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 template to render the introduction of the GLUON gauge as mass-coupled quark inducer necessary.

Then 2(RGB+BGR)=2VPE neutralises the original massless gauges now in inertial associations.

ElectromagnetoGravitational Unification precedes the subsequent unifications however in the quantum spin equilibrium between the EMMR gauge, the Graviton gauge coupled to the AntiEMMR gauge in a Weak Association.

As the BGRs carry a down-spin remnant in 1-2=-1, the Gluon gauge will renormalise in a spin induction coupled to a Higgsian supersymmetric particle with a downspin to allow overall unification or superrenormalisation between all the gauges.

This is the RMP or RestMassPhoton with downspin and colour charge mixing YYCCMM.

Setting the EMMR gauge as identical to the Gluon gauge across the unified manifold in onesided SelfRelativity; will demand the RMP to provide the StrongWeak Coupling between the inertial and gravitational mass definitions and so the unification between the laws of Planck and Einstein as previously described.

So the Gluon is in supersymmetry to the RMP and the EMMR gauge is in supersymmetry to the Graviton, albeit in conjunction with a coupled AntiEMMR gauge which is suppressed.

As all five gauges are massless, BUT the RMP allows the hybrid states for energy in the supersymmetries to mass induce a common Higgsian scalar template via its defintion as a blueprint for matter in YCM; this Higgsian template must assume a general quantum geometric form, which allows all subsequent particle generations of the standard model to emerge from it as 'substructures'.

In most elementary terms, the RMP is a squared or doubled VPE-string state which enables the concept of mass to be described as transformed energy eigenstate from the demetricated string plenum of the cosmology. Hence the definition of the RMP must directly relate to the ob served manifestation of inertia, coupled to its precursor in the gravitational mass equivalence as stringed monopolic electricity and fundamentally defined in frequency.

Subsequently, assigning the StarCoulomb the units of V.df/dt will allow identification of spacetime itself and in the form of the ZPE=VPE acted upon as volume element by an angular acceleration df/dt, which in string terms can be described as 'awareness' about the Self-Eigenstates illustrated before.

This then leads to a physical description of consciousness in terms of the StarCoulomb (C*) and many details are embodied in the text following and can be found elsewhere on my site or the forum contributions.

The first mass induction is required to manifest the nature of the suppressed antiradiation gauge as that of so called weakons, which become defined in the coupling of a leptonic ring as subquark structure to a quarkian core or kernel, which is anti(neutrinoic). ElectroWeak Unification so must occur at the energy eigenstates of either charged- or neutral  weakon currents.  Neutral weakon currents (of Zo particles) are defined in precisely the 'squared' eigenstate of the RMP as substructure of the Higgs template and so in the superposition of antineutrinos in the case of matter.

To particularise the subHiggsian structure in the quark-antiquark or matter-antimatter couplings the quarks must be defined as diquarks or quark molecules associated with the trisection of the colour sectors. An intermediary and mesonic ring so will be necessary to define the down-quark oscillation wrt to the leptonic ring as the CER, coincident with the weakon scale, the strange quark level and the gluonic asymptotic confinement of those colour charges as the scale of the Higgs Boson itself.

This superposition of massless base neutrinos from the original massless Higgs Boson then defines a minimum of three neutrino generations; two massless ones (say electron and muon) and an inertial one (called tau) with a scalar mediating agent labeled Higgs neutrino, the latter being the mass induction of the kernel  as gluonic-neutrinoic unification of the quantum gravity via the quantum geometry of the intrinsic curvature of the strings.

Those strings are now greatly reduced from their original string energy defined in the gauges and e* and their Planckian transformation classes.

StrongWeak Unification so becomes the gluon-kernel-neutrino coupling, which electroweakly manifests in the inertia of the weakons.

The unification of the electromagnetic- and the gravitational interaction is inherent in the topological structure of the quantum geometry itself and is primarily independent on mass as the communication of the string gauges, initialised in the Gauged Radiation and AntiRadiation.

It becomes however a property of metric spacetime by the equivalence principle, which describes the gravitational mass equivalent as a monopolic string current.

Details are described in the treatize below and engage Maxwell's Law of Classical Electromagnetism and in particular his Displacement Current as an inherent form of spacetime itself.

This essay then justifies Maxwell's notion of an etheric medium of stress in identifying this 'stressable' etheric medium as the string background demetricated as the inherent curvature of spacetime in the nature of the ZPE as VPE and the elementary monad for the universe in the Weylian String Quantum, defining the omniscient magnetocharge as the 'Self- or EigenState' of the "God-Particle'.

Hi all!
This article generously shared by Hossein Javadi of cph group is dramatically affirming my post on the "Origins of Mass as a Monopole Mass Transformation". The mainstream is converging to the string cosmology as the discerning reader can ascertain in comparing my post of definitive initial conditions with the data contained in this article.
quote from below:
 
"In the universe before the bounce, all the general features will be the same, said Singh. It will follow the same dynamical equations, the Einstein's equations when the universe is large. Our model predicts that this happens when the universe becomes of the order 100 times larger than the Planck size. Further, the matter content will be the same, and it will have the same evolution. Since the pre-bounce universe is contracting, it will look as if we were looking at ours backward in time."

Before the Big Bang: A Twin Universe?

The new study suggests that the universe that came before our own universe was its identical twin.
Image credit: NASA and ESA. 

Until very recently, asking what happened at or before the Big Bang was considered by physicists to be a religious question. General relativity theory just doesn't go there  at T=0, it spews out zeros, infinities, and errors  and so the question didn't make sense from a scientific view. 

But in the past few years, a new theory called Loop Quantum Gravity (LQG) has emerged. The theory suggests the possibility of a quantum bounce, where our universe stems from the collapse of a previous universe. Yet what that previous universe looked like was still beyond answering.

Now, physicists Alejandro Corichi from Universidad Nacional Autonoma de Mexico and Parampreet Singh from the Perimeter Institute for Theoretical Physics in Ontario have developed a simplified LQG model that gives an intriguing answer: a pre-Big Bang universe might have looked a lot like ours. Their study will appear in an upcoming issue of Physical Review Letters.

The significance of this concept is that it answers what happened to the universe before the Big Bang, Singh told PhysOrg.com. It has remained a mystery, for models that could resolve the Big Bang singularity, whether it is a quantum foam or a classical space-time on the other side. For instance, if it were a quantum foam, we could not speak about a space-time, a notion of time, etc. Our study shows that the universe on the other side is very classical as ours.

The finding builds on previous research, with some important differences. Last year, Penn State physicist Martin Bojowald used a simplified version of LQG to show that a universe on the other side of the bounce could have existed. However, although that model produced valid math, no observations of our current universe could have lead to any understanding of the state of the pre-bounce universe, as nothing was preserved across the bounce. Bojowald described this as a sort of cosmic amnesia.

But Corichi and Singh have modified the simplified LQG theory further by approximating a key equation called the quantum constraint. Using their version, called sLQG, the researchers show that the relative fluctuations of volume and momentum in the pre-bounce universe are conserved across the bounce.

This means that the twin universe will have the same laws of physics and, in particular, the same notion of time as in ours, Singh said. The laws of physics will not change because the evolution is always unitary, which is the nicest way a quantum system can evolve. In our analogy, it will look identical to its twin when seen from afar; one could not distinguish them.

That means that our universe today, roughly 13.7 billion years after the bounce, would share many of the same properties of the pre-bounce universe at 13.7 billion years before the bounce. In a sense, our universe has a mirror image of itself, with the Big Bang (or bounce) as the line of symmetry.

In the universe before the bounce, all the general features will be the same, said Singh. It will follow the same dynamical equations, the Einstein's equations when the universe is large. Our model predicts that this happens when the universe becomes of the order 100 times larger than the Planck size. Further, the matter content will be the same, and it will have the same evolution. Since the pre-bounce universe is contracting, it will look as if we were looking at ours backward in time.

Specifically, Corichi and Singh calculate that the change in relative fluctuations across the bounce is less than 10^-56, a number which becomes even smaller for universes that grow larger than 1 megaparsec (our universe is somewhere between 3,000 and 6,000 megaparsecs).

As the researchers explain, having an identical twin universe would not necessarily mean that every single feature of both universes would be identical. For instance, it doesn't imply that there was another you that existed at some point, a person who has already lived your life.

If one were able to look at certain microscopic properties with a very strong microscope,  a very high-energy experiment probing the Planck scale  one might see differences in some quantities, just as one might see that twins have different fingerprints or one has a mole and the other does not, or a different DNA, Singh said.

As Singh explained, there are still many questions regarding the details of the possible pre-bounce universe.

The biggest question is whether these features survive when we consider more complex situations, he said. For example, one would like to know whether some structures present in the previous universe  like galaxies  will leave some imprint in the new expanding one that will give rise to identical structure or just 'similar.' For instance, it could happen that, in the previous universe, galaxies formed in a different way, so one might have a different distribution of galaxies on the other side. We will be able to answer this question when we understand these models.

Ultimately, Corichi and Singh's model might even tell us what a future universe would look like. Depending on how fast our present universe is accelerating  which will ultimately determine its fate  there's a possibility that a generalization of the model would predict a re-collapse of our own universe.

Such a universe will have many bounces from one branch to another, Singh said. It is also possible that universes in different branches will be identical. 
 
Tony B.:
Mainstream physics is converging, but misses in the details. There was actually no bounce of a twin universe as such, but this bounce is the Oscillation of the Planck-Length from my works as the Squarerrot of Alpha, the finestructure constant which emerges the Stoney-Planck units of measurement in the unification of electric charge with the Planck units.
Its value is about 11.7.
 
The quote above describes the Modular Duality of string theory as the inversion duality of a small radius to a large radius (its inverse) in a coupling to the string modes of vibration or high energy and frequency (my ps-eigenstates of say the Weyl-Loop) and the string modes of winding as low energy and kow frequency (my ss-eigenstates).
 
The significant statement in the quote is the calculation, that this 'twin universe' does not happen at the Planck-Scale, but at a magnified Planck-Scale, so 100 times bigger.
 
This describes in QR the string transform of the Planck-String (class I open and closed) to the Monopole-String (class IIB, closed and selfdual as the missing monopoles in Maxwell's theories).
 
In QR this transformation is precise and gives the ratio between the Planck-Length and the Monopole-Length as:
 
LPlanck/LMonopole=√{Gh/2πc³}/{h/2π.mmonopole.c}=√{Gh/2πc³}.{2πec²/h}=2.85/1000 or a factor of 351.2 (or ~56 for the nonreduced Planck Constant h).
 
The overall 'bouncing' also engages a monopole mass increased by a factor of 30 in the unification of the finestructures of gravitation and electromagnetism.
 
The 'Twin-universe' of the article is thus identical to the Moebian connected 12th dimensional one in my posts, but is part of a single universe and as mapped in the history of the QR cosmology described in the posts.
 
Tony B.

http://farside.ph.utexas.edu/teaching/em/lectures/node46.html

Michael Faraday revolutionized physics in 1830 by showing that electricity and magnetism were interrelated phenomena. He achieved this breakthrough by careful experimentation. Between 1864 and 1873, James Clerk Maxwell achieved a similar breakthrough by pure thought. Of course, this was only possible because he was able to take the experimental results of Faraday, Ampère, etc., as his starting point. Prior to 1864, the laws of electromagnetism were written in integral form. Thus, Gauss's law was (in S.I. units) the flux of the electric field through a closed surface equals the total enclosed charge, divided by . The no magnetic monopole law was the flux of the magnetic field through any closed surface is zero. Faraday's law was the electromotive force generated around a closed loop equals minus the rate of change of the magnetic flux through the loop. Finally, Ampère's circuital law was the line integral of the magnetic field around a closed loop equals the total current flowing through the loop, multiplied by . Maxwell's first great achievement was to realize that these laws could be expressed as a set of first-order partial differential equations. Of course, he wrote his equations out in component form, because modern vector notation did not come into vogue until about the time of the First World War. In modern notation, Maxwell first wrote:

			(400)
			(401)
			(402)
			(403)

Maxwell's second great achievement was to realize that these equations are wrong.

We can see that there is something slightly unusual about Eqs. (400)-(403). They are very unfair to electric fields! After all, time-varying magnetic fields can induce electric fields, but electric fields apparently cannot affect magnetic fields in any way. However, there is a far more serious problem associated with the above equations, which we alluded to earlier on. Consider the integral form of the last Maxwell equation (i.e., Ampère's circuital law)

(404)

This says that the line integral of the magnetic field around a closed loop is equal to times the flux of the current density through the loop. The problem is that the flux of the current density through a loop is not, in general, a well-defined quantity. In order for the flux to be well-defined, the integral of over some surface attached to a loop must depend on , but not on the details of . This is only the case if

(405)

Unfortunately, the above condition is only satisfied for non time-varying fields.

Why do we say that, in general, ? Well, consider the flux of out of some closed surface enclosing a volume . This is clearly equivalent to the rate at which charge flows out of . However, if charge is a conserved quantity (and we certainly believe that it is) then the rate at which charge flows out of must equal the rate of decrease of the charge contained in volume . Thus,

(406)

Making use of Gauss' theorem, this yields

(407)

Thus, is only true in a steady-state (i.e., when ).

The problem with Ampère's circuital law is well illustrated by the following very famous example. Consider a long straight wire interrupted by a parallel plate capacitor. Suppose that is some loop which circles the wire. In the non time-dependent situation, the capacitor acts like a break in the wire, so no current flows, and no magnetic field is generated. There is clearly no problem with Ampère's law in this case. However, in the time-dependent situation, a transient current flows in the wire as the capacitor charges up, or charges down, and so a transient magnetic field is generated. Thus, the line integral of the magnetic field around is (transiently) non-zero. According to Ampère's circuital law, the flux of the current through any surface attached to should also be (transiently) non-zero. Let us consider two such surfaces. The first surface, , intersects the wire. This surface causes us no problem, since the flux of though the surface is clearly non-zero (because it intersects a current carrying wire). The second surface, , passes between the plates of the capacitor, and, therefore, does not intersect the wire at all. Clearly, the flux of the current through this surface is zero. The current fluxes through surfaces and are obviously different. However, both surfaces are attached to the same loop , so the fluxes should be the same, according to Ampère's law (404). It would appear that Ampère's circuital law is about to disintegrate! However, we notice that although the surface does not intersect any electric current, it does pass through a region of strong changing electric field as it threads between the plates of the charging (or discharging) capacitor. Perhaps, if we add a term involving to the right-hand side of Eq. (403) then we can somehow fix up Ampère's circuital law? This is, essentially, how Maxwell reasoned more than one hundred years ago.

Let us try out this scheme. Suppose that we write

(408)

instead of Eq. (403). Here, is some constant. Does this resolve our problem? We want the flux of the right-hand side of the above equation through some loop to be well-defined; i.e., it should only depend on , and not the particular surface (which spans ) upon which it is evaluated. This is another way of saying that we want the divergence of the right-hand side to be zero. In fact, we can see that this is necessary for self-consistency, since the divergence of the left-hand side is automatically zero. So, taking the divergence of Eq. (408), we obtain

(409)

But, we know that

(410)

so combining the previous two equations we arrive at

(411)

Now, our charge conservation law (407) can be written

(412)

The previous two equations are in agreement provided . So, if we modify the final Maxwell equation such that it reads

(413)

then we find that the divergence of the right-hand side is zero as a consequence of charge conservation. The extra term is called the displacement current (this name was invented by Maxwell). In summary, we have shown that although the flux of the real current through a loop is not well-defined, if we form the sum of the real current and the displacement current then the flux of this new quantity through a loop is well-defined.

Of course, the displacement current is not a current at all. It is, in fact, associated with the generation of magnetic fields by time-varying electric fields. Maxwell came up with this rather curious name because many of his ideas regarding electric and magnetic fields were completely wrong. For instance, Maxwell believed in the æther, and he thought that electric and magnetic fields were some sort of stresses in this medium. He also thought that the displacement current was associated with displacements of the æther (hence, the name). The reason that these misconceptions did not invalidate his equations is quite simple. Maxwell based his equations on the results of experiments, and he added in his extra term so as to make these equations mathematically self-consistent. Both of these steps are valid irrespective of the existence or non-existence of the æther.

``But, hang on a minute,'' you might say, ``you can't go around adding terms to laws of physics just because you feel like it! The field equations (400)-(403) are derived directly from the results of famous nineteenth century experiments. If there is a new term involving the time derivative of the electric field which needs to be added into these equations, how come there is no corresponding nineteenth century experiment which demonstrates this? We have Faraday's law which shows that changing magnetic fields generate electric fields. Why is there no ``Joe Blogg's'' law that says that changing electric fields generate magnetic fields?'' This is a perfectly reasonable question. The answer is that the new term describes an effect which is far too small to have been observed in nineteenth century experiments. Let us demonstrate this.

First, we shall show that it is comparatively easy to detect the induction of an electric field by a changing magnetic field in a desktop laboratory experiment. The Earth's magnetic field is about 1 gauss (that is, tesla). Magnetic fields generated by electromagnets (which will fit on a laboratory desktop) are typically about one hundred times bigger that this. Let us, therefore, consider a hypothetical experiment in which a 100 gauss magnetic field is switched on suddenly. Suppose that the field ramps up in one tenth of a second. What electromotive force is generated in a 10 centimeter square loop of wire located in this field? Faraday's law is written

(414)

where B=0.01 tesla is the field-strength, A=0.01 m² is the area of the loop, and t=0.1 seconds is the ramp time. It follows that V~1 millivolt. Well, one millivolt is easily detectable. In fact, most hand-held laboratory voltmeters are calibrated in millivolts. It is clear that we would have no difficulty whatsoever detecting the magnetic induction of electric fields in a nineteenth century style laboratory experiment.

Let us now consider the electric induction of magnetic fields. Suppose that our electric field is generated by a parallel plate capacitor of spacing one centimeter which is charged up to 100 volts. This gives a field of 10⁴ volts per meter. Suppose, further, that the capacitor is discharged in one tenth of a second. The law of electric induction is obtained by integrating Eq. (413), and neglecting the first term on the right-hand side. Thus,

(415)

Let us consider a loop 10 centimeters square. What is the magnetic field generated around this loop (we could try to measure this with a Hall probe). Very approximately, we find that

(416)

where l=0.1 meters is the dimensions of the loop, B is the magnetic field-strength, E=10⁴ volts per meter is the electric field, and t=0.1 seconds is the decay time of the field. We find that B~10^-9 gauss. Modern technology is unable to detect such a small magnetic field, so we cannot really blame Faraday for not noticing electric induction in 1830.

``So,'' you might say, ``why did you bother mentioning this displacement current thing in the first place if it is undetectable?'' Again, a perfectly fair question. The answer is that the displacement current is detectable in some experiments. Suppose that we take an FM radio signal, amplify it so that its peak voltage is one hundred volts, and then apply it to the parallel plate capacitor in the previous hypothetical experiment. What size of magnetic field would this generate? Well, a typical FM signal oscillates at 10⁹ Hz, so t in the previous example changes from 0.1 seconds to 10^-9 seconds. Thus, the induced magnetic field is about 10^-1 gauss. This is certainly detectable by modern technology. So, it would seem that if the electric field is oscillating fast then electric induction of magnetic fields is an observable effect. In fact, there is a virtually infallible rule for deciding whether or not the displacement current can be neglected in Eq. (413). If electromagnetic radiation is important then the displacement current must be included. On the other hand, if electromagnetic radiation is unimportant then the displacement current can be safely neglected. Clearly, Maxwell's inclusion of the displacement current in Eq. (413) was a vital step in his later realization that his equations allowed propagating wave-like solutions. These solutions are, of course, electromagnetic waves. But, more of this later.

We are now in a position to write out Maxwell's equations in all their glory! We get

			(417)
			(418)
			(419)
			(420)

These four partial differential equations constitute a complete description of the behaviour of electric and magnetic fields. The first equation describes how electric fields are induced by charges. The second equation says that there is no such thing as a magnetic monopole. The third equation describes the induction of electric fields by changing magnetic fields, and the fourth equation describes the generation of magnetic fields by electric currents and the induction of magnetic fields by changing electric fields. Note that with the inclusion of the displacement current these equations treat electric and magnetic fields on an equal footing: i.e., electric fields can induce magnetic fields, and vice versa. Equations (417)-(420) sum up the experimental results of Coulomb, Ampère, and Faraday very succinctly: they are called Maxwell's equations because James Clerk Maxwell was the first to write them down (in component form). Maxwell also fixed them up so that they made mathematical sense.

Next: Potential formulation Up: Time-dependent Maxwell's equations Previous: Gauge transformations

The Origin of Mass as Monopole-Mass Transformation


"Maxwell came up with this rather curious name because many of his ideas regarding electric and magnetic fields were completely wrong. For instance, Maxwell believed in the æther, and he thought that electric and magnetic fields were some sort of stresses in this medium. He also thought that the displacement current was associated with displacements of the æther (hence, the name)."   
 

I shall try to show that Maxwell's Ether is real in the sense of the stringed ZPE background.  This will embody a imo beautiful mapping of displacement scales as fundamental cosmology.

1. MagnetoCharge                e*= 2Re.c²

to define the atomic scale manifested via stringed monopolic magnetism;

2. ElectroCharge                   e= √(Alpha).Planck-Length.c²

to define the Planck-Length manifested via electricity;

3. Magnetic Constant   μo= (Radian definition).Weyl-Perimeter.c²

to define the 9-micron scale  as a 'lifeforce' for biovitality in the universe.


We recall equation (13):
 

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.
 
Now recall the Newtonian- and Coulombian ForceLaws describing the inverse square expression for the 'infinite' interactions between 'pointcharges e' and between 'pointmasses m' and separated by a distance r:
 
Fe=ke²/r²  and  Fm=Gm²/r²  and from which the Energy formulas describe electric- and gravitational potential energy in the forms:  Ve=ke²/r   and Vm=Gm²/r.
 
Substituting the action parameter  hc/2π  for  displacement r then crystallises the dimensionless finestrycture for the energy interactions of electromagnetism and gravitation.
 
This leads for example to a description of chemistry in form of the Rydberg spectra, derived from the Bohr atom and where for the Rydberg-Constant      R∞=Alpha³/4πRe  we find  hc.R∞=Alpha².mec²/2   as the Rydberg Energy with Ry finestructuring in the wave quantum numbers  k for the atomic spectra as: 
 
k=R∞(1/n²  -1/m² )Z² 

and with Z the atomic number for the elements.   Modular  Duality connects these two potential energy expressions in an inversion energy, we have termed Magneto-Charge as inversed Weyl-Energy however and we write the so called ZPE as a potential energy and as VPE=Vortex-Potential-Energy: 

1/ZPEWeyl=e*=[360Re/8π](√μo)²/λWeyl
 for  μo =e*.[8π/360].λWeyl/Re=120π/c        (14)
                                                    
We have used the the 'lower dimensional' manifestation of the StarCoulomb C* as the unit for inverted Zero-Point-Energy or ZPE=VPE in [1/J].   This crystallises the CER as:

Re =10¹⁰.λWeyl/360 = [2π/360]10¹⁰.rWeyl =e*/2c² = λWeyl/2hc³  
for             EWeyl=1/e*=hc/λWeyl    and   h=1/e*fWeyl               (15)

The StarCoulomb so has 'higher dimensional' string units as Volume.Angular Acceleration or V.df/dt, but manifests as the 'inverted' ZPE. 

We now introduce a Generalised Action Law:

ACTION=CHARGE² ; which manifests in the lower dimensions in the form of supercoductivity, say in the Quantum Hall Effect (RH=VH/IH=h/ne²); Josephson Frequencies (f=2e.V/h) and the Conductance Quantum (G=2e²/h); all of which describe a unified Resistance in Ohms (Ω) via a: 

Free Space Impedance:

Zo = √(μo/εo) = (2h/e²).Alpha = 120π (Ω) 

for      Alpha=Zo /2RH        for n=2 in the quantised Hall effect.     (16)
 

Maxwell's equation for the displacement current:   jD  = εo.∂/∂t∫E.dS   from      

and

   
   
now gives the dimensional analysis:  [jD]=[C²/Jm][1/s][V/m][m²]=[C/s]=[A] -> 2ef=I for current in the lower dimensional realm becoming the magnetocurrent:  [ec]=[efλ]=[imλm] in the higher dimensional scenario of its transpositional  mapping. 

We so define the mass equivalence for a mass m quantised in N to magnetocurrent as follows: 

    For any mass m:       m= N'.mss = N'(efss)λm  

The elementary monopolic current quantum is:    efss = ec²mss/h ~ 5.353x10^-50 Ampere* for mss=hfss/c²=2.4691358..x10^-81 kg* ; manifests however in the Cooper-Pairing Iss=2Nefss, that is the mass current is quantised in the zero-spin bosonification of the fermionic double-electron charge and for integer count N.
  
The stringmass quantum  mss=(efss)λm=e.hfss/(ec)c  is the Inertial Mass Quantum and where (efss) ~ 5.353x10^-50 Ampere*   is the equivalent Gravitational Mass Quantum as a monopolic mass current, manifesting at the unification wavelength scale of the GUT-Monopole of energy 2.7x10¹⁶ GeV and as the monopolic perimeter of λm =mss /(efss)=h/ec² = 4.611023....x10^-32 m* and as a magnified and transformed Planck-Length λPlanck =2πRPlanck.
 
λm /λPlanck={h/ec² }/{√(2πhG/c³)}
                 =√(15h/π)/e=√(10^-32/π)/e=(10^-16/e)/√π      (17) 

These definitions take the transformation mapping of the mensuration units between the dimensions and so the generalised action law for unitised resistance and impedance into account. The squared Impedance is measured in Ω²=H(enry)/F(arad) and so in a sense defines an Impedance Action h*=ee* from Zo = √(μo/εo).

As the PLO=√(Alpha).√(hG/2πc³)=e/c²,  {h/ec²}=h.PLO/e²  as a transformed displacement unit.
The modular duality between  the elctric potential  Ve=ke²/r   and the gravitational potential  Vm=Gm²/r so describes an inversion lightpath for gravitation in the identity: 

For Electromagnetism:    c = λemr .femr    in m/s.
For Gravitation:             c = 1/(λgr .fgr)    in s/m,   subject to the string duality: 

λps λss=fps.fss=1  and the maximum- and minimum boundary/initial conditions for the 'awareness' or angular acceleration differential df/dt being: 

  (df/dt)max = fps²   and   (df/dt)min = fss²=1/fps²          (18)


Magneto-Charge e*=2Re.c²=2(1=¹⁰λps/360)c² =(10¹⁰/180){λps.c²}=(10¹⁰/180){λμ} for a Infrared-Unification-Wavelength: {λμ}IR=180e*/10¹⁰=180c.Lo=9 microns* and for
c=fIR.λIR=(6x10¹⁵/180 Hz*).(9x10^-6 m*).

Light-Constant Lo=1/(6x10¹⁵) is a fundamental algorithmic constant of frequency transduction,
where Lo.fps=5x10¹⁴ Hz* defines the Optical-Unification-Frequency at 6000 Angstroms* and for Orange Light by λoptical=c/(Lo.fps)=6x10^-7m*.



The CIRCULAR GRAVITO-MAGNETO-ELECTRIC SPECTRUM (GME-Spectrum):

femr.....λemr-------------------fgr.........λgr--femrλemr=c=1/(fgrλgr).................

fps......λps--------MinMax------fss........λss--as ElectroMagnetic Wavelength λps

fpsLo...λoptical------------------fss/Lo....1/λoptical----as Optical Unification λoptical

fIR......λμ=λIR=λps.c²-----------1/fIR........λss/c²------as InfraRed Unification λμ

c........1----------Unity---------1/c.........1------as EMR-GR-Wave Unification

2700...1/λIR--------------------1/2700....λIR-----as InfraRed Inversion Modality

180.....1/λoptical----------------1/180......λoptical---as Optical Inversion Modality

1/fIR....λss-------MaxMin-------fIR..........λps----as Gravitational Wavelength λss

fss.......cfps--------------------fps..........fss/c-----as Inflation-Wavelength cfps.



One effect of the GME-Spectrum becomes the proportion of a 'frozen GR-Wave' in any defined 'local universe' and as given by the lightspeed inversion. The acceleration am=cfps =3x10³⁸ m/s² so represents a modular dualised wavelength in the circular closure of the continnum of the GME-Spectrum.

As a 'winded superstring', Ess propagates as a local GR-Wave with Inversion-Lightspeed 1/c, which for a npresent cycletime npresent/Hoc ~ 2,010,264,772 m* for a distance so 5% the Venusian orbit, relative to the centre of the planet Earth.

This 'resistance field' grows at about 10.52 cm* annually.

  

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.Alpha⁹, to relate this to the gravitational finestructure Alpha-G=Alpha¹⁸.  
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.

The superposed acceleration am=cfps=9x10³⁸ m/s² is now applied in frequency-awareness modulation.
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/Alpha⁹=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=½hA=1.618221145..x10^-19 C* and for the fundamental algorithmic 'current' constant A²=14x15²⁴. 

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/Alpha⁹=efss.mP/mc  :  

sinΘw=CX......................Θw(n).........n-cycletime........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=9.29052714 x10^-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 per unit electron mass me√Yⁿ:

 1/C={me/efss}.{mc/mP}= 1.017336976{√Yⁿ}     (22)
           
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..x10⁵⁰ 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..}/δFeigenbaum 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:
 
Re=ke²/mec²= Alpha.h/2πmec²         (1)

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... fermi to Re=2.82872... fermi*, which calibrate to 2.824 fermi (SI) using m=0.9983318783m*.