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

Abstract

In a previous paper (AP4.7), a self-consistent theory called Model 1 was developed that appears to answer twelve 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?

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 and resolved here.

The Problems

In AP4.7, several problems were left for future efforts. In this paper, two connected ones have been singled out for effort.

Matter and Anti-matter. As noted in section 6 of AP4.7, the particles start entering the black hole as matter particles. They end after the big bang, as equal numbers of matter and anti matter particles. They then annihilate each other and are reduced again down to a few matter particles. How exactly does this happen.

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:

They must survive at extremely high energy (~ 10¹⁷ to 10¹⁹ GeV).
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.
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.
The force exchange photons must be able to ignore each other’s barrier potential to generate interacting forces.
They must unify the four forces of particle space into one force at about 10¹⁷ GeV (the known potential unification energy).
When the super particles break down, they must generate the particles associated with the four forces in matter and anti matter forms.
The high energy of the particles implies relativistic characteristics.

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. We start with the results of AP4.7.

The Solution

Super Particle Model 1A

Model 1A 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 1A are:

The super particle comes from a particle in particle space, which passes through a black hole where it gains energy to become a super particle, and enters high-energy vacuum space where it operates as dark matter.
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.
The coupling strengths for the electromagnetic force, the weak force and the strong force converge to a single super force at ~ 10¹⁷ GeV. The super particle provides the charge and potential energy needed to generate this super force.
The super particle has an SU(5) symmetry, a spin, an anti matter opposite, an average kinetic energy of ~10¹⁷ GeV, and a size ~ 3 x 10^-20 cm.
A super particle in this high potential energy space has the potential energy density (~10³⁵ GeV/cc) needed to generate the barrier potential shell that surrounds it, contains the high vacuum potential and separates vacuum space from particle space.
When the kinetic energy of a super particle nears the Planck energy, it bounces and enters vacuum space where it loses some average kinetic energy (temperature) in the larger volume of vacuum space (see AP4.7B) and becomes dark matter where it generates a dynamic equilibrium between particles and super particles in the high vacuum potential environment. Note that in this high-energy environment, the speed of light is high.
As high-energy super particles are added from the black hole, the temperature increases, and when the kinetic energy of the super particles reach the potential energy of the barrier shell, they flow over and initiate a big bang.
When the super particles then enter the even larger volume of particle space, the temperature drops dramatically. They cannot reenter vacuum space because the kinetic energy is below the barrier potential, so the vacuum potential is low, and they can no longer participate in the dynamic equilibrium of vacuum space. They must then decompose into particles, and the reverse process regenerating super particles is not possible.
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 particles, the CP violation that would normally produce an excess of matter, produces a dynamic equilibrium and forms both particles and anti particles. The potential energy is temporarily still high, so the pressure is negative, and space expands. Potential energy loss, and the expansion of space reduce the vacuum potential energy, and the expansion slows, so light speed drops. The particles lose contact with each other, and the CP violation starts to produce an excess of matter. We end up with our particle space, and a significant amount of matter.
The matter and anti matter particles annihilate each other to produce photons, which, as space expands, eventually become the microwave background.
Super particles tunneling through the barrier from the remaining super particles in vacuum space, show up as cosmic ray events that we observe beyond the GZK cutoff.
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.

Model 1A Detailed Characteristics

We start with some preparatory exercises to obtain some key equations. 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.

[-(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 would distort the particle orbital structures enough to increase the internal energy of the particle. Then the creation and destruction operators of the Schrödinger equation can be used to take this potential energy to create particles. Here, 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 black hole environment. Note that in the Schrödinger equation, the potential energy term with its charge determines the characteristics of the particle it describes.

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_iare 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 so will not be chosen, although it is not known to be precluded. We should ask if the unification of forces implies a change in the detailed characteristics of the particles involved in the forces. This will be explored more below, but generally, there does not seem to be any reason to change the general characteristics of the particles involved, since the SU(5) symmetry incorporates the other three symmetries. 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 high energy of vacuum space.

In the final one of these preparatory exercises, we will explore the problem of living in a world of matter when charge conservation requires matter and anti matter to be generated in equal amounts (note that this paragraph comes mostly from Kane). Particles appear in matter and anti matter forms, and, under normal circumstances annihilate to form photons, The evidence of our existence indicates that after the big bang, matter and anti matter particles were created and most were annihilated leaving a slight excess of matter. The photons went to make up the microwave background, and the matter went to make up the galaxies. Thus there is roughly one baryon excess for 10¹⁰ photons in particle space. This result can happen only if:

Conservation of baryon number is violated.
Charge-parity (CP) is violated.

Particle space is not in thermodynamic equilibrium while the above conditions are satisfied.

For the conservation of baryon number violation, the matter entering the black holes has an excess of matter over anti matter. The super particles that come out of a big bang create equal numbers of particles and anti particles, so there must be a process in vacuum space that eliminates the excess matter to generate the equality of matter and anti matter that exits vacuum space. Thus baryon number is violated somewhere in vacuum space or the initial big bang cooling phase. For the CP violation, it was originally thought that although C and P were separately not conserved by weak interactions, the combined CP would be a valid symmetry. However, it was found that although the processes and their conjugates that produce baryons occur, the probabilities of occurrence are slightly different-about one part in one thousand. This is the CP violation, and it has been found by experiment to be valid. Finally, there must be no thermodynamic equilibrium to get excess matter, because if there is, the excess matter would have an option to reverse and reform anti matter, and then make a dynamic equilibrium. Without equilibrium, a dynamic equilibrium cannot be obtained, so the excess matter remains for galaxy formation. This is a critical point as will be seen later.

We must ask if a black hole has enough potential energy to provide the required 10¹⁷ GeV. The first thing to notice is that the potential energy necessary to obtain this more energetic 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 a black hole requires a gravitational potential of ~ 10¹⁷ to 10¹⁹ GeV which requires the gravitational potential obtained from a black hole mass in the range of 10⁵ < 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. A 10⁶ solar mass black hole in the center of a galaxy was used as the example for the work done in this paper and in AP4.7, and it can give the appropriate kinetic and potential energy (see Thorne, 911). The energy of the final super particle generated is limited by the Planck energy to 10¹⁹ GeV, because at this energy it is bounced into vacuum space. It is thus concluded that at 10¹⁷ GeV, a particle is formed from the gravitational potential energy with SU(5) symmetry which carries the charge and potential for unified force. We will call this particle a super particle.

Now, we need to estimate the super particle properties. 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 gravity. Here, however, we have shown how the black hole potential energy can form a high-energy super particle in vacuum space, where the super particle has a much higher energy. 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.

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 U(1) symmetry with L = 0 (spherical symmetry, see Appendix 1 of AP4.7). This is one of the symmetries of the SU(5) group that the super particle was assumed to belong to. 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 of AP4.7), so by Noether’s theorem, there must be a charge. Also, as shown above, 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 of ~ 10³⁵ GeV/cc. 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.

Inside a black hole, 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 the characteristics of a proton (or neutron) change into the characteristics of a super particle, the process starts. 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. 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 at the high temperature extant. 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, where the group of particles 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 its components 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 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. 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. 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 in the black hole. 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 the ionized gas of super particles mentioned in AP4.7, which spreads out, and becomes the cloud of ionized dark matter around a galaxy described in 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 AP4.7 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 indicated in AP4.7B.

Now the temperature drops as the super particles expand into particle space, and the resultant reduction of the kinetic energy term means the potential energy term dominates, and the pressure term (see above) turns sharply negative. Particle space expands rapidly, so the high vacuum potential is rapidly diluted in particle space, and the expansion slows down. The speed of light, which was high in the beginning because of the high energy (Magueijo, 31), then starts to drop, and the universe loses its thermodynamic contact. The reverse process in the dynamic equilibrium that generates particles from super particles then dominates the equilibrium. No new super particles are formed because of the low potential. Then the kinetic energy behind the barrier drops below the barrier potential, and the particle flow and the big bang dies. The super particles in vacuum space begin slowly to be renewed through new black holes in a renewed particle space. As mentioned in AP4.7, the big bang vacuum potential is reduced by making particles until it is the same as that caused by the vacuum potential buildup caused by particles tunneling through the renewed vacuum barriers. These particles are the ones that cause the high-energy cosmic rays beyond the GZK cutoff. Then the vacuum energy in particle space increases as the super particles convert to particles and give up their potential. This potential is the dark energy that causes the accelerated expansion of space, which we observe in our time.

The details of the process that generates particles are important now. For the super particles that pass over the barrier and flow into particle space in a big bang, there is a rapidly diminishing particle temperature and density and especially a diminishing potential energy density. Once a super particle passes over the barrier, it cools and encounters a lower potential energy, so it cannot reestablish the barrier and reenter vacuum space without going through a black hole to provide the new potential energy. Thus, it is a naked, high-energy super particle in low energy particle space, and it must decompose into its component particles with lower symmetry. In this early phase of the big bang, the energy is still high, so light speed is still high, and the super particles are still in thermodynamic equilibrium. It is still matter as opposed to anti matter, as it has been since entering the black hole, and it is in an extremely unstable condition. It therefore transforms into energy according to the uncertainty principal, and returns to particle space as particles. Since there is thermodynamic equilibrium, both particles and anti particles are produced. Therefore, an equal number of matter and anti matter particles begin to be formed. As this process continues, the rapid expansion of particle space reduces the kinetic and potential energy, and so reduces light speed and shuts down the thermodynamic equilibrium. Then, as particles continue to be formed, the CP violation starts producing an excess of matter because there is no longer thermodynamic equilibrium. The matter and anti matter particles annihilate each other, leaving an excess of matter. Particle space is then left with a large number of photons, and a small excess of matter, from which galaxies are formed.

Testing Model 1A with Data

Model 1A must be tested with data. The tests that support the composite Model (Model1A along with Model 1 and Model 1B) are shown here. The composite Model does the following.

It correctly predicts interacting dark matter in and around a galaxy, and it shows why the matter is dark.
It describes a source for this dark matter, namely a black hole. This source does not violate the laws of physics as presently understood.
It correctly describes the distribution of this dark matter with respect to the galaxies and shows why this distribution happens.
It details the characteristics of the dark matter particles to within our ability to measure them.
It connects with a property predicted by the standard model of particle physics-namely the unification of forces, and predicts the impact of this unification.
It provides an explanation for the difference in vacuum potential energies as measured (low) and as predicted (high).
It provides a physically defendable procedure for describing what happens in a black hole other than “a singularity forms”.
It describes the cause of the Big Bang, what triggers it, what stops it and where the energy causing it comes from. All of this description is in keeping with the data currently available.
It correctly describes the immediate aftermath of the big bang; how early thermodynamic contact is maintained, why the expansion, why it stops, and where the energy causing it comes from.
It correctly describes the later aftermath of the big bang; where the matter and anti matter came from, why we have cosmic background radiation and where our excess of matter over anti matter came from.
It describes how quantum mechanical state details can be transmitted faster than the speed of light if coherence is maintained. Recent experiments have shown that this happens.
It correctly predicts extremely high-energy cosmic rays beyond the GZK cutoff, and describes where they come from. These cosmic rays have been observed.
It correctly predicts dark energy that accelerates the expansion of space, and describes where it came from, and the value of the dark energy. The accelerated expansion of space has been observed.
It predicts the existence of a future new big bang, and estimates when it will happen.

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.

It is not clear how the Higgs field and particle fit into the details of Model 1A. This problem should be investigated.

Model 1A is dependent on a series of rate equations that make the steps outlined above occur in the proper sequence. These rate equations should be detailed. The rate constants needed to ensure proper step sequence could probably be established.

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. Initial checks with existing data have been made, and Model 1A has been found to be in agreement with the data. Possible problems with the model have been analyzed, and a theoretical program proposed as a fix. Experiments that would check the accuracy of the model have been proposed. Model 1A has been found to be valid as far as the current checks can determine.

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. Thorne, Miguel and Wheeler, Gravitation, New York, Freeman and Co., 1973.