j. gregory moxness - a more natural reference model integrating relativity and quantum mechanics

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A More Natural Reference Model

Integrating Relativity and Quantum Mechanics

J Gregory Moxness

(Dated: OriginalApril 13, 1997, CurrentNovember 22, 2007)M Theory and/or Loop Quantum Gravity hold the promise of resolving the conflict between

general relativity and quantum mechanics but lack experimental connections to predictability inphysics. A connection is made to these and other theories vying for the title of a Theory ofEverything by questioning the value of the traditional Planck unit reference point for the scalesat which they operate. It also suggests a cosmological model which has acceleration as beingfundamental. It provides for an intuitive understanding of the Standard Model and its relationshipto particle masses and the structure of the atom. The prediction of particle mass and lifetimes is agood indicator for its validity.

PACS numbers: 03.65, 04.20.-q, 11.25.-w, 11.27.+d, 12.10.-g,12.60.-i, 95.30. 95.35.+d, 95.75.Wx, 98.80-kKeywords: M Theory, LQG, E8, Quantum Mechanics, Relativity, Cosmology, Standard Mo del, CKM

I. INTRODUCTION

This paper will present a new more natural refer-ence model for integrating General Relativity (GR) andQuantum Mechanics (QM) by contrasting it with the de-velopment of a reference model based on the more tradi-tional Planck units. The new unit-of-measure (UoM) isbased on the non-linear expansion or acceleration of theuniverse [1]. It provides a testable framework for par-ticle mass prediction in support of the Standard Model(SM) as well as M Theory (MT), Loop Quantum Grav-ity (LQG) and A. Garret Lisis recent An ExceptionallySimple Theory of Everything (aESToE) based on an E8Lie Group Theory [2].

The fact that the universe is found to be accelerat-ing indicates that an exponential model which accommo-dates this acceleration could be more natural than thetraditional linear model. The key to defining this newmodel relies on deriving unity as the center of scalesfor length (L), time (T), mass (M), and charge (Q) thatare exponentially expanding.

Grand Unified Theories (GUTs) hold in high regardthe Planck scale for its natural proximity to the unifica-tion energies. This scale is set by setting the fundamentalparameters of the velocity of light (c), Plancks constant(), and Newtons Constant (GN) to unity. Planck unitsare derived by combining powers of these constants into

their dimensions of L, T, M, and Q. In terms of space-time, it seems to identify a possible lower limit to thelength scale at one unit Planck length (lP =

GN/c3).

Cosmological models logically define an upper limitbased on the age and extent of the universe. In addi-tion to an upper and lower limit (e.g. infinity () andzero= 1/ respectively), an exponential model should

URL: http://www.TheoryOfEverything.org/TOE/JGM;mailto:[email protected]

identify a center (unity) in order to be well defined. Inphysics, the upper limit is naturally thought to be in-

dicated by the macro world of GN and GR. The lowerlimit is the micro world ofand QM. Fortunately, c is athome in both the micro and macro worlds. In the Planckunit model, the expanse between unity and zero is whereGR and QM require the new physics beyond SM. Asa reference model for scaling the universe, it offers no di-rect prescription for phenomena associated with atomicscales; therefore, using Planck units as a reference framefor the center of an exponentially scaling model seemscounter-intuitive.

A new model is offered that uses this same generalapproach in defining natural dimensions but with inter-esting results achieved by associating with it two morefundamental parameters - the macro Hubble (H0) andthe micro fine structure (). This approach does not de-tract from the significance of the Planck scale and its as-sociated theoretical frameworks; however, it adds a pointof view that puts it properly at the micro edge of an ac-celerating universal expansion.

II. DEFINING THE NEW MODEL

Except for the Hubble parameter, the fundamental pa-rameters of , c, GN, and are typically thought to beconstant. A new model based on an accelerating universeis achieved by considering that all of these fundamentalparameters vary with time[]. It is also necessary to re-define the relationships between the measurable aspectsor dimensions of our reality.

[] Measuring synchronous time variation of multiple fundamentalconstants is problematic due to the principle of covariance. Timevariation per tunit is 1 in Nt = 8 = 1 .2435904532 1017.


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A. Relating Length to Time

In Planck units, c sets up the relationship betweenspace and time by being driven to an effective dimen-sionless unity (a.k.a. geometrized units). This is doneby setting unit (Planck) time as that taken by a photonto traverse 1 unit lP, such that tP = lP/c = 1. In termsof experimental precision, c is a defined measurementwith no standard error. That is, its value is used to definelength and time by counting its particle/wave oscillationsor pulses.

The concept of using c to drive the relationship of spaceand time is also used in the new model with the differ-ence focusing on the fact that the universe is found tobe accelerating. This new model creates a relationshipbetween the fundamental constants which provides anopportunity to normalize them to that universal accel-eration. It does this by defining their magnitudes to bevarying with time. For consistency, it also modifies thetraditional understanding of the relationship between thedimensionality of L and T. The fundamental constantsare now more properly referred to as fundamental pa-rameters.

For the assumptions in this new model, accelerationbecomes a dimensionless unity and requires setting Lto be equivalent to the square of the time dimension[]:

L = T2 (1)

or alternatively T=L/2 and I=1 =

T.

With c as the indicator for the expansion of space-timethrough its integral relationship with the impedance offree space (0) derived from permittivity (0) and perme-

ability (0), it is natural to be defined as covariant withan accelerating universe. Since LT1 = T, c can also bedirectly associated with the age of the universe insteadof Plancks (dimensionless) unity. Of course, since H0 ofdimension T1 is directly related to the age of the uni-verse, it can be incorporated into the new model as wellwith[]:

aU = 4H0c = 1 Unit Acceleration

= 1 Dimensionless U nit (2)

= 86.648 Angstroms/s2

where:

c = H0 = 1 Dimensionless U nit (3)

H0 is defined using the space metric (a) is a function oftime. It can also be defined as a function redshift factor

[] Procedural note: in terms of the traditional dimensionality of L,T, M, Q, the extra time dimensions found are associated withthe complex plane.

[] This is an explicit acceleration in terms of dimension and doesnot rely on the modified relationship between L and T.

(z) as a(z). Depending on cosmological model, this cangive the age of the universe:

tU = a(0)/H0 (4)

The normalization is made possible by (2) and thismodels definition of:

H0 = 8

/(4tunit) (5)c = 8lunit/tunit = 1/(4H0) =

8tunit (6)

For the purposes of this work, the assumption is thatthis relationship is correct and that the analysis of ex-perimental evidence for the constraints on multiple timevarying fundamental parameters will corroborate this.

A less dramatic alternative is also offered by definingL=T and a dimensionless c = 1/(4H0 tunit) = 8.There is evidence from the relationships defined belowthat this is just as reasonable. This alternative has simi-lar dimensionality to that of the traditional Planck UoM,along with its constant fundamental parameters. Unfor-

tunately, it negates several interesting results related tothis models tie to E8 and/or MT. Some of these resultscan be recovered by instead relating the 8 dimensions ofcharge to Degrees of Freedom (DoF). Unfortunately, thisstill leaves open the interpretation for the value of .

B. The Constancy of Constants

An analysis of the possible time dependence of c, GN,the cosmological constant (), and the dark energydensity () has determined [3] that if:

= 2 cc

GNGN

(7)

then is constant. The new model has:

c

c= GN

GN=

=

1

tU(8)

implying that is not constant.Current experimental evidence for (and constraints on)

the magnitude of the time variation in the fundamentalparameters is on the order of 1 part in 1014 per yearfor GN (from type Ia supernova data [4]) and 1 part in

1016

per year for (from quasar dust cloud and Okloreactor data [5]). Of course, these calculations assumedthat the other fundamental parameters were constant.This assumption could account for the discrepancy inthis models GN and varying at 1 part in 109 per year,which is too large by a factor of 105 for GN and 107 for.

In the case where these fundamental parameters areconsidered unity and constant, as in Natural and PlanckUoM, their scaling may be accounted for in the scalingof other related parameters, such as in gauge theoriesand/or Running Coupling Constants (RCC).


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C. Relating Length to Mass

Typically, equating dimensions of L to M in Planckunits uses the QM based Compton effect. SettingPlancks constant (h or = h/2) and c to unity ef-fectively associates a Compton (wave) length to be theinverse of mass or L = M1. The association of L to Mcan also be accomplished in GR by associating mass toits gravitational radius. This method establishes L=Mat odds with the Compton method. While this GR ap-proach removes the dimensionality of GN, it leaves a di-mensionality to of L2, which is used by Veneziano [6]to link GR to MT by setting to the square of stringlength (lP). Another motivation for Planck units is de-rived from the fact that it is only at lP that these twomethods for relating length to mass converge.

In the new UoM model, as in Planck units, it usesthe Compton effect to set = lunitmunitc while givingsignificantly different results due to c being associatedwith time and not (dimensionless) unity. This begs thequestion of whether to simply take the Compton effectas natures indicator of the dimensional relationship be-tween length and mass. Compton relates mass to a 1Dwavelength. In 4D GR space-time, the inter-relationshipbetween mass and gravity is spherically symmetric. Theability to link GR and QM in an intuitive way becomesproblematic.

A more natural alternative to rationalizing this prob-lem is offered. The Compton effect is the indicatorof the inter-dependence between a particles rest massand the corresponding quantized wavelength and angleof its emissions. It is merely one aspect of how massrelates to length given the wave-particle duality of na-ture. It is reasonable to understand a particlesrest mass in terms of both a QM-like linear wavefrom the Compton effect (L = M1) and a GR-like point particle from a spherically symmetricvolume compression (or deceleration) of space forsome period of time. That is:

M = L3T1 = T5 (9)

or in terms of a volume of space (V) simply M = V /6.This implies that the transformation of GR space-timeinto a particles rest mass is a separate transformationfrom that of QM transformations to the massless photon(). This idea is the key to particle mass prediction of

the new model.Since is a quantized angular momentum (mvr or

spin), its particle dimensionality in the new model is:

ML2T1 = T8 (10)

which indicates a linkage of QM and GR with E8 and/oran 11D MT space-time with 3 real dimensions of spaceand 8 dimensions associated with time, but allocated tocomplex imaginary space.

The model identifies a very natural unit length which isprecisely related to the inverse of the Rydberg Constant

(R):

lunit =

R=

2h

mec=

4

mec= 4a0 (11)

This is twice the circumference of the Bohr model of theatom (2a0). If this lunit is related to spin (), it is clearthat a fermion of spin /2 would then be precisely thecircumference of the Bohr atom. It should be noted thatlunit is being defined using the most accurately measuredparameters [7], where and me are calculated using Rknown to a standard error of 6.6 ppt or 6.6 1012 and at 0.7 ppb or 7.0 1010. This is accomplished usingthe definition of and the electron or elementary charge(e) less accurately known to 85 ppb:

=0e

2

4(12)

So from (11) and (12) with an error twice that of esgiving 170 ppb accuracy to:

me = 4R2c

= 0e2

R3c

= 0e2

R3

(13)

It is also interesting to note that R is theoreticallyderived by finding the smallest electron radius of a classi-cal (Bohr orbital) model allowed when incorporating thequantum model using the Hiesenberg uncertainty princi-ple. This may support the idea that the R = /lunit ismore deeply connected to the boundary of both classical-relativistic (macro) and quantum (micro) models of theuniverse than lP.

D. The New Model and Special Relativity (SR)

It is instructive to visualize the new model using theconcepts of SR. Normalizing c to aU allows for an explicitdescription of the mechanism for changing a particlesvelocity (v). It is done by constraining aU in one ormore dimensions. The velocity increases orthogonally tothe constraint ofaU. The explanation for Lorentz lengthcontraction (l), time dilation (t), and increase in mass(m) are a natural result of constraining aU. See Fig. 1.

E. Defining Mass Magnitude

Completing a minimally constrained definition inPlanck units is accomplished by locking in a specific unitof mass by the free selection of the magnitude for GN = 1.For the most part this affords a pleasing result. Unfortu-nately, it also results in a unit mass that is significantlylarger than the particles of the SM. This large unit massis rationalized with the hope that it will be the harbingerof particles in a GUT. This indeed may be the case andis not precluded in the definition of the new model.

Since the new UoM-based model is already over-constrained, the ad hoc selection of the magnitude ofGN


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FIG. 1: Visualizing the new model

is not possible. The new relationships between L, T, andM give GN a dimension of T

1, and a new relationshipwith H0 is possible:

GN = 4H0 (14)

in terms of both magnitude and dimension. Given ac-curate current measure of Newtons Constant at 14 ppm[8]:

GN = 6.674215 1011 m3

kg s2(15)

the Hubble parameter can be calculated very precisely interms of velocity per mega parsec (Mpc) as:

H0 = 81.3248km/s

Mpc(16)

This preliminary value is outside a rather large standarduncertainty of 5% by a factor of 3 [9], but will be el-egantly adjusted in a later section. More detailed sig-nificance of an interestingly small particle size munit =296.7397 eV/c2 [] and a rather large tunit = 0.2758466 swill also be discussed in a later section.

F. Defining Charge

The magnitude and dimensionality for a unit of chargestill needs to be defined explicitly. It has implications for

[] Representing mass as (eV/c2) is less common than simply (eV).Natural UoM facilitates ignoring fundamental parameters set tounity (, c, GN) and equates mass, energy, length and time. Thispaper exposes the risks of this habit based on UoM assumptions,and attempts to clarify and maintain complete and accurate rep-resentations.

Quantum Field Theory (QFT) linking Quantum Electro-Dynamics (QED) to Quantum ChromoDynamics (QCD),particle mass prediction, as well as a more general link-age between GR, QM, E8 and/or MT. In Planck units,charge is essentially a dimensionless parameter. It setse(Q) to the small fraction

4. Since the dimension-

ality of M has been redefined in terms of L and T, analternate definition to the dimensionality of Q is offered

with p ossible implications for Higgs mass prediction.Holding 0 to dimensionless unity and using the new

models dimensional definition for M sets the magnitudeof e2(Q) = 4 and the dimensionality to:

Q = M L1/2 = M T1 = L2 = T4 (17)

Charge can now be visualized as a measure ofthe quantum change in particle mass per unittime. In terms of an area (A): Q = M/5 = V /30 = A.In this model, with the possibility for complex space-

time, the quantization of charge seems necessary for themass transformation between the real spatial dimensionsof a 3D GR particle-like volume compression and itsdual 1D QM linear wave-like Compton effect. That is:M(3D)/M(1D) = Q(2D) = A = 1 [].

The significance of an intuitive choice for the magni-tude of the charges mass gives a testable prediction forwhat may be the mass of the Higgs boson (mH). Thiscan be shown to have new more natural relationships inthe definitions of the Fermi Constant (GF), ElectroWeak(EW) mixing angle (w), the Vacuum Expectation Value(VEV or v, and < 0 >0) [10], and Zero Point Field(ZPF):

mH =

2 lunit =

2/R

=

8

mec=

munitc/2

(18)

= 147.98904797 GeV/c2 G1/2F /2

and:

qunit = e = mH

4

2 lunit= mH

2R

= mH

mec2

=

4 =

2h (19)

This leaves the possibility of a new interpretation forthe parameter (4) traditionally equated in a Planckunit model to e2 where = 1.

[] Obviously, in this context, dimension D = Re[L] = T, or equiv-alently D = L = T2 if M[3D] = T M[T5].


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1. EW Mixing Angle (w)

The EW ratio (4) from (12) is used to define a weakmixing or Weinberg angle of:

w = sin1 xw = 28.3489498827 (20)

where:

xw =1

2

4 = 0.225473272505 (21)

Surprisingly, this value is easily derived from the stan-dard EW model [11] with a bit of algebraic manipulation,where:

g = e/

xw (22)

g = e/

1 xw (23)using a typical EW SM constraint:

g = xw8

0(24)

Of course, this also agrees with EW SM predictions:

e =gg

g2 + g2= g sin w = g cos w (25)

This prescription for the input parameters of the EWmodel is within the experimental standard error [7] of3.4 ppk when averaged with xw[OnShell] = 0.22215 andxw[MS] = 0.23124. Taking the average of the two xwschemes might be linked to RCC.

G. Completing the Model

Combining the discussion of magnitude and dimensionabove into a single equation, gives:

(T8)

lunitmunit= c =

1

GN=

1

4H0= 134.8678tunit 8tunit (26)

The inverse relationships between the fundamental pa-rameters and a more natural connection between gravita-tional attraction and Hubble expansion may suggest the

duality of MT relating the micro and macro worlds de-fined above. The proximity of the magnitudes to 8tunitmay extend the model even further. This exponent seemsto support the 8D time construct previously noted in thedimensionality of implying that fine structure is a frac-tional dimension (fractal) of time.

1. Linking GN and w

It is possible to adjust the Newtonian or GR value of

G(D=3+1=4)N to the MT value of G

(D=3+8=11)N using the

dimensionless gravitational coupling factor for open (go)and closed (gc) strings [12] where gc = g2o and GN =g2c

8/tunit. A value of:

g2c =

1 2( /2)2

cos w=

1 2( /2)21 3

/2

= 1.13612135987 (27)

which alters (26) and shifts the values for H0 =71.5811688427 km/s/Mpc and = 1/137.0359997094in precise alignment with the center of all currentexperimental values [13]! SM can now be directlylinked to GR and MT giving GN = 6.674220938621011 m3/kg s.

III. MODEL DETAIL AND PREDICTIONS

Combining these discussions of dimensions and magni-tude of the fundamental parameters results in an ability

to associate the results to familiar arguments as well aspredict new relationships in physics.

A. Charge Predictions

The complexity of charge in the SM involvesRCC, perturbation theory, Axial-Vector (A-V) currents,quark Cabibbo-Kobayashi-Maskawa (CKM) and neu-trino Maki-Nakagawa-Sakata (MNS) phased mixing ma-trices, Noethers theorem linking conservation rules andCPT symmetry (and its violations), the Unitary Tri-

angle, a dual Standard Model (dSM), and SU(5) SU(3)C SU(2)I U(1)Y /Z6 group theory. The newmodel builds on this by introducing a simplifying selfdual Standard Model (sdSM) while predicting and retroor post-dicting the parameters in the theories just men-tioned. It solves the hierarchy problem and explains finetuning of the fundamental parameters.

1. Linking RCC andxw

RCC, with its varying of at different energies ormasses, is a method that accommodates experimental

results and provides for the idea of grand unificationat (or near) the Planck mass (mP = /clP =

c/GN)

scale. If RCC is viewed as an accommodation of the effectthat the accelerating universe has on the fundamentalparameters, then by (21), xw and w will vary with dif-ferent . Using this as a guide to understanding the dif-ference between xw()[MS] and xw()[OnShell], calcu-lating xw()[MS] gives consistent results with (MZ) =1/127.037.

It will be interesting to see whether the strongcoupling constant in the modified-minimal-subtractionscheme s(MZ)[MS] = 0.1177(13) might also relate to


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s(mH)[MS] = xw/2 = 0.1127. The modification ofRCC using (26) as an indicator to the path to grand uni-fication is an interesting alternative to current thinking.

2. Linking CKM andxw

It is also found that xw may relate to the Cabibbo

angle (c) in the Wolfenstein parameterization of theCKM matrix [14] where = |Vus| = sin c. Morerecent data suggests that = xw may not be out-side a rather large standard error of > 1% for c [15].With = /3(60), = 1/A = 2/3, = /2, and = 1/(

3) gives:

VCK M =

1

2

2 A3ei

1 22 A2A3(1 ei ) A2 1

= 1 2

2 A3( i)

1

2

2A2

A3(1 ( + i)) A2 1 =

0.974580 0.225473 0.0057310.225473 0.974580 0.050838

0.011462 0.050838 1

(28)

where it is interesting to note, |VCK M[1, 3]| = /4and |VCK M[3, 1]| = /2. The error for each value (in1/parts per unit) gives:

VCK Merror =

1061 429 22429 5386 10

24 10 832

(29)

A simpler model which gives the same results, butwith a large error in |Vtd| = 50% is given where =/3(60), = 1/A = 1, = /2, and =

3 gives:

VCK M =

1

2

2 3ei

1 22

2

3(1 ei ) 2 1

=

0.974580 0.225473 0.0057310.225473 0.974580 0.050838

0.005731 0.050838 1

(30)

The error for each value (in 1/parts per unit) gives:

VCK Merror = 1061 429 22429 5386 10

2 10 832

(31)

3. Axial Vector Coupling (CAV)

It has been found that the Axial-Vector relationshipcan be defined within experimental error as:

CA V = l3unit H0tunit munit

= 5.583694478 1044 cm3MeV/c2 (32)

4. Fermi Constant (GF)

To a posteriori obtain the weak boson masses and thecharged lepton masses requires the theoretical derivationofGF and < 0 >0= v/

2. The definition ofmH in (18)

can be used such that:

GF =

GF(c)3

=

2mH1 + r

2= 1.166390 105 (GeV/c2)2 (33)

8

8m2unit= 1.141512 105 (GeV/c2)2

where r = 2.179195% due to radiative corrections inthe definition of GF []. As in the calculation of par-ticles anomalous magnetic moments (e.g. ae), the ra-diative corrections are precisely calculated by countingself induced perturbations as described in Feynman loopdiagrams. Unfortunately, this prescription for r is sig-

nificantly outside the very small experimental and the-oretical standard error of 8.6 ppm by a factor of 2500.When comparing the non-perturbative GF with an errorof 2.2 ppk, this error factor is reduced to 9. This erroris expected to be rationalized by changes in perturbationtheory based on the new model.

5. The Vacuum Energy (VEV orv, and < 0 >0)

The EW Fermi model, mH, e, and GF gives:

v = 1/

GF2 mH

22

= 248.886919 GeV/c2 (34)

< 0 >0 = v/

2 mH

2

= 175.989628 GeV/c2 (35)

6. The Self Dual Standard Model (sdSM)

The dual SM (dSM) [16] is based on the SU(5) SU(3)C SU(2)I U(1)Y/

Z6 group theory. It relatesthe SU(2)I representation of left-right (L,R) isospin (I),

the SU(3)C representation of red-green-blue (r,g,b) color(C), and U(1)Y representation of Yukawa hypercharge(Y) in SU(5). This is done using a diagonal transforma-

[] As explained in footnote [] re: Natural UoM, it is less com-monly (but more precisely) represented as GF = (c)

3/mass2.This model explicitly defines GF in terms of m

2H only. Depend-

ing on usage, the factor of (c)3 is only needed for proper con-versions.


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tion matrix T=(r,g,b,L,R):

TC = Diag(13

, 13

,2

3, 0, 0) (36a)

TI = Diag(0, 0, 0, 1, 1) (36b)TY = Diag(1, 1, 1, 3

2, 3

2) (36c)

These matrices are then used with the standard SU(3)monopole representation of each particle m(C,I,Y) pro-ducing the SU(5) group monopoles M(r,g,b,L,R) for thatparticle. The specific transformation is M(r,g,b,L,R) =mC TC + mI TI + mY TY . For example, the left andright handed spin electrons (eL,R) transform as follows:

eL = m(0, 1/2, 1) M(1, 1, 1, 2, 1)(37a)eR = m(0, 0, 2) M(2, 2, 2, 3, 3) (37b)

The sdSM model is essentially the same with the ad-dition of a factor of 3 and 2 for TC and TY respectively.In order to maintain SU(5) consistency, the typical mC

and mY values also change by an inverse factor (respec-tively). This has the effect of creating all integer matricesfor M and T. More importantly, it maintains integer par-ticle representations of m(C,I,Y) by factoring out simpleinteger fractions of 1/2 and/or 1/3.

It should also be noted that mI is a left handed rep-resentation with L=-R. In the absence of isospin, theparticle will be right handed. It is this rotational (I)symmetry that represents the assymetry of time (T) dueto aU. Color is slightly complicated with mC having aneven distribution of an arbitrarily chosen (negative) colorwith a 3-fold degenerate distribution of (r,g, or b) added(or subtracted). It is this translational color symmetry,

now labeled as (Clr) in order to avoid confusion uponthe introduction of Charge parity (C), that representsthe assymetry of sPace parity (P) also due to aU. It es-tablishes a complex linkage with the real dimensions ofspace (x,y,z), as well as the imaginary (x, y, z) dimensionsrelated to the discussion of (1). This has direct implica-tions for GR and the formation of the more significantmass of the 3 flavor generations and nucleons. Both mIand mC sum to zero within their representations. Hy-percharge is more complicated with an even distributionof color (r,g,b) and isospin (L,R) components, which sumto zero across (Clr) and (I). Hypercharge can be said torepresent the interchange of color and isospin.

In this model, eR = mY and represents an arbi-trarily chosen (negative) hypercharge. The down quarkrepresents a 1/3 interchange of hypercharge and colordR = (mY mC)/3. Of course, the W represents theinterchange of the up and down quarks, but it is inter-esting to note that they also represent the pure cou-plings WR = mY and WL = mI. Looking intocomposite 3 quark (baryon) particle representations, itis interesting to note that n0R(d

rR, d

gL, u

bR) = mC and

0R = 3dR + W+

R = 3mC.As in SM, strong Yukawa hypercharge (Y) and Isospin

(I, Ix,y,z , I3) is 0 for generation 2 and 3 particles.

Weak Yukawa hypercharge (YW) and isoTopic spin(T, Tx,y,z , T3) is related to strong hypercharge andIsospin through c and the CKM matrix.

Space parity and angular momentum quantum numbers

In standard representations [17], the principle integer

quantum number is n = 1 for fundamental SM particlesand n 1 for composite particles. This gives a specificorbital (or azimuthal) angular momentum (L = l 1 n 1 = 0). The orbital magnetic quantum number (m,not to be confused with the monopole matrix represen-tation above) is l m l. It affects the probabilitydistributions, but not the total momentum of the parti-cles.

Space parity transformation (P) has a translationaltransformation of Px,y,z Px,y,z and a quantum rota-tional transformation P = (1)L+1 (a.k.a. even or oddparity). P=CT violation is shown by a lack of evidencefor right handed neutrinos (R).

Spin has horizontal and vertical axial components(sy,z ) and vector components along the direction of mo-mentum (sx). A generic representation of a spin axisis (sx,y,z = s3). The specific particle angular momen-tum is (S = s3). Total angular momentum (J) is|L S| J L + S of dimension . For fundamen-tal SM particles where n = l = 1, L = 0, J = S = s.Single SM particle fermions (leptons and quarks) areJ = 1/2, while single gauge (and Higgs) boson (force)particles are J = 1. Leptons have only J transformations.For composite particles made up of multiple fundamentalfermions, J is half the difference of left and right handedparticles or simply J = |#L #R| /2 [].

Charge conjugation and time reversal

Total charge in this model is Q = (I+Y)J of dimensionq2unit = e

2. Charge conjugation is C = (1)L+S. C=PTviolation is the basis for the weak interactions.

The multiplicative parity transformation G = (1)I+Capplies only to mesons. The complete charge representa-tion for a particle is often shown as IG(JP C).

[] Alternate representations: orbital designations from tradi-

tional representation in atomic physics for l = 1 t o 8 a re(S,P,D,F,G,H,I,K) respectively. Other notations have n = s, J =ml, S = ms, sy,z = sx,y, sx = sz = sp, TZ = I

W. The ro-tational direction label for a clockwise right handed spin is (R)and (L) for counter-clockwise left handed spin (with the spinaxis pointing into the clock as opposed to being out from theclock). The translational direction label relative to (y, z) di-mensions for positive (a.k.a. up) spin is () and () for negativeor down spin. Chiral polarizations, with axis aligned with the di-rection of momentum (x), are also labeled up when parallel anddown when anti-parallel. Combining translational and rotationalnotations for spin up gives ((x,y,z)R,L) and ((x,y,z)R,L) for

spin down. These are typically identified through Stern-Gerlachexperiments on accelerated particles.


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8

As in translational space transformation, time reversalis (T T). Anti-particles (x) are T=CP transfor-mations giving the negative of a particle with oppositehandedness. The known violations of CP transforma-tions were originally found in the short and long lifetimesof the neutral kaons (K0S, K

0L) and more recently in BB

mesons from the BaBar collaboration. The arrow of timeis intuitively related to the second law of thermodynam-

ics (entropy). This model relates this to the accelerationof the universe as well. This is the basis for the newmodels ability to predict the parameters of all particles.The new models sdSM charge configurations are shownin Table I.

Fermions, Neutrinos, Twistors, and Particle-WaveDuality

The sdSM charge representation reveals a significantpattern related to neutrinos. Specifically, by adding (orsubtracting) the left handed neutrino (L) to e & d, it willchange the L R (or R L) symmetry of any particle.This is reversed for the u & W particles. This idea is sup-ported by a suggestion that the left-handed spin electronneutrino (Le) is made up of a spinless compressed vol-ume of space (a.k.a. particle rest mass m0) oscillating insuperposition with L. As in Penrose twistor theory [18],where points and lines are duals, the particle and waveare duals of each other. The spinless mass energy of theneutrino is of course equal to the wave energy by theCompton effect. Twistor theory has a unassigned spin0 particle with homogeneity of -2. The new model sug-gests this is in fact m0 referenced above. Twistor theoryhas Le and Re with homogeneity -1 and -3 respectively(a difference of m0).

Just as a particle-antiparticle fermion pair can be cre-ated out of the vacuum or with sufficiently energeticphotons, the neutrino particle-wave pair can be annihi-lated by being brought into superposition with its anti-neutrino partner. As in a closed string, like fermionscannot be in superposition. This is what differentiatesthe Bose-Einstein statistics for wave-like bosons from theFermi-Dirac statistics of the fermions. These fermionmasses must be separated at least by the distance of theradius of their wavelength.

CPT, Neutrinos, and Left Handed UniversalAcceleration

Studies of CPT invariance suggests a universal prefer-ence for L. In this model, the photons maintain thehorizontal {left right} = sy = 1/2 and vertical{up down} = sz = 1/2 spin orientations, while theneutrino(s) maintain the helical (or chiral) spin orienta-tion along the axis of momentum sx = 1/2 []. If theanti-symmetric superposition ofm0 and left handed pho-ton (L) symmetric boson wave becomes the model forthe observed left handed spin 1/2 fermion, the definitionof the right handed photon (R) must account for thelack of evidence for Re. Using the SU(5) charge con-figurations and turning again to Penrose twistor theory,

where the homogeneity of L and R are 0 and -4 re-spectively, it is suggested that the combination emergentfrom the VEV and time symmetric particle interactionshas Le + Re = (0, 0, 0) = R.

The Le is stable which means the particle-wave dual-ity does not simply separate or randomly decay into itsparts. The lack of evidence for Re also suggeststhat the source of stability in Le is obtained by

the assignment of universal acceleration to L inthe particle-wave duality of Le. This stable accel-eration may be visualized as the spiral generated fromGolden Sections and Fibonacci numbers. The L-R spinexchange may be visualized as the 3D Lorenz Attractorfrom chaos theory. This model for particle interactionwill be shown to support the transformation of space-time required in the much desired explanation for themeasured value of Dark Energy contained in .

Particle-Wave Duality and Pilot Wave Theory (PWT)

This begins to make clear the paradox of the particle-wave duality. It is consistent with the results of As-pects experiments on Bells Inequality and the Einstein-Podolsky-Rosen (EPR) paradox, which reveals that theuniverse is either deterministically non-local or locallyprobabilistic with action-at-a-distance [19]. Taking theformer view as that of the deBroglie-Bohm and Ghirardi-Rimini-Weber (GRW) PWT [20], this models descrip-tion of the neutrino identifies universal acceleration andmassless photons as the guiding waves and m0 withthe guided particles. Both are needed in order to re-main stable in an accelerating universe.

Continuing the pattern implies that due to a left

handed universal acceleration, eL is a stable superpo-sition of L and m0 that will be shown to be the in-verse of the neutrino mass. The neutrino mass is thusshown to be integrally related to the measured devia-tions in the value of the Bohr magneton (B = /2me),understood and precisely calculated theoretically as selfinduced perturbations (using a base of /2), namelythe anomalous magnetic moment of the electron (ae =0.115965218598%).

It is suggested that eR is generated by random super-positions with Le (eL eR + Le). Generating eL outofR requires the subtraction ofLe or the addition of ananti-neutrino (eR

eL

Le = eL + Re). Similar to the

polarization of photons, this is the source of randomnessfound in the spin selection of the electron.

B. Mass Predictions

The particle mass predictions are all based relation-ships with . Approximations based on the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) quark-gluonmomentum splitting structure functions (using a base of2) is also noted when appropriate.


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TABLE I: sdSM Particle Charge Configurations

Particle Charge Q=(I+Y)J m(C,I,Y) J = |#R #L| /2 M(r,g,b,L,R)R = R + m0 = 0 0 2(0, 0, 0) 1/2 (0, 0, 0, 0, 0)L = L + m0 0 (0, 1,1) 1/2 (1,1,1, 2, 1)eR 1 mY = 2(0, 0,1) 1/2 TY = (2, 2, 2,3,3)eL = eR L 1 (0,1,1) 1/2 (1,1,1, 1, 2)dR 1/3 2(1, 0,1)/3 1/2 (1,1, 0, 1, 1)dL = dR L 1/3 (2,3, 1)/3 1/2 (0, 0, 1,1, 0)uR = dR + W+R = dR eR +2/3 2(1, 0, 2)/3 1/2 (1, 1, 2,2,2)uL = uR + L +2/3 (2, 3, 1)/3 1/2 (0, 0, 1, 0,1)R = L + R 0 2(0, 0, 0) 1 (0, 0, 0, 0, 0)L = aU 0 (0, 1,1) 1 (1,1,1, 2, 1)WR = uR dR = eR 1 mY = (0, 0, 1) 1a TY = (2, 2, 2,3,3)WL = W

R 2L 1 mI = (0, 1, 0) 1 TI = (0, 0, 0, 1,1)

Z0 = W + W 0 (0, 0, 0) 1 (0, 0, 0, 0, 0)(drR, u

gL) 1 mY = (0, 0, 1) 1b TY = (2, 2, 2,3,3)

(drL, ugR) 1 mI = (0, 1, 0) 1b TI = (0, 0, 0, 1,1)

L,R(d, u) 1 (0, 1, 1) 1/2bc (1,1,1, 1, 2)0L,R((u + u) (d + d))/

2 0 (0,1,1)/2 0 (0, 0, 0, 0, 0)

0LR((u + u) (d + d))/

2 0 (0, 0, 0) 0 (0, 0, 0, 0, 0)+L,R(d, u) +1 (0, 1, 1) 1/2

bc (1, 1, 1,

1,

2)

+(drR, ugL) +1 mI = (0, 1, 0) 1b TI = (0, 0, 0, 1,1)

+(drL, u

gR) +1 mY = (0, 0, 1) 1

b TY = (2, 2, 2,3,3)K0LR(d, s) = R 0 2(0, 0, 0) 0 (0, 0, 0, 0, 0)K0L,R(d, s) = L 0 (0,1,1) 1/2bc (1,1,1, 2, 1)K0Short(K

0L,R + K

0

L,R)/

2 0 (0, 0, 0)/

2 0 (0, 0, 0, 0, 0)K0Long(K

0L,R + K

0R,L)/

2 0 (0, 0, 0)/

2 1bc (0, 0, 0, 0, 0)

n0R(drR, d

gL, u

bR) 0 mC = 2(1, 0, 0) 1/2 TC = (1,1, 2, 0, 0)

n0R(drR, d

gR, u

bL) 0 (2, 1,1) 1/2 (2,2, 1, 2, 1)

n0L(drL, d

gL, u

bR) 0 2(1,1, 1) 1/2 (1, 1, 4,4,2)

n0L(drL, d

gR, u

bL) 0 (2,1, 1) 1/2 (0, 0, 3,2,1)

p+R(drR, u

gL, u

bR) +1 (2, 1, 1) 1/2 (0, 0, 3,1,2)

p+R(drL, u

gR, u

bR) +1 (2,1, 3) 1/2 (2, 2, 5,5,4)

p+L(drR, u

gL, u

bL) +1 2(1, 1, 0) 1/2 (

1,

1, 2, 1,

1)

p+L(drL, ugR, ubL) +1 2(1, 0, 1) 1/2 (1, 1, 4,3,3)R(d

rR, d

gR, d

bR) 1 2(1, 0,1)/3 3/2 3(1,1, 0, 1, 1)

L (drL, d

gL, d

bL) 1 (2,3, 1)/3 3/2 3(0, 0, 1,1, 0)

0R(drR, d

gR, u

bR) 0 mC = 2(1, 0, 0)/3 3/2 TC = (1,1, 2, 0, 0)

0L(drL, d

gL, u

bL) 0 (2,1, 1)/3 3/2 (0, 0, 3,2,1)

+R(drR, u

gR, u

bR) +1 2(1, 0, 1)/3 3/2 (1, 1, 4,3,3)

+L(drL, u

gL, u

bL) +1 (2, 1, 1)/3 3/2 (0, 0, 3,1,2)

++R (urR, u

gR, u

bR) +2 2(1, 0, 2)/3 3/2 3(1, 1, 2,2,2)

++L (urL, u

gL, u

bL) +2 (2, 3, 1)/3 3/2 3(0, 0, 1, 0,1)

aLack of evidence for WR may be explained by its associationwith the electron charge configuration.bThis is inconsistent with SM particle spin.cSpin calculation is avg. of (0+1)/2 vs. just 0.

1. Unit Mass (munit)

munit can be defined using the Compton effect:

munit =

lunitc=

R c

=me

4= 296.739860919 eV/c2 (38)

m2e

mp

cos w+

me2

= 296.742 eV/c2

The addition ofme /2 is due to the aforementioned con-nection with ae and B.


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2. Weak Bosons (mW,Z0)

By standard definition of the EW model, the weakboson masses:

mW =gwGF

= xw

2/GF xw25/4mH (39)

= (

/2)1/327/44munit

= 79.3619 GeV/c2

mZ0 = mW/ cos w 90.1766 GeV/c2 (40)Driven by the error in r in the definition of GF, the

error in this prescription of weak boson masses is outsidethe experimental standard error of 3.4 ppk by a factor of4.

The new definition of e (already related to GF by mHand a non-unity ) has created an opportunity to simplifythe EW model. The standard definition above for gw =

xw

2 = e and its role in (39) is based on Natural UoM.Using the new UoM from (18), (19), (22), and (24), then:

gw = e = gxw = (2xw)3 (41)and in terms of g:

mW xw25/4mH = xw25/4e

2lunit4

= xw25/4g

xw

2lunit4

=

2gtunit (42)

mZ0 =mW1 xw

=

2

1 xw gtunit

=

2

1 xwe

xwtunit =

2

xwgtunit (43)

3. Charged Leptons (me,,)

Decay modes of the first generation of SM particleshave not been observed, they are stable.

Stable Electron Mass (me)

By definition in this model, from (13), (19), and (38):

me =4R

2

c

=0e

2R

3

c

=4

munit (44)

exactly. Notice the connection to the CKM matrix inthat me/munit = (2xw)3 = 8 |VCK M[3, 1]| = 8 |Vtd| =16 |VCK M[1, 3]| = 16 |Vub|. Also of potential interest, it isfound to be approximated by a relationship with DGLAPexponents:

me (2)(4/3)2

munit (45)

Unfortunately, this interesting prescription is signifi-cantly outside the very small experimental standard errorof 170 ppb by a factor of 3470.

Muon Mass (m) and Lifetime ()

In SM, m, and , are known relative to GF. Usingthe Weisskopf-Wigner relation for mass energy, the decaywidth mass () is known as well:

=

c2 G

2Fm

5

3(4)3(46)

In this new model, the stable particle lifetimes increasewith tU 48tunit. This indicates it is reasonable toset e = p = 4

8tunit. A remarkable pattern is de-veloped, such that each generation (n=1,2,3) of chargedleptons (e,,) gives:

[n]e,, m[n]113ne,, = tunitm

113nunit (2)

20 (47)2

2n2(1+12n)3(1n)(4n)/28(3n)

This single equation reduces the input parameters of theSM by three, such that only a prescription for the mass(or lifetime) of the leptons is needed. The results for this

equation using experimental values for either the mass(or the lifetime) of the charged leptons are within ex-perimental bounds. They are similar in nature to theexponent in the theory of RCC (11 2nf/3), where nfis the number of fermions. It indicates a link to an 11DMT and/or the E8 aESToE via triality relationships. The

Mass(V)Lifetime() tied to the suggested 3 real dimen-sions of space (P) and the 8 imaginary dimensions oftime (T) make up the charge (C) configurations listedin Table I. Since the L-R charge configuration does notaffect the mass of the particles and the generational im-pact on mass is significant, it is suggested that it is thenumber (n-1) of additional compressed imaginary timedimensions (multiplied by a factor of three, one for eachreal dimension: x,y,z) which is affecting the particlesmass. This defines the limit on the number of parti-cle generations, since n=4 would require more than 11D.Another interesting result is that with [0] = tunit, thenm[0] = 142.58291278 MeV/c2, which is on the order ofthe pion mass.

A prescription for the mass of the muon is offered:

m 3me2

(48)

Tau Mass and Lifetime (m, )

Following the pattern for m gives a prescription forthe mass of the tau:

m m8

(49)

While the non-perturbative mass and lifetime prescrip-tions for and have an error (


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11

TABLE II: Charged Lepton Mass and Lifetime

Mass Lifetimee 510.99944123 KeV/c2 13.6 Billion years 105.03797892 MeV/c2 2.35 s 1.7992480561 GeV/c2 282 Femto s

4. Uncharged Leptons or Neutrinos (me,,)

Given current experimental constraints that all valuesof e,, 0.3 eV/c2 with their sum < 0.7 eV/c2 [21], itis suggested that:

me =m2unit

me= 0.172318 eV/c2 (50a)

m = me m2unit

m

= me 8.33389 104 eV/c2 (50b)

m = m m2

unitm

= m 4.95526 105 eV/c2 (50c)

5. Quark Fermions (mu,d, mc,s, mt,b)

Given the ratio of masses in (50), it is interesting tonote that from (38) by rough approximation that:

mp m2e

munit(51)

suggesting that the mass of the first generation of lightquarks (mu,d) is in some way inversely related to theelectron neutrino mass. Generalizing this across the threegenerations of SM, these baryon masses would be in-versely related to neutrino masses with munit and thecharged lepton masses as conversion factors. For the pre-cisely measured mp (using me and the electron-proton-mass-ratio with standard error of 460 ppb) (51) is merelya non-perturbative approximation.

Stable First Generation Quark (Up/Down) Mass (mu,d)

Simply setting the mass of the down quark (d) to:

md = 2me = 3.210704 MeV/c2 (52)

and the mass of the up quark (u):

mu = md/2 = 1.605352 MeV/c2 (53)

give values very close to current measurements and cre-ates a simple relationship that supports the sdSM modelof charge and mass prescriptions.

Up Quark Flavor (Up-Charm-Top) Mass (mu,c,t) andLifetime (u,c,t)

TABLE III: (d-s-b) & (u-c-t) Quark Masses

Quark Massesd = 3.210704 MeV/c2 u = 1.605352 MeV/c2

s = 98.10558 MeV/c2 c = 1.319946 GeV/c2

b = 3.270126 GeV/c2 ta = 175.9896 GeV/c2

aConsistent with SM prediction of t = 0, the top quark does not

hadronize. It has a measured constraint of < 1024

s. This is anoted exception to the lifetimes inferred from Table II and III.

Following the pattern established in (47), using the lep-ton masses as a basis for the quark masses and assumingthe quark lifetimes are the same as the leptons, a simplequark mass and lifetime pattern emerges:

[n]u,c,t m[n]113nu,c,t = [n]e,,m[n]

113ne,,

2

232n

8

2

1

12

1

4

(1n)(2n)/2(54)

Down Quark Flavor (Down-Strange-Bottom) Mass(md,s,b) and Lifetime (d,s,b)

Continuing the pattern for the down series of quarksand using the up flavor series as a basis for the downflavor series:

[n]d,s,b m[n]113nd,s,b = [n]u,c,tm[n]

113nu,c,t

232n

2

8

(n(2n)2)/2(55)

It is interesting to note the identification of the EW fac-

tor

2 as well as the inverse (or dual) relationshipsbetween the up and down series of quarks, as well as be-tween the leptons and the up series. These values werealso guided by the assignment of < 0 >0 to the mass ofthe top quark, which nicely closes the sdSM mass pro-gression with its link to mH. These equations give theresults in Table III.

6. Composite 2 Quark Hadrons (Mesons)

For this section, several important meson particle pa-rameter predictions (PPPs) are reviewed. The branch-ing ratios (i/) and resonant cross sections (R) for themany decay modes of composite particles are determinedfrom the specific masses and lifetimes. The complete me-son PPPs will be reviewed in Appendix A.

Pion Mass (m0,) and Lifetime (0,)

Speculating on the masses of the pions using the massrelationships above and a modified Weinberg relation [22]


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12

gives:

m =3

R2

c/gc =

8/3munit/gc

= 3

munitm2H/2/gc 1

2gc3

munit

GF(56)

= 138.959 MeV/c2

where:

R =g2c

GN4H0 =

tunit

l3unitmunit

= 1 Dimensionless Unit (57)

and:

m0 = m/

gc =3

megc

mHgc

2gc

2mp

= 134.596 MeV/c2 (58)

This intriguing prescription for the mass of the pionis outside the experimental standard error of 5ppm by afactor of 875.

Neutral Kaon Mass (mK0S,L

) and Lifetime (K0S,L

)

In order to understand the detail relating to the CPTsymmetry and their violations (e.g. CP T), it is crit-ical to understand the mass and (more importantly) the

lifetime of (K0S(ds ds)/

2, K0L = (ds + ds)/

2).

7. Composite 3 Quark Hadrons (Baryons)

The complete baryon PPPs will be reviewed in Ap-pendix A.

Stable Proton Mass (mp) and Radius (rp)

The quark composition of the proton has the mass ofthe up quarks precisely equal to the mass of the downquark. It is this equality that provides for the stabilityof the proton. Equations (45) and (51) give:

mp 4

2

munit (2)(4/3)4

munit (59)

It is interesting to note that by extending this rela-tionship to the 3 generations of SM, the mass of the 3rd

generation particles (p+, ++) approach that of the mP.This would suggest that the Cosmic Egg or Primor-dial Atom responsible for the Big Bang (BB) mayhave been 3rd generation leptons which would imme-diately disintegrate into the naturally inflationary ac-celerating universal expansion of protons and electronsthat we know today. It can be shown that when form-ing a black hole from the current estimate for the massof the universe derived from the matter density (m)

and the Hubble radius (RH = c/H0), if compressed intoPlanck volumes (VP = 4l3P/3) each of mass mP, itresults in a radius precisely 2 times the proton radius(rp = 0.8 1015m). The proton radius link to thePlanck and matter densities is the first indicator of theduality that resolves the hierarchy problem related toVEV, Higgs, and matter densities.

C. Cosmological Predictions

This new model is able to give reasonable causes formany cosmological unknowns and their experimentallydetermined values.

1. Milne-Dirac, Eddington, and Weinberg Relations

All of these notable physicists attempted to reduce thenumber of fundamental parameters in physics by creatingrelationships between them. Some were approximationslimited by experimental accuracy. To this end, under-standing the intentions as they relate to the new morenatural model is interesting. From (14), it is easy to as-sociate this new model to the Milne-Dirac Large NumberHypothesis (LNH) and a time varying GN [22].

Eddington attempted to quantify the LNH with thenumber of baryons in the universe using and binarynumerology. Unfortunately, he used an integer value of1/ = 136 (and subsequently 137) giving NE = 137 2256. LNH and NE were modified by Weinberg resultingin the relation:

h2H0

GNc m3nucleon (60)

while:

mnucleon =3

H0GN

h2

c= 207.9 MeV/c2 (61)

is referenced as being on the order of m, yet withcurrent measures of H0 giving 3m/2, it is not evenclose to being within current experimental standard er-ror. Following Milne-Dirac, Eddington and Weinberg,the new model offers a better approximation of the pionmass(es) to within 0.4% using the most accurate currentvalue of and a binary exponent in E8 and MT dimen-

sions, it also gives a very precise value for a large numberrelated to time as:

Nt = 8 = 1.2435904532 1017 (62)

and similar in form to (60), the new model has moreprecisely:

4H0 = GNg2c

munittunit

2c tunit = UnitEnergy (63)

Using the new models definition for m from (56)gives Weinbergs number (now closely associated with


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13

VEV) for the number of nucleons (pions) in the observ-able universe (MU = MH/4), where MH is the mass inthe observable volume of the universe (VU = 4R3H/3)from Hoyles Steady State (SS) model and the criticalmass energy density of the vacuum

c = 3H20/8GN/g

2c (64)

Specifically:

NW = MU/m = (c3/8GNH0)gc

8/3/munit

= gc112/3/2 = 9.97684762939 1079 (65)

2. The New Physics of Black Hole Singularities

Given the definition of mass (9) and charge (17), it isproposed that the process for increasing the mass den-sity of a volume is limited to the stopping of universalacceleration and expansion in the space which that vol-ume occupies (Q = M /5 = V /30 = 0). This would re-

quire a compressive force. By SRs link between massand velocity, if a given mass experiences no compres-sive force (or change in velocity) relative to free space(cspace = cmass), it is seen as expanding and acceleratingwith space. There is no change to its mass density andits charge is 0.

Therefore, without invoking time reversal (T) sym-metries, the lower limit of compressibility in terms of achange in mass density per unit time is cspacecmass = 0.The given mass experiences no change in mass density.This is of course a particle traveling at the speed oflight (which is the rate of universal expansion as definedabove).

If a given mass experiences maximum compressibilityrelative to free space, the space it occupies has stoppedexpanding cmass = 0 and its mass density changes at thesame rate as the universe expands space = cspace. Theupper limit of compressibility in terms of a change inmass density per unit time is cspacecmass = space0 =1. The given mass and charge is seen as a black holesingularity at the limit of GR physics.

This eliminates the need for any new physics beyondblack hole singularities. It also offers more natural expla-nations relating to Hawking radiation in the evaporationof black holes, entropy and information loss (or not) inblack hole physics.

3. The Cosmological Constant

In terms of billions of light-years (Gly), the Hubbleradius is:

RH = c/H0 = 13.660008445 Gly (66)

The Lambda Cold Dark Matter (CDM) model of aFriedmann-Lematre-Robertson-Walker (FLRW) metric[23] for an accelerating universe has density parameters

for energy, matter, and curvature (k), with space metric(a(z)=R), is now given by:

H20 =

R

R

2=

2

34

GNg2c

c +

3 kR2H (67)

While is properly defined as an energy (or m=E/c2)

per volume (a.k.a. density = ML3

), its representa-tion varies due to a lack of understanding on its origin. Itis sometimes represented in terms of dimension L2 (us-ing R2H ) or simply as T

2 (using H20 ), where the valuein this new model can be given as:

= 8GN = x3H20 (68)

where the factor x is introduced such that = xc.Another, even more common, representation has:

= /3H20 = /c = x (69a)

= m + + k = 1 (69b)

The new model suggests a natural dark energy com-ponent originating from universal acceleration that fitsvery nicely with recent cosmological data [24]:

0 =

10

c dt = 2/3 (70a)

0 = 2H20 (70b)

Introducing dark matter (dm), visible baryon (b)and radiation () components to the model :

mc

= dm + b (71a)

m = dm + b + = m/c +

= 1 + (71b)k = k/H

20 = (1 (m + )) = (71c)

= (3/2)2/3(H0tunit/2)

1/5 = 1/4737.01 (71d)

It is suggested that without visible (baryonic) matter,the dark universe has dm0 = 10 = 1/3. This modelincorporates the idea that part of dm has contributionsfrom neutrinos (), which are made up of 2/3 and1/3 m0. Given the structure of the new sdSM, the ad-dition of baryons is calculated by adding 2 parts to theuniversal acceleration (dark energy), which is now in the

form of dark neutrino-bound R, while subtracting 1 partm0 and 2 parts L from the dark matter, which are nowvisible as baryons. Based on an integer approximation forthe measured value of the visible mass in the observableuniverse:

b = 1/4! = 1/24 = 4.166 . . . % (72a)

= 0 + 2b = 3/4 = 75% (72b)

= ( 3/2)2H20 (72c)

dm = dm0 3b = 5/24 = 20.833 . . . % (72d)m = dm + b = 1/4 = 25% (72e)


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14

and using an FLRW age factor of:

a(z) =

11+z

0

da/a2 + m/a + k + a2

(73a)

a(0) = 1.012701315 (73b)

gives a very precise calculation for the current age of the

universe of:

tU =a(0)

H0= 13, 842, 982, 880(78) years (74)

Just as M(3D)/M(1D)=Q(2D)=A, there is an equiva-lence in this model between [ML

3 = T1] by a GRconversion, and [M

4 = L4 = (cT)4] by QM conver-sions. Getting to the L2 or T2 requires selective L=Mconversions by assuming gravitational radii and Planckunits. Comparing the critical mass density to that ofthe expected Higgs field shows that they are related bya factor of:

H/ = 35 =

35k (75)since:

H(M4) = (mHv/

8)2 = m2H/(4GF)

= m4H = 4(4munit)

4 (76a)

(M4) = (/c)3c = (T

1)

= (4/3)2H0/2 = 9(4)3(8/8)/tunit

= 9(4)3GFm2unit/tunit (76b)

It is shown that instead of a paradoxical disparity in their

magnitudes, they are in fact precisely dual.

4. Gravitational Coupling and String Length

In natural units, gc and GN have a direct relationshipto the string length (lstring ) of order lP. This model hasan inverse relationship to time on a universal scale:

tstring = 1/(4H0) = 8tunit 109 years

=

lstring =

RH/4

1Gly (77)

This is consistent with recent findings related to thelarge-scale structure of the universe.

5. Baryon to Photon Ratio

A baryon to photon ratio of:

= nb/n =

5/

2 = 1/1.83662 109 (78)

is within experimental error.

6. Cosmic Microwave Background Radiation (CMBR)

Recent studies of CMBR by the Wilkinson MicrowaveAnisotropy Probe (WMAP) have precisely determinedits temperature to be 2.72528K [9]. By Boltzmannsconstant (kB), CMBR translates to a mass energy valueof 234.8469 eV/c2. This familiar reference to tempera-ture is a conversion from the determination of the Wienpoint in the measured Maxwell-Boltzmann blackbodyspectrum by using Planck radiation law and the Stefan-Boltzmann constant SB = Li4(1)(4)k

4b /(

3(2c)2)represented here in terms of polylogarithms or deJon-quieres function (which are also related to the Bose-Einstein and Fermi-Dirac statistics mentioned previ-ously). The Wien point was found at wavelength1.874827 mm (or frequency of 159.9040 GHz).

From WMAP, the CMBR redshift from first light de-coupling from the surface of the universe is z = 1089 1.The age of the universe at the time of decoupling is then:

a(z)/H0 = 304.306 Ky r (79)

The comoving radius (RU), angular size (DA), and lu-minosity distance (DL) of the observable universe are:

RU = a(z)RH = 14.2089 Gpc = 46.3438 Gly(80a)

DA = RU/(1 + z) = 42.5172 M ly (80b)

DL = RU(1 + z) = 50.5147 T ly (80c)

where:

a(z) =

11

1+z

da

a/a2 + m/a + k + a2(81)

7. Black Hole Evaporation and the Casimir Force

Confirmation of the assignment of universal accelera-tion to a Theory of Everything (ToE), is found in theidentification of the Casimir force (in a blackbody of theMinkowski vacuum) with that of the gravitational accel-eration at the surface of black holes with a thermalizedHawking radiation (TH). This is accomplished by apply-ing the Fulling-Davies-Unruh (FDU) effect [25] to boththeories where:

T

F DU = T

H = a

/2kBc (82)This results in a thermal bath of Rindler particles (e.g.Re and unstable protons) in accelerated reference frameswith acceleration a/K = 2.466085 1020 m/s2/K. Itshould be noted that by definition:

2TF DU/a = TP/aP = /kBc (83)

where Planck unit temperature and acceleration are:

TP = mPc2/kB (84a)

aP = lP/t2P (84b)


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15

Since a black hole increases its thermal radiation as itgets smaller, TP can be characterized as the maximalthermal radiation just before being totally evaporated.Using universal scales in the new model:

TF DU = T

H = T

U (85)

resulting from the universal mass now linked to m with:

MU = mVUc (86)

which gives a Casimir blackbody acceleration, or equiv-alently the acceleration on the surface of a black holeof gravitational radius, which is 1/2 the Schwarzschildradius:

RU bh = RU s/2 = GNMU/(gcc)2 = RH/8 = lstring /2

= 1.7075425741 Gly (87)

Using (2) gives an acceleration:

c4/(4GNMU) = 2cH0 = aU/2 (88)

As done for Planck units, restating this result in termsof the new model gives a surprising result:

2TF DU/a = T

P/aP = T

U/aU = /kBc (89)

This implies that today the ZPF, VEV, and repre-sent the minimal change in mass density (charge) fromuniversal acceleration, while black holes represent max-imal change in mass density (e.g. where mP is withinlP) relative to the current rate of acceleration. Theseimplications will be significant in resolving the debateconcerning the origin of inertia, Machs principle, and an

ether related to the ZPF and VEV.

8. The Observable Universe at tU 1 tunit

In terms of the observable universe today, a black holeof mass MU = 9.994897 1059mP, if compressed into asmany VP, results in sphere of radius 2rp = 1.6f m. Thissuggests that a BB matter-antimatter vacuum fluctua-tion resulted in 1060 3rd generation primordial atomsof mass mP within universal radius 2rp immediately de-cayed within tunit. Over time tU they inflated to ra-dius RH with acceleration aU leaving radiation (such as

CMBR), leptons (, e) and baryons (p,n of radius rp).In order to understand the universe at tunit, it is a sim-

ple matter to set = 1. This has mP = munit at lunitand is the point where Planck units become synonymouswith the new units of this model and where grand uni-fication is realized as a natural result! The observableuniverse (to a hypothetical observer) is lunit. This begsthe question; at tU 1 tunit and lU 1 lunit, wherewere todays 1060mP (then 1060munit) which arecurrently found within RH? The answer comes from un-derstanding that c and m can be assigned to VEV(and mH) by (32). They are either to be found within

2rp as the BB model might suggest or present through-out space-time as VEV (a function of time) which the SSmodel might suggest.

Fundamental parameters and objects scale into frac-tions as Nt = 8 1. This model predicts the behav-ior observed in todays particle accelerators as well as thescaled interactions of the sdSM at tunit, and before. Ifthe universe is non-locally deterministic (by GRW) and

spin synchronized (by Bell and Aspect), it logically im-plies that aU and the laws of physics are non-local. Thiseliminates the constraint that only interactions which arewithin a common events light cone can exhibit similar(not necessarily coherent) behavior. With this, it seemsthat both BB and SS cosmologies could be synonymous!

9. Loop Quantum Gravity (LQG) and an AcceleratingUniverse

The accelerating universe provides for the absolutetime lacking in GR without significantly altering the basis

for GRs success - namely the space-time metric. It alsoprovides the means for QM to be linked to GR throughthe FDU effect being equated with both Casimir andHawking radiation. Quantization is naturally providedby atomic scale unit L, T, M, Q dimensions and unit ac-celeration. The infinite divisibility of space-time in GRis now limited by the background of an acceleration andits finite measure - time (in tunits). LQG is indicated inaESToE. The evidence for linkage with this new modelis interesting.

IV. CONCLUSION

To summarize, the new dimensionality relations from(1), (9), and (17):

L = T2 (90a)

M = L3T1 = T5 (90b)

Q = ML1/2 = M T1 = T4 (90c)

The dimensional relationships relate CPT and E8and/or MT by:

M T(11D) = C(4D) + P(6D) + T(1D)

= C([T

8

]) + P(L3

= T6

) + T1

= Re[P(3D)] + Im[T(8D)] (91)

= P({x,y,z}) + i({x, y, z},C(SU(5) = {r,g,b}, {L, R}))

To within all most current experimental error:

munitlunit= c =

g2cGN

=1

4H0= 8tunit (92)

The new units to MKS conversions in Table IV havebeen generated from (92). A comprehensive sdSM pre-


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16

TABLE IV: NEW Units to MKS Conversions

NEW Units MKS Units1 Unit Time (tunit) = 0.27584662291 s1 Unit Length (lunit) = 6.64983692227 1010 m1 Unit Mass (munit) = 5.28986280466 1034 kg1 Unit Charge (qunit) = 1.50032062662 1027 Coul

scription for fundamental particles summarized in TableV.

This model could be described using terms from [6]

as a one (not-so) constant party view. In this model,the fundamental parameters c, , GN, and H0 are de-rived from . It restores the idea of an absolute refer-ence frame for time which is embedded in the very core ofthese fundamental parameters of physics, which helps inunderstanding the arrow of time, entropy and cosmicinflation. The micro and macro scales of the universe arelimited in magnitude by time in such a way that infin-

ity becomes only a mathematical concept not physicallyrealized as the universe unfolds.

The universe itself becomes the clock upon which timecan be measured.

[1] A. Riess, A. Filippenko, P. Challis, A. Clocchiattia,A. Diercks, P. Garnavich, R. Gilliland, C. Hogan, S. Jha,R. Kirshner, et al., Arxiv preprint astro-ph/9805201(1998).

[2] A. G. Lisi, An exceptionally simple theory of everything

(2007), URL http://www.citebase.org/abstract?id=oai:arXiv.org:0711.0770.[3] A. Albrecht and J. Magueijo, Physical Review D 59,

43516 (1999).[4] S. Nesseris and L. Perivolaropoulos, Physical Review D

75, 23517 (2007).[5] J. Barrow, Journal of Physics: Conference Series 24, 253

(2005).[6] M. Duff, L. Okun, and G. Veneziano, Journal of High

Energy Physics 2002, 19 (2002).[7] P. Mohr and B. Taylor, Reviews of Modern Physics 77,

1 (2005).[8] J. Gundlach and S. Merkowitz, Physical Review Letters

85, 2869 (2000).[9] C. Bennett, M. Halpern, G. Hinshaw, N. Jarosik,

A. Kogut, M. Limon, S. Meyer, L. Page, D. Spergel,G. Tucker, et al., Astrophysical Journal, Supplement Se-ries 148, 1 (2003).

[10] J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley Publishing, 1967).

[11] C. Quigg, Gauge Theories of the Strong, Weak, and Elec-tromagnetic Interactions (Westview Press, 1997).

[12] B. Zwiebach, A First Course in String Theory (Cam-bridge University Press, 2004).

[13] M. Passera, Physical Review D 75, 13002 (2007).[14] L. Wolfenstein, Physical Review Letters 51, 1945 (1983).[15] E. Blucher and W. Marciano, V ud, V us, the Cabibbo

angle and CKM unitarity (2006).[16] H. Liu and T. Vachaspati, Physical Review D 56, 1300

(1997).[17] W. Yao, J. Phys. G: Nucl. Part. Phys. 33, 1 (2006).[18] F. Peat, Superstrings and the Search for the Theory of

Everything (Cardinal, 1991).[19] A. Aspect, Atomic Physics 8 (1983).[20] G. Ghirardi, A. Rimini, and T. Weber, Physical Review

D 34, 470 (1986).[21] A. Smirnov, Arxiv preprint hep-ph/0512303 (2002).[22] M. Berman and L. Trevisan, Arxiv preprint gr-

qc/0112011 (2001).[23] P. Peebles, Principles of Physical Cosmology (Princeton

University Press, 1993).

[24] M. Tegmark, D. Eisenstein, W. Hu, and R. Kron, Arxivpreprint astro-ph/9805117 (1998).

[25] G. Matsas and D. Vanzella, Arxiv preprint gr-qc/0205078(2002).


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TABLE V: Complete sdSM Prescriptions

[ Mass Generations (in munits) ] [ Charge (in q2units) Q=(I+Y)J, J = |#L #R| /2 ]

Particle 1(e) 2() 3() Q m(C , I , Y ) J M(r,g,b,L,R)(in tunits) 4

8 2((4/9)/2)2 (2)6/3R = R + m0 = 0 2(0, 0, 0) 0 (0, 0, 0, 0, 0)

L = L + m0 1/e 1/e 1/ 1/ 1/ 0 (0, 1,1) 1/2 (1,1,1, 2, 1)eR mY = 2(0, 0,1) 1/2 TY = (2, 2, 2,3,3)

eL = eR L 4/ 3e/2 /8 1 (0,1,1) 1/2 (1,1,1, 1, 2)dR 2(1, 0,1)/3 1/2 (1,1, 0, 1, 1)

dL = dR L 2u1 u2/241/4 u3/261/4 1/3 (2,3, 1)/3 1/2 (0, 0, 1,1, 0)uR = dR + W

+

R = dR eR 2(1, 0, 2)/3 1/2 (1, 1, 2,2,2)uL = uR + L e 4 <

0 >0 +2/3 (2, 3, 1)/3 1/2 (0, 0, 1, 0,1)R = L + R 2(0, 0, 0) 1 (0, 0, 0, 0, 0)

L = aU 0 0 (0, 1,1) 1 (1,1,1, 2, 1)WR = uR dR = eR mY = (0, 0, 1) 1 TY = (2, 2, 2,3,3)

WL = WR 2L 2xw < 0 >0 1 mI = (0, 1, 0) 1 TI = (0, 0, 0, 1,1)

Z0 = W + W W/ cos w 0 (0, 0, 0) 1 (0, 0, 0, 0, 0)

mH

24

< 0 >0

2mHxw = sin

2 w= sin c 3 /2s xw/2

Acknowledgments

I would like to thank my family for their love andpatience and those in academia who might take the time(and unfortunately risk) to simply help in the reviewof this work. For without the support of family, theadventure of this journey would be more lonely; withoutthe support of academia, more difficult!

APPENDIX A: COMPLETE PPP

These tables are a work in progress. They aregenerated from Particle Data Group (PDG) exper-imental data [17]. Specifically, the upgraded file(http://pdg.lbl.gov/2006/mcdata/mass width 2006.csv)for use in Monte Carlo based lattice QCD cal-

culations. An improved version of this file(http://www.TheoryOfEverything.org/TOE/JGM/ToE.xls)is available, which has been created based on this modelby generating the data (with few exceptions) from thequark configuration, L and S. Eventually, it will containall mass, decay width predictions, and error factors. Anerror factor of 1 is within standard experimental error.An error factor of 0 implies it has yet to be predicted.


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TABLE VI: Complete sdSM Fundamental Particle Parameter Predictions

Name Quarksa L S Clr I Y G J P C Q q l Mass(MeV) ExpErr f(Err) (MeV) f(Err)L aU 1 0 0 0 0 1 1 1 0 0 0 0Def 0WL W

R 2L 1 0 0 1 0 1 1 79361.83467 25 41.65 2140 0

Z0 + W 1 0 0 0 0 1 0 90176.52482 21 48.15 2495.2 0mH

24 0 0 0 0 0 0 0 147988.8981 10000 0.20 0

eL 1/e 0 0 0 1/2 1/2 0 0 1.72318E 07 2.E 07 0.14L 1/ 0 0 0 1/2 1/2 0 0 8.38311E 10 3.E 09 0.72L 1/ 0 0 0 1/2 1/2 0 0 4.89396E 11 5.E 11 0.02eR 4/ 0 1/2 0 0 1 1/2 1 0.510998924 4.E 08 0DefR 3e/2 0 1/2 0 0 1 1/2 1 105.0378725 9.E 06 68944.05 2.79861E 16 3946.022251R /8 0 1/2 0 0 1 1/2 1 1799.246234 0.29 76.75 2.3E 09 8dR 2u1 0 1/2 1/3 0 1/3 1/2 1 1/3 2.568560743 2 1.22uR e 0 1/2 1/3 0 2/3 1/2 1 2/3 1.284280372 0.8 1.14sR u2/2

41/4 0 1/2 1/3 0 1/3 1/2 1 1/3 98.1054868 25 0.12cR 4 0 1/2 1/3 0 2/3 1/2 1 2/3 1319.944835 90 0.78bR u3/2

61/4 0 1/2 1/3 0 1/3 1/2 1 1/3 4624.653065 70 6.07tR <

0 >0 0 1/2 1/3 0 2/3 1/2 1 2/3 175989.4505 3300 0.54

aCapitals anti-quarks, x or y wave function coefficients,p or q CP violation parameters.


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TABLE VII: Complete sdSM Meson Parameter Predictions

Name Quarks L S Clr I Y G J P C Q q l Mass(MeV) ExpErr f(Err) (MeV) f(Err) uD 0 0 0 1 0 1 0 1 0 1 12 25 138.9597037 3.5E 04 1.7E+ 03 2.5E 14 00 (uU dD)2 0 0 0 1 1 1 0 1 1 0 12 25 134.5961689 6.0E 04 6.3E+ 02 7.8E 06 0 x(uU + dD) + y(sS) 0 0 0 0 0 1 0 1 1 0 12 25 547.51 0.18 0 0.0013 0f0(600) ? non qQ 0 0 0 0 0 1 0 1 1 0 800 400 0 800 0(770) uD 0 1 0 1 0 ? 1 1 1 39 36 775.5 0.4 0 149.4 00

(770) (uU dD)2 0 1 0 1 1 1 1 1 1 0 39 36 775.5 0.4 0 149.4 0(782) x(uU + dD) + y(sS) 0 1 0 0 0 1 1 1 1 0 39 36 782.65 0.12 0 8.49 0(958) x(uU + dD) + y(sS) 0 0 0 0 0 1 0 1 1 0 12 25 957.78 0.14 0 0.203 0f0(980) ? non qQ 0 0 0 0 0 1 0 1 1 0 980 10 0 70 0a0 (980) ? non qQ 0 0 0 0 0 ? 0 1 1 984.7 1.2 0 75 0a00(980) ? non qQ 0 0 0 0 0 1 0 1 1 0 984.7 1.2 0 75 0(1020) x(uU + dD) + y(sS) 0 1 0 0 0 1 1 1 1 0 39 36 1019.46 0.019 0 4.26 0h1(1170) x(uU + dD) + y(sS) 2 1 0 0 0 1 1 1 1 0 1170 20 0 360 0b1 (1235) uD 1 0 0 1/2 1/2 ? 1 1 1 1229.5 3.2 0 142 0b01(1235) (uU dD)

2 1 0 0 1/2 1/2 1 1 1 1 0 1229.5 3.2 0 142 0

a1 (1260) uD 0 1 0 1/2 1/2 ? 1 1 1 1230 40 0 420 0a01(1260) (uU dD)

2 1 0 0 1/2 1/2 1 1 1 1 0 1230 40 0 420 0

f2(1270) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 2 1 1 0 30 28 1275.4 1.1 0 185.2 0f1(1285) x(uU + dD) + y(sS) 1 0 0 1/2

1/2 1 1 1 1 0 1281.8 0.6 0 24.2 0

(1295) x(uU + dD) + y(sS) 0 0 0 0 0 1 0 1 1 0 1294 4 0 55 0(1300) uD 0 0 0 1 0 ? 0 1 1 1300 100 0 400 00(1300) (uU dD)2 0 0 0 0 0 1 0 1 1 0 1300 100 0 400 0a2 (1320) uD 1 1 0 1/2 1/2 ? 2 1 1 30 28 1318.3 0.6 0 107 0a02(1320) (uU dD)

2 0 0 0 1/2 1/2 1 2 1 1 0 1318.3 0.6 0 107 0

f0(1370) x(uU + dD) + y(sS) 1 0 0 1/2 1/2 1 1 1 1 0 1350 150 0 350 0h1(1380) x(uU + dD) + y(sS) 1 0 0 1/2 1/2 1 1 1 1 0 1386 19 0 91 01 (1400) ? non qQ 0 1 0 0 0 ? 1 1 0 1376 17 0 300 001(1400) ? non qQ 0 1 0 0 0 1 1 1 1 0 1376 17 0 300 0(1405) x(uU + dD) + y(sS) 0 0 0 0 0 1 0 1 1 0 1409.8 2.5 0 51.1 0f1(1420) x(uU + dD) + y(sS) 1 0 0 1/2 1/2 1 1 1 1 0 1426.3 0.9 0 54.9 0(1420) x(uU + dD) + y(sS) 1 0 0 0 0 1 1 1 1 0 1425 25 0 215 0f2(1430) x(uU + dD) + y(sS) 1 0 0 1/2 1/2 1 1 1 1 0 1453 4 0 13 0a0 (1450) uD 1 1 0 1/2 1/2 ? 0 1 1 1474 19 0 265 0

a00(1450) (uU dD)2 1 1 0 1/2 1/2 1 0 1 1 0 1474 19 0 265 0(1450) uD 0 1 0 1 0 ? 1 1 1 1459 11 0 150 00(1450) (uU dD)2 0 1 0 0 0 1 1 1 1 0 1459 11 0 150 0(1475) x(uU + dD) + y(sS) 0 0 0 0 0 1 0 1 1 0 1476 4 0 87 0f0(1500) ? non qQ 0 0 0 0 0 1 0 1 1 0 1507 5 0 109 0f1(1510) x(uU + dD) + y(sS) 0 1 0 1/2 1/2 1 1 1 1 0 1518 5 0 73 0f2(1525) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 2 1 1 0 30 28 1525 5 0 73 0f2(1565) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 2 1 1 0 1546 12 0 126 0h1(1595) x(uU + dD) + y(sS) 0 1 0 1/2 1/2 1 1 1 1 0 1594 18 0 380 01 (1600) ? non qQ 0 1 0 0 0 ? 1 1 0 1653 18 0 225 001(1600) ? non qQ 0 1 0 0 0 1 1 1 1 0 1653 18 0 225 0a1 (1640) uD 0 1 0 1/2 1/2 ? 1 1 1 1647 22 0 254 0a1(1640) (uU dD)

2 0 1 0 1/2 1/2 1 1 1 1 0 1647 22 0 254 0

f2(1640) x(uU + dD) + y(sS) 1

1 0 1/2

1/2 1 2 1 1 0 1638 6 0 99 02(1645) x(uU + dD) + y(sS) 2 0 0 0 0 1 2 1 1 0 1617 5 0 181 0(1650) x(uU + dD) + y(sS) 2 1 0 0 0 1 1 1 1 0 1670 30 0 315 03(1670) x(uU + dD) + y(sS) 2 1 0 0 0 1 3 1 1 0 32 31 1667 4 0 168 02 (1670) uD 2 0 0 1 0 ? 2 1 1 1672.4 3.2 0 259 002(1670) (uU dD)

2 2 0 0 0 0 1 2 1 1 0 1672.4 3.2 0 259 0

(1680) x(uU + dD) + y(sS) 0 1 0 0 0 1 1 1 1 0 1680 20 0 150 03 (1690) uD 2 1 0 1 0 ? 3 1 1 32 31 1688.8 2.1 0 161 003(1690) (uU dD)

2 2 1 0 0 0 1 1 1 1 0 1688.8 2.1 0 161 0

(1700) uD 2 1 0 1 0 ? 1 1 1 1720 20 0 250 0


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TABLE VIII: Complete sdSM Meson Parameter Predictions (cont.)

Name Quarks L S Clr I Y G J P C Q q l Mass(MeV) ExpErr f(Err) (MeV) f(Err)0(1700) (uU dD)2 2 1 0 0 0 1 1 1 1 0 1720 20 0 250 0a2 (1700) uD 1 1 0 1/2 1/2 ? 2 1 1 1732 16 0 190 0a02(1700) (uU dD)

2 3 1 0 1/2 1/2 1 2 1 1 0 1732 16 0 190 0

f0(1710) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 0 1 1 0 1718 6 0 137 0(1760) x(uU + dD) + y(sS) 0 0 0 0 0 1 0

1 1 0 1760 11 0 60 0

(1800) uD 0 0 0 1 0 ? 0 1 1 1812 14 0 207 00(1800) (uU dD)2 1 1 0 0 0 1 0 1 1 0 1812 14 0 207 0f2(1810) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 2 1 1 0 1815 12 0 197 0X(1835) x(uU + dD) + y(sS) 0 0 0 0 0 1 0 1 1 0 1834 7 0 68 03(1850) x(uU + dD) + y(sS) 2 1 0 0 0 1 3 1 1 0 32 31 1854 7 0 87 02(1870) x(uU + dD) + y(sS) 2 0 0 0 0 1 2 1 1 0 1842 8 0 225 0(1900) uD 0 1 0 1 0 ? 1 1 1 1860 20 0 160 00(1900) (uU dD)2 0 1 0 0 0 1 1 1 1 0 1860 20 0 160 0f2(1910) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 2 1 1 0 1915 7 0 160 0f2(1950) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 2 1 1 0 1944 12 0 472 03 (1990) uD 4 1 0 1 0 ? 3 1 1 1982 14 0 188 003(1990) (uU dD)

2 2 1 0 0 0 1 1 1 1 0 1982 14 0 188 0

f2(2010) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 2 1 1 0 2010 60 0 200 0f0(2020) x(uU + dD) + y(sS) 1 1 0 1/2

1/2 1 0 1 1 0 1992 16 0 440 0

a4 (2040) uD 3 3 0 1/2 1/2 ? 4 1 1 2001 10 0 313 0a04(2040) (uU dD)

2 3 3 0 1/2 1/2 1 4 1 1 0 2001 10 0 313 0

f4(2050) x(uU + dD) + y(sS) 3 3 0 1/2 1/2 1 4 1 1 0 2025 10 0 225 02 (2100) uD 3 1 0 1 0 ? 2 1 1 2090 29 0 620 002(2100) (uU dD)

2 1 1 0 0 0 1 0 1 1 0 2090 29 0 620 0

f0(2100) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 0 1 1 0 2103 7 0 206 0f2(2150) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 2 1 1 0 2156 11 0 167 0(2150) uD 0 1 0 1 0 ? 1 1 1 2149 17 0 360 00(2150) (uU dD)2 0 1 0 0 0 1 1 1 1 0 2149 17 0 360 0f0(2200) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 0 1 1 0 2189 13 0 240 0fJ(2220) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 2 1 1 0 2231.1 3.5 0 23 0(2225) x(uU + dD) + y(sS) 0 0 0 0 0 1 0 1 1 0 2220 18 0 150 03 (2250) uD 4 1 0 1 0 ? 3 1 1 2260 20 0 160 003(2250) (uU

dD)

2 2

1 0 0 0 1 1

1

1 0 2260 20 0 160 0f2(2300) x(uU + dD) + y(sS) 3 1 0 1/2 1/2 1 2 1 1 0 2297 28 0 150 0f4(2300) x(uU + dD) + y(sS) 5 1 0 1/2 1/2 1 4 1 1 0 2332 15 0 260 0f2(2340) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 2 1 1 0 2340 60 0 320 05 (2350) uD 4 1 0 1 0 ? 5 1 1 2330 35 0 400 005(2350) (uU + dD)

2 4 1 0 1 1 1 5 1 1 0 2330 35 0 400 0

a6 (2450) uD 5 3 0 1/2 1/2 ? 6 1 1 2450 130 0 400 0a06(2450) (uU + dD)

2 5 3 0 1/2 1/2 1 6 1 1 0 2450 130 0 400 0

f6(2510) x(uU + dD) + y(sS) 5 3 0 1/2 1/2 1 6 1 1 0 2460 50 0 260 0X(1070) ?? 0 0 0 0 0 1 0 1 1 0 1072.4 0.8 0 3.5 0X(1110) ?? 1 1 0 1/2 1/2 1 2 1 1 0 1107 4 0 111 0f0(12 1600) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 0 1 1 0 1480 100 0 1030 0X(1420) ?? 0 0 0 0 0 1 0 1 1 0 1420 20 0 160 0X(1600) ?? 1 1 0 0 0 1 2 1 1 0 1600 100 0 400 0X(1650) ?? 0 ? 0 0 0 ? ? ? ? 0 1652 7 0 50 ?X(1750) ?? 0 1 0 0 0 1 1 1 1 0 1753.5 1.5 0 122 0X(1775) ?? 0 1 0 0 0 ? 1 1 ? 0 1763 20 0 190 0X(1855) ?? 0 ? 0 0 0 ? ? ? ? 0 1857 5 0 20 0X(1870) ?? 0 ? 0 0 0 ? ? ? ? 0 1870 40 0 250 0a3(1875) (uU dD)

2 4 1 0 1/2 1/2 1 3 1 1 0 1870 40 0 380 0

2(1880) (uU dD)

2 1 1 0 0 0 1 0 1 1 0 1880 20 0 260 0a1(1930) (uU dD)

2 0 1 0 1/2 1/2 1 1 1 1 0 1930 30 0 160 0

X(1935) ?? 0 1 0 0 0 ? 1 1 ? 0 1935 20 0 215 02(1940) (uU dD)

2 1 1 0 1/2 1/2 1 0 1 1 0 1940 40 0 160 0

3(1945) x(uU + dD) + y(sS) 4 1 0 0 0 1 3 1 1 0 1945 20 0 115 0(1960) x(uU + dD) + y(sS) 0 1 0 0 0 1 1 1 1 0 1960 25 0 200 0b1(1960) (uU dD)

2 0 1 0 1/2 1/2 1 1 1 1 0 1960 40 0 210 0

(1965) (uU dD)2 0 1 0 0 0 1 1 1 1 0 1965 30 0 165 0h1(1965) x(uU + dD) + y(sS) 0 1 0 1/2 1/2 1 1 1 1 0 1960 40 0 340 0f1(1970) x(uU + dD) + y(sS) 0 1 0 1/2 1/2 1 1 1 1 0 1971 15 0 240 0


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TABLE IX: Complete sdSM Meson Parameter Predictions (cont.)

Name Quarks L S Clr I Y G J P C Q q l Mass(MeV) ExpErr f(Err) (MeV) f(Err)X(1970) ?? 0 ? 0 0 0 ? ? ? ? 0 1970 10 0 40 0X(1975) ?? 0 ? 0 0 0 ? ? ? ? 0 1973 15 0 80 ?2(1975) x(uU + dD) + y(sS) 3 1 0 0 0 1 2 1 1 0 1975 20 0 175 0a2(1990) (uU dD)

2 3 1 0 1/2 1/2 1 2 1 1 0 2003 10 0 249 0

(2000) (uU

dD)

2 0

1 0 0 0 1 1

1

1 0 2000 30 0 300 0

f2(2000) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 2 1 1 0 2001 10 0 312 0X(2000) ?? 0 ? 0 0 0 ? ? ? ? 0 2214 15 0 355 0X(2000) ?? 3 1 0 0 0 1 4 1 1 0 1998 3 0 15 ?2(2005) (uU dD)

2 1 1 0 0 0 1 0 1 1 0 2005 15 0 200 0

(2010) x(uU + dD) + y(sS) 0 0 0 0 0 1 0 1 1 0 2010 35 0 270 01(2015) (uU dD)

2 0 1 0 0 0 1 1 1 1 0 2014 20 0 230 0

a0(2020) (uU dD)

2 0 0 0 1/2 1/2 1 2 1 1 0 2025 30 0 330 0X(2020) ?? 0 ? 0 0 0 ? ? ? ? 0 2015 3 0 10 0h3(2025) x(uU + dD) + y(sS) 4 1 0 1/2 1/2 1 3 1 1 0 2025 20 0 145 0b3(2025) (uU dD)

2 4 1 0 1/2 1/2 1 3 1 1 0 2025 15 0 107 0

2(2030) x(uU + dD) + y(sS) 3 1 0 0 0 1 2 1 1 0 2030 5 0 205 0f3(2050) x(uU + dD) + y(sS) 4 1 0 1/2 1/2 1 3 1 1 0 2048 8 0 213 0f0(2060) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 0 1 1 0 2060 0 ? 50 ?(2070) (uU

dD)

2 0 0 0 0 0

1 0

1 1 0 2070 35 0 310 0

a3(2070) (uU dD)2 2 1 0 1/2 1/2 1 1 1 1 0 2070 20 0 170 0X(2075) ?? 0 ? 0 0 0 ? ? ? ? 0 2075 12 0 90 0a2(2080) (uU dD)

2 1 1 0 1/2 1/2 1 0 1 1 0 2060 20 0 195 0

X(2080) ?? 0 ? 0 0 0 ? ? ? ? 0 2080 10 0 110 0X(2080) ?? 4 1 0 0 0 ? 3 1 ? 0 2080 10 0 190 0a1(2095) (uU dD)

2 0 1 0 1/2 1/2 1 1 1 1 0 2096 17 0 450 0

(2100) x(uU + dD) + y(sS) 0 0 0 0 0 1 0 1 1 0 2100 50 0 190 0X(2100) ?? 0 ? 0 0 0 ? ? ? ? 0 2100 40 0 250 0X(2110) ?? 4 1 0 0 0 ? 3 1 ? 0 2110 10 0 330 0f2(2140) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 2 1 1 0 2141 12 0 49 0(2145) x(uU + dD) + y(sS) 0 1 0 1 1 1 1 1 1 0 2150 20 0 235 0X(2150) ?? 1 1 0 0 0 ? 2 1 ? 0 2150 10 0 260 0a2(2175) (uU dD)

2 1 1 0 1/2 1/2 1 0 1 1 0 2180 40 0 310 0

(2190) x(uU + dD) + y(sS) 0 0 0 0 0 1 0

1 1 0 2190 50 0 850 02(2195) x(uU + dD) + y(sS) 3 1 0 0 0 1 2 1 1 0 2195 30 0 220 0(2205) x(uU + dD) + y(sS) 0 1 0 0 0 1 1 1 1 0 2205 30 0 350 0X(2210) ?? 0 ? 0 0 0 ? ? ? ? 0 2210 79 0 200 0X(2210) ?? 0 ? 0 0 0 ? ? ? ? 0 2207 22 0 130 ?h1(2215) x(uU + dD) + y(sS) 0 1 0 1/2 1/2 1 1 1 1 0 2220 40 0 320 0b1(2240) (uU dD)

2 0 1 0 1/2 1/2 1 1 1 1 0 2240 35 0 320 0

2(2240) (uU dD)

2 3 1 0 0 0 1 2 1 1 0 2240 60 0 330 04(2240) (uU dD)

2 5 1 0 0 0 1 4 1 1 0 2240 25 0 190 0

2(2245) (uU dD)

2 3 1 0 0 0 1 2 1 1 0 2240 60 0 320 02(2250) x(uU + dD) + y(sS) 3 1 0 0 0 1 2 1 1 0 2248 20 0 280 04(2250) (uU dD)

2 5 1 0 0 0 1 4 1 1 0 2250 15 0 215 0

4(2250) x(uU + dD) + y(sS) 5 1 0 0 0 1 4 1 1 0 2250 30 0 150 03(2255) x(uU + dD) + y(sS) 4 1 0 0 0 1 3 1 1 0 2250 20 0 200 0X(2260) ?? 3 1 0 0 0 ? 4 1 ? 0 2260 20 0 400 0(2265) (uU dD)2 0 1 0 0 0 1 1 1 1 0 2260 40 0 320 0a1(2270) (uU dD)

2 0 1 0 1/2 1/2 1 1 1 1 0 2270 60 0 300 0

a2(2270) (uU dD)

2 1 1 0 1/2 1/2 1 0 1 1 0 2265 20 0 235 0h3(2275) x(uU + dD) + y(sS) 4 1 0 1/2 1/2 1 3 1 1 0 2275 25 0 190 0a4(2280) (uU dD)

2 3 1 0 1/2 1/2 1 2 1 1 0 2300 20 0 230 0

(2280) x(uU + dD) + y(sS) 0 0 0 0 0 1 0 1 1 0 2285 20 0 325 0(2280) (uU dD)2 0 1 0 0 0 1 1 1 1 0 2280 50 0 440 03(2285) x(uU + dD) + y(sS) 4 1 0 0 0 1 3 1 1 0 2280 60 0 230 0X(2290) ?? 0 1 0 0 0 1 1 1 1 0 2290 20 0 275 0f3(2300) x(uU + dD) + y(sS) 4 1 0 1/2 1/2 1 3 1 1 0 2303 15 0 214 03(2300) (uU dD)

2 4 1 0 0 0 1 3 1 1 0 2300 50 0 340 0

a3(2310) (uU dD)

2 2 1 0 1/2 1/2 1 1 1 1 0 2310 40 0 180 0f1(2310) x(uU + dD) + y(sS) 0 1 0 1/2 1/2 1 1 1 1 0 2310 60 0 260 0


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TABLE X: Complete sdSM Meson Parameter Predictions (cont.)

Name Quarks L S Clr I Y G J P C Q q l Mass(MeV) ExpErr f(Err) (MeV) f(Err)4(2320) x(uU + dD) + y(sS) 5 1 0 0 0 1 4 1 1 0 2330 40 0 240 0f0(2330) x(uU + dD) + y(sS) 1 1 0 1/2 1/2 1 0 1 1 0 2337 14 0 217 0(2330) x(uU + dD) + y(sS) 0 1 0 0 0 1 1 1 1 0 2330 30 0 440 0a1(2340) (uU dD)

2 0 1 0 1/2 1/2 1 1 1 1 0 2340 40 0 230 0

X(2340) ?? 0 ? 0 0 0 ? ? ? ? 0 2340 20 0 180 0

(2360) (uU dD)2 0 0 0 0 0 1 0 1 1 0 2360 25 0 300 0X(2360) ?? 3 1 0 0 0 ? 4 1 ? 0 2360 10 0 430 0X(2440) ?? 6 1 0 0 0 ? 5 1 ? 0 2440 10 0 310 0X(2632) ?? 0 ? 0 0 0 ? ? ? ? 0 2631.6 2.1 0 0 ?X(2680) ?? 0 ? 0 0 0 ? ? ? ? 0 2676 27 0 150 ?X(2710) ?? 5 1 0 0 0 ? 6 1 ? 0 2710 20 0 170 0X(2750) ?? 6 1 0 0 0 ? 7 1 ? 0 2747 32 0 200 0f6(3100) x(uU + dD) + y(sS) 7 1 0 1/2 1/2 1 6 1 1 0 3100 100 0 700 0X(3250) ?? 0 ? 0 0 0 ? ? ? ? 0 3250 8 0 45 0X(3250) ?? 0 ? 0 0 0 ? ? ? ? 0 3245 8 0 25 0K uS 0 0 0 0 1 ? 0 1 1 12 25 493.677 0.016 0 5.315E 14 0K0 dS 0 0 0 0 0 ? 0 1 0 12 25 497.648 0.022 0 0 ?K0S p(dS) + q(Ds) 0 0 0 0 0 ? 0 1 0 497.648 0.022 0 7.352E 12 0K0L p(dS) q(Ds) 0 0 0 0 0 ? 0 1 0 497.648 0.022 0 1.287E 14 0K0 (800) uS 1 1 0 1/2 1/2 ? 0 1 1 840 80 0 620 0

K00 (800) dS 1 1 0 1/2 1/2 ? 0 1 0 840 80 0 620 0K(892) uS 1 0 0 0 1 ? 1 1 1 39 36 891.66 0.26 0 50.8 0K0(892) dS 0 1 0 0 0 ? 1 1 0 39 36 896 0.25 0 50.3 0K1 (1270) uS 1 2 0 1/2 1/2 ? 1 1 1 1272 7 0 90 0K01(1270) dS 1 0 0 1/2 1/2 ? 1 1 0 1272 7 0 90 0K1 (1400) uS 1 0 0 1/2 1/2 ? 1 1 1 1402 7 0 174 0K01(1400) dS 1 0 0 1/2 1/2 ? 1 1 0 1402 7 0 174 0K uS 0 1 0 0 1 ? 1 1 1 1414 15 0 232 0K0 dS 0 1 0 0 0 ? 1 1 0 1414 15 0 232 0K0 (1430) uS 1 0 0 1/2 1/2 ? 1 1 1 1414 6 0 290 0K00 (1430) dS 1 1 0 1/2 1/2 ? 0 1 0 1414 6 0 290 0K2 (1430) uS 2 2 0 1/2 1/2 ? 2 1 1 30 28 1425.6 1.5 0 98.5 0K02 (1430) dS 2 2 0

1/2 1/2 ? 2 1 0 30 28 1432.4 1.3 0 109 0

K(1460) uS 0 0 0 0 1 ? 0 1 1 1460 0 ? 260 ?K0(1460) dS 0 0 0 0 0 ? 0 1 0 1460 0 ? 260 ?K2 (1580) uS 3 1 0 0 1 ? 2 1 1 1580 0 ? 110 ?K2(1580) dS 2 0 0 0 0 ? 2 1 0 1580 0 ? 110 ?K(1630) uS ? 0 0 0 1 ? ? ? 1 1629 7 0 16 0K0(1630) dS ? 0 0 1/2 1/2 ? ? ? 0 1629 7 0 16 0K1 (1650) uS 1 0 0 1/2 1/2 ? 1 1 1 1650 50 0 150 0K01(1650) dS 1 0 0 1/2 1/2 ? 1 1 0 1650 50 0 150 0K(1680) uS 2 1 0 0 1 ? 1 1 1 1717 27 0 320 0K0(1680) dS 2 1 0 0 0 ? 1 1 0 1717 27 0 320 0K2 (1770) uS 2 0 0 0 1 ? 2 1 1 1773 8 0 186 0K02(1770) dS 2 0 0 0 0 ? 2 1 0 1773 8 0 186 0K3 (1780) uS 2 1 0 0 1 ? 3 1 1 32 31 1776 7 0 159 0K03 (1780) dS 2 1 0 0 0 ? 3

1 0 32 31 1776

j. gregory moxness - a more natural reference model integrating relativity and quantum mechanics

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