Unified Electro-Gravity (UEG) Theory and Quantum Electrodynamics

Nirod K. DasDepartment of Electrical and Computer Engineering, Tandon School of Engineering,

New York University, 5 Metrotech Center, Brooklyn, NY 11201(Dated: June 24, 2019)

The Unified Electro-Gravity (UEG) theory, originally developed to model a stable static charge, isextended to a spinning charge using a “quasi-static” UEG model. The results from the new theory,evaluated in comparison with concepts and parameters from basic quantum mechanics (QM) andquantum electrodynamics (QED), show that the QM and the QED trace their fundamental originsto the UEG theory. The fine structure constant and the electron g-factor, which are key QEDparameters, can be directly related to the proportionality constant (referred to as the UEG constant)used in the UEG theory. A QM wave function is shown to be equivalent to a space-time ripple inthe permittivity function of the free space, produced by the UEG fields surrounding a spinningcharge, and the basic QM relationships between energy and frequency naturally emerge from theUEG model. Further extension and generalization of the theory may also explain all other quantummechanical concepts including particle-wave duality, frequency shift in electrodynamic scattering,and charge quantization, leading to full unification of the electromagnetics and gravity with thequantum mechanics.

I. INTRODUCTION

A new theory unifying the electromagnetic and grav-itational concepts, referred to as the Unifed Electro-Gravity (UEG) theory, was proposed in [1] to model astable, static electronic charge, referred to as a staticUEG electron. In its most basic form, the UEG theoryintroduces a gravitational field proportional to the en-ergy density surrounding the charge, with the constantof proportionality γ, referred to as the UEG constant,which results in a strong gradient of the the permittivityfunction εr(r) around the charge. With the success of thestatic UEG theory, an electron with a spin angular mo-mentum ~/2 may be conceived in terms of the static UEGelectron, that physically spins at a certain radial distancer0 to produce the given angular momentum. The centralacceleration of the spinning electron would be supportedby suitable UEG forces produced by the surrounding elec-tric and magnetic fields. The spinning electron would beself-supported by the radial forces due to the electron’sown UEG fields, in distinct contrast with orbiting of anelectron around the nucleus of an atom, which instead isexternally supported by the radial forces due the electricfield of the central nucleus. The permittivity functionεr(r) of the static UEG electron, would transform intoa space-time-dependent permittivity function εr(r, t) forthe spinning electron, which would be equivalent to hav-ing a space-time ripple, representing a quantum mechan-ical wave function. The spinning radius, speed, associ-ated wave frequency, angular momentum, energy/massmay be modeled by extending the static UEG theory of[1], by including additional dynamic UEG effects due tothe magnetic field and field momentum-distribution ofthe spinning electron.

A rigorous, dynamic version of the static UEG theoryof [1] would be needed to fully model the spinning elec-tron, which is premature at this point. In the absenceof the rigorous dynamic UEG theory, we will use suit-

able extension of the basic static UEG theory of [1]. Theextended model, referred to as the “quasi-static” UEGmodel, will be guided by existing concepts from Newto-nian mechanics and gravity [2], relativistic mechanics [3],electromagnetics [4] and general relativity [5], and buildupon the basic principles of the static UEG theory of [1].The objective is to explain different quantum-mechanicaland quantum-electrodynamic concepts and parameters,such as the wave function [6], Planck’s constant [7] andangular momentum [8], fine structure constant [9, 10]and g-factor [11], in terms of UEG concepts and param-eters such as the permittivity function, the UEG con-stant(s) and different UEG forces [1]. Further exten-sion of the principles of the quasi-static UEG model ofthe spinning electron may physically explain energy andfrequency shift in an electrodynamic scattering process,charge quantization linked to quantization of the angularmomentum, and wave-particle duality based on a pilot-wave concept. In any event, development of the UEGtheory would open a wider unified theoretical framework,combining electromagnetic, gravitational, together withthe quantum mechanical and electrodynamic concepts,that would be applicable to all elementary particles. Thiswould provide a unified alternative to the standard modelof particle physics [12], without need for additional strongand weak nuclear forces.

The sequence of presentation in different sectionsmaybe outlined as follows:

Section II presents the basic model of a spinning elec-tron, in equivalence to an orbiting electron, and extractsbasic relations between the mass of the static UEG elec-tron, the total mass of the spinning electron, the electrong-factor and the spin angular momentum.

This is followed in section III by identifying differentUEG forces in a spinning electron, and formulating thetotal UEG acceleration that would support the spinningmotion, based on first-order estimates. This would allowrelating the fine structure constant from quantum elec-

2

trodynamics to the UEG constant in section IV, in anapproximate form, that can be verified with the UEGconstant available from the static UEG model of elec-tron in [1]. A much closer evaluation is explored in sub-section IV A, with deeper insights into the UEG spinmodel, which may assist in future development of a rig-orous UEG theory.

Section V models the UEGravito-Magnetic effect dueto field momentum associated with the spinning motion,which is shown to cancel with the basic UEG effect dueto the magnetic energy density of the spinning charge.This allowed the formulations presented in the sectionsII, III and IV using only the UEG acceleration due to theelectric energy density, in order to support the spinningmotion.

Section VI relates the quantum-mechanical wave fre-quency to the spinning frequency in terms of the spinvelocity and the g-factor. This is based on relativistictransformation between the spinning frame and a station-ary external frame. The value of the g-factor is shownto be estimated from the UEG spin model in differentdegrees of accuracy, as compared with its known mea-sured value. This is to reinforce validity of the spin UEGmodel, and illustrate finer predictive power of the model.

Fundamental significance of the spin UEG model, andpotential implications of the UEG theory in general, arediscussed in section VII, outlining concepts for full unifi-cation of electromagnetics and gravity, together with thephysics of quantum mechanics and elementary particles.

II. ELECTRON SPIN MODELED AS ORBITINGOF A STATIC UEG ELECTRON, AROUND ITS

OWN FIELDS

Consider a static UEG electron, which is originallymodeled as a stable charge body using the basic, staticUEG theory of [1]. Then, consider the static UEG elec-tron to spin at radius r0 at a speed v0, close to thespeed of light c, the central acceleration of which couldbe sustained by suitable UEG force(s). Clearly, the ba-sic UEG theory of [1] which rigorously models the staticUEG charge without spin, may no longer be rigorouslyvalid for the spinning charge. A dynamic UEG theory fora moving charge would be required, that would includeadditional UEG forces due to energy density of the mag-netic field, as well as UEGravito-magnetic effects due tothe field momentum associated with the electromagneticfields. The development of a such a complete dynamictheory, referred to as a Unified Electro-Gravito-Magnetic(UEGM) theory, is premature at this point, beyond thescope of the present work. However, in absence of sucha full dynamic theory, we will model the spin behaviorusing a quasi-static UEG model, complemented by estab-lished results and insights from quantum electrodynam-ics.

A static UEG electron (modeled by a static UEG the-ory) may spin at a specific radial distance and velocity,

that could be sustained by the UEG forces due to its ownfields. The spinning of the static UEG electron maybeconsidered equivalent to orbiting of a complete electronstructure (that already spins) around a central nucleus ata suitable orbital radius. Except, the complete-electronorbiting is sustained by the electric fields of an externalbody, the nucleus, whereas the spinning of the electronis sustained by the UEG forces due to the fields pro-duced by the electron itself. The spinning electron maybe treated similar to an orbiting electron with orbitalquantum number equal to one, where the complete elec-tron mass me (already including the spin effects) for theorbiting electron is substituted by the static UEG massm′e of the “bare” (without the spin) electron. We knowfrom quantum electrodynamics, that the magnetic mo-ment µJ due to an orbiting electron with orbital quantumnumber equal to one, is about the same as that due to aspinning electron, different by a factor g = g/2 [13] closeto unity. This means the velocity-radius products of theorbiting and the spinning electrons are also close to eachother, different with the same above factor g. In addition,we also know from quantum electrodynamics, that theangular momentum J of the orbiting and spinning statesare ~ and ~/2, respectively, different exactly by a factorof two. Based on the above information we already have,it can be deduced that the total mass me (with spin) ofthe orbiting electron is g(= 2g) times, or about twice, the

mass m′e of a static UEG electron (without spin, modeledby a static UEG theory). Also can be deduced, that theangular momentum of the spinning electron is exactlyequal to the above mass m′e of the bare static UEG elec-tron, multiplied by the velocity-radius product, (v0r0) ofthe spinning electron.

µJ = q2 × (vr),

µJ (spin) ' µJ (orbital) = ~q2me

= 1gµJ (spin),

(vr)spin ' (vr)orbital = ~me

= 1g (vr)spin,

g = g2 = 1.00115965218091,

J = m× (vr), J(spin) = 12J(orbital) = ~

2 ,

m′e(vr)spin = 12me(vr)orbital = ~

2

m′e ' 12me = gm′e, me = gm′e,

J(spin) = ~2 =

J(orbital)2 = me

2 (vr)orbital

= (gm′e) 1g (vr)spin = m′e(vr)spin = m′ev0r0. (1)

As we deduced, the ratio between the spinning andthe static electron masses is approximately equal to two.One might casually expect the ratio to be equal to therelativistic boost factor, which is dependent on the spinspeed, as per special relativity. However, as mentionedbefore, we anticipate the spinning speed v0 to be close tothe speed of light c, in which case the relativistic boost

3

factor would be much larger than the above ratio close totwo. Accordingly, this might appear, at first, to be a con-tradiction to the casual expectation, but that may not bea valid observation. The mass transformation relation ofspecial relativity is applicable only to a complete, stablemassive particle in motion, but not for transformation ofmass of the static UEG electron as it spins. This is be-cause, the static UEG electron is an ideal state that is notdynamically stable in motion, and therefore does not con-stitute a complete, valid particle by itself to which spe-cial relativity can be independently applied. The staticUEG electron is only a part of the internal formation ofthe complete electron structure, and the special relativ-ity can only be applied to the complete structure. Fur-ther, the environment around a spinning electron, whichis governed by the UEG theory involving non-linear de-formation of the free-space structure around the electron,is significantly different from a simple free-space mediumassumed in the special relativity. Accordingly, the prin-ciples of special relativity may not apply strictly in theirconventional forms, in this spinning environment, partic-ularly for transformation of mass.

The angular momentum relation of (1) may now beused to express the ratio of the spin radius r0 and anequivalent radius r′e of the static UEG electron, in termsof the fine structure constant α [9, 14]. The ratio is ap-proximately equal to 1/α, assuming that the spin velocityv0 is close to the speed of light c.

m′er0v0 =q2r0v0

8πε0r′ec

2 = ~2 , m

′e = q2

8πε0r′ec

2 ,

r0r′e

=4πε0~cq2

( cv0) = 1

α ( cv0) ' 1

α , v0 ' c. (2)

III. UEG ACCELERATION COMPONENTSTHAT SUPPORT THE SPINNING CENTRAL

MOTION)

The fields and dynamics of a moving charged bodywith an expected speed close to the speed of light wouldneed special modeling and interpretation. We wouldshow in the following section V that the UEG acceler-ation due to the energy density of the magnetic field ofthe spinning charge would cancel with the UEGravito-Magnetic acceleration produced by the momentum distri-bution associated with the equivalent UEG mass/energydistribution. Therefore, the central acceleration of thespinning charge would be sustained only by the remain-ing UEG acceleration due to energy density of the elec-tric field. The central spinning motion of the electron,thus balanced by all the UEG and the UEG-Magnetic ef-fects, may all be viewed as gravitational in nature in thefundamental sense. Accordingly, consistent with generalrelativity, a moving frame attached to the spinning orbitmay be interpreted as an orbiting inertial frame (primedframe), moving along with the charge body, and the or-biting frame would be inertially equivalent to an external

stationary frame (unprimed frame) far from the spinningcenter. We would estimate the electric field, electric en-ergy density, and the associated UEG acceleration in theexternal stationary frame. This UEG-acceleration dueto the electric energy density of the spinning electron,as seen in the external unprimed frame, would supportthe central acceleration of the spinning body. Space-timerelations of special relativity may be used, for relativis-tic transformation between the external unprimed frameand the spinning primed frame.

A length parameter, radius r′e of the charge, along theorbital motion, as seen at a given instant in the orbit-ing primed frame, would be multiplied by the relativis-tic boost factor (= N) as seen in the external unprimedframe. Accordingly, one may interpret that the electroniccharge would “look stretched” along the orbit by theboost factor (N). If N = 2πr0/r

′e, the charge may appear

wrapped around the spinning orbit, satisfying a suitableperiodic physical condition. The periodic condition maybe assumed to be a required “resonant” condition in adynamic UEG theory, yet to be rigorously developed, inorder to maintain a stable spin structure. Under this res-onant condition, the stretched charge may be viewed inthe form of N number of virtual unit cells, that are peri-odically arranged with proper overlap (assumed overlapfactor 2) between neighboring units, over the entire cir-cumference of the spin orbit (see Fig.1). Accordingly, thespinning charge may be viewed as a ring-charge, as wellas a ring-current distribution. In fact, because the spin-ning orbit is actually in random orientations, with thespin-axis pointing randomly in all possible directions, thecharge may be viewed to be wrapped around the entiresurface of a sphere of radius equal to the spin radius r0.Accordingly, the structure may be approximately mod-eled as a spinning surface-charge distribution, uniformlydistributed over the sphere of radius r0, with axis of thespinning randomly changing in time.

As per the above model, we would derive the aver-age electric energy density at radial distance r0, as seenby the external unprimed frame, by assuming a spher-ically symmetric electric field. The average electric en-ergy density may first be expressed assuming that theuniform charge distribution on the sphere of radius r0is stationary with respect to the unprimed frame, hav-ing only radial electric field. When the charge spins, theradial electric field at a given point, which is directed or-thogonal to the spinning velocity at the point, is expectedto be increased by the relativistic boost factor N , as perspecial relativity. Consequently, the average electric en-ergy density that we derived first, assuming the station-ary charge distribution, may now be multiplied by thesquare of the boost factor, in order to find the averageelectric energy density of the spinning electron. This av-erage electric energy density would be used to calculatethe UEG acceleration to support the central accelerationof the spinning charge.

4

FIG. 1.

E = q

4πε0r20

1√1−

v20c2

= qN

4πε0r20

,

N =

√1−

v20c2

= a× (2πr0r′e

) ' (2πr0r′e

), a ' 1. (3)

IV. PLANCK’S AND FINE STRUCTURECONSTANTS RELATED TO THE UEGCONSTANT USING THE SPIN MODEL

As discussed earlier, the central acceleration of the spinis to be sustained only by the UEG force due to theaverage electric energy density at the radius r0. TheUEG force due to magnetic energy density is assumed tobe balanced by the UEGravito magnetic force, as shownin section V.

As per the charge model discussed above, the chargestructure of Fig.1 maybe effectively interpreted in theform of overlapping (overlapping factor 2) square gridsof 2r′e x 2r′e size each, wrapped in a ring configurationaround the sphere of radius r0. Further, because the axisof the ring structure of Fig.1 is randomly changing intime, the 2r′e x 2r′e sized grid structure would be effec-tively overlapping in two dimensions, wrapped over thesurface of the sphere. Therefore, the UEG force at thecenter of the grid may be calculated by multiplying theaverage energy density on the spherical surface by a fac-tor (4/π). The factor is equal to the ratio of the area of ar′e x r′e (excluding overlap region) square grid to that ofan enclosed circle of radius r′e. This geometric factor may

be considered an empirical “filling factor,” necessary forproper estimation of the effective UEG force seen at thecenter of the spinning electron.

W τ =ε02 E

2 =ε02 ( q

4πε0r20

)2(N)2 ' ε0

2 ( q

4πε0r20

)2(

2πr0r′e

)2,

Eg ' γWτ ( 4r′2

πr′2) ' γ ε02 ( q

4πε0r20

)2(

2πr0r′e

)2( 4π ) =

v20r0' c2r0,

γm′er′e

2 = γ q2

8πε0r′e3c2' r0

4r′e,

r0r′e' 4

γm′er′e

2 = 138.359 (UEG Theory),

r0r′e

= 1α ( cv0

) = 1α ( 1√

1− 1N2

)

' 1α =

4πε0~cq2

' 137.036 (QED). (4)

The angular momentum associated with the abovespinning would be equal to ~/2, as expected from quan-tum electrodynamics. The required ratio of the spin-radius r0 and the charge-radius r′e, as derived in (2) fromquantum electrodynamics, is approximately equal to theinverse of the fine structure constant α [14]. This ratior0/r

′e is shown above in (4) to approximately compare to

that r0/r′e = 4γm′e/(r′e

2) independently estimated from

the UEG theory, based on the spinning model of Fig.1,using the UEG constant γ derived in [1] from a staticUEG model of an electron. The small fractional differ-ence between the above two results for the ratio r0/r

′e is

calculated to be of the order of the fine structure con-

5

stant. Conversely, if one would estimate the UEG con-

stant γ = r′e2/(4αm′e) from the above UEG theory and

spin model, using the ratio 1/α = r0/r′e (2) from quan-

tum electrodynamics, and known values of the electronmass m′e = me/g from (1) and corresponding electron ra-dius r′e from (3), the value of γ would be different fromthat in [1] derived from a static UEG electron model.The two different independent values of γ would intro-duce a fractional ambiguity close to the fine structureconstant, which we will address shortly in the followingsection IV A.

γ(UEG) = 138.359× r′e2

4m′e

= 138.359× r2eg3

4me' 6.017× 102(ms-2)/(Jm-3),

γ(QED) = 137.036× r′e2

4m′e

= 137.036× r2eg3

4me' 5.96× 102(ms-2)/(Jm-3),

γ(UEG)− γ(QED)

' γ(QED)× 1.32α ∼ γ(QED)× α. (5)

Leaving aside the small fractional ambiguity, discussedabove, the close results from the UEG theory and quan-tum electrodynamics point to a definite fundamental con-nection between the two theories, relating the UEG con-stant γ to the fine structure constant α. This is a signif-icant development, also providing a direct physical rela-tion between the UEG constant γ and the Plancks con-stant ~, via the fine structure constant α to which boththe γ and ~ are related to, founded on the dynamic mod-eling of the spin, sustained by the UEG forces. In otherwords, the Planck’s constant ~, with its origin in quan-tum mechanics, may no longer be considered a fully inde-pendent natural constant, but is rather unified togetherwith the UEG constant γ. Accordingly, the UEG theory,which already unifies the electric and gravitational prin-ciples, is now positioned to be fully unified with quantummechanics as well.

A. Closer Relationship Between the UEG andQuantum Electrodynamics

It may be noted that the UEG theory from which theconstant γ was estimated in (4) is only a basic theory,where the UEG acceleration is assumed to be propor-tional to the energy density, with γ as the constant of theproportionality. A rigorous UEG theory would includehigher-order acceleration proportional to higher powersof the energy density, which is expected to reduce thevalue of the stable mass m′e, as compared to that fromthe basic theory with a given γ without the higher-orderterms [1]. Conversely, in order to have the same final sta-ble mass m′e, one may need to start with a basic UEG the-ory producing a higher stable mass, or equivalently with

a lower γ, before introducing higher-order UEG terms.In other words, the actual value of γ in the dominantacceleration in a rigorous UEG theory, which is the theconstant of proportionality between the UEG accelera-tion and the energy density, in the low energy-densityrange, is expected to be lower than than the value of γin [1] obtained from a basic UEG theory without anyhigher-order effects. This is under the condition that therigorous and the basic UEG theories produce the samestatic electron mass m′e. The lower value of γ in the rig-orous theory would be associated with a reduction of theeffective radius r′e, in proportion to the cube-root of γ [1].

Based on the above discussion, we may recognize thatin principle there are three theoretical values for the con-stant γ. (I) The value of γ obtained from a basic UEGtheory [1], that produces a stable electron mass equalto m′e = me/g. (II) The actual value of the γ, whichis the constant of proportionality between the UEG ac-celeration and the energy density, valid when the energydensity is sufficiently small. This would be the dominantterm, or the first order approximation, in a fully rigorous

UEG theory. And, (III) the value of the γ = αr′e2/(4m′e)

that is indirectly estimated from an ideal spin model ofthe electron, as derived in section IV, which expects theknown fine structure constant from quantum electrody-namics to be related to the γ, and the known values of theelectron mass m′e and the electron radius r′e. A higher-order UEG theory for a bare, static electron, combinedwith a rigorous, dynamic UEG model for a spinning elec-tron would be needed to explain any differences or spe-cific relationship between the three parameters, which isbeyond any scope of the present work. The parameters(I) and (III) are shown in (5) to be close to each otherwith a fractional difference of the order of the fine struc-ture constant, and we may suspect similar closeness ofthe parameter (II) to the other two values. Additionalinsight may assist in more accurate evaluation for theparameter (II), which is the actual constant of propor-tionality between UEG acceleration and energy density,in an environment with low energy density.

The effective radius used in an ideal spin model of sec-tion II, Fig.1, is assumed to be the classical radius r′eof the bare electron, which determines the required rela-tivistic boost factor to be ideally equal to N = 2πr0/r

′e.

The actual value of the boost factor is slightly larger thanthis ideal value, represented by the factor a, the value ofwhich can be estimated as shown in (7), from the knownvalues of the fine structure constant α and electron g-factor. This increase is equivalent to having an effectiveradius r′e to be smaller than the ideal value by the samefactor a. It may be reasonable to estimate that the ac-tual increased value of the boost factor N = 2πr0a/r

′e,

and the corresponding reduced effective radius r′e/a, isassociated with the average between the two values ofγ (I) and (II), that is the average between the valuesneeded in a basic UEG model and in a rigorous UEGmodel to produce the same stable mass m′e. Whereas,the ideal value of the boost factor N = 2πr0/r

′e, and the

6

corresponding effective radius r′e, is associated with thefirst value of γ (I), that is the value needed in a basicUEG model to produce the stable mass m′e. As per theearlier discussion on the effect of the higher-order UEGtheory, the reduction in the effective radius would meanthat the average of the two values of γ (I) and (II) wouldbe lower than the first value of γ (I), by a factor equalto a3 ' 1.0045 ' 1 + 0.62α (see (7)). This would place theestimate for the actual value of γ (II), fractionally about(1+1.24α) lower than the estimate of γ (I) from the basicUEG theory. This estimate for the actual value of theγ (II) is fairly close to the estimate (III) from quantumelectrodynamics, which we know from (5) to be fraction-ally about (1 + 1.32α) lower than the estimate (I). Inother words, the estimates of γ (II) and (III) would beessentially equal to each other with a fractional differenceof less than 0.1α, or within 0.1%.

γ(actual) ' γ(Basic UEG)

(1+2a3)

=γ(Basic UEG)

(1+1.24α)= 5.963× 102(ms-2)/(Jm-3),

γ(QED) ' γ(Basic UEG)(1+1.32α)

= 5.96× 102(ms-2)/(Jm-3),

γ(actual) ' γ(QED),γ(actual)γ(QED)

< 1.001 . (6)

The parameter a, used in the above discussion and de-duction, is expressed as follows, using (2) for the ratior0/r

′e, and (15) to relate the boost factor N to the fac-

tor g. The value of a may be calculated using knownmeasured values of the fine structure constant α and theelectron g-factor g = 2g .

r0r′e

=4πε0~cq2

( cv0) = 1

α ( cv0) = 1

α ( 1√1− 1

N2

),

N = a× (2πr0r′e

) = 2πaα ( 1√

1− 1N2

),

1a =

2π/α

N

√1− 1

N2

=(2π/α)(g−1)√

1−(g−1)2

= (2π/α)× 0.0011596529 = 1− 0.0015126724 . (7)

Based on the close estimated values (II) and (III) of γ,as discussed above, it may be suggested that the two val-ues (II) and (III), namely, the value of γ from a rigorous

UEG model of electron, and the value γ = αr′e2/(4m′e) de-

rived from quantum electrodynamics, could be, after all,equal to each other, or close to each other with relativelyhigher precision. This proposition may be supported byfurther insights and more accurate modeling of the cen-tral acceleration of the spinning electron.

The above modeling in (4) of the spinning electron us-ing the UEG theory was established in an approximateform, in the absence of a rigorous dynamic UEG the-ory, as an initial estimate in order to illustrate funda-mental relations between the UEG and the fine structure

constants. Conversely, when a rigorous dynamic UEGtheory would be established and it validates the basicprinciples of the modeling (4), the fine structure and thePlanck’s constants could in principle be derived and pre-dicted exactly from the UEG theory. For now, we mayevaluate the fine structure constant α, which is the in-verse of ratio of the spin radius and the electron radius,more accurately from the modeling of (4), guided by thefollowing insight.

We know from (7) that the boost factor N is slightlylarger than the ratio (2πr0/r

′e) obtained from the angular

momentum in (2), by the factor a. This is equivalent tohaving increased overlap between the neighboring parti-cles in the ring model of section II, Fig.1. The averageenergy density in (4) maybe properly redistributed overthe surface of the spin sphere, weighted in proportionto the actual energy/mass distribution. Accordingly, theredistributed energy density at the particle center wouldbe inversely proportional to the square of the overlap fac-tor a, considering overlap of the spinning particle in twodimensions over the surface of the spin sphere. More isthe overlap, which is on the outer edges of the particle,more energy density needs to be redistributed away fromthe center, leaving less energy density at the particle cen-ter. This redistributed energy density, evaluated at thecenter of the particle, would be multiplied with the UEGconstant γ, in order to obtain the UEG acceleration thatsupports the central acceleration. Accordingly, the UEGacceleration would be reduced by a factor a2. This maybe introduced as an multiplying factor 1/a2, in additionto the ideal redistribution factor 4/π that we already havein our model of (4).

W τ =ε02 E

2 =ε02 ( q

4πε0r20

)2(N)2 =

ε02 ( q

4πε0r20

)2(

2πr0r′e

)2(a)2,

Eg = γWτ (4r′e

2

πr′e2 )( 1

a )2

= γε02 ( q

4πε0r20

)2(

2πr0r′e

)2( 4π ) =

v20r0,

γm′er′e

2 = γ q2

8πε0r′e3c2

= (r04r′e

)(v0c )

2

= (r04r′e

)(1− 1N2 ) = (

r04r′e

)(1− (1− g)2). (8)

The expression for the ratio of the spin and classical staticelectron radii, derived from spin angular momentum re-lation (2), may now be used for a closer relationship be-tween the rigorous UEG constant γ to the fine structureconstant α.

r0r′e

=4πε0~cq2

( cv0) = 1

α ( cv0) = 1

α ( 1√1− 1

N2

) = 1α ( 1√

1−(1−g)2),

4γm′er′e

2 = (r0r′e

)(1− (1− g2)) = 1α

√1− (1− g2) = 1

α

√1− 1

N2 ,

(4γm′er′e

2 )(r0r′e

) = ( 1α )

2. (9)

The dimensionless constant 4γm′e/r′e2, where γ is the

rigorous UEG constant, and the other dimensional con-

7

stant 1/α, which is the inverse of fine structure constant,are now shown in (9) to be close to each other with frac-tional difference of approximately 1/(2N2). This frac-tional difference is of the order of the square of α/(2π),which would amount to having the above two dimension-less constants essentially equal to each other, with theirratio different from unity only in the sixth or higher dec-imal places. This is a significant development, which, inaddition to reinforcing unmistakable unified connectionbetween the UEG theory and quantum electrodynamics,opens valuable insights for any future development of afully rigorous UEG theory. The effective γ for a rigor-ous UEG theory is now very accurately estimated from abasic UEG theory and available information from quan-tum electrodynamics. Additional details for a rigorousUEG theory could also be extracted from the g-factor,the measured value of which is available with very highprecision. This would be possible through the parametera in (7), which is the change of the effective radius ofthe particle as compared to its ideal classical value r′e,carrying information that would constrain any variationof a general UEG function γ(Wτ ) in a rigorous UEG the-ory. This is in addition to the effective γ deduced above,which would be the first-order constant coefficient of thegeneral UEG function, which is only an approximationof the general UEG function for low energy density Wτ .

V. THE UEG ACCELERATION DUE TO THEMAGNETIC FIELD, AND THE UEGM

(UEGRAVITO-MAGNETIC) ACCELERATIONDUE TO THE FIELD MOMENTUM

We will find the expression of the velocity due to spin-ning at a given radius r. This may be derived fromthe electromagnetic field momentum, using the Coulombelectric field due to the electron charge and the magneticfield produced due to spin magnetic moment µS . The ve-locity may also be estimated from a quantum-mechanicalmodel where the spinning of the static mass m′e is treatedsimilar to the orbital motion of the total electron massme. The two velocity expressions from the electromag-netic and the quantum models are similar except the sin θ

factors.

µS = ~q2me

z, H = θµS

4πr3sin θ + r

µS2πr3

cos θ,

E = r q

4πεr2, v(EM) = E×H

( ε2E2)

= φ2µS sin θ

qr = φ~ sin θmer

,

S = m′er0 × v0 = 12mer × v

= z 12mevφr sin θ = z ~2 , v(QM) = φ ~

mer sin θ . (10)

The energy density in the magnetic field would producean UEG acceleration Egum, which may be expressed bymultiplying the average energy density in the magneticfield with the UEG constant γ.

Egum = −r < γ(µ2H2) >= −r

γµµ2S

32π2r6< (sin2θ + 4cos2θ) >

= −rγµµ2

S32π2r6

π∫0

(sin2θ+4cos2θ) sin θdθ

π∫0

sin θdθ

= −rγµµ2

S16π2r6

= −r γµq2~2

64π2m2er

6 . (11)

Unlike a static electron without any spin, which pro-duces a UEG force field and is associated with a gravi-tational mass distribution (mass-density) as per Gauss’Law, a spinning electron would in addition be asso-ciated with an effective UEG momentum distribution(momentum-density) that may be expressed by multi-plying the UEG mass density and the velocity derivedabove. This momentum-density due to the moving UEGmass-density is expected to produce a gravito-magneticfield, in a very similar way as an electric current distribu-tion due to a moving electric charge distribution producesa magnetic field as per the Ampere’s Law of the electro-magnetic theory. Accordingly, the gravito-magnetic fieldmay also be derived from the UEG momentum densityusing an equivalent version of the Ampere’s Law.

The acceleration due to the gravito-magnetic field maybe expressed as the cross-product of gravito-magneticfield and the velocity. Note that there are two ve-locity terms in the above derivation: (I) the velocityused in derivation of the gravito-magnetic field to be-gin with, and then (II) the velocity that multiplies withthe gravito-magnetic field to find the gravito-magneticacceleration. As a reasonable approach to estimate theaverage gravito-magnetic acceleration, we choose the twovelocity terms to be expressed differently as in (10) - theformer derived electromagnetically (v(EM)) and the laterquantum-mechanically (v(QM)). Also note that we treatthe gravito-magnetic acceleration Egm in (12) just likean equivalent acceleration in an electromagnetic model-ing, without any adjustment factor. This is unlike con-ventional gravito-magnetic modeling [15] where an addi-tional factor of 1/4 might be needed. This is because,in conventional gravito-magnetic modeling [15] the mass,which is the source of gravitation, relativistically varieswith velocity. Whereas, the average mass density ρvu inthe present modeling, associated with the azimuthal (φ-directed) is assumed to be independent of the velocity v,just like the electric charge density, which is the sourceof an electromagnetic field, would be in an equivalentelectromagnetic modeling.

8

Egue = −rγ( ε2E2) = −r γq2

32π2εr4,

ρvu = −ε∇ · Egue = − γq2

16π2r5,

∇ × Hgu = Jgu = ρvuv(EM), Hgu = θHguθ,

1r

∂(rHguθ)

∂r = ρvuvφ(EM) = − γq2~ sin θ

16π2mer6,

Hguθ = γq2~ sin θ

64π2mer5,

Egm = −µ < v × Hgu >= −µv(QM)× Hgu

= rµvφ(QM)Hguθ = rµ( ~mer sin θ )( γq

2~ sin θ

64π2mer5)

= r γµq2~2

64π2m2er

6 . (12)

It is shown that the gravito-magnetic acceleration (12)due to UEG momentum density is negative of the UEGacceleration (11) due to the energy density in the mag-netic field. Therefore, the total UEG force is simply theUEG force due to the energy density in the electric field,independent of the magnetic field generated due to thespin.

Egm + Egum = 0,

Eg = Egue + Egm + Egum

= Egue = −rγ( ε2E2) = −r γq2

32π2εr4. (13)

The theory developed in this section is an impor-tant recognition of the existence and significance of thegravito-magnetic effect surrounding the electron, pro-duced as per the new UEG theory. The gravito-magneticeffect constitutes a critical physical mechanism of thecomplete internal structure of the electron.

VI. QUANTUM MECHANICAL WAVE IS ARIPPLE IN THE “NON-LINEAR” FREE-SPACE

MEDIUM, WITH THE QUANTUM FREQUENCYCLOSE TO THE SPIN FREQUENCY

The quantum mechanical (QM) wave of frequency ω

may be viewed as a ripple in the free space produced dueto the spinning of the electron, as a result of the strongUEG force. The non-linear permittivity function of thefree-space in the UEG (static) theory would transforminto the QM wave function of the “free-space” as a resultof the spinning. It was discussed in sections III, V, thatthe strong UEG field around the spinning charge wouldproduce an equivalent rotating inertial frame, draggedalong with the moving charge due to the UEGravito-Magnetic (UEGM) effect. The frequency ω of the QMwave maybe intuitively “seen” as a difference-frequencyω − ω0 relative to the rotating frame spinning with thefrequency ω0. The difference frequency ω − ω0, and theactual QM frequency ω may be related with each other

by the relativistic boost factor N between the rotatingframe (primed frame) and a stationary frame (unprimedframe) far from the spin center. Accordingly, the QMfrequency ω may be shown to be slightly larger than thespin frequency ω0, with a small difference of ω/N . The in-tuitive relationships may also be established using space-time transformation between the primed and unprimedframes, and enforcing a periodic symmetry condition (βx (2πr0) =2π) around the circumference 2πr0 of the ro-tating frame.

This is a significant development, which provides a di-rect physical process that represents the QM wave, in theform of ripples produced due to spinning in a a non-linearfree-space medium. This may be established by directlyrelating the QM wave frequency ω to the physical spin-ning frequency ω0 of the charge.

ejωte−jβs = ejω′t′e−jβ

′s′ , t =t′+s′v0/c2√

1−v20c2

, s =s′+t′v0√

1−v20c2

,

ω′ =ω−βv0√

1−v20c2

, β′ =β−ωv0/c2√

1−v20c2

,

ω′ = ω =ω−v0/r0√

1−v20c2

=ω−ω0√1−

v20c2

;

β × (2πr0) = 2π, β = 1r0. (14)

For a general interpretation of the above concept of thequantum/UEG wave, first consider a “stationary” spin-ning charged body with a total mass m (including spinand static UEG mass) and linear momentum p = 0, withno linear motion of the center of spinning. The regionsurrounding the charge will be associated with a space-time dependent permittivity function εr(r, t) expressed inthe harmonic form (14), which would represent the quan-tum/UEG wave function of the stationary particle. Thewave will be seen by a stationary observer to be oscil-lating as ejωt with frequency ω, but having no spatialdependence with wave number β = 1/r = 0, in the re-gion far from the center (r = ∞). We may assume thatthe wave amplitude in the far region is uniform in space,independent of the spatial variation of the UEG field.This wave function would be consistent with quantummechanics, with the expected energy-wave frequency re-lationship w = mc2 = ~ω, and momentum-wave numberrelationship p = mv = ~β = 0.

Now, the above quantum-mechanical relationships forthe “stationary” spinning charge may be extended as wellwhen the charged body undergoes a linear motion of thecenter of spinning, with velocity v in a given direction s.Applying space-time transformation of special relativity,the above wave function ejωt of the stationary charge inthe far region, dependent only on time, maybe shown

to transform into a wave ejω(t−sv/c2)η = ejω′te−jβ

′s,with both space and time variation, as seen by a sta-tionary observer. The new frequency ω′ = ηω = ηmc2/~

9

= m′c2/~, and the new wave number β′ = ω′v/c2 = m′v/~= p′/~, are related to the new mass m′ = ηm and mo-mentum p′ = m′v, where η = (1 − v2/c2)−0.5 is the rela-tivistic boost factor associated with the velocity v. Thebasic quantum mechanical energy/momentum and fre-quency/wave number relationships, W ′ = m′c2 = ω′~ andp′ = m′v = β′~, are clearly established between the waveparameters in the region far from the center of the mov-ing charge, and the mass m′ and linear momentum p′ ofthe physical charged body moving at the center of wave.

Clearly, the above quantum-mechanical relationshipsfor the quantum/UEG wave would not be valid in theregion closer to the central charge. A full dynamic UEGtheory may be needed to rigorously model the wave func-tion in the central region, particularly in the immediatevicinity of the charge with strong energy density.

A. Electron g-Factor Related to Relativistic Boostfactor, and to the Spin and Quantum Wave

Frequencies

Based on the above quantum-mechanical interpreta-tion, the frequency ω in (14) may be related to the totalelectron mass me. On the other hand, the spin frequencyω0 is related to the static electron mass m′e through thespin angular momentum ~/2. Accordingly, given thatthe two frequencies ω and ω0 are related to each otherin (14) by the boost factor N , the total and the staticmasses would also be related to each other by the boostfactor. Consequently, the electron g-factor, which is theratio of the total and the static masses, would be directlyrelated to the boost factor.

1√1−

v20c2

= N,ω−ω0√1−

v20c2

= N(ω − ω0) = ω,

ω(1− 1N ) = ω0, ~ω = mec

2,

J = m′er0v0 = m′ev20ω0

= ~2 , v0 = ω0r0,

mec2

~ (1− 1N ) =

2m′ev20

~ , m′e = mec2

2v20

(1− 1N )

= me2(1− 1

N2 )(1− 1

N ) = me2(1+ 1

N)

= meg ,

1N = g

2 − 1 = 0.001159652 (measured). (15)

B. Estimating g-Factor from the Fine Structureand UEG Constants, Based on the Spin Model

The small difference between the quantum wave andthe spinning frequencies appears in the form of the g-factor of the electron. The value of the g-factor maybe estimated directly from the UEG constant, or equiv-alently from the fine structure constant, to the first or-

der, consistent with the prediction from quantum elec-trodynamics (QED). This estimate for the g-factor, whenrounded up, is accurate up to the 5th decimal point, ascompared to the currently measured value.

µJ = qf0πr20 = q

2w0r20 = q

2v0r0, J = m′ev0r0,

µJJ = q

2m′e= q

2me2(1 + 1

N ) ' q2me

2(1 +r′e

2πr0)

= q2me

2(1 + α2π ) = q

2meg, g = 2(1 + α

2π ),

g2 = (1 + α

2π ) = 1.0011614097; 1α = 137.035999139 ,

g2 (measured) = 1.0011596521 . (16)

C. Higher Order Corrections to the g-factor

Higher order correction to the g-factor may also be es-timated from the UEG/QM theory. This follows up onthe above result that the total electron mass is slightlylarger than twice (factor of about 2(1 +α/(2π)) the UEGelectrostatic mass, which is different from the ideal factorof 2 assumed in a simple spinning model with an idealrelativistic boost factor N = 2πr0/r

′e = 2π/α Accordingly,

we need the electric and magnetic energies of the spinningelectron to be each slightly larger than the static electricenergy. This would be accomplished by having a slightlylarger relativistic boost factor than the ideal value of2π/α (boost factor increased to (2π/α)(1 + α/(2π))). Fol-lowing the similar derivation for the g-factor presentedearlier, this would lead to a smaller g-factor than thefirst order estimate above, the trend being consistentwith the measured g-factor and the theoretical deriva-tion from quantum electrodynamics.

g = 2(1 + α2π /(1 + α

2π ))

' 2(1 + α2π (1− α

2π )) = 2(1 + α2π − ( α2π )2),

g2 ' (1 + α

2π − ( α2π )2) = 1.0011600608 ,g2 (measured) = 1.0011596521 . (17)

The above estimate for the g-factor, when rounded up,is accurate up to the sixth decimal point, as compared tothe currently measured value. This is one order improve-ment compared to the first order estimation deduced ear-lier.

This above estimation is based on the assumptionthat the mass/energy of the spinning electron increasesproportional to the boost factor. This trend is consis-tent with the special relativity, which is expected not tostrictly apply in the dynamic UEGM model. Alternateimprovement in accuracy of estimation of the g-factor ispossible by assuming that the difference between the finestructure constant and the UEG dimension-less constant4γm′e/r′e

2is related to the higher-order correction term

of the g-factor (see section IV A).

10

g = 2(1 + 1N ) = 2(1 +

r′e2πr0a

)

' 2(1 + α2π × (

(1/α)

(4γm′e/r′e2

))1/6

)

= 2(1 + α2π × (137.0360

138.3588 )1/6

) = 2(1 + α2π × (1− 0.0016)),

g2 ' (1 + α

2π × (1− 0.0016)) = 1.0011595514 ,g2 (measured) = 1.0011596521 . (18)

This is improvement in the higher-order corrections ofthe g-factor, compared to the earlier estimation in (17),with improvement showing in the seventh and eighth dec-imal points. This estimation uses a simple averaging ofthe two UEG constants γ, one from the basic UEG the-ory of electron [1] and the other from QED using the finestructure constant, as reasoned in section IV A, in orderto deduce an effective γ. This effective γ determines aneffective radius (=r′e/a) for estimation of the boost fac-tor N , from which the g-factor is estimated as shown in(18). Accordingly, a more accurate prediction/estimationof the g-factor would be possible by deducing a more ac-curate effective γ using a higher-order UEG model of [1].

An exact value of the g-factor can be predicted directlyfrom an exact boost factor N , if it could be available,using the exact relationship g = 2(1+1/N) (see 15), (18)).

In principle, the N = 1/√

1− (v0/c)2 could be solved from

a fully rigorous (both static and dynamic parts) UEGmodel, as the required relativistic boost factor for anelectron with a static UEG mass m′e, spinning at a radiusr0 = ~/(2v0m

′e) and speed v0, to acquire its total known

dynamic mass me = gm′e = 2m′e(1 + 1/N) and an angularmomentum ~/2. Such a rigorous and dynamic UnifiedElectro-Gravito-Magnetic (UEGM) theory maybe at thispoint premature, and is beyond the scope of the presentwork.

VII. DISCUSSION: FUNDAMENTALIMPLICATIONS FROM THE UEG THEORY OF

QUANTUM ELECTRODYNAMICS

The fine structure constant α, first introduced by Som-merfeld [9] as a dimensionless number relating physicalconstants from quantum mechanics (~), electromagnetics(q and ε0) and relativity (c), remained mysterious in itsorigin [10, 16, 17], even though the constant has beenwidely used in all quantum field theories [11, 12]. Asper the current work, it is now clear that the fine struc-ture constant has its fundamental origin in a new Uni-fied Electro-Gravity (UEG) theory, developed for model-ing of elementary particles [1]. A dimensionless constantemerges in the UEG theory, relating a constant used inthe theory (the UEG constant γ) with an elementaryparticle’s stable mass and the particle’s classical radius,which appeared to be closely related (numerically) to thefine structure constant [1]. In the present work, this di-mensionless constant from the UEG theory of [1] is shown

to also govern the spin dynamics of the electron that de-termines the spin angular momentum, and consequentlyis shown to be directly related (on physical basis) to thefine structure constant. Interestingly, the dimensionlessconstant from the UEG theory, which is now related tothe fine structure constant, is a normalized-parameterindependent of any specific mass or charge of a parti-cle, and therefore is a mathematically-based number, re-quired to maintain a stable static particle (based on theUEG theory, before any spin is introduced) with a givencharge q and a given UEG constant γ. Considering thatit is a mathematically-based number, independent of anyspecific particle mass or charge, the dimensionless UEGconstant or equivalently the fine structure constant is ex-pected to carry a general scope of application to any ele-mentary particle (electron/positron, proton/anti-proton,for example). By extension, the scope of the constantwould cover composite charged as well as neutral par-ticles, consisting of of multiple charge layers. However,in the present work the theory is specifically applied tothe spin dynamics of an electron, which is the simplestparticle.

A. Quantization of Charge and AngularMomentum as Complementary, Emergent Concepts

The discovery of the new UEG theory of such sig-nificance, to which the fundamental origin of the finestructure constant of quantum electrodynamics couldbe traced, is bound to open reexamination of manyrelated physical phenomena, that remained mysteriousand unsolved to date. Consider an immediate conse-quence of the discovery. Once the fine structure constantα = q2/(4πε0~c) is independently established as a funda-mental dimensionless constant that determines the stablemass and spin dynamics of an elementary particle, thenthe required constant α, for a given angular-momentumparameter ~ and a reference value of c, would force theelementary quantity q2/ε0 (or equivalently q/

√ε0) to be a

fixed, quantized value. This would be the case, when anynew charge is created in the form of a particle-antiparticlepair. The available quantized angular momenta, in inte-gral multiples of ~ from any transitional “photon packets”(see later discussion on the photon concept), are expectedto dynamically force the two charges (positive and neg-ative) in the particle-antiparticle pair, to each acquirea fixed value of magnitude q (given ε0 and c as refer-ence constants). This is a significant new understand-ing of the elementary charge q as a dynamically emer-gent, fixed quantity, no longer a pre-assigned parameteras currently understood. The new understanding couldsolve the current mystery of the natural quantization ofall available charges, because they all would consist ofan integral number of the elementary charge (+q or −q),each having the same magnitude, which is dynamicallyfixed at the time of their production, enforced by theUEG theory and quantization of the available angular

11

momenta.Conversely, given the fixed magnitude q of an elemen-

tary charge already available, the required (dictated bythe UEG theory) constant α = q2/(4πε0~c) would fix thecharge’s angular momentum ~/2 (given ε0 and c as refer-ence constants), as well as its energy-frequency relation-ship W ′ = ~ω′ (section VI). Consequently, all “photonpackets” (light radiation), that are naturally producedthrough a coupling process with the non-linear UEGfields of the elementary charge (see later discussion onthe photon concept), would be each associated with aquantized angular momentum (= ~) and energy (= ~ω),which are pre-fixed by the angular momentum ~/2 of thecoupling charge. These available transitional “photons,”which are assumed to be general exchange media in thecharge creation process discussed earlier, would, in turn,determine the magnitude of each new elementary charge±q created. Accordingly, the Planck’s constant ~ and theelementary charge magnitude q would constitute a com-plementary pair of constants, that are naturally emer-gent, balanced with each other through the dynamics ofthe UEG theory and the classical electromagnetic theory.

The continual balancing process between the elemen-tary charge q and the Planck’s constant ~, as discussedabove, may be traced back to the beginning of the cur-rent universe. All naturally-existing elementary chargeswere created in this beginning phase, possibly through achained reaction process that was originally balanced bythe angular momentum of a transitional photon, which inturn was synchronized with the annihilating elementarycharges from a preceding collapsing universe. This maypresume a cyclic universe, where the same fixed mag-nitude of the elementary charge in the current universewould also be maintained through annihilation in a col-lapsing phase in the future, into re-creation in a newbouncing universe, by repeating the above q− ~ synchro-nization process.

B. Wave-Particle Duality

As the new model of electron spin clearly establishes,the charged center of the electron is surrounded by the“quantum ripples” which are actual ripples or variationsin the structure or characteristics (permittivity) of the“free-space” itself. Accordingly, the electron would ex-hibit particle-like behavior governed by its central core,and as well exhibit its wave-like behavior due to the sur-rounding ripples. This would explain the wave-particledual behavior of the electron, which has been experimen-tally observed, but is considered to be mysterious basedon the current quantum-mechanical understanding. Theripples are produced by non-linear spin dynamics of thecentral electron, based on the UEG theory which is fun-damentally non-linear. The central particle and the sur-rounding quantum ripples can not be de-linked from eachother, and are expected to complement each other in allphysical processes. Any motion of the electron at the cen-

ter would also be guided by the surrounding quantum rip-ples, that are constrained by suitable UEG principles, orequivalently governed by the quantum-mechanical princi-ples [6, 8, 18]. These ripples in the free-space may repre-sent the pilot wave proposed by de Broglie [19, 20], whichcould be used to physically explain the measured inter-ference pattern of the electron when it passes through ascreen with two closely-spaced slits. The central core ofthe particle could be physically guided by the interferencepattern created by its own surrounding pilot wave [21].This would result in having the physical locations, wherethe central charged particle is actually detected by a suit-able measurement, to be probabilistically distributed bythe same pattern as the pilot-wave’s interference.

C. Electrodynamic Scattering, PhotoelectricEffect, and the Photon Concept

Further, a non-linear UEG process similar tothat responsible for generation of the UEG/quantum-mechanical ripple or wave of a spinning electron, withits energy (momentum) directly related in proportion tothe wave frequency (wave number), could also be respon-sible for non-linear interaction of the UEG/quantum-mechanical wave of an electron with a UEG/field waveof an incident or outgoing light (photon). This wouldresult in dynamic “mixing” between the UEG/quantum-mechanical/field waves of the electron and the photon.The process would be analogous to frequency up- ordown-conversion in transistor electronic circuits [22], pro-duced due to non-linear mixing of two time-dependentelectrical signals of different frequencies, having the con-cept extended for both time- and space-dependent sig-nals. Based on a suitable non-linear mixing process, itis conceivable that any change of the light’s frequency(wave number) would be negative of that of the elec-tron’s UEG/quantum-mechanical frequency (wave num-ber). The change of the electron’s frequency (wave num-ber) would be in direct proportion to that of its energy(momentum), with the constant of proportionality equalto ~, as per the UEG theory of the electron. In addition,the change of the electron’s energy (momentum) wouldbe equal to the negative change of the light’s energy (mo-mentum), as per the principle of energy (momentum)conservation. Therefore, combining the above three con-ditions, the change of the light’s frequency (wave num-ber) would be in direct proportion to that of its own,or equivalently negative of the electron’s, energy (mo-mentum), with the constant of proportionality equal to~. This mechanism could physically explain the Comp-ton scattering [23], without having to accept it as somemysterious fundamental “quantum phenomenon”.

A similar non-linear, dynamic mixing process couldalso explain the nature of quantized absorption/radiationof light (photon) energy, by/from a given material, byassociating the process with a known quantized energytransition of the material’s electrons (due to material’s

12

atomic or molecular structure). As per the non-linearmixing process and the principle of energy conserva-tion, the wave frequency and energy quanta of any ab-sorbed/radiated light (photon) could be explained tobe equal to positive/negative changes in UEG-quantum-mechanical wave frequency and energy of a transitioningelectron of the material, respectively. The changes inthe electron’s radian frequency and energy are known tobe proportional to each other, with the constant of pro-portionality equal to ~, as per the UEG theory of theelectron. Therefore, combining the above conditions, theabsorbed/radiated light’s radian frequency and the en-ergy quantum would also be directly related in propor-tion to each other, with the constant of proportionality~. Extending this principle, in case an incident light’sfrequency exceeds the above threshold frequency of ab-sorption, the process would be associated with a scat-tered light of a lower frequency. In this process, using asimilar explanation as above, the energy quantum of elec-tron transition can be shown to be proportional to thedifference in the radian frequencies between the incidentand scattered light, with the constant of proportionality~. This could physically explain Raman type scattering[24] as well as Einstein’s photoelectric effect [25], withoutinvoking any “quantum mystery”.

Further, using known relationship between the light’s

energy and the angular momentum (in a circularly-polarized state), with their ratio equal to the radian fre-quency (= ω) as per the classical electromagnetic the-ory [26, 27], the spin-like angular momentum associatedwith each energy-quantum of light (= ~ω), as deducedabove, would be equal to ~. All these combined prin-ciples of light would now provide a complete physicalexplanation, based on the UEG theory and classical elec-tromagnetic theory, for the nature of a “photon packet”in the Einstein’s photoelectric effect [25], or the Comp-ton/Raman type scatterings [23, 24], and similarly in thePlanck’s black-body radiation [7]. Accordingly, Planck’sinitial suspicion - that the quantum-mechanical “photonpacket” might not represent any “mysterious” fundamen-tal nature of the light itself, but could simply be a book-keeping tool that happened to properly model the absorp-tion/radiation of light [28, 29] - may after all be validatedby the new UEG theory.

The underlying mechanism of a dynamic, non-linearmixing processes, as discussed above, seem conceptuallyclear. However, its detailed understanding and modelingmay require development of a complete, dynamic UnifiedElectro-Gravito-Magnetic (UEGM) theory of an elemen-tary charge, interacting or mixing in the presence of anexternal electromagnetic radiation (light). Such a gen-eral theory is at this point premature, beyond the scopeof the present work.

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[3] A. Einstein, Annalen der Physik 322, 891 (1905).[4] J. C. Maxwell, A Treatise on Electricity and Magnetism,

Vol. I and II (Reprint from 1873) (Dover Publications,2007).

[5] A. Einstein, Annalen der Physik 354, 769 (1916).[6] E. Schrodinger, Annalen der Physik 384, 361 (1926).[7] M. Planck, Annalen der Physik 309, 553 (1901).[8] P. A. M. Dirac, Proceedings of the Royal Society A:

Mathematical, Physical and Engineering Sciences 117,610 (1928).

[9] A. Sommerfeld, Atomic Structure and Spectral Lines.(Translated by H. L. Brose) (Methuen, 1923).

[10] R. P. Feynman, QED: The Strange Theory of Light andMatter (p. 129) (Princeton University Press, 1985).

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[12] N. Cottingham and D. Greenwood, An Introduction tothe Standard Model of Particle Physics (2Ed) (Cam-bridge University Press, 2007).

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wiki/G_factor_(physics), Retrieved (2017).

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//en.wikipedia.org/wiki/Fine_structure_constant,Retrieved (2017).

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