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The GEM (Gravity-EM)Theory : the Unification

of the Strong, EM , Weak ,and Gravity Forces

of Nature

John E. Brandenburg PhD , Morningstar Applied Physics LLC

Madison USA

(Abstract)

This manuscript presents the initial results of the GEM

(Gravity-Electro-Magnetism) theory which unifies the

four forces of nature. The two long range forces

Gravity and Electro-Magnetism are first unified, and

out of this unification also proceeds the unification of

the short range Weak and Strong Forces. They are

unified under the two postulates that: 1. Gravity fields

are an array of electromagnetic cells and 2. The

separate appearance of Gravity and EM fields from

each other is correlated with the separation of protons

and electrons from each other as they emerge from

the Planck scale with the appearance of a compact or

hidden dimension. In the Standard Model all massive

particles are charged and move freely at short

distances and even photons spend time as charged

particles. The quark-electron split occurs based on the

asymmetry in dimensionality between space and time.

The proton mass is found by assuming Planckian

neutral pion fields inside the proton. The theory

produces the value of G: the Newton gravitation

constant, and the proton mass accurately from the

Planck scale with no free parameters. The theory

produces the values of the masses, charges and

spins for the pions of the Strong Force and the W and

Z bosons of the Weak Force as quantum Mie

scatterings off the compact dimension structures

associated with the proton and electron masses. The

Higgs Boson mass follows from similar formalism. The

GEM theory extends the Standard Model to include

Gravitation. The theory predicts a short lived, neutral

spin 0 particle will be found at approximately 22MeV,

that matter can emerge from the bare vacuum, and

that a basic cosmic parameter is the number 42.8503.

Keywords—GEM Unification Gravitation

Electromagnetism quarks, Strong Force, Weak

Force, Pions, W and Z Bosons, Higgs Boson

I. INTRODUCTION

According to present understandings, the cosmos, as

we know it, began with a tremendous explosion, the

Big Bang, that became the expansion of the universe.

This can be interpreted as the sudden appearance of

charged massive particles from the vacuum, along

with entropy. Such an occurrence can be understood,

in turn, as the result of the formation of a compact or

hidden dimension, leading to the appearance of other

particles and forces. This scenario is proposed in the

GEM (Grandis et Medianis) “the unity of the great and

middle” theory [1-5]. The GEM theory unites the

“middle” or “mesoscale” of particle classical radii with

“great” scales of both the Cosmos and Planck Scale.

The GEM theory is combination of two concepts- the

compact 5th dimension concept of the Kaluza-Klein [6]

theory unifying gravity and electromagnetism, and the

Sakharov [7,8] concepts of an electro-dynamic

vacuum-spacetime as the origin of an electro-dynamic

gravity, and CP Violation (favoring matter over

antimatter) in the Big Bang giving rise to hydrogen.

Under the conjecture of Dr. Alfred Luhen, (Private

Communication) one cannot create mass without

creating gravity, meaning the Higgs Boson, the quanta

of the mass generating scalar Higgs field, must be

fundamentally connected to General Relativity. This

fundamental connection is illuminated by the GEM

unification theory, as will be shown and is also

discussed in more depth in ref. [5].

A. The Theory in Summary

The four forces of nature consist of two long range

forces Gravitation and Electro-Magnetism with infinite

effective range, and two short range forces, the

Strong and Weak forces, with effective ranges of only

subatomic distances. Gravity shapes the stars,

planets, and galaxies, Electromagnetism illuminates

the universe and determines basic atomic structure.

The Strong force is responsible for basic nuclear

structure, binding the protons together against their

mutual electrostatic repulsion, and also causes the

massive energy releases in fusion that lights the Sun

and stars, and also the fission reactions that generate

power on Earth. The Weak force is responsible for

beta decay of radioactive nuclei. Whereas the long

range forces are well described by exchanges of

massless bosons, the photon and graviton, the short

range forces are best described as exchanges of

massive bosons. The pion is the exchange boson of

the Strong force outside the nucleons and the W and

Z bosons are exchange quanta of the Weak Force.

The effort to unify these forces began with unification

of the two long range forces, and then continued with

the discovery that the short range forces were unified

as well. In the GEM theory quantum electro-

magnetism is the basic underlying force that creates

the other forces, this reflected in the charged

character of all fundamental massive particles in the

Standard Model and their free movement at short

distances.

The resulting theory can be summarized briefly: 1.

It is postulated that gravity fields can be modeled as

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an array of ExB drift cells familiar from plasma

physics, making spacetime electrodynamic and

cellular in structure due to the presence of a compact

dimension. 2. It is also postulated that the separation

of EM from gravity is correlated with the separation of

protons and electrons from the Planck scale with the

appearance of a compact 5th dimension of subatomic

size. The presence of the compact 5th Kaluza-Klein

dimension required to have separate EM and gravity

fields in the vacuum also destabilizes the vacuum by

breaking its scale symmetry at the physical size ( in

cgs) ro =e2/moc2 where mo=(mpme) ½ with mp and

me, being the proton and electron masses

respectively. This predisposes the cosmos to the be

dominated by hydrogen. As proposed by Witten [9]

the presence of the compact dimension makes the

vacuum unstable. In the GEM theory the instability of

the vacuum leads to its decay into proton-electron

pairs, or hydrogen[3]. A physical interpretation of this

compact dimension is as electric charge.

In order to preserve a vacuum interval of zero length

the charges must split into a time-like charge: the

electron, and spatial part with three sub-dimensions:

the quarks in an image of spacetime. Since this can

occur many ways this must introduce entropy. The

mass of the proton is found by assuming Planckian

pion fields inside a classical radius. The proton is thus

stabilized and the quarks confined by a geometric

constraint of maintaining compact dimensionality.

This geometric constraint allows the proton to be dealt

with as a fundamental particle in the theory.

In a strange quantum phenomenon, the classical

electrodynamic radii of the electron and proton

support resonant Mie scatterings off the background

quantum ZPF (Zero Point Fluctuation) giving the

masses, spins and charges of the exchange bosons

of the Strong and Weak nuclear forces, which are the

pions and W and Z particles respectively and creates

a resonant Mie scattering Higgs Boson mass of

approximately mp/ ~128 GeV. It is found that the

spins and charges of the exchange bosons reflect the

intrinsic dimensionality of electrons and protons that

they scatter off of. The theory predicts a new, elusive,

neutral particle called an M* at approximately 22MeV

and that rare vacuum decays will occur, making

hydrogen and radiation out of empty space [5].

B. Outline of Approach

The GEM theory is based on simple physical concepts

and mathematical models derived from them. Like a

pathfinding journey across a vast wilderness, one

must travel light, carrying only basic essentials. The

GEM theory essentially combines the Kaluza-Klein 5th

dimensional approach with the Sakharov concept of

‘metric elasticity of space’ due to the ZPF. The

Kaluza-Klein approach gives both Maxwell’s

equations of EM and the Einstein Equations of

General Relativity with proper couplings. It also

requires a scalar EM field which resembles the Higg’s

field. Thus the mass producing scalar field and gravity

are born together in this theory. The Sakharov

approach gives the physical picture of spacetime and

particles as electrodynamic. Given the difficulty of

unifying the four forces of nature, it was decided to

achieve this by successive approximations, this theory

being the first level, with minimal constraints and

conditions. Thus, a rudimentary “Bohr Model” of field

unification results, that extends the Standard Model to

include Gravitation at low energies. Hopefully, like the

Bohr model of the hydrogen atom, the GEM theory

can form the basis for deeper and more sophisticated

understandings in the future and at length become the

basis for the engineering of the future.

In the remainder of this brief article, the basic physical

models of the GEM theory will be presented along

with their results. The quarks and electron will be

shown to arise from preservation of charge and

vacuum interval as an image of normal spacetime. It

is found that the proton, at least at the low energies of

interest here, is geometrically constrained to confine

its quarks and to be stable, and thus can treated as a

fundamental particle. A physical model of gravity as

electrodynamic will be presented. The separate

appearance of the proton and electron with the

appearance of the compact 5th dimension will be

modeled with precise calculations of the proton mass

and value of Newton Gravitation constant G resulting

from the vacuum. The line path integral method giving

rise to the Higgs Boson mass and exchange boson

masses will then be analyzed in terms of an exchange

of quanta with a background quantum ZPF.

II. THE POSTULATES, MODELS, AND BASIC RESULTS

OF THE GEM THEORY

The following explains how the basic concepts of

the GEM theory are turned into models and their basic

results.

A. Gravity Fields and Spacetime as Electrodynamic

The first basic postulate of the GEM theory is that

gravity fields can be synthesized as arrays of ExB

drifts familiar from plasma physics. The concept for a

synthesis of a gravity field from electromagnetism was

the outgrowth of the effort to achieve controlled

thermonuclear fusion, most specifically the magnetic

confinement of plasmas for fusion. As part of this

effort the motion of charged particles in magnetic and

electric fields was carefully studied and an effect

called an “E-cross-B drift” or ExB drift[10], was

identified.

Fig. 1. The ExB drift caused by crossed electric and

magnetic fields affects all charged particles identically and in

non-uniform E fields, but uniform B fields, can cause

acceleration.

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This effect is remarkable in that it affects all

charged particles identically regardless of charge or

mass. We can derive this model of a gravity field

simply by first assuming uniform E and B fields at right

angles to each other, as in Figure 1, for example, Ex

and Bz in the x and z directions respectively. We have

then for motion of a charged particle in the x and y

directions or r, , using esu units:

z

y

x

xB

c

V

qE

t

V

m

(1)

(2)

Where we have included an Ey for a curvilinear E

field. We can solve this by assuming a velocity

function of two parts, in x and y coordinates. Here we

make the simplification that Ex >>Ey , i.e. a particle at

the center of the region between the two plates in

Figure 1.

dosc VVV

(3)

z

x

dB

cE

V

(4)

in the y direction with the definitions

)(sin tVV c

y

osc

(5)

)(cos tVV c

x

osc

(6)

Where V is assumed to be a constant with V

Vd and we have defined

mceB

c/

(7)

Note this drift velocity shown in Eq. 4 is

independent of charge and mass.

If we leave the magnetic field uniform and vary the

E field at right angles to its direction, in the direction of

the drift, the particle will experience an acceleration in

the direction of its ExB drift in the y direction:

yy

E

B

Ec

t

Vx

z

xd

2

2

(8)

2

2

2

2

1c

B

E

z

x

(9)

This is easily confirmed by a particle simulation

where an electron and a ‘heavy positron’ of positive

charge but 10x the mass of electron are released in

uniform magnetic field but between two plates set at

an angle between each other, as seen in Figure 2.

Fig. 2. A simulation of an EM-synthetic gravity field with

the trajectories of an electron and a “heavy positron” of 10x

an electron mass are seen.

The gyro-motion radius ao of the particles seen

here vanishes in the limit of very strong magnetic

fields (Bz ) thought to be present in the vacuum

due to the quantum ZPF (Zero Point Fluctuation)

whereas the gravity produced velocity is cEx/Bz is

much less than light for ordinary gravity fields.

0

2

2 e

mc

B

E

a

z

x

o

(10)

We have found this physical model of gravity

fields as being composed of locally uniform magnetic

and varying electric fields. Flat spacetime then, we

can conceive of as being composed of uniform

magnetic and electric fields. But the vacuum is

observed to be massless, or even to have a tiny

negative mass density. How then, is the vacuum full of

powerful fields to create an ExB drift array to create

gravity, but yet has no mass density? To be

consistent with GR, the mass density of the very E

and B fields causing gravity must be considered as a

source of gravity. This problem is not unique to the

GEM theory but is a pressing problem for any theory

of a quantum vacuum.

Einstein discovered the ZPF (Zero Point

Fluctuation) in 1910, showing that as a consequence

of the Heisenberg Uncertainty principle the vacuum

itself must be populated with EM modes. The physical

z

x

y

yB

c

V

qE

t

V

m

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presence of these modes can be seen in the

existence of the Casimir Effect. However, the fact that

these modes do not create an observable mass-

energy density in the vacuum is one of the great

mysteries of physics. This problem was considered by

the great Russian physicist Yakov Zeldovich [11] who

argued that a ZPF mass density term would appear as

a Cosmological Constant term, allowed by General

Relativity, and that another such term existed to

cancel the ZPF term. The Zeldovich Cancelation term

would then be required for a massless vacuum that

we experience. Here we have the basic field equation

for GR including the Cosmological Constant :

gT

c

G

RgR 4

8

2

1

(11a)

0

84

gT

c

G

(11b)

GEM theory is an alloy of the concepts of

Sahkarov [7], in gravity’s relationship to the EM ZPF,

and the Kaluza-Klein theory [6] of EM-gravity

unification, and its relationship to a hidden 5th

dimension. To see this we begin with the Hilbert

action principle in 4 spacetime dimensions with a zero

cosmological constant.

41

)16(dxgRGW

(12)

where R is the Curvature Scalar. Finding the

extremum of this action leads to the vacuum gravity

equations with canceled ZPF EM fields.

0

2

1 RgR

(13)

Sakharov interpreted the integrand as a real

energy density. He equated this energy density to a

perturbed quantum EM ground state spectrum of ZPF

(Zero Point Fluctuation) due to the Heisenberg

Uncertainty principle applied to the vacuum EM field.

The zeroth-order ZPF is assumed to vanish due to a

canceling cosmological constant term proposed by

Yakov Zeldovich [11], who was a colleague of

Sakharov’s. This “Zeldovich Cancelation” ensures that

only the perturbations due to curved space cause the

effect of the ZPF to appear. Sakharov calculated the

perturbed part of the ZPF due to spacetime curvature.

He then derived a formula for G in terms of an integral

over the perturbed ZPF:

5

2

*

5

2

1c

d

o

c

GW P

(14)

oP

PTrc

rc

G2

4

23

(15)

where P is the Planck frequency c/rP, where rP =

(G

/c3)1/2 and the energy density To =

c/rP4 is the

Planck scale energy density. This is consistent with a

physical model of gravity forces as due to imbalances

of the EM Poynting vector, S= cExB/4 ( in esu) or a

radiation pressure P=<S>/c. The second example of

radiation pressure or Poynting vector acting on

particles in a box whose walls absorb and emit

radiation is shown in Figure 3. In Figure 3, the left

figure shows hot-bright particles in a dark-cold

enclosure, the right figure shows cold–dark particles in

a hot–bright enclosure. Mutual radiation pressure

forces are shown by block arrows.

Fig. 3. Radiation Pressure Affecting Particles in an

Enclosure. Left: Two hot ideal radiaiors in a cold box repel

each other by mutal radiation pressure. Right : Two cold

ideal radiators in a hot box attract each other due to mutual

shadowing.

As was shown in the first section an ExB or

Poynting drift field, with constant B and E growing

stronger in the direction of the drift, can produce

gravitational-like acceleration of charged particles of

all charges and masses, as shown in Figure 1. The

Sakharov model for the gravitational force is basically

that of a radiation pressure Poynting field produced by

non-uniformities in the ZPF and is successful in the

sense that is self-consistent (see Figure 3). It is

understandable that Sakharov would arrive at this

physical model for gravity, since he worked on the

Soviet Hydrogen Bomb where radiation pressure is

crucial. We can derive the same idea, in relativistic-

covariant form, from the expressions in the first GEM

article [3], where the zeroth-order ZPF stress energy

was caused to vanish. That is we will explain the

Zeldovich Cancelation as EM-gravity unification

physics.

The following equations show this theory in

covariant form. It can be seen that if the metric tensor

for gravity is written as a normalized first part of the

EM momentum-stress tensor:

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However, if the fundamental structure of

spacetime is electro-magnetic we can write the metric

tensor as an electromagnetic tensor[3] :

(16)

For the case of statistically uniform isotropic

vacuum fields it is easy to see that the elements of the

gradient of the metric will vanish.

When this expression is used, the EM stress

tensor for the ZPF can be made to vanish as shown in

the first article on the GEM theory [2].

(17)

Here we assume a model of spacetime containing

adjacent regions of strong E or B fields. The particles

however, travel as wave packets and sample a

volume swept out by a wave-front, thus they see an

average spacetime. An average over volume so that

<B2>=<E2> and <EB>=0 results in a volume average

of two metric forms one dominated by electric flux, for

instance, in its local direction Ey

0000

0200

0000

0002

g

(18)

And another, in an adjacent region, by magnetic

flux also in By

2000

0000

0020

0000

g

(19)

Upon volume average, assuming large scale

isotropy, we recover the familiar Lorentzian flat space

metric.

1000

0100

0010

0001

g

(20)

Using the observation that, for nearly flat

spacetime, gravity fields and their potentials are

linearly additive, we can derive the effective gravity

potential for the ExB drift model of gravity assuming

the EM form of the metric tensor required for self-

censorship. We then find for the upper left diagonal

element of the metric tensor: goo , and from it the

effective Newtonian gravity potential.

222

222

222

2

1

22

000

000

000

000

2

xyz

zxy

zyx

BBE

BBE

BBE

E

EBg

(21)

We have then for perturbing fields and a gravity

potential in terms of an E×B drift model of gravity that

is valid for both DC and oscillating E fields, where

charged particles are accelerated into the strongest

part of the perturbing E field. How then does the

Newtonian gravity potential between charged particles

come about? We begin with the expression for a

gravity potential in terms of E and B fields in the

vacuum, where VD is the particle drift velocity in the

crossed E and B fields:

2

2

22

2

2

00 ,/21 x

EE

EB E

cg

(22)

We obtain from GEM Metric tensor to first order in

Ex/Bz <<1 and averaging with a flat metric.

2

2

2

/21 B

E

cx

(23)

As was first proposed by Puthoff [12], it can be shown

[13] that point charges floating in a ZPF will create

and interference pattern E2 between their scattered

1/r radiation E fields and the impinging ZPF E fields,

leading to a Newtonian potential around each particle.

It was also pointed out by Puthoff that under the

Standard Model all fundamental massive particles are

charged and move freely at short distances,

consistent with electrodynamic gravity. QED ensures

that even photons spend part of their time as charged

particles and are thus subject to electrodynamic

gravity [5]. Using the metric formulation of Eq. 16 and

spatial averaging a full Schwarzchild Metric: grr= 1/(1-

2GM/c2r) , arises statistically around each charged

particle [13, 5].

FF

FF

g4

0

4

FF

gFFT

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B. Particles From the Vacuum: The GEM Concept

We have the vacuum quantities associated with the

Planck scale, the Planck length, the Planck mass,and

the Planck charge , respectively:

3

c

G

rP

(24a)

G

c

MP

(24b)

cqP

(24c)

The simplest result then would use the vacuum

derived Planck charge qv as the length of the path in

the 5th dimension. Using this we could obtain the

proton mass as the simplest result.

We must now consider other constraints to such a

theory. Nothing, especially the cosmos itself, is by

definition simple. In particular, the appearance of one

particle does not increase entropy in the universe, and

entropy requires complexity. Also, we must consider

that a charged particle cannot simply pop out of the

vacuum without violating the electromagnetic

constraint of charge neutrality. So the same simple

process of a path integral allowing the appearance of

a proton must also allow the appearance of an

electron to balance it and to maximize entropy.

Therefore, we must have the proton appear as part of

a system that includes the electron, so that hydrogen

results:

ep qq

(25a)

ep qeeq ,

(25b)

Another constraint occurs because the path length in

the vacuum that cannot be simply a distance, but

must be a spacetime interval. In the vacuum state all

particles must be masses and move at the speed of

light and have a spacetime interval of zero:

)( 222

2

oooo zyxr

(26a)

0

222 oo tcr

(26b)

It is seen that the appearance of the new hidden

dimension occurs in a form analogous to the splitting

of a canceling charge pair of particles from the

vacuum, by splitting of a quantized light-like, or

vacuum, space-time interval of length zero. In the

GEM theory the hidden dimension size, where the

hidden dimension can mix with the non-hidden

dimensions, is the quantized particle size. The hidden

dimension quantities are thus able to mix with the

normal spacetime quantities because they are similar

at smaller scales. This will lead to, as we experience

them, two particle types. One is associated with the

time-like portion of the constrained interval, leading to

a one-dimensional scalar character, an electron, and

another of equal size with a space-like vector

character having three constrained sub-dimensions, a

proton. The gravitation constant G, functions in the

vacuum as the “interpreter” of charge into either mass

or distance. Thus, ironically, charge and mass, the

source terms for EM and gravity, are unified already in

the vacuum quantity G, which has units of charge to

mass ratio squared in the esu system used here.

o

rcGq

4

/

(27a)

))(/( 222

42

zyxo qqqcGr

(27b)

2

4222 )/( too qcGtcr

(27c)

Therefore, the quantized vacuum scale length, the

Planck length, gives birth to a quantized larger scale

hidden dimension. Because the quantized hidden

dimension is an image of macroscopic space-time in a

light-like interval, and its structure is part of a split

“lightlike” spacetime where charge q is analogous to

macroscopic dimensions as a length, we have charge

conservation and interval conservation. We obtain

from these conditions the following constraints on the

charges of the particles:

3214 qqqqqo

(28)

2

3

2

2

2

1

2

4

2qqqqqo

(29)

where the subscripts, 1,2,3,4 denote x,y,z,t the

corresponding time or space dimensions in the

unconstrained Cosmos.

Thus, the space-like portion of the split interval, the

proton, has three sub-dimensions that we interpret as

quarks or sub-charges, while the electron acts like a

single entity.

This concept then makes the electron-quark family a

reflection of the dimensional assymetric of spacetime,

with a scalar time and a three dimensional spatial

dimensions. However, we have here specified the

Planck length as the shared radius of the quarks and

electrons. But the physics of the world depends on

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the much larger scale of subatomic particles. Here the

electrostatic radius of the electron enters as the final

“deployed” length for the electron. By the requirement

The default radius upon “full deployment” of the

hidden dimension and its physics would be the

electron electrostatic radius rc=½ e2/mec2=1.4x10-13cm

where we assume this radius will be shared by the

quarks so that we have also rc = ½ ( q12 + q22 + q32)

/mec2 and this is the nucleon radius rn 1.4 x10-13cm

[14]determined by Strong force scattering, and also

the charged pion Compton wavelength, considered

the range of the Strong Force.

Thus, the conservation of vacuum interval and charge

neutrality requires that the electron and proton share

the same radius, as is approximately observed. This

requires two conditions on the three dimensional array

of quark charges

This concept of the electron and proton being born

together explains both quark confinement and the

absence of proton decay as geometric requirements,

seeing as the proton must preserve its dimensionality

in quark space. That is, it is three dimensional and

like any three dimensional object it cannot become an

object of lower dimensionality.

This can only be satisfied by a SO(3) symmetry group,

similar to the SU(3) symmetry group of conventional

quark theory.

C. The Charges of the Quarks

Quarks in three colors appear naturally in the GEM

theory. As was previously discussed the Kaluza-Klein

fifth dimension can be considered to be a new

dimension which can replace either time or space in a

light-like interval, as was seen in Eq. 26 a, b. The

fifth-dimension then becomes a constrained image of

either the time or space portion of spacetime and thus

has four sub-dimensions. The electron corresponds

to a “time-like” or scalar entity while the proton

corresponds to a space-like component, having three

sub-dimensions. We can minimize the volume of this

three-space, given the two constraints of charge

conservation and the conservation of mesoscale

radius, defined in Eq. 28, 29, which is a constraint on

the sum of the quark charges, and sum of the squares

of quark charges. We have then the constrained

relaxation of the system, in the form a Lagrange

multiplier system:

)()( 3212

2

3

2

2

2

11321 qqqqqqqqq

(30)

Where we minimize the three-volume formed by the

quark charges: q1q2q3, subject to the constraints on

their total charge and interval from Eq. is that of the

electron (in electron units)

Where we minimize the three-volume formed by the

quark charges: q1q2q3, subject to the constraints that

their total charge is that of the electron (in electron

units)

1

321 qqq

(31)

And the sum of their squares is also unitary, so the

classical radius of the compound particle is that of an

electron:

1

2

3

2

2

2

1 qqq

(32)

We have then, upon varying the values of q1, q2, q3

respectively, the three equations:

02 23121

qqq

(33)

02 22131

qqq

(34)

02 21123

qqq

(35)

which have the solutions:

9

2

3

1

21

(36)

3

2

,

3

1

321 qqq

(37)

This corresponds to the standard quark model, and

the second, trivial, solution is that of an electron with

q1 =-1 and q2 and q3 =0. Thus, in solving the problem

of the structure of a 5th dimension, one finds that its 3-

volume, upon being minimized, with constraints, yields

the charges of the quark system. Thus, the GEM

theory is actually compatible with the standard model.

In the GEM theory, the splitting apart of the proton

and electron is correlated to the splitting apart of the

gravity and EM forces. In the Standard Model

context, this means that baryon and lepton number: B

and L respectively, are not conserved but their

difference (B-L) is conserved and the non-

conservation of B and L separately occurs at the

Planck scale, where gravity and EM unify. The

appearance of charge and mass at the subatomic

scale occurs with the appearance and deployment of

the 5th dimension, which is slightly smaller than the

EM cross-section of the electron. This means that,

instead of subatomic particles being considered

points, they must be treated as objects of definite size

similar to the 5th dimension radius. This means that in

the presence of the vacuum ZPF the structural sizes

of the particles support resonances, and these

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resonances in-turn take on a quantum existence of

their own.

In quantum electrodynamics, it is found that the sizes

of various quantum objects can be understood as

being created through orders of EM interaction. The

Bohr radius of the hydrogen atom, and the Compton

radius of the electron, for instance, can be found as

the electron classical radius re =e2/mec2 for instance,

can be found as the 1/

2, and 1/

respectively times

the electron classical radius. However, the

electrostatic radius for the electron is ½ the electron

classical radius. This factor of ½ can be understood

as the difference between monopole or “scalar” EM

interactions, which cannot propagate farther than re

and dipole “vector” EM waves which can propagate.

C. The Mass of the Proton

The proton has inside its radius of approximately

rc, three dynamic entities, quarks, as a reflection of

the space-like structure is acquires when the 5th

dimension split the vacuum spacetime interval. The

quarks are inseparable, and cannot be seen in

isolation. In the GEM theory this is due to the fact that

the proton is a three-dimensional object and cannot

be made into something of lower dimensionality, just

like a rubber ball can be squashed but not reduced to

infinitesimal thickness, when released from pressure it

rebounds to its normal spherical shape. What also

occurs in the GEM theory is that the proton is isotropic

and spherical and this means that the quarks are best

modeled as chaotically mixed at all times. In the GEM

theory the proton is full of entropy.

We can therefore model the proton, since we consider

it full of chaotic EM fields as, a spherical shell of

radius rc full of Planckian radiation fields, one field for

each of the 3 color charge fields(see Figure 4.) We

will consider that the electric charge resides on the

surface of the shell, which is full of neutral

mesons.

We will consider the shell to be thin. We will assume

an emissivity of close to one

1.0 so the Black Body

model will be valid. We will choose the temperature of

the Planckian fields to be kT = m

oc2 = 264.15mec2,

the mass of the neutral pion, which is what would

occur if every quark was accompanied by its

corresponding anti-quark. Black Body modes of

longer wavelength than the radius of a spherical cavity

are cut off, however, the wavelength of energy

maximum for a Planckian distribution is

approximately-1/5 that of

= kT/(hc) =9.183 x 10-13

cm where h is the normal form of Planck’s constant. A

cutoff of wavelengths longer than that corresponding

to kT thus leaves approximately 97% of the energy in

shorter wavelength modes intact, thus such a cutoff

does not violate our Planckian assumption.

Fig. 4. A. A model of the proton has having three rapidly and

chaotically moving quarks. B. A model of the fields in the

proton as being at maximum entropy, due to quark free

motion, that is: Planckian.

Therefore, we will assume the proton is full of EM

energy W in 3 Planckian modes or colors in a volume

Vc =4rc3/3 of a sphere of radius rc:

3

45

)( )(

15

8

30.97 hc

kT

VW c

(38)

Here the Planckian modes must be considered

independent, so they simply add to each other. Using

the fact that rc(m

oc2/hc) = 1/6.518, and assuming an

emissivity = 97% we obtain approximately:

3

3

25 )15.264(

45

16

0.946

o

c

e

r

cmW

(39)

)004.1(6

06.277 15.264

12.1)94.0(6 2525 cmcmW ee

(40)

25

6cmW e

(41)

Therefore, the Lenz-Wyler formula, mp/me =65 which

is accurate to 17 parts per million, can be derived to

high accuracy from a simple model of the proton as

containing 3 independent Planckian fields of

temperature corresponding to the rest energy of the

neutral

meson. This means that the proton-electron

mass ratio hides in the Stefan-Boltzmann constant,

and that entropy exists even in the subatomic scale.

Thus we can see that the basic electron-quark picture

of the structure of matter can be derived from its

appearance from the vacuum as a charge opposed

pair but also with the constraint that the charges act

as spatial lengths and preserve a vacuum interval.

However this analysis also indicates that quark

confinement and proton stability have their origins in

topology, and hence, at least for low energies, the

proton-electron pair can be treated as a pair of

fundamental particles.

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D. The Value of G and the Proton Mass From the

Planck scale

The second GEM postulate is that Gravity and EM

forces separate in correlated way with the appearance

of electrons and protons from the Planck Scale. We

can examine this by a Gedanken experiment where

we squeeze a single atom of hydrogen in sphere until

it becomes the size of a Planck radius and forms a

Blackhole. The Blackhole then evaporates via

Hawking radiation [15] into a shower of gamma rays

and particles and antiparticles and thus destroys the

baryon and lepton number of the original electron ad

proton.

Let us consider a “Gedanken” experiment [3]

where a single atom of hydrogen is confined in a

sphere whose size is shrunk continuously until it

reaches approximately the radius of a Planck length rP

= (G/c3)1/2, (See Figure 5.) at this point the electron

and proton making up the hydrogen will have long

since ionized and increased in mass due to

Heisenberg Uncertainty. The proton and electron will

then form a Black Hole which will then undergo

Hawking Evaporation [15] (Figure 5.) into a shower of

photons, particles and their anti-particles. It is noticed

that this evaporation will destroy the baryon and

lepton number of the proton and electron, leaving only

the quantum numbers of the vacuum. This is in

accordance with the observation that many of the

quantities we observe in the present day cosmos are

“running constants” and change under radically

smaller spacetime curvature, to merge eventually with

Planck Scale quantities. Therefore, what we consider

to be physical constants may be tied to specific range

of scale-size for the radius of curvature of spacetime,

and these physical quantities will change dramatically

when the radius of curvature approaches the Planck

Scale.

Fig. 5. A Gedanken experiment where 1. A single atom

of hydrogen, a proton and an electron, is shrunk within a

sphere 2. And ionizes. Finally it reaches the Planck size 3.

And becomes a Black Hole, whereupon, 4., it undergoes

Hawking Evaporation and becomes a cloud of gamma rays,

matter and antimatter so that original hydrogen is lost.

In the previous chapter we were able to formulate

gravity fields as electro-magnetic but this appeared to

require a cellular nature for spacetime, in order to

allow gravity fields, and spacetime itself, to be

composed of regions of powerful electric and

magnetic fields. At first, such a physical picture seems

perfectly consistent with the concept of the Planck

Scale, where spacetime is a foam of scale size equal

to the Planck Length: rP = (G/c3)1/2. However, at the

Planck scale only a limited group of physical

constants are possible and these do not include many

of those constants that describe the universe we

experience. We can imagine that in the primordial first

instants of the Big Bang the entire universe was in a

compressed state at the Planck Scale but that it

expanded form this scale to “deploy” a new larger

scale that carried with it the physics of the cosmos we

know. Therefore, in this chapter we must further

quantify the concept of cellular spacetime to define a

range of scale size for a cellular structure in

spacetime that is distinct from the Planck Scale and

represents an expanded scale that emerges from that

primordial scale.

Thus, based on our Gedanken experiment, we

consider that any cellular scale size in the vacuum is

“fully deployed” to its proper size in the present

cosmos, and helps determine its physics, but this

scale size is crushed out of existence at the Planck

scale, where hydrogen disappears. Accordingly, our

Gedanken experiment to squeeze a proton-electron

pair into the vacuum, also squeezes the cellular scale-

size into the Planckian vacuum.

Let us assume however, in our thought

experiment, that the wave functions of the proton and

electron, carrying with them all their identifying

quantum numbers have merged as the Black Hole

forms at the Planck Scale, that is, the radius of

spacetime local spacetime curvature r rP before

this happens. To model this behavior we will use a

simple U(1) symmetry model for the proton and

electron masses, considering that since all information

disappears we will formulate the model only in terms

of charge q ,mass m, and mass ratio mp/me = .

Accordingly we have a simple U(1) mass model:

)sin()cos(

oo immm

(42)

The U(1) symmetry is complex valued with real

and imaginary mixed together. Particles with

imaginary rest masses are tachyons, particles that

move faster than light. The simplest physical

interpretation we can make for such imaginary

particles is that they are particles that have fallen

inside the event horizon of a Black Hole, accelerating

beyond the speed of light in the process and being out

of communication with the real particles of the

universe. This is important at the Planck scale

because there particles appear out of the vacuum,

form black holes and disappear, so that spacetime is

effectively a “foam.” Foamy spacetime features Black

Holes that are so closely packed that it is impossible

to determine whether a particle is inside or outside an

event horizon. Thus particles at the Planck scale can

be physically represented as complex, half real and

half imaginary, with masses satisfying a U(1)

symmetry. So the Planck scale is completely chaotic,

mixing imaginary masses with real ones.

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Let us imagine that at the Planck scale everything

becomes simple, the EM and gravity forces unify to

one force obeying U(1) symmetry and lepton and

baryon number also disappear, in fact everything

disappears but “vacuum” quantities: G, c, and , the

Newton gravitation constant, the speed of light , and

the rationalized Planck’s constant respectively. These

determine the Planck Length: rP = (G/c3)1/2. Planck

mass MP = (c/G)1/2, and Planck charge qP = (c)1/2

However, let us assume also that since EM forces still

exist and enforce quantization of charge and the

charge neutrality of the vacuum, so that quarks

remain grouped in groups of 3 having one positive

electron charge to cancel the charges of electrons.

Thus, a plasma consisting of quarks and electrons

occurs at the Planck scale, but protons are still

identifiable as groups of quarks because the vacuum

must be charge neutral.

Therefore, at the Planck scale we can have

Planck masses of real and imaginary masses

consisting of a quark-electron plasma which can still

be represented as relativistic mass-dilated electrons

and protons because of the requirement of charge

neutrality.

On the other end of the spectrum of sizes we

assume a “fully deployed” cellular scale of subatomic

size, which we propose to be of the size range

2

2

cme

r

o

o

(43)

where moc2= (mpme)1/2c2=21.897MeV so that the

size scale is neutral between protons and electrons,

and a size parameter which is determined entirely by

low energy physics quantities. We will call this energy

and size scale the “mesoscale” because it lies

between the Planck Scale and the Cosmic Scale.

This is all based on the GEM postulate that

baryon and lepton number disappear at the Planck

scale coincidentally with the separate identity of

Gravity and EM fields. The vacuum is thus as simple

as possible at the Planck scale, only particles and

anti-particles of Planck mass and charge exist there

and gravity and EM are basically merged.

In contrast the appearance of the cellular scale

size as the universe expands from the Planck scale

represents the appearance of a new degree of

freedom. This is similar to when a molecular layer

evaporates from a surface and becomes a 3-

dimensional gas. We will consider then, accordingly,

that the expansion from the Planck Scale allows the

appearance of a 5th dimension, represented by the

appearance of a new scale size : ro, which is the

appearance of particles: electrons and protons with

their classical radii. That is, the appearance of the 5th

dimension allows the appearance of the mesoscale.

The expansion of the universe from the Planck Scale

thus allows a new 5th dimension, a new degree of

freedom, of much larger scale size than the Planck

Scale, to appear, and with it new physics. But how

shall we include this into our U(1) mass model?

The angle , we will consider, in this model,

corresponds to charge state and is thus quantized as

a canceling pair o, even in the Planck Scale.

However let us model the appearance of the fifth

dimension by allowing this angle to become an

imaginary rotation angle to give two real particle

masses corresponding to an "up" quantum state and

"down" quantum state from the U(1) symmetry. Let us

therefore assume a model of a scale dependent

vacuum where the existence of a 5th dimension

breaks the vacuum scale invariance. We now have for

the mass model:

)exp( oo

mm

(44)

Where is a parameter such that = 0 at r ~ rP .

That is, near the Planck scale, when the 5th

dimension does not exist and thus protons and

electrons are identical. At the other extreme = o

when the 5th dimension is “fully deployed” and

separate particle masses are generated at o from Eq.

44 as r ro. This suggests a formula o~ln ln (r/rP),

so that o very strongly near the Planck scale but

varies very little at everyday scale.

)exp( o

e

p

m

m

(45)

Where is a mass asymmetry parameter, being

the square root of the mass ratio of the electron to the

proton.

Thus, even though mass symmetry is broken in

terms of the new 5 space we experience, it is actually

preserved in terms of a geometry involving the

imaginary angles in the original U(1) symmetry. That

is, the new particle dimension looks symmetric in the

space of imaginary angle.

We require that this simple mass model give the

behavior as mo MP , 1 as r/rP 1

To obtain a smooth transition to the Planck scale

as curvature collapses to the Planck length the angle

o must be dependent on curvature near the Planck

length but very insensitive to it at larger curvatures,

where the new fifth dimension is fully deployed. Based

on the lack of observation of proton decay, lepton and

baryon numbers are obviously strongly conserved.

The simplest model to obtain this mixture of scale

sensitivity with curvature r is for the rotation angle to

have the dependence on our 5th dimensional

deployment parameter

)ln(

(46)

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)/ln( P

rr

(47)

So that lepton and baryon numbers disappear,

with 1 as r rP

Therefore, in the GEM model, the separate

appearance of proton and electron pairs from the

vacuum is, like the separate appearance of EM and

gravity forces, linked to the appearance and full

development of the fifth dimension. The physical

description of this new 5th dimension is that it comes

into being at scale size that corresponds to the size of

a particle classical radius ro.

However, it is apparent Eq. 47 cannot be correct

near r = rP where 1, thus we must modify the

formula slightly so that both the right and left side go

to zero smoothly at r = rP and = 1 , where we

assume goes to one with the vanishing of a small

parameter 0

1

(48)

We rewrite Eq. 29:

2

1

ln

P

r

r

(49)

We now see that both sides of this expression go

to zero as both quantities r/rP and 1 as they should.

We have added the correction factor as second order

in , that is -2 = me/mp to be similar to the reduced

mass correction of the conventional dynamics of the

electron-proton system. Therefore, when the new 5th

dimension is “fully deployed” we have for

=42.8503…

2

1

ln

P

or

r

(50)

We note how both sides of this expression go to

zero with leading order in , as r/rP 1:

3

1

ln 2

P

r

r

(51)

We must also correct the mass formula so that mo

= MP at the Planck scale. So we must write, using the

Planck charge qP . We will assume that the normalized

charge state assumes the role of determining mass

q/e but that as we approach r = rP that e qP = (c)1/2

so that 1 and also all masses approach the

Planck mass mo MP

)lnexp(

eq

mm o

(52)

This formula gives the observed mass difference

between the electron and proton and also ensures that

this difference disappears as r/rP 1. However, not

only mass the mass difference disappear but the mass

mo must undergo the process mo MP, as 1 We

therefore extending this formula, where normalized

charge controls mass, to obtain

)lnexp(

e

q

Mm P

Po

(53)

Where this gives the proper limit as mo MP , 1.

However, we also require the condition, as mo

MP that we must have the condition that r , rP , mo and

MP have the proper quantum relationship ro = /(moc)

so that near the Planck scale

033lnlnln

P

o

P

o

oP

Po r

r

M

m

rM rm

(54)

We obtain this behavior in for the mo system by

modifying Eq. 53, like we did the expression in Eq.

50, with a second order term to ensure the proper

behavior for mo, as -1/2 and 1

)lnexp(()ln)1(exp( 2/1

e

q

Mm P

(55)

This requires, at normal spacetime curvature and

charge state q/e =+1 the expression for the proton

mass , with MP = 2.17645x10-5g :

gxMm Pp

242/1 106665.1)ln)(exp(

(56)

This expression agrees with the observed rest

mass of the proton 1.67262 x10 -24 g , to 3.6 parts per

thousand and goes to the proper limit of mp = MP as

1.

We now return to primary expression relating

normalized spacetime curvature to the mass ratio.

The expansion of the effective curvature to ro,

which we will term the “mesoscale” radius -since it is

the range of scales of classical particle radii and lies

between the Planck and Cosmic scales- then yields,

by Eq. 50 the relation:

....850.42

1

ln 2

P

or

r

(57)

If we examine the ratio of the mesoscale radius to

the Planck radius, we discover it is also a quantum

normalized ratio of coupling constants between gravity

and EM,

2

2

o

P

oGm

e

r

r

(58)

This suggests that the gravitational interaction

between two masses is mediated by the emission and

absorption of EM photons. This is as we would expect

if both EM and Gravity were both part of the same

general phenomenon. The formula of Eq. 39 can be

inverted to find an accurate expression for the

gravitation constant.

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We thus obtain for the gravity constant, using the

measured value of the proton electron mass ratio, to

first order:

228

2

2

1067384.6

)/1(2exp

gcmdynex

mme

G

ep

(59)

this expression is within 3.6 parts per 100

thousand of the measured value of G:

6.67408 x10-8 dyne-cm2 gm-2. Note that the

expression gives proper limiting behavior at the

Planck scale, yielding G even as all masses go to MP ,

e2 c and and 1.

Therefore , a simple mass model, bridging the

lepton-baryon mass system at its lowest energy end-

members the electron and proton, that fulfills the

expectation of our Gedanken experiment and has

proper limiting behavior at both the Planck scale and

scale of the fifth dimension, which is the subatomic

scale, yields accurate expressions for both the proton

mass and the gravitation constant.

A formula similar to Eq. 59 was originally

published in approximate form in 1987 and corrected

in1988 [1] and bears some resemblance to the

formula published by T’Hooft [16] based on

“Instanton” theory that combines Hawking Evaporation

with Thermal physics.

III. THE EXCHANGE BOSON MASSES AND SELECTION

RULES GOVERNING THEIR GENERATION

The existence of a hidden 5th dimension in an

otherwise 4 dimensional space time breaks the scale

symmetry of the vacuum by inserting a length at which

physics must change. Since the 5th dimension is

independent of the other coordinates, the 5th

dimension looks like a spherical particle from a

distance in any direction, that is, it looks like a particle

of a certain size. It is a well-known phenomenon in

physics that particles of well-defined sizes in

otherwise uniform media support Mie scattering, that

is, they support both radial and surface resonances.

At the suggestion of Dr. Eric Davis (Private

Communication) the consequences of such structural

resonances were explored.

Mie scattering would be expected on a hidden

dimensional structure in the presence of the ZPF and

would give rise to particle quanta. We will also

consider the classical particle surface of charged

particles as a spherical surface that can support Mie

structural resonances. This seems, at first, very

unlikely, even bizarre. It is like General Motors

walking into a bar, and having a drink. The classical

surface of a charged particle appears, at first glance,

to be a mathematical artifice and not to define a real

dynamic entity. However, since this is quantum

mechanics, even seemingly unlikely and bizarre

events can contribute to observables. This also shows

the underlying electromagnetic character of the short

range forces. We will call the particles caused by

these quantum Mie scattering events “Mieons.” Two

fields are available in the ZPF to drive quantum Mie

scattering, these are the EM field and Radion field,

which must come into being as part of the Kaluza-

Klein scheme for having both EM and Gravity and

which has the source term E2-B2 [17]. We will identify

EM resonances with the factor 1/ and we will identify

the Radion resonances with the factor . This will give

rise to new particles, Mieons, at resonances on the

hidden dimension. The EM resonances will be vector

resonances around the circumference of the spherical

classical surface. The Radion field, being a scalar

field, would be expected to produce, at least in lowest

order, a simple radial mode inside the spherical

classical particle surface. It will also give rise to

Mieons on resonances on the classical electrostatic

radii of the electron and proton, which will behave like

conducting surfaces to first order. The fundamental

and lowest order resonances can be expected to be

most important as determined by radial and

circumferential resonances. The fundamental

resonance will be considered as well as a 5-fold

resonances because the 5 dimensionality of the entire

system for low intensity oscillations.

Since the concept of a quantum resonant path on

a classical charged particle surface seems to be but

one of many quantum possibilities, we will generalize

it to include alternative paths of lower quantum

probabilty, in orders of our coupling strengths, and

1/. Therefore, we express mathematically this

concept of Mie resonances, generalized to include

virtual paths of reduced probability of order , for the

EM ZPF, or 1/, for the Radion field, by the

following, for each spin component of the boson:

NhcE EM /

(60)

c

e

NcE R

2

/

(61)

Where we have for the path lengths for EM ZPF

excitations, where N and P are integer multiples of ½,

and express for the Mie quanta agency:

)22( ccEM rPr

(62)

And likewise for Radion excitations, which are

radial:

)2/2( ccR rPr

(63)

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Where E is the particle rest energy, c, is the

speed of light h is Planck’s constant. Rearranging we

obtain for the EM ZPF:

)1()22( Pr

cN

rPr

Nhc

Eccc

(64)

)1(

22

P

cNm

Ec

(65)

Where mc is the particle mass generating the

classical radius

c

e

NcE 2

/

(66)

)2/2( cc rPr

(67)

)/1(

22

P

cNm

Ec

(68)

The scattering of quanta out of the ZPF by a

particle will imprint the quanta with the character of

the particle form which it scatters. It must give a spin-

state dimensionality of a scalar spin-0 particle off the

time-like-scalar nature of the electron and a vector

spin-1 particle off the space-like-vector proton. The

simplest scatterings will be reactive charge state off

the charges of the electron-proton system.

Fig. 6. A quantum Mie scattering caused by a

fundamental resonant excitation vector on a classical

particle surface

Fig. 7. A quantum Mie scattering caused by a

fundamental Radion ZPF resonant scalar excitation of a

classical particle shell.

A. The Simple Mie Scattering Results

We begin with the simplest case where N=1/2 and

P=0 at classical radius of the mesoscale particle rc =

ro/2. We then obtain the mass of the proton as a

Radion excitation.

op mm

(69)

We then obtain , under the same circumstances of

N=1/2 , M=0 for an EM ZPF scattering, with

mo=21.896 MeV

MeVcmm oc 6.3000/

2

(70)

This mass is then the EM ZPF Mieon associated

with hidden dimension and is very close to the mass

of the elusive (3000) baryon [18] at a mass of

3000MeV, the eta-c charmed scalar meson, at a mass

of 2983.6 MeV with no charge or spin, and the much

longer lived long lived J/ vector meson at

3096.9MeV with spin 1. So this a mass- energy region

of much activity, as we would expect if it

corresponded to a Compton wavelength nearly

matching the hidden dimension size.

We then proceed to look at the simple cases N=1,

P=0, or first order, Mieons resulting from resonant

modes on the electron classical surface. We obtain

from Eq. 45:

MeVcmm e0.140/2 2

(71)

Which is the mass of the charged -meson which

has spin 0. At first it is confusing to associate the

electron classical radius with the proton, however

because CP violation favors matter over anti-matter

the existence of positive charge of +e must induce

negative electrons to appear in the vacuum at that

radius. This means even though it is a proton, virtual

electrons are present around it because of QED. This,

and fact that positive charges are treated differently by

nature than negative ones- protons and electrons are

both stable- means that a positive charge e can have

associated with it a radius associated with an electron

and ‘strike forth’ pions. When we look at the electric

classical radius of the proton we obtain, from Eq. 65:

GeVcmm pW 41.8022

(72)

This is the mass of the charged W-boson which

has spin 1 reflecting the dimensionality of the proton

as having 3 sub-dimensions. These formulas are quite

accurate as is seen in Table 1. In both cases the spin

of the Mieon is the spin on the classical surface of the

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parent particle is plus or minus /2. We can take the

ratio of the masses of these two bosons:

(73)

This is versus the actual experimental value mW /

mπ± = 574.2, so again agreement is good. The

particles resulting from simple Mie scattering ( P=0) in

the GEM theory are summarized in Table 1.

TABLE 1. Particle Masses Predicted by the GEM theory for

Simple Mie , P=0, Scattering Theory and Observed Masses

Particles

Particle Properties

Predicted

Mass

Measured

Mass

%

error

140.05MeV

139.6MeV

0.3%

W

80.409GeV

80.398GeV

0.01%

c

3000.6MeV

2985MeV

0.7%

We understand from this that the charged nature

of the particles results from the polarization of the

vacuum at the classical particle surfaces of the

electron and proton. The spin states of the pion and W

particles reflect the dimensionality of the electron as a

one dimensional particle-yielding a scalar pion, and

the three dimensional spin 1 vector character of the W

particle is required for it to interact with the three

quarks.

B. The Complex Mie Scattering Results

We can consider that the path integrals on

classical particle surfaces “tumble” in 5 space and to

first order all the degrees of freedom are identical.

This will allow 5-fold perturbations to develop on the

path integral so that virtual paths exist that add or

subtract to the effective length of the path, (see

Figure 8 and 9) so we will have M=5.

Fig. 8. A quantum Mie scattering caused by a resonant

excitation on a classical particle surface plus a five-fold

alternative quantum path.

Fig. 9. A quantum Mie scattering caused by a resonant

excitation on a classical particle structure with a 5-fold

alternative path also being excited.

)51(

22

cNm

Eo

(74)

for the electron we obtain the neutral pion:

2

/1.135

)51(

2cMeV

m

me

o

(75)

We have then for the case of N=1/2 and P= - 5 for

mo

2

//2.3114

)51( cMeV

m

mo

J

(76)

This result is within 6 parts per thousand of actual J/

particle mass of 3096.6MeV.

We can look thus propose a similar “tumbling in

5 dimensions” process operating in the Radion field

except that in case it gives a negative “backflow” or

“shortcut” contribution to the path integral.

We return to the path integral model for Mieons

generated by the Radion field where mc the particle

mass generating the classical radius, in this case me

)/1(

2

P

Nm

Eo

(78)

Where we have P=-5 N=1 scattering off the

proton. As before, the particle must be a spin 1 vector

boson because of the “vector” or triune character of

the proton. This perturbation features the “backflow”,

or “shortcut” negative contribution to the path integral:

2

/03.91

)/51(

2cGeV

m

mp

Z

(79)

3574.3

W

M

m

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The perturbed pathway mechanism generally

takes charge off of particles because is an averaging

over neutral space.

Following this procedure for N=1/2 M=0 we obtain

for the scalar excitation off the uncharged scalar

eta-c particle with the uncharged scalar result

2

/1.124)51/( cGeVmm cH

(80a)

We also obtain EM ZPF excitation off the proton

classical surface at spin 0:

2

/1.124)51(/ cGeVmm pH

(80b)

These both give the approximate mass of the

Higgs Boson [19] of spin 0 and charge 0. This result

(as mH mp/) was obtained and presented at the

2012 STAIF Meeting in Albuquerque NM , four

months before it was known [4].

So that we have approximately

85035.42

e

p

c

Hm

m

m

m

(81)

The experimental value is mH/mc 42.6, so

agreement is good.

Finally, we have for N=1/2 and for P=0 a Radion

scattering off the electron, which is a new particle.

MeVmm eo 9.21

(82)

This is the mesoscale particle, which we will term

the M* (“Morningstar”) particle in honor of the

sponsors of this research. It has never been

observed, but some evidence for its existence can be

found, and will be discussed in the next section of this

chapter. We would expect it to be charge-neutral and

have spin 0 like the Higgs Boson. It should decay into

electron-positron pairs and photons.

The predicted particle masses and those

experimentally observed are summarized in Table 2.

TABLE 2. Particle Masses Predicted by the GEM theory and

Observed Masses Including the New Predicted M* Particle

Particles

Particle Properties

Predicted

Mass

Measured

Mass

%

error

o

135.12MeV

134.98MeV

0.1%

Z

91.03GeV

91.19GeV

0.2%

Higgs

124.1GeV

125.1GeV

0.8%

M*

21.98MeV

****

***

Unexpectedly, the GEM theory created a doorway

to understanding with two short-range forces of

nature the Weak and Strong nuclear forces, because

in unifying gravity and EM in a geometric theory, it

produced a geometric scale regime for subatomic

particles and the regime for their interactions. The

quantum particles which create the short range forces

are thus scatterings out of the full spectrum of the ZPF

by these resonant structures. The fact that the

scattering structures are EM classical radii shows the

underlying electromagnetic character of the short

range forces. The GEM theory produced the picture of

EM forces not only between charged objects but also

between uncharged structures that can be extended

to include short-range nuclear forces.

IV. SUMMARY AND DISCUSSION

Under the conjecture of Dr. Alfred Luhen, (Private

Communication) one cannot create mass without

creating gravity. The Higgs Boson thus cannot exist

and generate mass outside the context of General

Relativity. Accordingly, the simplest way for this to

occur in the GEM context is that the Higgs scalar field

occurs in Kaluza-Klien theory as the Radion scalar

field so that both gravity, EM-mass energy as gravity

source term, and particles are born together with the

Radion field. The concept of the Higgs Boson as the

creator of mass in the GEM theory is obvious because

of the relationship mHiggs mp/ so that the Compton

radius of the Higgs Boson is the EM interaction length

of the proton:

2

2

cm

e

p

Higgs

(83)

Thus, the known source of mass in the universe,

the proton, is in EM resonance with the Higgs Boson,

that is, the proton EM self-interaction time is the

Compton oscillation time of the Higgs. The Higgs

boson can thus be viewed as the most general

excitation, by both EM and Radion fields, of a

structural resonance of the hidden Kaluza-Klien 5th

LEAVE BLANK

LEAVE BLANK

dimension, and thus part of the mechanism in the

vacuum that gives rise to separate EM and gravity

fields and also a cosmos dominated by hydrogen.

The GEM theory had its original goal as the

unification of the two long range forces of nature, EM

and gravity, however, it was found that could not be

done without a hidden dimension whose size

corresponded to the size of classical radii of protons

and electrons. It was found that particle masses of

first and second generations from this hidden

dimension size could be generated by quantum Mie

scattering. In this quantum model, the classical

particle surfaces themselves support quantum Mie

scattering resonances. This process appears to create

a pattern of changes of spin and charge, creating

bosons from fermions and vice versa, and charged

and neutral particles. The central importance of the

EM classical radii in this unification theory suggests

the underlying EM character of the forces. The model

gives the correct masses, spins and charges reflecting

the dimensionality of the electron or proton they

scatter off of.

The result is a rudimentary “Bohr Model“ of field

unification which gives G, the mass of the proton, and

the masses of the pions and W and Z exchange

bosons of the Strong and Weak force. It also gives an

accurate estimate of the Higgs Boson mass. It also

predicts a new particle and other phenomena,

particularly that hydrogen and radiation can appear

occasionally from the vacuum, particularly at Black

Hole mergers [5] This theory suggests that

manipulation of Gravity, Strong, and Weak Forces by

Electromagnetism may be possible. It is hoped this

work can form the basis for future advances in

understanding and engineering.

ACKNOWLEDGMENT

The author wishes to thank Morgan Boardman

and Paul Murad of Morningstar Applied Physics and

Eric Rice of Orbital Technologies Corporation and

Jess Sponable of DARPA for their support and

encouragement of this research as well as Abe

Meghed for many useful comments, and finally thanks

to my industrious cousin Axel for his good example.

The author is also very grateful to JMESS for this

opportunity to codify the GEM theory in its present,

early, state. Laus Deo

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