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!
Here is a completion of my work of sorts. It provides the groundwork for
someone more adept than me in the ways of unifying various branches of theoretical physics.
The
Equivalence Principle between inertial mass and gravitational mass is shown to derive from inertial mass being equivalent
to a superconductive source current and as known in the data base as the impedance of free space.
Spacetime curvature in General Relativity is shown not to be truly elementary in terms of mass content or inertia;
but to be inherent in the opening and closing of elementary supermembranes. It so must be derived from the inherent topology
of spacetime and say related differential geometries.
What is truly fundamental,
is the notion of supercharge as inverted energy. This is evidenced as the Colour-Charge or the
gluon charge of the Standard Model in particle physics and unifies all of physics cosmologically in the quantum gravity manifesting
as string transformations.
This supercharge is so not subject to experimental analysis as
the well known Coulomb charge of electric fields.
It is more elementary, in describing the electric
charges to have a higher dimensional progenitor in a magneto charge, which then hitherto manifests as the strong interaction
in the nucleus in the quantum physics of the lower dimensions of the inertial parameters. In the higher dimensions, this colour-charge
defines space and time in the invariance of the lightpath x=ct, where this 'linearised' time t is however coupled
to a dimensionless cycle time n=Hot for dn/dt=Ho a nodal Hubble-Frequency; the
latter being in modular duality or inversion properties relating the quantum geometry of the strings to the classical geometry
of a curved spacetime containing mass.
The most basic physical principle so becomes rather
simple.
The circular closing and opening of the smallest physical entities in the strings;
is a simple holographic projection for this same opening and closing of a fractal universe defined in the metrics of Black
Holes.
The elementary particles are stable in a fundamental fermionic quark-lepton hierarchy
of a neutron as a boundary transformation from a supersymmetry, namely the bosonic manifestation of this fermionically
bifurcated eigenstate as a dineutron or Higgs-Bosonic neutron. This dineutron or Higgs-Eigenstate derived from a massless
string transformation and then allowed fermionic plasma to be born in a primordial neutron beta decay.
All protons and electrons in the universe derived from this process.
There never
existed any antimatter to equilibriate the mass content of those dineutrons however. The parental string, known as the
heterotic symmetry group 32, did not generate a matter-antimatter coupling in the X-Boson and the Anti-X-Boson; but it bifurcated
into a leptonic ring-part and a quarkian kernel-part under the gravitational mass equivalent described in a flow of frequency
as say a string current, which was by definition superconductive as no media for the manifestation of inertia yet existed.
The equivalence principle then 'seeded' the primordial universe with the bosonic dineutrons
bifurcating into neutron couplings, which then beta decayed. This decay manifested the inertial properties of spacetime under
the guidance of a 'seedling' mechanism related to the Black Hole metrics manifesting as hyperstrings and which mapped
the ZPE=VPE as the vortices for potential string energies as a hybrid eigenstate between the fermions and the bosons in a
supersymmetric coupling.
The original massless Higgs-Bosonic eigenstate became magnetocharge
induced in a breaking of an even earlier supersymmetry; namely the supersymmetry between radiation and antiradiation in terms
of chirally different gauge transformations and eigenstates.
This must prove definitive
in any unifying cosmology. The noninertial cosmology of a massless universe can yet be gravitational in its inherent curvature
of the quantum gravity of superstrings; whose energy will define the colour-charge as magnetic precursor for the electro charges
measured in inertia physics.
The prior supersymmetry so will be spin- or chiral different;
say in a definition for the EMMR (as magnetocharged EMR independent on the existence of mass) gauge as selfinteracting in
two spin directions, say up and down or clockwise and anticlockwise.
This selfinteraction
must be topologically multiconnected and allow a Moebian connectivity to selfenfold this differential geometry in a primal
definition of multiconnected spacetime.
Because of this selfenfoldment then, the chiral
orientations can manifest on a onesided surface or manifold and produce a dimensional divide, such as is used in this and
related paper as 'higher' and 'lower'.
So the massless eigenstate can selfinteract
and allow projection of two spin-different eigenstates, say the divided dimensionalities.
Here
then, the colour charge manifests in a trisection for the enclosed area as a 'magneto-charge flux'; albeit in a 'colour
mixing', which can be modelled on say 120 degree sectors of a circle. Introducing cyclicity in permutations, will now
allow an additional sense of differentiation between the EMMR gauges.
In particular the
Principle of Quantum Relativity will be introduced as the Self-Relativity of the multiconnected manifold flux for the colour
charges.
Self-Relative to a Onesided manifold; a cyclic permutation RGB=GBR=BRG will provide
a different colour-mixing, say (R+R)(G+G)(B+B) or (R+G=Y)(G+B=C)(B+R=M) or the cyclic permutation YCM=CMY=MYC; than a TwoSided
manifold.
The doublesided surface will so define the 'dimensional' divide as the inside
and the outside of say a 2-Sphere or 3-Ball embedded in 3-dimensional Riemann-Space R3.
This dimensional
divide will then become geometrically equivalent to a 180 degree inversion of say the sinusoidal waveform.
So then the EMMR colour charge gauge defined in RGB now can redefine itself as say a Matter-Template YCM for a halfcycle
of the aforesaid sinusoidal waveform, geometrically identical to 'half of the cipher 8 or the symbol for infinity (∞)).
This blueprint for matter is bosonic and massless.
Completing the sinusoidal waveform so
defines a 'Point of Inflexion' where the gauge flips from one cyclicity to its anticycle and RGB becomes BGR and YCM
becomes MCY.
So the Anti-EMMR gauge for bosonic AntiRadiation becomes BGR with definition
of an AntiMatter-Template MCY, (Neutrinos will be BBGGRR and AntiNeutrinos RRGGBB in a later definition say).
This process can be easily ascertained to now iteratively repeat as the scenario of closed superstrings
nonlinearly propagating themselves as those sinuisoidal geometrical waveforms in a coupling and flipping of EMMR+AntiEMMR->AntiEMMR+EMMR->EMMR+AntiEMMR->......
In terms of colour-mixing RGB+RGB in the onesidedness results in the colour charge transformations:
YCM->MCY->YCM->.....
To 'Break the Symmetry'; the continuity of the
inflexion points at 180-degree intervals must be broken.
Equivalent to an infinite computer-loop
based on binary qubit eigenstates; one complete traversion of sinx+sin(-x)=sinx-sinx=0 will suffice to manifest the bosonic
matter-antimatter eigenstates in term of transmuted colour charges e*.
Those colour
charges e* will in due course give rise to yet another eigenstate, namely the eigenstates embodied in the physical laws of
Max Planck in E=hf and of Albert Einstein in E=mc2.
The bosonic eigenstate will
then assume the Planck-Law and the fermionic eigenstate will associate with the Einstein-Law.
The
bosonic primordial string eigenstate is massless but becomes subject to inertia in a transformation of the colour charges
from one dimension in to the other.
In particular, there are 8 permutative eigenstates for
the gauge trisection in quantum geometry. Defining a 'pure' radiative eigenstate as W(hite) and a 'pure' inertial
eigenstate as B(lack); gives 6 hybrid eigenstates as energy transitories between E=hf and E=mc2.
For a matter (or antimatter) trisection this will be: WWW for the Planck-Law and transforming into the BBB for the
Einstein-Law via hybrid states WWB and WBW and BWW and BBW and BWB and WBB.
For a matter-antimatter
coupling, there will be four such eigen states in: WW and WB and BW and BB.
This scenario of
course is manifested and observable in the decay of the higher energy 'particles' or 'wavelets' into their
neutron-defined elementary eigenstates of string-bosonic origins.
But the Origin of Mass
is yet in the making. The Radiation-AntiRadiation symmetry must be broken to allow the still MASSLESS Matter-AntiMatter 'Mirror-Symmetry'
to become MASSINDUCED by the colour charge string transformation described in the above.
So
after the completion of a single waveform; the AntiEMMR gauge DOES NOT INFLECT; but the EMMR gauge does.
So in Lucifer- or LasufeR-like fashion of RefusaL, the Supersymmetry between the gauges is broken in a Double-Up-Spin
(say) now requiring renormalisation in the creation of the GRAVITON gauge.
Defining the
EMMR gauge as RGB with up-spin will now define a SUPPRESSED AntiEMMR gauge as BGR with up-spin and a Graviton gauge
as BGR with doubledown-spin.
The BGR gauge becomes suppressed, because now the onesidedness
must become doublesided to harbour the new gauge definition in ENERGY and in SPIN.
The e*
energy of the EMMR gauge is now mapped onto the e* energy of the Graviton gauge, rendering the energy of the AntiEMMR gauge
superfluous in a 'transfer' or superposition of that energy e*.
A new cosmological
scenario now eventuates in a gauge unification across dimensions, which seeks a new form of equilibrium.
The previous 0-spin or scalar nature of the Higgs-Boson now bifurcates into fermionic quantum spin eigenstates
in inducing EITHER the Matter-template or the AntiMatter-template. This is decisive, as the SPIN of the EMMR-Antigauge
is still required in the cosmology to conserve the quantum spin.
The suppression of
the AntiRadiation so for one creates the Graviton and for two allows the Higgs-Bosonic Mastertemplate to become a universal
inertial massinducer in a coupling to the new Graviton master gauge BGR of doubledown spin.
But what is the effect of choosing either the matter template or the antimatter template?
This is just the SUPERSYMMETRY between the EMMR-gauge and the Graviton-gauge in energy in that now the twosidedness
will give a different colour-mixing, which describes the quark-antiquark or mesonic coupling in RGB+BGR=(R+B)(G+G)(B+R)=MGGM=CRRC=YBBY
colour charge eigenstates from the permutative cyclicities. The latter eigenstate is known as the base pionic VPE and
as a direct manifestation from the ZPE of the 'nonvirtual' Heisenbergian gauge background defined in e*.
This VPE-background so describes the metrics in an inertial spacetime continuum, yet string discretised
or quantised quantum gravitationally in the monopolic string currents, which are identical to the gravitational mass of massless
gauges under Planck's Law and the inertial mass of Einstein's Law.
And so it is,
that no antimatter is required, EXCEPT as emergence from the VPE background as described. This VPE is supersymmetric in not
differentiating between the eigenstates of RGB+BGR=MGGM=GGMM=GMMG=MMGG=... in permutative cyclicity for three colours
reducing to just two colours.
The Higgsian MassInduction now takes the form of renormalising
the suppressed BGR colour-charge mix with the initially massless matter template YCM.
YCM
is scalar as a Higgsian quantum geometric template and becomes gravitational in coupling to the BGR graviton gauge in tandem
with the 'suppressed' BGR te