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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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