2 R_{e}

1+½√2 =

1.707106781

-0.085786437

±0.914213562

0.828427125

x-root is real

-1 = i^{2}

y-root is complex

[3.41/3.41]m_{e}√(1-x)

3.848262343x10^{-31}

3.833873334x10^{-31}0.910

8.77216401x10^{-18}c

2.631649203x10^{-9}

1.150593228x10^{-15}

0.414213562 R_{e}

=( √2 - 1) R_{e}

3.414213562 R_{e}

= (2+√2) R_{e}2 0 ± ½√(3) 0.866025403 -0.866025403

[4]⅙m_{e}√(1-x)

3.400568951x10^{-31}

3.387853908x10^{-31}0.931

1.123396092x10^{-17}c

3.370188275x10^{-9}

1.01673724x10^{-15}

= 0.36602540 R_{e}4 R _{e}2.472136030.095491515 ± 0.8090169860.904508501-0.7135255471[4.94/4.94]m_{e}√(1-x)

2.870930718x10^{-31}

2.860196042x10^{-31}0.951

1.576125021x10^{-17}c

4.728375064x10^{-9}

R_{proton}= 0.85838052x10^{-15}

= 0.309016987 R_{e }

4.94427206 R_{e}3 ⅙ ± √(7/12) 0.930429282 -0.597195949

[6]⅙m_{e}√(1-x)

2.450493743x10^{-31}

2.44133112x10^{-31}0.965

2.163360455x10^{-17}c

6.490081364x10^{-9}

7.32673935x10^{-16}

= 0.26376262 R_{e}6 R _{e}4 ¼ ± √(½) 0.957106781 -0.457106781

[8]⅛m_{e}√(1-x)

1.924131173x10^{-31}

1.916936668x10^{-31}0.978

3.50886558x10^{-17}c

1.052659674x10^{-8}

5.75296616x10^{-16}

= 0.20710678 R_{e}8 R _{e}

174,532,925.3

-{1±1/√[1-ß^{2}]} /ß^{2}

~-1{1±1+½ß^{2}}/ß^{2}

0.499999..4 ±

0.500000..5

~ ½^{-}± ½^{+}

0.999999999.....

{m_{e}/αm_{ps}}^{2 }=

1-3.282806345x10^{-17}

-0.000000..1

[#/#]m_{e}√(1-x)

5.323079946x10^{-39}

5.303176457x10^{-39}

minimum mass (electron-neutrino)

0.00297104794 eV*

m_{νe}=mv_{τ}^{2}

= 0. 002982..eV*0.999

qbb boundary of physicality

0.045798805 c

13,739,641.79

r_{ec}= r_{ps}=(m_{e}/αm_{ps})R_{e}

1.59154943x10^{-23}

= 5.7296x10^{-9}R_{e}349,065,850.6 R_{e}∞½^{- }± ½^{+}1^{-}0^{-}

[∞^{-}]0^{+}m_{e}√(1-x)=m_{e}

m_{eo}=0+1^{-}

algorithmic metaphysicality

inflaton spacetime as complex v_{ps}= ic = ci[∞] R_{e}

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=∞: ß^{2}=½^{-}±½^{+}for roots x=1^{-}and y=0^{-}; for v=c with U_{m}= (½v^{2})μ_{o}e^{2}/8πR_{e}= (½v^{2})μ_{o}e^{2}/4πR_{e}= ½m_{e}c^{2}= m_{magnetic}c^{2}= m_{electric}c^{2 }and m_{o}= 0m_{e}

Aß^{2}= ([1-ß^{2}]^{-½}-1) = 1+½ß^{2}-3ß^{4}/8+5ß^{6}/16 -35ß^{8}/128+...-1

The Binomial Identity gives the limit of A=½ in: A=½ - ß^{2}{3/8 - 5ß^{2}/16 + 35ß^{4}/128 -...} and as the non-relativistic low velocity approximation of E=mc² as KE=½m_{o}v².

Letting ß^{2}=n, we obtain the Feynman-Summation or Path-Integral for dimensionless cycle time n = H_{o}t = ct/R_{Hubble}with H_{o}=dn/dt in the UFoQR for 1 = (1-ß^{2})(1+ß^{2})^{2}as ß^{4}+ß^{2}-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 γ^{3}in the manifestation of relativistic force as the time rate of change of relativistic momentum p_{rel}. Furthermore, the mass-charge ratio {e/m_{eo}} relation of the electron implies that a precision measurement in either the restmass m_{oe}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 m_{e}from its restmass resulting in m_{eo}γ = m_{e}γ^{2}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 - ß^{2}} describes the ß^{2}distribution of relativistic velocity in the unitary interval from A=0 to A=1, letting {1 - ß^{2}} = {√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 m_{oe}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: m_{electric}+ m_{magnetic }+ δm_{monopolic}= m_{ec}{½+½[v/c]²} + δ_{ps}m_{ec}= m_{ec }with m_{e}c^{2}√{1 + v^{2}γ^{2}/c^{2}} = m_{e}c^{2}γ = m_{ec}c^{2}for m = m_{ec}from the energy-momentum relation E^{2}= E_{o}^{2}+ p^{2}c^{2}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 3x10^{8}(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 μ_{o}= 4πx10^{-7}H/m which becomes numerically equal in the Maxwell constant μ_{o}= 1/ε_{o}c^{2}in an applied fine structure μ_{o}.ε_{o}= {120π/c}.{1/120πc} = 1/c^{2}(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.

{https://cosmosdawn.net/index.php/en...-alpha-variation-and-an-accelerating-universe}

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 α..............................................................................._{var}= 1 - (1.6021119x10^{-19}/1.60217662x10^{-19})^{2}= 1 - 0.9999192 = 8.08x10^{-5}[Eq.10]

Alpha α = μ_{o}ce^{2}/2h = 2π.(2.99792458)(1.6021119)^{2}x10^{-37}/(6.62607004x10^{-34}) = 60πe^{2}/h = 7.2967696x10^{-3}= 1/137.047072

{s} = 1.000978394 {s*} = 0.999022562 {s} {m} = 1.001671357 {m*} = 0.998331431 {m} {kg} = 1.003753126 {kg*] = 0.996260907 {kg} {C} = 1.002711702 {C*} = 0.997295631 {C} {J} = 1.005143377 {J*} = 0.994882942 {J} {eV} = 1.00246560 {eV*} = 0.997540464 {eV} {K} 0.98301975 {K*} = 1.017273559 {K}

From the unification polynomial U(x) = x^{4}+ 2x^{3}- x^{2}- 2x + 1 = 0 and derivative U'(x) = 4x^{3}+ 6x^{2}- 2x - 2 with minimum roots at x_{1}= X and x_{2}= -(X+1) = Y and maximum root at x_{3}= 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 redefines 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 ß^{2}distribution for the electron mass.

SNI:EMI [1-X]:[X] X X

#:#^{3}

#^{-2}

α^{-⅔}

1/∛α^{2}

Invariant

Upper BoundX-Boson SNI:WNI [1-X]:[1+X] [2X-1] X ^{3}

#:#^{18}

#^{-17}

α^{-⅓(17)}

1/∛α^{17}SNI:GI [1-X]:[2+X] [1-X] ^{2}X ^{4}

#:#^{54}

#^{-53}

α^{-⅓(53)}

1/∛α^{53}EMI:WNI [X]:[1+X] [1-X] X ^{2}

#^{3}:#^{18}

#^{-15}

α^{-5}

1/∛α^{15}EMI:GI [X]:[2+X] [2X-1] X ^{3}

#^{3}:#^{54}

#^{-51}

α^{-17}

1/∛α^{51}WNI:GI [1+X]:[2+X] X

#^{18}:#^{54}

#^{-36}

α^{-12}

1/∛α^{36}

Invariant

Lower BoundL-Boson

For the unitary interval at A=½ the Compton constant defines m_{e}.R_{e}, but at A=1, the constancy becomes ½m_{e}.2R_{e}and at the average value at A=¾ it is ⅔m_{e}.(3/2)R_{e}.

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 ß^{2}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 ⅔m_{e }and 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 this paper.

In the diagram above the mass of the electron is distributed as m_{ec}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 m_{e}, which 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 v_{ps}= 1.50506548x10^{-18}c and manifesting not as a dynamic external motion, but as f_{αω}= 2.84108945x10^{-16}= ∑f_{ss}= ∑m_{ss}c^{2}/h = f_{αω}/f_{ss}= 8.52326834x10^{14}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 m_{e}at A=½ and more than half of m_{e}at the absolute 0 state at A=0.

We know this discrepancy to be ⅓m_{e}on mathematical grounds and so one might relate the Compton constant in the ⅓R_{e}to set the ⅓m_{e}interval as being centred on A=½ for two bounds A_{1}and A_{2}in the 'complex' region where ß^{2}is negative and where ß^{2}is positive respectively. To approximate the two bounds, we shall define the sought interval for the bare electron mass m_{eo}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 E_{ps }= 1/e* = 1/2R_{e}c^{2}and using the modular string duality we use the magneto charge quantum not as inverse energy E_{weyl}, but as energy to set m*= E*/c^{2}= 2R_{e}* and so the unification factor for the electron mass m_{ec}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 = α^{⅔ }to set the electron's interaction relative to the SNI and a decreasing size of the electron centred at the R_{e}scale decreasing towards the nuclear centre with increasing speed in the 'real interval'.

As we require ⅔m_{e}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^{⅔}+ ⅓α^{⅔}= ⅔α^{⅔}.

The lower bound for m_{eo}so is A_{lb}= ½ - ⅓α^{⅔ }= 0.487459961.... and the upper bound becomes A_{ub}= ½ + ⅓α^{⅔ }= 0.512540039... for a total A-interval of A_{lb}+ A_{ub}= 0.0025080078... = 2(0.012540039).

We so can define m_{e}(m_{eo};ß^{2}) = m_{e}/ √(1 - ß^{2}) = m_{eo}/ (1 - ß^{2}) for any m_{eo}in the interval defined in the ß^{2}distribution and [Eq.8] with the effective restmass m_{e }= 9.290527148x10^{-31}kg* in * units.

ß_{lb}^{2}(0.487459961..) = -1.55145054.. + 1.517053242.. = -0.034397297.. (equilibrium in x-root) for m_{eo}= m_{e}√(1 - i^{2}ß^{2}) = 9.129344446x10^{-31}kg* for 9.095208981x10^{-31}kg.

ß_{o}^{2}(0.5000000000) = -1.50000000.. + 1.5000000000.. = 0.000000000.. (complex in x-root) for m_{eo}= m_{e}√(1 - 0) = 9.290527148x10^{-31}kg* for 9.255789006x10^{-31}kg.

ß_{ub}^{2}(0.512540039..) = -1.451067085.. + 1.483599368.. = 0.032532283.. (real in x-root) for m_{eo}= m_{e}√(1 - ß^{2}) = 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 m_{e}in the complex region of the unitary interval.

To correlate the complex solution for m_{eo}with the real solution for m_{eo}, we are required to shorten the interval A_{ub}- Al_{b}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 ß^{2}, 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 constant 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* = 1/2R_{e}c^{2}being of the same order as alpha as α/E_{weyl}= αe* = 3.648381483 or e*= 0.274094144.α.

Additionally, a conformal mapping of the minimum Planck energy as a Planck oscillator E_{o}= ½hf_{o}at the Planck energy of superstring class I onto the heterotic superstring HE(8x8) in the qbb energy quantum E_{ps}= E_{weyl}associates and couples the unitary interval to the displacement bounce of the inflaton. We denote the E_{ps}energy quantum as |E_{ps}| in its unified modular self state where E_{ps}.e* = 1 = E*e*

As ß^{2}= (1 - {m_{e}/m_{ec}}^{2}) and (1 - {m_{eo}/m_{e}}^{2}) as a distribution of mass ratios, it can be linked to the Compton constant in m_{e}/m_{ec}= r_{ec}/R_{e}in an inverse proportionality and so the unitary interval and the electron's mass and spacial extent distribution.

We set the interval A_{2}= A_{ub}- ½|E_{ps}| = 0.512540039...- 0.001 = 0.511540039... and the conjugate interval as A_{1}= A_{lb}+ ½|E_{ps}| = 0.487459961... + 0.001 = 0.488459961...

ß_{1}^{2}(0.488459961..) = -1.547250706.. + 1.515668402.. = -0.031582303.. (complex in x-root) for m_{eo}= m_{e}√(1 - i^{2}ß^{2}) = 9.142642017x10^{-31}kg* for 9.108456831x10^{-31}kg.

ß_{2}^{2}(0.511540039..) = -1.45488119.. + 1.484884234.. = 0.030003044..(real in x-root) for m_{eo}= m_{e}√(1 - ß^{2}) = 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 near the fractional divergent parts.

{A_{ub}- ½} + {½ - A_{lb}} = 2(0.012540039) = 0.025080078 = 2(⅓α^{⅔}) = 1/40 + 0.000080078... = ½|E_{ps}|(25) + 0.000080078... = ½|E_{ps}|(25) + [~]α_{var}in 7.22x10^{-7}parts.

A_{ub}- A_{4l}= A_{3u}- A_{lb}= 0.0010808... = 0.001 + 0.0000080078 = ½|E_{ps}| + [~]α_{var}.

A_{ub}= ½ + ⅓α^{⅔ }= 0.512540039...= 0.51254 + 0.000000039.. and A_{lb}= 0.487459961.. = 1 - 0.5124 - 0.00000039..

The alpha variation α_{var}= 1 - (1.6021119x10^{-19}/1.60217662x10^{-19})^{2}= 1 - 0.9999192 = 8.08x10^{-5}by [Eq.10]

A_{3l}= A_{1}+ ½α_{var}= 0.488459961.. + 0.0000404.. = 0.488500361.. and its image is A_{4u}= A_{2}- ½α_{var}= 0.511540039... - 0.0000404.. = 0.511499639..

A_{3u}= A_{1}+ α_{var}= 0.488459961.. + 0.0000808.. = 0.488540761.. and its image is A_{4l}= A_{2}- α_{var}= 0.511540039... - 0.0000808.. = 0.511459239...

ß_{3l}^{2}(0.488500361..) = -1.547081394.. + 1.515612547.. = -0.031468846.. (complex in x-root) for m_{eo}= m_{e}√(1 - i^{2}ß^{2}) = 9.143177565x10^{-31}kg* for 9.108990376x10^{-31}kg.

ß_{3u}^{2}(0.488540761..) = -1.54691211.. + 1.5155567.. = -0.03135541.. (complex in x-root) for m_{eo}= m_{e}√(1 - i^{2}ß^{2}) = 9.143712983x10^{-31}kg* for 9.109523792x10^{-31}kg.

ß_{4u}^{2}(0.511499639..) = -1.455035593.. + 1.484936225.. = 0.029900632..(real in x-root) for m_{eo}= m_{e}√(1 - ß^{2}) = 9.15057674x10^{-31}kg* for 9.116361885x10^{-31}kg.

ß_{4l}^{2}(0.511459239..) = -1.455190021.. + 1.484988222.. = 0.029798201..(real in x-root) for m_{eo}= m_{e}√(1 - ß^{2}) = 9.151059822x10^{-31}kg* for 9.1163843161x10^{-31}kg.

The bare electron mass m_{eo}should be found in two intervals defined in the alpha variation applied to both a complex halving part A_{3 upper bound}- A_{3 lower bound}for a minimised δ_{min}added to ½α_{var}and a real halving part A_{6 lower bound}- A_{6 upper bound}for a maximised δ_{max}subtracted from ½α_{var}.

To calibrate the units of the (*) mensuration system with the SI-measurement system, the mass-charge ratio for the electron and assuming a unit defined consistency, is applied in: {e/m_{eo }= 1.606456344x10^{-19 }C*/9.143202823x10^{-31}kg* = 1.756995196x10^{11}C*/kg* } and {e/m_{eo}= 1.602111894x10^{-19}C/9.10901554x10^{-31}kg = 1.758820024x10^{11}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 and the minimum Planck Oscillator |E_{o}= E_{ps}= E_{weyl}| at the cosmogenesis of the inflaton. We recall the super membrane displacement transformation of [Eq.9]:

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]:

Monopolar charge quantum e*/c^{2}= 2R_{e}⇐ super-membrane displacement transformation ⇒ √α.l_{planck}= e/c^{2}as Electropolar charge quantum

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 ß^{2}distribution.

⅔α.................................................................................................................................................................................................^{⅔}∝ (√α)^{3}in ⅔α^{⅔}≈ 1/40 + α_{var}= {⅔α^{-⅚}}(√α)^{3 }[Eq.12]

for proportionality constant {⅔α^{-⅚}} = 1/{1/40 - 1.477074222x10^{-4}} = 1/{1/40 - 1.828.α_{var}}

For (√α)^{3}= 6.232974608x10^{-4}then:

A_{5l}= A_{3l}+ 6.232974608x10^{-4}= 0.488500361..+ 6.232974608x10^{-4}= 0.489123658...

A_{5u}= A_{3u}+ 6.232974608x10^{-4}= 0.488540761..+ 6.232974608x10^{-4}= 0.489164058..

A_{6u}= A_{4u}+ 6.232974608x10^{-4}= 0.511499639..+ 6.232974608x10^{-4}= 0.512122936..

A_{6l}= A_{4l}+ 6.232974608x10^{-4}= 0.511459239..+ 6.232974608x10^{-4}= 0.512082536...

for the ß^{2}solutions:

ß_{5l}^{2}(0.489123658..) = -1.54447277.. + 1.514751719.. = -0.029721051.. (complex in x-root) for m_{eo}= m_{e}√(1 - i^{2}ß^{2}) = 9.151423661x10^{-31}kg* for 9.117205639x10^{-31}kg.

ß_{5u}^{2}(0.489164058..) = -1.544303917.. + 1.514695982.. = -0.029607935.. (complex in x-root) for m_{eo}= m_{e}√(1 - i^{2}ß^{2}) = 9.151957085x10^{-31}kg* for 9.117737069x10^{-31}kg.

ß_{6u}^{2}(0.512122936..) = -1.452656072.. + 1.484134815.. = 0.031478742..(real in x-root) for m_{eo}= m_{e}√(1 - ß^{2}) = 9.143130852x10^{-31}kg* for 9.108943838x10^{-31}kg.

ß_{6l}^{2}(0.512082536..) = -1.452810201.. + 1.484186714.. = 0.031376512..(real in x-root) for m_{eo}= m_{e}√(1 - ß^{2}) = 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 {m_{eo}/m_{e}}^{2}in the ß^{2}distribution

As the ß^{2}distribution is bounded in {A_{ub}- A_{lb}= ⅔α^{⅔}} as a sub-unitary interval in a smaller sub-interval of ½α_{var}; 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|E _{o}|⇔ |E_{ps}|* = 1/|e*|½|E _{ps}|¾|E _{ps}|1|E _{ps}|5/4|E _{ps}|3/2|E _{ps}|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}|E _{ps}|*/|e*| to reunitize-renormalize E*e*=12x10 ^{-6}3x10 ^{-6}4x10 ^{-6}5x10 ^{-6}6x10 ^{-6}⅔-value in partition interval ⅔m _{e}.(3/2)R_{e }for mean A=¾1/2 3/4 1 5/4 3/2 Fraction of Renormalization effect 1/3 1/2 2/3 5/6 1 Value of Δ(½α _{var}} in A_{6lb}- A_{6ub}and in A_{3ub}- A_{3lb}

2x10^{-6}

complex minimum3x10 ^{-6}4x10 ^{-6}5x10 ^{-6}

6x10^{-6}

real maximumThe ½a_{var}sub-interval so is adjusted by 6x10^{-6}from A_{6ub }- Δ(½α_{var}} = A_{SI}for ß_{SI}^{2}for m_{eo}SI 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

L_{P}√α = e/c^{2}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 'c^{2}' 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 E_{ps}to the 10-dimensional superstring sinksource energy E_{ss}as the 11-dimensional super-membrane E_{ps}E_{ss}.

{G_{o}k=1 for G_{o}=4πε_{o}and represents 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*' = 2R_{e}.c^{2}= 1/hf_{ps}= 1/E_{Weyl wormhole}by the application of the mirror/T duality of the super membrane E_{ps}E_{ss }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 = i^{2}= -1 = cos(π)+isin(π) = ℮^{iπ}

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 ß^{2}= x = 0, the Compton constant defines the required electron restmass of electrostasis as ½m_{e}c^{2}= e^{2}c²/8πε_{o}R_{e}} for an effective elecetron size of R_{e}, whilst for A=1 the m_{e}c^{2}= e^{2}c²/4πε_{o}R_{e}for a doubling of this radius to 2R_{e}for ß^{2}= x = X.

In the Feynman lecture the discrepancy 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} = 3/4 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 m_{ec}r_{ec}= m_{e}R_{e }for ß^{2}= 0 and at A=1, the Compton constant gives m_{ec}r_{ec}= ½m_{e}.2R_{e}for ß^{2}= 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 R_{p}= ½XR_{e }and where the factor X represents the symmetry equilibrium for a ß=(v/c} velocity ratio distribution for the effective electron restmass m_{e}proportional to the spacial extent of the electron.

For the proton then, its 'charge distribution' radius becomes averaged as R_{proton}= 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 v_{e}= 1.50506548x10^{-18 }c for its electrostatic potential, where U_{e}=∫{q²/8πε_{o}r²}dr = q²/8πε_{o}R_{e }= ½m_{e}c^{2}for a classical velocity of v_{e}=0 in a non-interacting magnetic field B=0.

2U_{e}=m_{e}c^{2}so implies a halving of the classical electron radius to obtain the electron mass m_{e}=2U_{e}/c^{2}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

We consider the universe's thermodynamic expansion to proceed at an initializing time t_{ps}=f_{ss}at lightspeed for a lightpath x=ct to describe the hypersphere radii as the volume of the inflaton made manifest by the instanton as a lower dimensional subspace and consisting of a summation of a single spacetime quantum with a quantized toroidal volume 2π²r_{weyl}and where r_{weyl}=r_{ps}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 t_{G}, say so 18.85 minutes later, the count of space time quanta can be said to be 9.677x10^{102}for a universal 'total hypersphere radius' of about r_{G}=3.391558005x10^{11}meters and for a G-Hypersphere volume of so 7.69x10^{35 }cubic meters from N{2π^{2}.r_{ps}^{3}} = Volume = 2π^{2}.R_{Hk}^{3}.

{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 can then be used to indicate the mapping of the wormhole scale onto the scale of the sun as a quasi conformal scaling of the fermi scale of the classical electron radius onto a typical gravitational star system.

r_{weyl}/R_{sun}=R_{e}/r_{E}for R_{sun}=r_{weyl}.r_{E}/R_{e}=1,971,030 meters. This gives an 'inner' solar core of diameter about 3.94x10^{5}meters.

As the classical electron radius is quantized in the wormhole radius in the formulation R_{e}=10^{10}r_{weyl}/360, rendering a finestructure for Planck's Constant as a 'superstring parametric': h=2πr_{weyl}/2R_{e}c^{3}; the 'outer' solar scale becomes R_{sun[o]}=360.R_{sun}=7.092x10^{8}meters as the observed radius for the solar disk.

19 seconds later; a F-Hypersphere radius is about r_{F}=3.451077503x10^{11}meters for a F-count of so 1.02x10^{103}spacetime quanta for the thermodynamically expanding universe from the instanton.

We also define an E-Hypersphere radius at r_{E}=3.435971077x10^{14}meters and an E-count of so 10^{112}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 to be independent on mensuration physics of any kind.

{https://cosmosdawn.net/index.php/en...stanton-to-continuon-four-pillars-of-creation}

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 to 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 (IR).

A down-quark so is a unitary ring coupled to a kernel-quark. The proton's quark-content so can be rewritten and without any loss of any of the properties and generalities in unitary symmetry obtained from the Standard Model of particle physics and 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 (OR) 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 (Sigma^{o}Resonance); usd (Sigma^{o}) and the sud (Lambda^{o}) 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 R_{e}=ke²/m_{e}c² 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 R_{compton }= h/2πmc with m the mass of the nucleus, say a proton; the latter so having a scale reduced from R_{e}by some partitioning of the classical electron size.

As the Planck Oscillator E_{o}=½hf_{o}of the Zero-Point-Energy or ZPE as Vortex-Potential-Energy or VPE defines its ground state at half its effective energy of E_{k}=hf_{k}, and as a conformal mapping from the string energy scale of the inflaton onto the qbb scale of the instanton in the E_{weyl}= E_{ps}=/e*=1/2R_{e}c^{2}|_{mod}gauge boson; we define a subatomic scale at half of R_{e}as r_{mean}=½R_{e}.

The wave-matter (after de Broglie generalising wavespeed v_{dB}from c in R_{compton}c) then relates the classical electron radius as the 'confinement limit' to the Compton scale in the electromagnetic finestructure constant in R_{e}=Alpha.R_{compton}.

The extension to the hydrogen-atom is obtained in the expression R_{e}=Alpha².R_{bohr1}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: r_{M}=½(r_{F}+r_{G}) =3.421317754x10^{11}meters and set the macro-leptonic radius to r_{E}=3.435971077x10^{14}meters.

Secondly, we map the macro-scale onto the micro-scale, say in the simple proportionality relation for the micro-mesonic scale R_{mean}= R_{e}.r_{M}/r_{E}= 2.765931439x10^{-18}meters.

So reducing the apparent measured 'size' of a halving of R_{e}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 r_{weyl }= r_{ps}=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=mc^{2}, which describe the baryonic- and hyperonic 'quark-sectors' in: mc^{2}=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 Z^{o}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 and in a way revisiting the transformation of a bosonic ancestry for the fermionic matter structures, discussed further on in the string class transformations of the inflaton era. There exists so a natural and generic supersymmetry in the quark-lepton hierarchy and no additional supersymmetric particles are necessary.

Then the Outer Ring contracts along its magnetoaxis defining its asymptotic confinement and 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 2πR_{e}and the wormhole perimeter λ_{weyl}=2πr_{weyl}.

But in this process of the 'shrinking' classical electron radius towards the gluonic kernel; 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 then indicates a neutrino-oscillation potential at the Inner Ring-Boundary. Using our proportions and assigning any neutrino-masses m_{ν }as part of the electronmass m_{e}, 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:

m............................................_{Higgs/Tauon}= m_{e}λ_{weyl}.r_{E}/(2πr_{M}R_{e}) = m_{e}λ_{weyl}.r_{E}/(2πr_{M}R_{e})~ 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 (Neutrino 2000), 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 referred to in the 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:

r_{E}= 3.435971077x10^{14}meters and an E-count of (26x65^{61}) = 1.00x10^{112}spacetime quanta:

m_{νHiggs-E }= m_{νelectron}= m_{e}.r_{ps}{r_{E}/r_{E}}/R_{e}= 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 E_{ps}.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 {R_{e}^{2}/r_{ps}}:

|m.........................................................................._{νHiggs-E }= m_{νelectron}|_{modular}= m_{e}.r_{ps}{R_{e}^{2}/r_{ps}}/R_{e}= alpha.h/2πc = 2.580701988x10^{-45}(kg/m)*[Eq.14]

r_{F}= 3.451077503x10^{11}metres for the F-count of (13x66^{56}) = 1.02x10^{103}spacetime quanta:

m_{νHiggs-F }= m_{νmuon}=m_{e}.r_{ps}{r_{E}/r_{F}}/R_{e}= 5.299779196x10^{-36 }kg* or 2.969144661 eV* as Weak Interaction Higgs Mass induction.

r_{G}= 3.39155805x10^{11}metres for the G-count of (67x36^{65}) = 9.68x10^{102}spacetime quanta:

m_{νHiggs-G }= m_{ν}_{tauon}= m_{e}.r_{ps}{r_{E}/r_{G}}/R_{e}= 5.392786657x10^{-36 }kg* or 3.021251097 eV* as Weak Interaction Higgs Mass Induction.

The mass difference for the Muon-Tauon-(Anti)Neutrino Oscillation, then defines the Mesonic Inner Ring Higgs Induction:...........................[Eq.15]

m_{νHiggs }= m_{e}.r_{ps}{r_{E}/r_{G }- r_{E}/r_{F}}/R_{e}= 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 R_{E}nexus for R_{E }= r_{ps}∛(26x65^{61}) m* and for m_{νHiggs-E }= m_{νelectron }= μ_{o}e^{2}c^{2}.r_{ps}/4πR_{e}^{2}c^{2}= 30e^{2}λ_{ps}/2πcR_{e}^{2}or μ_{o}{Monopole GUT masses ec}^{2}r_{ps}/4πR_{e}^{2}c^{2}= 2.982198661x10^{-3}eV* and for:

m............................................................................._{νElectron}c^{2}= m_{v}(ν_{Tauon}^{2})c^{2}= m_{ν}(ν_{Muon}^{2}+ν_{Higgs}^{2})c^{2}= μ_{o}{Monopole GUT masses ec}^{2}r_{ps}/4πR_{e}^{2}[Eq.16]

This can also be written as m_{νHiggs-E}=m_{νelectron}=m_{νTauon}^{2}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.

m_{νTauon}= B^{4}G^{4}R^{4}[0]+B^{2}G^{2}R^{2}[-½] = B^{6}G^{6}R^{6}[-½] = √(m_{νelectron}) = √(0.002982) = 0.0546... eV*

m_{νHiggs }= B^{4}G^{4}R^{4}[0] = m_{e}λ_{ps}.r_{E}{1/r_{G}-1/r_{F}}/(2πR_{e}) ~ 9.301x10^{-38}kg* or 0.0521... eV*

m_{νMuon}= B^{2}G^{2}R^{2}[-½] = √(m_{νTauon}^{2}- m_{νHiggs}^{2}) = √(0.00298-0.00271) = √(0.00027) = 0.0164... eV*

m_{νElectron}= B^{2}G^{2}R^{2}[-½] = (m_{νTauon})^{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:

(m_{ν3}+ m_{ν2}).(m_{ν3}- m_{ν2}) = m_{ν3}^{2}- m_{ν2}^{2}= 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 R_{E}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 [ec^{3}=2.7x10^{16}GeV*]_{unifiedinmodularduality}manifests in their masses. The premise of the older Standard Model for a massless (anti)neutrino so remains valid 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: (R^{4}G^{4}B^{4})[0] and the Tauon Anti(Neutrino) in (R^{6}G^{6}B^{6})[½].

The twinned neutrino state so becomes apparent in a coupling of the scalar Higgs-Neutrino with a massless base neutrino in a (R^{6}G^{6}B^{6})[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.

m_{νHiggs}+ m_{νelectron}= m_{νHiggs}+ (m_{νTauon})^{2}for the 'squared' ground state of a massless base (anti)neutrino for a perturbation Higgsian (anti)neutrino in (m_{νTauon})^{2}= (m_{νHiggs}+ Δ)^{2}= m_{νElectron}for the quadratic m_{νHiggs}^{2}+ 2m_{νHiggs}Δ+ Δ^{2}= 0.002982 from (m_{νHiggs}+ Δ) = √(m_{νelectron})

and for a Δ = √(m_{νelectron}) - m_{νHiggs}= m_{νTauon}- m_{νHiggs}= 0.0546 eV - 0.0521 eV = 0.0025 eV.

m_{νHiggs}+ Δ = 0.0521 + 0.0025 = (m_{νHiggs}) + (m_{νelectron}) - 0.00048 = m_{νtauon}= 0.0521+0.00298 - 0.00048 + ... = 0.0546 eV* as a perturbation expression for the 'squared' scalar Higgs (Anti)Neutrino.

(m_{νMuon}- m_{νElectron}){(m_{νMuon}+ m_{νElectron}) - (m_{νMuon}- m_{νElectron})} = 2m_{νElectron}(m_{νMuon}- m_{νElectron}) as the squared mass difference:

m_{νMuon}^{2}- m_{νElectron}^{2}= 2m_{νElectron}(m_{νMuon}- m_{νElectron}) + (m_{νMuon}- m_{νElectron})^{2}

and for m_{νMuon}2 = m_{νElectron}- m_{νHiggs}^{2}= (0.002982 - 0.00271 = 0.00027) for √(0.00027) = m_{νMuon}= 0.01643 = 5.51 m_{νElectron}.

{m_{νMuon}^{2}- m_{νElectron}^{2}} - m_{νMuon}2 + 2m_{νMuon}m_{νElectron}- m_{νElectron}^{2}= 2m_{νMuon}m_{νElectron}- 2m_{νElectron}^{2}= 2m_{νElectron}{m_{νMuon}- m_{νElectron}}

= 2mν_{Electron}^{2}{m_{νMuon}/m_{νElectron}- 1} = 8.892x10^{-6}{11.02-1} = 8.910x10^{-5}, approximating the KamLAND 2005 neutrino mass induction value of 7.997..x10^{-5}eV^{2}obtained for a ratio of 11m_{νElectron}= 2m_{νMuon}.

For 3 (anti)neutrinos then, the cosmological summation lower and upper bounds for (anti)neutrino oscillations are:

0 + m_{νelectron-muon}+ m_{νelectron-tauon}+ m_{νmuon-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].

∑m_{ν}= m_{νElectron}+ m_{νMuon}+ m_{νHiggs }+ m_{νTauon}= 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 R^{2}G^{2}B^{2}[+½] for the AntiNeutrinos and in B^{2}G^{2}R^{2}[-½] for the Neutrinos.

{s} = 1.000978394 {s*} = 0.999022562 {s} {m} = 1.001671357 {m*} = 0.998331431 {m} {kg} = 1.003753126 {kg*] = 0.996260907 {kg} {C} = 1.002711702 {C*} = 0.997295631 {C} {J} = 1.005143377 {J*} = 0.994882942 {J} {eV} = 1.00246560 {eV*} = 0.997540464 {eV} {K} 0.98301975 {K*} = 1.017273559 {K} The Wave Matter of de Broglie: λ_{deBroglie}= 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: λ

_{deBroglie}= h/p = hc/pc for (pc) = √{E^{2}- E_{o}^{2}}= m_{o}c^{2}.√{[v/c]^{2}/(1-[v/c]^{2})}

(a) Example:

A pellet of 10g moves at 10 m/s for a de Broglie wavelength v_{dB}= h/mv = h/0.1 = 6.7x10^{-33}m*

This matter wavelength requires diffraction interference pattern of the order of λ_{dB}to be observable and subject to measurement

(b) Example:

An electron, moving at 80% of light speed 'c' requires relativistic development

E_{o }= m_{o}c^{2}with E = mc^{2}= m_{o}c^{2}/√{1-[v/c]^{2}}, a 66.66% increase in the electron's energy describing the Kinetic Energy E - E_{o}= {m - m_{o}}c^{2}

for a relativistic momentum p = m_{o}c.√{[0.8]^{2}/(1-[0.8]^{2})} = (1.333..) m_{o}c = h/λ_{deBroglie}and for a relativistic de Broglie wavelength, 60% smaller, than for the non-relativistic electron in λ_{deBroglie }= h/1.333..m_{o}c < h/0.8m_{o}c =λ_{deBroglie}(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'

v_{phase}= wavelength.frequency = (h/mv_{group})(mc^{2}/h) = c^{2}/v_{group}> c for all v_{group}< c

m = Energy/c^{2}= hf/c^{2}= hc/λ_{deBroglie}c^{2}= h/λ_{deBroglie}c = m_{deBroglie}= [Action as Charge^{2}]_{mod}/c(Planck-Length Oscillation)

= [e^{2}]_{mod}/cl_{Planck}√alpha = [e^{2}c^{2}/ce]_{mod}= [ec]_{modular}

as monopole mass of GUT-string IIB and as string displacement current mass equivalent for the classical electron displacement 2R_{e}= e*/c^{2}= [ec]_{modular}as Wormhole minimum spacetime configuration for the Big Bang Instanton of Big Bang wormhole energy quantum E_{ps}=hf_{ps}=m_{ps}c^{2}=kT_{ps}as a function of e*=1/E_{ps}of Heterotic superstring class HE 8x8 and relating the Classical Electron Diameter {2R_{e}} as Monopole Mass [ec]_{mod}in mass M=E/c^{2}modular dual in Curvature Radius r_{ps}=λ_{ps}/2π=2G_{o}M_{c}/c^{2}⇒ G_{o}m_{ps}/c^{2 }quantum gravitationally.

The factor 2G_{o}/c^{2}multiplied by the factor 4π becomes Einstein's Constant κ = 8πG_{o}/c^{2}= 3.102776531x10^{-26 }m/kg describing how spacetime curvature relates to the mass embedded in that spacetime in the theory of General Relativity coupled to the theory of Quantum Relativity.

The selfduality of the superstring IIB aka the Magnetic Monopole selfstate in GUT Unification 2R_{e}/30[ec]_{mod}= 2R_{e}c^{2}/30[ec^{3}]_{mod}= e*/30[ec^{3}]_{mod}∝ κ for a proportionality constant {κ*}=2R_{e}/30κ[ec]_{mod}= 2R_{e}.c^{2}/8πe = e*/8πe =1.2384..x10^{20}kg*/m* in string units for Star Charge in Star Colomb C*/Electro Charge in Coulomb C unified.

The monopolar Grand Unification (SEWG ⇒ sEwG ⇒ gravitational decoupling SEW.G) has a Planck string energy reduced at the IIB string level of e*=[ec^{3}]_{modular}for m_{ps}c^{2}c/[ec]_{modular}= [c^{3}]_{modular}= 2.7x10^{25}eV* or 4.3362x10^{6}J* for a monopole mass [ec]_{modular }= m_{monopole }= 4.818x10^{-11}kg*.

Mass M = n.m_{ss}= Σm_{ss}= n.{h/2πr_{deBroglie}c} .[E_{ss}.e*]_{mod}= n.m_{ps}.[E_{ss}.{9x10^{60}}.2π^{2}R_{rmp}^{3}]_{mod}= n.m_{ps}.[E_{ss}.{2R_{e}.c^{2}}]_{mod}= n.[E_{ps}.E_{ss}]_{mod}.[2R_{e}]_{mod}

for λ_{deBroglie}=λ_{ps}=h/m_{ps}c and [E_{ps}.e*]_{mod}=1

{2R_{e}c^{2}} = 4G_{o}M_{Hyper}for the classical electron radius R_{e}=ke^{2}/m_{e}c^{2}and describes its Hyper-Mass M_{Hyper-electron}= R_{e}c^{2}/2G_{o}= ke^{2}/2G_{o}m_{e}= 1.125x10^{12}kg* for an effective electron mass of m_{e}= ke^{2}/2G_{o}(1.125x10^{12}) =9.290527148x10^{-31 }kg* in string units and where k = 1/4πε_{o }= [G_{o}]_{u}= [30c]_{u}= 9x10^{9}(Nm^{2}/C^{2})*.

The curvature radius for the electron mass m_{e}= r_{electron}c^{2}/2G_{o}then becomes r_{electron}= 2G_{o}m_{e}/c^{2}= 2.293957...x10^{-57}m* in string-membrane inflaton space as 1.44133588x10^{-34 }r_{ps}in the wormhole instanton space.

R_{e}/r_{inflaton-electron}= M_{Hyper-electron}/m_{e}= 1.2109108..x10^{42}= ½(EMI/GI) = ½(e^{2}/G_{o}^{2}m_{e}^{2}) =½ {e/G_{o}m_{e}}^{2}= ½(2.421821677x10^{42 }) for the classical electron radius R_{e}halved from the classical electron diameter 2R_{e}from the definition for the modulated supermembrane coupled in E_{ps}E_{ss}=h^{2 }and E_{ps}/E_{ss}=f_{ps}^{2}=1/f_{ss}^{2}.

Mass M = n.m_{ss}= Σm_{ss}= n.{m_{ps}} .[E_{ss}.e*]_{mod}= n.{m_{ps}}[{hf_{ss}}.2π^{2}R_{rmp}^{3}]_{mod}= n.[m_{ps}f_{ss}^{2}]_{mod}= n.[hf_{ss}/c^{2}] = n.m_{ss}

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

For magnetic field B = vxE/c^{2 }= v.E.sinθ/c^{2}the momentum density ε_{o}ExB = ε_{o}v.E^{2}sinθ/c^{2}electric energy density U_{e}=½ε_{o}E^{2 }and E=q/(4πε_{o}r^{2}) and dV = 2πr^{2}.sinθ.dθ.dr for the spacetime interval from some minimum boundary a to ∞ and with ∫1/r^{2}dr = |-1/r|[∞,a] = 0^{-}+ 1/a = 1/a for a=R_{e}for the waved particle electron

p = ∫ε_{o}v(Esinθ/c)^{2}dV = p_{rel}= {2πε_{o}vγ/c^{2}}{q^{2}/16π^{2}ε_{o}^{2}}∫r^{-2}.{sin^{3}θ.dθ}.dr = {vγq^{2}/8πε_{o}c^{2}}∫r^{-2}.{sin^{3}θ.dθ}.dr

= {vγq^{2}/8π.a.ε_{o}c^{2}}∫sin^{3}θ.dθ = {vγq^{2}/8π.a.ε_{o}c^{2}}∫{1-cos^{2}θ}sinθ.dθ

= {vγq^{2}/8π.a.ε_{o}c^{2}}|⅓cos^{3}θ -cosθ|[π,0] = {vγq^{2}/8π.a.ε_{o}c^{2}} |-⅓+1-⅓+1| = vγq^{2}/6π.a.ε_{o}c^{2}= μ_{o}vγe^{2}/6π.R_{e}

p_{rel}= μ_{o}vγe^{2}/6π.R_{e }for m_{emr}= μ_{o}γe^{2}/6π.R_{e }= {4/3}½m_{e }= ⅔m_{e }> ½m_{e }

The electromagnetic mass must however be exactly U_{e}/c^{2}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 m_{emr }= m_{o }= m_{e}/2A = μ_{o}γe^{2}/6π.R_{e }= {4/3}½m_{e }= ⅔m_{e }defines A=¾ in the (v/c)^{2}distribution and for a velocity:

B^{2}={v/c}^{2 }= -⅚±√(19/12) for roots x=0.425 and y=-2.092; with v_{electron}= 0.65189908 c in U_{m}= (½v^{2})μ_{o}e^{2}/4πR_{e}= ½m_{e}v^{2 }

{4/3}.U_{e}/c^{2}= {4/3}γe^{2}/8π.ε_{o}R_{e }c^{2}= {4/3}½m_{e}= {4/3}.U_{m}/c^{2}= {4/3}.μ_{o}γe^{2}/8π.R_{e}= {4/3}γke^{2}/e* = {4/3}γke^{2}.hf* = (1-⅓)m_{e}for an apparent restmass ⅔m_{e}.

The corresponding energy level for this mass increase of ⅓m_{e}for a velocity of 0.745 c is is 2.788x10^{-14}Joules* or 0.17350 MeV* (0.17307 MeV) for a dynamic mass m_{e}.

The classical electromagnetic mass m

_{emr}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 (3/2)R_{e}=αh/(2πc.⅔m_{e}) = αh/2πcm_{e}= 4.1666.x10^{-15}m* (4.15971430x10^{-15}m) normalizes the {4/3} factor from the classical derivation of the electromagnetic mass for the electron in the mean value for the A=½ to A=1 interval for the ß^{2}distribution.

E* = E..............................................................................._{ps }= hf_{ps }= hc/λ_{ps }= m_{ps}c^{2}= (m_{e}/2e).√[2πG_{o}/αhc] = {m_{e}/m_{P}}/{2e√α} = 1/2R_{e}c^{2 }= 1/e*[Eq.17]

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 R_{e}in x/c^{2}= λ_{ps}/2π for x = r_{ps}c^{2}= 2G_{o}M_{Hubble}= Wormhole Radius of the Instanton of the quantum gravitational Big Bang creation event.

Modular duality E_{ps}= hf_{ps}=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 λ_{ps}=10^{-22}m* onto the the classical electron radius as: R_{wormhole}/R_{electron}= 360/(2π.10^{10}).

This can be defined as a form of angular acceleration |alphaomega = αω| = |df/dt|_{e}= e*/V* = λ_{ps}/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.

m_{emr}= μ_{o}γe^{2}/6π.R_{e }= {4/3}.U_{e}/c^{2}= {4/3}γe^{2}/8π.ε_{o}R_{e }c^{2}= {4/3}½m_{e}= {4/3}.U_{m}/c^{2}= {4/3}.μ_{o}γe^{2}/8π.R_{e}= {4/3}γke^{2}/e* = {4/3}γke^{2}.hf*

As the electromagnetic mass must however be exactly U_{e}/c^{2}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 d^{3}x/dt^{3}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 dp_{rel}/dt = d(m_{o}γv)/dt = m_{o}d(γv)/dt + γvd(m_{o})/dt = m_{o}d(γv)/dt + {γvh/c^{2}}df/dt = m_{o}γ^{3}.dv/dt + {γvh/c^{2}}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 2R_{e}c^{2}=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 2R

_{e}c^{2}= 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 m_{e}c^{2}=ke^{2}/R_{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 L_{P}√α = e/c^{2}in a unitary coupling between the quantum gravitational and electromagnetic fine structures.

G_{o}k=1 for G_{o}=4πε_{o}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*' = 2R_{e}.c^{2}= 1/hf_{ps}= 1/E_{Weyl wormhole}by the application of the mirror/T duality of the super membrane E_{ps}E_{ss }of heterotic string class HE(8x8).

Also in a model of quantum relativity (QR), there is a quantization of exactly 10^{10}wormhole 'singularity-bounce' radii defining the radian-trigonometric Pi ratio as R_{wormhole}/R_{electron}= 360/2π.10^{10}or 10^{10}= {360/2π}{R_{e}/r_{wormhole}} 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 10^{26}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.

{https://cosmosdawn.net/index.php/en...he-weyl-curvature-hypothesis-of-roger-penrose}

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 m_{p}=u.d.u=K.KIR.K=(939.776+1.5013-0.5205-0.1735) MeV* = 940.5833 MeV* (938.270 MeV).

Neutron m_{n}=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 c^{2}= 1/ε_{o}μ_{o}and the inverse of the product between electric permittivity ε_{o}=1/120cπ and magnetic permeability μ_{o}=120π/c for 'free space' impedance:

Z_{o}= electric field strength E/magnetic field strength H = √(μ_{o}/ε_{o}) = cμ_{o}= 1/cε_{o}= 120π}.

Coulomb Electro Charge e = L)_{P}.√α.c^{2}↔ 2R_{e}.c^{2 }= e* (Star Coulomb Magneto Charge

e* = 2R_{e}c^{2}= 2ke^{2}/m_{e}= e^{2}/2πε_{o}m_{e}= αhc/πm_{e}with Alpha-Variation (1.6021119x10^{-19}/1.60217662x10^{-19})^{2}= 0.99991921...for the calibration

{R_{e}m_{e}} = μ_{o}e^{2}/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*) = μ_{o}e^{2}/4π for e=1.606456344x10^{-19}C*

for the quantum mechanical electron and adjusted in the [SI/*] alpha variation [mkg/C^{2}] = Alpha Variation α_{var}in {R_{e}m_{e}.α_{var}}_{SI}= {α_{var}.μ_{o}e^{2}/4π}_{SI}= {R_{e}m_{e}}* = {μ_{o}e^{2}/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 R_{e}= 2.773142866x10^{-15}m for an increased electron effective restmass of m_{e}= 9.255789006x10^{-31}kg or for (R_{e}m_{e}) = (μ_{o}e^{2}/4π) = 2.566762525x10^{-45}mkg.

From wikipedia:https://en.wikipedia.org/wiki/ElectronThe 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.

Thereisalso 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 r_{ps}=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 R_{e}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 theycouldstraighten out the classical difficulty andthenmake 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 aself-consistentquantum theory out ofanyof 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 Naturehasbeen 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.

Thenuclearforces 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 mc^{2}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 thesignis wrong! The neutron isheavierthan 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 objectexceptfor 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 π^{o}-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 nonetcharge, itdoeshave a charge distribution inside it—it is only thenetcharge 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 (Sigma^{o}Resonance); usd (Sigma^{o}) and the sud (Lambda^{o}) 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 R_{e}=ke²/m_{e}c² 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 m_{p}=u.d.u=K.KIR.K=(939.776+1.5013-0.5205-0.1735) MeV* = 940.5833 MeV* (938.270 MeV).

Neutron m_{n}=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 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 or Gγ 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] + Antiν_{electron}[+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] + Antiν_{electron}[+½]+GP[-1]} ⇒ n^{o}[-½] + ν_{electron}[-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] + ν_{electron}[-½]}_{W+}+ Graviphoton[+1])

⇒ d[+½]u[-½]{u[-½] + IR^{-}[0]}*{KIR-Oscillation (OR-IR)^{o}[-½]+e^{+}[+½]+v_{electron}[-½]} ⇒ d[+½]u[-½]d[-½] + {(OR-IR)^{+}[0]} +ν_{electron}[-½]

⇒ n^{o}[+½]+ν_{electron}[-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 R^{2}G^{2}B^{2}[+½]+B^{2}G^{2}R^{2}[-½] = BY^{2}B[0]=GM^{2}G[0]=RC^{2}R[0] = VPE[0].

An Anti-Neutrino template R^{2}G^{2}B^{2}[+½] = W^{2}[+½] = B^{2}G^{2}R^{2}[-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 R^{2}G^{2}B^{2}[+½] being the anti-state for the Neutrino template B^{2}G^{2}R^{2}[-½] and without or following the Graviphoton 'flip'.

CP violation in the weak nuclear interaction

The difference between matter and antimatter subsequently derives from the difference between the Outer Ring charge of the W^{+}for antimatter and the W^{-}for matter and so becomes related to the nature of constituent neutrinos and anti-neutrinos in the Kernel-Ring oscillations respectively.

The described gluon-anti-neutrino-electron oscillation from Kernel to mesonic IR to leptonic OR so becomes an inherent supersymmetry between bosonic gluons and fermionic (anti)neutrinos manifesting in the weak interaction and its associated parity violations in Charge-Parity (CP) symmetry.

All quark-antiquark states engaging outer ring oscillations, such as the neutral kaon pairing d.sbar and dbar.s and bottom quark energy states such as b.sbar =(ud)bar.sbar = so will exhibit a difference between matter and antimatter.

For matter IR with antimatter ORbar, for the neutral kaon K^{o}oscillates from its kernel VPE K.Kbar or u.ubar a matter IR to an antimatter ORbar for the antimatter weakon:

K^{o }= d.sbar = [K+IR].[Kbar+ORbar] = [K.Kbar][0]+[IR*ORbar][0] = [K.Kbar][0]+[IR*{ORbar+ν_{electron}][-1]}_{W+ }+Gγ[+1]

⇒ {u.ubar+d.dbar or u.dbar+ubar.d} + {strongweak anti-gluon-neutrino kernel-ring interaction suppressing any lepton decay products}[-½-½+1]} ⇒ {π^{o}+π^{o}or π^{+}+π^{-}} ⇒ K_{short}^{o}or

⇒ {ubar.d+e^{+}[½]+ν_{electron}[-½]} ⇒ π^{-}[0] + e^{+}[½]+ν_{electron}[-½] ⇒ K_{long}^{o}, if the W^{+}manifests from its quantum geometric VPE structure in a ORbar-IR oscillation.

For antimatter IRbar with matter OR, for the neutral kaon K^{o}bar oscillates from its kernel VPE K.Kbar or u.ubar an antimatter IRbar to a matter OR for the matter weakon:

K^{o}= dbar.s = [Kbar+IRbar].[K+OR] = [K.Kbar][0]+[IRbar*OR][0] = [K.Kbar][0]+[IRbar{OR+antiν_{electron}][+1]}_{W- }+Gγ[-1]

⇒ {u.ubar+d.dbar or u.dbar+ubar.d} + {strongweak gluon-anti-neutrino kernel-ring interaction suppressing any lepton decay products}[-½-½+1]} ⇒ {π^{o}+π^{o}or π^{+}+π^{-}} ⇒ K_{short}^{o}or ⇒ {u.dbar+e^{-}[-½]+ν_{electron}[+½]} ⇒ K_{long}^{o}, if the W^{-}manifests from its quantum geometric VPE structure in a IRbar-OR oscillation.

But an exchange of the inner and outer rings in their matter and antimatter nature is also possible resulting in the superpositioning of the neutral kaon's wavefunctions and leading to CP violation in that mixing between matter and antimatter in characteristics defined in the weakon quantum geometry.

Here, the Graviphoton does not neutralize the interacting weakon spin, but spininduces the interacting mesonic inner ring in the IR-ORbar or IRbar-OR oscillation and delaying the strongweak kernel-ring interactions for the antigluon-neutrino or gluon-anti-neutrino kernel templates respectively.

K^{o }= d.sbar = [K+IR].[Kbar+ORbar] = [K.Kbar][0]+[IR*ORbar][0] = [K.Kbar][0]+[IR*[0]{ORbar+ν_{electron}][-1]}_{W+ }+Gγ[+1]

⇒ [u.ubar][0]+{IR*[+1]+ORbar[-1]+ν_{electron}[0]} ⇒ [u.ubar][0]+[KIR.KIRbar][0] ⇒ {u.ubar+d.dbar} as a two particle decay in anti-gluon-neutrino strongweak interaction and with the Graviphoton[+1] spin inducing the matter based Inner Ring to neutralize the opposite spin of the interacting W^{+}[-1] weakon.

K^{o}= dbar.s = [Kbar+IRbar].[K+OR] = [K.Kbar][0]+[IRbar*OR][0] = [K.Kbar][0]+[IRbar{OR+antiν_{electron}][+1]}_{W- }+Gγ[-1]

⇒ [u.ubar][0]+{IRbar*[-1]+OR[-1]+antiν_{electron}[0]} ⇒ [u.ubar][0]+[KIRbar.KIR][0] ⇒ {u.ubar+d.dbar} as a two particle decay in gluon-anti-neutrino strongweak interaction and with the Graviphoton[-1] spin inducing the antimatter based Inner Ring to neutralize the opposite spin of the interacting W^{-}[+1] weakon.

The difference in the antimatter to matter and matter to antimatter kernel-ring oscillation so results in the mixing of the wave functions to exemplify the CP violation in the neutral kaon as decaying in different fashion and decay rates as the K_{short}^{o}= {d.sbar+dbar.s}/√2 and the K_{long}^{o}= {d.sbar-dbar.s}/√2 in decay times differing in a factor of the light-matter interaction probability α in t_{Ks}^{o}=8.95x10^{-11}s* in a two particle decay {π^{o}+π^{o}or π^{+}+π^{-}} and 5.18x10^{-8}s* in a three particle decay {π^{o}+π^{o}+π^{o}or π^{o}+π^{+}+π^{-}or π^{+}+e^{-}+ν_{electron}or π^{-}+e^{+}+ν or similar pion-lepton combinations from the weakon templates} respectively.

This superposition so shows the K_{short}^{o}to engage the W^{-}and the K_{long}^{o}to utilize the W^{+}in a distinct quantum geometric difference between the kernel-inner ring - outer ring oscillations between that of interacting matter weakons and that of interacting antimatter weakons.

The discovery by in 1964 of the K_{long}^{o}also at times manifesting a two particle decay proved the CP violation at the Brookhaven Alternating Gradient Synchrotron Laboratory by a collaboration led by James Cronin and Val Fitch of Princeton University.

As shown above, this CP violation becomes a consequence of wave-quarkian quantum geometry applied to quantum chromodynamics.

For the neutral B-mesons defined in a diquark structure (U=[uu] for c=U.ubar; b=[ud].ubar; t=[ds].U) detailed further on in this paper, the CP violation at an higher energy level becomes more pronounced and susceptible to the measurement of the manifesting energies.

Because the K_{long}^{o}decay pattern also allows a two particle decay in the form of the mesonic ring part of the b-quark being spininduced by the Graviphoton, instead of the latter spin neutralizing the weakon spin; an excess of the matter based diquark b=ud.ubar decay patterns relative to the antimatter based anti-diquark bbar=ud.bar.u will be observed in the experimental evidence in the subtraction of the K_{long}^{o}decay patterns becoming added to the decay patterns of the K_{short}^{o}.

Typical decay patterns for the B-mesons are:

B^{-}= b.ubar = [ud.ubar].ubar = [U+IR+Kbar].[Kbar] = [K.Kbar] + [K+Kbar]+{IR*-OR[+½]+antiν[+½]}_{W- }+Gγ[-1] ⇒ UUbar+OR[-½]+antiν[+½]

⇒ ucbar[0] + OR[-½] + antiν[+½] ⇒ D^{o}[0] + (e^{-};μ^{-})[-½] + antiν[+½]

B^{+}= bbar.u = [udbar.u].u = [Ubar+IRbar+K].[K] = [K.Kbar] + [Kbar+K] + {IRbar*-ORbar[-½]+ν[-½]}_{W+}+Gγ[+1] ⇒ Ubar+KIRbar*-ORbar[+½]+ν[-½]

⇒ c.ubar[0] + ORbar[+½] + ν[-½] ⇒ D^{o}[0]+(e^{+};μ^{+})[+½] + ν[-½]

B_{d}^{o}= b.dbar = [ud.ubar].dbar = [U+IR+Kbar].[KIRbar] = [U.Kbar+KIRbar] + {IR*-OR[+½]+antiν[+½]}_{W- }+Gγ[-1] ⇒ Uubar+KIRbar+OR[-½]+antiν[+½]

⇒ c.dbar + OR[-½]+antiν[+½] ⇒ D^{+}[0] + (e^{-};μ^{-})[-½]+antiν[+½]

B_{d}^{o}= bbar.d = [udbar.u].d = [Ubar+IRbar+K].[KIR] = [K.Kbar] + [Ubar.K+KIR]+{IRbar*-ORbar[-½]+ν[-½]}_{W+ }+Gγ[-1] ⇒ Ubar.u+OR[-½]+antiν[+½]

⇒ cbar.d + ORbar[+½] + ν[-½] ⇒ D^{-}[0] + (e^{+};μ^{+})[+½] + ν[-½]

For antimatter IR and matter OR, a possible decay mode is: B_{s}^{o}= bbar.s = [udbar.u].s = [Ubar+IRbar+K].[K+OR]

⇒ [Ubar+IRbar+K].[K[0]+({OR+antiν_{electron}][+1]}_{W-}+Gγ[-1]) ⇒ [Ubar+IRbar+K].[K[0]+(OR[0]+antiν_{electron}[0]) ⇒ ([Kbar.Kbar]+K+IRbar)(K+OR)

⇒ [Kbar.K] +[KIRbar.KOR] + {strongweak kernel-ring gluon-anti-neutrino interaction suppressing any lepton decay products} ⇒ uubar + dbar.s ⇒ π^{o}+ K^{o}

⇒ [Kbar.KOR]+[K.KIRbar] {strongweak kernel-ring gluon-anti-neutrino interaction suppressing any lepton decay products} ⇒ ubar.s + udbar ⇒ K^{-}+ π^{+}

For matter IR and antimatter OR, a possible decay mode is: B_{s}^{o}bar = b.sbar = [ud.ubar].sbar = [U+IR+Kbar].[Kbar+ORbar]

⇒ [U+IR+Kbar].[Kbar[0]+({ORbar+ν_{electron}][-1]}_{W+}+Gγ[+1]) ⇒ [U+IR+Kbar].[Kbar[0]+(ORbar[0]+ν_{electron}[0]) ⇒ ([Kbar.Kbar]+Kbar+IR)(Kbar+ORbar)

⇒ [Kbar.K] +[KIR.KORbar] + {strongweak kernel-ring gluon-neutrino interaction suppressing any lepton decay products} ⇒ uubar + d.sbar ⇒ π^{o}+ K^{o}

⇒ [K.KORbar]+[Kbar.KIR] {strongweak kernel-ring gluon-neutrino interaction suppressing any lepton decay products} ⇒ u.sbar + ubar.d ⇒ K^{+}+ π^{-}

In both cases the creation of the neutral kaon K^{o}d.sbar-dbar.s quark content superposition repeats the CP violation in the manner indicated.

{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] + Antiν_{electron}[+½] ⇒ p^{+}[-½] + {Antiν_{electron}[+½] + (Electron e^{-}[+½]}_{W-}+ Positron e^{+}[+½]_{VPEo[+1]}+ Graviphoton[-1]

⇒ p^{+}[-½] + {Electron e^{-}[-½] + Antiν_{electron}[+½]} + Positron e^{+}[+½] ⇒ {p^{+}[-½]+IR^{-}[0]+K^{o}[-½+½]} + e^{+}[+½] ⇒ n^{o}[-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 n^{o}[-½] + ν_{muon}[-½] ⇒ n^{o}[-½] + ν_{muon}[-½] + ({Antiν_{muon}[+½] + (Muon μ^{-}[+½]}_{W-}+GP[-1])

⇒ d[-½]u[+½]d[-½] + *{KIROR-Oscillation (OR-IR-K)[+½] +Antiν_{muon}[+½]+ν_{muon}[-½] + GP[-1]}

⇒ d[-½]u[+½]u[-½] + IR^{-}[0] + {OR^{-}[+½]+GP[-1]} +{R^{2}G^{2}B^{2}[-½]+B^{2}G^{2}R^{2}[+½]} ⇒ p^{+}[-½] + μ^{-}[-½] + VPE[0]

⇒ p^{+}[-½] + μ^{-}[-½] +VPE[0] ⇒ p^{+}[-½] + *{KIROR-Oscillation (OR-IR-K)[-½]}({e^{-}[+½] + Antiν_{electron}[+½]}_{W-}+ GP[-1])

⇒ p^{+}[-½] + ν_{muon}[-½] + e^{-}[-½] + Antiν_{electron}[+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.

mν_{Higgs}=m_{e}λ_{w}.r_{E}/(2πr_{M}R_{e}){1/r_{G}-1/r_{F}} ~ 9.3x10^{-38}kg or 0.052 eV for a scalar blueprint Antiν_{Higgs}= R^{4}G^{4}B^{4}[0] with anti-state ν_{Higgs}= B^{4}G^{4}R^{4}[0]

and coupling as the Tauon (Anti) Neutrino as

Antiν_{tauon}= R^{2}G^{2}B^{2}[+½] + R^{4}G^{4}B^{4}[0] = R^{6}G^{6}B^{6}[+½] = Antiν_{electron}+ Antiν_{Higgs}and

ν_{tauon}= B^{2}G^{2}R^{2}[-½] + B^{4}G^{4}R^{4}[0] = B^{6}G^{6}R^{6}[-½] = ν_{electron}+ ν_{Higgs}

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

∇^{2}∅ - {r/R_{e}}^{2}= 0 = (1/r).∂^{2}/∂r^{2}{r∅} - {r/R_{e}}^{2}.∅

∂^{2}/∂r^{2}{r∅} = {r/R_{e}}^{2}.(r∅) for a solution

r∅ = constant.exp[-r/R_{e}] for the Yukawa Potential with μ = 1/R_{e }= 4πε_{o}m_{e}c^{2}/e^{2}= 4πm_{e}/μ_{o}e^{2}

∅ = constant.(1/r).exp[-r/R_{e}] ⇒ m_{e}c^{2}= (μ_{o}e^{2}c^{2}/4πR).exp[-R/R_{e}] for R/R_{e}= exp[-R/R_{e}]

f(R/R_{e}) = R/R_{e}- exp[-R/R_{e}] = f(x) = x - exp[-x] = 0 with derivative f'(R/R_{e}) = f'(x) = 1 + exp(-x)

and x_{k+1 }= x_{k}- f(x)/f'(_{x}) for a Newton-Raphson solution x_{o}=½ for

x_{1}= ½ - (-0.10653066)/(1.6065307) = 0.56631100;

x_{2}= 0.56631100 - (-0.00130508243)/(1.56761552) = 0.56714353

x_{3}= 0.56714353 - (0.00000037547)/(1.56714316) = 0.56714330... for R = 0.5671433 R_{e}

For the potential energy of the electron with effective mass m_{e}= μ_{o}e^{2}/4πR, the Yukawa potential for the nucleus reduces the classical electron radius to 0.5671433 R_{e}, which approximates the radius of the proton as ½R_{e}, but diverges from the proton's charge radius by the factor X approximately.

We have shown that the sought after reduction of the classical radius of the electron occurs in the interval from A=½ to A=1 and where the Yukawa potential results in ½XR_{e}or= 0.85838x10^{-15}m* for the charge radius of the proton at A=1 as precisely half of the reduced monopolar quantum relativistic electron radius at 1.716761063x10^{-15}m*. The Yukawa potential applied to the classical electromagnetic electron in electrostasis so approximates the monopolar quantum relativistic electron in 0.5671433/0.618034 or 91.77%.

From the Feynman Lecture:This function is called theYukawa potential. For an attractive force,Kis 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 ≈10^{15}m^{−1}.

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

Besides conventional string class considerations, the graviton must have spin 2 as a consequence of quantum angular momentum conservation.

Before spacetime creation in the instanton of the quantum Big Bang, the transformation of the five string classes manifested in the inflaton using a prior supersymmetry between matter- and antimatter templates., represented in say sinx+sin(-x)=0 and where the positive region becomes a quantum geometric matter conformal mapping and the negative region becomes its conjugative for antimatter. As the linearisation of the circle inflects at 180 degrees, matter and antimatter become defined in adjacent clockwise and anticlockwise semi cyclicities.

If now the arbitrary boundaries are defined in some unitary interval between 0 and 360 degrees or [-∞,0,+∞] or [-1,0,+1] or [0,½,1] or [-(X+1),-½,X]; then the left boundary dynamics of say righthandedness cancels the right boundary dynamic of lefthandedness throughout the 2 semicycles, say described in a Moebian connectivity and topology of surface non-orientability in a conformal mapping of a 2D surface onto a 11D supermembrane in a membrane-mirror space.

After the completion of a full cycle, the matter- and antimatter templates exist in the membrane space of the inflaton, say as a supersymmetry between the righthanded electromagneto monopolar radiation (emmr) and its antistate in a lefthanded electromagneto monopolar antiradiation. This supersymmetry between radiative selfstates precedes any possible supersymmetry between the matter and antimatter blueprints, as the dynamic of the emmr eigenstate defines the former as a secondary manifestation of potential manifestation, once the instanton of spacetime creation supercedes that of the prior string-brane epoch.

To realise the matter-antimatter potential, the completion of the full emmr cycle breaks its own supersymmetry in the exchange of the right- and left boundary and initial conditions.

The original righthanded (Weyl-gauge photon say of the left mirror) now situated at the right mirror extends the unitary interval towards the positive abscissa (aleph null enumerability) and inflects its anticlockwise parity into its original clockwise parity or chirality.

The original Weyl-antiphoton from the right mirror, now situated at the left mirror retraces the path of the Weyl-gauge photon however and so does not inflect and so creates the necessity to negate two clockwise quantum spins by a doubled anticlockwise spin angular momentum.

This demands the birth of quantum gravity and of its gauge agent of the graviton in the formation of a new universal wavefunction transversing in the opposite direction of the now twinned electromagneto monopolar propagation of the original emmr supersymmetry.

A consequence of this 'changing of the fundamental supersymmetry' becomes the restriction of any matter-antimatter symmetry to become confined to the concept of pair production in the presence of existing matter or antimatter in nonparity.

Defining matter to couple in a Goldstone gauge boson form to the original Weyl-photon (RGB) then forces the Weyl-antiphoton (anticyclic BGR) to suppress the antimatter (MCY anticyclic to matter YCM) template in lieu of a 'twinned' emergent blueprint known as the scalar 0-spin Higgs Boson (Y

^{2}C^{2}M^{2}).

Imagine a Moebian strip without thickness und so restricted to be two dimensional. The perimeter of the quasi-inner ring so defines a self-intersection with its quasi-outer ring and depicts half of the total 2D-space of the Möbius strip for the inflection at 180 degrees. Then the Möbian strip breaks its own non-orientable nature and symmetry to create the 3rd dimension. The second parameter space can now become orientable (without the Möbian twist of 180 degrees) and the self-relativity of the first part becomes now 3-dimensional relative and allows a new mixing of the tripartite sectors of the quantum chromodynamics of the constituent Goldstone bosons. From this point in the cosmogony onwards an older non-manifested matter-antimatter supersymmetry can eventuate in the observed pair-production, being otherwise suppressed by the earlier radiation-antiradiation supersymmetry described.

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

Quantum Gravitation 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.

{Capitalisation of letters infers emphasis and decapitalisation of letters implies suppression of respective fundamental interactions}.

String-BosonDecoupling Time s*Wavelength (λ=2πl) m*Energy (hc/λ) J* & eV*Modular Wavelength m*Temperature

K*Significance1. Planck-Boson

I/SEWG⇒sEwGt _{P}=2πr_{P}/c

4.377x10^{-43}1.313x10 ^{-34}1.523 GJ* or 9.482x10 ^{27}eV*7.617x10 ^{33}1.079x10 ^{32 }Outside Hubble Horizon Limit in Protoverse 2. Monopole-Boson

IIB/sEwG⇒SEWg

GI-GUT decouplingt _{M}=2πr_{M}/c

1.537x10^{-40}4.6110x10 ^{-32}4.337 MJ* or 2.700x10 ^{25}eV*2.169x10 ^{31}3.072x10 ^{29}Outside Hubble Horizon Limit in Protoverse 3. XL-Boson

HO32/SEW.Gt _{XL}=2πr_{XL}/c

2.202x10^{-39}6.605x10 ^{-31}302.817 kJ* or 1.885x10 ^{24}eV*1.514x10 ^{30}2.145x10 ^{28}Outside Hubble Horizon Limit in Protoverse 4. ECosmic Bosons

IIA/SeW.G

SNI decouplingt _{EC}=2πr_{EC}/c

6.717x10^{-34}2.015x10 ^{-25}0.9927 J* or 6.180x10 ^{18}eV*4.964x10 ^{24}7.032x10 ^{22}Galactic Supercluster Sarkar

M_{o}=R_{Sarkar}c^{2}/2G_{o}Scale5. False Higgs Vacuum t _{HiggsPE}=2πr_{HiggsPE}/c

t_{ps}.T(n_{ps})/T_{algo}

1.297x10^{-32}[max] to 2.8473697...x10^{-32 }[min]3.891x10 ^{-24}0.0514 J* or 3.200x10 ^{17}eV*2.570x10 ^{23}3.641x10 ^{21}Galactic Supercluster Scale 6. Weyl-Boson

HE64/S.EW.G

Big Bang-Instanton

EMI decouplingt _{ps}=2πr_{ps}/c

3.333x10^{-31}1.000x10 ^{-22}0.002 J* or 1.245x10 ^{16}eV*1.000x10 ^{22}1.417x10 ^{20}Galactic Halo(Group) Scale 7. T(n)=T _{ps}

Bosonic Unificationt _{BU}=n_{BU}/H_{o}

1.897x10^{-9}0.56902

ProtoverseT(n) ^{4}= {[n+1]^{2}/n^{3}}H_{o}M_{o}c^{2}/(2π^{2}sR_{H}^{2}[550]) = 18.1995{[n+1]^{2}/n^{3}} (K^{4}/V)*1.757

Protoverse

T_{ps}-bosonic

T_{EW}^{4}=

18.2[n+1]^{2}/n^{3}

n=H_{o}t_{BU}Unitary Modular Geometric Mean Scale 8. Higgs Boson Vacuum

Electroweak WNI decouplingt _{EW}=n_{EW}/H_{o}

0.00274~1/3654.167x10 ^{-18}

Quantum Scale4.799x10 ^{-8}J* or 298.785 GeV*2.400x10 ^{17}3.400x10 ^{15}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: : #.(m_{ps}/m_{Planck})f(G) and for the L-Boson it is written as: #^{54}.(m_{Planck}/m_{ps})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' θ_{ps}is defined via constant X ⇒ {ℵ}^{3}⇒ alpha α as X = ϖ(n). sin θ_{ps}for a unitary force action ϖ(n) acting on the inflaton acceleration cf_{ps}modulated from the inflaton source hyper-acceleration of the de Broglie matter wave for phase speed R_{H}f_{ps}in R_{H}f_{ps}^{2}=1.43790791x10^{87}(m/s^{2})* in the displacement lightpath for the nodal Hubble constant H_{o}= dn/dt = c/R_{H}defining the frequency ratio

n_{ps }= λ_{ps}/R_{H}= 2πr_{ps}/R_{H}=f_{ps}/H_{o }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}= H_{o}= 58.04 km/Mpc.s (extrapolated to 66.9 km/Mpc.s for a present n_{present}=1.13271... cycle time coordinate) and in inverse proportion to its maximum as the wormhole frequency f_{ps}, 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 lower dimensional spacetime itself.

The inflaton angle θ_{ps}so is maximised at 90° at X = ϖ(n). sin θ_{ps}for θ_{ps}= 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 t_{P}=2πr_{P}/c = 4.377x10^{-43}is connected to the X/L string via the monopole string at the unified SEWG level in the self-duality of the GUT-monopole at [ec.c^{2}]_{uimd}= 2.7x10^{16}GeV* and at a brane inflaton time of t_{M}=2πr_{M}/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 t_{XL}=2πr_{XL}/c=2.202x10^{-39}s* and string class HO(32) decouples gravity in replacing f(G)/m_{Planck}by the monopole mass #^{2}/[ec]_{uimd}modular dual to f(S)m_{Planck}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.

m_{XB}= alpha.m_{ps}/[ec]_{uimd}= #^{3}.m_{ps}/[ec]_{uimd}= 3.364554269x10^{-12}kg* = 1.884955575x10^{15}GeV* unifying SEW in the monopolar electron boson energy m_{ec}|_{max}= αm_{ps}

m_{LB}= alpha^{18}.[ec]u_{imd}/#^{2}.m_{ps}=#^{52}.[ec]u_{imd}/#^{2}.m_{ps}= 1.982105788x10^{-28}kg* = 111.0453587 MeV* unifying EWG at the bosonic muon energy

The X-Boson mass and the L-Boson mass then transform into the string class IIA, as the coupling from the self-dual monopole class, here termed the ECosmic Boson to indicate its native characterization as primordial cosmic string ancestor for a spectrum of cosmic rays, tabulated following this discussion.

The ECosmic Boson manifests at an inflaton time of t_{EC}=2πr_{EC}/c = 6.717x10^{-34}s* at an energy of 0.9927 J* or 6.180x10^{9}eV* and as a consequence of the universal wavefunction B(n) = {2e/hA}.exp{-Alpha.T(n)} and where T(n)=n(n+1) defines X and Y in the Euler identity for T(n)=1.

The electromagnetic interaction, which was emphasized in the decoupling of the gravitational interaction in the sEwG to form the X/L-Boson in SEW.G now becomes suppressed in SeW.G in the B(n) for n=n_{ps}=6.259093473x10^{-49 }⇒0 and T(0)=0 for B(n_{ps})=2e/hA= 0.992729794..in units of inverse energy that is as units of the magneto charge under modular string duality.

The constant A=4.854663436x10^{14}Ampere* can be defined as a cosmic string magneto current and derives from particular algorithmic encodings underpinning the numerical values for the fundamental constants of nature.

The ECosmic boson then triggers a 'false vacuum' in a brane time interval from t_{HiggsPE }= 2πr_{HiggsPE}/c = t_{ps}.T(n_{ps})/T_{algo}= 1.297x10^{-32}[max] to 2.8473697...x10^{-32 }[min] defined in a non-kinematic temperature gradient of the cosmogenesis and related to the hyper acceleration gradient between the de Broglie inflaton wave phase speed a_{dB}= R_{H}f_{ps}^{2}and the boundary cosmological (dark energy) constant Λ_{Einstein}(n_{ps}) = G_{o}M_{o}/λ_{ps}^{2}=with 2.Λ_{Einstein}(n_{ps})/a_{dB}= M_{o}/M_{H}=0.02803.. descriptive for the baryonic matter content at the instanton as a proportional coupling between the 'mother black hole' defined in the Schwarzschild metric with an event horizon he size of the Hubble radius R_{H}= 2G_{o}M_{H}/c^{2}.

It can be said, that the universal wave function B(n) remains 'frozen' within this encompassing inflaton event horizon about the FRB (Functional Riemann Bound) at the x=-½ coordinate and between a cosmic uncertainty interval {X: -1,0} defining the Witten-M-space in this presentation; until it is observed and/or defined in accordance with the premises of quantum mechanics applied to the universe in total. In particular the 'unfreezing' of B(n) requires the linearization of the quantum geometric circularity of the Compton wavelength into its particularized quantum radius.

Quark-Lepton Unification in XL-Boson Class HO(32)

SEWg --- SEW.G

Following the creation of the 'false Higgs vacuum' as a potential spacetime quantum and as a prototypical holofractal of the brane volumar; the Planck string and now as a ECosmic string of increased spacial extent and of lower energy transforms into the Weyl-E_{ps}Boson of the quantum big bang event as the instanton.

This results in an integration or summation of E_{ps}-quanta evolving at the speed of light from the original Weylian wormhole as the 'creation singularity'.

This 'filling' of the inflaton M-space with lower dimensional instanton C-space represents however an attempt by the wormhole summation, which is expanding originally at the speed of light to become retarded by a force opposing the linear expansion and so decurving of the original wormhole definition. This effect of anti-curvature or the attempt to recircularise the linearization of the lower dimensional expanded membrane space by its higher dimensional contracting (or collapsing) membrane space is known as gravity in the macrocosmic cosmology of General Relativity, but represents the integrated effect of quantum gravity as a summation of spacetime quanta as wormhole volumars inhabiting expanding space as boundary and initial condition for contracting spacetime.

The expanding qbb or the integration and multiplication of wormhole quanta now enables the X/L bosons to transform into a quark-lepton hierarchy at instanton time t_{ps}=f_{ss}=1/f_{ps}=3.333..x10^{-31}s*.

The Higgs vacuum is now rendered as physical in spacetime occupancy and the relative sizes of elementary particles is defined in the the diameter of the electron and its parameters of energy and momentum. In particular e*=2R_{e}c^{2}=1/E_{ps}restricts the extent of the Compton constant in the mass and size of the electron and quantizing the quantization of monopolar energy in the volumar equivalent of the inversed source energy quantum of the Weyl-E_{ps}Boson conformally transformed from the Planck scale onto the Weyl wormhole scale in the superstring transformations.

Magnetopolar charge e* as inversed energy quantum in its higher dimensional form assumes the characteristic of a region of space acted upon by the time rate change of frequency or df/dt. As said this allows a definition of physical consciousness as the action of a quasi angular acceleration as df/dt onto the dynamics of anything occupying any space, if this space represents a summation of E_{ps}- gauge photon quanta. The concept of physical consciousness so finds it resolution in the quantum geometry of superbrane volumars.

The Higgs field of physical consciousness so applies action on spacially occupied dynamics, such as elementary particles or collections and conglomerations of particles, irrspective of those particles exhibiting inertial mass or gravitational mass and as a consequence of the photonic energy equivalence to mass in E=hf=mc^{2}.

The X-Boson of energy 1.885x10^{15}GeV* so transforms into a K-Boson of energy given by the transformed Planck boson into the K-Boson with m_{c}=m_{Planck}.Alpha^{9}=keα^{8.5}=(e/G_{o})α^{8.5}=9.924724514x10^{-28}kg or 556.0220853.. MeV* under Planck-Stoney unification for electric charge and mass.

The primordial K-Boson so becomes the ancestor for all nucleons and hyperons as a base kernel energy as a function of cycletime n in m(n)=m_{c}Y^{n}.

For a invariance of the Gravitational parameter GM=G_{o}X^{n}.MY^{n}= constant , a mass evolution in the constancy of XY=X+Y=e^{iπ}=i^{2}=-1 ∀n can be applied to 'evolve' the mass of the K-Boson as a function of cycletime n from its initial self-state n_{ps}=H_{o}/f_{ps}=λ_{ps}/R_{H}and to relate the history in time to a history of space in a timeless cosmogenesis.

This evolution of mass as a fundamental cosmological parameter relates to the 'missing' mass in the M_{o}/M_{H}= 0.02803.. ratio say as the Omega of the deceleration parameter in the Friedman cosmology. Considering a time evolution of a restmass seedling M_{o}towards a Black Hole closure mass M_{H}in the form of 'massless eternal Strominger branes' will crystallize the existence of a multiverse as a function of the wormhole radius r_{ps}expanding in higher dimensional brane spacetime until the Hubble radius R_{H}is reached in a time of about 4 trillion years. A formula to describe this is: nlnY=ln(R_{H}/r_{ps}) or equivalently nlnY=ln(M_{H}/M_{curvature}) for the quantum gravitational transformation of the Planck mass into the curvature mass of 6445.775.. kg* as the minimum mass a Black Hole can have in the quantum relativistic cosmology.

When a Strominger eternal (there is no Hawking radiation) black hole has reached its macro state from its micro state, say after 234.47 cycles in a protoverse, then the entire old universe will quantum tunnel into a new universe which was born as a multiverse at the completion of the first cycle for n=1 and when a second inflaton holographically repeated the cosmogenesis parallel in time but not in space to ensure the eternal continuity for the first universe created as a protoverse. The quantum tunneling wall so is a interval of time defined in n_{ps}and not any boundary in space. (Details on this can be found in another paper called:

"A Revision of the Friedmann Cosmology", available on request and {https://cosmosdawn.net/index.php?lang=en}

The upper bound for the kernel mass so becomes m_{c}Y^{npresent }=1.71175285x10^{-27}kg* or 958.9912423.. MeV* for n_{present}set at 1.132711...

The K-Boson then assumes the form of a trisected subatomic core in distributing the K-superstring energy in three quantum geometric parts or sectors depictable in three 120 degree regions of a gluon field for the 8 gluon permutations between the SU(3) self-states:

E=mc^{2}: {BBB; BBW; WBB; BWB; WBW; BWW; WWB; WWW}:E=hf, for the hyperon SU(3) unitary quark or antiquark distribution and E=mc^{2}:{BB; BW; WB; WW}:E=hf for the mesonic quark-antiquark couplings for SU(2), with the (W)hite state implying complete emr-emmr dematerialization and the (B)lack state inferring complete materialization in the chromodynamics of the coulor mixing and gluon charge exchanges.

The L-Boson then induces the outer leptonic OR ring structure as the ancestor of the muon fermion and the inner mesonic ring or IR becomes the oscillatory potential for the OR to reduce in size to approach the kernel K trisected in the gluon distribution.

The precursive X/L-Boson transforming into the quark-lepton hierarchy of fermions, so manifests a native supersymmetry or supergravity without any necessity for additional particles or string vibrations in unifcation physics.

It can then be said, that the meeting or intersection of the OR with the Kernel K occurs at the IR in the form of neutrinos and anti-neutrinos emitted by the kernel as the partners for the OR manifesting as three leptonic generations in electron, muon and tauon to define the weak interaction bosons in the weakons and the Z-Boson. The weakons so display the bosonic nature of the original X/L bosons but allow a partitioning of the boson integral spin momentum in a sharing between the fermionic kernel and the fermionic outer ring. The quantum geometry indicated then allows a decomposition of the weakons into leptonic generations and the Z-Boson to assume the weak interaction energy in the form of massless gluons becoming mass induced by the quantum geometric template of a scalar Higgs field as majorana neutrinos. This can be illustrated in the quantum chromodynamics of the trisection of both kernel and rings as the mixing of colour charges as indicated.

Subtracting the L-Boson mass from the K-Boson mass then sets particular energy intervals shown following in the diquark hierarchies found in the quantum geometry of Quantum Relativity. The energy interval for the KKK kernel then becomes (282.65 MeV* - 319.66 MeV*) and is defined as a Kernel-Ring-Cross-Coupling constant:

Kernel-Ring Mixing Constant: K.........................................................................................._{X}/R_{L}= m_{c}Y^{n}/3m_{LB}) =2.878677247......for n_{present}=1.132711[Eq.18]

Nucleonic Upper Limit: m_{c}Y^{npresent}= 958.9912423 MeV*

Unitary Coupling Force: ϖ(n_{present})/√{Y^{npresent}} = #f(G).cf_{ps}{alpha_{E}/alpha}

= 2πcG_{o}m_{planck}m_{ps}m_{e}m_{c}√(Y^{npresent})/eh^{2}= 1.33606051

alpha_{E }= 2πG_{o}m_{c}m_{e}/hc for m_{c}√(Y^{n}); as ring masses m_{e,μ,τ}are constant in kernel masses

alpha_{G }= 2πG_{o}m_{c}^{2}/hc for kernel mass m_{c}as m_{c}Y^{n}

Graviton-GI mass: #f(G)=alpha.m_{planck}/[ec]_{uimd}transforms m_{ps}from m_{planck}in m_{XB}

Coupling angle: θ_{ps}(n_{present}) = Arcsin(X/ϖ(n_{present})) = 27.553674°

Upper Bound Multiplier = 1/Lower Bound Multiplier

ULM = 1/LBM = 90°/θ_{ps}(n_{present}) = 3.2663521

Using those definitions allows construction for the diquark hierarchies following.

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 y^{2}dV 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:

{v...................................................................................................................................................._{ps}/c}^{2}= 1/{1 + 4π^{2}r_{ec}^{4}/α^{2}λ_{ps}^{4}} = 1/{1 + r_{ec}^{4}/4π^{2}α^{2}r_{ps}^{4}}[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 = i^{2}as the complex origin. But 0.236067..= X^{3}, 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 = √e^{2}/2ε_{o}hc = √(60πe^{2}/h) in standard and in string units, reduces the SNI finestructure constant # by a factor Alpha^{1/6 }; 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 E_{ps}E_{ss}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) = J_{o }= 2e/hA = 0.9927298 1/J* or 6.2705x10^{9}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 2.7x10^{16}GeV*.

The Unity of the SNI transforms to [1-X] = X^{2}and the EMI transforms as the Interaction of Invariance from X to X.

The Weak Nuclear Interaction or WNI as X^{2}becomes [1+X] = 1/X and the Gravitational Interaction or GI transforms as X^{3}transforms to [2+X] = 1/X^{2}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) = u^{4}+2u^{3}-u^{2}-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 X^{2}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 = ct_{k}:

t_{SNI}= R_{e}/c = 2.777..x10^{-15}m*/3x10^{8}m*/s* = 0.925925...10^{-24}s* ~ Order (10^{-23}s*)

t_{EMI}= t_{SNI}/α = 10^{-23}s*/(7.30x10^{-3}) = 1.37x10^{-21}s* ~ Order (10^{-21 }s*)

t_{WNI}=t_{SNI}/α^{6}= 10^{-23}s*/(1.51x10^{-13}) = 6.62x10^{-11}s* ~ Order (10^{-10}s*)

t_{GI}= t_{SNI}/α^{18}= 10^{-23}s*/(3.44x10^{-39}) = 2.91x10^{15}s* ~ Order (10^{15}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→x^{3}with the Alpha-Unity squaring in the functionality of the WNI and defining G-Alpha as Alpha^{18}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):

m

_{c }= m_{planck }Alpha^{9}from the electromagnetic string unification with gravitation in the two dimensionless finestructures:

For Gravitational Mass Charge from higher D Magnetic Charge: 1 = 2πG

_{o}.m_{planck}^{2}/hc

For Electromagnetic Coulomb Charge as lower D Electric Charge: Alpha = 2πke^{2}/hc

Alpha as the universal masterconstant of creation, then becomes defined via the Riemann Analysis from XY = i^{2}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. A symmetry for B(n) is found for i^{2}.U(u)=0 for a FRB=½ indicating a cosmological relationship to the Riemann hypothesis with respect to the distribution of prime numbers and Riemann's zeta function.

The derivation of the HBRMI draws upon this definition process and sets the coupling angle as arcsin(X/@) for a Unitary 'Force' @=(#f_{G}).cf_{ps}E-Alpha/Alpha and with the electron mass replacing the fundamental nucleon mass m_{c}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 f

_{G}f_{S }= 1 in modular definition of a characteristic GI-mass #f_{G}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.

Wikipedia reference:F-theory is a branch of string theorydeveloped 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 and residing in the 2-toroidal bulk space of Vafa as our Riemann 3-dimensional surface describing the VPE-ZPE of the microquantum of the qbb. The E_{ps}-Weyl wormhole of topological closure so is holographically and conformally mapped onto the bulk space in 12 dimensions as a braned volumar evolving by mirror duality of the 11-dimensional closed AdS membrane space of Witten's M-space as Vafa's F-space and mirroring the hyperbolic topology of 10-dimensional C-space as an open dS cosmology in an overall measured and observed Euclidean flatness of zero curvature.

Vafa's F-space so can be named the omniverse hosting multiple universes which are nested in parallel timespace and defined in particular initial and boundary conditions valid and applicable for mall universes as a multiversal parameter space.

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: E_{ps}=E_{primary sourcesink }= hf_{ps }= m_{ps}c^{2}and the 'winding' and coupled selfstate is denoted by: E_{ss }= E_{secondary sinksource }= hf_{ss }= m_{ss}c^{2}

The F-Space Unitary symmetry condition becomes: f_{ps}f_{ss }= r_{ps}r_{ss }= (λ_{ps}/2π)(2πλ_{ss}) = 1

The coupling constants between the two eigenstates are so: E_{ps}E_{ss }= h^{2}and E_{ps}/E_{ss }= f_{ps}^{2 }= 1/f_{ss}^{2}

The Supermembrane E_{ps}E_{ss}then denotes the coupled superstrings in their 'vibratory' high energy and 'winded' low energy selfstate within an encompassing super eigen state of quantum entanglement.

The coupling constant for the vibratory high energy describes a maximised frequency differential over time in df/dt|_{max }= f_{ps}^{2}and the coupling constant for the winded low energy describes its minimised reciprocal in df/dt|_{min }= f_{ss}^{2}.

F-Theory also crystallizes the following string formulations from the E_{ps}E_{ss}superbrane parameters.

Electromagnetic Finestructure: α_{e}= 2πke^{2}/hc = e^{2}/2ε_{0}hc = μ_{o}e^{2}c/2h = 60πe^{2}/h .......... (Planck-Stoney-QR units *)

Gravitational Finestructure (Electron): α_{g}= 2πG_{o}m_{e}^{2}/hc = {m_{e}/m_{Planck}}^{2}

Gravitational Finestructure (Primordial Nucleon): α_{n}= 2πG_{o}m_{c}^{2}/hc

Gravitational Finestructure (Planck Boson): α_{Planck}= 2πG_{o}m_{Planck}^{2}/hc

1/E_{ps }= e* = 2R_{e}c^{2 }= √{4αhce^{2}/2πG_{o}m_{e}^{2}} = 2e√α[m_{P}/m_{e }= 2e√{α_{e}/α_{g}} = {2e^{2}/m_{e}}√(k/G_{o}) = 2e^{2}/G_{o}m_{e}= e^{2}/2πε_{o}m_{e}

for G_{o}= 1/k = 4πε_{o}for a cosmological unification of finestructures in unitary coupling E*.e*=1 in [Nm^{2}/kg^{2}]=[m^{3}s^{-2}/kg]=1/[Nm^{2}/C^{2}]=[C^{2}m^{-3}s^{2}/kg] for [C^{2}]=[m^{6}/s^{4}] and [C]=[m^{3}/s^{2}].

E_{ps }= 1/E_{ss}= 1/e* = √{α_{g}/α_{e}}/2e = G_{o}m_{e}/2e^{2}

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

R_{e}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: m_{e}c^{2 }= ke^{2}/R_{e}; and for the electronic monopolar restmass m_{e}.

Alpha α is the electromagnetic finestructure coupling constant α = 2πke^{2}/hc for the electric charge quantum e, Planck's constant h and lightspeed constant c.

G_{o}is the Newtonian gravitational constant as applicable in the Planck-Mass m_{P }= √(hc/2πG_{o}). and the invariance of the gravitational parameter G(n)M(n)=G_{o}X^{n}.m_{c}Y^{n}.

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 =μ_{o}qv/4πr^{2 }= μ_{o}i/4πr = μ_{o}qω/4πr = μ_{o}Nef/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:

μ_{o}ε_{o}= 1/c^{2 }= (120π/c)(1/120πc) to crystallise the 'free space impedance' Z_{o }= √(μ_{o}/ε_{o}) = 120π~377 Ohm (Ω).

This vacuum resistance Z_{o}so defines a 'Unified Action Law' in a coupling of the electric permittivity component (ε_{o}) of inertial mass and the magnetic permeability component (μ_{o}) 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 = 2πGm_{P}^{2}/hc and the Planck-Charge derives from Alpha=2πke^{2}/hc and where k=1/4πε_{o}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 L_{P }= √(hG/2πc^{3}) 'oscillates' in its Planck-Energy m_{P }= h/λ_{P}c = h/2πcL_{P}to give √Alpha).L_{P }= e/c^{2}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 G_{o }= 4πε_{o}, describing the 'Action Law' for the Vacuum Impedance as Action=Charge^{2}, say via dimensional analysis:

Z_{o }= √([Js^{2}/C^{2}m]/[C^{2}/Jm]) = [Js]/[C^{2}] = [Action/Charge^{2}] in Ohms [Ω = V/I = Js/C^{2}] and proportional to [h/e^{2}] as the 'higher dimensional source' for the manifesting superconductivity of the lower dimensions in the Quantum Hall Effect (~e^{2}/h), the conductance quantum (2e^{2}/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 G_{o }= 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 m_{P}by a proto-nucleonic mass:

m_{c }= √(hc/2πG_{o}).f(alpha) = f(Alpha).m_{P}and where f(Alpha) = Alpha^{9}.

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= i^{2 }= exp(iπ).

One can write a Unification Polynomial: (1-X)(X)(1+X)(2+X) = 1 or X^{4}+2X^{3}-X^{2}-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]¦(X^{2})[Weak short]¦(X^{3})[Gravitational long]

as 1¦X¦X^{2}¦X^{3}= (1-X)¦(X)¦(1+X)¦(2+X).

Unity 1 maps as (1-X) transforming as f(S) in the equality (1-X) = X^{2}; X maps as invariant of f(E) in the equality (X) = (X); X^{2}maps as (1+X) transforming as f(W) in the equality (1+X) = 1/X; and X^{3}maps as (2+X) transforming as f(G) in the equality (2+X) = 1/X^{2 }= 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 R^{5}to Minkowski R^{4}or Membrane-Space R^{11}to String Space R^{10}).

The monopole class so 'unifies' E with G via the gravitational finestructure assuming not a Weylian fermionic nucleon, but the bosonic monopole from the kG_{o }= 1 initial-boundary condition Gm_{M}^{2 }= ke^{2}for m_{M }= ke = 30[ec] = m_{P}√Alpha.

The Planck-Monopole coupling so becomes m_{P}/m_{M }= m_{P}/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 short-range coupling becomes f(S)/f(W) = #/#^{18 }= 1/#^{17 }= Cuberoot(Alpha)/Alpha^{6}and the long-range coupling is Alpha/Omega = 1/Alpha^{17 }= #^{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 α_{Z}= 0.1184 at the energy level of the Z^{o}weakon at about 92 GeV.

The monopole quasimass [ec] describes a monopolic source current ef from the unification identity 1/e*f_{ps}= h = E*/f_{ps}as a fine structure for Planck's constant h, manifesting for a displacement λ=c/f. This is of course the GUT unification energy of the Dirac Monopole at precisely [c^{3}] eV or 2.7x10^{16}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 proto nucleon mass is defined in the modular duality of the heterosis in: Omega = Alpha^{18 }= 2πG_{o}m_{c}^{2}/hc = (m_{c}/m_{P})^{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 m_{W}, 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 3.4x10^{15}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 T_{Weyl }= T_{max }= E_{Weyl}/k = 1.4x10^{20}K as the maximum Black Hole temperature maximised in the Hawking MT modulus and the Hawking-Gibbons formulation: M_{critical}T_{min }= ½M_{Planck}T_{Planck }= (hc/2πG_{o})(c^{2}/2k) = hc^{3}/4πkG_{o}for T_{min }= 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 4λ_{ps}.

The XL-Boson mass is given in the quark-component: m_{X}= #^{3}m_{W}/[ec] = Alpha.m_{W}/m_{P }= #^{3}{m_{W}/m_{P}}~1.9x10^{15}GeV; and the lepton-component: m_{L }= Omega.[ec]/#^{2 }= #^{52}[ec/m_{W}] ~ 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 L_{1}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.partitioning

for groundstates g_{k}(+Δ)energy values

energy *

MeV*

energy SI

MeVparticle name p ^{+}u.d.u=KKIRK m _{K}+[L_{2}}-[e^{-}]-⅓[e^{-}]939.776+1.5013-0.5205-0.1735 940.5833 938.270 charged proton n ^{o}d.u.d=KIRKKIR m _{K}+2[L_{2}]-2[e^{-}]+⅓[e^{-}]939.776+3.0026-1.0410+0.1735 941.9111 939.594 neutral neutron μ ^{±}OR* in 1st OR oscillation

m_{L}- L_{1}- Δ

n[L_{s : }98.19-111.05]111.04536-(4.9028+Δ) 106.143-Δ 105.658375 charged muon τ ^{±}OR** in 2nd ORoscillationL _{M}- m_{L}+ 2g_{s}+ L_{s}+ L_{ud}+ Δ

1822.88-111.05+0.9837+52.31+16.01+Δ

=1712.81+68.32+Δ1781.13+Δ 1776.86 charged tauon π ^{o}u.ubar; d.dbar m _{gu,d}- L_{u,d}+ e^{-}+ ⅓e^{- }+ Δ150.5781-16.014+0.6940+Δ 135.258+Δ 134.9776

neutral pion

groundstateπ ^{±}u.dbar; ubar.d

m_{gu,d}- L_{u,d}+ L_{1}+ e^{-}+ Δ

π^{o}+ L_{1}- ⅓e^{-}+ Δ

150.5781-16.014+4.9028+~e^{-}+Δ

135.258+4.9028-0.1735+Δ

139.987+Δ

139.987+Δ139.5702 charged pion λ ^{o}d.u.s m _{no}+ m_{πo }+ g_{L2}- L_{1}+ Δ941.911+135.26+46.100-4.903+Δ 1118.37+Δ 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]xm_{ps}/[ec]) modulated in (SNI/EMI=∛{Alpha}/[Alpha]), the intrisic unified Interaction-Strength and as the L-Boson's mass in: ([Omega]x([ec])/(m_{ps}.∛(α^{2}).

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 LevelKernel-Energy in MeV*K-Mean(x½) in MeV*Ring-Energy in MeV*IR-OR.Mean.in.MeV*Comment

VPE-Level

[K-IR]

26.4924-29.9618g_{L2}= 14.11355

2.8175-3.1865L _{2}= 1.5010K-IR VPE

VPE-Level

[IR-OR]

86.5334-97.8657g_{L1}= 46.100

9.2030-10.408L _{1}= 4.9028

IR-OR VPE

Ground-OR

electron level

UP/DOWN-Level

u=K; d=K+IR

ubar=Kbar; dbar=Kbar+IRbar282.6487-319.6637 g_{u,d}= 150.5781

30.060-33.997L _{u,d}= 16.014

K-KIR

basis

STRANGE-Level

s=K+OR

sbar=Kbar+ORbar

923.2302-1,044.13g_{s}= 491.8401

98.187-111.045

muon energyLs = 52.308

KIR-KOR

basis

1st (K)-OR-Muon level

CHARM-Level c=U.ubar; U=uu

cbar=Ubar.u; Ubar=uu.bar

3,015.59-3,410.51g_{cU}= 1,606.53

320.71-362.71L _{cU }= 170.86

singlet

apparent

BEAUTY-Level

b=ud.ubar

bbar=udbar.u

9,849.99-11,139.93g_{b}= 5,247.48

1,047.6-1,184.7L _{b }= 558.08

doublet

apparent

MAGIC-Level

M=us.ubar

Mbar=usbar.u

32,173.6-36,386.9g_{M}= 17,140.13

3,421.7-3,869.8L _{M}= 1,822.88

max Tauon energy

doublet

suppressed

in 2nd K-OR-Tauon level M=us and M.Mbar=VPE

in b.bbar resonance

DAINTY-Level

D=dd.U=udd.u

Dbar=ddbar.Ubar=uddbar.ubar

105,090-118,852g_{D}= 55,985.5

11,177-12,640L _{D}= 5,954.25

triplet

suppressed

in D=dd and D.Dbar=VPE

in no IROR oscillation

TRUTH-Level

t=ds.U=uds.u

tbar=dsbar.Ubar=udsbar.ubar

343,261-388,214g_{t}= 182,869

36,506-41,287L _{t}= 19,448.25

triplet

apparent

SUPER-Level

S=ss.U=uss.u

Sbar=ssbar.Ubar=ussbar.ubar

1,120,592-1,268,044g_{S}= 597,159.0

119,243-134,858L _{S}= 63,525.27

triplet

suppressed

in S=ss and S.Sbar=VPE

in no ORIR oscillation

The K-Means define individual materialising families of elementary particles;

a (UP/DOWN-Mean) sets the (PION-FAMILY: π^{o}, π^{+}, π^{-});

a (STRANGE-Mean) specifies the (KAON-FAMILY: K^{o}, K^{+}, K^{-});

a (CHARM-Mean) defines the (J/PSI=J/Ψ-Charmonium-FAMILY);

a (BEAUTY-Mean) sets the (UPSILON=Υ-Bottonium-FAMILY);

a (MAGIC-Mean) specifies the (EPSILON=Ε-FAMILY);

a (DAINTY-Mean) bases the (OMICRON-Ο-FAMILY);

a (TRUTH-Mean) sets the (KOPPA=Κ-Topomium-FAMILY) and

a (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(+)=60.214 MeV* and K(-)=31.986 MeV* and the IROR-Ring-Mixing gives (L(+)=6.404 MeV* and L(-)=3.402 MeV*) for a (L-K-Mean of 1.5010 MeV*) and a (L-IROR-Mean of 4.9028 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 (m_{c}=9.9247245x10^{-28}kg*=(√(Omegaxm_{P}) for n_{p}as 1.71175286x10^{-27}kg* or 958.99 MeV* and setting 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(n^{0};p^{+})=939.776 MeV*}.

A best approximation for Newton's Gravitational constant '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.

A basic nucleon restmass is m_{c}=√Omega.m_{P}=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 m_{p}=u.d.u=K.KIR.K=(939.776+1.5013-0.5205-0.1735) MeV* = 940.5833 MeV* (938.270 MeV).

Neutron m_{n}=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 Higgs Boson 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 Z^{o}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 80.622 GeV* and 80.424 GeV mass of the weak-interaction gauge boson must represent the basic form of the Higgs Boson and that is 161.244 GeV* or 160.847 GeV as a function of the electro-weak coupling and related as a 'charged current' weak interaction to a 'neutral current' interaction mediated by the Z^{o}boson of energy about 91 GeV* to sum for a 'Vacuum Expectation Value' of about 252 GeV*.

From Electro-Weak Unification parameters: {1eV = 1.0024656 eV*} with T(n_{EW}=4.67x10^{-21}) =3.40x10^{15}K*

M_{W±}= Σ_{Kernel-Mean}= m_{up-down}+m_{strange}+m_{charm}+m_{magic}+m_{dainty}+m_{bottom}= 0.151+0.492+1.607+5.247+17.140+55.986 = 80.622 GeV* or 80.424 GeV

M_{Zo}= 91.435 GeV* or 91.210 GeV

M_{Hχ}= 298.580 GeV* or 297.846 GeV

√2.Fermi Constant G = √2.G_{F}= √2{πα/(√2.M_{W}^{2}[1-M_{W}^{2}/M_{Z}^{2}])} = (1/Higgs-Vacuum-Expectation HVE)^{2}= 1.5848x10^{-5}GeV^{-2}* for HVE=251.19 GeV* or 250.58 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=U.u(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].ubar and m=[us].ubar} and the diquark triplet of dainty-top-super {D=[dd].U and t=[ds].U and S=[ss].U} 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.

M_{W-}+ M_{W+}+ M_{Zo}= 252.68 GeV* ≈ HVE + m_{charm}- (m_{K(+)}+m_{K(-)}+m_{L(+)}+m_{L(-)}) = (251.19 + 1.60653 - [0.0922+0.009806]) = 252.69 GeV* or 252.07 GeV

m_{charm}- (m_{K(+)}+m_{K(-)}+m_{L(+)}+m_{L(-)}) = 1.60653 - 0.102 = 1.5045 ≈ M_{W-}+ M_{W+}+ M_{Zo}- HEV = 1.49 GeV*

HEV = M_{Hχ}- m_{D}+ m_{ud}+ 2xm_{charm}+ m_{u,d}= 298.580 - 55.986 + 5.24748 + 3.21306 + 0.15058 = 251.205 GeV* ≈ HEV in Kernel -Inner Ring mixing

HEV = HB+anti-HB = 2xM_{higgsboson}for a Higgs Boson mean of: ½{252.68} = 126.34 GeV* or 126.03 GeV SI.

M_{higgs boson}= 2x{55.986+5.247+1.607+0.492+0.151+0.046+0.014} GeV* = 127.09 GeV* = 126.77 GeV SI for an upper bound including the base quarks u,d,s.

Using the 3 Diquark energy levels U,D and S yield M_{higgsboson}= 2x{55.986+5.247+1.607} GeV* = 125.68 GeV* and 125.37 GeV SI.

Subtracting the u,d means and the VPE mixing corrections gives: 125.68 - (g_{L2}+g_{L1}+g_{u,d}+L2+L1+L_{u,d}) = 125.68 - 0.23321 = 125.447 GeV* or 125.138 GeV SI for a measured mass of the Higgs Boson.

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 5,247.48 MeV* and the topomium triplet minimum is at 55,985.5 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(5.24748+55.9855) GeV* = 122.466 GeV* (or 122.165 GeV SI).

These are the two means from ATLAS {116-130 GeV as 123 GeV} and CMS {115-127 GeV as 121 GeV} respectively.

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{55.986+5.247+1.607+0.492+0.151+0.046+0.014} GeV* = 127.09 GeV*, which become about 126.77 GeV SI as an upper bound 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{55.986+5.247+1.607} GeV* = 125.68 GeV* and 125.37 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's 'Diphoton' - December 15th, 2015

As can be calculated from the table entries below; a (suppressed Top-Super Diquark Resonance is predicted as a (ds)UUbar(ss)=(ds).u.ubar.u.ubar.(ss) quark complex or diquark molecule averaged at (182.869+597.159)GeV=780.03 GeV.

In the diquark triplet {dd; ds; ss}={Dainty; Top; Super} a Super-Superbar resonance at 1.1943 TeV can also be inferred with a 'IR-OR triplet suppressed' Super-Dainty resonance at 653.145 GeV* and the Top-Dainty resonance at 238.855 GeV* 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 Z^{o}decay pattern, which engage the boson spin of the Z^{o}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 Z^{o}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 Z^{o}Boson energy level explicitely as an upper boundary relative to the displacement scale set for the kernel at the wormhole radius r_{ps}=λ_{ps}/2π and the classical electron radius as the limit for the nuclear interaction scale at 3 fermis in: R_{compton}Alpha.

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 R_{MIR}=2.777..x10^{-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 (R_{Sarkar }= (M_{o}/M_{critical}.R_{Hubble}) = 0.028.R_{Hubble}~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 = μ_{o}qv/4πr^{2 }= μ_{o}i/4πr = μ_{o}Nef/2r = μ_{o}Neω/4πr for angular velocity ω=v/r transforms into B = constant(e/c^{3})gxω

in using a_{centripetal }= v^{2}/r = rω^{2}for g = GM/r^{2 }= (2GM/c^{2})(c^{2}/2r^{2}) = (R_{S}c^{2}/2R^{2}) for a Schwarzschild solution R_{S }= 2GM/c^{2}.

B = constant(eω/rc)(v/c)^{2 }= μ_{o}Neω/4πr yields constant = μ_{o}Nc/4π = (120πN/4π) = 30N with e = m_{M}/30c for

30N(eω/c^{3})(GM/R^{2}) = 30N(m_{M}/30c)ω(2GM/c^{2})/(2cR^{2}) = NmM(ω/2c^{2}R)(R_{S}/R) = {M}ω/2c^{2}R.

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

But any mass M has a Schwarzschild radius R_{S}for N = (M/m_{M}){R/R_{S}} = (M/m_{M}){Rc^{2}/2GM} = {Rc^{2}/2Gm_{M}} = {R/R_{M}} for a monopolic Schwarzschild radius R_{M }= 2Gm_{M}/c^{2 }= 2G(30ec)/c^{2 }= 60ec/30c^{3 }= 2e/c^{2 }= 2L_{P}√Alpha = 2OL_{P}.

Any mass M is quantised in the Monopole mass m_{M }= m_{P}√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 2L_{P}√Alpha~L_{P}/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 'L_{P}-bounce': OL_{P }= L_{P}√Alpha = e/c^{2}in the higher (collapsed or enfolded) string dimensions, the electropole e = OL_{P}.c^{2}maps the magnetopole e*= 2R_{e}.c^{2}as 'inverse source energy' E_{Weyl }= hf_{Weyl}and as function of the classical electron radius R_{e}= ke^{2}/m_{e}c^{2 }= R_{Compton}.Alpha = R_{Bohr1}.Alpha^{2 }= Alpha^{3}/4πR_{Rydberg }= 10^{10}{2πR_{W}/360} = {e*/2e}.OL_{P}.

The resulting reflection-mirror space of the M-Membrane space (in 11D) so manifests the 'higher D' magnetocharge 'e*' as inertial 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 E_{8}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/2Rc^{2}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 = i^{2}= -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:

E_{ps }= E_{primary sourcesink }= hf_{ps }= m_{ps}c^{2}and the 'winding' and coupled selfstate is denoted by: E_{ss }= E_{secondary sinksource }= hf_{ss }= m_{ss}c^{2}

The F-Space Unitary symmetry condition becomes: f_{ps}f_{ss }= r_{ps}r_{ss }= (λ_{ps}/2π)(2πλ_{ss}) = 1

The coupling constants between the two eigenstates are so: E_{ps}E_{ss }= h^{2}and E_{ps}/E_{ss }= f_{ps}^{2 }= 1/f_{ss}^{2}

The Supermembrane E_{ps}E_{ss}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 }= f_{ps}^{2}and the coupling constant for the winded low energy describes its minimised reciprocal in df/dt|_{min }= f_{ss}^{2}.

F-Theory also crystallizes the following string formulations from the E_{ps}E_{ss}superbrane parameters.

1/E_{ps }= e*= 2R_{e}c^{2 }= √{4αhce^{2}/2πG_{o}m_{e}^{2}} = 2e√α{m_{P}/m_{e}} = 2ke^{2}/m_{e }= αhc/πm_{e}

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

R_{e}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: m_{e}c^{2 }= ke^{2}/R_{e}; and for the electronic restmass m_{e}.

Alpha α is the electromagnetic finestructure coupling constant a =2πke^{2}/hc for the electric charge quantum e, Planck's constant h and lightspeed constant c.

G_{o}is the Newtonian gravitational constant as applicable in the Planck-Mass m_{P }= √(hc/2πG_{o}).

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.

Cosmic Ray Unification in XL-Boson Class IA

SEW.G --- SeW.G

An 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-BosonWavelength (λ) mEnergy (hc/λ) J & eVModular Wavelength mSignificance1. Planck-Boson 1.2x10 ^{-34}m1.6 GJ or 9.9x10 ^{27}eV8.0x10 ^{33}mOutside Hubble Horizon Limit 2. Monopole-Boson 4.6x10 ^{-32}m4.3 MJ or 2.7x10 ^{25}eV2.2x10 ^{31}mOutside Hubble Horizon Limit 3. XL-Boson 6.6x10 ^{-31}m303 kJ or 1.9x10 ^{24}eV1.5x10 ^{30}mOutside Hubble Horizon Limit 4. X-K-Boson transit (+) 8.8x10 ^{-28}m227 J or 1.6x10 ^{21}eV1.1x10 ^{27}m2πR _{Hubble11D}5. X-K-Boson transit (-) 1.0x10 ^{-27}m201 J or 1.2x10 ^{21}eV1.0x10 ^{27}m2πR _{HubbleHorizonLimit}6. CosmicRayToe 1.9x10 ^{-27}m106 J or 6.6x10 ^{20}eV5.3x10 ^{26}m2πR _{Hubble10D}7. CosmicRayAnkle 2.0x10 ^{-25}m1.0 J or 6.2x10 ^{18}eV5.0x10 ^{24}mGalactic Supercluster Scale 8. CosmicRayKnee (+) 1.0x10 ^{-22}m0.002 J or 1.24x10 ^{16}eV1.0x10 ^{22}mGalactic Halo(Group) Scale 9. CosmicRayKnee (-) 6.3x10 ^{-22}m0.3 mJ or 2.0x10 ^{15}eV1.6x10 ^{21}mGalactic Disc(Halo) Scale 10.CosmicRay 1.4x10 ^{-20}m0.002 mJ or 1.4x10 ^{13}eV7.1x10 ^{19}mGalactic Core Scale

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 bosonic proto-di-nucleons (m_{c}'s) as George Gamow's primordial neutron matter or ylem in his proposed cosmology descriptive of the QBB.

The stability of stars is a function of the equilibrium condition, which balances the inward pull of gravity with the outward pressure of the thermodynamic energy or enthalpy of the star (H=PV+U). The Jeans Mass M_{J}and the Jeans Length R_{J}a used to describe the stability conditions for collapsing molecular hydrogen clouds to form stars say, are well known in the scientific data base, say in formulations such as:

M_{J}=3kTR/2Gm for a Jeans Length of: R_{J}=√{15kT/(4πρGm)}=R_{J}=√(kT/Gnm²).

Now the Ideal Gas Law of basic thermodynamics states that the internal pressure P and Volume of such an ideal gas are given by PV=nRT=NkT for n moles of substance being the Number N of molecules (say) divided by Avogadro's Constant L in n=N/L .

Since the Ideal Gas Constant R divided by Avogadro's Constant L and defines Boltzmann's Constant k=R/L. Now the statistical analysis of kinetic energy KE of particles in motion in a gas (say) gives a root-mean-square velocity (rms) and the familiar 2.KE=mv²(rms) from the distribution of individual velocities v in such a system.

It is found that PV=(2/3)N.KE as a total system described by the v(rms). Now set the KE equal to the Gravitational PE=GMm/R for a spherical gas cloud and you get the Jeans Mass. (3/2N).(NkT)=GMm/R with m the mass of a nucleon or Hydrogen atom and M=M_{J}=3kTR/2Gm as stated.

The Jeans' Length is the critical radius of a cloud (typically a cloud of interstellar dust) where thermal energy, which causes the cloud to expand, is counter acted by gravity, which causes the cloud to collapse. It is named after the British astronomer Sir James Jeans, who first derived the quantity; where k is Boltzmann Constant, T is the temperature of the cloud, r is the radius of the cloud, μ is the mass per particle in the cloud, G is the Gravitational Constant and ρ is the cloud's mass density (i.e. the cloud's mass divided by the cloud's volume).

Now following the Big Bang, there were of course no gas clouds in the early expanding universe and the Jeans formulations are not applicable to the mass seedling M_{o}; in the manner of the Jeans formulations as given.

However, the universe's dynamics is in the form of the expansion parameter of GR and so the R(n)=R_{max}(n/(n+1)) scalefactor of Quantum Relativity.

So we can certainly analyse this expansion in the form of the Jeans Radius of the first proto-stars, which so obey the equilibrium conditions and equations of state of the much later gas clouds, for which the Jeans formulations then apply on a say molecular level.

This analysis so defines the ylemic neutron stars as 'Gamov proto-stars' and the first stars in the cosmogenesis and the universe.

Let the thermal internal energy or ITE=H be the outward pressure in equilibrium with the gravitational potential energy of GPE=Ω. The nuclear density in terms of the superbrane parameters is ρ_{critical}=m_{c}/V_{critical}with m_{c}a base-nuleon mass for a 'ylemic neutron'.

V

_{critical}= 4πR_{e}^{3}/3 or the volume for the ylemic neutron as given by the classical electron radius R_{e}=10^{10}λ_{wormhole}/360=e*/2c^{2}and related to the ground state (Dirac Sea) Fermi energy E_{fermi}= ½mv^{2}and the Fermi velocity v_{fermi}= h/2πm∛(3π^{2}N/V) for a N-particle Fermi-Dirac system of volume V by the Compton constant m_{ec}r_{ec}=αh/2πc=m_{e}R_{e}.

A spherical space defined by the classical maximised electron radius R

_{e}then would be partitioned in:N = 4πR

_{e}^{3}/6π^{2}r_{ps}^{3}= 2R_{e}^{3}/3πr_{ps}^{3}= (2/3π)(2π.10^{10}/360)^{3}= π^{2}.10^{30}/8,748,000 = 1.1282..x10^{24}wormhole radii of the quantum mechanical electron approximated by the minimised 'point particular' electron as the N/V ground state in the Fermi energy.

The electron's Fermi velocity then becomes v

_{fermi}= h/2πm_{e}∛(3π^{4}.10^{30}/8,748,000) = 36,781.195.. m*/s* or 0.0001226. c for this ground state for a Fermi energy of 6.28437422x10^{-22}J* ~ [2π.λ_{wormhole}]_{unified}J* or 0.0039119..eV* and 0.00093 eV* above the mass of the electron (anti)neutrino at 0.002982 eV*.

H=(molarity)kT for molar volume as N=(R/R

_{e})^{3}for dH=3kTR^{2}/R_{e}^{3}.

Ω(R)= -∫G

_{o}Mdm/R = -{3G_{o}m_{c}^{2}/(R_{e}^{3})^{2}}∫R^{4}dR = -3G_{o}m_{c}^{2}R^{5}/R_{e}^{6}fordm/dR=d(ρV)/dR=4πρR

^{2}and for ρ=3m_{c}/4πR_{e}^{3}For equilibrium, the requirement is that dH=dΩ in the minimum condition dH+dΩ=0.

This gives: dH+dΩ=3kTR

^{2}/R_{e}^{3}- 16G_{o}π^{2}ρ^{2}R^{4}/3=0 and the ylemic radius in 'Gamow's Ylem' law:

R..........................................................................................................................................................................................._{ylem}=√{kTR_{e}^{3}/G_{o}m_{c}^{2}}[Eq.19]

as the Jeans-Length precursor or progenitor for subsequent stellar and galactic generation.

The ylemic (Jeans) radii are all independent of the mass of the star as a function of its nuclear generated temperature. Applied to the proto-stars of the vortex neutron matter or ylem, the radii are all neutron star radii and define a specific range of radii for the gravitational collapse of the electron degenerate matter.

This spans from the 'First Three Minutes' scenario of Steven Weinberg to the cosmogenesis to 1.1 million seconds (or about 13 days) and encompasses the standard beta decay of the neutron (underpinning radioactivity). The upper limit defines a trillion degree temperature and a radius of over 40 km; the trivial Schwarzschild solution gives a typical ylem radius of so 7.4 kilometers and the lower limit defines the 'mysterious' planetesimal limit as 1.8 km.

For long a cosmological conundrum, it could not be modelled just how the molecular and electromagnetic forces applicable to conglomerate matter distributions (say gaseous hydrogen as cosmic dust) on the quantum scale of molecules could become strong enough to form say 1 km mass concentrations, required for 'ordinary' gravity to assume control.

The ylem radii's lower limit is defined in this cosmology then show, that it is the ylemic temperature of the 1.2 billion degrees K, which perform the trick under the Ylem-Jeans formulation and which then is applied to the normal collapse of hydrogenic atoms in summation.

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 2πx10^{22}metres.

10. is the massless ancestor of the Higgs-template and defined through the Weyl-String-Eigenenergy E* = kT* = hf*= m*c

^{2}= 1/e* = 1/2R_{e }c^{2}.The scale of (10) emerges from the holographic principle as 2π

^{2}R*^{3}.f*^{2 }= e* for R*=h/(2πm'c)=1.41188..x10^{-20 }m for a Compton Energy of E' = m'c^{2 }= 2.2545..x10^{-6}J or 14.03 TeV, which serendipitously is the maximum energy regime for which the LHC is presently designed.

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

Conclusion:

As David Tong in his lecture at the Royal Institute proposed; the extension of the quantum field theory and the standard model of particle physics can proceed in revisiting the nature of the classical electron.

The electron field of QFT as a universal wavefunction becomes naturally embedded in the spacetime matrix of General Relativity, should the large scale curved classical geometry of GR be applied to QFT as a quantum geometry.

A quantum geometry derived from the transformation of five superstring classes manifesting their characteristic energy scales in the inflaton preceding the Quantum Big Bang cosmology of the instanton naturally renders the spacetime parameters of the inflaton as quantum gravitational in the application of a higher dimensional modular duality.

It is then a mirror duality inherent in the spacetime potential created in the inflaton epoch, which enables the thermodynamic Planck-Einstein cosmology of the QBB to utilize itself in the volume of spacetime it dynamically occupies and in holographically and conformally coupling the microcosm of the quantum relativity to the macrocosm of general relativity as the curvature of spacetimes.

The electron field of QFT so allows the curvature of spacetime in a geometric sense to interact with a Higgs field of inertia in a dual nature of the energy quanta defining this inertia as mass and electromagnetic quanta.

The curvature of spacetime therefore becomes an effect of the linearization of primordial wormhole parameters defined in the inflaton epoch and the physics of 11-dimensional supermembrane manifolds and is evidenced and observable in the relationship between de Broglie matter waves and the Compton wavelengths to relate the wave-particle duality of the quantum mechanics on all scales to the original boundary conditions of displacement scales.

In particular a Planck-Stoney 'bounce' relating the minimum energy of the Zero-Point Planck Oscillator to a coupling between electropolic charge e and magnetopolic charge e* at the Planck energy and as a minimum displacement parameter, becomes the precursor for all subsequent quantum fluctuations, which are however not based on a virtuality of the matter-antimatter coupling, but are found in an inherent gauge physics of originally massless Goldstone bosons, giving rise to the fundamental interactions.

Quantum geometric gravity then allows the unfolding of a wormhole event horizon to manifest as mass in transforming the waved de Broglie matter into particularised matter as a 'decurving' of the Compton wavelength into a Compton radius, the elementary building unit for this process being the electron of QFT.

The foundation of QFT and the Standard Model so are encapsulated in the parameters of the electron in its mass and its charge as derivatives and effects of its nature exhibited in the inflaton, now rendered observable and measurable in the continuation of the cosmological history of the instanton.

Examination and analysis of the electron's origins, so crystallizes its monopolar origin of quantum relativistic self-interaction as its own initial condition and when the qbb created its boundary mass or inertia as the mass of the Weyl-E_{ps}wormhole as a transformed Planck boson defined at the start of the inflaton and the string epoch.

As this initial electron mass is inherently defined in the Compton constant, setting the proportionality between mass and displacement from the Planck scale to the electron scale; the nature of the electron is related to the manifestation of energy and momentum on all other scales allowed by the natural boundary conditions defined by the instanton-inflaton parameters.

The electron is not a point particle, but has a size upper and lower bounded by its Weyl-E_{ps}limit from above and its classical diameter from below. It's minimum size, being that of the wormhole of creation, so can be associated with the limits for physical measurement and the success of QFT remains valid in this case, but without any need for infinite regressions or divergences from the mathematical viewpoint.

Its classical size directly relates to its monopolar self-interaction and has been known for long as the 'missing' energy of the electron in its self-interaction and its mass as of being of a purely electromagnetic origin in electrostasis, that is its restmass at zero velocity and the absence of any external magnetic field.

The internal charge distribution of the electron so becomes a direct effect of its volume occupied as a minimized string-brane volumar in the inflaton quantum fluctuation of the Planck-Stoney bounce relating displacement to charge via the electromagnetic finestructure constant.

This charge-displacement coupling then enables the birth of a space-inherent form of angular acceleration or the time rate change of frequency coupled to any volumar to define the diameter of the electron with the ratio of energy over time as the quantum of magnetopolar charge.

Modular mirror and T-duality then renders the magnetopolar charge quantum e* as the precise inversion of the wormhole energy E*=hf*

This paper has shown, that the electron is a magnetic monopole as a direct derivative of the decay of the magnetic monopole boson also known as the supermembrane or self-dual superstring class IIB. The electron so possesses an internal magnetopolar field descriptive of its self-interaction, with its self-energy so as form of angular acceleration as the square of frequency, maximised in its upper bound of its cosmogenesis.

Applying the modular string duality, it has been shown, that the electron has both a minimum restmass, independent from its effective mass and a maximum mass as per its creation.

At the core of physical consciousness lies quantum consciousness; but there it is called self-interaction of a particle or dynamical system in motion relative to its charge distribution.

We have shown, that it is indeed the charge distribution within such a system and quantized in the fundamental nature of the electron and the proton as the base constituent of atomic hydrogen and so matter; that defines an internal monopolar charge distrubition as a quantum geometric formation minimised in the classical size of the electron and the energy scale explored at that displacement scale.

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Rev. Mod. Phys. 17, 97 – Published 1 April 1945

W. Pauli

Niels Bohr on His 60th Birthday

Translations from original sources:

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https://en.wikisource.org/wiki/Tran...d_Relativistic_Theory_of_Electromagnetic_Mass

Max Born; 1909:

http://gallica.bnf.fr/ark:/12148/bpt6k15334h.image.f7

https://en.wikisource.org/wiki/Tran...the_Kinematics_of_the_Principle_of_Relativity

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.191101

Indications of a Spatial Variation of the Fine Structure Constant

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Neutrino 2000

http://www.physik.uni-mainz.de/exakt/neutrino/en_experiment.html

https://arxiv.org/abs/hep-ex/9805021

Measurements of the Solar Neutrino Flux from Super-Kamiokande's First 300 Days

https://arxiv.org/abs/1006.1623

Observation of a first ντ candidate in the OPERA experiment in the CNGS beam

https://arxiv.org/abs/astro-ph/0602155

The neutrino mass bound from WMAP-3, the baryon acoustic peak, the SNLS supernovae and the Lyman-alpha forest

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https://en.wikipedia.org/wiki/George_Gamow

David Tong; Cambridge University; Published on Feb 15, 2017

Quantum Fields: The Real Building Blocks of the Universe

Published on Feb 15, 2017

According to our best theories of physics, the fundamental building blocks of matter are not particles, but continuous fluid-like substances known as 'quantum fields'. David Tong explains what we know about these fields, and how they fit into our understanding of the Universe.

https://youtu.be/QUMeKDlgKmk

April 25th, 2018