Abstract

There are currently eight connected major unanswered questions in physics and astrophysics. The most important of these are:

• How can dark matter be explained and described?
• How can dark energy be explained and described?
• How can the theories of symmetry and the Higgs field be used to calculate the masses of the fundamental particles? 

A self-consistent theory called Model 1  has been developed that answers these questions quantitatively. The unique features of this model are:

• There are two spaces in the universe, particle space and quantum vacuum space. A potential barrier composed of Higgs field 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 (energy ~10¹⁷GeV) that operate with unified force. They then pass into the high-energy vacuum space where they become dark matter (super particles) operating behind the potential barrier (potential energy ~10¹⁹GeV).

• Dark matter particles interact with each other and form a slowly building and moving bubble centered on a galaxy. Corridors of dark matter form a cosmic web between the galaxies, which guide the development of new galaxies and connect the bubbles of dark matter to each other.

• The dark matter particles in vacuum space gain energy and eventually exceed the ability of the barrier to contain them. They then explode back into particle space as a big bang (Type 1). This process repeats to make a series of new universes, each with higher entropy.  Eventually, the entropy is high enough that a Type 1 big bang cannot occur, and the balance of pressure and density in particle space shifts, causing a complete collapse and a different type of big bang (Type 2). This Type 2 big bang restarts the Type 1 cycles. 

• 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. 

Considerable work has been done to show how Model 1 answers the important questions named and is an accurate description of nature (ref 3, AP4.7). In working out mass rotation for Model 1, some questions over the origin and operation of the enormous mass (~10¹⁷GeV) of the shielded super particles surfaced. In order to answer these questions, it became necessary to work out a model that allows us to calculate the mass of the proton and the fundamental particles that make it up from the theories of Symmetry and the Higgs field (ref 8, AP4.7V). This mass model (part of Model 1) then allowed us to work out a theory of the mass of the super particle, and its shield. However, this mass model left one of its parts unspecified, namely, the origin of the Higgs field and the connection between the Higgs field and general relativity. This paper will fill this hole in the mass model.

 

The Problem

Higgs found out that elementary particle mass is connected to a field that permeates space (Kane, 97). Schumm points out that mass appears to be the charge for the gravitational field (Schumm, 10). Shumm also notes that mass can be modeled by a screening effect with the Higgs field (see Shumm, 293-299). Most important, Einstein described a background independent way to connect mass to the curvature of space in the field equation (Misner, 431 and 41). In all of this, it seems that there is not an intrinsic mass in the fundamental particles of the nucleus. The mass appears to come from the interaction of the Higgs field and the mass charge of the particle.

In a prior paper (ref 8, AP4.7V), it was noted that a value of the Higgs field is specified by the value of the Boson particle masses. Further, we hinted that the Higgs field is the same as the real, scalar field of general relativity that controls space expansion (Peebles, 396). These facts introduce an important issue that was not addressed in reference 8, namely, the connection between the Higgs field and general relativity. This issue will be pursued here.

 

The Solution

There are five effects connected with mass that are usually treated separately.

• The origin of the Higgs field
• The inertial effects of mass
• The expansion and contraction of space
• The gravitational effects of mass
• The quantum connection between mass and the Higgs field

These effects are usually described with different theories, but they are closely related, and seem to require a unified theory. Such a theory will be described here. 

Origin of the Higgs Field

We expect a field to have a source-its charge. For example, the electric field has a source-the conserved electric charge Q. This charge results from the invariance of electromagnetic radiation phase throughout space (Noether’s theorem). The result is the electric field equation:

            ε = K_eQ/r²

Now we determine by experiment that the laws governing the generation of mass by Higgs field are invariant throughout space. Then there must again be a conserved quantity by Noether’s theorem-the conserved mass charge m. The mass as a charge was also suggested by Schumm (Schumm, 10). The result is the Higgs field equation:

            φ_h = K_ho m /r²               

We expect the Higgs field to be uniform in space, because the mass we measure, which is generated by the Higgs field is uniform in space, but the above equation indicates that the Higgs field might be lumpy, i.e. concentrated around mass particles. To explain why this conflict does not occur, we must look at three cases.

• The Higgs field averaged over the bubble universe. Here, the Higgs field comes mostly from the total distribution of mass in the universe. That distribution is uniform and smooth on a large scale, even though it is not on a small scale. Also, the constant K_ho is small. Thus a large amount of mass is required to generate a significant field, so the field must come from a distance that encompasses a large mass. For this reason, the Higgs field is relatively smooth and dominated by the average mass density of the universe until a test particle passes close to a localized mass. More important, mass formation is a quantum process, and as such it operates on thresholds. If the Higgs field is above the threshold necessary to generate mass, the correct mass will be generated, and it will not follow the variations in the Higgs field. In this case (particle space), the threshold is low, so the Higgs field required to generate mass is modest, and ordinary particles (~1 GeV) are generated with correct masses, and the mass remains constant even when the field fluctuates.
• The Higgs field averaged over the bubble shell of the super particle. Here, the Higgs field comes mostly from the mass of the bubble shell, which surrounds the bubble, and thus provides a smooth field. Some field also comes from the mass and kinetic energy of the super particle moving within the bubble shell, and this will cause fluctuations in local values. Again, the quantum nature of mass formation ensures that the correct mass is generated, and it remains constant. In this case (vacuum space), the threshold is high, so the Higgs field is high, and super particles (~10¹⁷ GeV) are generated with correct masses, and the mass remains constant even when the field fluctuates. The massive shell around the super particle maintains the Higgs field at a level above the threshold. If the shell is removed, the super particle decays to a particle space proton.
• The Higgs field averaged over the diffusion zone of the black hole where super particles are formed Here, the Higgs field is dominated by the mass and kinetic energy of the many particles in the black hole. The field is smoothed out in the diffusion zone where super particles are generated, and the threshold is high, so the Higgs field is high. The field can fluctuate, but super particles can form only where the Higgs field is high enough (above the threshold), so super particles are generated with the correct mass, and the mass remains constant even when the field fluctuates. After the super particles are generated, they are covered with a barrier shell, and they become stabilized, and can (and do) leave the black hole.

We note that the Higgs field emitted by the mass charge is a complex field containing both real and imaginary components.

The Inertial Effects of Mass Through the Higgs Field

The inertial effects of mass such as maintenance of velocity and resistance to acceleration can be modeled by a screening effect from the Higgs field (see Shumm, 293-299) that explains inertial 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 interfere with the oscillation of the original photon field. Thus the electric field in the medium will oppose the constant oscillation of the original photon field, and reduce it. 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. This screening range is similar to the range of a field with massive exchange particles, shown in the equation (see Kane, 29).

           φ = φ_o /4πr exp(-mr) (natural units 

Note that the field is significant in size only out to a range of r ~ 1/m (natural units), where m is the “effective mass”.

In a similar manner, we can model the mass of a quark or proton with a Higgs field that “drags” on the quark as it accelerates. If a free, decelerating proton passes through a medium (vacuum) filled with particles that create a relatively uniform Higgs field (visible and dark matter), the decelerating proton generates a decelerating Higgs field that interferes with the ambient Higgs field in particle space, and causes it to push back to reduce the relative motion toward zero deceleration. Thus the Higgs field in the vacuum will oppose the deceleration, and slow its movement down toward a lower constant velocity. We can model this effect by saying that the screening Higgs field generates an “effective mass” for the decelerating proton as shown above. We can, however, apply a force over a distance to the proton, and thus accelerate the particle to the energy necessary to raise the proton velocity up to its original (and higher) constant velocity. Note that this behavior is the inertial behavior of massive particles, and the particle obeys Newton’s laws. There does not appear to be any free inertial mass in a proton other than the Higgs “effective” mass. 

It is important to understand that the field described here is a real, scalar field, so the real part of the Higgs field can account for the inertial effects of mass, since in two prior papers (ref 8, AP4.7V and ref 9, AP4.7G) reasons are given to equate the Higgs field with the real part of the real, scalar field. 

The Expansion and Contraction of Space

In order to deal with the expansion and contraction of space, Peebles postulates the existence of a new real scalar field, and develops the equations for the field density ρ_f, and the pressure p in space from general relativity.The expansion and contraction of space in this zone is controlled by the following field density (ρ_f) and pressure (p) equations from general relativity (see Peebles, 396). 

            ρ_f = φ’ ²/2+ V = field density

            p = φ’ ²/2 – V = pressure 

            Where:

            V = a potential energy density

            φ = a new real scalar field = Higgs field

            φ’=the time rate of change of the field

            f’’ ²/2 = a field kinetic energy term

Also, from the field equation of general relativity, Peebles develops the cosmological equation for the time evolution of the expansion parameter (a(t)) due to mass density (ρ_m) and pressure (p) (see Peebles, 75):

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

Note from the field pressure equation, that if the potential energy exceeds the field kinetic energy, the field pressure is negative. Also, if the negative field pressure is large enough, it can dominate the density. 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.

It is important to understand that the field described here is a real, scalar field, so the real part of the Higgs field, and mass density can account for the expansion and contraction of space, since in a prior paper ( ref 8, AP4.7V) reasons are given to equate the Higgs field with the real part of the real, scalar field. 

Gravitational Effects of Mass

Einstein described a background independent way to connect mass to the curvature of space in the field equation (Misner, 431 and 41). He then used the field equation to show that gravitational attraction is due mass curving space, and does not require a force of attraction acting at a distance. The Newtonian equation for the gravitational force can be developed from Einstein’s field equaation (Meisner, 412).

Always remember, however, that mass is not the only thing that controls spatial curvature. There is a real, scalar field embedded in space that controls the shape of space as well (see Peebles, 396), and this field is the real part of the Higgs field.

The Quantum Expression for Particle Mass from the Higgs field

In reference 8, AP4.7V, the generation of mass m_p by the Higgs field f was described in some detail to yield the following quantum expression for particle mass-energy:

             m_p = (m_η²-λ_t φ ^2p)φ ².

                     = Km_η²φ^2p (1- λ_tφ ^2p/m _η²)

                     = Higgs mass corrected for self interaction              

            Where:

            K determines units of energy

            p = boson number

            λ_tf ^2p/m _η² = (single internal states factor)f ^2p /

                                       (external states factor)(total internal states factor)

                                   = H / (external states Higgs factor)

            H = internal states ratio or Higgs quantum number

Note here that the field used here is a complex Higgs field with an imaginary part, so both the real and imaginary parts are required to show how particle mass is generated from the complex Higgs field

 

Summary

We see that a complex Higgs field originating from the mass-energy of the particles in the universe and imbedded in space can account for all the effects of mass. We notice that:

• Mass generates the Higgs field in space.
• The Higgs field generates the inertial effects of mass
• The Higgs field works with the mass generated curvature of space to generate the expansion and contraction of space.
• The mass generated curvature of space works with the massive particles to generate the gravitational force on those particles.
• The complex Higgs field works with particle charge to generate the mass-energy of the basic particles.

In a simpler form, we may say that gravitational charge (mass-energy) generates the Higgs field; the Higgs field generates the mass-energy of particles. The mass-energy, and the Higgs field generate the curvature of space. The Inertial effects, gravitation and the expansion-contraction of space are side effects of the generation process.

 

Conclusion

We see that the real, scalar field in general relativity is compatible with and part of the Higgs field, but the real part of the field contains the dynamics of mass, and the imaginary part is required to generate mass. We may summarize the origin and operation of the Higgs field by saying; gravitational charge (mass-energy) generates the Higgs field, and the Higgs field generates the mass-energy of particles. The mass-energy, and the Higgs field generate the curvature of space. The Inertial effects, gravitation and the expansion-contraction of space are side effects of these generation processes

 

References

1. B. A. Schumm, Deep Down Things, Baltimore, Johns Hopkins University Press, 2004. G. Kane, Modern Elementary Particle Physics, Ann Arbor, Michigan, Perseus Publishing, 1993 
2. L. H. Wald, “AP4.7 DARK MATTER AND ENERGY-FUNDAMENTAL PROBLEMS IN ASTROPHYSICS” www.Aquater2050.com/2016/10/
3. Misner, Thorne and Wheeler, Gravitation, New York, Freeman and Co., 1973.
4. L. H. Wald, “AP4.7D HOW TO PROVE A THEORY’S CORRECTNESS” www.Aquater2050.com/2016/10/
5. L. H. Wald, “AP4.7I THE SUPER PARTICLE AS A COSMIC RAY” www.Aquater2050.com/2015/11/
6. L. H. Wald, “AP4.7L EXTRACTING SUPER PARTICLES FROM THE BARRIER SHELL” www.Aquater2050.com/2016/05/
7. L. H. Wald, “AP4.7V THE COMPONENTS OF MASS FOR MODEL 1” www.Aquater2050.com/2016/09/
8. L. H. Wald, “AP4.7G ORIGIN OF THE NEW SCALAR FIELD” www.Aquater2050.com/2015/12/