Abstract

 

There are currently three important connected major unanswered questions in physics and astrophysics.

(1)  How can the theories of symmetry and the Higgs field be used to calculate the masses of the fundamental particles?

(2)  How can dark matter be explained and described?

(3)  How can dark energy be explained and described?

A self-consistent theory (called Model 1 in this paper) has been developed that appears to answer questions 2 and 3 quantitatively. In order to derive and justify Model 1, however, it became necessary to calculate the mass-energy of the proton and other fundamental particles that make it up, which answers question 1. This procedure then gave a path for calculating the mass of the Super Particle, which is the primary particle of Model 1. The super particle was found to be a Grand Unified Particle, which unifies the electromagnetic, weak and the strong forces. In investigating the properties of this super particle, it became obvious that it had the properties of dark matter, and when it breaks down, it generates dark energy. This paper describes the means of calculating mass-energy for any particle and the properties of the shielded super particle. In a sequence of related papers (Wald, Model 1-B; Wald, Model 1-C; Wald, Model 1-D; Wald, Model 1-E; and Wald, Model 1-F), Model 1 is detailed and expanded.

 

 

 

                              I. THE PROBLEM

 

Schumm points out that mass appears to be the charge for the gravitational field (Schumm, 10). Higgs found out that elementary particle mass is connected to a field that permeates space (Kane, 97). The mass comes from the interaction of the Higgs field and the mass charge of the particle, so it should be calculable using quantum mechanical techniques. The ability to calculate the mass of particles allows us to calculate the mass and characteristics of the grand unified particle or super particle. The super particle is the basic particle of Model 1, and it appears to explain dark matter and dark energy. The unique features of Model 1 are:

• There are two spaces in the universe, low-energy particle space and high-energy quantum vacuum space. A potential barrier separates them. One space contains visible matter, and the other space contains dark matter.

• There is a cycling of mass-energy between these spaces through the black holes that connect them. Particles pass from particle space to vacuum space through black holes where they are converted into super particles (energy ~10¹⁷GeV).  They are then wrapped with a potential energy barrier shield (~10¹⁹GeV) to stabilize them. The barrier shield forms the boundary of high-energy vacuum space. These stabilized, shielded super particles are then able to escape from the black hole into particle space. The shielded super particles have a low interaction cross-section with ordinary particles except through gravity, and so are observed as dark matter.

• Dark matter particles interact with each other and form a slowly building bubble centered on a galaxy that stabilizes its outer edges. Corridors of dark matter are also generated which form a cosmic web between the galaxies. These corridors guide the development of new galaxies.

• The super particles can tunnel through the barrier into particle space. Upon reaching particle space, the super particles become unstable and break down into particles (cosmic ray protons) with ultra high kinetic energy (UHECR’s). In doing so, they give up potential energy from their barrier shields into particle space which becomes the dark energy that we observe as the cause of our accelerating, expanding universe.

 In this paper, we will show that the mass of particles can be calculated by adding a Higgs state to the Standard Model particle states. Further, we will extend the theory that allows us to determine the standard model masses to deduce the existence of the shielded super particle of Model 1. The super particle will also be shown to be a Grand Unification Particle. The shield for this particle will further be shown to be a Complete Unification Field unifying electromagnetic, weak, strong and gravitational forces. Finally, the super particle will be shown to have the characteristics of dark matter, and yield dark energy and cosmic rays when it tunnels through the shield and breaks down.

 

                                II. THE SOLUTION

 

This paper will proceed by:

A. Developing the theory that allows us to calculate the mass of particles.

B. Proving the accuracy of the theory by calculating the masses of the particles, and comparing them with experiment.

C. Calculating the mass of the Grand Unified Particle, showing that it fits the characteristics of the Super Particle, and then calculating the mass of the barrier shell needed to stabilize the super particle.

D. Showing how a black hole in the center of a galaxy can form shielded super particles, and then showing how it can escape the black hole as dark matter.

E. Showing how escaping dark matter can stabilize the edge of a galaxy.

F. Showing how super particles can penetrate the barrier shell by quantum tunneling, and then break down to form ultra high-energy protons and potential energy (dark energy).

 

A. Particle Mass-energy Theory

 

Kane (Kane, 261) describes mass as due to three sources:

(1). Higgs free mass of the particles

(2). Confinement mass-i.e. the mass-energy that holds the particles together.

(3). Interaction mass.

Free mass is given to quarks and leptons through interaction of symmetry with the Higgs field. As will be shown below, confined (or constituent) mass is given to confined particles by interaction of quarks confined into protons with the Higgs field. The interaction mass is small and calculable and will not be pursued further here because it is treated elsewhere (Kane, 262). Here we will work out the theory for, and the values of, each component of mass-energy.

 (1). Higgs Free Mass of the Particles

Energy of an Electron in Orbit Around a Proton

As a development guide and for comparison with the final form of Model 1, let us describe a known physical phenomenon-electron orbital motion in quantum shells around a proton nucleus-the atom. According to classical mechanics, the potential energy levels of this system can be obtained by noting that the electric field around the nucleus is:

            ε = 10^-7 c²q_e/r² (nt/coul)             

Then the force on the electron in orbit is:

            f = 10^-7c²q_e²/r² = εq_e (nt)                     

And the potential energy of the electron in its shell is:

            V = -(10^-7 c²q_e/r²) q_er = εq_er (J)

So if the electron orbit moves outward a distance d, the amount of potential energy given up is:

            ΔV = -(10^-7c²q_{e /} r²) q_ed = -εq_ed (J)   

But the probability of presence of the electron in the shell n is low due to destructive interference of the electron with itself unless the radius is such that the electron orbit distance traveled around its shell is exactly n electron wavelengths long (n = 1,2,3…). When this condition is met, the electron interferes with itself constructively, the probability of presence is 1, and the potential energy of the electron as it moves around the orbit in its shell is:

            V_n = -((1)hcR_∞/n²) (J)

Here the quantum field ((1)hcR_∞/n²) has replaced the classical field (10^-7c²q_e / r²). Note the quantity (1) is the quantum symmetry value for symmetry U(1), which applies to the electromagnetic force. The quantum number n appears in the denominator to replace r as the measure of how many wavelengths are needed to circle an orbit. Note also that the square of the charge q_e²is incorporated into the term R_∞.           

Now if the electron moves from orbit 1 to orbit 2 and loses potential energy, a photon of wavelength λ_l and energy hc/ λ_l is emitted, where:

            1/ λ_l  = R_∞(1/ n₁² – 1/ n₂²)

            Where:

            n = orbital quantum number

            R_∞ = Rydburg number (1/meters)

            h =Planck’s constant (J sec)

            c = speed of light (m/sec)

            q_e = electromagnetic charge (coulomb)

 

Particle mass due to orbital motion in a Higgs field

Here we give a description of the quantization of the Fermion and Boson mass-energy in the Higgs fields due to orbital motion. Now we will use the same procedure to develop the mass of a particle from the Higgs field and compare it with the quantum electron case. Kane starts with the Lagrangian (see Kane, 98) of a Higgs field of a particle passing through an ambient Higgs field caused by many particles in a vacuum.

            T – V = ½∂_μ φ∂ ^μφ – (½μ²φ ²+ ¼ λφ⁴)

Note that the potential energy V is related to the Higgs field as follows

            V = -(½μ²φ ²+ ¼ λ φ⁴) =-(½μ² φ_h ² (1-¼ λ_tφ_h² / ½μ² )

            Where:

            λ = self interaction coefficient

            φ_h  = Higgs field (a complex quantity), so φ_h ² = φ^† φ 

 

The first term appears to be the interaction of the particle with the ambient Higgs field. The second term appears to be the interaction of the particle with its own field and the ambient Higgs field. To find the excitation energies, and thus the masses, we must find the minimum of the potential and expand around the minimum to get excitations, which are the particles. As Kane notes (Kane, 98), “In field theory, it is conventional to call the ground state the vacuum, and the excitations are the particles.” The form of the Lagrangian determines the mass of the particles. If these operations are performed, the result is:

            m _η²  = -2 μ² =  mass              

Here particle mass m_p (real), is obtained from m _η² (complex). Then, V can be written:          

            V = – m _η² φ²+ ¼ λφ ⁴= –m _η²φ ² (1- ¼ λ_tφ_h ²/ m _η² )          (1)

We call the quantized particle mass energy m_pη.  Then if the quantum state of the potential energy changes, a massive particle is formed as follows 

            ΔV_η = m_pη = – m_η²φ_h ² (1- 1/4 φ_h ² λ_t /m _η²) = particle mass energy        (2)

                     = – (S_o)K_hohcn (1 – λ_t m/4)

            Where:

            m_η²φ ² = K_hohcn

            1/4 φ_h ² λ_t /m _η²= (φ_h ²/m _η²) λ_t /4  =  m(λ_t /4)

            (φ_h ²/m _η²) = m = Higgs quantum number

Here we note that as with the electron, each Fermion is moving within the nucleus in a reentrant pattern determined by its symmetry, so the mass energy is low due to destructive interference unless the particle orbit distance traveled is exactly n_o particle wavelengths long (n_o = 1,2,3…). Then the particle interferes constructively, and the mass energy is high. In a similar way, each Higgs particle moves in a reentrant pattern within the nucleus of m particle wavelengths, and the mass energy is high when the particle interferes constructively. Note that for convenience, a descending quantum number ((4-n) = 4,3,2,1) is used instead of an ascending n to make the final expression simpler.

In addition, the first Higgs field is modified by the quantum number m of the Higgs particle (m) orbiting the nucleus in the following way:

            m _η² φ² = K_hohcn_o^2m

Then the potential energy of a particle as it moves around its orbit in its symmetry pattern is the product of factors (see Kane, 90) as shown in the equation:

            ΔV_η = – (S_o)K_hohcn_o^2m (1 – λ_t (4-m)/4)

                     = (symmetry factor)x(charge factor)x(field factor)

The value of each factor is as follows.

The Symmetry factor specifies the symmetry that is active in a particle, and because of constructive interference, each symmetry factor (S_o) becomes:

            (S_o) = (n!)

            Electromagnetic factor U(1) = (1) for the electron

            Isospin factor SU(2) = (2×1) for the isospin state

            Color factor SU(3) = (3x2x1) for the quark

            Higgs factor SU(4) = (4x3x2x1) for the Higgs particle

Note that only the quantum numbers for the symmetries active in the particle appear in the factor. Note also that a particle is formed for each set of active symmetries, and the families of particles stem from the sequence of sets.

The Charge factor specifies which charge is active in a particle. Its value is:

            f ^s = charge factor = 0.9909 for s = 1

            s = symmetry number (1,2,3,4,6,10)

            (Electromagnetic charge) = -q_e

            (Isospin charge) = q_i

              (Color charge) = q_c

              (Mass charge) = m_p = the charge that generates mass-energy.

Note that the electromagnetic charge has a different sign than the other charges because it is different from the other charges. Electromagnetic charge can both repel and attract; the others cannot.

The Field factor is more complicated. Two Higgs fields are important in mass generation, the ambient and the self-interaction fields. 

The first Higgs field is from the distributed mass in the universe, which is uniform on a large scale. We call this the ambient field. It can be described by the equation:

            m _η²φ ² = K_hohcn_o^2m

           

In writing this equation, it is noted that the density of particles is small, so on average one particle is not close to another particle. It is also noted that enough total particles exist so that the total field density from the sum of all particles K_hohcΣ q_t²/r² is above the threshold needed to generate a quantized particle. Then the field is quantized, and m _η² φ² becomes K_hohcn^2m). It is further noted that as with atoms, the square of the charge is incorporated into the constant K_ho.  It is finally noted that the particles have a closed orbit in the ambient Higgs field around the nucleus, and the probability of orbit occupation of a Fermion or Boson is high only when the constructive interference of the nuclear particle with itself as it completes its closed loop is exactly n wavelengths (n = 1,2,3…). It will be seen, then, that the quantum number n is in the numerator because the summed Higgs field strength is uniform in space rather than radial around the nucleus as it was for the electron in an atom.

The second Higgs field is due to self-interaction, and so is controlled by the quantum number of the Higgs particles m _η that are close. So the field is determined by the quantum number of the Higgs particle that is orbiting near the charge of the particle. This field can then be described for the Higgs quantum number m by the equation:

            φ_h2² m =  mrK_ho ¼ ( λ_t /m _ηh²) m _ηh²/r².= m K_ho ¼ ( λ_t )/r

Recalling that the field is small unless r is such that the distance traveled in a pattern orbit is an integral multiple of the particle wavelength, we find for a particle influenced by an orbiting Higgs particle with quantum number m:

            φ_h2² m = λ_t (4-m)/4,

Here we have incorporated the K_ho /r into the λ_t term as we did with the atomic results. If we insert the two Higgs terms into equation (2), we get:

            φ_h² =  φ_h1²(1- φ_h2² )=  n_p(1- λ_t (4-m)/4)             (3)

But as Kane noted (Kane, 105) the Higgs field must be assigned an SU(2) doublet m’(up or down) with the following characteristics:

            m’ = either of the two quantities, down or up:

 

            down- (m) = variable internal field term, so all m fields apply.

            m’ = (m) = 0,1,2,3,4,6,10

Note that assuming λ_t remains constant at 1,

            (1-λ_t((4-m)/4) = (1-4/4), (1-3/4), (1-2/4), (1-1/4), (1-0/4), (1-0/4)

   

            up- (m+(m-1)) = constant internal field term, so only m = 2 applies.

            (m) = 1,2,3,4,6,10 (the m=0 case does not exist)

             m’ = (m+(m-1)) = 1,3,5,7,…

Again, assuming λ_t remains constant at 1, and m = 2

             (1-λ_t(4-m)/4) = (1-2/4), (1-2/4), (1-2/4)

 

Particle mass due to spin in a Higgs field

Again, the spin mass of the particle is a product of three factors operating in a Higgs field, except the motion is spin rather than orbital motion.

            V_n= m _η²φ ² (1- φ ² ¼ ( λ_t /m _η²))  = (symmetry factor)(charge factor)(field factor)

Spin Symmetry factor

The Symmetry factor specifies which symmetry is active in a particle, and for

Higgs Boson, the spin factor becomes:

            (Spin factor SP(0)) = (0)

Fermion, the spin factor becomes:

            (Spin factor SP(1/2)) = (1/2)

For a Boson, the spin factor becomes:

            (Spin factor SP(1)) = (1)

For three Fermion particles combined into one, such as in the proton, the spin factor is:

            (Spin factor) = (3/2)

 

Spin Charge factor

The spin charge factor that is active is mass charge.

            (Mass charge) = m_sp = the charge that generates mass-energy

 

Spin Field factor

Two Higgs fields are important in mass generation, the ambient and the self-interaction fields.

The first Spin field is again from the ambient field. It can be described by the equation:

            φ_h1² n_s = K_ohcn_s                     

It is noted again that as with atoms, the square of the charges is incorporated into the constant K_o.  It is finally noted that the particles have a closed spin in the ambient field, and the probability of orbit occupation of a Fermion or Boson is low due to destructive interference of the particle with itself unless the spin rotated by the particle around its axis is exactly (n_sp = +1/2, +1, +3/2, -3/2, -1, -1/2). It will be seen, then, that the quantum number n_sp is in the numerator and linear.

The second spin field is due to self-interaction, and so is controlled by the quantum number of the Higgs particles m _ηthat are close. But the quantum spin number is in a half-integral sequence (m/2), so the second field is:

            φ_h² =  φ_h1²(1- φ_h2² )=  n_sp² (1- λ_t (8-m)/2×4))             (4 

But as Kane noted (Kane, 105) as part of the Higgs mechanism, that the Higgs field must be assigned an SU(2) doublet m’(up or down) with the following characteristics:

            m’ = m’(down) or m’(up) where:

 

            down- (m) = variable internal field term, so all m fields apply.

            (m) = 1, 2, 3, 4, 6, 10.

Note that assuming λ_t remains constant at 1,

            (1-λ_t((8-m)/2×4) = (1-7/8), (1-6/8), (1-5/8), (1-4/8), (1-2/8), (1-0/8)

           

            up- (m+(m-1)) = constant ambient field term,

            (m) = 1,2,3,4,6,10 (the m=0 case does not apply)

            (m+(m-1)) = 1, 3, 5, 7,…

Again, assuming λ_t remains constant at 1, but m = 2 is the only Higgs number that applies for the constant ambient field.

            (1-λ_t((8-m)/2×4) = (1-7/8), (1-7/8), (1-7/8)

           

Note that spin is –1/2, 1/2, 2/2…, so m=0 is precluded, and the term (1-λ_t((8-m)/2×4)cannot be zero. Thus the neutrino is formed.

Then comparison with the field equation (2) allows us to replace it with the following equation to get the quantized field factor:

                    (Field factor) = (S_o)n^2m’(1- λ_t(4-m)/4)) + (S_sp)n_p^2m’(1- λ_t((8-m)/8))       (4)            

Mass-energy Coefficient for Orbitals and Spin

Note finally that the coefficient K_o hc  is determined by a few basic constants and an equation with the following form for each family of particles. It should be noted that the atomic orbitals for hydrogen are included in this equation.

            K_o hc  = mu(½r_e/a_e)^z f ^s t^p               

            p = (s+z)-q_r

   Where:

            mu= basic mass-energy units of the particle family (eV)

            a_e = Bohr radius = 5.28×10^-11m

            r_e = classical electron radius = 2.82×10^-15m

            (r_e/a_e) = radius ratio = 0.534×10^-4

            t^p = mass-energy factor = 10³ for p = 1

            f ^s = symmetry factor = 0.9909 for s = 1

            s = symmetry number (0,1,2,3,4,6,10)

            p = mass number (0,1,2,3,4)

            z = radius ratio number (0,1)

            q_r = charge ratio number= q_e /q_eo = -1 for electric charge which insures opposition to the color charge

                 = q_i /q_eo = 1 for the isospin charge

                 = q_c / q_eo = 1 for the color charge

                  = m_p / q_eo = 1 for the mass charge           

The basic mass energy unit of eV was chosen for simplicity. Using this basic unit, the charges of all of the four forces are automatically incorporated into the coefficient.

 

There are eight families of interest here.

1.Coefficient for energy of the atomic orbitals for hydrogen.

             mu = eV

             m_t = 0.511

             (½r_e/a_e)^z = (½ 0.534×10^-4)¹ for z = 1

             f ^s =  (0.9909)⁰ =1 for s=0, q=-1, p = s+z-q = 2

             t^p = (10³)^p = 10⁶ for p = 2

             R_∞ hc  = m_t K_o hc  = 0.51×10⁶x½0.534×10^-4 eV = 13.6eV

2.Coefficient for mass-energy of the spin for Neutrinos

             K_n hc= ~ 0.9909 eV, s = 1, best fit of data

             mu= eV

             f ^s = (0.9909)¹ for s=1, q=+1, p = s+z-q = 0

             t^p = (10³)^p  = 1 for p = 0

             K_onhc= (0.9909) eV

 3.Coefficient for mass-energy of free Electrons

             K_me hc = 0.990910⁶ eV, s = 1 best fit of data

             mu = eV

             f ^s  =  (0.9909)¹ = 0.9909 for s=1, q=-1, p = s+z-q = 2

             t^p = (10³)^p = 10⁶ for p = 2

             K_of hc = (0.9909) 10⁶ ev

4.Coefficients for Free Mu and Tau particles

             K_mt hc= (0.9909)¹ 10⁶ eV, s = 1 best fit of data

             mu = eV

             f ^s = (0.9909)¹ = 0.9909 for s=1, q=-1, p = s+z-q = 2

             t^p = (10³)^p = 10⁶ for p = 2

             K_omt hc= (0.9909) 10⁶ 

5.Coefficients for Quarks

             K_mqhc= (0.973)10⁶eV, s = 3 best fit of data

             mu = eV

             f ^s = (0.9909)³ = 0.973 for s=3, q=+1, p = s+z-q = 2,

             t^p = (10³)^p = 10⁶ for p = 2

             K_omt hc= (0.973)10⁶ eV

6.Coefficients for Higgs particles

             K_mhhc  = 0.973, s = 3 best fit of data

             Mu = eV

             f ^s = (0.9909)⁴ = 0.964 for s=4, q=+1, p = s+z-q = 3

             t^p = (10³)^p = 10⁹ for p = 3

             K_omt hc= (0.964)10⁹

7.Coefficients for W and Z particles

             K_mwzhc= (0.964)10⁹ eV, s = 4 best fit of data

             Mu = eV

             f ^s = (0.9909)⁴ = 0.964 for s=4, q=+1, p = s+z-q = 3

             t^p = (10³)^p = 10⁹ for p = 3

             K_omt hc= (0.964)10⁹ eV

8.Coefficients for Confinement

             K_mcmhc  = (938) 10⁶ eV, s = 7 best fit of data

             mu = eV

             f ^s = (0.9909)⁷ = 0.938 for s=3+4=7, q=+1, p=(s+z-q)=(3-1)=2 (note (b))

             t^p = (10³)^p = 10⁶ for p = 2

             K_omt hc=  (938) 10⁶ eV

Notes

(a). In two of the eight families, the formulas differ slightly from the best fit of data, families 3 and 5. In each case, the best fit quantum number should be one quantum number lower.

(b). For confinement, have p = 3(quarks)+4(confinement) = 7, p=(3-1) is for quarks only. 

Total Particle Mass

Note finally that the total particle mass is as follows:

             m_pη = K_ohc m_t mu                                         (5)

 

             Where:

             K_ohc = 1/2 (r_e/a_e) f ^s t

             (r_e/a_e) = 0.534×10^-4

             f ^s = (0.9909)^s , for s = 1,2,3,4

             t = (10³)^p, for p = 1,2,3

             m_t = [(S_o) n_o^2m’(1- λ_t(4-m)/4)) + (S_s)n_sp^2m’(1- λ_t((8-m)/8))]

             n_o = 1,2,3,4…

             n_sp = +1/2, +1, +3/2, -3/2, -1, -1/2

             m’(down) = m = 1, 2, 3, 4, 6, 10.

             m’(up) = (m+(m-1)) = 1, 3, 5, 7,11,19

             mu = eV

 (2). Confinement mass

Now we have the power to calculate the mass of the primary particles, but we still must establish how to calculate the confinement mass of composite particles such as the proton and the neutron. For composite particles, a procedure similar to the above one for primary particles yields:

             m_nc = (Particle 1 factor)(Particle 2 factor)(Particle 3 factor) 

                         x (Symmetry factor)(Charge factor)(Field factor)

                     = (V_n1)(V_n2)(V_n3)( S_o)(hcK_c n^2m’ (1- λ_tm/4))        (6)

  (3). λ_t Definition for Single and Multiple Particles

There are four different cases for λ_t.

(1). For a single particle is: 

            (1-λ_tm/4) = (1- (m/4)),             

(2). If three bosons are acting together on fermions (as in two cases of the Higgs mechanism with SU(2) symmetry), the self interaction term becomes:     

             (1-λ_tm/4) = (1-(1/3×2/4)) if one particle of three is acting at a time                

                                = (1-(2/3×2/4)) if two particles of three are acting at a time

(3). If three bosons and two fermions are acting together at a time (as in the second case of the Higgs mechanism with SU(2) symmetry), then: 

             (1-λ_tm/4)  = (1-2/3(2/4(2/4+3/4)) = (1–2/3×5/8)

(4). If two fermions are acting together (as in proton formation from quarks), the self interaction term becomes:

             (1-λ_tm/4) = (1-(2/4(2/4+3/4)) = (1-5/8) 

 

B. Primary Particle Mass-energy Calculation

 

In order to prove the accuracy of this mass calculation procedure, we will now calculate the mass of the principle fermions and bosons.

(1). Calculation of Higgs Free Mass of the Particles 

Table I. Leptons Free Mass

(n,m) values 

(1,(1-4/4))     (1,(1-2/4)        (2,(1-4/4))      (2,(1-2/4))      (2,(1-3/4))      (2,(1-2/4))                                                                                                                  

Experimental lepton mass (Kane,8, and en.wikipedia.org/wiki/Neutrino#mass)

ν_e                     e(0.511MeV)  ν_μ                     μ(105.7MeV)  ν_τ                       τ(1,777MeV)

ν_e + ν_μ + ν_τ < 0.3 eV. At least one > 0.04.

Lepton masses from Orbital motion in a Higgs field

(1-4/4)             (1-2/4)             (1-4/4)         (1-2/4×1/3)      (1-4/4(3/4?)   (1-3/8×1/3)(2/4?))

                         x(1×1)                                         x(1×2)                                        x(1×2)

                         x1^2×1                                           x2²⁽²⁺¹⁾                                     x2²⁽³⁺²⁾

(0)                   (0.50)                (0)                   (106.9)             (0)                   (1,792)

Lepton masses from Spin

(1-7/8)             (1-7/8)             (1-7/8)             (1-6/8)            (1-7/8)             (1-5/8)

x1/2                 x(1/2)                x2/2                 x2/2                 x2/2                 x(2/2)

x(1/2)^2×1         x(1/2)^2×1            x2/2^2×2           x2/2²⁽²⁺¹⁾      x2/2^2×3              x2/2²⁽³⁺²⁾

(0.016)            (0.016)              (0.125)             (0.25)             (0.125)             (0.375) 

Total mass (m_t)

(0.0160)          (0.516)              (0.125)             (107)               (0.125)             (1,792)

Correction for the neutrino (K_onhc (mu) = f ^s t (eV) = (0.9909)¹ (10³)⁰ = 0.9909 (eV)

(0.0159eV)                                (0.124eV)                                 (0.124eV)

Correction for the electron (K_onhc (mu) = f ^s t (eV) = (0.9909)¹ (10³)² = 0.9909((10⁶)(eV)

                          (0.511)(10⁶)eV)                                 

Correction for the mu, tau (K_onhc (mu) = f ^s t (eV) = (0.9909)¹(10³)² = 0.9909((10⁶)(eV)  

                                                                              (106.0(10⁶)eV)                         (1776(10⁶)eV)

Notes

(a). The orbital and spin motion from one family with symmetry SU(1), and produce an electron with mass within experimental accuracy of the observed mass. Also a neutrino is formed with mass within the estimated neutrino mass limits. The orbital and spin motion also form a second family with symmetry SU(2) and produces two particles and two neutrinos.

(b). The (2,(1-3/4)) case fits the (2,(1-4/4) data best. Also the (2,(1-2/4)) case fits the (2,(1-3/8)).data best. This is expected because the tau particle and its neutrino then fit the SU(6) and SU(10) cases which are the only acceptable higher symmetry cases (see C below). The tau and its neutrino are the leptons for the grand Unification Proton. 

(c). The (2,(1-2/4)) case shows the 1/3 term of 3 particles acting together to become (2,(1-2/4×1/3))

Table II Fermion Free mass

(n,m) values

 (3,(1-3/4))       (3,(1-2/4))      (3,(1-2/4))              (3,(1-2/4))           (3,(1-1/4))              (3,(1-2/4))                                                                                                                  

Experimental quark mass (MeV)

 u(1.7-3.3)         d(4.1-5.8)       s(101+29-21)          c(1270+70-90)   b(4.19-4.67(10³))  t(172(10³))

Quark masses from Orbital motion in a Higgs Field

(1-3/4)                 (1-2/4)         (1-2/4(2/3)5/4)       (1-2/4(1/3))         (1-0(1/4?))          (1-2/4)

x(1×1)                   x(1×1)                   x(1×2)                  x(1×2)                   x(1x2x3)              x(1x2x3)

x3^2×1                    x3^2×1                     x3^2×2                   x3^2x(2+1)              x3^2×3                    x3^2x(3+2)          

u(2.25)                d(4.50)                 s(94.5)                c(1217)                 b(4.37(10³))        t(177(10³))      

Quark masses from Spin motion in a Higgs Field

(1-7/8)                (1-3/4)                  (1-7/8(2/3))      (1-3/4(1/3))        (1-7/8)                  (1-3/4)

x(1/2)                  x(1/2)                    x(2/2)                 x(2/2)                  x(3/2)                   x(3/2)

x3/2^2×1                x3/2^2×1                 x3/2^2×2              x3/2^2x(2+1)          x3/2^2×3                 x3/2^2x(3+2)       

u(0.144)              d(0.28)                 s(2.11)                c(9.97)                  b(10.8)                  t(21.6)

Total mass (m_t)

u(2.39)                d(4.78)                 s(96.6)                c(1227)                 b(4.38(10³))        t(177(10³))                       

Correction for quarks (K_onhc (mu) = f ^s t (eV) = (0.9909)³(10³)²= 0.973(10⁶)(eV)  

u(2.33(10⁶eV)   d(4.65(10⁶eV)    s(94.0(10⁶eV)    c(1194(10⁶eV)     b(4.26(10⁶eV)    t(172(10⁶eV)                                

Notes

(a). For the (3,(1-2/4)) case, three bosons and two fermions are acting together at a time, so the term becomes:

(1-2/4(2/3(2/4+3/4)) = (1– 2/4(2/3)5/4) = (1-5/12)

(b). For the (3,(1-2/4)) case, three bosons are acting together, one at a time, so the term becomes:

            (1-2/4(1/3))

(c). The (3,(1-1/4)) case fits the (3,(1-0)) data best. The (3,(1-2/4)) remains the same for both cases. This anomaly hints that this tau particle is a grand unification lepton, and matches with the Grand Unification Proton with symmetry SU(6) described below. This case is significant, so more will be said about it below.

Table III Higgs Bosons Free Mass Including Possible Grand Unification SU(6) and Complete Unification SU(10) Bosons

(n,m) values

(4,0)                (4,1)                    (4,2)                (4,3)                (4,6)                 (4,10)                                                                                                     

Experimental and other possible Higgs masses

                        H^o(125GeV)                                                                                  (~10¹⁹GeV)

Masses from Orbital Motion in a Higgs Field

(1-4/4)             (1-3/4)             (1-2/4)             (1-1/4)             (1-0/4)             (1-0/4)

x(1)                  x(1×2)              x(1x2x3)          x(1x2x3x4)      x(1×2…x6)        x(1×2…x10)

x4^2×1                   x4^2×2                  x4^2×3                   x4^2×4                   x4^2×6                 x4^2×10

(0)                   (128)               (12,300)          (1.18×10⁶)        (1.20×10¹⁰)      (4.00×10¹⁸)

Higgs masses from Spin motion in a Higgs Field

(1-7/8)             (1-6/8)           (1-5/8)            (1-4/8)             (1-2/8)              (1-0/8)

x(0)                  x(0)                 x(0)                 x(0)                    x(0)                  x(0)

x4^2×1                x4^2×1               x4^2×2               x4^2x(2+1)           x4^2×3                 x4^2x(3+2)          

(0)                   (0)                   (0)                   (0)                      (0)                      (0)      

Total mass (m_t)

(0)                (128)              (1.23 x10⁴)        (1.18×10⁶)          (1.20×10¹⁰)      (4.00×10¹⁸)                    

Correction for Higgs (K_onhc (mu) = f ^s t (eV) = (0.9909)³(10³)³= 0.973(10⁹)(eV)  

(0GeV)     (124.5(10⁹eV)  (12.0(10¹²eV)   (1.15 (10¹⁵eV)   (1.17(10¹⁹eV)   (3.89(10²⁷eV)                     

Notes

(a). There is no (m, m+(m-1)) column for the Higgs because the Higgs interacts only with the ambient field.

(b). One other possible Higgs particle shows on the table-(4,4), but it has a 0 GeV energy, so it does not appear to exist. No lower energy Higgs particle has been found, but a systematic search has not been made.

(c). The Higgs field (4,1) appears to be the one that reacts with (3,(1-3/4)) and (3,(1-2/4)) cases.

(d). The next Higgs field (4,2) appears to be the one that interacts with (3,(1-1/4)) and the two (3,(1-2/4)) cases to make a heavier quark.

(e). The (4,6) and (4,10) Higgs  match the expected values for the super proton and the barrier shell. 

Table IV Boson Free Mass for the W and Z bosons

 (n,m) values

 (-)                   (-)                    (3,2)                (2,(2+1))         (4,3)                (3,(3+2))        

 Experimental boson mass

                                                 W(80.4)          Z(91.1)            W’(?)                Z’(?)

 Boson masses from Orbital motion in a Higgs field

                                                (1-2/4)             (1-1/4)             (1-2/4)             (1-2/4)

                                                x(1×2)               x(1×2)              x(1x2x3)          x(1x2x3)        

                                                x3^2×2                x2²⁽²⁺¹⁾            x4^2×3               x3²⁽³⁺²⁾                                                                                                           (81)                   (96)                  (1.2×10⁴ )        (1.77×10⁵)      

Quark masses from Spin motion in a Higgs Field

                                             (1-7/8(2/3))     (1-6/8(1/3))     (1-7/8(2/3))     (1-6/8(1/3))

                                               x(2/2)              x(2/2)              x(3/2)              x(3/2)

                                               x3/2^2×2           x2/2^2x(2+1)      x4/2^2×3           x3/2^2x(3+2)       

                                              (2.11)               (0.75)                (40.0)              (64.9)  

Total mass (m_t)

                                             (83.1)               (96.75)              (12.0(10³))      (177(10³))                       

Correction for Higgs (K_onhc (mu) = f ^s t (eV) = (0.9909)⁴(10³)³= 0.964(10⁹)(eV)  

                                             (80.1(10⁹eV)   (93.3(10⁹eV)   (11.6(10¹²eV)  (171(10¹²eV)         

Notes.

a). The interaction is mixed. The first results are from SU(2), yet for W, the number of dimensions is 3. and the Higgs field is 2. Still for Z, the number of dimensions is 2 and the number of the Higgs field is 2. The same crossing is assumed for W’ and Z’. This mixing appears to be due to the peculiarities of the weak force. 

b). The W’ and Z’ particles probably do not exist,   not been found because the energy is too high for current machines, but they are expected to exist. 

c). The next pair of particles may not exist, because the SU(5) group appears to be forbidden

(see section C below).

 

(2). Calculation of the Confinement Mass for the Primary Composite Particles

The confinement mass component for the proton can be described as the energy component due to the exchange of the gluons between the quarks to maintain the confinement of the quarks. The quark combinations to make nuclei are as follows:

• u, u, d. This is the common proton in particle space
• u, d, d. This is the common neutron in particle space.
• t, t, b. This may be a grand unification proton or super proton in vacuum space

A different combination of u and d gives the neutron, but the neutron is not important for the purposes of this paper, so it will not be pursued here.            

Table V Confinement Mass for the Proton, Neutron and of the Grand Unification Proton (Super Proton)

(n,m) values

            (3,(1+0))                                   (3,(2+1))                                    (3,(6+5))                                                                                                                    

Experimental proton mass    Experimental neutron mass     Possible Super proton mass

uud(938.28MeV)                    udd(939.58MeV)                    ttb(~10¹⁷GeV)

 

Proton, Neutron and Super proton masses  from Higgs charges and fields

u(2.31MeV)    (1-2/8)             u(2.31MeV)    (1-5/8)             t(172GeV)         (1-5/8)

d(4.63MeV)    x(1x2x3)          d(4.63MeV)    x(1x2x3)          b(4.26GeV)       x(1x2x3x6)

(uud)=24.71    x3^2x(1+0)         (udd)=49.52    x3^2x(1+0)        (ttb)=1.26×10⁵  x3^2x(6+5)                     

            uud(1001)                               udd(1002.7)                             ttb(5.46 10¹⁶)                                                                      

Correction for Higgs (K_onhc (mu) = f ^s t (eV) = (0.9909)⁷ (10³)³ = 0.938(10⁹)(eV) 

            (938.9(10⁶eV )                      (940.5(10⁶eV)                         (5.093(10²⁵eV)                                                                    

Notes

(a). The mass energy for a proton matches the experimental data, and so there is reason to believe the formula is correct.

(b). The mass energy for ttb super proton matches the value for Grand Unified Force (Kane, 281) obtained by other means. This is strong evidence for the existence of a super proton.

(c). The self-interaction factor for the proton (uud) is (1-5/8), and fits the data quite well. This factor results from the fact that the self-interaction term comes from interaction with two Fermions rather than one as for a particle, and so is:

            (1-λ_tf ^2p/m _η²)= (1-2/4(2/4+3/4)) = (1-2/4(5/4)) = (1–5/8)

(d). The self-interaction factor for the neutron (udd) is (1-2/8), and fits the data well. This factor results from the fact that the self-interaction term comes from interaction with one Higgs boson rather than two as for a proton, and so is:

            (1-λ_t φ^2p/m _η²)= (1-2/4(2/4)) = (1–2/8)

 

C.    Shielded Super Particle Mass Calculation

 

Kane notes that three forces appear to achieve the same value at ~10¹⁷ GeV. It also appears that four forces (including gravity) may unify at a somewhat higher value (10¹⁹ GeV-see Kane, 281), and this fact fuels the speculation that the forces unify at high energy. We note the following combinations:

• U(1)xSU(2)xSU(3) = SU(6) = The electromagnetic, weak and strong forces are all combined (Grand Unification)
• U(1)xSU(2)xSU(3)xSU(4) = SU(10) = All forces are combined. (Complete Unification)

In contrast, we note the following:

• SU(5) = SU(2)xSU(3) = unification of only weak and strong forces.
• SU(7), SU(8) and SU(9) have the same problem. They can unify only some of the forces.

The symmetry term in section A above, demands that we must account for the symmetry of all of the lower symmetry forces in order to calculate the mass of a particle, however. Thus all higher combinations are forbidden except SU(6) and SU(10). As a result, the proton decay lifetime experiment, with lifetime calculations based on SU(5), is expected to fail, as it appears to be doing (Kane, 289). But the super proton SU(6) and the barrier shell SU(10) are expected to be formed along with the standard model particles if the energy conditions are correct.

For the quark (3,1) case above, the (1-1/4) value for internal states was expected, which would give a mass value of 3.28GeV, but this value is a poor fit to data. However, the (1-0) value, which was used, gave the best fit to data. The (3,(3+2)) case would give the same value for either case. But the (1-0) value goes with the (4,6) case, which is the Grand Unification value. Note that the (3,2) value is too high as well, and it is also a down quark. It appears that Grand Unification case dominates the particle formation process. It appears that we have accidentally stumbled on the components of a Grand Unification proton in cases (3,3) and (3,(3+2)). When we combine these quarks into a super proton, as shown above, we get a mass energy value of ttb-5.8×10¹⁶ GeV, a value very close to the expected ~10¹⁷ GeV. Also, the τ particle (1,777MeV), case (2,(3+2)) appears to be the electron equivalent for this super particle, and will be called the super electron.

The super proton is expected to be unstable in low energy particle space, and break down into an ultra high kinetic energy proton and give up potential energy. In order to maintain a high potential energy environment where it can recombine into a super particle and so maintain its existence, a potential energy barrier shell is required. It must have a potential energy greater than the super proton energy (5.8×10¹⁶ GeV) to contain it, but less than the Planck energy (1.22×10¹⁹ GeV), say ~10¹⁹ GeV. The (4,10) Higgs field appears to fit at potential energy 4.00×10¹⁸ GeV. Note also that as a Higgs field, it acts on mass, so electromagnetic force and photons penetrate the barrier, but mass does not, except by tunneling.

The barrier shell can be approximated by a thin potential energy shell of thickness “a” that obeys the following equations (see Wald, Model 1-D Appendix H for more details).

 

            If E> V₀

            T = 1/(1+V₀²sin²(k₁a)/4E(E-V₀)               (7)

                = transmission through the barrier shell

            Where:

             V₀ = shell potential energy    

           

            If E< V₀,

            T = 1/(1+V_o² sinh²(k₁a)/4E(V₀-E),

            Where:

            k₁= (8p²m(V₀-E)/h²)) ^1/2

 

We see, then that massive particles with kinetic energy less than the potential energy (4.00×10¹⁸GeV) are mostly reflected, but some can tunnel through.

 

D.    Formation of Shielded Super Particles

 

To determine how the super particles and barrier shells are formed and operate, we must determine the equations for the processes that are valid in black holes. The expansion and contraction of space in high- energy zones are controlled by the following field density (r_f) and pressure (p) equations from general relativity (see Peebles, 396):

 

           ρ_φ = φ ²/2+ V = field density

            p = φ ²/2 – V = pressure                   (8)

            Where:

            V = a potential energy density

            φ = a new real scalar field = Higgs field

            φ’= the time rate of change of the field

            φ’ ²/2 = a field kinetic energy term

 

Also, from the field equation of general relativity, Peebles develops the cosmological equation for the time evolution of the expansion parameter (a(t)) due to average mass-energy density (r_m), pressure (p) and the cosmological constant (Λ) (see Peebles, 75):

 

            ä/a = -4/3πG (ρ_m+ 3p) + Λ                 (9)

                    = acceleration of the cosmological expansion parameter        

            Where:

            m = particle mass

            ρ_m = Σm/vol

            vol = volume of space containing the particles

 

Note from the field pressure equation (8), that if the potential energy density exceeds the field kinetic energy, the pressure is negative. Then, if the potential energy increases enough, the negative pressure term in equation (9) can become large enough to exceed the mass density and Λ terms in equation (9), and the acceleration of the cosmological expansion parameter (ä/a) turns positive, and space will expand. If the potential energy V is small compared to the field kinetic energy term, however, the field pressure term is positive, and if Λ is small, the acceleration ä/a becomes negative, and space will  contract. 

Further, it has been suggested that mass is the conserved charge for the gravitational (Higgs) field by Schumm (Schumm, 10) and others. If this suggestion is true, we would expect the field f to obey the following equation as it emanates from a massive particle:

           φ = K_ho m /r²              (10)           

The field described above is a real, scalar field, and is associated with spatial curvature as is mass-energy, and has the general characteristics of the real part of the Higgs field. So we will assume that the real part of the Higgs field accounts for the expansion and contraction of space.

Higgs found that potential energy is connected (see equation (1) above) to the Higgs field and mass. Also, the Higgs field is related to mass through equation 10. Now as the radius from the black hole center decreases, r_m increases, and so the field density (φ/vol) increases as well. From equation (1), we see that V increases faster than ρ_m, and so a contraction zone gradually turns into an expansion zone as a particle descends toward the center of the black hole. Therefore at some radius from the black hole center, ä/a will turn positive, form a barrier and reflect most of the particles. So a particle will descend through the contraction zone toward the black hole center, and then be reflected back by the expansion zone inside it, and then return again in the contraction zone under the influence of gravity. This cycling back and forth in two zones characterizes the high-energy diffusion zone where super particles are formed. 

Note that the volume of the diffusion zone is dependent on the mass of the black hole because of the r dependence of r_m. The area of this diffusion zone is:

             A_d = Km_bh 4/3π r_o²                (9)                     

             Where:

             m_bh = black hole mass

             r_o = event horizon radius

As the particle kinetic energy, and the spatial potential energy approach the unification energy (10¹⁷ GeV), the particles can convert to super particles. At the same time, potential energy barrier shells are being formed in the higher energy of the expansion zone. The super particles increase their kinetic energy during recycling to nearly 10¹⁹ GeV, where they can penetrate the shell and become stabilized as recycling shielded super particles. These shielded super particles then become dark matter. 

As the particle kinetic energy, and the spatial potential energy approach the unification energy (10¹⁷ GeV), the particles can convert to super particles. At the same time, potential energy barrier shells are being formed in the higher energy of the expansion zone. The super particles increase their kinetic energy during recycling to nearly 10¹⁹ GeV, where they can penetrate the shell and become stabilized as recycling shielded super particles. These shielded super particles are dark matter.

Once the shielded super particles are formed, they can then penetrate the black hole event horizon in the following way. The speed of light is determined by the energy in the high-energy granules of Planck space (Wald, Model 1-D Appendix A for more details). When the kinetic energy of a particle nears the Planck energy (1.22×10¹⁹ GeV), the speed of light increases above 2.99×10¹⁰ cm/sec in order for the Planck length to remain constant under relativistic foreshortening. Thus it is above the escape velocity (2.99 x 10¹⁰ cm/sec) of the event horizon formed at lower energies, so the shielded super particle escapes. In a general relativistic way of looking at this problem, a particle near Planck energy exceeds the ability of the gravitational well generated by black hole particles to contain it.

We note that low energy protons are shielded from interacting with super particles by the barrier shell. This interaction cross section is similar to the interaction of a proton with a neutron, and it is calculable. The proton-shell interaction cross section has been calculated to be ~10^-45 cm² (Wald, Model 1-C Appendix2), and so is small enough to warrant the name “Dark Matter”.

 

E.    Stabilization of Galaxies with Dark Matter

 

Beyond the event horizon, the density of shielded super particles is low enough that the mean free path is greater than the distance to the edge of the galaxy, and so the super particles fly free to intergalactic space creating a dark matter density that reduces as ~1/r² from the black hole at the galactic center.

Peebles (Peebles, 47) has described the problem of galactic rotation of spirals quantitatively in his Figure 3.12. The density of the visible matter at a given radius from the galactic center (ρ_t(r)) can be obtained by measuring the emission from the galaxy per unit area. The circular rotation velocity (ν_c) can be obtained by measuring the doppler of the emitted light. The astronomical data for spiral galaxies show that ν_c of visible matter in a spiral galaxy starts lowtoward the center of the galaxy and rises to a maximum and then flattens out to a constant velocity thereafter. Newtonian gravity requires, however, that ν_c reduce beyond the maximum, or some of the matter beyond the maximum would escape from the galaxy’s gravity until the total mass density ρ_t(r) at radius r matches the equation:

             ρ_t(r) = ρ_v(r) = ν_c² / 4πGr²              (11)

               Where

             ρ_v(r) = mass density of the visible matter

             ν_c = circular rotation velocity as a function of radius.

             G = gravitational constant.

In order for spiral galaxies to have the constant velocity beyond the maximum observed, there must be an added component of non-visible or “dark” matter (ρ_d(r)) beyond the maximum that is decreasing with radius at a slower rate than the visible component. Then the sum of the visible and dark matter components would have the mass density as a function of radius needed to account for the flattening of the circular rotation velocity observed, namely:

             ρ_t(r) = ρ_v(r) + ρ_d(r) = ν_c² / 4πGr² (observed)           (12)

Equation 12 shows clearly that if ν_c² is constant beyond the maximum, the dark matter component of density (ρ_d(r)) must be inversely proportional to the square of the radius (~1/r²) as the visible component dies away. This behavior matches the behavior of the shielded super particles traveling to the edge of the galaxy.

In addition to the dark matter, it has been observed that there is a relation between the mass of the central black hole of a galaxy and velocity dispersion of the stars dust and gas of the bulge in those galaxies. This relation is called the M-sigma relation (Ferraese, 539). Recall that the area of the central black hole diffusion zone (equation 9) increases with the black hole mass, and so the dark matter density ρ_d(r) in equation (12) increases with black hole mass. This increase in ρ_d(r) increases the dust, gas and stars accumulated due to the dark matter increase. Now the dust, gas and stars gained from ρ_d(r) has higher ν_c than that due to ρ_v(r) because it is due to higher mass in the galaxy. Thus an increase in ρ_d(r) from an increase in black hole mass increases the maximum ν_c. The minimum ν_c due to ρ_v(r) remains the same. Thus the dispersion of the velocity of stars, dust and gas in the bulge of a galaxy with higher central black hole mass will be higher.

Note finally that the dark matter moves away from the black holes in each galaxy preferentially in the direction of other black holes, thus forming a net like structure with galaxies as nodes.(the cosmic web). So intergalactic gas and dust tend to form galaxies around this structure in groups, strings and walls.

These observed data imply that shielded super particles satisfy three of the primary requirements of dark matter. More details on this dark matter halo are given in Wald, Model 1-C 

 

F.    Tunneling Super Particles, Cosmic Rays and Dark Energy

 

It has been noted that a super particle is unstable outside of its barrier shell, so when it tunnels through the barrier shell, it will become a proton with ultra high energy (up to ~10¹⁹ GeV) and a significant amount of potential energy that came from the barrier shell and is added to particle space. Thus Model 1 predicts the existence of ultra high-energy cosmic rays (UHECR’s), and a buildup of potential energy in particle space.

Such cosmic ray events have been observed with energy up to ~ 10²² EV, and there is evidence that the energy goes higher. These events should not exist, since they are beyond the GZK cutoff, and no known local omni directional cosmic ray sources with this energy exist except for tunneling super particles. The GZK cutoff is formed when high-energy protons above a certain energy interact with microwaves to form lower energy particles. Since microwaves are everywhere (the GZK energy), cosmic rays should be limited to that energy. Yet such cosmic rays are observed. They occur anywhere there is dark matter-i.e. anywhere within a galaxy, and at lesser frequency, beyond (see Wald, Model 1-E for details).

In addition to ultra high-energy protons, the tunneling super particles yield potential energy from the barrier shells upon breaking down. It has been found (Wald, Model 1-E Appendix 1) that a barrier shell thickness of 10^-31 cm will yield enough tunneling super particles over ~10¹⁰ years to account for the dark energy (potential energy density) we observe in our universe (~10^-4 GeV/cc).

 

                 III. SUMMARY/CONCLUSIONS

 

In this paper, a procedure has been developed that allows us to calculate the mass of the particles of the universe with considerable accuracy from the Higgs theory and the theory of Symmetry.

Following Model 1, the mass of a super particle was calculated, and found to match the expected Grand Unification energy (~10¹⁷GeV) (Kane, 281), and consists of a quantum combination of the t and b quarks. We found finally, that the barrier shell of the shielded super particle fits the characteristics of a Higgs field that satisfies the SU(10) symmetry (Total Unification of the electromagnetic, weak, strong, and gravitational forces).

 This shielded super particle was found to have the low interaction cross section of dark matter, stabilize the outer edges of galaxies, explain the existence of ultra high-energy cosmic rays (UHECR’s), and explain the dark energy that is expanding the universe.

Model 1 as described here lacks a detailed and coherent description of the Higgs field. This lack is addressed in Reference 1-Wald, Model 1-B.

 

                        IV. REFERENCES

 

1.  L. H. Wald, Model 1-B “The Origin of the Higgs Field for Model 1” www.Aquater2050.com/2017/01/
2.  L. H. Wald, Model 1-D “The Recycling Universe” www.Aquater2050.com/2017/02/
3.  L. H. Wald, Model 1-E “The Super Particle as a Cosmic Ray” www.Aquater2050.com/2017/03/
4.  L. H. Wald, Model 1-F “How to Prove a Theory’s Correctness” www.Aquater2050.com/2017/03/
5.  B. A. Schumm, Deep Down Things, Baltimore, Johns Hopkins University Press, 2004.
6.  G. Kane, Modern Elementary Particle Physics, Ann Arbor, Michigan, Perseus Publishing, 1993 

7.  P. J. E. Peebles, Principles of Physical Cosmology, Princeton, New Jersey, Princeton University Press.

8.  Ferraese, L. and Merritt, D. “A Fundamental Relation Between Supermassive Black Holes and their Host Galaxies” The Astrophysical Journal The American Astronomical Society. 539 (1) (2000-08-10) 
9. L. H. Wald, Model 1-C “Shaping the Dark Matter Cloud” www.Aquater2050.com/2017/02/