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

Abstract

In a previous paper (ref 7, 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:1

• 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 connected 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 (protons) 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 working out this model, some problems arose that are connected with it. The most important of those problems are on the detailed characteristics of the dark matter super particle that is the core of Model 1. Those problems will be addressed here and some will be resolved.

 

The Problem

In AP4.7, several problems were left for future efforts. In this paper, one has been singled out for effort.

 

Super Particles. AP 4.7 postulated the existence of a set of super particles with characteristics similar to bosons, electrons and photons, but at much higher energy. These super particles were then shown to be consistent with the current data on dark matter. As noted in AP4.7, the characteristics of the super particles were indicated briefly, but they were not defined in detail. This task will be accomplished here. The overall characteristics required of the super particles are:

1. They must survive at extremely high kinetic energy (~ 10¹⁷ to 10¹⁹ GeV).
2. They must generate something equivalent to an exchange force in order to interact with each other and form a dark matter ionized cloud around a galaxy.
3. They must generate a potential barrier to separate the high-energy space from the low energy space, and ensure that the super particles interact with particles only on the level of an elastic scattering, which has a very low cross section. The potential barrier must have a strength of  ~ 10¹⁹ GeV.
4. The force exchange photons must be able to ignore each other’s barrier potential to generate interacting forces.
5. They must unify the four forces of particle space into one force at about 10¹⁷ GeV (the known potential unification energy).
6. When the super particles break down, they must generate the particles associated with the four forces in matter and anti matter forms.
7. Under some circumstances, the super particle must generate extremely high-energy protons, which are observed as cosmic rays.

In this paper, we will define the super particles in some detail, and take them through their various incarnations to describe where matter and anti matter come from. For the purposes of this paper, the particle of interest will be a proton and an electron. A deuteron also appears possible. The super particles will be essentially a high energy state of a proton and a high energy state of an electron. We start with the results of AP4.7.

 

The Solution

A Super Particle for Model 1

Model 1 is a basic, self-consistent physical model for a super particle that will fit the roll of dark matter and generate dark energy. The unique features of Model 1 are, then:

1. The super particle comes from a particle in particle space (baryon conservation), which passes through a black hole where it gains enough potential energy to become a super particle, and then enters high-energy vacuum space where it operates as dark matter.
2. The potential energy of the high gravitational field in a black hole provides the potential energy needed to make a particle into a super particle, and appears to be the only place in the universe that can provide it.
3. The coupling strengths for the electromagnetic force, the weak force and the strong force converge to a single super force at ~ 10¹⁷ GeV (Kane, 281). The super particle components are assumed to provide the charges and potential energies needed to generate this super force.
4. Since the baryon is conserved in the transition, the super particle is assumed to have an SU(5) symmetry, a spin and an anti matter opposite. 
5. Since the kinetic energy is in the range ~ 10¹⁷ to 10¹⁹ GeV, and the potential energy is 10¹⁹ GeV, the uncertainty principle says that its size is ~ 3 x 10^-20 cm.
6. In order to remain stable, a super particle must operate in a high potential energy vacuum space with a density of ~10³³ GeV/cc. (see ref 8, AP4.7C). The barrier potential shell that surrounds and contains this high potential energy space operates with an even higher potential energy density ~ 10³⁵ GeV/cc. This shell separates vacuum space from particle space. The barrier shell is ~ 10^-5 cm in diameter, and ~ 10^-7 cm thick (see Appendix 1). Thus the barrier is a wall ~ 10¹⁹ GeV high. It is expected to be s wave scattering because the kinetic energy of the particle is so much less than the potential energy of the super particle.
7. In order to pass the barrier of the shell, a super particle needs activation kinetic energy that boosts its total kinetic energy to ~10¹⁹ GeV, which is near the Planck energy. The addition of energetic particles through the black hole provides this energy. With this energy, the particle bounces on the Planck energy and enters vacuum space where it loses some average kinetic energy (temperature) in the larger volume there. At this point, it becomes a dark matter ionized gas where it generates a dynamic equilibrium between particles and super particles in the high vacuum potential environment (see ref 8, AP4.7C).
8. As high-energy super particles are added from the black hole, they form a kinetic equilibrium with a temperature, and the temperature increases. When the mean kinetic energy of the super particles nears the potential energy of the barrier shell, the particles in the high-energy tail flow over it and initiate a big bang. Note that in this high-energy environment, the speed of light is high (Magueijo, 31). The super particles rush to the principal (highest super particle energy) black hole to pass into particle space, leaving a feint, residual imprint of the old cosmic web (see ref 9, AP4.7B for details).
9. When the super particles enter the even larger volume of particle space, the temperature drops. They cannot reenter vacuum space because the kinetic energy is below the barrier potential, so the vacuum potential is low. They can no longer participate in the dynamic equilibrium of vacuum space, so they must decompose into particles. Since the kinetic energy has actually exceeded the shell potential energy, the super particles have enough kinetic energy (at the Planck energy) after flowing into particle space, that collisions can cause complete disruption of the super particle into energy. Note that both positive and negative ions from the ionized gas of super particles are temporarily converted to energy, so charge is conserved
10. In the initial phase after the big bang, the temperature is still high, so the speed of light is high and produces thermodynamic equilibrium. As particles are formed from super particle energy, the CP violation that would normally produce an excess of matter, produces a dynamic equilibrium and forms both particles and anti particles in roughly equal amounts. The particles and anti particles annihilate each other and produce photons. The potential energy is still high, so the pressure is negative, and space expands. Potential energy loss, and the expansion of space reduce the vacuum potential energy, so the expansion slows. Temperature drops more, so light speed drops. The particles lose contact with each other, and the CP violation starts to produce an excess of matter. The particles and forces freeze out of the energy, one sub particle and its force at a time.  We end up with a lot of photons and a significant amount of matter, but very little anti matter.
11. As space expands, the photons eventually become the microwave background we observe in our time.
12. Super particles tunneling through the barrier from the remaining super particles in vacuum space, show up as cosmic ray events that we observe in the energy range of ~ 10¹⁷ to 10¹⁹ GeV, which is beyond the GZK cutoff. They appear everywhere in the galaxies, as the observations show.
13. Potential energy from the tunneling super particles is dumped in particle space as the super particles break down. This potential energy builds up in particle space to become dark energy. This dark energy causes the accelerated expansion of particle space we observe.  

 

Note that these processes involve a sequence of rate processes that will be quantified in ref 8, AP4.7C.

 

 

Super Particle Detailed Characteristics

 

We will start with size. Take as an example, the electromagnetic force with an electron circling a proton. The highest energy state is obtained when the wavelength of the electron fits exactly once around the proton. Interference will keep the electron from trying to get closer to the proton even though the electrostatic attraction tries to force it closer. Lesser energy states fit the orbits at larger diameters, but with an increased circumference. Note that the circumference must be an integral number of wavelengths larger, however. Thus (in a much simplified fashion) we can define the energy states of chemistry. If the energy is higher, however, the wavelength is smaller, and the electron will try to get closer, but it cannot achieve it in a stable state. In fact, the next step in getting closer in a stable state is to force the electron into the proton to make a neutron (~ 10^-13 cm radius). Thus we observe the existence of neutron stars where this step is achieved with the help of the potential energy of the gravity of a 2 solar mass star. Here, however, we have shown how the black hole potential energy can form a higher energy super particle state in vacuum space. The electron and the proton and its quarks find a new relatively stable state in a much higher energy super particle. The super particle, in its higher energy state, is smaller. Using the uncertainty relation and the known size of the proton in particle space (10^-13 cm with energy ~ 1 GeV), one can estimate, for a super proton with energy 10¹⁷ GeV, a size of ~ 3 x 10^-20 cm. Note finally, that the super particle is not completely stable. It exists in a dynamic equilibrium with its particle. Thus it must remain in an environment (a black hole or high energy vacuum space) filled with the potential energy needed to convert a particle into a super particle. This equilibrium environment and its rate equations are described in ref 8. AP4.7C.

 

The most critical property in this high-energy space is the ability to generate the barrier shell that separates vacuum space from particle space. The shell shows itself to have a spherical symmetry (see Appendix 1 below). This is one of the symmetries of the SU(5) group that the super particle is assumed to have. Thus the right symmetry is available for use. Now the coherence of a super particle (the wave function and its derivative is continuous at the barrier boundaries) is maintained in both vacuum and particle spaces and in the barrier (coherence requirement-see Appendix 1), so by Noether’s theorem, there must be a charge. Also, as shown below, there is enough potential energy from the gravitational potential of the black hole to form the potential energy shell. Thus, since all of the components needed for the shell plus the energy are available, the shell will be generated. Note that the vacuum space within the shell walls will be filled with a vacuum energy ~10³⁵ GeV/cc obtained from the gravitational curvature. Also, the vacuum space within the shell volume is filled with a vacuum energy density of ~ 10³³ GeV/cc, which provides the potential needed for the dynamic equilibrium of the super particle mentioned above. This vacuum energy density is the same as the potential energy of spontaneous symmetry breaking obtained from the Higgs field (Appendix 5). Thus the Higgs field apparently provides the vacuum potential in vacuum space that is used for super particle construction. Note finally that the shell size (~ 10^-5 cm) is large compared to the super particle size (~ 3 x 10^-20 cm), so there is room for the particle to move around within the barrier.

 

The super particle is generated inside the black hole. There, the operating conditions for particle generation are set as follows. When a particle sinks inside the black hole to the point where the gravitational curvature gives enough potential energy (~ 10¹⁷ GeV) to make a proton (or neutron) change into a super particle, the process starts (Appendix 3). In order to fit the characteristics it must have, this change starts at ~ 10¹⁷ GeV which is also the energy of unification of the three forces (Appendix 2). The potential energy in the proton started at ~ 1 GeV (compatible with particle space). At 10¹⁷ GeV, the quarks get closer and the gluons orbit tighter, so the inward force is greater. The same is true of the electron, which gets closer, so the force is higher. Thus, we get a smaller, tighter, more energetic particle. Now these super particles are formed in the high potential energy environment of a black hole and the conversion process takes place rapidly (see ref 8 AP4.7C for rate details)). At the same time, with the high kinetic energy, the super particles break down into particles rapidly, so a dynamic equilibrium is formed between super particles and particles. The higher the potential and kinetic energies, the higher the concentration of super particles, until when it nears the Planck energy, the matter is nearly all super particles. The energy is now high enough, also, that the super particles are nearly all ionized. Note that if the high vacuum potential energy of the black hole is lost, the reverse reaction that disrupts super particles into particles will dominate, and the super particles will rapidly be reduced to particles-as happened after the big bang. 

 

As the kinetic energy of a super particle in particle space (in the black hole) reaches the Planck level of ~ 10¹⁹ GeV, it can bounce on the Planck barrier and pass into vacuum space as mentioned by Smolin (Smolin, 250). With the particles in vacuum space, conditions are right to form the barrier potential that separates this new vacuum space from particle space (see ref 8 AP4.7C for sequence details). The high vacuum potential and the high temperature needed to keep a high concentration of super particles will be maintained by the barrier potential, even if the super particles travel away from the black hole, as they must to form dark matter. Now in vacuum space, there is a somewhat larger volume and so a lower average kinetic energy (temperature) of super particles results. The high vacuum potential that exists behind the barrier now exceeds the kinetic energy, so the pressure turns negative and reverses the contraction toward the black hole center. The dark matter starts to expand and counters the contraction due to black hole gravity. If the expansion goes too far, the vacuum potential becomes less than the kinetic energy due to increased volume and particle formation, and the contraction starts again. Here, super particles are still ionized, and form an ionized gas of super particles, which spreads out, and becomes the cloud of ionized dark matter around a galaxy as detailed in ref10 AP4.7B. Note that the electromagnetic force operates as an exchange super force as in particle space, except that the exchange virtual super photon energy is higher. Note, also (see Appendix 1) that the exchange virtual super photon with its high energy, and zero rest mass will pass right through the barrier potential, and the super force will operate undisturbed in vacuum space even though surrounded by particle space outside the barrier. In vacuum space, the dark matter cloud builds up kinetic energy (and thus temperature) by adding energetic super particles from the black hole by the bounce process into vacuum space. Eventually, the kinetic energy reaches Planck energy and then flows over the barrier to become a new big bang, as detailed in ref 8, AP4.7C..

 

Testing Model 1 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 Super Particle Model 1A

Certain problems with Super Particle Model 1A were discovered in the course of this work. Those problems will be discussed here.

• Model 1A is dependent on a series of rate equations that make the steps outlined above occur in the proper sequence. These rate equations are detailed in ref 8, AP4.7C.

 

Further Proof of Super Particle Model 1A

• Some of the rate equations can be checked experimentally. If they ensure proper step sequence, it will provide major support for Model 1A.

 

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 was predicted in a new space (vacuum space) that constitutes this dark matter, and generates this dark energy and the high-energy cosmic rays. The details of these super particles were not pursued in AP4.7, and so they have been pursued in this paper. The super particles have been found to be essentially high-energy states of protons and electrons, where a spherical shell barrier that contains a high potential energy density surrounds the proton. Initial checks with existing data have been made, and Model 1 has been found to be in agreement with the data. Certain details of Model 1 are given in two other papers (ref 8, AP4.7C, and ref 10, AP4.7B). Model 1 has been found to be valid as far as the currently available data can determine.

 

Appendix 1

First compare Schrödinger’s equation (an energy balance in quantum space), and the energy balance from general relativity. Both have kinetic energy and potential energy terms. In general relativity, the potential energy is in the curvature of space and shows up as pressure in the energy balance equation (Peebles, 394).

 

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

 

The pressure here 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 due to gravity

            f = a new real scalar field

            f’ ²/2 = the kinetic energy term

           

Note that under the correct circumstances, the pressure p can be either positive (contracting) or negative (expanding), depending on the potential or kinetic energy terms.

 

The Schrödinger equation is as follows (see ref 7 AP4.7 for more details).

 

[-(h²/8p²m)Ñ ²+V]Y = EY

 

Where:

            V = potential energy of a quantum field

            E = total energy

            (h²/8p²m)Ñ ² = kinetic energy

 

Here, we identify the potential energy from the curvature of space-time due to mass in a black hole with the potential energy of the Schrödinger equation. The gravitational spatial curvature of a black hole could distort the particle orbital structures enough to increase the internal energy of the particle to the super particle level. Then the creation and destruction operators can be used in the Schrödinger equation to create super particles. We rely on the Loop Quantum Gravity results of Smolin (Smolin, 250-see also 11 in AP4.7) to justify using these equations in a high-energy, black hole, quantum gravity environment.

 

Now, we note:

            E = the energy of the super particle.

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

 

Where:

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

            a = the barrier potential width.

 

Note that what we are describing is a spherical shell of radius r_o and thickness a around a super particle.

 

In solving this equation, 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+V_o² 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 r_o 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:

 

r_o = 10^-5 cm

a =  10^-7 cm

 

 

Appendix 2

Now Kane (Kane, 279) shows that the couplings of the forces satisfy the equation:

           

            1/α_i (M²) = 1/ α_i (μ²) + b_i /4π ln M²/ μ²

 

            Where:

            α_i  are the couplings for the forces

            M is the mass scale at which we want to calculate α_i

            μ is a scale where the coupling is measured

b_1, b_{2 ,} b₃are calculated for the U(1) (electromagnetic), SU(2) (weak) and SU(3) (strong) interactions.

 

Kane then develops the equation to show the coupling strengths as a function of the mass (energy) at which we want to calculate them. They are shown to converge close to a single value at a mass M_G  ~ 10¹⁷ GeV. The convergence is not exact, because it is sensitive to radiative corrections, but it is close. If they meet exactly, that would be taken as a very strong indicator of a grand unification into a single force (a GUT). There are several kinds of GUT’s. For our purposes here, a GUT with SU(5) symmetry will be chosen because one of its sub symmetries (U(1)) will be needed for the barrier potential (see below). Super symmetry is not necessary, and there are problems with its use (see ref 9, AP4.7D), so it will not be chosen. We should ask if the unification of forces implies a change in the detailed characteristics of its particles and forces. This will be explored more below, but generally, since baryons are conserver at this point, there does not seem to be any reason to change the detailed characteristics of the sub particles and forces involved. Also, we will need one of the symmetries later. Because the operating energy is high, the super particle is relativistic and so has spin and anti matter. Thus the particles that are in the standard model should exist in some form, and a super force for the super particle is still accompanied by the exchange of a photon. The potential energy involved in the function of these particles, of course, increases in the extreme energy of vacuum space.

 

Appendix 3

We must ask if a black hole has the ability to provide the required 10¹⁷ GeV to 10¹⁹ GeV in kinetic energy and 10¹⁹ GeV in potential energy needed to form super particles from particles and provide a barrier. We note that the kinetic and potential energy varies inversely with r (Misner, 911). Thus there is an r with the proper energies. However, the Planck energy must be reached before the Planck radius is reached. It was found that energy is reached easily by a 10⁶ solar mass black hole worked.  It was also noted that such a massive black hole was common for galactic centers. So it was used as the example for the work done in this paper and in AP4.7. It was also noticed that the potential energy necessary to obtain the super particle state is very high. To get an electron to move into orbit near a nucleus requires a potential energy ~ electron volts. To get an electron to merge with a proton and make a neutron in a neutron star requires a potential energy ~ GeV, which requires the gravitational potential obtained from ~ 2 solar masses. To get a proton to become a super proton in vacuum space requires a gravitational potential of ~ 10¹⁷ GeV, and a kinetic energy of ~ 10¹⁹ GeV which requires the gravitational potential obtained from a black hole mass in the range of 10⁴ < m < 10⁹ solar masses. This implies that the central black hole in a galaxy is the principle provider of dark matter in the universe, although very large stars that might be able to generate such energetic particles do exist, and were common in the early universe

 

Appendix 4

Kane (Kane, 112) has estimated the contribution of spontaneous symmetry breaking to the vacuum energy density of the universe. This energy density estimate came from calculations based on the Higgs mechanism. He obtains a value of ~ 10⁴⁹ GeV/cc. This value is admittedly approximate. He must guess at the value of the Higgs self coupling. However, the vacuum energy density varies only linearly on this self-coupling value, so the energy density is not very sensitive to this value-perhaps a few orders of magnitude out of 49. Now Model 1 estimates the potential energy needed to generate the barrier wall as (see exercise 6) ~ 10¹⁹ GeV. This energy requires that the energy density within the wall is ~ 10³⁵ GeV/cc, and the energy density within the spherical shell is ~10³³ GeV/cc. Thus it appears that there is more potential energy in spontaneous symmetry breaking than is required for super particle construction. In order to push a super particle behind the barrier, excitation energy is required (see 7, above). This energy is expected to show up in the energy density that comes out into particle space. This energy (10² GeV/10^-15 cc) closes the gap between the symmetry breaking energy ~ 10⁴⁹ GeV and the vacuum space energy density ~ 10³³ GeV/cc (See 7, above). The error is within the uncertainty in the two estimates.

 

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/030545v3.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.      Misner, Thorne, and Wheeler, Gravitation, New York, Freeman and Co., 1973.

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

8.      L. H. Wald, “AP4.7C DARK MATTER RATE EQUATIONS” 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, “AP4.7B SHAPING THE DARK MATTER CLOUD” www.Aquater2050.com/2015/07/