Abstract

Of the major unanswered questions in physics and astrophysics, three are arguably the most important.

• How can dark matter be explained and described?
• How can dark energy be explained and described?
• Is it possible to explain what happened before the big bang and what initiated it and what happened afterward?

A five part self-consistent theory called Model 1 has been developed that answers these questions quantitatively. The papers Model 1-A “Mass and the Function of the Standard Model Particles”, Model 1-B “The Origin of the Higgs Field for Model 1” and Model 1-C “Shaping the Dark Matter Cloud” (see Wald, 1 Model 1A, Model 1B and Model 1C) answer the first question. Next, the paper Model 1E “The Super Particle as a Cosmic Ray” (see Wald, Model 1E) answers the second question. In this paper, a sequence of creation and destruction steps was formulated and justified that describes the current data on the big bang that initiated our universe and thus answers question 3. These steps describe a recycling universe that rotates mass-energy through several states that start and end with a big bang. However, two types of big bangs can occur that feed back to each other. The existence of these states ensures that there will always be a universe in one state or another.

 

The Problem

Of the major unanswered questions in physics and astrophysics, three are arguably the most important.

• How can dark matter be explained and described?
• How can dark energy be explained and described?
• Is it possible to explain what happened before the big bang and what initiated it and what happened afterward?

A self-consistent theory called Model 1 has been developed that answers these questions quantitatively. The unique features of this model are:

1. There are two spaces in the universe, particle space and quantum vacuum space. A potential barrier composed of Higgs field separates them. One space contains visible matter, and the other space contains dark matter.
2. There is a cycling of mass-energy between these spaces through the black holes that connect them. Particles pass from visible matter space through black holes where they are converted into super particles (energy ~10¹⁷GeV) that operate with unified force behind the potential barrier (potential energy ~10¹⁹GeV), and become shielded super particles or dark matter.
3. Dark matter particles interact with each other and form a bubble halo centered on a galaxy. Corridors of dark matter (the cosmic web) connect the bubble halos of dark matter to each other. This web guides the development and organization of new galaxies.
4. 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 into particle space which is the dark energy that we observe as the cause of our accelerating, expanding universe.
5. The dark matter particles in vacuum space gain energy and density, and eventually exceed the ability of the barrier to contain them. They then explode back into particle space as a big bang (Type 1). This process repeats to make a series of new universes, each with higher entropy.  Eventually, the entropy is high enough that a Type 1 big bang cannot occur, and the balance of pressure and density in particle space shifts, causing a complete collapse and a different type of big bang (Type 2). This Type 2 big bang reduces the entropy and restarts the Type 1 cycles. 

A five part self-consistent theory called Model 1 has been developed that answers these questions quantitatively. The papers Model 1A “Mass and the Function of the Standard Model Particles”, Model 1B “The Origin of the Higgs Field for Model 1” and Model 1C “Shaping the Dark Matter Cloud” (see ref 1 Model 1A, ref 2 Model 1B and ref 3 Model 1C) answer the first question. Next, the paper Model 1E “The Super Particle as a Cosmic Ray” (see ref 4 Model 1E) answers the second question.

In the papers “Mass and the Function of the Standard Model Particles” and “The Origin of the Higgs Field for Model 1” a case was made for the existence of the super particle and its shield. This case was based on the ability to calculate the mass-energy of existing particles by use of Higgs theory and Symmetry. Using this same theory, it was found to be possible to calculate the mass energy of the super particle and its shield, and the characteristics of the shielded super particle fit neatly into the standard model. Thus we were able to provide a case for the correctness of the mass of Model 1. In addition, in the paper “Shaping the Dark Matter Cloud” the shielded super particle was shown to fit the requirements of dark matter, so a case was made for their equivalence. Finally, in the paper “The Super Particle as a Cosmic Ray” the decay products of the shielded super particle were shown to fit the requirements of dark energy and UHECR cosmic rays, so a case was made for the identity of dark energy.

In this paper, a sequence of creation and destruction steps was formulated and justified that match the current data on the big bang that initiated our universe and thus answers question 3. It will be shown that there is a possibility for two types of big bangs. Furthermore, the two types feed back on each other, and ensure that there will always be a universe in a rotating state. In addition to describing these steps, a case will be made for their correctness. 

 

The Solution

In searching for a complete and comprehensive cycle of mass-energy through its states, we will use the theories of general relativity, quantum mechanics and classical (Newtonian) mechanics in each step where it appears to apply. There will be steps where quantum mechanics and general relativity are both used in the same physical situation, so properly; a complete theory of quantum gravity should be applied, but currently, none exists. We will nonetheless assume these theories can be used together, and see if the result compares well with experiment. The applicable equations from these theories will be shown here. 

 

Expansion and Contraction of Space

First we will describe the equations that control the expansion and contraction of space. In order to provide this control, Peebles postulates the existence of a new real scalar field, and develops the equations for the field density ρ, and the pressure p in space from general relativity.The expansion and contraction of space is controlled by the following field density (ρ) and pressure (p) equations from general relativity (see Peebles, 396):

 

            ρ = φ’ ²/2+ V = field density        (1)

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

 

            Where:

            V = a potential energy density

            φ = a new real scalar 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 (ρ_m), pressure (p) and the cosmological constant (Λ) (see Peebles, 75):

 

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

                    = acceleration of the cosmological expansion parameter

           

Note from the field pressure equation (2), that if the potential energy density exceeds the field kinetic energy, the pressure is negative. The field kinetic energy term is slowly varying, however, because it depends primarily on the total mass in the general vicinity (see Wald, Model 1-B), so the potential energy controls the pressure. Then, if the potential energy increases enough, the negative pressure term in equation (3) can become large enough to exceed the mass density term in equation (3), and the acceleration of the cosmological expansion parameter (ä/a) turns positive, and space will eventually 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 eventually contract. Even if the (ä/a) term is negative, however, space will continue to expand for a while, thus maintaining its prior state, but eventually, expansion velocity will reduce below zero and space will contract. Thus, if ä/a is positive, space will expand faster and faster as time goes on. On the other hand, if ä/a is negative, space will expand slower and slower until the expansion velocity reverses sign, and then space will contract.

 

Source of the Real Scalar Field

Now we must establish the source of the real scalar field (see ref 2, Wald Model 1B). We expect a field to have a source-its charge. For example, the electric field has a source-the conserved electric charge Q. This charge results from the invariance of the phase of electromagnetic radiation throughout space (Noether’s theorem). The result is the equation for the electric field (ε):

 

            ε = K_eQ/r²

 

Now it has been suggested that mass is the conserved charge for the field for gravity by Schumm (Schumm, 10) and others. If this suggestion is true, it will result in the following equation for a field emanating from a massive particle mass, which we will call f_h.

 

            φ_h = K_ho m /r²                          (4)            

 

It is important to understand that the field described here as a real, scalar field, 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, and so we conclude f  = f_h.

 

Diffusion Equations

In the diffusion zone, the average kinetic energy is high enough to ionize the super particles. Therefore, at this radius, the high concentration gradient and the electric fields cause an ionized diffusion zone to form where the following equations are expected to be valid (Cobine, 51). 

 

            V⁺ = -D⁺/n⁺ dn⁺/dx + K⁺E

            V^– =-D^–/n^– dn^–/dx – K^–E

 

            Where:

            D = Diffusion coefficient

            K = Ion mobility under the influence of electric field 

            V = Ion velocity

            n = Ion concentration

            E = Electric field

            n^g = source of particles from the black hole

           

We set:

            V+ = V-  = V ;  n⁺ = n ^– = n ;  dn⁺/dx = dn^–/dx = dn/dx

 

We solve these equations, and get:

 

             n = (N_o(r)/4pDt)^3/2 exp(–r²/4Dt)         (5)

 

            Where:

            D = (D⁺ K^– + D^– K⁺ ) / ( K⁺+ K^– – 2 K⁺ K^– ) = total diffusion coefficient

                r= Radius from black hole source

            t= Time

            N_o(r) = particles diffusing from an “instantaneous” point source  

 

It should be noted that an “instantaneous” point source was chosen because it can represent the time span that the black hole is feeding, which is short compared to the lifetime of a galaxy. There are expected to be many short feeding episodes at higher intensities with lower, longer, smoother episodes in between. The solution shows that the relaxation time (the time needed for the resulting bubble of particles to flatten out) can be long for intense matter intakes. Thus a large input (N_o) into the black hole will take a long time to diffuse out into the galaxy. So the procedure for formation and distribution of super particles tends to smooth out the unevenness in the formation rate of super particles in the diffusion zone of the black hole.

The principal portion of the diffusion coefficient can be approximated by the equation:

 

            D = v L = v / 3nπd²

 

            Where:

            v = mean velocity of the super particles

            d = effective diameter of the super particle.

            L = mean free path = 1 / 3nπd²

            n =  super particle density.

 

The mean free path of the super particles is small enough to be called diffusion in the diffusion zone of the black hole. These super particles within their barrier shell are called dark matter (n = ρ_d(r)), because they have a low interaction cross-section with protons (~10^-45 sq cm) and so are difficult to detect with visible matter detectors (see Wald Model 1A). Using the total matter density expression obtained by Peebles for matter just beyond the event horizon (say r ~ 10⁵ cm), and using an effective super particle diameter of d < 10^-11cm, the mean free path of a super particle just outside the event horizon is >10²⁶ cm. This is further than the distance from the black hole center to the critical radius (~ 10²² cm), so super particles exiting the black hole event horizon will fly straight to intergalactic space with few collisions. Furthermore, they have a large enough kinetic energy (>10¹⁷ GeV) that they will not be stopped at the event horizon (see next section). Thus the super particle (dark matter) density ρ_d(r) will vary as:

 

            ρ_d(r) ~ K / r².

 

When the super particles reach intergalactic space, the density will gradually flatten out to the residual value of intergalactic space. This intersection point is somewhat beyond the critical radius. The rotation of these super particles around the galactic center is small because they originate from the central black hole of the galaxy.

 

Conditions for Change of State

Mass Formation

• High temperature
• High potential energy
• Low field KE

 

Space Expansion

• High temperature
• High potential energy
• Low mass density
• Low field KE
• Note

 

Space Contraction

• Low temperature
• Low potential energy
• High mass density
• High field KE

 

Big Bang

• High temperature (KE above barrier potential)
• High potential energy
• High mass-energy density
• Low field KE

 

Comprehensive Rotation of Mass-energy Through its States in the Universe

Now we can describe the mass-energy rotation through space. To describe this rotation, we must start with an unjustified set of initial conditions, but we will end with a set of conditions that justify the initial conditions.

• We start with a huge number of high kinetic energy super particles passing through their barrier shields in a first principle black hole and colliding. The colliding super particles are disrupted into energy and can become any high temperature particle. High potential energy seeded with charges for the four forces builds up in particle space along with the shadow net of low temperature dark matter from a prior universe. The speed of light is high (Appendix A) due to the high average kinetic energy (high temperature) of the colliding super particles. The high potential energy causes space to expand rapidly (see equations 2 and 3 above). The energy is in thermodynamic equilibrium throughout particle space even though the volume is large because the speed of light is high.
• The expansion results in cooling (see Appendix B) and the forces freeze out, so particles can form. Matter and anti matter particles are formed from potential energy and annihilate into photons that are later observed as microwave background radiation. The speed of light drops with the cooling (Appendix A), and thermodynamic equilibrium throughout the zone created by the big bang is lost. An excess of matter is formed as a result of the loss of equilibrium (Appendix C).
• Potential energy is converted into matter. Loss of potential energy and increase of mass density (matter) causes expansion to slow dramatically, but not halt (see equations 1 and 2). Local high mass density zones of cold dark matter attract the newly formed matter particles and aid in star formation, and the stars formed gather in galaxies (see ref 3, Wald, Model 1C).
• Dust, gas and stars spiral down toward the center of the galaxies and increase the mass there. The mass in the central zone of each galaxy determines the velocity v_c needed to remain in orbit. Particles with velocity < v_c fall toward the center of the galaxy. Where v_c = c all particles (including photons) fall toward the center of the galaxy, and an event horizon is formed. In this way, a central black hole is formed (see Appendix D).
• Massive particles fall to a diffusion zone within the event horizon formed by a contraction zone layer with an expansion layer beneath it. Massive particles fall through the contraction zone and then are reflected by the expansion zone, and then fall back through the contraction zone again thus forming a circulation of particles within the zone that generates the conditions for diffusion. The diffusion moves the highest energy super particles outward toward the event horizon (see Appendix E for details).
• Super particles are formed in the contraction zone, and covered in a barrier shell in the expansion layer to form a shielded super particle (see Appendix F for details).
• Note that there is no mass singularity at the center of the black hole. The diffusion will tend to drive particles from the high-density interior, and the potential barrier will reflect most of the others, and so slow their return. Finally, the size of the central zone will expand to ensure that the space occupied by each shielded super particle is limited to the shield volume, so the growth of the central mass density of the black hole is controlled.  
• The highest kinetic energy shielded super particles escape through the event horizon into the galaxy, and from there into intergalactic space. The mass of the escaping shielded super particles stabilizes the outer edge of the galaxy and is observed as dark matter (see Appendix G for details).
• In intergalactic space, the acceleration of the expansion parameter ä/a and the temperature start high after the big bang, and both reduce as particles form from potential energy and space expands. Eventually, particle formation and spatial expansion from the big bang stop because potential energy and temperature have become too low to sustain them, and space contraction begins. Note, however that intergalactic space does not immediately contract because it takes time for ä/a to overcome the residual high positive velocity of the expansion parameter. In addition, the expansion effect of the cosmological constant Λ must be overcome.
• The shielded super particles build up slowly in intergalactic space as the galaxies with central black holes and the dark matter escaping from them increase. Note that the mass density ρ_m buildup is with hot particles, so the average shielded super particle temperature increases. The super particles tunnel through the shield into intergalactic space and break down and the breakdown products are cosmic rays (UHECR’s) and potential energy. The increase in potential energy causes pressure to turn negative and space to start expanding again (see Appendix H for details). The increase in the temperature of the shielded super particles causes them to diffuse away from each other, so the increased temperature of the super particles aids the expansion process. The net effect is to counter the contraction of intergalactic space that had begun. However, the mass density builds up faster than the potential energy, because the tunneling (which provides V ) is slower than the mass escape from black holes. And the increase in mass density ρ_m increases the density of the scalar field φ and its field kinetic energy φ’ ²/2, thus countering the pressure (see equations 2, 3 and 4). This process takes time, but eventually the acceleration turns negative, and space continues to contract.
• The only thing that can halt this contraction process is lack of mass entering the black holes and thus keeping the black holes from providing a stream of shielded super particles to intergalactic space. This can happen if there is insufficient mass in the galaxies. This can happen over time if too much mass becomes tied up in the shadow net of cold dark matter.
• The shielded super particles in intergalactic space have low and high kinetic energy (temperature) groupings. The low temperature grouping of shielded super particles comes mostly from the shadow net of dark matter from the prior universe. The high temperature group is more distributed and fluid.
• The low energy shielded super particles in the diffusion zone of the central black holes gain energy as they recycle from the expansion zone to the contraction zone, and the highest temperature portion preferentially passes through the event horizon into the galaxy and eventually into intergalactic space to heat the shielded super particles there.
• Eventually, the average kinetic energy of shielded super particles in both intergalactic space and the central black hole diffusion zone nears the barrier shell potential energy (~10¹⁹ GeV) in both zones, and the speed of light exceeds 2.99 x 10¹⁰ cm/sec as well. The first black hole to reach this maximum potential energy condition is referred to as the first principal black hole.
• The shielded super particles from intergalactic space and lesser black holes then flow rapidly to the first principal black hole under the influence of gravity, and simultaneously flow over the potential barrier in a new big bang. They leave a feint tracery of low temperature dark matter (shadow net) in intergalactic space and in galaxies because the particles involved didn’t have enough energy to exceed the 2.99 x 10¹⁰ cm/sec speed barrier. Thus the initial conditions noted above for a big bang have been generated around the first principle black hole, and so a limited Type 1 big bang begins in this local zone. The volume of the Type 1 big bang that starts is determined by the volume around the first principal black hole that obtains an energy near ~10¹⁹ GeV. We see, however, that a shadow web of low temperature shielded super particles remains after the Type 1 big bang occurs.
• The escaping high temperature shielded super particles from limited big bangs, plus the normal high temperature shielded super particles from the galaxies heat the intergalactic shielded super particles as the Type 1 big bangs recur until the average intergalactic temperature reaches the barrier potential. In addition, the density of super particles increases until the cosmological expansion parameter ä/a to turn negative, and intergalactic space begins to contract. Then the intergalactic and black hole super particles flow together to a principle black hole and start a Type 2 big bang that cleans out most of the shadow net. After a cleansing Type 2 big bang, the initial conditions noted above have been achieved

We note that the data show that our current state is that the universe is undergoing accelerated expansion. So our current situation in this cycle is: 

• The acceleration of the expansion parameter is positive, and the universe is expanding.

 

Summary and Conclusions

Of the major unanswered questions in physics and astrophysics, three are arguably the most important.

• How can dark matter be explained and described?
• How can dark energy be explained and described?
• Is it possible to explain what happened before the big bang and what initiated it and what happened afterward?

A five part self-consistent theory called Model 1 has been developed that answers these questions quantitatively. The papers Model 1A “Mass and the Function of the Standard Model Particles”, Model 1B “The Origin of the Higgs Field for Model 1” and Model 1C “Shaping the Dark Matter Cloud” (see ref 1 Model 1A, ref 2 Model 1B and ref 3 Model 1C) answer the first question. Next, the paper Model 1E “The Super Particle as a Cosmic Ray” (see ref 4 Model 1E) answers the second question.

In this paper, a sequence of creation and destruction steps was formulated and justified that describes the current data on the big bang that initiated our universe and thus answer question 3. These steps describe a recycling universe that rotates mass-energy through several states that start and end with a big bang. However, two types of big bangs can occur that feed back to each other. The existence of these states ensures that there will always be a universe in one state or another. The steps may be summarized as follows.

• A big bang starts, expands and cools
• Four forces freeze out
• Matter is formed
• Galaxies are formed
• Central black holes are formed within galaxies
• Shielded super particles are formed within galaxies
• Shielded super particles escape the black hole and move to intergalactic space
• The number and temperature of shielded super particles increases and space contraction begins
• Kinetic energy reaches barrier potential level, and shielded super particles pass the barrier shield as a new big bang.
• First some Type 1, and then a final Type 2 big bang forms, and then the cycle restarts.

 

Appendix A

In order to make both constant speed of light and constant Planck length compatible, Amelino-Camelia and Magueijo (Amelino-Camelia, 6 and ref 8, Magueijo, 251 and ref 7, Magueijo, 31) developed a modified light speed relation. This relation shows that when the energy increases enough, the speeds of particles and photons increase to values greater than the speed of light in a vacuum at moderate energy (2.99 x 10¹⁰ cm/sec). This relationship has been developed further, and incorporated into Model 1. There it was found, using the theory of granulated Planck space, that the velocities of particles in vacuum space reach extreme values much higher than 2.99 x 10¹⁰ cm/sec, when the super particle kinetic energy (E_sp) approaches E_pl. A summary of the necessary conditions is given here.

Consider the condition where super particles have a potential energy V_sbo, which is only slightly less than the Planck energy. Particles and photons are roughly the same size as Planck granules, and moving in and out of each granule is important. For example, when super particles gain enough energy to operate freely in barrier space, they are operating in the zone 10¹⁹< E < 1.22 x 10¹⁹ GeV. Thus since the length of travel for a particle is n Planck lengths long, and N is the number of disruptions along the travel length, then the distance traveled is nl_p, and the time used for this travel is just Nt_p, for these disruptions, then the speed of light v_o as it moves in and out of each Planck granule is:

 

            v_o = nl_p/ Nt_p ½[(1 + (E_smo+ E_ske)/(E_smo+E_ske– V_sbo)]

                 = 2.99 x 10¹⁰n / N ½[(1 + (E_smo+ E_ske)/(E_smo+E_ske– V_sbo)] cm/sec

 

            Where:

            E_ske = super particle kinetic energy

            E_smo = super particle rest mass energy

Now, as the super particle energy moves up from the lower limit (V_sbo) we see that:

            (E_smo+E_ske) > V_sbo

Then:

            ½[(1 + (E_smo+ E_ske)/(E_smo+E_ske– V_sbo)] ~ 1

And since the energy is still removed from the Planck energy, N = n, so:

            v_o = nl_p/ Nt_p = c = 2.99 x 10¹⁰ cm/sec

Now recall that the potential energy of a Planck granule is the Planck energy, so as the super particle kinetic energy moves higher still toward the Planck energy, the super particle can pass right through the potential energy of the Planck granule just like a super particle passes through the super particle barrier shell when the kinetic energy equals the barrier potential energy. Thus the particle cannot detect the potential energy edge of a Planck granule. Then the number of disruptions along the travel length (N) is reduced from n to the large edges like disruptions in space such as the shock at an edge of a solar system, a galaxy, a boundary of a corridor in the cosmic web or an edge of the observable universe. This is a much smaller number than n, so n/N >> 1, and:

            v_o = nl_p/ Nt_p >> 2.99 x 10¹⁰ cm/sec 

Note that the same argument holds for photon velocities, except E_smo is zero. Note also that v_o is never infinite.

 

Appendix B

As space expands, the particles contained in it fly apart, and the relative velocity of particles is reduced. Thus the particles collide with lesser and lesser velocity, and so the average relative kinetic energy (temperature) becomes less and less. Under these conditions, the group of particles undergoing expansion cools. This condition is summarized in the gas law. Now temperature reduction occurs only if the particles are in thermodynamic contact, i.e.-the particles must collide and exchange energy. Contact of particles in a large volume is determined by the speed of light. If the time necessary for a photon to travel at the speed of light from one extreme of the volume to the other exceeds the time of existence of the particles, the particles are not in contact.  On the other hand, if the travel time is less than the existence time, the particles are in contact, and can even be in thermodynamic equilibrium. For more details, see Cobine, p 1, ff.

 

Appendix C

In the formation of matter and anti matter, our current particle data show that there was roughly one matter baryon excess for 10¹⁰ photons in particle space. This result can happen only if (Kane, 290):

1. Conservation of baryon number is violated.
2. Charge-parity (CP) is violated.
3. Particle space is not in thermodynamic equilibrium while the above conditions are satisfied.

Now we see that the conservation of baryon number was violated as soon as the super particles flowed over the potential barrier and were disrupted. The potential energy from the disrupted super particles was reformed into matter and anti matter particles while still in thermodynamic equilibrium due to the high light speed at the high energy existing then. Since there was thermodynamic equilibrium at that time, a roughly equal number of particles and anti particles were produced. The matter and anti matter particles annihilated each other producing photons that eventually become our microwave background radiation. As this process continued, light speed dropped as kinetic energy dropped, and then thermodynamic equilibrium was lost. Charge-parity was violated, and without thermodynamic equilibrium to overcome it, an excess of matter particles was produced. Particle space was then left with a large number of photons, and a small excess of matter particles, from which galaxies were eventually formed.  

 

Appendix D

The shadow web of residual dark matter from a prior universe provides the nucleation super particles needed to form galaxies out of the thin soup of matter left from the particle formation step. How this occurs can be illustrated with the following simplified example. Some of this matter soup moves toward the high curvature of the center of mass of each forming galaxy, and gains circular speed ν_c around that center. The speed ν_c increases as mass increases and the matter particles move toward the center until a portion of the particles reaches a speed of 2.99 x 10¹⁰ cm/sec according to the equation (Peebles, 47),

            M(r) = mass within radius r = ν_c²r /G

At this speed, the energy increases, but the speed ν_c cannot because it has reached the speed limit for light in low energy particle space, so the increasing energy becomes mass. The mass keeps falling toward the center of mass of the galaxy, since it cannot maintain that radius with centrifugal force. The radius from the center at which this speed is reached is referred to as the event horizon for the black hole, and a black hole is born. The matter that passes through the event horizon is torn apart into particles by tidal forces as it moves deeper. Note that this is not the only way a central, super massive black hole is formed, and it is not the only thing that happens in the formation, but it is the most significant one for mass recycling. A black hole near the center of a galaxy will feed on dust, stars and gas moving to the center and become a central growing, super massive black hole.

 

Appendix E

As particles move toward the black hole center, they encounter two zones separated by a barrier. In these two zones, the time rate of change of field φ’ due to the motion of particles across zones varies according to the zone:

1. Contraction zone— As particles move past the event horizon toward the black hole center, they become more and more concentrated, and the mass density ρ_m increases. This increase causes a corresponding increase in field φ according to equation 4. So particles with high average velocity toward the black hole center will pass through this zone with high φ’. Potential energy V increases as radius to the center decreases (Misner, 911), but φ’ ²/2 increases faster, so φ’ ²/2 exceeds V, and this is a space contraction zone.
2. Expansion zone—As the particle concentration increases deeper in the contraction zone, diffusion moves particles away from the deep, concentrated zone toward the shallow lower particle density zone, and particle density gradient diminishes (see equation 5). The result for a sinking particle is a reduction in φ’ ²/2. This movement to lower density is faster for higher kinetic energy particles. Thus φ’ reduces, but V is increasing, so φ’ ²/2 eventually becomes smaller than V . and this zone becomes an expansion zone.
3. Barrier—When particles move across a boundary between low and high potential energy, the boundary acts like a barrier, and if the kinetic energy is lower than the potential energy, most of the particles are reflected. This reflection accentuates the action of the diffusion, and reduces φ’ ²/2 even more.

Thus there will be a shell where space will contract, and just inside it there will be a shell where space will expand. The boundary between will reflect particles. So a particle will descend through the contraction zone toward the black hole center, and then most will be reflected back by the expansion zone inside it (see Appendix H). The higher the kinetic energy of the reflected particle, the closer it will get to the event horizon. If it is high enough, the kinetic energy will near the Planck energy (1.22×10¹⁹ GeV), and the speed of light will increase above 2.99×10¹⁰ cm/sec in order for the Planck length to remain constant under relativistic foreshortening. When the speed increases above 2.99 x 10¹⁰ cm/sec, it is above the escape velocity of the event horizon formed at lower energies, so the shielded super particle will escape the black hole. These escaping particles may be the radiation from the black hole proposed by Hawking. If the kinetic energy is too low, the shielded super particle will fall back to the barrier and gain kinetic energy in the fall. There it will be reflected again and thus recycle until the shielded super particle gains enough kinetic energy to escape the event horizon.

 

Appendix F

Here we give a more complete description of the quantization of the fermion and Higgs fields. We will use the same procedure to develop the mass of a particle from the Higgs field that is used to develop the energy of a photon from the electric field of an atom, and 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∂_μφ∂ ^μφ – (½μ²φ ² + ¼ λφ ⁴)

 

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

 

            V = ½μ²φ ²+ ¼ λφ ⁴

 

            Where:

            λ = self interaction coefficient

            φ  = Higgs field – a complex quantity

The first term appears to be the interaction of the particle Higgs field with the ambient Higgs field. The second term appears to be the interaction of the particle field with itself 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. In field theory, it is conventional to call the minimum the ground or vacuum state, and the perturbation terms are excitations. The form of the Lagrangian determines the mass of the particles. If these operations are performed, the result is:

            m _η²  = -2 μ² = mass               

Note m _η is a complex quantity, so to get particle mass m_p (real), we must use m _η² to get the real quantity. Then, V can be written:        

            V = – m _η²φ ²+ ¼ λφ ⁴= -(m _η²– λ_tφ ²)φ ²         (1)

And if we note that particle mass energy is quantized as m_pη, then if the quantum state of the Higgs potential energy shifts, a massive particle is formed as follows:

 

            ΔV_η = m_pη = m_η²φ ² (1- λ_tφ ²/m _η²) = particle mass energy        (2)

 

            Where:

            m _η² = mass charge         

Now we note that as with the electron, each charged particle is moving 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 particle wavelengths long (n = 1,2,3…). This interference causes the quantization of the potential energy. Then the particle interferes constructively, and the potential energy wave function 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:

 

            V_n= m _η²φ ² = (symmetry factor)(charge factor)(field factor)

 

The value of each factor is as follows.

The Symmetry factor specifies which symmetry is active in a particle, and because of constructive interference, each term becomes:

(Electromagnetic factor U(1)) = (1) 

(Isospin factor SU(2)) = (2)

(Color factor SU(3)) = (3)

(Higgs factor SU(4)) = (4)

So the (symmetry factor) = (1x2x3x4) = (n!) where only the quantum numbers active in the particle appear in the factor.

 

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

(Electromagnetic charge) = q_e

(Isospin charge) = q_i

(Color charge) = q_c

(Mass charge) = m_p = the charge that generates mass-energy (ref 2, Model 1B).

So the (charge factor) = (q_e q_i q_c m_p) = q_t where only the charges active in the particle appear in the factor.

 

The field factor is more complicated. Two Higgs fields are important in mass generation. One Higgs field is from the distributed mass in the universe, which is relatively uniform on a large scale. We call this the ambient field. It can be described by the equation:

            φ_h1² = K_ho Σ m_p /r² = K_ho Σ m _η²/r² ~ K_ho n

Here it is assumed the density of particles is small, so on average a test particle is not close to another massive particle.

The second Higgs field is due to self-interaction, and so is controlled by the mass of Higgs particles m _η that are close. This field can then be described by the equation:

            φ_h2² =  K_ho λ_t m _η²/r², where λ_t is the self interaction constant.

Recalling that m _η² is small unless r is such that the distance traveled in a pattern orbit is an integral multiple of the particle wavelength (n), we find:

            φ_h2² =  λ_t (1/n), Where λ_t is the self interaction constant.

If m nearby Higgs particles are active with charge, and recalling that the self-interaction term is negative (see 2), then the total is:

            φ_h² =  φ_h1² + φ_h2² =  n² (1- λ_t (m/n))             (3)

But as Kane noted (Kane, 105), as part of the Higgs mechanism, the Higgs field must be assigned an SU(2) doublet m’, where:

            m’ = either of the two quantities:

            m = Higgs charge operating with ambient field

            (m+(m-1)) = Higgs charge operating with ambient and internal fields

            Then:

            n² becomes n^2m’

Comparison with the field equation derived by Kane (2) allows us to replace it with (4) to get the quantized field factor:

            (Field factor) = n^2m’(1- λ_t(m/n_m)),              (4)

            Where:

            n = symmetry number for the particle of interest

            n_m = 4 = quantum number for mass.

            m’ = m (up), or

                  = (m+(m-1)) (down)

Then the total potential energy term is:

            V_n= m _η²φ ² = (symmetry factor)(charge factor)(field factor)              

                 = n! q_t hcK_o n^2m’ (1- λ_tm/4)          (5)

                 = mass energy of the primary particles (see equation 2)      

 

            Where:

            q_t = total charge

            hcK_o = Higgs mass-energy constant (analogous to R_∞(q_e) for the electron case)

            λ_t = self interaction factor

            m = Higgs field number

 

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 yields:

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

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

                  = (V_n1)(V_n2)(V_n3)(n! q_t hcK_o n^2m’ (1- λ_tm/4))

We note here that if many particles become active together, we get modifications in equation (5). There are three cases.

(1)  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-λ_t(1/3×2/4)) if one particle of three is acting on m at a time                

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

(2)  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-λ_t2/3(2/4(2/4+3/4)) = (1–λ_t 2/3×5/8)

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

            (1-λ_tm/4) = (1-λ_t(2/4(2/4+3/4)) = (1-λ_t5/8)

Finally, we must specify the units of the mass-energy for the particles. There are two cases.

(1)  If hcK_o = 1, and λ_t = 1, the energy for each Fermion is given in MeV

(2) If hcK_o = 1, and λ_t = 1, the energy for each Boson is given in GeV

 

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 part of the forces.

The symmetry term shown 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. Thus all combinations are forbidden except SU(6) and SU(10). As a result, the proton decay lifetime experiment, with short 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 (3,3) 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, and it even distorts the (3, 2) value for d. 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 lifetime, 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 under special circumstances.

 

Appendix G

Beyond the event horizon of the central black hole, 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 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. Now Peebles (Peebles, 47) shows that the matter density ρ_t(r) in a galaxy at a radius r is:

 

            ρ_t(r) = ν_c² / 4πGr²

 

            Where

            ν_c = circular rotation velocity as a function of radius.

            G = gravitational constant.

 

The astronomical data for spiral galaxies show that ν_c starts low toward the center of the galaxy and rises to a maximum and then flattens out to a constant value. Newtonian gravity requires that ν_c reduce beyond the maximum, or the matter beyond the maximum would escape from the galaxy’s gravity. Since ν_c is constant beyond the maximum, the density must increase and vary as ~1/r² out there. Now if the density of the dark matter that is decreasing at a slower rate (~1/r²) becomes equal to the density of the visible matter (~ν_c² / 4πGr² ) at the maximum ν_c , then the density of the dark plus the visible matter would vary as ν_c ~1/r². This, of course is what we observe.

In addition to this relation, 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 of the bulge in those galaxies. This relation is called the M-sigma relation (Ferraese, 539). Note in section D that the volume of the diffusion zone where shielded super particles are formed, and thus the number of shielded super particles formed, is directly dependent on the black hole mass (the number increases as the mass increases). Thus when the shielded super particle mass equals the visible matter mass, matter with velocity greater than the escape velocity of visible plus dark matter will escape, causing the dependence of the black hole mass on the velocity dispersion.

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.

 

Appendix H

Consider the following three-dimensional time independent Schrödinger equation.

 

            [-(h²/8p²m)Ѳ+V(x, y, z)]Y(x, y, z) = EY(x, y, z)

 

            Where:

            V(x, y, z) = barrier potential

            E = particle energy

If we convert to spherical coordinates, and let:

            Y(r, q, f) = R(r) Y(q, f)

            Where:

            Y(l, m) = Spherical Harmonics = (4p) ^-1/2  , for  l = 0 (spherical symmetry)

Now, let:

            R(r) = U(r)/r,

            then:

            Y(r, q, f) = (4p) ^-1/2  U(r)/r   

Now, consider:

            [-(h²/2m d²/dr² + V(r)]U(r) = EU(r)

            Where

            E = the energy of the particle = p²/2m for a super particle.

            V(r) = V_o[Q(r) – Q(r-a)] = the vacuum barrier potential.

            Q(x) = the Heavyside step function of width a starting at x =0

            a = the barrier potential width.

Note that if any solution to the equation is unchanged if the step function is moved along the r axis to r_o.  Then one can think of starting at 0 and moving in vacuum space to r_o, then moving through the barrier potential for a distance a, and then for x>a, we move in particle space. Thus the equation governs passage from vacuum space through the barrier into particle space, and vice versa. For convenience, we will let r_o = 0 for solving the equation. Note also, that what we are describing is a spherical shell of radius r_o and thickness a around a super particle.

What we will calculate is the transmission probability density (T = t²  = r) or probability of transmission. The solution to the equation is a combination of left and right moving wave functions that are continuous at the boundaries of the barrier (r = 0 and r = a) along with their derivatives.

The solution can be used to generate the transmission through the barrier T (see Ref 9), which is as follows:

            If E>V

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

            Where k₁= (8p²m(E-V₀)/h²)) ^1/2          

            If E<V,

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

            Where k₁= (8p²m(V₀-E)/h²)) ^1/2

Here we have set up the equations for either of two shells, a vacuum space shell and a barrier shell. The rate of passage of a particle through either spherical shell for a galaxy is:

 

            R = T h/2p k_o n_sp / m r_ob particles/sec galaxy

 

The best fit for the vacuum space sphere and the barrier shell of the very rough data available is:      

            r_ov = 10^-20 cm which defines the inner boundary of the vacuum shell

            r_ob = 10^-11 cm which defines the outer boundary of the vacuum shell

            a = 10^-31 cm which defines the outer boundary of the barrier shel 

There are three important cases.

 

            Case 1

            E > 10¹⁷ GeV

            V_ov = potential energy ~ 10¹⁷ GeV

            V_ov/cc = potential energy density ~ 10⁵⁰ GeV/cc

            n_sp = number of super particles in vacuum space = 10⁶⁹ /galaxy

 

This is the vacuum space case for particles with potential energy ~ 10¹⁷ GeV-i.e. super particles. We note that super particles with kinetic energy greater than 10¹⁷ GeV move freely in vacuum space. If the kinetic energy drops below 10¹⁷ GeV, however, the probability of operating in and passage through quickly attenuates toward zero.

 

            Case 2

            E > 10¹⁷ GeV

            V_ob = 10¹⁹ GeV

            V_ob/cc = potential energy density ~ 10⁷² GeV/cc

            n_sp = number of super particles in vacuum space = 10⁶⁹ /galaxy

 

This is the case of leakage of super particles into particle space by tunneling through the barrier. In this case, T ~ 10^-50, and R is ~ 10³⁵ particles/sec galaxy. For all 10⁸ galaxies of particle space, R is ~10⁴³ particles/sec. When these particles reach particle space, they break down to ordinary particles and give up their phase change energy (10¹⁷ GeV/particle) into the particle space vacuum energy, or dark energy, which over 10¹⁰ years has made a dark energy of ~ 10^-4 GeV/cc. This is the same dark energy that causes the accelerated expansion of space that requires a potential energy of ~ 10^-4 GeV/cc.

 

            Case 3

            10¹⁹ < E < 1.19 x 10¹⁹ GeV

             V_ob = 10¹⁹ GeV

 

This is the case of big bang passage over the barrier. In this case, T = 1, and R = 10⁹³ particles/sec. When these particles reach particle space, they break down into ordinary particles and give up their phase change energy into particle space vacuum energy, or expansion energy, which expands particle space.

 

Appendix I

Rate of Production and Re-Conversion of Super Particles.

Consider the production of super particles S and re-conversion back to particles P. Note that this is a conservative process in which the baryon and its components are conserved. Only the symmetry and potential energy and therefore the internal dynamics of the baryon components are changed. Thus, S may be considered an excited state of P. These processes can therefore be described in a way similar to chemical reactions as a rate process. We start with the equation:

            P + V  = S

            Where:

            P is particle energy

            S is super particl energy

            V is the potential energy required for the conversion from P to S.

            The = sign shows that the process can go in either direction.

The equation indicates that the rate of production of S from P should be a first order reaction, and so we can write:

 

            Rate = d[P]/d t = – k_p[P]

           

            Where:

            [P] is the concentration of particles P

            [S] is the concentration of super particles S

            k_p is the rate constant

The integrated rate production equation is:

 

            [P] = [P_o]exp(-k_pt)

 

The rate of production of P from S is:

 

            Rate = d[S]/d t = – k_s[S]

 

And the integrated rate production equation is:

 

            [S] = [S_o]exp(-k_st)

           

Super particles are produced from particles and the potential energy V that comes from the distortion of vacuum space by mass in a black hole (see ref 2, AP4.7A). The potential energy V[r] is a function of r, which is the distance from the center of the black hole, and M, which is the mass of the black hole (see Misner, 911). This is not a single valued function of r, but a distribution dependent on mass, electromagnetic field, and rotation distributions within the black hole. This distribution can be approximated by a Gaussian function F_g[r,M], which will be shortened to show only the principle dependence F_g[r].

The dependence of the rate constant k_p on V for S production from P can be described as:

 

            k_p = A_pexp(-V_g(r_o) / F_g[r])

 

            Where:                                                           

            V_g(r_o) = force unification potential = S particle excitation potential = 10¹⁷ GeV

            r_o = Black hole radius at which the Gaussian mean is ~ 10¹⁷ GeV

Also an appropriate amount of potential energy is taken from particle space to facilitate this reaction. Note that when F_g[r] increases (more excitation potential is available), the rate constant increases toward A_p. When F_g[r] decreases (less excitation potential is available), the rate constant decreases toward zero, the [P] conversion rate is reduced toward zero, and [P] remains near the initial value of [P_o]. Recall that the conversion rate does not go completely to zero because F_g[r] is a Gaussian and has high-energy tails.

The rate constant for [P] production from [S] is:

 

            k_s = A_sexp(V_g(r_o) / F_g[r])      

 

Also an appropriate amount of potential energy is given up into particle space in this process. Note that when F_g[r] increases (more excitation potential is available), the rate constant decreases toward A_s. When F_g[r] decreases (less excitation potential is available), the rate constant increases, and [S] rapidly converts to [P], giving up its potential energy to particle space.

These expressions for k come from the fact that we can expect that in a Gaussian distribution of potential energy quanta, the number with potential energy greater than V_g will be equal to exp(V_g(r_o) / F_g[r]). The coefficient A_p is a frequency factor.

When the particles P are converted into super particles S, the super particles gain a charge for the barrier potential shell, and it forms. This charge exists because the continuity of the wave function and its derivative are maintained in passage of a super particle through the shell, so Noether’s theorem requires it (see Appendix 1). However, the super particle does not pass beyond the barrier into vacuum space until it gains enough kinetic energy (activation energy) to bounce against the Planck limit and then penetrate the barrier into vacuum space

 

References

1. L. H. Wald, Model 1-A “Mass and Function of the Standard Model Particles” www.Aquater2050.com/2017/01/
2. L. H. Wald, Model 1-B “The Origin of the Higgs Field for Model 1” www.Aquater2050.com/2017/01/
3. L. H. Wald, Model 1-C “Shaping the Dark Matter Cloud” www.Aquater2050.com/2017/01/
4. L. H. Wald, Model 1-E “The Super Particle as a Cosmic Ray” www.Aquater2050.com/2017/01/
5. P. J. E. Peebles, Principles of Physical Cosmology, Princeton, New Jersey, Princeton University Press.
6. B. A. Schumm, Deep Down Things, Baltimore, Johns Hopkins University Press, 2004.
7. J. D. Cobine, Gaseous Conductors, Dover publications, Inc., New York, 1958
8. G. Kane, Modern Elementary Particle Physics, Ann Arbor, Michigan, Perseus Publishing.
9. Misner, Thorne and Wheeler, Gravitation, New York, Freeman and Co., 1973