AQUATER PAPER 4.7 DARK MATTER AND ENERGY-FUNDAMENTAL PROBLEMS IN ASTROPHYSICL

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

Abstract

There are currently ten connected major unanswered questions in astrophysics. The most important of these 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 in the energy range beyond the GZK cutoff come from?

A self-consistent theory called Model 1 has been developed that answers these questions quantitatively. This model will be described and defended with data from astronomers in this paper.

 

 

The Most Significant Current Questions in Astrophysics

There are ten connected major unanswered questions in astrophysics.

  1. What is dark matter and where does it come from? Are particles and forces unified?
  2. Why is there such a huge disparity between different estimates of vacuum energy (the vacuum catastrophe)?
  3. Can the distribution of dark matter into bubbles and lattices that are connected to galaxies be explained?
  4. Does the speed of light change with energy?
  5. Is it possible to explain what happened before the big bang and what initiated it and what happened afterward?
  6. Is it possible to explain the accelerated expansion of space and dark energy?
  7. Is it possible to explain the large-scale cutoff and asymmetry in the Microwave Background Energy?
  8. Can the experiments that show an instantaneous transfer of state at long distances in conflict with the speed of light maximum on the transfer of information be explained?
  9. Is there a practical procedure for obtaining answers on questions that arise in the area of quantum gravity-especially for questions involving black holes?
  10. Extremely high-energy cosmic rays have been observed in the range 1017 GeV to 1019 GeV. They should interact with the microwave background, and disappear above the BZK cutoff. Can this be explained?

 

Model 1 described below addresses all of these questions and answers them with apparent success. Only a simplified version of these answers will be given here. The details will be given in connected papers referred to in the references. Together, they appear to give a complete answer to these questions.

 

Model 1. A Basic Physical Model Describing Dark Matter and Dark Energy.

The unique features of this model are:

  • There are two spaces (particle space and quantum vacuum space) in the universe separated by a potential barrier. One space contains visible matter, and the other space contains dark matter.
  • Coherence requirements form the boundary conditions for passage of particles through the potential barrier. 
  • There is a cycling of mass-energy in the universe through black holes that connect the two spaces. Particles pass from our space through black holes where they are converted into super particles in vacuum space. There, they become dark matter operating behind the potential barrier.
  • Dark matter particles interact with each other and form a slowly increasing bubble centered on galaxies. The bubbles of dark matter connect with each other in corridors of dark matter forming a lattice called the cosmic web on which other new galaxies are formed.
  • There, behind a potential barrier they gain energy, build up in number and eventually exceed the ability of the high-energy barrier to contain them. They then explode back into our space as a big bang. This process cycles repetitively.
  • Super particles tunnel through the barrier into particle space where they are unstable. They break down into particles with extreme kinetic energy and give up potential energy into particle spade. The potential energy gradually builds up in particle space to become the dark energy that we observe as the cause of our accelerating, expanding universe. The particles are observed as extreme energy cosmic rays with energy beyond the GZK cutoff.

 

Model 1 Characteristics

The primary characteristics of Model 1 are given in this section. The details, equations and calculations for Model 1 are given in the 7 Appendices. Details are given in separate papers that are referenced.

  1. There are several particles that carry energy in two spaces of the universe. A potential barrier separates the two spaces (see Appendix 1). One space will be called Quantum Vacuum space (vacuum space for short), and the other will be called particle space hereafter. We live in particle space. The primary entities in the two spaces that carry energy are wave packets or photons and particles such as electrons and baryons (combined quarks). In vacuum space, the energy density is extremely high, and the photons, electrons and baryons have a high energy form that will be called super photons, super electrons and super baryons hereafter (see ref 14, AP4.7A). The potential barrier consists of a spherical shell that surrounds each super particle (see Appendix 1). In particle space, photons, electrons and baryons have the low energy form we are familiar with. Four forces act on these entities in particle space. Super particles carry a combined charge for a unified force that is hidden behind the potential barrier. The super particle spin, if any, would not show beyond the barrier either. Thus they will not interact with the detectors we normally use. It is important to point out that super particles travel in particle space behind their barrier, which they carry with them. Thus a super particle and a particle see the barrier between them, but super particles pass through each other’s barriers as if they are not there and that allows the super particles to interact directly. A particle, however, sees the barrier potential shell of a super particle as a smooth spherical shell, and can scatter off of it. This scattering cross section is S scattering (like billiard ball) like that of a neutron off of a proton.  The scattering cross section has been calculated, and the value obtained (s = 10-45 cm2 – see Appendix 6) is very small. Thus super particles would be extremely difficult to detect in particle space, so we call super particles dark matter. Nonetheless it appears possible to do so (see ref 17, AP4.7E). But the particles do see each other easily through the gravitational force.

 

  1. In vacuum space, the four forces become unified in the high energy (both kinetic and potential) that exists there. This force acts on the super electrons and super baryons through super photons and so it will be called the super force. This unification has been predicted for a long time (Kane, 281) The energy of unification is ~ 1017 GeV as determined by extrapolating the four separate forces to high energy. Vacuum space has a high energy density (Kane estimates ~ 1049 GeV/cc-Kane, 112). The cosmological constant carries its own vacuum potential energy in particle space. It has been calculated to be ~ 10-5 GeV/cc from the acceleration of the expansion of the universe. Clearly, this difference in potential energy in the two spaces demands a barrier between them. The potential barrier is a spherical shell of radius ro and thickness a around the super baryon, and it has a potential energy value of ~ 1019 GeV (see Appendix 1). Note that super particles can become ionized-an important point as will be seen later, The structure of particle space is expanding, and is shown by the expansion rate equation (see Appendix 2), which has three terms, the density term, the curvature term and the cosmological constant term. Each term carries energy. The curvature term carries energy in the pressure. As a particle descends into a black hole, it gains both kinetic energy (due to increased particle velocity) and potential energy (due to increased curvature) until the potential energy provides the expansion necessary to break the grip of the gravitational attraction (see Appendix 4). Then, the potential energy is used to make super particles, and the expansion stops and we are left with high-energy dark matter in vacuum space (see details in ref 16, AP4.7C).

 

  1. The generation of dark matter occurs as follows. Particles from particle space fall into black holes, and the kinetic energy increases because the particles are falling. The particles are moving into a smaller volume as well, so the energy per particle and potential energy density increases dramatically (see Appendix 4, also Misner, 910). The particles collide and reach equilibrium and so have an average energy and a temperature. At the same time, the gravitational potential energy increases due to the increasing curvature of space. As the particle potential and kinetic energy approach the unification energy (1017 GeV), the particles can convert to super particles by increasing their potential energy by 1017 GeV. This potential energy comes from the gravitational potential energy of the black hole. The super particles then increase their potential energy to nearly 1019 GeV. They then generate the spherical potential barrier, which has a strength of ~ 1019 GeV. The kinetic energy increases as well. This kinetic energy gives the activation energy needed to bounce the super particle into vacuum space. The vacuum potential energy density of vacuum space becomes 1033 GeV/cc because the potential energy is high (1019 GeV) and the volume of the shell in which it operates is small (10-14 cc). This vacuum space potential energy density is large compared to the vacuum potential of particle space (~ 10-5 GeV/cc) because it is in a separate small space, and shielded from the large particle space by the barrier potential. According to Smolin (Smolin, 250) the particles that near the Planck energy bounce, and enter a different space (vacuum space). Note that the particles in vacuum space are super particles in order to remain stable. The super particles (including super photons), at extreme energy, are ionized, and interact with each other through an electromagnetic super force using exchange super photons. The super particles also feel other forces, namely, the gravitational force, the centrifugal force and the kinetic energy pressure of a gas at high temperature (see Appendix 4). Thus the super particles, as they enter vacuum space, first experience an expansion that breaks the grip of gravity due to the gravitational potential. Then, as the gravitational potential is used up making particles, the gravity starts to reassert itself, and the centrifugal, kinetic energy and electromagnetic forces become important (see Appendix 4). These forces allow us to lay out the equations of motion (see Appendix 5) for dark matter. The solution for the resulting equations show a dark matter bubble centered on the galaxy’s central black hole and connecting corridors of dark matter between the bubbles. They diffuse away from the black holes primarily in the direction of other black holes. The dispersion pressure, electromagnetic force, gravitational force and centrifugal force interact, and slow the particles down, so they do not keep spreading and thinning too rapidly. Thus they form a net like structure (the cosmic net) not visible in particle space that is a nucleation zone for galaxies to coalesce on through gravity. So particles tend to form galaxies around this structure in groups, strings and walls. The dark matter diffusing from the central black hole of a galaxy also forms a bump or bubble in mass centered on the central black hole, which tends to control the amount of mass gathered into a galaxy centered on that black hole. Note that gravity operates in both spaces, but the super particle force (other than the gravity portion) does not operate in particle space because of the barrier. This fits generally with the data on dark matter obtained by observing galaxies (see ref 16, AP4.7C for more details).

 

  1. Note that in order to have the huge diffusion coefficient (Appendix 5) needed for such huge bubbles as are observed with galaxies, the particles involved must travel faster than 3 x 1010 cm/sec. This fits well with the experimental data on the varying fine structure constant, and the calculations that predict higher light speed at higher energies in order to keep the Planck length constant (see Appendix 3).

 

  1. The big bang occurs as follows. As the very energetic super baryons build up in vacuum space, they increase the average kinetic energy (and thus temperature) in vacuum space until the kinetic energy of most of the particles approaches the Planck energy. Thus the kinetic energy of the particles approaches the potential energy of the vacuum barrier, and the transmission probability goes to unity (see Appendix 1).  When this happens, the super particles flow rapidly through the barrier into particle space where the kinetic energy and density are low (see ref 16, AP4.7C). Also the super particles flow to the site of the black hole with the highest energy and density (see ref 18, AP4.7F). This is the Big Bang. There, the super baryons and super electrons have high enough kinetic energy to convert totally into energy for a short time. The energy converts back into particles with equal parts matter and anti matter. They annihilate each other and become photons. Space expands and cools rapidly under the influence of the gravitational potential (see ref 16, AP4.7C for details).  The speed of light drops, and the particles lose thermodynamic contact, so the CP violation takes hold. Then the particles obtained have a slight excess of matter. At this point, a series of phase changes occur, and the particles and forces of particle space begin to freeze out. This process of conversion of potential into particles takes about 5 billion years. Note here that the Big Bang flow ends when the vacuum space kinetic energy falls below the barrier potential. This cut off happens over a span of time because the super particles are in a Gaussian distribution, and so the particles will not all reach the barrier potential at the same time (see ref 18, AP4.7F for details). In the new particle space, vacuum space fills up again, and a new big bang happens. A calculation assuming the rate constant for refilling vacuum space does not change beyond now, gives the time of the next big bang to be ~ 1012 years from now (Appendix 5). This calculation is very rough and requires many assumptions, however.

 

  1. The residual super particles behind the barrier leak super particles even after the big bang is over. These tunnel through the barrier at a low rate (see Appendix 1). When these particles reach particle space, they break down into ordinary particles and give up their potential energy into an increasing particle space vacuum potential. Eventually, this increasing potential passes the decreasing big bang potential (at about 5 billion years from the big bang) and increases to the value we observe now (10-5 GeV/cc). This is the potential that in our time we call dark energy, which causes the accelerated expansion we observe (See Appendix 4). Note that as a result, the acceleration we observe should go through a minimum and then start gradually increasing (see ref 16, AP4.7C for details).

 

  1. There is a reduction in the spatial spectrum of the microwave background energy of the universe at a distance R (R~1027 cm), which is close to the radius of the visible universe. This reduction is coincident with the edge of the dark matter bubble that marks the edge of the visible universe. This universe bubble consists of the dark matter bubbles of each galaxy along with the lattice of dark matter corridors that stretch between them. This bubble provides a gravitational edge for our local portion of the universe and so provides an edge to the background expansion zone, and also the microwave background (see 18, AP4.7F for details).

 

  1. There is a set of experiments that show an instantaneous transfer of state information over distances too large to allow for transfer of information at the speed of light. In order for this transfer to take place, the particles involved must remain coherent. This can be explained in terms of transfer of state through the potential barrier, and then through vacuum space. In the development of the barrier transfer equations, a boundary condition for the transfer was that the particle wave function be continuous along with its derivative. This is equivalent to saying that particles being transferred must remain coherent. If coherence is conserved in both spaces, there must be a charge common to both spaces from Noether’s theorem. This means that there is a fundamental coherence connection between a charge of vacuum space and a separate charge of particle space. This conclusion was hinted at by the convergence of the four forces at ~ 1017 GeV. Thus a photon in particle space can maintain its coherence with a photon in vacuum space, travel at very high speed there because of high vacuum space energy, and then connect with another particle in particle space. Thus state is transferred at speeds higher than the speed of light in particle space. Note that neither a massive particle nor a photon has to pass through the barrier in order to carry this information, so the vacuum potential energy difference does not have to be paid in this process.
  2. In doing this work, it was necessary to answer certain basic questions about physics in black holes. Loop Quantum Gravity theory provided a way to accomplish this aim. A group of results (Smolin, 250) are already available from Loop Quantum Gravity that is compatible with Model 1. For example, loop Quantum Gravity is finite. It is background independent. It fits into the notation used for the Standard Model, and for General Relativity as well. It predicts gravitons at low energy. Especially, it predicts a Newtonian type gravitational force. It can also be used to predict some important states in black holes. For example, it shows particles sinking into black holes, bouncing at the Plank energy and expanding into a new space. These are fundamental steps in this paper, and so they provide a defensible, background independent basis for constructing this model in such a high-energy environment.
  3. Model 1 predicts the existence of extremely high cosmic ray energy events (up to ~ 1028 EV), which are beyond the GZK cutoff. A cosmic ray is essentially a very high-energy proton. It was found, using the standard model of particle physics, that a proton with energy above a certain energy (the GZK cutoff) interacts with the microwave background in particle space to form other particles. Since microwave background is everywhere, protons with extremely high energy (i.e. from super nova etc.) should not last very long in particle space.  Yet such cosmic rays are observed (Magueijo, 33). Model 1 predicts super particles tunneling through the potential barrier. These super particles are unstable in particle space, and break down in particle space into protons with energy in the range of ~ 1017 to ~ 1019 GeV. They occur anywhere there is dark energy-i.e. anywhere within a galaxy. Thus these protons will appear too close to the earth to react with microwaves before interacting with the earth’s upper atmosphere and causing a cosmic ray. Thus we have high-energy cosmic rays (see ref 16, AP4.7C for more details).           

 

Gaining Acceptance for Model 1

Model 1 must be tested with data. A summary of the tests that support Model 1 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.

 

Summary and Conclusions

  • A model has been developed that predicts dark matter and energy and the extremely high-energy protons, which operate beyond the GZK cutoff. Initial order of magnitude checks with existing data have been made, and the model is found to be in agreement with the data. Possible problems with the model have been analyzed. The most important of the problems have been analyzed and resolved in companion papers ref14, AP4.7A; ref15, AP4.7B; and ref16, AP4.7C. Experiments that would check the accuracy of the model have been proposed. The model has been found to be valid as far as the current checks can determine.

 

Appendix 1. The Basic Equation

Consider the following non-relativistic three-dimensional time independent Schrödinger equation.

 

            [-(h2/8p2m)Ñ2+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  , if  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.

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

And,

            Q(x) = the Heaviside 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 ro.  Then one can think of starting at 0 and moving in vacuum space to ro, 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 ro = 0for solving the equation. Note also, that what we are describing is a spherical shell of radius ro and thickness a around a super particle.

 

Note that 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 8), which is as follows:

 

            If E>V

 

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

           

            If E<V,

 

            T = 1/(1+Vo2 sinh2(k1a)/4E(V0-E),

 

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

 

Here we have set up the equations for a super particle with spherical vacuum barrier of radius ro and thickness a. Inside the radius is vacuum space. Outside the radius is the barrier shell of thickness a, and outside that is particle space. The rate of passage of a particle through the spherical vacuum barrier is:

 

            R = T h/2p k1

 

The best fit of the very rough data available to the writer is:

 

            ro = 10-5 cm

            a =  10-7 cm

 

There are two important cases.

 

            Case 1

            E = 1017 GeV

            V0 = 1019 GeV

            N = number of super particles in vacuum space = 1060 super particles

 

In this case, T = 10-50, and R = 1074 GeV/cm2 sec. This is the case of leakage of super particles for the whole universe by tunneling through the barrier. 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 ~ 10-5 GeV/cc. This is the same dark energy that causes the accelerated expansion of space that requires a potential energy of ~ 10-5 GeV/cc (see Appendix 4). Note that the number of particles N that has built up in a thermal equilibrium at energy E and remained there, did so because the gravitational energy of contraction in the black hole was used up in converting particles into super particles at this cross over energy for making them.

 

            Case 2

            E = 1019 GeV

            V0 = 1019 GeV

 

In this case, T = 1, and R = 10124 GeV/cm2 sec. This is the case of big bang passage over the barrier. 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 inflation energy, which causes inflation. The amount needed is estimated to be ~1094 GeV/cc (see ref 9), where the volume of space at the beginning of inflation is estimated to be (for one super particle barrier shell) 10-14 cc. Thus the inflation potential energy required is ~ 1080 GeV. The phase change energy (~1017 GeV/particle) from the ~1060 particles in particle space including the dark matter is ~ 1077 GeV. The discrepancy seen is not surprising considering the roughness of the calculation, and the fact that the theories used to obtain the estimates have not been matched for assumptions and conditions.

 

Appendix 2. The Expansion Rate of the Universe

The expansion rate equation of the universe (Peebles, 76) is,

 

            H2 = (a’/a)2 = 8/3 p Grb+ 1/ a2R2+L/3

            Where:

            H = Hubble’s constant

            R = Radius of curvature

            G = Gravitational constant

            a = Expansion parameter

            r = Density

            a’ = Rate of change

 

Appendix 3. The Speed of Light at Extreme Energy

In order to make constant speed of light and constant Planck length compatible, Amelino-Camelia (Amelino-Camelia, 6) develops a modified dispersion relation for photons as follows.

 

            E2 ~   c2p2 + Lp c E p2  

            Where:

            E= energy

            P= momentum

            Lp= Planck length

            c= velocity of light in vacuum

               

 

This corresponds to a deformed speed of light law:

 

            vg (p) = c (1+Lp ! p! / 2)

 

This law is approximately valid when Lp <1.

 

For higher energies, the following can be used:

            c ~ (3 x 1010 cm/sec) / (1-E/Em ) 

            Where:

            Em = Planck energy

(see ref 10 Magueijo, 31, where some assumptions have been made)

 

Note that when the energy increases, the speed of light increases. Magueijo (Magueijo, 251) describes it thus, “It was as if the speed of light became larger and larger as we approached the border between classical and quantum gravity. At the border, the speed of light seemed to become infinite and absolute space and time could be recovered, not in general, but for one specific length and time- Lp, and tp …”.

 

Appendix 4. Potential Energy and Expansion Pressure

Particles around and in a black hole operate under the influence of four forces.

  • A central force operating toward the center of the black hole due to gravitational attraction or repulsion.
  • A central force operating away from the center of the black hole due to the centrifugal force of the particle’s rotation around the black hole’s center.
  • A dispersive force due to the motions and collisions of particles due to their high temperature (kinetic energy pressure).
  • An electromagnetic force 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.

 

As a particle falls into a black hole, gravitational attraction first controls. Loop quantum gravity has established the existence of this attraction in background independent terms. When the particle nears Planck energy, it bounces and expands into a new space, where gravitational repulsion takes over and the attraction of the black hole center can finally be balanced by a new set of forces as follows.

 The gravitational force. The energy conservation equation (Peebles, 395) is,

 

            r’ = -3 (r + p) a’/a

 

            Where:

            p = pressure

            r = energy density

            r’ = rate of change of energy density

            a = space expansion factor

            a’ = rate of change of space expansion factor

 

There are conditions when the net pressure is negative,

           

            p < –r/3

 

Then the Robertson-Walker line element and thus the spatial distances diverge. The divergent condition applies when:

 

            p = f’ 2/2 – V

 

            Where:

            V = a potential energy density

            f = a new real scalar field

 

Here, it is assumed that V is a slowly varying function of f and the initial value of the time derivative of f is not too large. Then the kinetic energy f’ 2/2 is small compared to V, and the pressure is negative, and depends on V. Then space expands under the expansion pressure of V, and the attractive pressure of gravity in the black hole is overcome.

 

Then Model 1 shows that V is decaying with time into super particles. Also the kinetic energy is increasing due to the addition of new energetic particles through the black hole. Eventually, the kinetic energy term exceeds the potential energy, and the gravitational force turns attractive, balanced by diffusion and electromagnetic forces and tempered by the centrifugal force. The effect of these forces on the particle ion cloud is explored in Appendix 5.

 

At the same time, according to Model 1, super particles are tunneling slowly through the vacuum barrier between vacuum space and particle space and then breaking down into low energy particles, and thus adding phase change potential energy to the vacuum potential V in particle space. This is a potential energy rate that increases with time along with the number and size of black holes. Recall that the potential energy from the big bang is decreasing as the vacuum energy is used up to make particles since there is no input from over the barrier because the big bang has stopped. Thus, the potential energy density reached a minimum (at about 5 billion years ago according to the data), as the two rates become equal, and then begin to increase. This increase continues until it reaches the value that exists at this epoch (10-5 GeV/cc). At the same time, particles (protons) are being added to particle space with extremely high kinetic energy (up to 1019 GeV). They are entering distributed in space, but preferentially in the vicinity of galaxies, where the dark matter is in highest concentration. They are distributed in energy because the vacuum space dark matter is a Gaussian energy distribution of particles.

 

Appendix 5. Energy Density Estimates

The Model 1 description of the ion cloud unfolds as follows.

  1.  An object, or a cloud of particles that enters a black hole trades gravitational potential energy for kinetic energy. At the same time the potential energy increases due to increasing curvature of space. The objects are torn apart into particles by shear forces in the black hole, and as they gain kinetic energy, they come into thermal equilibrium with other particles, and therefore have an increasing temperature. When the particles gain enough energy (on average), to be beyond the energy of unification of all four forces (~ 1017 GeV-see Kane, 281); but before they reach the Planck energy limit (1.22 x 1019 GeV), and the potential energy is also beyond the unification limit, they do the following. The particle ion cloud uses gravitational potential energy to expand (see Appendix 4), then the particles start to convert into super particles using up that same potential, so the expansion slows and the particles form into an ionized cloud of super particles under the influence of gravity, centrifugal force, kinetic energy pressure and electromagnetic force (see Appendix 4 above). Once the super particles form, they generate the unified force and the spherical potential energy barrier (see Appendix 1 above) that isolates Particle space from Vacuum space. The super particles will then operate between 1017 and 1019 GeV and be ionized at this temperature. As an example, a particles that descend to ~ 10-6 cm from the center of a 106 sun black hole will gain enough kinetic and potential energy to generate a super particle.
  2. After the super particles enter Vacuum space and expand away from the black hole, they become dark matter to Particle space (our space). In Vacuum space, this cloud of particles becomes an ionized gas cloud having both super baryons and super electrons as well as super photons. The temperature is much too high for the super baryons and super electrons to combine into super atoms, but it is assumed that the super force is strong enough so that the super baryons will not break down into super quarks. It is above the ~10 17 GeV threshold that makes the super force possible. It thus appears possible to analyze this ionized gas with the tools developed for ionized gasses in Particle space (Cobine, 50). The method given here is different because of the extra forces, but closely related to the method given there. We begin with the diffusion velocities of the ionized gaseous components.

 

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

 

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

 

                      Vg = KgG

 

            Where:

                       D = Diffusion coefficient

                       K = Ion or grav 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 Appendix 4)

                       ng = source of particles from the black hole

           

            We set:

                        V+ = V- = Vg = V,  n+ = n – = ng = n,  dn+/dx = dn–/dx = dn/dx

 

            We solve this equation, and get:

 

                        n= (No/4pDt)3/2 exp(–r2/4Dt)  

 

            Where:

 

                        D = (D+ K– + D– K+ ) / ( K+ + K– –  2 K+ K– / Kg ) 

                                   r= Radius from black hole source

                        t= Time

                        No = particles diffusing from an “instantaneous”  point source  

           

            From basic kinetic theory we find:

 

                        D = Lc/3

 

            Where:

 

                        L = 1/npd2 and d is the diameter of the shielded  super ion.

                        And c = the average velocity = 1.128co

                        And co ~ c or less (co is limited by the speed of light).

                        And c ~ (3 x 1010 cm/sec) / (1-E/Em)

                        And Em = maximum energy = Planck energy

 

            Note also that:

 

                        D/K  = kT/e and,

                       

                        E = 3kT/2

           

            Where:

 

                        T = Temperature of the plasma.

                        E = Energy of the ions.     

 

We note from the above equations that:

a) The solution is the equation for a peaked function (bubble) that centers on the black hole in the galaxy, and sags with time just as the dark matter appears to do. Note that n falls off rapidly for r2 > 4Dt.

b) The shape of the function is normally spherical, but can have tails if D Which is proportional to K is different in different directions. This is especially important for Kg (gravitational mobility). Any local increase in n in a radial direction will make a decrease in D, which will start to build up n in that corridor. Thus there is a tendency for lattices of dense dark matter corridors to build between bubbles.

c) In order to make the center dense part of the bubble have a diameter of the order of a galactic core (~1020 cm for example), D must be large (~1028 cm2/sec), and t must be large, (~1012 sec, ~ the lifetime of a galaxy). In order to make D this large, d must be ~10-5 cm, and c must be ~ 1 x 1012 cm/sec and n is estimated as ~ 10-6 particles/cc. This d is the diameter of the potential barrier shell, so collisions with the barrier shell apparently dominate diffusion. This value for c is clearly greater than the standard light speed as proposed by Amelino-Camelia, and Magueijo (see esp. Ref 10, Magueijo, 31). To quote from (Ref 11, Magueijo, 251), “It was as if the speed of light became larger and larger as we approached the border between classical and quantum gravity. At this border, the speed of light seemed to become infinite, and absolute space and time could be recovered, not in general, but for one specific length and time-Lp and tp-so that everyone could agree on what belonged to classical and to quantum gravity.”  

d) Note that this super fast light throughout the bubble is also required to maintain the conditions for the validity of kinetic theory that has been assumed to make the equations above. Certainly the energy of the particles is high enough since we are operating near the Planck energy.

e) Note that No is an impulse source in the above equation, and acts like the black hole fed for a time short compared to the life of the galaxy and then stopped. Later, it started again. It is the average of a series of these feeding impulses that is convenient to use to calculate the characteristics of the dark matter bubble. This, of course, is how the black holes have been observed to operate. This impulse behavior can also explain how donut shaped bubbles of dark matter can form.  

f) Eventually, these super particles escape into intergalactic space to build up a uniform base of super particles in the universe.

g) Note that this explanation is only order of magnitude based on average galactic characteristics. More accurate calculations based on detailed dark matter data are necessary to confirm the model.  

  1. The equations of Appendices 1, 4 and 5 above make it possible to estimate the time between big bangs. As mentioned above, the leakage of super particles into intergalactic space is a leakage into the base of super particles in Vacuum space. This base has the galactic bubble of super particles superimposed on it. A galactic bubble is expected to reach the spillover point first, so galactic parameters will be used for this calculation. At the present time, an average galaxy is estimated to have the value ~1060 GeV which was built up over ~1010 years (the lifetime of our universe). The rate of buildup started at 0 because there were no black holes. As the number of black holes increased, the rate increased in vacuum space according to the formula

 

                      Rvti2 

 

             Where:

                      Rv = vacuum space rate constant = 1017 GeV/sec2

                      ti  = time fromthe big bang to now = 1010 years= 3 x 1017 sec

 

Now the vacuum potential energy barrier has an estimated value of 1019 GeV. Also, the super particles build energy from E = 1017 to 1019 GeV. Assuming the same buildup rate continues in the future, the time required for the kinetic energy to reach the vacuum potential, and start spilling out into a new big bang is 1019 sec or 1012 years.

4.      It is important to note that dark matter is a result of two competing effects, namely:

O The ingestion of matter from particle space into black holes at a certain average rate.

O The leakage of dark matter from the dark matter bubble into interstellar vacuum space.

The buildup of dark matter into the dark matter bubble around a galaxy means that more matter is being ingested by black holes than is being leaked into interstellar space. The difference goes into the buildup around the galaxy. The buildup rate calculated in 3 above is the net difference between these rates. Eventually, all dark matter will find its way into the base in interstellar vacuum space and contribute to the kinetic energy behind the vacuum potential, but the bubble around the galaxy will hit the limit first, so its value is most important. Thus the calculation of the dark matter buildup rate to the big bang is only roughly valid. It is useful, however to give a description for what will happen.

5.     It is also important to note that the use of kinetic theory from particle space in the very high-energy zone of vacuum space may introduce errors in the results.  Its use is justified only if the theory can later be justified and/or the experimental results match the experimental results (see Problems with Model 1, above).

 

Appendix 6. Dark Energy and Dark Matter

There are two kinds of material we are attempting to account for, dark matter and dark energy. They are separate problems, and will be handled separately.

  • Dark Matter. It has been shown in Appendix 5 how two spaces connected by the black holes of Model 1 can account roughly for the observed distribution characteristics of dark matter. 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/(Vo + E)

 

            Where:

                      M = ms mp/ (ms + mp)

                      mp = mass of particle space baryons = 1 GeV.

                      ms = mass of super baryons = 1017 GeV.

                      Vo = 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.

 

  • Dark Energy. Using the upper limit of the cosmological constant, the vacuum energy of particle space is estimated to be ~ 10-5 GeV/cc. This is the vacuum potential energy we observe now causing the accelerated expansion we observe now. (see experimental results 8).

During inflation, the potential energy of particle space is estimated as ~ 1071 gm/cc or ~ 6 x 1094 GeV/cc (see ref 9). It is believed that as particles were formed, this large potential was gradually used up.  

It is difficult to determine the quantum expectation value of a vacuum due to the interacting particles and anti particles exactly, but the value is not expected to be zero. It is estimated to be roughly one particle in every volume equal to the Compton wavelength of the particle cubed. Using the Planck mass (the highest) as the particle mass, one obtains a value of ~ 1091 gm/cc or ~ 10115 GeV/cc. A calculation using the Planck volume gives ~ 10125 GeV/cc. Other estimates have been published, but most are in the range of ~ 10115 to 10125 GeV/cc. It should be noted that not all of the particles and anti particles interacting in vacuum have even close to Planck mass. Indeed, one estimate based on the potential of the Higgs particle (Kane, 112), is ~ 1049 gm/cc. It might be expected that an average value including other particles might be even lower. Thus the value used for the purpose of this model will be  ~ 1035 GeV/cc.      

One of the results of the dark matter of Modle1 (see Appendix 1 Case 1) is that there is a rate of particles that tunnel from vacuum space through the vacuum barrier into particle space, and thus add phase change energy to the vacuum energy in particle space until it reaches ~ 10-5 GeV/cc in our time as expected.   

  • The results of these estimates show that it is possible to explain the dark matter and the dark energy in the sense that one can see roughly where they came from what they are doing now, and predict what will happen to them in the future.

  

Appendix 7. Prior Experimental and Theoretical Results

It is necessary to describe the prior experimental and theoretical results that Model 1 must satisfy in order to be a successful theory. Note by way of definition, that “accepted” means that some data exist that support the results given. Note also that “proved” means that the data supporting the results given have been cross-checked by different people and re-checked by different methods, and are thus accepted as valid.

 

References

  1. L. Smolin, The Trouble with Physics, Boston, New York: Mariner Books, 2006.
  2. B. A. Schumm, Deep Down Things, Baltimore, Johns Hopkins University Press, 2004.
  3. Misner, Thorne and Wheeler, Gravitation, New York, Freeman and Co., 1973.
  4. G. Kane, Modern Elementary Particle Physics, Ann Arbor, Michigan, Perseus Publishing.
  5. P. J. E. Peebles, Principles of Physical Cosmology, Princeton, New Jersey, Princeton University Press.
  6. “Dark Matter Drops a Clue”, Pg 35, Scientific American, New York, June 2015.
  7. I. G. Amelino-Camelia, “Testable Scenario for Relativity with Minimum-Length” hep-th/0012238. 
  8. HTTPS://en.wikipedia.org/wiki/Rectangular_potential_barrier. 
  9. WWW.astro.edu/~wright/cosmo_constant.html
  10. J. Magueijo, New Varying Speed of Light Theories, arxiv.org/pdf/astro-ph/030545v3.pdf
  11. J. Magueijo, Faster than the Speed of Light, Penguin Books, New York, New York, 2003.
  12. J. D. Cobine, Gaseous Conductors, Dover publications, Inc., New York, 1958
  13. D. Halliday, Introductory Nuclear Physics, John Wiley and Sons, New York, 1955.
  14. L. H. Wald, “AP4.7A SUPER PARTICLE CHARACTERISTICS” www.Aquater2050.com/2015/08/
  15. L. H. Wald, “AP4.7B SHAPING THE DARK MATTER CLOUD” www.Aquater2050.com/2015/08/
  16. L. H. Wald, “AP4.7C DARK MATTER RATE EQUATIONS” www.Aquater2050.com/2015/08/
  17. L. H. Wald, “AP4.7E INTERACTION RATE OF DARK WITH VISIBLE MATTER” www.Aquater2050.com/2015/08/
  18. L. H. Wald, “AP4.7F GATHERING FOR THE BIG BANG” www.Aquater2050.com/2015/08/
  19. L. H. Wald, “AP4.7G ORIGIN OF THE NEW SCALAR FIELD” www.Aquater2050.com/2015/08/
  20. L. H. Wald, “AP4.7D HOW TO PROVE A THEORY’S CORRECTNESS” www.Aquater2050.com/2015/08/