Hi All!
 
This is a most important post to me and this is written plainly with a link to the University of Texas, where Maxwell's Displacement Current is analysed. This will allow anyone wishing to investigate further to do so.
 
The equations are crucial to show where the inertial mass comes from.

So I shall continue in this post to describe the general cosmology as it occurred relative to the paradigm of Quantum Relativity.
This post will be of immense importance and shall prove of profound interest to future cosmologists and physicists. It will allow a number of techniques to test the data given in this essay by well designed experiments.

First of all, I would like to give honorary mention to William MacArthur aka Mac, who is active on a number of these forums, a retired biologist and science teacher, residing in Queensland, Australia.

Mac has written extensively on the topic, which I am about to discuss under his titles of: "The Gravitational Electron" and similar; discussing a possible unification scenario between gravitation and electromagnetism. Mac's papers can be found on a multitude of forum libraries for anyone interested in someone else's realisations as to the 'logically selfconsistent' and 'correct' cosmology. And William MacArthur is an excellent teacher of scientific principles and I hope, that the amateur reader can follow his style of authorship somewhat better and easier, than my expositions.

Mac has independently from myself, I might say, and dating to an earlier time period in the 1970's and 1980's used the 'Gravitational Electron' to relate the electron's inertial and noninertial properties, meaning its mass and its Coulombic charge content respectively. He correctly applied the relationship between dimensionless finestructures for those parameters, but then failed to extrapolate those parameters into the Planck parameters of the string epoch.

QR uses the same theoretical basis, but then takes the consequences much further and avoids certain theoretical 'cul de sacs', which imo prevented Mac to pursue his theoretically well established facts much further. But I give honorary mention here, because Mac's idea of the gravitational electron as a quantum Black Hole proves decisive in the QR paradigm. Mac had the intuitive eureka moment, but then became sidetracked by applying the appropriate formalism of Special Relativity in an 'inappropriate' manner; such as 'gravitational time dilation' over cosmic chronological time and a subsequent 'infinite recessional' time specifying the Big Bang.

So I shall begin to describe the cosmology in words and without equations for the casual, but scientifically informed reader. Only after this 'story' has been told, will I 'fill in the gaps' with the actual formulations.

Where does mass come from?

The supposed Big Bang has happened so 14 Billion years ago, the casual reader is told from the echelons of the academic establishment!
All the energy of the universe and everything, which now constitutes the cosmos and including space and time originated in this Big Bang, the pundits state and since spacetime itself was created then, a point of nothingness or a mathematical singularity began to expand outwards and filled the cocreated spacetime with matter and antimatter and the parameters of the physical sciences.

The dynamics for this cosmological expansion is found in the laws of thermodynamics, of kinetic energy and momentum conservation and the 'arrow of entropy'.
Basically, the Big Bang Cosmology describes a Planck Radiator as a 'Perfect Black Body' which in expanding, also cools down and in this process of Temperature dispersion, also gains in disorder or entropy.
The energy of the singularity so was extremely 'hot' and would be infinite for a true physical point-singularity in 0 dimensions; but would be very large, yet finite in a 'smearing out' or fuzziness or 'uncertainty fluctuation' about this 'Point-Space'.

Mathematical models, such as Quantum-Loop-Gravity, String-Theory or Quantum-Foam-Metrics then become ever more elaborate in complexities and technical detail to describe this Planckian Black Body in the metricated physicality of the reality of the material universe.
This universe is then observed and measured as such in quantities such as displacement or length, temporal time, mass and the postulated charges associated with mass to allow laws of attraction and repulsion to interact between constituents, such as atome, molecules, bodies, stars and galaxies.

When the phyicist, mathematician or researcher uses the formulations of the parameters, describing the basic physical quantities; certain paradoxes seem to emerge.

A major paradox relates the parameter of the 'lightest particle' which is conclusively measured by scientists - namely the electron.

Experiments clearly indicate, that the electron is a 'point-particle' of no or very limited apparent spacial extent (currently postulated to be of a radius smaller than about 10^-19 metres say). Yet the very successful theory of Quantum-Electro-Dynamics or QED, clearly indicates, that the 'preferred' scale of the electron's manifestation is a so called Classical Electron Radius (CER=Re). The entire dynamics of electron-photon interaction for example falls beautifully into place, if this CER permeates the physics from the subatomic realm of the Electron's Compton-Radius to the atomic realm of the Hydrogen Atom in the First Bohr Radius to the Ryberg Spectra, which then extend the basic hydrogenic proton to the higher elements.
I shall give those interrelated formulations later, but they all have a common factor in the Alpha-Finestructure Constant, which determines the interaction probability between mass and light (or electromagnetic radiotion in the form of photons).

So without further ado; the reason for this dilemma in regards to the 'size of the electron' is the gravity of the electron as a function of its mass and primordially the emergence of the electronmass from its stringed 'premass'.

We have encountered the PREMASS in the previous 'parent' essay on the Big Bang revisitation.
We have said there, that the notion of GRAVITATION manifests as the curvature of spacetime a la General Relativity as a third modulation; the second modulation being the introduction of MASS to cause this GRAVITATION, necessary in the first modulation of a LIMIT for the invariance of the lightpath as the unitary assumption for the entire cosmology.

The fourth modulation is however the cause of the CURVATURE from first principles, that is the topology for the universe without any mass. This becomes the Quantum Geometry of QR, which somehow relates to the Classical Geometry of GR by necessity.

And the details of this solve the 'Gravitational Electron' problem and with it the rest of the apparent cosmological paradoxes, known under labels such as the horizon-, the monopole-, the lambda-, and the 'you-name-it'-problem.

So the story in words is this.

The 'Point-Space' of the Null Dimension becomes 'fuzzy' or 'smeared out' in a Principle of Uncertainty (HUP after Werner Heisenberg).
How does this happen?
The HUP makes the abstract mathematics physical.
The universe is DEFINED in something including the 'Natural Laws', which is METAPHYSICAL and inclusive of whatever any or all mathematical formalisms can invent or discover or rediscover. A distinction between the latter is unnecessary, as the idea of chronological time of past, present and future emerges as a physical property and so is not causative of some other notion of time, which only requires a mathematical principality of ORDER.

So then the fuzzy singularity becomes physical and requires some rather peculiar properties to manifest the thermodynamic Big Bang in the Planck Black Body Radiator model.

If the universe has some required critical mass today to close it in a flat curvature; and as it is observed by the experiments; then all this mass must be in the 'fuzzy' singularity, which must be very very small by necessity of its own fuzziness and the HUP.

The universe so uses Nature's 'Big Trick'. This 'Big Trick' is called Modular Duality and this is not a new thing under the sun.
The basic mathematical principle can be seen in the physics of simple optics, in say the focalisation of images in convex and concave lenses and mirrors. Some images are real, others are virtual, some images are upright and others are inverted, such as in the retina in the eye. Those optics also apply to a 'Cosmological Principle of Holography' and this in modern terminology by renown physicists such as Leonard Susskind for example.

So the primal physical application of Modular Duality becomes that of relating the Mirror-Dimension of the 11D Hubble-Node to the 'fuzzy' Planck-Singularity.
The latter defines the smallest 'physicality' in a so called Planck-Length, a Planck-Time, a Planck-Temperature and a Planck-Energy and so on.

In particular we find here the PRECURSOR for our Planck Black Body Radiator in the so called Zero-Point-Enery of a minimum Quantum Energy Eigenstate EPlanck=½hf and where h is Planck's Constant and f stands for a physical parameter called frequency. Let us call this minimum ZPE-Energy Eigenstate, the Planck-Oscillator.

So our 'fuzzy' singularity becomes physical in a say, transformed Planck-Oscillator, then specifying entire spectra of energy eigenstates, such as in the formulations in quantum mechanics and its 'wavefunctions'.

The Modular Duality as 'Nature's Mastertrick' now does the following.
The singularity - now finitised - becomes MODULAR DUALISTIC to its MIRROR singularity.
What is this mirrored singularity?

It is the LIMIT of our Hubble-Event-Horizon as the Hubble-Node, where we 'modularily dualise' a maximum mass with a minimum mass.

This minimum mass IS NOT the Planck-Mass, as the Planck-Mass is so 1.6x10^-8 kilograms and which is rather larger, than the mass of a subatomic particle say.

So one of the conundrums in modern physics is, how the Planck-Oscillator can represent the minimum eigenstate in mass.
It can do so in displacement, specifying the Planck-Length as so 2x10^-35 meters and as say the 'fuzzy realised' radius redefining the singularity of the 'Point-Space'.

The minimum mass is the mass of the electron at so 9x10^-31 kilograms however as the smallest known inertial mass known to physics.

{The neutrino masses are constituent of the electron mass in the tau generation in QR and so cannot be used as this minimum; and especially as QR predicts the electron- and muon neutrino generations to be massless as base neutrino classes}.

So the situation for the Planck-Oscillator becomes an expanding thermodynamic universe with a duality mapping between the mass total of the universe and the mass of a singular electron mapped onto the Hubble-Event-Horizon.


Using Special Relativity and the actual definitions for the electron's parameters, the details are derived in due course; but with the result described in a physics of Black Hole Cosmology.

The electron as a GRAVITATIONAL and NONINERTIAL RELATIVISTIC ELECTRON is the parent electron for the INERTIAL RELATIVISTIC ELECTRON of QED and the massparameters of the manifested Planck-Oscillator as the Planck-Black Body Radiator.

This gravitational electron has noninertial mass, meaning, that it is defined in a curvature scenario for the universe before the mass via m=E/c² manifested in even a single electron.

The Hubble-Radius defines a MOTHER-BLACK HOLE, which is 'collapsed' at the Planck-Oscillator singularity and which as such an extremal Black Hole forms a boundary or initial condition and does not Hawking radiate. It so serves as an invariant for the proceeding thermodynamic cosmic evolution.

Now because this Mother-BH is by definition a spherical boundary; set by a string-epoch in chronological time, which 'inflated' the Planck-Oscillator's Planck-Scale to the Hubble-Scale; it by the principle of modular duality must also define a particular Planck-Oscillator scale.

And that scale is the physics of the Gravitational Electron as a Planckian-String-BH with Schwarzschild Radius Ro say.

This then is the reason as to why the Planck-Oscillator can carry the entire mass of the universe required for its sperical closure at the 'smeared out' singularity.

Mathematically, the 'Point-Space' becomes physically 'real' as the Planck-String. The latter transforms into less energetic Planck-Strings with the effect of an increasing 'Planck-Length' and a decreasing Planck-Mass, because this displacement scale is defined in say the Compton Radius or de Broglie Radius of matter waves in QED and where mass m is inversely proportional to the wavelength (λ) via m=h/λc.

The 'Point-Space' is however completely defined and physicalised in terms of the lightpath x=ct, which became 'inflated' in a de Broglie phase transition defining the string epoch to be the mirrored 'Point-Space' as the Hubble-Event-Horizon.

So you the reader and the entire universe resides within a Mother-BH.

The crucial matter in this scenario is however the 'Size of the Electron'. How big is the gravitational electron?
It is the modular dual of the Mother-BH, which is closed with the mass total of the universe defining its parameters in the Schwarzschild metric.
The gravitational electron also has a Schwarzschild Radius and one which is vastly smaller than the Planck-Length in so 2.3x10^-57 meters. So all the physical models, which use the Planck-Length as a minimum for the physical spacetime metrics become inapplicable.

But here Mother Nature uses its modular trickery once again.

The gravitational electron becomes itself 'fuzzy' and 'smeared out' as the entire surface area of the Mother-BH and so never manifests as a physical inertial 'particle'. The gravitational electron itself becomes MASSLESS as an extremal Black Hole, also known as a 'Strominger Brane' in 11-dimensional brane theory.

But this of course, allows the modular duality to state the next 'strange' but absolutely necessary condition.

The Mother-BH is also MASSLESS as a Strominger-Brane and subject to evolution in any number of DAUGHTER-BHs, which are not boundary- or initial conditions and so subject to transformation in energy exchanges as in Hawking radiation.

And this is what we require; as we have said, that the mass total of the universe is situated at the singularity and yet is massless simultaneously.
The Black Hole Cosmology then crystallises the experimentally observed parameters in terms of cosmological redshift and the Einstein-Friedmann-Walker-de Maitre Cosmologies and the like; albeit inclusive of a demetrication for the scalefactors to allow the mass-independent definition for the overall cosmic topology to establish itself.

In particular the BH-Evolution becomes a function for the dimensionless cycletime or Now-Time for the lightpath intersection described in the parent paper on the Big Bang thought experiment.

The physics, will describe the harmonic, meaning equilibriumised emergence of more complex cosmic structures in the Planck Black Body Radiator filling the prespace created by the de Broglie wavematter inflation.

A first manifestation of the Mother-BH will occur 236.5 Million years into the cosmology; where at a redshift of z=7.477, a 'quasar-wall' is established.
This will instigate a significant phase transition in the first 'seeding' of the cosmos in homogenuity and isotropy; meaning things look and are the same in all directions, without 'irregularities' such as a star or a galaxy.

The Superclusters of galaxies will then specify the large scale geometry for the universe in the Sarkar-BH, which has precisely the mass required to seed the entire universe baryonically; meaning in terms of the protons and neutrons, which constitute the observed mass in the cosmologies.

A paradox in cosmology, namely how the observed superclusters could form so early in a young universe under their mutual gravity, so becomes elucidated as the coupling of the Sarkar-BH to sub-supercluster galactic evolution.

It will be shown, how a basic neutron mass then coupled to an EFFECTIVE and then inertial electronmass as a function of the Planck-Mass itself.
We will find a googol count of spacetime quanta, which are of course the Planck-Oscillators as the ZPE of the Standard Models.

Then the Sarkar-Mass will become defined in the subatomic parameters, showing how the quantum physics relates to the classical physics.

But this Sarkar-BH differs from the Mother-BH in that the Sarkar-BH is physically observable in the MANIFESTED mass (albeit with missing energy) of actual galactic superclusters.

The Mother-BH has no mass and also has the total mass required for its positive curvature and so cannot be observed from within. And as ANY observer is located cosmically at the singularity of the Mother-BH; any physical observer is in its cosmic womb, as yet 'unborn' (into the 12th dimension say).

We shall also derive the electron's inertial mass and revisit other cosmological scenarios as required.

To 'prove' all this mathematically, using the well-established and textbook available parameters; will be the next exercise.

Tony B.
 
 
There exists a most important issue in quantum mechanics, namely the stability of the electron and the nature of its mass. QED postulates the electron as a point-particle of a size smaller than 10^-18 metres; yet the extremely successful calculations in Quantum ElectroDynamics or QED are required to 'scale up' the electron to its 'classical' size of Re so 3x10^-15 metres.
Postulating a 'Dirac Sea' of 'virtual particles' within this classical electron radius, the electron should be unstable due to the repulsion of the 'virtual electrons' of that 'uncertainty soup'.

Re=ke²/mec²= Alpha.h/2πmec²    (1)

and where kG=1 in modular duality as described elsewhere and k=1/4πεo and Alpha=2πke²/hc.

We begin in assigning the Planck-Oscillator as the Gravitational Electron Mass me as a noninertial string energy in terms of the electric permittivity εo.



EPlanck=½hf=½mec²=Gme²/Ro       (2)

and where Ro  is the Schwarzschild Radius for the gravitational electron. We here see straight away, that combining (1) and (2) will define the electron's Schwarzschild Radius: Ro=2Gme²/c² and relate the CER to the latter in (3).

Ro/2Re=Gme²/ke²=G²me²/e²      (3)

The unification condition kG=1 now requires a crucial identity for dimensional consistency between the Planck- or String parameters.
One knows, that the Newtonian Force-Law expression is dimensionally consistent with the Coulomb Force-Law expression (both measuring force units in Newtons); but that the 'charge e' in the Coulomb-Law becomes the 'mass m' in the Gravity-Law.
Using the kG=1 identity , it is easy to show, that the product of the Planck-Length and the Squareroot of Alpha becomes: √(Alpha).Planck-Length, defining the Planck-Length-Oscillation or PLO for the Planck-Oscillator:

PLO=√(Alpha).LPlanck=√(2πke²/hc).√(hG/2πc³)=e/c²    (4)

So now we have a length dimension expressed in the 'Stoney-Unit' of the Coulombic Charge quantum and as related to the Planck-Units.
The PLO now allows a string definition for the Coulombic Charge quantum as:

Stringed Coulombic Charge Quantum:

 e=PLO.c²     (5)

The stringed Coulombic Charge quantum so MANIFESTS as a INERTIAL charge quantum in a mass parfametric universe. This can be ascertained in the nature of electromagnetic radiation or EMR.
EMR is generated by the acceleration of Coulombic charges; where these charges are however ALWAYS associated with inertia, that is INERTIAL MASS.

The stringed Coulombic charge quantum is NOT associated with Inertial Mass, but represents its parental GRAVITATIONAL MASS.
So it is here, that the Equivalence Principle of Albert Einstein originates between them as two energy EIGENSTATES. These two eigenstates can be said to connect the boson-string epoch for a massless cosmic inflation to the mass parametric and general relativistic inertial cosmology of the thermodynamic Planck Black Body universe.

So, the informed and inquisitive reader may ask a pertinent question.

If the string epoch couples to the electric fields in the Coulombic charge quantum and the physical universe defines the electric field in electromagnetism as an invariant coupling to a magnetic field; where then is the magnetic string coupling in regards to the string epoch?

The answer is straight forward. The magnetic string coupling is the PREMASS as the Gravitational Mass and precursive to the Inertial Mass in the Equivalence Principle of General Relativity.
This of course solves many conundrums in modern cosmology all at once. The absence of magnetic monopoles in isolation becomes the effect of inertial mass being coupled electrically and gravitational mass being coupled magnetically.

Then, as inertia of mass is fundamentally magnetic string energy and no antimass is required for the thermodynamic mass evolution; no magnetic monopoles are necessary to implement the dynamics for the latter.

But now the question arises, as how to define inertial mass magnetically through and by those 'absent' magnetic monopoles.

We require an ACCELERATION of MagnetoCharges to generate the 'parental EMR' and an EMR which we may term String-EMR or EMMR for ElectroMagneticMonopolic Radiation.
The way for EMR to become generated, is by angular acceleration of say inertial protons in nuclear fusion reactions, such as occurs in stars, say the sun.
The way EMMR is generated, is by angular acceleration of stringed bosonic protons in something related to stars in say massless protostars of a premassive or preinertial or stringed scenario of Planckioan energy, related to the energy of Black Holes.

This of course has been detailed many times in QR in the Ylemic NeutronStars, which mapped the primordial Beta-minus decay as the first implementation of the weak nuclear interaction in the first 1036 seconds or so of the cosmogenesis of the thermodynamic universe.
The ylemic protostars are defined in the modern scientific literature in terms of the Jeans Radius of gravitationally collapsing hydrogen clouds. The Jeans radius is much more fundamental in defining the ylemic protostars purely in terms of subatomic parameters; a stringed neutron mass (mc) and the CER.
The formulation describes the equilibrium between the gravitational inward pressure of contraction based on the nucleonic stringmass and the thermal outward pressure of expansion due to the thermodynamic temperature of the universe itself, albeit as modulated by the kinetic energy of Vortex-Potential-Energy or VPE, which reprents the ZPE of the Planck-Oscillator under self-transformation of the stringed energies.
The expression for the ylemic radius is:

Rylem = √(kT.Re³/Gmc²)      (6)

The ylemic neutron stars are the parental neutron stars and describe the transition between neutron stars and Black Holes in the reversed sense as it is observed in the astrophysics of today.
Today, a limiting mass, called the Chandrasekhar Mass (MCH) defines 'electron degeneracy' in normally gravitating matter, which 'collapses' the atomic orbitals of electrons and so results in the electron degeneracy in the astrophysics of white dwarves.
The ylemic stars reverse this process in the astrophysics of nuclear stringed 'plasma' matter expanding to allow the electrons to define the atomic structure of hydrogen and the higher elements in the appropriate nucleosynthesis of the chemical elements.

Details are found in the library on the topics of Quantum Relativity and are discussed elsewhere. The important consequence of the ylems for the present derivation for the magnetic origin for all inertial mass are the subatomic string parameters of the Re scale as the interaction scale for the strong- and weak nuclear interactions in the Standard Model of Particle Physics with a nucleon string mass mc, which becomes defined in QR as a direct function of the Planck-Mass and the Alpha-Finestructures:

mc²=hc.Alpha¹⁸/2πG=mPlanck².Alpha¹⁸   (7)

We so have a mapping for the Planck-Mass as a gravitational stringed mass onto a manifestation of the inertial and nonstringed mass equivalence.
A detailed analysis, shows then, that this nucleonic string mass represents a phase transition from a stringed mass originating in the inflationary string epoch. It is known in the modern literature as a Grand-Unification-Theoretical GUT-mass of the X-Boson. It can also be identified as a particular heterotic string class of a symmetry group HO(32) in M-braned string theory.

Now it is here, that we shall find the magnetic orgin for mass; as the parent of the X-String-Boson is the Magnetic Monopole String-Boson of GUT-Energy mm=2.7x10¹⁶ GeV.
It's definition is decisive in QR in the generalisation of the kG=1 identity of the modular duality.

Using k=1/4πεo and finestructuring the Maxwell Constant  μo.εo=1/c²=(120π/c)(1/120πc)  in incorporating the finestructure of free space impedance or resistance defines k=1/G=30c in string parametric terms.

Letting ke²=GM² for M²=k²e²=(30ec)² for the decisive monopolic source mass:

Mm=30[ec]=30mm     (8)

In other words all inertial mass mi has a monopolic and gravitational mass mg equivalent which is of monopolic magnetic origin and can be expressed as a magnetocharge current which incorporates the displacement element in the form (Monopolic Current ef)x(Displacement λ)=Inertial Mass.
We now extend our mass generalisation even further in defining the following identity as the Gravitational Alpha Finestructure:

2πGMo²/hc =2πGmc²/hc.{E.mPlanck²/me²}    (9)

and where E represents a googol (a number greater than 10¹⁰⁰) as a spacetime quanta counter; i.e. the number of Weyl-String Volumes at a particular chronologiocal n-time in the cosmology.
This 'special' time then defines the Sarkar-Black Hole to have the Schwarzschild metric:
 
Mo=RSarkarc²/2G=√(E){mPlanck.mc/me}
           =√(E).{mPlanck²/me}.Alpha⁹
           =√(E).{mc²/me}/Alpha⁹                 (10)
 
Crystallising the basic fundamental nucleon/electron ratio mc/me, we so relate the BH-Cosmology of the massless gravitational universe to the inertially massive universe defined in the couplings between nucleons and electrons, ergo the Planck Black Body thermodynamic cosmology of the Standard Model.
But how do we define the monopolic mass equivalence in terms of the Coulombic charge quantum e?
We must derive a magneto charge quantum e*; which will be the modular dual for the Weyl-String Energy quantum: EWeyl=hfWeyl=mWeyl.c=kTWeyl  as a transformed Planck-String after the end of the inflationary epoch and as the fundamental metric basis for the cosmology.

We so use the electromagnetic finestructure: Alpha=2πke²/hc = Ee²/Eo²  to define a 'Charge-Seed' Eo to induct the Sarkarian Mass-Seedling Mo with its magneto charge equivalent Eo.
So the googol E becomes a higher dimensional 'Super-Alpha' as the ratio:

Alpha/Alpha*=(e²/Eo²)=Alpha/E and with 
√(E)=(Mo.me/mc²)Alpha⁹  from (10).

One can now predict the number of nucleons of the universe comprising the Sarkar metric in stating that (Mo/mc) nucleons will be the this number, say as the ylemic neutron VPE energy eigenstates.
As the charges must be doubled for a bifurcation into positive and negative inertia associated electric charges, say proton- and electron charges, in say the primordial ylemic neutron-mc weak interaction decay; the number of Coulombic charge quantums now must be:
 
2e((Mo/mc).{e/e*)=Eo     (11)
 
It is now easy to derive the elementary definition for the Weyl-Loop Energy Eigenstate:
 
EWeyl=hfWeyl=mWeyl.c²=kTWeyl =√2πGme²/4Alpha.e².hc}
=(me/mPlanck)(1/2e)/√Alpha=(me/2ke²)=1/2Rec²
={me/mc}{1/2e}√(Alpha¹⁷)=1/e*       (12)
 
This equation represents the unification equation for the entirety of physical science.
 
The Weyl-String eigenstate is the ZPE quantum inherent in spacetime itself. A Planckian Action Energy activates the ZPE or VPE eigenstate in transformation of the inherent magnetic monopolic string energy into a initial magneto charge current given in IWeyl=2efWeyl=2eEWeyl/h=2emWeyl.c²/h and where the Weylian mass quantum mWeyl=hfWeyl/c² becomes magneto current in modular duality of the Weyl-String in Planck-oscillation vibration to its winded string duality and as expressed in the heterotic superstring class HE(64)=HE(8x8).
In QR the vibratory eigenstate is denoted as 'primary state' 'ps' and the winded state is denoted as its 'secondary' duality 'ss'.
Then, as the Weyl-mass quantum is a transformed Planck-mass of mWeyl=mps=2.22x10^-20 kg in QR; its winded string dual must become the absolute minimum frequency eigenstate for inertia as the 'inflation-defining' timeinstanton fss=3.33x10^-31 seconds.
All inertial mass so has this value as its intrinsic eigenfrequency and avoiding so any physical singularity calculations in accordance with the physical genesis of the Weyl-Loop.
All inertial mass also becomes quantised in the modular dual winded string mass-quantum:

mss=Ess/c² =hfss/c²=2.469..x10^-81 kg

This defines a low-frequency and winded magneto-electricity quantum in the form Iss=2efss as the quantisation for Coulombic flow of inertia associated electricity, in that a medium is required for the currents to flow.
 
We can now relate the Weyl-Eigenstate for the Planck-Oscillator to the Scale of the Electron in the CER using (12):
 
As Eps=(me/mPlanck)(1/2e)/√Alpha=1/2Rec²=1/e* , we are now we are able to finetune our Gravitational Electron in (2), (3) and (4) in a more precise definition:
 
EPlanck=½ hf=½ mec²=Gme²/Ro    (2)

Ro/2Re=Gme²/ke²=G²me²/e²       (3)

PLO = √(Alpha).LPlanck=√(2πke²/hc).√(hG/2πc³)=e/c²     (4)
 
Ro/2Re=Gme²/ke²=G²me²/e²=LPlanck².Alpha/Re²=(2e/e*)² for the 12-dimensional Energy Hamiltonian expression:
 
2Re.c²=e* <-> e=PLO.c²    (13)
 
This becomes the mapping transformation of the magnetocharge e* and AS A MAGNETIC CHARGE from the 'higher' dimension as the CER in the 'lower dimension' and AS A DISPLACEMENT.
Modular Duality now reverses the process in mapping the ELECTRIC CHARGE from the 'lower' dimension as a now SUBPLANCKIAN DISPLACEMENT in the Planck-Length-Oscillation.
This last sentence describes the profundity of Quantum Relativity in terms of a new scientific understanding and the reformation and renewal of the paradigmatic standard models in both, the cosmology of the classical relativities and the cosmology of the quantum.
I'll end for now and attempt to share this in a readable manner with the forum member and whoever finds value in the self consistent and encompassing logos of QR.
 
Tony B.


CALCULATION OF THE ELECTRONMASS

The magnetic energy stored in a magnetic field B of volume V for a (n-turn toroidal) current inductor i for velocity v and selfinduction L is:

Um=½Li²=½(μon²v)(B/μon)²=½B²V/μo and the Magnetic Energy Density per unit volume is then Um/V=½B²/μo.

Similarly, the Electric Energy density per unit volume is: Ue/V=½εoE² say via the Maxwell equations and Gauss' law.

By the Biot-Savart and Ampere Law: B=μoq.v./4πr² and εo=1/c²μo for the E=cB foundation for electrodynamic theory.

So for integrating a spherical surface charge distribution dV=4πr².dr from Re to ∞:
Um=∫{μoq²v²/8πr²}dr = μoq²v²/8πRe.

Similarly, Ue=∫dUe=q²v²/8πεoRe =kq²/2Re=½mec² as per definition of the classical electron radius and for the total electron energy mec² set equal to the electric potential energy.

We term me here the EFFECTIVE electronmass and so differ it from an actual 'bare' restmass mo.
We now define the electric electromagnetic mass as:

melectric=kq²/2Rec²=Ue/c²=½me

and consider the electric electron energy to be half the total energy (akin the virial theorem for PE=2KE, say in the Bohr atom's PE=(-)ke²/RBohr = e²/4πεoRBohr = (2)e²/8πεoRBohr =2KE).

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

and which must be the KE by Einstein's c²dm=c²(mr-mo) and for the relativistic electronmass mr=mo/√(1-B)  for  B=(v/c)².

But we can see, that should one use the measured electron mass from the Re-definition as the electron's restmass, that is:
 

mmagnetic+melectric=me{½+½(v/c)²}<me,

because of the mass-velocity dependency factor B and the groupvelocities v<c.
Halving the electronmass so into its magnetic and electric components requires this electronmass to be photonic-bosonic as a lightspeed bosonic string of the Planck-String transformations.
This then represents the SUPERSYMMETRIC ELECTRON of the string/inflation epoch.

For the classical fermionic electron, we introduce the relativistic restmass mo=hf/c² and set Constant Amo=μoe²/8πRe  for  AB=1/√[1-B] -1.

This leads to the quadratic: A²B²+(2A-A²)B+(1-2A)=0

and the solutions:

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

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

mmagnetic=μoe²[v/c]²/8πRe=mo.AB=½me.(v/c)²

then finestructures mmagnetic in the relation moA=½me  and allows correlation between the relativistic and kinetic restmass mo and the effective electron groundmass me as a stringmass, transformed into an electron moving at relativistic speed v say.

In particular me =2Amo and is moA for A=½ AS the NEW minimisation condition.
In string parameters and with me in *units, the following is found:

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

This implies, that for A=1, mo=½me, where me=9.290527147x10^-31 kg*=60(ec)(e/e*)=(6000e)² kg* precisely and if the prequantum algorithmic associations, based on the magnetic constant defining the Classical Electronic Radius, are used in the numeracy.

In SI-units (CODATA), the (*) units are calibrated as:

m=0.9983318783m*; s=0.9990230094s*; kg=0.99626135kg* and C=0.0997296076C* depending on precision measurements for h=6.2607596x10^-34 Js and c=2.99792458x10⁸ m/s and e=1.60217653(14)x10^-19 C.

Also, the bare electron is measured as: mo=9.1093826(16)x10^-31 kg=9.1435672x10^-31 kg*; but as function of Re and e and εo with the effective electronic restmass then becoming mo'=9.255793118x10^-31 kg for a mo/mo'=0.98418.. or a relativistic mass-increase of 1.58%.

So if we allow the 'bare' electron to become effective in a 'counter-oscillation' with respect to the Planck-Length-Oscillation; we have a reduced CER for a relativistic electron moving say, through an electric potential of 8.191 keV with a relativistic speed of 0.1772c and representing the stringed supersymmetric electron as a leptonic fermion.

This effect is also a direct consequence from the definition of the CER.

In QR it is precise as a quantisation of the Weyl-Radius and the definition of the radian in:

Re=10¹⁰.rps(2π/360)=2.777..x10^-15 m*=2.773144x10^-15 m.

The latter value deviates from the SI-value in 2.773144/2.817940=0.9841 and which represent the mo/mo' percentage from before.

The mensuration systems are calibrated by the magnetic constant being measured as an identity in both, the SI- and the (*) systems as μo=120π/c=4π/10⁷=1/εoc² and as c=3x10⁸ (m/s)* precisely by definition.

There is however an interval of uncertainty in regards to the charge quantum e, as say observed in the Alpha-Variation of Webb and co from quasar spectra in hydrogenic absorption lines.

The SI-value for e is modified from e'=1.602112608x10^-19 C in [μo/μo*]=0.994599463/C² in the unit of the Henry for magnetic induction in [H]=[Js²/C²].
This breaks the perfect calibration applied with introduction of the [kg] unit in terms of inertia, previously dependent only on lightspeed c in the Maxwell constant.

C²=0.994599463C²* then recalibrates the Coulombic charge quantum e from e=1.606456344x10^-19 C*=1.602112608x10^-19 C=e' from the measured e=1.60217653(14)x10^-19 C.

e/e'=1.00004, which squared, represents the alpha variation as so 8 parts in 100,000.

The alpha variance is so an effect of inertia and relates to the CER in the PLO, which manifests in the inertial properties of the electron.

As B≥0 for all velocities v, bounded as groupspeed (not de Broglie Phasespeed always >c) in c for which B=1; a natural limit is found for the B distribution at A=½ and A=∞.
The 'bare' electron's restmass mo so is binomially distributed for the B quadratic.

Its minimum value is half its effective mass me and as given in melectric=kq²/2Rec²=Ue/c²=½me for A=½ and its maximum for A=∞ is the unity v=c for B=1.

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

For A=½: B=-3/2±3/2 for roots x=0 and y=-3;
for A=¾: B=-5/6±√(19/12) for roots x=0.425 and y=-2.092;
for A=1: B=-½± ½√(5) for roots x=X and y=Y;
for A=∞: B=½[-]±½[+] for roots x=1[-] and y=0[-];

Letting B=n, we obtain the Feynman-Summation and the Binomial Identity gives the limit of A=½ in:

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

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

The unifying condition is the Euler Identity: XY=X+Y=i²=-1=℮^iπ.

This concludes this introduction to the electron's electromagnetic restmass.

Hi all!