ABSTRACT

There are currently eight 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 that consists of many parts has been developed that answers these questions quantitatively. These parts have been collected into a self-consistent set, which will be referred to as Model 1. 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. Corridors of dark matter forming a cosmic web, which guide the development of new galaxies connect the bubbles of dark matter to each other.

• 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 a long series of new universes.

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

One of the most important underlying pieces of Model 1 is the underlying vacuum. In reference 1, AP4.7P, it was shown that the underlying vacuum sets the primary physical constants E_pl, l_pl, and t_pl. When the mass-energy E_o of the universe is added, the basic components of the universe are determined. The basic structure and origin of the underlying vacuum was not specified, however. In this paper, the structure and origin of the underlying vacuum for Model 1 will be detailed.

 

The Problem

The basic components and operation procedures of the universe according to Model 1 are determined by the following physical constants (ref 1, AP4.7P).

A). The primary physical constants are set by the underlying granularity of space. They are as follows:

• The Planck energy E_pl is fundamental and unchanging. This constant sets the maximum energy for a particle in the universe. If the maximum is too small, no locally stable, recycling universe can exist.
• The Planck time t_pl is fundamental. This constant sets the minimum increment of time in the universe. The maximum time scale is set by the cycle time of the universe (see ref 2, AP4.7J).
• The Planck length l_pl is fundamental and unchanging. This constant sets the minimum increment of size in the universe. The maximum scale is set by the amount of mass in the universe.
• The amount of low entropy energy (mass-energy) that enters the universe E_o in the big bang is fundamental. This sets the maximum scale of the universe. If the amount is too small, no stable, recycling universe can exist (see Appendix 4). Thus it is set by natural selection (see C below).

Note that these constants appear to be primary because they define the Planck grain and it appears to be the fundamental factor for the granular vacuum.

B). The secondary physical constants are determined by the primary physical constants.  The secondary constants are:

• The constant c is truly constant, and is determined as:

            c = l_pl / t_p 

Note that c is the same as the velocity of light v only for photons in the mid energy range. For photons in the very high and very low energy ranges, light speed v is altered by the vacuum potential energy, and can be higher or lower than c, respectively (see ref 1, AP4.7M).

• The Planck mass m_p is truly constant, and is determined as:

            m_p =  ђ / c² t_pl= E_pl / c 

• The Planck constant is truly constant, and is determined as 

            ђ  =  E_pl t_p           

This constant sets the limit of uncertainty in measurement of energy and time in our universe (the energy uncertainty principle). Note that it also sets the limit of uncertainty in measurement of size (l_pl) and momentum (p_pl) ((the momentum uncertainty principle) in our universe as follows:

            ђ =  p_pl l_pl = (2 m_pl E_pl)^½ l_pl

• The gravitational constant G is truly constant, and is determined as 

            G = c⁵ t_pl² / ђ 

This constant defines how much mass is needed to make a black hole, and so how much mass is needed to make a long lived universe, because black holes are needed to make a locally stable, recycling universe (see ref 6, AP4.7N).

• The Lie symmetry groups determine how the energy that enters the universe in the big bang are partitioned into particles under the principle of equipartition of energy.  These groups come into play only if E_pl and E_o are large enough. Note that several different symmetry groups can partition the energy. Thus the one nature uses must be chosen by natural selection (see C below).
• The charges of the electromagnetic, weak, and strong forces must be related in a hierarchy of strength, or stable nuclei and atoms cannot form. The Higgs constants and the total mass of the universe must also be fixed correctly, or the mass-energy of the universe cannot recycle. Thus even though they appear independent, their choice is determined by natural selection to maximize recycle time (see C below).

C). The total mass energy E_o, the symmetry groups, and the charges can vary, and are determined by a natural selection process.

• The total mass energy E_o can vary, and is determined in a quantum collapse process by the amount needed to result in a long lasting, recycling universe.
• The symmetry group provides a particle energy organization principle to fit the particles within the energy span bounded by the maximum energy (E_pl), and allow them to function without interfering with each other. 
• The charges work with the symmetry group in a way that ensures a maximum recycle time.

Thus setting the total universe mass-energy E_o along with the fundamental constants would completely define the basic characteristics of the resulting universe through natural selection. If E_o is too small, no universe will form. If it is large enough, a natural selection process will concentrate the mass energy into the particles with symmetry groups and charges similar to ours. Note that the resulting universe will allow for the existence of life, but that characteristic is not the reason it is the most probable (see ref 3, AP4.7Q for more details).

The purpose of this paper is to explore the structure, origin and operation of the underlying vacuum space for Model 1 by describing its structure, showing how the primary physical constants are set, and how E_o is provided.

 

The Solution

Model 1 is based on a basic axiom-that the universe is fundamentally causal. That is, each particle and action we observe has a cause, whether we can discover it or not. This axiom must be kept in mind to understand this paper. Further, we note that the time dependent version of the Schrödinger equation and the General Relativity equations are used together even though the quantum gravity theory is not yet complete. An attempt has been made to consolidate the two theories in Loop theory (see Appendix A), but this theory is not yet ready to be used for physical predictions. Therefore we will use the existing versions of the equations assuming the results have meaning, and explore the results to see if they agree with existing experiments.

1). Granular Space

We start with an underlying granular space. We adopt Wheeler’s model of space with some modifications (ref 8). In 1955, John Wheeler proposed that a concept called Quantum Foam be used to describe the foundation of the fabric of the universe. At scales of the order of a Planck length, the Heisenberg uncertainty principle allows energy to decay into virtual particles and anti particles and then annihilate back into energy without violating physical conservation laws. Any particle with energy less than E_p (and thus all particles) can appear this way. At the Planck scale, the energy density involved is extremely high, and so according to general relativity, it would curve space-time tightly and cause a significant departure from the smooth space-time observed at larger scales. 

We see then that the energy in a grain of space would be expected to oscillate between the potential energy, the mass and the kinetic energy forms as seen in the Schrödinger equation in a time less than the Planck time, and this oscillation would not be noticed on a scale larger than the Planck scale. Because of this rapid oscillation, the total of the potential energy, kinetic energy and mass energy would average to zero, and so the large-scale curvature of space alone would be zero and space flat. We see further that at tiny scales (a Planck scale), space would have a “foamy” or “grainy” character even though on a large scale, space would appear smooth, flat and empty. Then virtual particles could pop in and out of existence from Planck potential energy for a Planck time. According to this proposal, the Planck grain size is the smallest possible size, and the Planck energy is the largest possible energy, and the separation of the edges of these grains must be at least a Planck distance. Note that the time of existence of a virtual particle as determined by the uncertainty principle is extremely small, so the flickering of the energy to virtual particles and back from the grains would not be noticeable to the real particles or photons passing through, but real particles and photons would notice the high energy of the grains, and thus be aware of the grain’s existence. Thus we have defined a vacuum composed of grains with high potential energy that yield virtual particles that flicker in and out of existence so fast that a particle or photon passing through will only see the high energy of the grains, not the particle or photon.

2). The Primary Physical Constants

According to Model 1, in the original, primal granular space, the primary physical constants are in a mixed (combined) quantum state, until they are tested by trial in a real universe. The mixed state is unstable, and wants to collapse, but it will collapse into a single state only when tested by successful trial in a real universe. If the single state is not long-lived, the universe will revert back to the mixed quantum state. In our universe, the state happened to collapse onto a set of values that created a long-lived universe. The primary physical constants collapsed into the following values:

            l_p = 1.62 x 10^-33 cm

            t_p =  5.38 x 10^-44 sec

            E_p = 1.22 x 10¹⁹ GeV

These constants are independent and define the structure of the underlying granular space. These primary constants then define most secondary constants. There was an absolute independent time unconnected to space consisting of the sum of the times t_p. There was a space unconnected to time consisting of the sum of the lengths l_p in any direction. There was an energy consisting of the sum of the energies E_p. Time, space and energy were linear sums of l_p, t_p, and E_p at this primal time.

The energy in the grains of the primal universe continued to oscillate between the potential energy, the mass and the kinetic energy forms in a time less than the Planck time until, by chance, the energy in a huge number of grains all oscillated to mass at one time and in one local zone. At this time, a significant quantity of real mass-energy E_o has been generated in one zone, and if large enough, it would begin to move from the local zone and start the formation of matter (see section 3). This matter formation would cause a collapse into one real quantum state with single values of l_p, t_p, and E_p. After the collapse, the primary physical constants are the same everywhere and everywhen in granular space, so the laws of physics are the same, and there must be a universal charge (Noether’s theorem). In this case, the charge is the potential energy in each granule, which is conserved. Also, after this time, there is long-lived mass-energy in a local zone, so the laws of general relativity become relevant. Finally, after this time, the Higgs field has come into existence controlled by the mass as its charge (see Appendix C), and effectively increases E_o by a Higgs screening effect (see ref 9, AP4.7S for more details).

3). Variable Physical Parameters, and Natural selection.

Now we must determine how the other physical parameters are determined. For comparison purposes recall (ref 1, AP4.7P), that in the case of recycling universes, the particles that result from the prior universes are determined as follows:

• Particles that collide and create real energy in an accelerator (much less than the Planck energy) don’t disturb the laws of their universe, and so create new particles with symmetry and charge consistent with the physical laws of their universe.
• Super particles that collide and create real energy at less than Planck energy level after flowing over the barrier shell in a big bang retain their symmetry and charge values and the universe retains its physical laws.
• Particles and super particles that collide and create real energy at the Planck energy level after collapsing in a big crunch lose their symmetry and charge values and the universe has the possibility of changing the physical laws determined by them.

For these cases, the amount of mass-energy in the new universe is determined by the amount passing from the old to the new universe. That amount is equal to the amount present in the old universe.

In the case of the formation of the very first universe, the process is more complicated. This process can be summarized as follows.

• A random process selects primary physical constants, and a large group of matter and anti matter particles forms by a chance collection of mass-energy E_o in the granules of a local zone of the granular space. This happening is very rare.
• The matter and anti matter particles can collect together only for a large mass in a local zone (Appendix B). The large mass then may or may not form a bubble universe. If the amount of matter (from E_o) gathered into the bubble is large enough, the acceleration of the expansion parameter ä/a can turn negative (appendix B), the particles formed will move toward each other, an edge of the local zone can be defined, and a bubble universe can form, thus collapsing the mixed state into a single state (see equations, Appendix B). If the amount of matter is too small, the potential energy density will control, ä/a will always be positive, and the matter particles temporarily formed will move away from each other and not form a bubble universe. Then granular space will revert to the mixed quantum state.
• Once sufficient mass-energy E_o is collected and a bubble universe is started by the collapse of the mixed to the single state, the process of forming matter and anti matter with an excess of matter will start (see Appendix B)
• Any number of universes can start in the same granular space, and all of the universes started would have the same primary physical constants because they originate from the granular space where the conserved charge (potential energy) exists. The secondary constants subject to natural selection to lengthen the lifetime can be different in each universe, but the changes are limited by the fixed primary physical constants. One universe in the single state vacuum will confirm and maintain its existence
• If the incipient universe can complete the matter formation step, it will have a complete test of its state, the collapse will be permanent, and it will then start oscillating in a series of big bangs as described in reference 5, AP4.7N 

We have seen that space has a relatively complex structure. Its structure and operation have been described and appear to be understandable. We note that the energy of our universe does not have to come from outside the universe because it is built into its structure. The causal nature of the universe implies that the origin of space involves a discussion of the cause of its structure. Thus we must ask here, “Why is there something, rather than nothing at all?” This discussion is beyond the scope of this paper because the answer lies beyond the realm of physics.

With this description, the structure and operation of the underlying vacuum of space for Model 1 has been described

 

Summary and Conclusions

In this paper the structure and operation of the underlying vacuum of space for Model 1 has been described by showing its structure, and how the primary physical constants are set, and how E_o is provided. The origin of vacuum space with all its complexity, involves a discussion of a first cause, and so is beyond the scope of this paper and was not discussed here.

 

Appendix A

In doing this work, it was necessary to answer certain basic questions about physics. This requires the use of Schrödinger’s equation of quantum physics, the results of the Standard Model of particle physics, and general relativity. Some of these results (Smolin, 250) are already available from Loop Quantum Gravity, and they appear to be 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 therefore Schrödinger’s equation and for General Relativity as well (Gambini, 161). It predicts gravitons at low energy. Especially, it predicts a Newtonian type gravitational force. 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. However, the Loop Quantum Gravity basis is not complete, so the precise form of Schrödinger’s equation needed here is not available (Gambini, 237). Therefore we will use the standard forms and see if the results agree with experimental results.

Appendix B

The details of the process that generates matter particles are important (ref 1, AP4.7N). As indicated above, matter and anti matter particles are formed from the potential energy in the Planck granules, and then annihilate back into energy in less than a Planck time. A slight excess of matter particles can result. This excess can happen only if (Kane, 290):

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

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

Now the conservation of baryon number was violated as soon as the particles formed from the Planck granules. Also CP is normally violated in the particle formation process. However, particle space will be in thermodynamic equilibrium during this process, because the granules are in close proximity and cannot diffuse away from each other, so no excess matter will form. Thus the granules in the vacuum will maintain a steady and uniform formation and annihilation cycle, so space will remain smooth and flat. On the other hand, when quantum chance causes many matter and anti matter particles to form in a local zone at one time, the particles can and will diffuse away rapidly from the over dense zone, thermodynamic equilibrium will be lost, and an excess of matter particles and annihilation photons will be formed. The matter particles will obey the laws of general relativity, and so form a cycling bubble universe following the field density ( ρ_f) and pressure (p) equations from general relativity (see Peebles, 396):

 ρ_f = ø’ ²/2+ V = field density

 p = ø’ ²/2 – V = pressure

            Where:

            V = a potential energy density

            ø = a new real scalar field

            ø’=the time rate of change of the field

            ø’ ²/2 = a field kinetic energy term 

Also, the cosmological equation for the time evolution of the expansion parameter (a(t)) due to mass density (r_m) is (see Peebles, 75):

            ä/a = -4/3πG ( ρ_m+ 3p) = acceleration of the cosmological expansion paramete           

Note from the field pressure equation, that if the potential energy exceeds the field kinetic energy, the field pressure is negative. Also if the field pressure is large enough, it can dominate the pressure. Thus if the negative field pressure term is large enough to exceed the mass density term, the acceleration of the cosmological expansion parameter ä/a turns positive, and space expands. If the potential energy V is small compared to the field kinetic energy term, field pressure is positive, the acceleration ä/a is negative, and space contracts. The changing conditions of potential energy and mass density in the universe will then cause the universe to cycle (see ref 5, AP4.7N).

It is important to observe that if the amount of matter (from E_o) gathered into the bubble is large enough, ä/a can turn negative, an edge of the zone containing the matter can be defined, and a bubble universe can form. If the amount of matter is too small, potential energy density will control, ä/a will always be positive, and the matter particles formed will diffuse away and not form a bubble universe. 

Appendix C

The relation between the potential energy density, the rest mass of particles and the Higgs field f_h is as follows. Recall that in reference 12, AP4.7G, a connection was made between the above-mentioned new real scalar field of general relativity f and the Higgs field f_h, so we will only use one field f. We start with the Lagrangian (Kane, 98):

            Lagrangian = T – V = ½∂_μf ∂ ^μf – (½μ²f ²+ ¼ λf ⁴)                (3 

            Where:

            T = kinetic energy

            V = ½μ²f ²+ ¼ λf ⁴ = potential energy               (4 

By expanding around the minimum of V, and using perturbation theory, the equation is found to describe a particle with mass m_η (Kane, 100) where:

            m_η² = -2 μ²  

 

If the kinetic energy of the particle is zero, m_η is the rest mass. This is only one example of several that describe the complete Higgs field operating in the standard model. It is generally typical.

 

This rest mass can be modeled by a screening effect with the Higgs field (see Shumm, 293-299) that explains mass formation. To explain this effect, we compare it with the screening effect of electrons on photons. If a photon passes through a medium filled with free electrons, its oscillating electric field oscillates the electron charges, and they generate opposing photons that tend to cancel the original photon. This tendency is called screening, and it gives a finite range to a photon in conducting media. We can model this effect by saying that the screening electric field generates an “effective mass” for the photon even though the photon has zero mass and infinite range (see Kane, 29). In a similar manner, we can model the mass of a particle with a Higgs field that “drags” on the particle as it accelerates. If an accelerating particle passes through a medium filled with a uniform Higgs field in such a way as to reduce its acceleration, it gives its accelerated motion a finite range. We can model this effect by saying that the screening Higgs field generates an “effective mass” for the accelerating particle even if the particle has zero intrinsic mass (see Kane, 29). If the particle has small kinetic energy, we will call this effective mass the rest mass of the particle.

To complete this description, we must describe where the Higgs field comes from. The electric field has a source-the electric charge. Schumm points out (Schumm, 10) that mass appears to be the charge for the gravitational field. Then perhaps the Higgs field has as its source the particle mass charge. If so, the field diverges from its particle mass source and becomes less with distance according to the equation:

             ø = ø_o m_η /r²               (5) 

We might therefore expect the Higgs field to be lumpy. But to get the mass generation effects we observe, the Higgs field should be relatively uniform. To explain why this conflict does not exist, we must look at the following situation.

• The Higgs field in the universe comes from the total distribution of mass in the universe. That distribution is smooth on a large scale. Thus the Higgs field from mass at a long distance is smooth, and there is a significant amount of it because of the huge mass in the universe. The Higgs field from a medium distance mass is only slightly lumpy, and it is slightly important because the source is nearer, and the interaction frequent. The Higgs field from very close mass could be important because it is close, but it is not. A particle only feels the Higgs source from close masses for a very short time because of the high relative velocity of the particle and the mass, and such a glimpse is rare except in black holes, so the particle does not experience a screen that gives an effective mass. Thus the field comes from a distance, it is smooth, and the screen is effective.

 

References

1. L. H. Wald, “AP4.7P RELATIONSHIPS BETWEEN THE PHYSICAL CONSTANTS” www.Aquater2050.com/2016/05/
2. L. H. Wald, “AP4.7J CYCLE 1 AND THE CYCLICAL UNIVERSE” www.Aquater2050.com/2016/01/
3. L. H. Wald, “AP4.7Q THE CHARACTERISTICS OF THE PRIMAL UNIVERSE” www.Aquater2050.com/2016/05/
4. L. H. Wald, “AP4.7M VARIABLE LIGHT SPEED AND MODEL 1” www.Aquater2050.com/2015/12/
5. L. H. Wald, “AP4.7N A NEW CONCEPT OF MASS FOR MODEL 1” www.Aquater2050.com/2016/01/
6. L. Smolin, The Trouble with Physics, Boston, New York: Mariner Books, 2006.
7. G. Kane, Modern Elementary Particle Physics, Ann Arbor, Michigan, Perseus Publishing
8. Quantum Foam, HTTP:/en.wikipedia,org/wiki/Quantum_foam/
9. L. H. Wald, “AP4.7S STRUCTURE OF THE BARRIER SHELL” www.Aquater2050.com/2016/07/
10. B. A. Schumm, Deep Down Things, Baltimore, Johns Hopkins University Press, 2004.
11. R. Gambini and J. Pullin, Loops, Knots, Guage Theories and Quantum Gravity, Cambridge University Press, 1996.
12. L. H. Wald, “AP4.7G ORIGIN OF THE NEW SCALAR FIELD” www.Aquater2050.com/2015/12/