Electroweak DeCoupling

If we unitise our 'Awareness-Differential' under modular duality, we can now finetune our investigations in the proton/electron energy ratio by utility of a modified finestructure for gravitation.

We have used Unity as 1=2πGmPlanck²/hc to define the Planckian mass mP and have used the basic nucleon mass mc=mP.Alpha^9, to relate this to the gravitational finestructure Alpha-G=Alpha^18.

We then substitute the effective electron mass me for one of the mc's in Alpha-G to define the finestructure coupling Alpha-E between the bosonic string bifurcation into the quark-nucleon kernel and leptonic ring parts which are themselves coupled in the neutrinoic core definitions in strongweak associativity.

The electromagnetic-gravitational coupling then is dimensionless as:
Alpha/Alpha-E=ke²/Gmcme=[30ec]²/mcme (19)

in terms of the unification of electro charge with inertial mass as a monopolic magneto charge current.

We recall, from the Big Bang thought experiment and the beginning of this post, that the electron as a bosonic string became mapped onto the de Broglie phase transition, which defined the Hubble Oscillation for the cosmology.

For the defining cycletime nps=Hotps=λps /Rmax; the de Broglie matter wave had a phase acceleration: adB=Rmaxfps²=λps fps²/nps.

So the ratio between the minimum emergent metric λps and the 'inflated' maximum Rmax modulates the superluminal inflationary lightspeed to its invariance in the relativistically mass parametric universe. This becomes so a superposed acceleration am=cfps=9x10^38 m/s^2 and to which our frequency-awareness modulation is now applied.

df/dt=1 under modular duality implies that the frequency changes for the vibratory string eigenmodes are equivalent to time changes in the winded string eigenmodes.

Writing λps λss=fps.fss=1, so is equivalent of defining a nondual expression for:

1=df/dt=f²=C.{Alpha.mP/[ec]}.{cfps}/{Alpha/Alpha-E}.

Here, Alpha.mP/[ec] is the string transform and coupling between the Planck string and the monopole string described elsewhere and C is some constant for rendering the boundary condition for a unitised higher dimensional awareness equal to its lower dimensional manifestation in the coupling between electro charge and magnetocharge in the say Josephson ratio for Energy/Current in the action law.

We can so write: C={[ec]/mP}.{cfps}/{Alpha-E}=hec/2πfps.GmPmcme ={efss.mP/me.mc}=0.982958472.

This can be written as a function of the electron mass as monopolic current equivalence as:

C.me=efss/Alpha^9=efss.mP/mc (20)

Here we used the effective electron mass me as a function of the CER and which differs from a 'bare' electronmass me in so 1.58% in QR calculations. This also relates to the alpha variation of so 8 parts per 100,000 as previously indicated; in that future research and analysis, might well be induced to consider the amplitude of the cosmic wavefunction: B(n)=(2e/hA).exp{-Alpha.T(n)} in considerable detail.

QR derives the value for the chargequantum e=1.606456344x10^-19 C* in solving the transcendental equation 1=Bo.exp{Alpha} for complex solution n={-½ ± i.½√3}, say by Newton-Raphson iteration with a first approximation for e1=hA/2=1.618221145..x10^-19 C* and for the fundamental algorithmic 'current' constant A²=14x15^24.

One might note here the approximation of e to Y=1/X=1.6180339..=½(√5+1) in a factor of 1.000116 or of so 1 part in 10,000.

One might also note that the Functional-Riemann-Bound for B(n) is the real abscissa n=-½ as the conjugate for the real root in the Riemann Hypothesis in regards to the Zeta function.

But the significance of the X to Alpha mapping in the underpinning pentagonal supersymmetry of the cosmology also emerges in our string transformation and the constant C.

Setting C=1, would decrease the effective electronmass me to a first approximation meo=hec/2πfps.GmPmc and about 9.1322x10^-31 kg* and differing now in a factor of 1.00124.. from the SI-measured 9.1435672x10^-31 kg*.
We can consider this to be a lower bound for the 'bare' electronmass meo.

Then allowing C to decrease in regards to the frequency modulations and considering the definition of inertial mass as magneto charge current and unified with gravitational mass; then brings us into the Higgs mass induction scenarios of the quantum cosmology.

Define a 'Weak-Mixing-Angle' Θw in: (1/C)sinΘw=X, where X is our supersymmetry parameter mapping Alpha in the string transformations.

Now allow C to vary as a function of cycletime n=Hot to define the electroweak mixing in terms of the cosmological Hubble-Oscillation and mapped linearly as an asymptotic deceleration of the intrinsic spacetime curvature of the quantum geometry.
Then:

Θw(n)=arcsin(CX) (21)

Using the effective electron mass me we set the amplitude 1/C=1.01733697 for the time instanton nps and as the maximum for the Planck-String to Monopole transformation in ElectroMagnetoGravito unification.

1/C=1 for Θw(n)=arcsin(X)=38.17270762... precisely for the StrongElectroWeak unification of the Monopole to XL-boson string transmutation.

This is preceded by 1/C=0 defining the 'singularity' for Θw(n)=90 (degrees) for the overall unification from the abstraction before the de Broglie inflation occurred.

Generally, we can compute the following table, using (20):
C.me=efss/Alpha^9=efss.mP/mc :

sinΘw=CX...................Θw(n).................. ...............Unification........me.............. ....

1/C=0, C=∞.................Undefined, nPlanck.................SEWG..........me=Undefined

1/C=X, C=Y.........................90°, nMonopole ...............sEwG.............me=5.644..x10^-31 kg*

1/C=1, C=1..........................38.173°, nXL..................SEW.G..........me=9.132x10^-31 kg*


1/C=1/Bo=1.0073..............37.847°, nECosmic..........SEW.......me=9.198.x10^-31 kg*

1/C=1.01733697................37.409°, nWeyl=nps ......S.EW.......me=9.29052714x10^-31 kg*

1/C=1.01733697{√Yⁿ}..... 37.409°, nEW=Ho.tEW....EW........me=9.29052714x10^-31 kg*

1/C=1.33596.......................27.556°, for npresent=Ho.tpresent.=1.1324........me=constant


At Higgs-Boson 'time' tEW~1/365 s* for a Fermi-Coupling-Constant of 298.453 GeV*=297.834 GeVSI; and which 'reduces' in 1.58% in unison with the effective electron mass to 293.73 GeV*=293.13 GeVSI approximately.

Gomcme=constant={GoXⁿ}.{mc√Yⁿ}me√Yⁿ and for:

1/C={me/efss}.{mc/mP}= 1.017336976{√Yⁿ} (22)

per unit electron mass me√Yⁿ.


We allow the electron mass to remain constant and allow a general mass evolution for the characteristic base nucleon mass mc to modify the constancy of Newton's gravitational constant G as function of cycletime n and as G(n)=GoXⁿ. Go=1/k then remains constant as string parameter, say applicable for Black Hole physics and the string scales in general.








The Bohr Magneton for the electron: μe=eh/4πme in Am²=J/T relates to the monopolic mass currents via elementary definitions:

Angular Quantum Spin Momentum applied to the electron as a Planck-Oscillator is: L= h/4π.

Magnetic Field Strength: H=B/μ in A/m=C/ms for a Magnetic Flux Density or Magnetic Induction: B=μH in T(esla)T=Wb/m²=Vs/m²=Js/Cm²=J/Am² as Energy/(Current.Area).

The torque produced by a quantum spinning electron has so units of energy/magnetic induction or [J/T]. The electron spins about its own magnetoaxis and represents the inertial current I=ef.

Lf/B=(h/4π).(I/eB)=(h/4eπ).(I²λ²/E)=(eh/4π)(λ²f²/mc²)=eh/4πm and for the inertial mass m.

But in the gravitational monopolic current mass equivalence this becomes under recall of [ec]=imλm :

Lf/B=(h/4π).(I/eB)=(h/4π).[ec/λm](imλm²/eE)=(h/4π).([ec]²/e.mc²) =(h/4πc).(ec/m)

So the Bohr Magneton for the electron incorporates the ratio of the electron mass to the monopole mass as:

(me/[ec])=h/4πcμe = 30hεo/μe (23)

The string units of V(olts)/c³ so calibrate the inertial and gravitational masses in the monopolic GUT-mass [ec]c² = c³ electron volts.


We now exemplify the electron mass from before:

An effective electron mass: me=9.290527147x10^-31 kg*=60(ec)(e/e*)=(6000e)² kg*, so consists of Ne=3.7626..x10^50 stringed mass quanta.

This reduces for the bare electron mass in the previously discussed variation in the CER.
Considering the topological universe as a Riemannian hypersphere (C∞) in the extended complex plane; the 3D-volumar can be described in the curvature factor (3π/2)VSphere =8.VTorus for a toroidal volume VTorus =2π².R³ for:
VSphere/VTorus =16/3π=1.697652726... ~ 8{0.99083..}/dFeigenbaum and where the Feigenbaum-Delta represents the 'Chaos-Constant' for an iterative 'doubling-process' as attractor in complexity theory and similar and related analysis.

If we now associate the dimensional reduction of generalised 'volumes' say as the magnification factors: 4π/3 -> 4π -> 8π from R3-Space to R2-Space to R1-Space in the lower dimensions for a single connected spherical volume; then the curvature factor 3π/2 maps the multiconnected toroidal volume in the reduction factors: 12π² -> 6π² -> 2π² in correspondence.

Our CER applicable for the effective electronmass so is extended in inverse proportion to the latter in (1):

Re=ke²/mec²= Alpha.h/2πmec²

In particular the doubling of the chaos constant infers an increase in the magnification of Re in 2(1-0.99083...)~1.834%, which serves as a first approximation for the 'magnification' of the CER wrt the 'bare' electronmass.

This first approximation, subject to perturbation and the 'reduced electron mass', so increases the CER from its 'precise' string value of Re=2.777... fermis to Re=2.82872... fermi*, which calibrate to 2.824 fermi (SI) using m=0.9983318783m*.



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