Abstract

There are currently four important connected major unanswered questions in physics and astrophysics.

(1) How can the theories of symmetry and the Higgs field be used to calculate the masses of the fundamental particles?

(2) How can dark matter be explained and described?

(3) How can dark energy be explained and described?

(4) Where do the ultra high-energy cosmic rays with energy beyond the GZK cutoff come from?

A self-consistent theory (called Model 1 in this paper) has been developed that appears to answer questions 2 and 3 quantitatively. In order to derive and justify Model 1, however, it became necessary to calculate the mass-energy of the proton and other fundamental particles that make it up, which answers question 1. This procedure then gave a path for calculating the mass of the Super Particle, which is the primary particle of Model 1. The super particle was found to be a Grand Unified Particle, which unifies the electromagnetic, weak and the strong forces. In investigating the properties of this super particle, it became obvious that it had the properties of dark matter, and when it breaks down, it generates dark energy. At this point, it was noticed that the Grand Unified Particle may be connected to the ultra high-energy cosmic rays that are observed with energy beyond the GZK cutoff (UHECR’s). In a sequence of related papers (Wald, Model 1-A; Wald, Model 1-B; Wald, Model 1-C; Wald, Model 1-D; Wald, Model 1-E and Wald, Model 1-F), Model 1 is detailed and expanded. But Model 1 is likely to be controversial, so a new question immediately arises for Model 1:

(5) How can we prove this theory’s correctness?

This paper is offered to address this final question.

The Problem

The Unique Features of Model 1

There are two spaces in the universe, low-energy particle space and high-energy 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 particle space to vacuum space through black holes where they are converted into super particles (energy ~10¹⁷GeV). They are then wrapped with a potential energy barrier shield (~10¹⁹GeV) to stabilize them. The barrier shield forms the boundary of high-energy vacuum space. These stabilized, shielded super particles are then able to escape from the black hole into particle space. The shielded super particles have a low interaction cross-section with ordinary particles except through gravity, and so are observed as dark matter.

Dark matter particles interact with each other and form a slowly building bubble centered on a galaxy that stabilizes its outer edges. Corridors of dark matter are also generated which form a cosmic web between the galaxies. These corridors guide the development of new galaxies.

The super particles can tunnel through the barrier into particle space. Upon reaching particle space, the super particles become unstable and break down into particles (cosmic ray protons) with ultra high kinetic energy (UHECR’s). In doing so, they give up potential energy from their barrier shields into particle space which becomes the dark energy that we observe as the cause of our accelerating, expanding universe.

Criteria for Success of Model 1

It has been possible to make a self-consistent model (Model 1) that answers all of the important questions shown in the abstract above. In spite of the apparent success of this model, it will not be accepted immediately. In order to be accepted, it must meet the following criteria.

Model 1 must be mathematically self consistent.
Model 1 must predict all the physical data currently known in this area of investigation.
Model 1 must connect with existing, accepted physical theories.
There must be no other simpler theoretical model that will satisfy all the physical data.
It is desirable that Model 1 predict something that is unknown at the time the model is presented, and then is discovered afterward.
Any particles fundamental to Model 1 should be directly observed.
Model 1 must provide a new window into physics and thus create new lines of research.

It should be noted that General Relativity and the Standard Model of particle physics both went through this process in order to gain acceptance, so the process is not unreasonable. In this paper, we will investigate Model 1 to see if it can satisfy the above criteria.

The Solution

Here, we will investigate to see how close Model 1 is to satisfying each of the acceptance criteria.

Mathematical Self-Consistency.

Model 1, by its very nature, must be couched in three separate, self-consistent mathematical disciplines: classical mechanics, quantum mechanics and general relativity. The first two have been mostly connected (Halliday, 21). The first and the last have been mostly connected (Misner, 3). The second and the third have been partially connected (Smolin, 251). Thus all three have not yet been smoothly connected into one consistent discipline, but the connection is close. What Model 1 used was the following.

The Schrödinger equation was used in the high-energy environment of a black hole. The environment (the black hole) was particle is a particle described by quantum mechanics with techniques developed made finite by limiting the energy of the system to Planck energy or less. The Schrödinger equation was then used to derive the barrier shell.
Classical mechanics was used to describe the dark matter as a kinetic gas made up of ionized super particles in a high-energy environment. The super particle is in the standard model. The assumption here is that the super particle’s spherical harmonics term is unimportant when describing this kinetic gas of super particles (see ref 6, AP4.7 Appendix 1).
General relativity equations were used to describe the curvature, expansion and contraction of space in and around a black hole. A scalar field f was used to obtain the spatial pressure relationship with the potential energy V (see ref 6, AP4.7 Appendix 5). The energy was limited to the Planck energy or less to keep the equations finite.
General relativity equations were also used to describe particles in the high-energy environment of a black hole. Again, the energy was limited to the Planck energy or less, so a singularity was avoided.
The use of quantum concepts in a situation usually described with general relativity is justified by results developed with Loop Quantum Gravity (Smolin, 251). These results are as follows. Loop Quantum Gravity is finite. It is background independent (as is general relativity). 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 at higher energy. 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 an intense and energetic environment. The equations used thus appear to be justified if the energy of the particles and of space under consideration are in the right energy range. Currently, however the details of the energy range where the equations are valid are somewhat vague.

Agreement with the Physical Data from Astronomers and Physists

Model 1 correctly predicts the physical data observed by astronomers (ref 6, AP4.7). The current physical data come in seven basic packages.

Ordinary Matter (ref 21, AP4.7V)

Model 1 provides a procedure to calculate the mass of particles in the Standard Model which agrees remarkably well with the measured values, and then calculates the energy of unification using the same procedure which agrees with the unification energy obtained with the Standard Model.

The dark matter (ref 8, AP4.7B)

Model 1 correctly predicts interacting dark matter in halos close to galaxies and in corridors between galaxies, 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 (a surrounding halo) and an intergalactic net (the cosmic web) and shows how this distribution happens.

The super particles (ref 7, AP4.7A)

Model 1 details the characteristics of the dark matter super particles to within our ability to measure them (a high energy state of a proton, possibly with SO(10) symmetry inside of a barrier shell).
It details the operating environment of the super particles, especially the boundary imposed by the barrier potential shell, and the high-energy vacuum space environment.

The course of matter as it transits from particle space, through a black hole, through vacuum space and through a big bang (ref 9, AP4.7C)

Model 1 provides a physically defendable procedure for describing what happens to the particles that descend through a black hole.
It describes the passage of particles through the black hole into vacuum space and back out again through a big bang into particle space.
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 space expands, why it stops, and where the energy causing it comes from.
It predicts the existence of a future new big bang, and estimates when it will happen.

The variations in the speed of light (ref 18, AP4.7M)

Model 1 correctly predicts the speed of light to be 2.99 x 10¹⁰ cm/sec.
It correctly predicts the slowing of the speed of light at cryogenic temperatures.
It predicts the increase of the speed of light at energies near the Planck energy.
It correctly predicts the Planck length to be invariant in spite of relativistic foreshortening.
It correctly predicts that particles with non-zero rest mass always move at less than light speed, while photons can move at light speed.

The matter, anti matter and the microwave background (ref 11, AP4.7F)

Model 1 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 correctly predicts the spatial spectrum of the microwave background radiation.

The dark energy (ref 15, AP4.7I)

Model 1 correctly predicts the 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.

Miscellaneous connected physical data (see 5, below)

Model 1 correctly predicts ultra high-energy cosmic rays (UHECRs) with energy in the energy range between the GZK cutoff and the Planck energy, and describes where they come from. These cosmic rays have been observed.
It provides an explanation for the difference in vacuum potential energies as measured (low) and as predicted (high)..

Connection with Currently Accepted Results of Physical Theories

The currently accepted results of accepted physical theories need to be connected to Model 1. These connections are as follows.

Model 1 provides a procedure to calculate the mass of particles in the Standard Model and then calculates the energy of unification using the same procedure. (ref 21, AP4.7V).
Model 1 connects with and predicts dark matter and dark energy (ref 6, AP4.7).
It connects with a property predicted by the Standard Model of particle physics-namely the unification of forces, and shows the results of this unification on super particles (ref 6, AP4.7). Further, it provides a procedure to calculate the mass of particles in the Standard Model which agrees remarkably well with the measured values, and then calculates the energy of unification using the same procedure which agrees with the unification energy obtained with the Standard Model.
It connects with a property derived from quantum mechanics, namely, the Planck energy, which is used as the limiting energy (ref 6, AP4.7).
It connects with a property predicted by quantum mechanics, namely that the speed of light increases at extremely high energy in order to maintain the Planck length constant (ref 18, AP4.7M).
It connects with properties predicted by general relativity; namely black hole properties and the expansion of space due to high potential energy (ref 9, AP4.7C).
It connects with and predicts the microwave background radiation spatial structure. (ref 11, AP4.7F).
The principle field in Model 1 appears to be the Higgs field from the Standard Model of particle physics. Thus it blends smoothly with the existence of the Higgs field from the standard model of particle physics (ref 12, AP4.7G).
It predicts and explains the existence of a big bang, and describes how it operates (ref 11, AP4.7F).
It connects with the Standard

Models other than Model 1 as competitors

Other models have been offered as competitors to Model 1 to explain dark matter and energy.

Neutrinos

Neutrinos have been offered as a candidate for dark matter, but its extremely low mass and high velocity does not fit the characteristics required. It is no longer seriously considered for this roll.

The Lightest Supersymmetric Particles (LSP)

LSPS have been seriously considered for dark matter. It has been proposed that the LSP might be a stable particle as an extension of the Standard Model. It is expected to be massive and therefore slow moving as required, but it is not clear how it would interact to form the galactic halo and the cosmic web that have been observed by astronomers. Further, it has no way to accomplish the other tasks shown in the list of necessary accomplishments for dark matter and dark energy, except for direct observation. Finally, it has not yet been directly observed. It has not been discarded yet, but there are serious problems. (Kane, 299)

Weakly interacting massive particles (WIMPS)

There has been some preliminary success in searching for WIMPS. Its characteristics have not been detailed, yet, however. It could be another name for Model 1’s super particle. Currently, there is no conflict in their characteristics. In fact, a calculation of the scattering characteristics of the super particle gives the same interaction rate as that of the preliminary WIMP experiment (ref 10, AP4.7E).

Microwave background radiation.

The spatial spectrum has a large peak, yet the most widely accepted theory for the early universe, Inflation, would predict a universe that is spatially uniform on a scale much larger than the radius of the observable universe R from very soon after the big bang. This is because there is no special physical reason for inflation to stop at a size R, and produce a cutoff. Thus the fluctuations should be more or less flat over the range of distances we can observe. On the other hand, Model 1 predicts a new universe that starts as a local zone drawing in dark matter from vacuum space and sending it out from the area around a principal black hole. This forms a new, small, growing zone of highly curved space of a size locked with R. The growth of this zone is accelerating due to a slowly increasing cosmological constant generated by super particles tunneling in from vacuum space that break down in particle space and leave their potential energy there as a slowly increasing cosmological constant. Thus the size of the universe and the principal spatial mode of the background radiation are locked together from the start. (Ref 11, AP4.7F)

Other versions of Model 1.

We ask now if there are other Models that could satisfy the requirements of dark matter, dark energy and the observed extreme energy cosmic rays.

The shape of the dark matter clouds is known roughly by experiments on gravitational lensing, and observations of galaxies (Peebles, 47). It is clear that the clouds are around and between galaxies. The clouds are found to move, but slowly. Clearly, the dark matter particles must interact with each other.

Also, the dark energy density was calculated by means of the accelerated expansion rate of space. It was found to be low (10^-4 GeV/cc). Yet the vacuum energy density calculated from Higgs theory, was high (10⁴⁹ GeV/cc). Clearly, there must be a barrier to separate the vacuum dark energy from the Higgs vacuum energy.

The maximum particle kinetic energy is limited by the Planck energy (~10¹⁹GeV). The force unification energy (if any) is estimated by the convergence of the forces to be ~ 10¹⁷ GeV. It is the only known significant energy convergence point. Also, unexplained cosmic rays are observed in the range of ~ 10¹⁷ to 10¹⁹ GeV. Thus the kinetic and potential energies of dark matter and perhaps dark energy must operate in the range ~ 10¹⁷ to 10¹⁹ GeV.

The size of the observable universe is roughly known. The visible matter particle density of the galaxies and the universe is roughly known. The dark matter particle density is roughly known. The kinetic and potential energy in a black hole has been calculated using general relativity. They are known to be high as the center is approached, and can reach the Planck energy.

Contemplation of the above facts shows that the features of Model 1 as shown in the Abstract above are the only ones that have a hope of satisfying the known characteristics of the universe. By calculating the appropriate numbers, it was found that a match was achieved to within an order of magnitude. Many of the basic numbers are not known better than that, so greater accuracy cannot yet be achieved. Some adjustments are possible in the Model, but barring radical new data, the general configuration appears to be set.

Predicting Unknown Phenomena

Model 1 predicts several unusual phenomena that cannot be explained with other theories.

Model 1 provides a procedure to calculate the mass of particles in the Standard Model which agrees remarkably well with the measured values, and then calculates the energy of unification using the same procedure which agrees with the unification energy obtained with the Standard Model (ref 21, AP4.7V).
Model 1 correctly predicts the existence and distribution of matter (both visible and dark matter) in and around galaxies (ref 8, AP4.7B). This distribution explains the unusual rotation of galaxies that is unexplainable otherwise.
It correctly predicts extremely high-energy cosmic rays with energy in the range between the GZK cutoff and the Planck energy, and describes their origin in our galaxy. Such high-energy protons must come from close around (our neighborhood of the galaxy), because if more distant, they would react with cosmic microwave background. It must also be omni directional. No nearby sources have been identified, yet these omni directional cosmic rays have been observed (Maguejo, 32).
It provides an explanation for the accelerated expansion of space.
It provides an explanation for the difference in vacuum potential energy as measured (low) and as predicted (high). As an example, see Kane, 112.
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 transmission happens wherever coherence is maintained (ref 6, AP4.7).
When galaxies collide, the luminous matter particles with high interaction cross-sections interact and coalesce, but the cold dark matter particles with low interaction cross sections will pass right through as seen by astronomers when observing the gravitational effects of light passing through colliding galaxies.

Direct Observation of the Super Particles

The quarks in the super particle (the top quark and the bottom quark) have been directly observed as shown in reference 21, AP4.7V.
Model 1 gives enough physical details to allow for calculation of interaction cross-sections between visible and dark matter. Such a calculation was accomplished, and the result compared with experiments currently underway. The comparison was favorable, but the data are preliminary (ref 10, AP4.7E).
The results of the breakdown of super particles in particle space are currently being observed as extreme energy cosmic rays (ref 15, AP4.7I).
A means of extracting a super particle out of its barrier shell and observing it has been proposed, and will be pursued (ref 16. AP4.7L)

New Lines of Research

Model 1 provides entry into some new lines of research, namely.

Most important, a method of extracting a super particle from its shell and observing it has been proposed (ref 16, AP4.7L).
The details of the extremely high-energy cosmic ray data may give some detailed information on super particles (ref 15, AP4.7I).
Model 1 provides a means of calculating the cross section of interaction between visible and dark matter. This can be used to search for dark matter particles, and their characteristics. This search has already begun (ref 10, AP4.7E)
Estimates of dark matter distributions have been proposed from astronomical observations of gravitational lensing. Those estimates can be checked in detail with the theory presented here (ref 8, AP4.7B).
Several lines of research resulted from the procedure to calculate particle mass (ref 21, AP4.7V).

Summary and Prognosis

We ask now what the current state of Model 1 is as follows.

Mathematical Self-Consistency

The relationship between the three mathematical disciplines used appears to boil down to the details of the energy and size range where the equations used are valid. Work is still needed in this area.

Agreement with the Physical Data from Astronomers

Model 1 correctly predicts the data obtained by astronomers.

Connection with Currently Accepted Results of Physical Theories

Model 1 connects with the standard model of particle physics, quantum mechanics, and general relativity in an apparently correct manner. Particle mass calculations provide excellent corroboration with the Standard Model.

Models other than Model 1 as competitors

None of the main competitors for theories of dark matter and dark energy can satisfy all of the experimental data currently available.

Predicting Unknown Phenomena

Model 1 predicts and satisfies at least three unusual phenomena that cannot be explained with any other theory. The particle mass calculations provide excellent corroboration with existing particle mass data.

Direct Observation of the Super Particles

Details from Model 1 were used to calculate an interaction rate for dark matter particles and a result was obtained. An existing program has obtained preliminary results that agree with the prediction, but confirmation is needed.

New Lines of Research

Four new lines of research were discovered in the course of this investigation. Most important is a method of extracting the super particle from its barrier shell and observing it.

Although some work is needed, it appears that Model 1 should be a leading contender for a theory of dark matter and dark energy. There are three remaining factors that have not been satisfied, however.

Several theoreticians must investigate model 1 over a span of time to insure that no mistakes have been made in its development.
A lot of data are being generated on these subjects right now. These new data must be investigated to be sure they do not conflict with Model 1.
Most important, a method of extracting the super particle from its barrier shell and observing it has been proposed. A result should be obtained.

In the final analysis, however, the most important issue is how well Model 1 fits the data. For example, some unusual methods of describing physical systems (Kane, 19ff) have been used in quantum mechanics. There, the only justification is that the methods work. They describe the physical systems well, however, and so have been accepted.

References

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L. H. Wald, Model 1-C “Explaining the Dark Matter Halo” www.Aquater2050.com/2017/02/
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