the natural philosophy of fundamental particles
TRANSCRIPT
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The atural Philosophy of Fundamental Particles
Riccardo C. Storti1
Key Words: Balmer Series, Bohr Radius, Buckingham Theory, Casimir Force, ElectroMagnetics, Equivalence Principle, Eulers Constant, Fourier Series, Fundamental Particles, General Relativity, Gravity, Harmonics, Hydrogen Spectrum, ewtonian Mechanics, Particle Physics,Physical Modelling, Planck Scale, Polarizable Vacuum, Quantum Mechanics, Zero-Point-Field.
Abstract
Theoretical estimates and correlations, based upon the Electro-Gravi-Magnetics (EGM)
method, are presented for the Root-Mean-Square (RMS) charge radius and mass-energy of many
well established subatomic particles. The EGM method is a set of engineering equations and
techniques derived from the purely mathematical construct known as Buckinghams (Pi)Theory. The estimates and correlations coincide to astonishing precision with experimental data
presented by the Particle Data Group (PDG), CDF, D0, L3, SELEX and ZEUS Collaborations. Our
tabulated results clearly demonstrate a possible natural harmonic pattern representing all
fundamental subatomic particles. In addition, our method predicts the possible existence of several
other subatomic particles not contained within the Standard Model (SM). The accuracy and
simplicity of our computational estimates demonstrate that EGM is a useful tool to gain insight into
the domain of subatomic particles.
Delta Group Engineering P/L
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1 ITRODUCTIO
1.1 HARMONIC REPRESENTATION OF GRAVITATIONAL ACCELERATION
Electro-Gravi-Magnetics (EGM) is a term describing a hypothetical harmonic relationship
between Electricity, Gravity and Magnetism. The hypothesis may be mathematically articulated by
the application of Dimensional Analysis Techniques (DATs) and Buckingham Theory (BPT),
both being well established and thoroughly tested geometric engineering principles [1-3], viaFourier harmonics. [4] The hypothesis may be tested by the correct derivation of experimentally
verified fundamental properties not predicted within the Standard Model (SM) of particle physics.
Storti et. al. derived the EGM relationship in [5-23] where it was shown that a theoreticalrepresentation of constant acceleration at a mathematical point in a gravitational field may be
defined by a summation of trigonometric terms utilizing modified complex Fourier series in
exponential form, according to the harmonic distribution nPV = -N, 2 - N ... N, where N is an
odd number harmonic. Hence, the magnitude of the gravitational acceleration vector g (via the
equivalence principle applied in [5-23]) may be usefully represented by Eq. (1) as |nPV|,
g r M,( )G M.
r2
n
PV
2 i.
n PV.
e n PV. PV 1 r, M,( )
. t. i...
(1)
such that, the frequency spectrum of the harmonic gravitational field PV is given by Eq.(2), [8]
PV n PV r, M,n PV
r
32 c. G. M.
r.. KPV r M,( )
.
(2)
where,
Variable Description Units
PV(1,r,M) Fundamental spectral frequency. Hz
KPV Refractive index of a gravitational field in the Polarizable Vacuum
(PV) model of gravity, [5] only contributing significantly when a large
gravitational mass (i.e. a strong gravitational field) is considered. For
all applications herein, the effect is approximated to KPV(r,M) = 1.nPV Harmonic modes of the gravitational field.
None
r Magnitude of position vector from centre of mass. m
M Mass. kg
G Gravitational constant. m3kg
-1s
-2
Table 1,
Subsequently, the harmonic (Fourier) representation of the magnitude of the gravitational
acceleration vector at the surface of the Earth up to N = 21 is graphically shown to be,
Time
GravitationalAcceleration g
Figure 1: harmonic representation of gravitational acceleration,
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As N , the magnitude of the gravitational acceleration vector becomes measurably constant.
Hence, Eq. (1, 2) illustrate that the Newtonian representation of g is easily harmonized over the
Fourier domain, from geometrically based methods (i.e. DATs and BPT). Therefore, unifying (inprinciple) Newtonian, geometric (relativistic) and quantum (harmonized) models of gravity.
1.2 BOUNDARY CONDITIONS
1.2.1 FREQUENCY
Storti et. al. showed in [8] that the spectrum defined by Eq. (2) is discrete and finite. The
lower boundary value is given by PV(1,r,M), whilst the upper boundary value (also termed
the harmonic cut-off frequency) is given by Eq. (3),
r M,( ) n r M,( ) PV 1 r, M,( ).
(3)
supported by Eq. (4-7),
n r M,( ) r M,( )
12
4
r M,( )1 (4)
r M,( )
3
108U
mr M,( )
U r M,( ). 12 768 81
Um
r M,( )
U r M,( )
2
.. (5)
U m r M,( )3 M. c
2.
4 . r3.
(6)
U r M,( )h
2 c3. PV 1 r, M,( )
4.
(7)
where,
Variable Description Units
n Harmonic cut-off mode [mode number at ].
Harmonic cut-off function.
None
Um Mass-energy density of a solid spherical gravitational object.
U Energy density of mass induced gravitational field scaled to
the fundamental spectral frequency.
Pa
h Plancks Constant [6.6260693 x10-34
]. Js
c Velocity of light in a vacuum. m/s
Table 2,
Since the relationship between trigonometric terms at each amplitude and corresponding
frequency is mathematically defined by the nature of Fourier series, the derivation of Eq. (4, 5) is
based on the compression of energy density to one change in odd harmonic mode whilst preserving
dynamic, kinematic and geometric similarity in accordance with BPT.
The preservation of similarity across one change in odd mode is due to the mathematical properties of constant functions utilizing Fourier series as discussed in [8]. The subsequent
application of these results to Eq. (1) acts to decompress the energy density over the Fourier domain
yielding a highly precise reciprocal harmonic representation of g whilst preserving dynamic,
kinematic and geometric similarity to Newtonian gravity, identified by the compression technique
stated above.
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1.2.2 POYNTING VECTOR
It was demonstrated by Haisch, Puthoff and Rueda in [24-26] that inertia may haveElectroMagnetic (EM) origins due to the Zero-Point-Field (ZPF) of Quantum-Electro-Dynamics
(QED), manifested by the Poynting vector, via the equivalence principle. Hence, it follows that
gravitational acceleration may also be EM in nature and the Polarizable Vacuum (PV) model of
gravity [27] is an EM polarized state of the ZPF with a Fourier distribution, assigning physical
meaning to Eq. (1).Subsequently, it follows that the energy density of a mass induced gravitational field may be
scaled to changes in odd harmonic mode numbers satisfying the mathematical properties of any
constant function described in terms of Fourier series utilizing Eq. (7) - such that,
U n PV r, M, U r M,( ) n PV 24
n PV4. (8)
Therefore, the Poynting vector2
of the polarized Zero-Point (ZP) gravitational field S
surrounding a solid spherical object with homogeneous mass-energy distribution is given by,
S n PV r, M, c U n PV r, M,. (9)
and may be graphically represented as follows,
Harmonic
ZPFPoyntingVector
S n PV RE, M E,
n PV
Figure 2,
where, RE and ME in Fig. (2) denote the radius and mass of the Earth respectively.
Fig. (2) illustrates that the Poynting vector of the ZP gravitational field increases with nPV.
Further work by Storti et. al. in [9] showed that >>99.99(%) of the effect in a gravitational field
exists well above the THz range. Hence, it becomes apparent that n and are important
characteristics of gravitational fields. We shall utilize these characteristics to quasi-unify particlephysics in harmonic form in the proceeding sections.
2 THE SIZE OF THE PROTO, EUTRO AD ELECTRO
In 2005, Storti et. al. derived the mass-energy threshold of the Photon utilizing n and theclassical Electron radius as shown in [12], to within 4.3(%) of the Particle Data Group (PDG)
value3 stated in [28], then proceeded to derive the mass-energies and radii of the Photon and
Graviton in [14] by the consistent utilization of n.
The method developed in [12] was re-applied in [13] to derive the sizes4 of the Electron,
Proton and Neutron. The motivation for this was to test the hypothesis presented in Section 1 by
direct comparison of the computed size values to experimentally measured fact. They believe that
2Per change in odd harmonic mode number.
3Consistent with experimental evidence and interpretation of data.
4 From first principles and from a single paradigm.
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highly precise computational predictions, agreeing with experimental evidence beyond the abilities
of the SM to do so, is conclusive evidence of the validity of the harmonic method developed.
To date, highly precise measurements have been made of the Root-Mean-Square (RMS)
charge radius of the Proton by [29] and the Mean-Square (MS) charge radius of the Neutron as
demonstrated in [30]. However, the calculations presented in [13] are considerably more accurate
than the physical measurements articulated in [29,30], lending support for the harmonic
representation of the magnitude of the gravitational acceleration vector stated in Eq. (1).
The basic approach utilized in [13] was to determine the equilibrium position between the polarized state of the ZPF and the mass-energy of the fundamental particle inducing space-time
curvature as would appear in General Relativity (GR). In other words, one may consider thecurvature of the space-time manifold surrounding an object to be a virtual fluid in equilibriumwith the object itself
5.
This concept is graphically represented in Fig. (3). A free fundamental particle with classical
form factor is depicted in equilibrium with the surrounding space-time manifold. The ZPF is
polarized by the presence of the particle in accordance with the PV model of gravity, which is (atleast) isomorphic to GR in the weak field. [27]
Figure 3: free fundamental particle with classical form factor,
In the case of the Proton, the ZPF equilibrium radius coincides with the RMS charge radius
r [Eq. (10)] producing the experimentally verified result rp by the SELEX Collaboration asstated in [29]6,
r
h m e.
16 c. 2. mp
3.
5
27 h. c.
4 . G.
m e4
mp
.. (10)
where, me and mp denote Electron and Proton rest-mass respectively.
In the case of the Neutron, the ZPF equilibrium radius coincides with the radial position of
zero charge density r [Eq. (11)] with respect to the Neutron charge distribution as illustrated in
Fig. (4). It is shown in [18] that r relates to the MS charge radius KS by a simple formula [Eq.
(12)] producing the experimentally verified result KX as presented in [30]7,
rh m e.
16 c. 2. m n
3.
5
27 h. c.
4 . G.
m e4
m n
..
(11)
where, mn denotes Neutron rest-mass.
5The intention is not to suggest that the space-time manifold is actually a fluid, it is merely to
present a method by which to solve a problem.6
r = 0.8306(fm), rp = 0.8307 0.012(fm).7 r = 0.8269(fm), KS = -0.1133(fm
2), KX = -0.113 0.005(fm2).
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r
dr
5
3
r
.
Charge Density
Maximum Charge Density
Minimum Charge Density
Neutron Charge Distribution
Radius
ChargeD
ensity
ch r( )
ch r0
ch rdr
r rdr
r
Figure 4: Neutron charge distribution,
KS
3 . r
2.
8
1 x( ) x3.
1 x x2
.
(12)
where, x is solved numerically8
within the MathCad environment by the following algorithm,
[18]
Given
ln x( )x2
x2
1
.1
3(13)
x Find x( ) (14)
Utilizing KS, KX may be converted to determine an experimental zero charge density radial
position value rX according to Eq. (15),
rX
r
KS
KS KX.. (15)
In the case of the Electron (as with the Proton), the ZPF equilibrium radius coincides with
the RMS charge radius r [Eq. (16)] producing an experimentally implied result9
as stated in [31],
r re1
2
ln 2 n re m e,. .
9
5
.
(16)
where, re and denote the classical Electron radius and Euler-Mascheroni constant [32]
respectively.
8x = 0.6829, rX = 0.8256 0.018(fm).
9 r 0.0118(fm), = 0.577215664901533.
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3 HARMOIC REPRESETATIO OF FUDAMETAL PARTICLES
3.1 ESTABLISHING THE FOUNDATIONS
Motivated by the physical validation of Eq. (10, 11), Storti et. al. conducted thoughtexperiments in [13] to investigate harmonic and trigonometric relationships by analyzing various
forms of radii combinations for the Electron, Proton and Neutron consistent with the DATs and
BPT derivations in [5-12] yielding the following useful approximations,
r m e,
r mp,
r m e,
r m n,2
(17)
r
r r
(18)
r
r
e
2
3.
(19)
where,
(i) and e denote the fine structure constant and exponential function respectively.(ii) Eq. (17) error:
(a) associated with (r,me)/(r,mp) = 2 is 8.876 x10-3
(%)
(b) associated with (r,me)/(r,mn) = 2 is 0.266(%).(iii) Eq. (18) error is 2.823(%).
(iv) Eq. (19) error is 0.042(%).
3.2 IMPROVING ACCURACY
Since the experimental value of the RMS charge radius of the Proton is considered by the
scientific community to be precisely known10
, [29] the accuracy of Eq. (18, 19) may be improved
by re-computing the value of r and r. This action further strengthens the validity of Eq. (17)
by verifying trivial deviation utilizing the re-computed values.
Hence, it follows that numerical solutions for r and r, constrained by exact
mathematical statements [Eq. (16 19)], suggests that the gravitational relationship between the
Electron and Proton, as inferred by the result (r,me)/(r,mp) = 2, is harmonic. The
computational algorithm supporting this contention may be stated as follows,
Given
r
re
r m e,
r mp,
r
r r
r
r
e
2
3. 1
2ln 2 n re m e,
. .
9
5
2
(20)
r
rFind r r,
(21)
yields,
r
r
0.826838
0.011802fm( ).
(22)
10 To a degree of accuracy significantly greater than the Electron or Neutron.
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where,
(i) Eq. (17) error:
(a) associated with (r,me)/(r,mp) = 2 is 4.493 x10-7(%).
(b) associated with (r,me)/(r,mn) = 2 is 0.282(%).(ii) Eq. (18) error is 1.11 x10
-13(%).
(iii) Eq. (19) error is 0.026(%).
3.3 FORMULATING AN HYPOTHESIS
In the preceding calculations utilizing known particle mass and radii as a reference, it was
found that the harmonic cut-off frequency ratio of an Electron to a Proton was precisely 2. This
provokes the hypothesis that a simple harmonic pattern may exist describing the relationship of all
fundamental particles relative to an arbitrarily chosen base particle according to,
r1 M 1,
r2 M 2,St
(23)
Performing the appropriate substitutions utilizing Eq.(3 - 7), Eq. (23) may be simplified to,
M1
M 2
2r
2r1
5
. St 9
(24)
where, St represents the ratio of two particle spectra. Subsequently, r may be simply
calculated according to,
r r
5
1
29
m e
mp
2
.. (25)
3.4 IDENTIFYING A MATHEMATICAL PATTERN
Utilizing Eq. (24), Storti et. al. identify mathematical patterns in [15-17] showing that St
may be represented in terms of the Proton, Electron and Quarkharmonic cut-off frequencies derivedfrom the respective particle. Potentially, three new Leptons (L2, L3, L5 and associated Neutrinos:
2, 3, 5) and two new Quark / Bosons (QB5 and QB6) are predicted, beyond the SM as shown in
table (3).
The EGM Harmonic Representation of Fundamental Particles (i.e. table (3)) is applicable to
the size relationship between the Proton and Neutron (i.e. to calculate r from r and vice-versa
utilising St = 1) as an approximation only. For precise calculations based upon similar forms, thereader should refer to [13].
ote: although the newly predicted Leptons are within the kinetic range11
and therefore shouldhave been experimentally detected, there are substantial explanations discussed inSection 5.2.
Existing and Theoretical Particles ProtonHarmonics ElectronHarmonics QuarkHarmonics
Proton (p), Neutron (n) St = 1 St = 1/2 St = 1/14
Electron (e), Electron Neutrino (e) 2 1 1/7
L2, 2 (Theoretical Lepton, Neutrino) 4 2 2/7
L3, 3 (Theoretical Lepton, Neutrino) 6 3 3/7
Muon (), Muon Neutrino () 8 4 4/7
L5, 5 (Theoretical Lepton, Neutrino) 10 5 5/7
11 A region extensively explored in particle physics experiments.
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Tau (), Tau Neutrino () 12 6 6/7
Up Quark (uq), Down Quark (dq) 14 7 1
Strange Quark (sq) 28 14 2
Charm Quark (cq) 42 21 3
Bottom Quark (bq) 56 28 4
QB5 (Theoretical Quark or Boson) 70 35 5
QB6 (Theoretical Quark or Boson) 84 42 6
W Boson 98 49 7Z Boson 112 56 8
Higgs Boson (H) (Theoretical) 126 63 9
Top Quark (tq) 140 70 10
Table 3: harmonic representation of fundamental particles,
4 RESULTS
4.1 HARMONIC EVIDENCE OF UNIFICATION
Exploiting the mathematical pattern articulated in table (3), EGM predicts the RMS charge
radius and mass-energy of less accurately known particles, comparing them to expert opinion. Thevalues of St shown in table (3), predict possible particle mass and radii for all Leptons,
Neutrinos, Quarks and Intermediate Vector Bosons (IVBs), in complete agreement with the SM,
PDG estimates and studies by Hirsch et. al in [33] as shown in table (4),
Particle EGM Radii
x10-16
(cm)
EGM Mass-Energy
(computed or utilized)
PDG Mass-Energy Range
(2005 Values)
Proton (p) r = 830.5957
Neutron (n) r = 826.8379
Electron (e) r = 11.8055
Muon () r = 8.2165
Tau () r = 12.2415
Mass-Energy precisely known,
See: National Institute of Standards and Technology
(NIST) [34]
Note: m = 10-100
Electron Neutrino (e) ren 0.0954 men(eV) 3 - m men(eV) < 3Muon Neutrino () rn 0.6556 mn(MeV) 0.19 - m mn(MeV) < 0.19
Tau Neutrino () rn 1.9588 mn(MeV) 18.2 - m mn(MeV) < 18.2
Up Quark (uq) ruq 0.7682 muq(MeV) 3.5060 1.5 < muq(MeV) < 4
Down Quark (dq) rdq 1.0136 mdq(MeV) 7.0121 3 < mdq(MeV) < 8
Strange Quark (sq) rsq 0.8879 msq(MeV) 113.9460 80 < msq(MeV) < 130
Charm Quark (cq) rcq 1.0913 mcq(GeV) 1.1833 1.15 < mcq(GeV) < 1.35
Bottom Quark (bq) rbq 1.071 mbq(GeV) 4.1196 4.1 < mbq(GeV) < 4.4
Top Quark (tq) rtq 0.9294 mtq(GeV) 178.4979 169.2 < mtq(GeV) < 179.4
W Boson rW 1.2839 mW(GeV) 80.425 80.387 < mW(GeV) < 80.463
Z Boson rZ 1.0616 mZ(GeV) 91.1876 91.1855 < mZ(GeV) < 91.1897
Higgs Boson (H) rH 0.9403 mH(GeV) 114.4 + m mH(GeV) > 114.4
Photon () r = Kh m 3.2 x10-45(eV) m < 6 x10
-17(eV)
Graviton (g) rgg = 2(2/5)
r mgg = 2m No definitive commitment
L2 (Lepton) mL(2) 9(MeV)
L3 (Lepton) mL(3) 57(MeV)
L5 (Lepton)
rL 10.7518
mL(5) 566(MeV)
2 (L2 Neutrino) m2 men
3 (L3 Neutrino) m3 mn
5 (L5 Neutrino)
r2,3,5
ren,n,n m5 mn
Not predicted or considered
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QB5(Quark or Boson) mQB(5) 10(GeV)
QB6(Quark or Boson)
rQB 1.0052
mQB(6) 22(GeV)
Not predicted or considered
Table 4: RMS charge radii and mass-energies of fundamental particles,
where,
(i) K denotes a Planck scaling factor, determined to be (/2)1/3
in [17].
(ii) h denotes Planck length [4.05131993288926 x10-35
(m)].
(iii) rL and rQB denote the average radii of SM Leptons and Quark / Bosons
(respectively) utilized to calculate the mass-energy of the proposed new particles.ote:
(a) a formalism for the approximation of2, 3 and5 mass-energy is shown in [19].
(b) it is shown in [12,14,17] that the RMS charge diameters of a Photon and Graviton are h and
1.5h respectively, in agreement with Quantum Mechanical (QM) models.
4.2 RECENT DEVELOPMENTS
4.2.1 PDG MASS-ENERGY RANGES
The EGM construct was finalized by Storti et. al. in 2004 and tested against published PDG
data of the day [i.e. the 2005 values shown in table (4)]. Annually, as part of their continuousimprovement cycle, the PDG reconciles its published values of particle properties against the latestexperimental and theoretical evidence. The 2006 changes in PDG mass-energy range values notimpacting EGM are as follows:
1. Strange Quark = 70 < msq(MeV) < 120.2. Charm Quark = 1.16 < mcq(GeV) < 1.34.3. W Boson = 80.374 < mW(GeV) < 80.432.4. Z Boson = 91.1855 < mZ(GeV) < 91.1897.
Therefore, we may conclude that the EGM construct continues to predict experimentally verifiedresults within the SM to high computational precision.
4.2.2 ELECTRON NEUTRINO AND UP / DOWN / BOTTOM QUARK MASS
Particle physics research is a highly dynamic field supporting a landscape of constantly
changing hues. The EGM construct relates mass to size in harmonic terms. If one applies Eq. (24)
and utilizes the Proton as the reference particle in accordance with table (3), one obtains a single
expression with two unknowns, as implied by Eq. (25).
Since contemporary Physics is currently incapable of specifying the mass and size of most
fundamental particles precisely and concurrently, EGM is required to approximate values of either
mass or radius to predict one or the other (i.e. mass or size). Subsequently, the EGM predictionsarticulated in table (4) denote values based upon estimates of either mass or radius.
Hence, some of the results in table (4) are approximations and subject to revision as new
experimental evidence regarding particle properties (particularly mass), come to light. The 2006
changes in PDG mass-energy values affecting table (4) are shown below. In this data set, the EGMradii is displayed as a range relating to its mass-energy influence.
ote: the average value of EGM Up + Down Quark mass from table (4) [i.e. 5.2574(MeV)]remains within the 2006 average mass range specified by the PDG [i.e. 2.5 to 5.5(MeV)].
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Particle EGM Radii x10-16
(cm) EGM Mass-Energy
(utilized)
PDG Mass-Energy
Range (2006 Values)
Electron Neutrino (e) ren< 0.0811 men(eV) < 2
Up Quark (uq) 0.5469 < ruq< 0.7217 1.5 < muq(MeV) < 3
Down Quark (dq) 0.7217 < rdq< 1.0128 3 < mdq(MeV) < 7
Bottom Quark (bq) 1.0719 > rbq > 1.0863
PDG Mass-Energy
Range (2006 Values)
4.13 < mbq(GeV) < 4.27
Table 5: RMS charge radii and mass-energies of fundamental particles,
The predicted radii ranges above demonstrate that no significant deviation from table (4)
values exists. This emphasizes that the EGM harmonic representation of fundamental particles is a
robust formulation and is insensitive to minor fluctuations in particle mass, particularly in the
absence of experimentally determined RMS charge radii.
Therefore, we may conclude that the EGM construct continues to predict experimentally verifiedresults within the SM to high computational precision.
4.2.3 TOP QUARK MASS
Dilemma
The Collider Detector at Fermilab (CDF) and D-ZERO (D0) Collaborations have recently
revised their world average value of Top Quark mass from 178.0(GeV/c2) in 2004 [35] to,
172.0 in 2005 [36], 172.5 in early 2006, then 171.4 in July 2006. [37]
ote: since the precise value of mtq is subject to frequent revision, we shall utilize the 2005 valuein the resolution of the dilemma as it sits between the 2006 values.
Resolution
The EGM method utilizes fundamental particle RMS charge radius to determine mass.
Currently, Quark radii are not precisely known and approximations were applied in the formulation
of mtq displayed in table (4). However, if one utilizes the revised experimental value of m tq =172.0(GeV/c
2) to calculate the RMS charge radius of the Top Quark rtq, based on Proton
harmonics, it is immediately evident that a decrease in rtq of < 1.508(%) produces the new
world average value precisely. The relevant calculations may be performed simply as follows,
The revised Top Quark radius based upon the new world average Top Quark mass,
r
5
1
1409
172GeV
c2
.
mp
2
.. 0.9156 1016
cm.=
(26)
The decrease in Top Quark RMS charge radius [relative to the table (4) value] based upon thenew world average Top Quark mass becomes,
rtq
r
5
1
1409
172GeV
c2
.
mp
2
..
1 1.5076 %( )=
(27)
where, rtq denotes the RMS charge radius of the Top Quark from table (4).
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Therefore, since the change in rtq is so small and its experimental value is not precisely known,we may conclude the EGM construct continues to predict experimentally verified results within theSM to high computational precision.
ote: the 2006 value for revised m tq modifies the error defined by Eq. (27) to < 1.65(%).
5 DISCUSSIO
5.1 EXPERIMENTAL EVIDENCE OF UNIFICATION
Table (3, 4, 5) display mathematical facts demonstrating that all fundamental particles may
be represented as harmonics of an arbitrarily selected reference particle, in complete agreement with
the SM. Considering that the EGM method is so radically different and quantifies the physical
world beyond contemporary solutions, one becomes tempted to disregard table (3, 4, 5) in favor of
concluding these to be coincidental.
However, it is inconceivable that such precision from a single paradigm spanning the entire
family of fundamental particles could be coincidental. The derivation of the Top Quark mass-
energy is in itself, an astonishing result which the SM is currently incapable of producing.
Moreover, the derivation of (a), EM radii characteristics of the Proton and Neutron (rE, rM
and rM) (b), the classical RMS charge radius of the Proton (c), the 1st term of the Hydrogen atomspectrum A and (d), the Bohr radius rx: all from the same paradigm, [18-20] strengthens theharmonic case.
Additionally, Storti et. al. demonstrate in Quinta Essentia, A Practical Guide to Space-Time Engineering, Part 3: pg. 54 (see: Ref.) that the probability of coincidence is
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5.2 THE ANSWERS TO SOME IMPORTANT QUESTIONS
5.2.1 WHAT CAUSES HARMONIC PATTERNS TO FORM?
(a) ZPF Equilibrium
A free fundamental particle is regarded by EGM as a bubble of energy equivalent mass.
Nature always seeks the lowest energy state: so surely, the lowest state for a free fundamental particle should be to diffuse itself to non-existence in the absence of something acting to
keep it contained?
This provokes the suggestion that a free fundamental particle is kept contained by the
surrounding space-time manifold. In other words, free fundamental particles are analogous to
neutrally buoyant bubbles floating in a locally static fluid (the space-time manifold). EGM is an
approximation method, developed by the application of standard engineering tools, which finds the
ZPF equilibrium point between the mass-energy equivalence of the particle and the space-time
manifold (the ZPF) surrounding it - as depicted by Fig. (3).
(b) Inherent Quantum Characteristics
If one assumes that the basic nature of the Universe is built upon quantum states ofexistence, it follows that ZPF equilibrium is a common and convenient feature amongst free
fundamental particles by which to test this assumption. Relativity tells us that no absolute frames of
reference exist, so a logical course of action is to define a datum as EGM is derived from a
gravitational base. In our case, it is an arbitrary choice of fundamental particle.
To be representative of the quantum realm, it follows that ZPF equilibrium between free
fundamental particles should also be analogous to quantum and fractional quantum numbers as
one finds with the Quantum Hall Effect. Subsequently, the harmonic patterns of table (3) form
because the determination of ZPF equilibrium is applied to inherently quantum characteristic
objects i.e. fundamental particles.Hence, it should be no surprise to the reader that comparing a set of inherently quantum
characterized objects to each other, each of which may be described by a single wavefunction at its
harmonic cut-off frequency, results in a globally harmonic description. That is, the EGM harmonic
representation of fundamental particles is a quantum statement of ZPF equilibrium as one would
expect. In-fact, it would be alarming if table (3), or a suitable variation thereof, could not be
formulated.
Therefore, harmonic patterns form due to inherent quantum characteristics and ZPF equilibrium.
5.2.2 WHY HAVENT THE NEW PARTICLES BEEN EXPERIMENTALLY DETECTED?
EGM approaches the question of particle existence, not just by mass as in the SM, but by
harmonic cut-off frequency (i.e. by mass andZPF equilibrium). Storti et. al. showed in [9]
that the bulk of the PV spectral energy
13
at the surface of the Earth exists well above the THzrange. Hence, generalizing this result to any mass implies that the harmonic cut-off period14
T
defines the minimum detection interval to confirm (or refute) the existence of the proposed L2, L3,
L5 Leptons and associated 2, 3, 5 Neutrinos. In other words, a particle exists forat least the
period specified by T i.e. its minimum lifetime.Quantum Field Theory (QFT) approaches this question from a highly useful, but extremely
limited perspective compared to the EGM construct. QFT utilizes particle mass to determine the
13>> 99.99(%).
14 The inverse of .
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minimum detection period (in terms of eV) to be designed into experiments. To date, this approach
has been highly successful, but results in the conclusion that no new Leptons exist beyond the SM
in the mass-energy range specified by the proposed Leptons. Whilst QFT is a highly useful
yardstick, it is by no means a definitive benchmark to warrant termination of exploratory
investigations for additional particles.
Typically in the SM, short lived particles are seen as resonances in cross sections of data
sets and many Hadrons in the data tables are revealed in this manner. Hence, the SM asserts that the
more unstable particles are, the stronger the interaction and the greater the likelihood of detection.The EGM construct regards the existing Leptons of the SM as long-lived particles. It also
asserts that the SM does not adequately address the existence or stability of the extremely short-livedLeptons proposed. This assertion is supported by the fact that detection of these particles issubstantially beyond current capabilities due to:
1. The minimum detection interval (with negligible experimental error) being < 10-29(s).2. The possibility that the proposed Leptons are transient (intermediate) states of particle
production processes which decay before detection. For example, perhaps an Electron
passes through an L2 phase prior to stabilization to Electronic form (for an appropriate
production process). Subsequently, this would be not be detected if the transition process is
very rapid and the accelerator energies are too low.
3. The possibility of statistically low production events.Hence:
1. The proposed Leptons are too short-lived to appear as resonances in cross-sections.2. The SM assertion that the more unstable particles are, the stronger the interaction and the
greater the likelihood of detection is invalid for the proposed Leptons.
Therefore, contemporary particle experiments are incapable of detecting the proposed Leptons atthe minimum accelerator energy levels required to refute the EGM construct.
5.2.3 WHY SHOULD ONE BELIEVE THAT ALL FUNDAMENTAL PARTICLES MAY BE
DESCRIBED AS HARMONIC MULTIPLES OF EACH OTHER?
Because of the precise experimental and mathematical evidence presented in table (3, 4, 6).
These results were achieved by construction of a model based upon a single gravitational paradigm.Moreover, Storti et. al. also derive the Casmir force in [11] from [5-10] utilizing Eq. (1 - 3).
5.2.4 WHY IS EGM A METHOD AND NOT A THEORY?
EGM is a method and not a theory because: (i) it is an engineering approximation and (ii),the mass and size of most subatomic particles are not precisely known. It harmonizes all
fundamental particles relative to an arbitrarily chosen reference particle by parameterizing ZPF
equilibrium in terms of harmonic cut-off frequency .
The formulation of table (3) is a robust approximation based upon PDG data. Otherinterpretations are possible, depending on the values utilized. For example, if one re-applies the
method presented in [16] based upon other data, the values of St in table (3) might differ.
However, in the absence of exact experimentally measured mass and size information, there is littlemotivation to postulate alternative harmonic sequences, particularly since the current formulation
fits the available experimental evidence extremely well.
If all mass and size values were exactly known by experimental measurement, the main
sequence formulated in [16] (or a suitable variation thereof) will produce a precise harmonic
representation of fundamental particles, invariant to interpretation. Table (3) values cannot be
dismissed due to potential multiplicity before reconciling how:
1. , which is the basis of the table (3) construct, produces Eq. (10, 11) as derived in [13].These generate radii values substantially more accurate than any other contemporary
method. In-fact, it is a noteworthy result that EGM is capable of producing the Neutron MS
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charge radius as a positive quantity. Conventional techniques favor the non-intuitive form of
a negative squared quantity.
2. is capable of producing a Top Quark mass value the SM cannot.3. EGM produces the results defined in table (6).4. Extremely short-lived Leptons [i.e. with lifetimes of < 10-29(s)] cannot exist, or do not
exist for a plausible harmonic interpretation.
5. Any other harmonic interpretation, in the absence of exact mass and size values determinedexperimentally, denote a superior formulation.
Therefore, EGM is a method facilitating the harmonic representation of fundamental particles.
5.2.5 WHAT WOULD ONE NEED TO DO, IN ORDER TO DISPROVE THE EGM METHOD?
Explain how experimental measurements of charge radii and mass-energy by international
collaborations such as CDF, D0, L3, SELEX and ZEUS in [29,35-40,44], do not correlate to EGM
calculations.
5.2.6 WHY DOES THE EGM METHOD PRODUCE CURRENT QUARK MASSES AND NOTCONSTITUENT MASSES?
The EGM method is capable of producing current and constituent Quark masses, only
current Quark masses are presented herein. This manuscript is limited to current Quark masses
because it is the simplest example of ZPF equilibrium applicable whereby a particle is treated as a
system and the equilibrium radius is calculated.
Determination of the constituent Quark mass is a more complicated process, but the method
of solution remains basically the same. For example, Storti et. al. calculate an experimentallyimplicit value of the Bohr radius in [20] by treating the atom as a system in equilibrium with the
polarized ZPF.
5.2.7 WHY DOES THE EGM METHOD YIELD ONLY THE THREE OBSERVED
FAMILIES?
This occurs because it treats all objects with mass as a system (e.g. the Bohr atom) inequilibrium with the polarized ZPF (the objects own gravitational field). Therefore, sincefundamental particles with classical form factor denote fundamental states (or systems: Quarks inthe Proton and eutron) of polarized ZPF equilibrium, it follows that only the three families will be
predicted.
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5.3 PERIODIC TABLE OF ELEMENTARY PARTICLES
Assuming QB5,6 to be Intermediate Vector Bosons (IVB's), we shall conjecture that the
periodic table of elementary particles may be constructed as follows,
TTyyppeess ooffMMaatttteerr
GGrroouupp II GGrroouupp IIII GGrroouupp IIIIII
Up 14
+2/3,1/2,[R,G,B]
uuqq1.5 < muq(MeV) < 3
Charm 42
+2/3,1/2,[R,G,B]
ccqq
1.1833(GeV)
Top 140
+2/3,1/2,[R,G,B]
ttqq
172.0(GeV)
QQuuaarrkkss
Down 14
-1/3,1/2,[R,G,B]
ddqq3 < mdq(MeV) < 7
Strange 28
-1/3,1/2,[R,G,B]
ssqq
113.9460(MeV)
Bottom 56
-1/3,1/2,[R,G,B]
bbqq4.13 < mbq(GeV) < 4.27
Electron 2
-1,1/2
ee= 0.5110(MeV)
Muon 8
-1,1/2
= 105.7(MeV)
Tau 12
-1,1/2
= 1.777(GeV)
SSttaann
ddaarrdd
MMooddeell
LLeepp
ttoonnss
Electron Neutrino 20,1/2
ee
< 2(eV)
Muon Neutrino 80,1/2
< 0.19(MeV)
Tau Neutrino 120,1/2
< 18.2(MeV)
L2 4
-1,1/2
LL22
9(MeV)
L3 6
-1,1/2
LL33
57(MeV)
L5 10
-1,1/2
LL55
566(MeV)
EEGGMM
LLeeppttoonnss
L2 Neutrino 4
0,1/2
22
men
L3 Neutrino 6
0,1/2
33
mn
L5 Neutrino 10
0,1/2
55
mnSSttaannddaarrdd MMooddeell aanndd EEGGMM BBoossoonnss
Photon N/A
1,Charge,
3.2 x10-45
(eV)
Gluon ?
1,Colour,1
ggll< 10(MeV)
QB6 84
1, Weak Charge,10-6
QQBB66
22(GeV)
Z Boson 112
1,Weak Charge,10-6
ZZ
91.1875(GeV)
Graviton N/A
2,Energy,10-39
gg
= 2m
QB5 70
1, Weak Charge,10-6
QQBB55
10(GeV)
W Boson 98
1,Weak Charge,10-6
WW
80.27(GeV)
Higgs Boson 126
0,Higgs Field,?
HH
> 114.4(GeV)
Table 7: predicted periodic table of elementary particles,
LLeeggeennddQQuuaarrkkss LLeeppttoonnss BBoossoonnss
Name St
Charge(e),Spin,Colour
SSyymmbboollMass-Energy
Name St
Charge(e),Spin
SSyymmbboollMass-Energy
Name
Spin,Source,*SC
SSyymmbboollMass-Energy
(i) *Where, SC denotes coupling strength at 1(GeV). [45]
(ii) The values of St in table (7) utilize the Proton as the reference particle. This is due to itsRMS charge radius and mass-energy being precisely known by physical measurement.
Table 7: particle legend,
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6 COCLUSIO
A concise mathematical relationship, based upon homogeneity concepts inherent in
Buckingham Theory, augmented with Fourier series, has been used to combine gravitational
acceleration and ElectroMagnetism into a method producing fundamental particle properties to
extraordinary precision. This also results in the representation of fundamental particles as harmonic
forms of each other. Additionally, the solution herein predicts the existence of new fundamental
particles not found within the Standard Model suggesting the following:1. An exciting avenue for community exploration, beyond the Standard Model.2. The potential for new Physics at higher accelerator energies.3. The potential for unification of fundamental particles.4. Physical limitations on the value of two extremely important mathematical constants [i.e.
and ] at the quantum mechanical level subject to uncertainty principles.
REFERECES
[1] B.S. Massey, Mechanics of Fluids sixth edition, Van Nostrand Reinhold (International), 1989,Ch. 9.
[2] Rogers & Mayhew, Engineering Thermodynamics Work & Heat Transfer third edition,Longman Scientific & Technical, 1980, Part IV, Ch. 22.
[3] Douglas, Gasiorek, Swaffield, Fluid Mechanics second edition, Longman Scientific &Technical, 1987, Part VII, Ch. 25.
[4] K.A. Stroud, Further Engineering Mathematics, MacMillan Education LTD, Camelot PressLTD, 1986, Programme 17.
Note: [5 - 20] refer to: http://www.deltagroupengineering.com/Docs/Metric_Engineering.pdf
Riccardo C. Storti, Quinta Essentia: A Practical Guide to Space-Time Engineering, Part 3, MetricEngineering & The Quasi-Unification of Particle Physics, ISBN 978-1-84753-942-7, In Press.
[5] Ch. 3.1, Dimensional Analysis, Pg(85 - 95):
This chapter appears in: Riccardo C. Storti, Todd J. Desiato, Electro-Gravi-Magnetics (EGM), Practical modelling methods of the polarizable vacuum I,
Physics Essays: Vol. 19, No. 1: March 2006.
[6] Ch. 3.2, General Modelling and the Critical Factor, Pg(97 - 105):
This chapter appears in: Riccardo C. Storti, Todd J. Desiato, Electro-Gravi-Magnetics (EGM), Practical modelling methods of the polarizable vacuum II,
Physics Essays: Vol. 19, No. 2: June 2006.
[7] Ch. 3.3, The Engineered Metric, Pg(107 - 114):
This chapter appears in: Riccardo C. Storti, Todd J. Desiato, Electro-Gravi-Magnetics (EGM), Practical modelling methods of the polarizable vacuum III,
Physics Essays: Vol. 19, No. 3: September 2006.
[8] Ch. 3.4, Amplitude and Frequency Spectra, Pg(115 - 123):
This chapter appears in: Riccardo C. Storti, Todd J. Desiato, Electro-Gravi-Magnetics (EGM), Practical modelling methods of the polarizable vacuum IV,
-
8/14/2019 The Natural Philosophy of Fundamental Particles
18/32
18
Physics Essays: Vol. 19, No. 4: December 2006.
[9] Ch. 3.5, General Similarity, Pg(125 - 143):
This chapter appears in: Riccardo C. Storti, Todd J. Desiato, Electro-Gravi-Magnetics (EGM), Practical modelling methods of the polarizable vacuum V,
Physics Essays: Vol. 20, No. 1: March 2007.
[10] Ch. 3.6, Harmonic and Spectral Similarity, Pg(145 - 157):
This chapter appears in: Riccardo C. Storti, Todd J. Desiato, Electro-Gravi-Magnetics (EGM), Practical modelling methods of the polarizable vacuum VI,
Physics Essays: Vol. 20, No. 2: June 2007.
[11] Ch. 3.7, The Casimir Effect, Pg(159 - 166):
This chapter appears in: Riccardo C. Storti, Todd J. Desiato, Electro-Gravi-Magnetics (EGM), Practical modelling methods of the polarizable vacuum VII,
Physics Essays: Vol. 20, No. 3: September 2007.
[12] Ch. 3.8, Derivation of the Photon Mass-Energy Threshold, Pg(169 - 173):This chapter appears in: Riccardo C. Storti, Todd J. Desiato, Derivation of thePhoton mass-energy threshold, The Nature of Light: What Is a Photon?, edited by C.
Roychoudhuri, K. Creath, A. Kracklauer, Proceedings of SPIE Vol. 5866 (SPIE,
Bellingham, WA, 2005) [pg. 207 - 213].
[13] Ch. 3.9, Derivation of Fundamental Particle Radii (Electron, Proton and Neutron),
Pg(175 - 182).
This chapter has been submitted to Physics Essays as: Riccardo C. Storti, Todd J.Desiato, Derivation of Fundamental Particle Radii (Electron, Proton and Neutron).
[14] Ch. 3.10, Derivation of the Photon and Graviton Mass-Energies and Radii,
Pg(183 - 187):
This chapter appears in: Riccardo C. Storti, Todd J. Desiato, Derivation of thePhoton & Graviton mass-energies & radii, The Nature of Light: What Is a Photon?,
edited by C. Roychoudhuri, K. Creath, A. Kracklauer, Proceedings of SPIE Vol.
5866 (SPIE, Bellingham, WA, 2005) [pg. 214 - 217].
[15] Ch. 3.11, Derivation of Lepton Radii, Pg(189 - 193).
[16] Ch. 3.12, Derivation of Quark and Boson Mass-Energies and Radii, Pg(195 - 203).
[17] Ch. 3.13, The Planck Scale, Photons, Predicting New Particles and Designing anExperiment to Test the Negative Energy Conjecture, Pg(205 - 216).
[18] App. 3.G, Derivation of ElectroMagnetic Radii, Pg(255 - 262).
[19] App. 3.H, Calculation of L2, L3 and L5 Associated Neutrino Radii, Pg(263).
[20] App. 3.I, Derivation of the Hydrogen Atom Spectrum (Balmer Series) and an
Experimentally Implicit Definition of the Bohr Radius, Pg(265 - 268).
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[21] App. 3.K, Numerical Simulations, MathCad 8 Professional, Complete Simulation,
Pg(283 - 363).
[22] App. 3.L, Numerical Simulations, MathCad 8 Professional, Calculation Engine,
Pg(367 - 386).
[23] App. 3.M, Numerical Simulations, MathCad 12, High Precision Calculation Results,
Pg(389 - 393).
[24] Alfonso Rueda, Bernard Haisch, Contribution to inertial mass by reaction of the vacuum toaccelerated motion, Found.Phys. 28 (1998) 1057-1108: http://www.arxiv.org/abs/physics/9802030
[25] Alfonso Rueda, Bernard Haisch, Inertia as reaction of the vacuum to accelerated motion,Phys.Lett. A240 (1998) 115-126: http://www.arxiv.org/abs/physics/9802031
[26] Bernard Haisch, Alfonso Rueda, Hal Puthoff, Advances in the proposed electromagneticzero-point field theory of inertia, presentation at 34th AIAA/ASME/SAE/ASEE Joint Propulsion
Conference, July 13-15, 1998, Cleveland, OH, 10 pages: http://www.arxiv.org/abs/physics/9807023
[27] Puthoff et. Al., Polarizable-Vacuum (PV) approach to general relativity, Found. Phys. 32,927 - 943 (2002): http://xxx.lanl.gov/abs/gr-qc/9909037
[28] Particle Data Group, Photon Mass-Energy Threshold: S. Eidelman et Al. Phys. Lett. B 592, 1(2004): http://pdg.lbl.gov/2006/listings/s000.pdf
[29] The SELEX Collaboration, Measurement of the -
Charge Radius by -
- Electron Elastic
Scattering, Phys.Lett. B522 (2001) 233-239: http://arxiv.org/hep-ex/0106053
[30] Karmanov et. Al., On Calculation of the Neutron Charge Radius, Contribution to the ThirdInternational Conference on Perspectives in Hadronic Physics, Trieste, Italy, 7-11 May 2001, Nucl.
Phys. A699 (2002) 148-151: http://arxiv.org/abs/hep-ph/0106349
[31] P. W. Milonni, The Quantum Vacuum An Introduction to Quantum Electrodynamics,Academic Press, Inc. 1994. Page 403.
[32] Mathworld, http://mathworld.wolfram.com/Euler-MascheroniConstant.html
[33] Hirsch et. Al., Bounds on the tau and muon neutrino vector and axial vector charge radius,Phys. Rev. D67: http://arxiv.org/abs/hep-ph/0210137
[34] National Institute of Standards and Technology (NIST): http://physics.nist.gov/cuu/
[35] The D-ZERO Collaboration, A Precision Measurement of the Mass of the Top Quark, Nature429 (2004) 638-642: http://arxiv.org/abs/hep-ex/0406031
[36] Progress in Top Quark Physics (Evelyn Thomson): Conference proceedings for PANIC05,
Particles & Nuclei International Conference, Santa Fe, New Mexico (USA), October 24 28, 2005.
http://arxiv.org/abs/hep-ex/0602024
[37] Combination of CDF and D0 Results on the Mass of the Top Quark, Fermilab-TM-2347-E,
TEVEWWG/top 2006/01, CDF-8162, D0-5064: http://arxiv.org/abs/hep-ex/0603039
-
8/14/2019 The Natural Philosophy of Fundamental Particles
20/32
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[38] The CDF & D0 Collaborations, W Mass & Properties, FERMILAB-CONF-05-507-E.
http://arxiv.org/abs/hep-ex/0511039
[39] The L3 Collaboration, Measurement of the Mass and the Width of the W Boson at LEP, Eur.
Phys.J. C45 (2006) 569-587: http://arxiv.org/abs/hep-ex/0511049
[40] The ALEPH, DELPHI, L3, OPAL, SLD Collaborations, the LEP Electroweak Working Group,
the SLD Electroweak & Heavy Flavor Groups, Precision Electroweak Measurements on the ZResonance, CERN-PH-EP/2005-041, SLAC-R-774: http://arxiv.org/abs/hep-ex/0509008
[41] Hammer and Meiner et. Al., Updated dispersion-theoretical analysis of the nucleonelectromagnetic form factors, Eur. Phys.J. A20 (2004) 469-473:
http://arxiv.org/abs/hep-ph/0312081
[42] Hammer et. Al, Nucleon Form Factors in Dispersion Theory, invited talk at the Symposium"20 Years of Physics at the Mainz Microtron MAMI", October 20-22, 2005, Mainz, Germany,
HISKP-TH-05/25: http://arxiv.org/abs/hep-ph/0602121
[43] Spectrum of the Hydrogen Atom, University of Tel Aviv.
http://www.tau.ac.il/~phchlab/experiments/hydrogen/balmer.htm
[44] The ZEUS Collaboration, Search for contact interactions, large extra dimensions and finite
quark radius in ep collisions at HERA, Phys. Lett. B591 (2004) 23-41:
http://arxiv.org/abs/hep-ex/0401009
[45] James William Rohlf, Modern Physics from to Z, John Wiley & Sons, Inc. 1994.
[46] J. F. Douglas, Solving Problems in Fluid Mechanics, Vol. 2, Third Edition, Longman
Scientific & Technical, ISBN 0-470-20776-0 (USA only), 1986.
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APPEDIX A
T r M,( )1
r M,( )(A1)
Illustrational (only) wavefunction [Eq. (A2)] based on Proton harmonics,
St t, sin St 2. . r mp,
. t. (A2)
0 5 .1029
1 .1028
1.5 .1028
2 .1028
2.5 .1028
3 .1028
3.5 .1028
Proton, Neutron
Electron, Electron Neutrino
L2, v2
L3, v3
1 t,( )
2 t,( )
4 t,( )
6 t,( )
1
2T r mp,.
t
Figure A1,
0 5 .1030
1 .1029
1.5 .1029
2 .1029
2.5 .1029
3 .1029
3.5 .1029
4 .1029
4.5 .1029
Muon, Muon Neutrino
L5, v5
Tau, Tau Neutrino
Up and Down Quark
8 t,( )
10 t,( )
12 t,( )
14 t,( )
1
16T r mp,.
t
Figure A2,
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0 1 .1030
2 .1030
3 .1030
4 .1030
5 .1030
6 .1030
7 .1030
8 .1030
9 .1030
1 .1029
1.1 .1029
1.2 .1029
1.3 .1029
Strange Quark
Charm Quark
Bottom Quark
QB5
28 t,( )
42 t,( )
56 t,( )
70 t,( )
1
56T r mp,.
t
Figure A3,
0 5 .1031
1 .1030
1.5 .1030
2 .1030
2.5 .1030
3 .1030
3.5 .1030
4 .1030
4.5 .1030
QB6
W Boson
Z Boson
Higgs Boson
Top Quark
84 t,( )
98 t,( )
112 t,( )
126 t,( )
140 t,( )
1
168T r mp,.
t
Figure A4,
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APPEDIX B
Graviton mass-energy, [14]
mgg = 2m (B1)
Photon mass-energy, [14]
mh
re3
3 re.
2 c. G. m e.
.512 G. m e
.
c 2.
2
.n re m e,
ln 2 n re m e,.
2
.
(B2)
Photon RMS charge radius 1st
representation, [14]
r re
5
m
m e c2.
2
. (B3)
Photon RMS charge radius 2nd
representation (in terms of the Planck scale), [17]
r KG h.
c3
.r
r
.
(B4)
Graviton RMS charge radius, [14]
rgg
54 r.
(B5)
Fine structure constant 2nd
representation, [15]
r
r
e
r
r. (B6)
Neutron charge distribution, [18]
ch r( )2
3
KS
3
r
5. x2
1.
. e
r
r
2
1
x3
e
r
x r
.
2
.. (B7)
Neutron Magnetic radius, [18]
Given
r ch rM.
r
rdr
r
r ch r( )d
(B8)
rM Find r M
Proton Electric radius, [18]
Given
r ch rE.
r
rdr
r ch r( )d (B9)
rE Find r E
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Proton Magnetic radius, [18]
Given
r ch rM.
rdr
r
r ch r( )d
(B10)
rM Find r M
Classical RMS charge radius of the Proton by the EGM method, [18]
rP rE1
2rM r
.
(B11)
1st
term of the Balmer series by the EGM method, [18]
A
PV 1 K rBohr., mp,
2 n K rBohr. mp,
.
(B12)
EGM wavelength, [8]
PV n PV r, M,c
PV n PV r, M,(B13)
Bohr radius, [43]
rBohr
0 h2.
m e. Q e
2.(B14)
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APPEDIX C
Illustration examples of Dimensional Analysis Techniques and Buckingham Theory
(for unfamiliar readers) have been taken from [46] and shown below,
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