For updated version—see www.Aquater2050.com/2015/11/

Abstract

In a previous paper (ref 8, AP4.7), a self-consistent theory called Model 1 was developed to answer ten major connected questions in astrophysics. The most important of these questions are:

• How can dark matter be explained and described?
• How can dark energy be explained and described?
• Where do the extremely high-energy cosmic rays that occur beyond the GZK cutoff come from?

 

Model 1 appears to successfully answer these questions. The unique features of this model are:

• There are two spaces in the universe, particle space and 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 our space through black holes where they are converted into super particles that operate with unified force. They then pass into the high-energy vacuum space where they become dark matter operating behind the potential barrier.

• Dark matter particles interact with each other and form a slowly building and moving bubble centered on a galaxy. The bubbles of dark matter are connect to each other by corridors of dark matter forming a cosmic web, which guides the development of new galaxies.

• There, behind a potential barrier, the dark matter particles gain energy, build up in number and eventually exceed the ability of the barrier to contain them. They then explode back into particle space as a big bang. This process repeats to make an endless series of new universes.

• After the big bang exhausts itself, super particles continue to tunnel through the barrier into particle space. The super particles are unstable and break down into particles with extreme kinetic energy. In doing so, they give up potential energy into particle space. The potential energy gradually builds up to become the dark energy that we observe as the cause of our accelerating, expanding universe. The extreme energy protons are observed as cosmic rays with energy between the energy of force unification and the Planck energy, which is beyond the GZK cutoff.  

 

In this paper, the formation and shaping of the dark matter clouds will be addressed and shown to conform to the existing data on dark matter. 

 

The Problem

In ref 8, AP4.7, several problems were left for future efforts. In this paper, one of these problems, the details of the formation of the dark matter cloud have been singled out for exploration.

 

The Dark Matter Cloud. AP 4.7 showed how an ionized cloud of super particles would form after entering vacuum space.  Some equations were developed for the cloud, and solved to give a contained, dark matter cloud roughly similar to the one obtained from studying the rotation data of galaxies. That was a simplified, first level treatment. Here, we will move to the next level. We start with the basic equations.

 

We begin with the diffusion velocities of the ionized gaseous components (see Cobine, 51).

 

            V⁺ = -D⁺/n⁺ dn⁺/dx + K⁺E + K⁺G

 

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

 

            V^g = K^gG

 

            Where:

            D = Diffusion coefficient

            K = Ion or gravitational mobility under the influence of electric or gravitational force 

            V = Ion velocity

            n = Ion concentration

            E = Electric field

            G = Gravitational field tempered by centrifugal force (see below)

             n^g = source of particles from the black hole

           

We set:

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

 

We solve these equations, and get:

 

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

 

                        Where:

                        D = (D⁺ K^– + D^– K⁺ ) / ( K⁺ + K^– –  2 K⁺ K^– / K^g ) 

                                   r= Radius from black hole source

                        t= Time

                        N_o = particles diffusing from an “instantaneous” point source  

 

The principal forces being described in this solution are the following:

• A diffusion force due to a concentration gradient and the motions and collisions of particles stemming from the kinetic nature of their motion.
• An electromagnetic force E pulling the components of an ionized particle cloud together due to the different diffusion rates of different particles (positive and negative particles} because of different diffusion coefficients.

We see an electric field in the velocity equations, yet the solution is independent of that field. We must ask how this can be.

 

In order to obtain this solution, we have simplified the G field into one central vector field pointed toward the particle source (the black hole). In reality, it is composed of the vector sum of a:

• A Newtonian type gravitational field pointed toward the center of the black hole that works on each particle. (Here we have taken advantage of the fact that Loop Quantum Gravity predicts a Newtonian type gravitational force even close to the black hole center (Smolin, 251). It is known that further from the black hole, a Newtonian type force works well.)
• A Centrifugal force field pointed away from the center of the black hole that works on each particle (Again, it is known that a centrifugal force works well further from the black hole).
• An expansive field that comes from the gravitational potential. Note that this field works on space itself.

 

The last force comes from a single new scalar field, f. The energy density and pressure equations that result are as follows (Peebles, 396):

 

            Here, ρ  = f’ ²/2+ V; and p = f’ ²/2 – V)

 

            Where:

            V = a potential energy density

            f = a new real scalar field

            f’ ²/2 = a kinetic energy term

 

Now, we assume V is a slowly varying function of the field, and the initial time derivative of the field is not too large. We also assume that V is large enough to make a significant contribution to the stress-energy tensor (Misner, 911). Then the pressure can satisfy the condition p < – ρ /3, which is the condition for the expansion of space. If V is less than the kinetic energy, f’ ²/2, gravitational attraction to the black hole will control.

 

It is necessary to see how V varies with R, the distance from the black hole center. This variance is given by Misner (Misner, 911), and we note that it increases as an observer is moved toward the black hole center. It eventually reaches ~10³⁵ GeV/cc, and it even rises somewhat higher as he/she moves closer.

 

The same potential energy density of ~10³⁵ GeV/cc is found within the barrier walls between vacuum and particle space.  Inside the barrier, around each super particle at a distance up to ~ 10^-5 cm from the super particle, V has a value of ~10³³ GeV/cc as indicated in AP4.7 Appendix 1. Beyond this distance is the vacuum value of particle space (10^-5 GeV/cc). As the particle approaches the center of the black hole, the high potential is used to form the barrier around the incoming particles, fill it with potential energy, accelerate the particles and thus make super particles and bounce them into vacuum space. Note that the super particles exist in dynamic equilibrium with particles in the high vacuum potential of vacuum space as shown in REF 10, AP4.7C.

 

The value of V is high enough in the vacuum space zone near the black hole center to generate the expansion condition mentioned above, and space expands. The expansion of space closer to the black hole than an imbedded particle moves the particle away from the black hole center. The use of potential energy to make particles, and the expansion of space away from the black hole center reduces V below the kinetic energy term (f’ ²/2), and the expansion dies. Then the particle is dragged back through space by the gravitational attraction of the black hole. Thus the particles tend to concentrate at a radius where these two actions balance. This radius supports an energy high enough to ionize the super particles. At this radius, the high concentration gradient and the electric fields formed cause the dispersion described above that generates the cloud of dark matter.

 

Note here, that when the super particles have expanded far enough away from the black hole center, they cool, and the super ions can combine into neutral particles. This is similar to combining an electron with a proton to form a neutron in neutron stars. For R far enough from the center of the black hole, the gravitational field is, of course:

 

                G = M₁G₀/R² 

 

Remember that it acts on the center of mass of a mass-energy source such as a particle.

 

More important, there is an extremely low interaction cross section between visible and dark matter. The low interaction and collision cross section results from the characteristics of the barrier potential shell (see Appendix 1).

 

Note finally that what we have described here is a pump that receives particles from particle space through the black hole, converts them into super particles, bounces them into vacuum space, and then pumps them away from the black hole center. We will call this pump the generation-expansion field. The super particle is pushed away from the black hole center, and comes under the influence of the central field. Here again, we see the central field G in the velocity equations, but the solution is independent of G. We need to investigate how this can be.

 

We have seen the problems, and so we must ask what the effect of the electric and the central field has on the solution to the velocity equations. The solution does not seem to show the effect of either the E, or more important, the G field. They seem to be able to be changed without any impact on the particle density function. This is this problem that we will investigate here.

 

The Solution

We will start our explanation by investigating the impact of the electric field. Cobine (Cobine, 51) describes in detail the interaction of the diffusion and the electromagnetic forces. He shows that the electric field is caused by the different diffusion rates of the positive and negative ions, and so is dependent on those rates. Thus the electric field can be eliminated from the equations because it cannot be changed independently of the diffusion. It should not appear in the final solution. If the initial conditions are changed, they can generate an electric field from a different source that is independent of diffusion. Then, the equations must be handled differently, and we will investigate that case below.

 

Now we investigate the impact of the central G field. Here, there are three cases of interest.

1. Assume the generation-expansion field plus the centrifugal force field roughly balances the gravitational field due to the black hole’s attraction on the particles, so the net radial average motion is roughly zero. Note, however, that the particles are moving through the expanding space under the influence of the gravitational field, so the 2 K⁺ K^– / K^g term in the D equation still has meaning. One would expect in this case, that the denominator of the term would be larger than the numerator, so the term would be small. Clearly, the solution to the equations shown above would be valid in this case.
2. Assume the generation-expansion field plus the centrifugal force dominate, and space expands faster than the gravitational attraction of the black hole can pull the particles back. In this case, a particle, trapped in space, moves away from the black hole even though it is attracted toward it. Note that the expansion does not last forever. It lasts only as long as the generation-expansion field is high, and we have seen that it drops fast as it expands and generates super particles. Thus the particle will move out until the generation-expansion field equals the gravitational field, and then it will slow, and move back at the rate demanded by the gravitational attraction tempered by the vacuum value of particle space (~ 10^-5 GeV/cc), which is low. Recall that the super particles involved are in a thermal, Gaussian distribution, so a thermally distributed band of super particles will form where the expansion field equals the gravitational field
3. Assume the gravitational attraction of the black hole to the particle dominates, because the particles are beyond the thermally distributed band of case 2. The particles are then attracted toward the black hole center by the central force. As this happens, the particles try to retreat to the radius where the expansion field equals the gravitational field, and a distributed band of super particles has formed.

 

Thus, we see that the super particles move radially to a quasi-stable minimum shell around the black hole center to form a source of incoming particles. This is an impulse source that gives out super particles as long as the black hole is feeding- a time short compared to the life of the galaxy. The particles do not remain at this equilibrium point, however, they diffuse away from it under the influence of the concentration gradient, and the electromagnetic force helped by the expanding space. Thus we must make a minor alteration to the above solution as follows:

 

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

 

                        Where:

                        D = (D⁺ K^– + D^– K⁺ ) / ( K⁺ + K^– –  2 K⁺ K^– / K^g ) 

                                   r= Radius from black hole source

                        t= Time

N_o(R)  = a Gaussian distribution of particles diffusing from a finite spherical shell source, where space expansion and the gravitational force balance.

 

Here we see that the solution is the same, except that the source is a spherical shell instead of a singularity (a delta function). Thus the solution is still valid, and it should be independent of the central force. Because the central force is self-determined, it cannot be changed unless the initial conditions are changed. Note that if the initial conditions change, the central force must be handled separately. We will investigate that case below. 

 

Special Case 1. Electric fields unrelated to diffusion.

Assume the black hole is feeding, and so has formed a rotating cloud of ions around the black hole. This rotating cloud forms an electric field that ionizes the particles, and then pumps ions and electrons from the rotating cloud out from the galaxy in a giant fast moving spike of radiating ions. This field is not connected with the diffusion electric field, so it must be analyzed separately.

 

The spike of radiating ions in particle space will not interact with ions in vacuum space, because the barrier from super particles would block the exchange photons that make the interaction possible. However, the gravitational attraction from the spike would tend to gather dark matter along the spike, and make a dark matter corridor coincident with the spike.

 

Special Case 2. Gravitational Fields that are dependent on more that one center of mass (one black hole). 

Assume that two galaxies are close at a distance R₀. Both have central black holes. The total gravitational field from the two galaxies is diminished along the corridor between them as follows:

 

                        G = M₁G₀/R² – M₂G₀/(R_O-R)²  (R> R₀₎

 

In this case, assume a super particle starts moving away from black hole 1 due to the potential expansion field surrounding the black hole center faster than the gravitational field can attract it to the black hole. The gravitational field is less along the radial toward black hole 2 than it is along other radials, so a corridor of diminished field is formed. Thus the super particle moves further along this corridor than along other radials, and a buildup of particles starts along that corridor. The presence of particles in the corridor increases the mass there and increases the resistance to movement, and so particles preferentially accumulate along that corridor. Over time, a lattice or cosmic web of super particle corridors forms using galaxies as nodes. This lattice acts as a nucleation net of dark matter along which dust and gas in particle space will be attracted. This dust and gas will then form galaxies preferentially along the net. This preferential formation of galaxies in strings and clumps and walls has been observed in the universe

 

It is important to note that when the super particles have expanded out to become a dark matter cloud, they cool and some super ions recombine to become neutral super particles. As such, they have a lower interaction and collision rate as super particles. More important, the barrier shell has a very low interaction and collision cross section with visible matter (see Appendix 1). Thus Model 1 correctly predicts the observed fact that when galaxies collide, the visible matter interacts with itself and coalesces while the dark matter passes right through the visible and dark matter.

 

Testing Model 1B with Data

This portion of Model 1 must be tested with data. A summary of the tests that support Model 1 including those supplied by this paper are shown here. A much more detailed description of the tests that support Model 1 is given in ref 20, AP4.7D.

1. Model 1 is constructed from elements of general relativity, quantum mechanics and classical physics in their appropriate energy realms. It is self-consistent in each of those realms. 
2. It satisfies all the physical data currently known in areas of dark matter and dark energy. No other model or theory is known that satisfies all these data.
3. It connects with the standard model of particle physics, a general relativity description of black holes, the theory of ionized gasses, the theory of the speed of light at extreme energies, the theory of the Planck high-energy limit of quantum mechanics and the theory of the Higgs field.
4. It predicts the existence of a cosmic ray with energy between ~ 10¹⁷ GeV and ~ 10¹⁹ GeV that can be observed beyond the GZK limit where it should not exist. This cosmic ray has been observed.
5. It predicts the existence of a new low cross section super particle with a barrier shield that can be directly observed. This super particle is now being searched for. Preliminary results are positive.

 

Problems with Model 1B

The primary problem is that to get a simple solution to the equations used, it was necessary to make certain simplifying assumptions. These assumptions can be justified in either of two ways.

• Each assumption must be shown mathematically to be small.
• The results must be shown to be in agreement with data.

In this set of papers, the latter procedure is the one used.

 

Further Proof of Model 1B

Theoretical Proof

Accomplishing the following tasks would strengthen the theory.

• Although the theoretical pieces of this development are justified separately, the development would be stronger if the assumptions were proved mathematically (see ref 9, AP4.7D).

 

Experimental Proof

Although Model 1B appears to satisfy all of the previous experimental results as shown above, it should also predict and satisfy one or more unique experimental results listed below.

• It is possible to do a simulation of dark matter formation and resultant galaxy formation. If the patterns are similar to those observed by astronomers, that similarity would constitute supporting evidence for this model.

 

Summary and Conclusions

A model (Model 1) has been developed in AP4.7 that predicts dark matter and energy and extremely high-energy cosmic rays, which operate beyond the GZK cutoff. As part of this model, a set of super particles in a new space (vacuum space) was predicted that constitutes this dark matter, and generates this dark energy and the high-energy cosmic rays. The details of the shaping of these super particles into dark matter clouds were not pursued in ref 8, AP4.7, and so they have been pursued in this paper. Initial checks with existing data have been made, and Model 1 has been found to be in agreement with the data. Possible problems with the model have been analyzed, and a program proposed as a fix. Experiments that would check the accuracy of the model have been proposed. Model 1 has been found to be valid as far as the current checks can determine.

 

Appendix 1

Here, we explore the characteristics of super particles to see if they can be observed in particle space- i.e. are they dark? First, super particles do not show charges associated with the electromagnetic, weak, and strong forces. They are combined into one super charge and hidden behind the barrier potential. The super particle spin, if any, would not show beyond the barrier as well. They have only the super charge associated with the unified force. Thus they will not interact with the detectors we normally use. Particles in particle space will scatter off the potential barrier surrounding the super particle, however, so it is necessary to calculate this scattering cross section. This scattering cross section is like the scattering of a proton off a neutron, but with different energies. This scattering cross-section has been calculated (Halliday, 47), and is as follows:

 

            s = h²π/M x  1/(V_o + E)

 

            Where:

            M = m_s m_p/ (m_{s +} m_p)

            m_p = mass of particle space baryons = 1 GeV.

            m_s = mass of super baryons = 10¹⁷ GeV.

            V_o = potential of super baryons = 10¹⁹ GeV

            E = kinetic energy of the particle space baryons = 1 GeV or less.

 

            Then:   s = 10^-45 cm² 

 

Clearly, this scattering cross section would be difficult if not impossible to detect. So matter is dark or difficult to detect in particle space. Also, the collision cross section of the dark matter particles is low enough that in colliding galaxies, the dark matter particles would pass right through each other, while the visible matter would interact and coalesce, as seen by astronomers.

 

References

1.      L. Smolin, The Trouble with Physics, Boston, New York: Mariner Books, 2006.

2.      G. Kane, Modern Elementary Particle Physics, Ann Arbor, Michigan, Perseus Publishing.

3.      J. Magueijo, New Varying Speed of Light Theories, arxiv.org/pdf/astro-ph/0305457.pdf

4.      J. Magueijo, Faster than the speed of light, Penguin Books, New York, New York, 2003.

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

6.      J. D. Cobine, Gaseous Conductors, Dover publications, Inc., New York, 1958

7.      Misner, Thorne and Wheeler, Gravitation, New York, Freeman and Co., 1973.

8.      L. H. Wald, “AP4.7 DARK MATTER AND ENERGY-FUNDAMENTAL PROBLEMS IN ASTROPHYSICS” www.Aquater2050.com/2015/07/

9.      L. H. Wald, “AP4.7D HOW TO PROVE A THEORY’S CORRECTNESS” www.Aquater2050.com/2015/07/

10.  L. H. Wald, “AP4.7C DARK MATTER RATE EQUATIONS” www.Aquater2050.com/2015/07/