Abstract

In a previous paper (ref 1, AP4.7), a self-consistent, cyclical theory for the universe called Model 1 was developed, that is complete, self-constructing and regenerating. 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 moving halo centered on a galaxy. The halos of dark matter are connected to each other by corridors of dark matter forming a cosmic web, which guides the development of new galaxies.

• There, behind a potential barrier, the dark matter particles gain energy, build up in number and eventually exceed the ability of the barrier to contain them. They then explode back into particle space as a big bang. This process repeats to make an endless series of new universes.

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

Several observables were noted in the paper that support the model (see below), but nothing would be more compelling as support, than to actually extract a super particle from its barrier shell and observe its properties. We might also find that its properties are useful to us in other areas than the ones that nature has used. Here we investigate the possibility that super particles might be extracted from their barrier shells and observed.

 

The Problem

Model 1describes a separate vacuum space filled with high vacuum energy as well as high-energy particles. Furthermore, this space can export its energy into particle space under some circumstances (by tunneling, if the particle energy is low, and spilling if the super particle kinetic energy exceeds the shell potential energy). Thus if we can determine a convenient procedure to release the super particle from behind the barrier where it could be detected as a cosmic ray, the procedure would provide exceptional proof of Model 1.

This super particle will be difficult to release, however. We should first see if there is reason to believe that Model 1 actually represents nature, and so justifies the effort necessary to do this extraction. There is one very strong argument in favor of the acceptance of Model 1. To construct Model 1 we start with two basic constants from quantum mechanics and the standard model of particle physics (Force Unification energy and the Planck energy), and choose two new constants (the spherical barrier radius and the barrier thickness). We can then quantitatively explain five observed phenomena that have yet to find a single consistent explanation, namely:

• The accelerating expansion of the universe (Dark energy)-see ref 4, AP4.7I.
• The matter needed for creation and rotation of the galaxies (Dark matter)-see ref 2, AP4.7B.
• The UHECRs (cosmic rays) that have been observed in the energy range beyond the GZK cutoff-see ref 4, AP4.7I.
• The huge disparity in the different estimates of the vacuum potential (Kane, 112).
• The large-scale cutoff and asymmetry in the Microwave Background Energy-see ref 5, AP4.7F.

It is difficult to satisfy five separate observed phenomena with one small set of variables (kinetic and potential energies) for one theory (Model 1) unless those phenomena are truly related to those phenomena. For a more complete description of the theory and data that support Model 1, see ref 12 AP4.7D.

Thus there appears to be good reason to believe that Model 1 describes nature accurately, so let us see if Model 1 can be confirmed by extracting a particle from behind its barrier for observation. In order to determine how this extraction can be accomplished, consider the Schrödinger equation in the following form (see ref 1, AP4.7):

            [-(h²/2m d²/dr² + V(r)]U(r) = EU(r)  

            Where

            E = p²/2m = the energy of the particle with mass m and momentum p.

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

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

            w = the width of the potential zone.

The solution can be used to generate the transmission through the barrier T (see Ref 8), which is as follows:

If E>V

            T = 1/(1+V₀²sin²(k₁w)/4E(E-V₀)

If E<V,

            T = 1/(1+V_o² sinh²(k₁w)/4E(V₀-E),

            Where

            k₁= (2m_sp(V₀-E)/ђ²) ^½ = momentum of the super particle in vacuum space

            k_o = (2m_sp (E)/ ђ²) ^½ = momentum of the super particle in particle space

            m_sp = super particle mass

Clearly the transmission T is very low unless E is close to or greater than V₀

On the other hand, for the case of photon penetration of the barrier shell, we note that the barrier shell has no electric charge, and no magnetic moment, so it will not interact with electromagnetic photons and thus impede the passage of photons through the shell to the super particle where interaction can take place. Thus exchange photons can reach super particles in vacuum space, and participate in a force interaction such as electromagnetic attraction and repulsion in an ionized gas of super particles if the photon energy is high enough. However, although a low energy exchange photon from a particle in particle space can reach through the barrier to a super particle in vacuum space, it doesn’t have enough energy to impact the super particle’s function and thus be observed. 

In this paper we ask the question of what will happen if a specially generated, extremely high-energy photon is passed through the super particle barrier. Can such extreme energy photons increase the energy of a super particle enough to force its passage through the barrier into particle space, so it can be observed as an extreme energy proton?

 

The Solution

First we must set up the rate of passage equations for super particles to particle space. Here we set up the equations for either of two shells, a vacuum space sphere and a barrier shell. The rate of passage of a particle through either spherical shell for a galaxy is:

            R = T ћ k_o n_sp / m_spr particles/se

Now if

            n_sp = N_g = number density of super particles in a galaxy, R will be rate of passage into a galaxy.

            r = r_op tor_ob = r_ov then the rate is for travel in and through vacuum space.

            r = r_ob to (r_ob + a) then the rate is for travel in and through the barrier.

The best fit for the vacuum space sphere and the barrier shell of the rough data available is (see ref 6, AP4.7G for details):         

            r_op = 10^-20 cm

            r_ob = 10^-11 cm

            a = 10^-31 cm

There are two important cases

Case 1

            E > 10¹⁷ GeV

            V_ov = potential energy ~ 10¹⁷ GeV

            V_ov/cc = potential energy density ~ 10⁵⁰ GeV/cc

            N_g = number of super particles in vacuum space = 10⁶⁹ /galax

This is the vacuum space case for particles with potential energy ~ 10¹⁷ GeV-i.e. super particles. We note that super particles with kinetic energy greater than 10¹⁷ GeV move freely in vacuum space. If the kinetic energy drops below 10¹⁷ GeV, however, the probability of operating in and passage through quickly attenuates toward zero

Case 2

            10¹⁷ < E < 1.19 x 10¹⁹ GeV

            V_ob = 10¹⁹ GeV

            V_ob/cc = potential energy density ~ 10⁷² GeV/cc

            N_g = number of super particles in vacuum space = 10⁶⁹ /galaxy

This is the case of the leakage of super particles into particle space by tunneling through the barrier. In this case, T ~ 10^-50, and R is ~ 10³⁵ particles/sec galaxy. For all ~10⁸ galaxies of particle space, R is ~10⁴³ particles/sec. When these particles reach particle space, they break down to ordinary extreme energy particles (protons) and give up their phase change energy (10¹⁷ GeV/particle) into the particle space vacuum energy (dark energy), which over 10¹⁰ years has accumulated as the dark energy of particle space (~ 10^-4 GeV/cc). This is the same dark energy that causes the accelerated expansion of space.

Now we want to give the super particles enough energy so that they will flow out from behind the barrier at a rate higher than the natural tunneling rate so we can observe them in the laboratory. We don’t have a particle or gamma source with enough energy to knock the super particle out with one ultra high-energy particle or photon, so we must take advantage of resonance within the barrier shell to pump the energy up one lower energy photon at a time to obtain an E ~ V₀. This pump must operate fast enough to overcome energy leakage so buildup can occur, however. Thus there are certain conditions that must be satisfied (Wylie, 75).

• We must use electromagnetic energy, which will penetrate the barrier shell because the barrier has no electric charge or magnetic moment to interact with the electromagnetic photons, and because it can act on super particle ions to increase their energy.
• We must pump at the resonant frequency to insure the rapid buildup of energy of the particles, and take advantage of magnification.
• We must pump fast enough to overwhelm the damping for low energy super particles due to the potential energy in vacuum space (see Case 1, above).

With these conditions, we can pump with gamma photons at less than V₀ energy. Note that we will start with equations from classical mechanics here, but with proper definition of terms from quantum mechanics, these equations appear to be convertible to quantum equations. 

In order to investigate these conditions, let us construct a force equation from the above results of the Schrödinger energy equation development to determine the resonant frequency. This force equation has the form (Wylie, 82):

            -1/2m d²r/dt² + C_o dr/dt + V_o r = F_ocos ω

Now we define critical damping as:

            C_oc = 2(V_o /m)

Also we define the magnification ratio as:

            M = the factor by which a deflection of r_ov by a constant force must be multiplied in order to give the amplitude of the vibrations that result when the same force acts dynamically with frequency ω.

Then, according to Wylie:

            M = 1 / [(1 – ω²_/ ω_r²) ² + (2 ω/ω_rC/C_oc )²] ^½ 

Furthermore, note that the damping ratio C/C_oc can approach (but never reach) zero, so the magnification ratio can approach (but never reach) infinity.

Here we must pause to answer a fundamental energy question. The equation we used above is a force equation. We must ask where the energy comes from that we gain when we obtain a magnification. If we multiply the original force equation by an increment of radius, it becomes an energy equation. By using the resulting energy equation the physical process becomes clearer. The mass oscillates by trading potential with kinetic energy. When the mass position is at its maximum radius, the potential energy is at its maximum, and the kinetic energy is at its minimum. When the mass is moving through the mean radius, the kinetic energy is at its maximum, and the potential energy is at its minimum. At resonance, the electromagnetic drive (gamma rays) pushes the mass on each cycle at just the right time to reinforce the motion, and thus pushes the mass position to a greater radius. Thus the mass position is magnified. The magnification we obtain is the magnification of the envelope of the oscillations of the super particle within the barrier shell. If the damping is enough to absorb the energy of each push (critical damping), the energy is used up in damping, the mass returns to its original position, and the magnification is one. If the damping is less than the amount needed to absorb each push, the radius will increase each cycle, and magnification will be greater than one. Thus as the number of cycles increases, the radius will continue to increase until the return force can no longer contain the mass, and the mass will break free. As time goes on, an equilibrium is established in which free particles are generated at a rate determined by the rate of energy entry into the system.

Now we will quantize the classical equation above. If each reinforcing tap of energy is a quantum of gamma ray energy (hυ_r) at the resonant frequency υ_r, then the super particle position is pushed a bit further into the barrier shell before being reflected, and the super particle maximum potential energy V is raised a bit more. Also the maximum kinetic energy KE of the super particle inside the barrier is raised a bit as well. Some of the gamma ray energy is absorbed by leakage of super particles (tunneling) through the barrier, thus generating the damping term in the quantum energy equation.

            R = T ћ A k₁ n_sp / m_spr = T ћ A n_sp (2m_sp(V₀-E)/ђ²) ^½ / m_spr particles/se

            Where:

            A = barrier area

If the kinetic energy is less than the potential energy, the system is under damped, and the photon energy is being used to increase the super particle energy toward the potential energy. When enough small quanta have been absorbed so that the kinetic energy is equal to the potential energy of the barrier (V_ob), the energy will be high enough to exceed the ability of the barrier to return the super particle, and the super particle will break through the barrier. If the kinetic energy is equal to the potential energy, the damping is critical and all the incoming photon energy is being used to push super particles out through the barrier. As in the classical system above, an equilibrium is finally established in which free particles pass through the barrier at a rate determined by the rate of energy entry of gamma photons into the system. Note, however, that the super particles are in a Gaussian distribution of energy, and so only the super particles in the upper portion of the distribution (those that gain enough energy in a dwell time) will reach this equilibrium and push out particles directly.

Finally, under the influence of the forcing gammas, the envelope of the oscillations rises exponentially toward V_ov as follows.

            E / E_m = 1 – Exp [-t(C_o /2m)] 

            Where:

            C_o /2m = T(E-V_ov) / 4r_ov ћ k₁

            E_m = V_ob

There are two important cases for this system.

Case 1 Vacuum space. V_ov>E> V_ob The super particle moves freely in the vacuum space bubble, but is blocked from exit by the barrier.

Classical force equation. Magnification ratio M of the super particle builds with each cycle until it exceeds the return force.

            1/2m d²r/dt² = inertial force in dynes

            m = super particle mass ~ 10¹⁷ GeV = 10^-7 gm

            V_o  = V_ov / r_ov² = return force per unit distance ~ 10^-8 dynes/cm

            C_o = mT(E-V_ov) / r_ov ћ k₁ = dissipation per unit speed in dynes/cm/sec

            E = energy of the super particle ~ 10¹⁷ GeV = 10¹⁴ erg

            T = transmission through the vacuum sphere ~ small if E<V_ov, and ~1 if E>V_ov.

            F_ocos ωt = electromagnetic driving force (gamma rays) in dynes          

Quantum energy equation. Energy E of the super particle builds with the absorption of each resonant photon until it breaks through the barrier.

            Then the resonant frequency if C_o is small is:

            ω_r =  ν_r /2p = 1/2p [V_ov / r_ov² m]^½

                   = 1/2p x 10²¹ cy/sec

            λ_r = 10^-11 cm (see Appendix 1)

            Photon energy = hc/ λ_r  = 10⁶ ev

            C_o /2m = T(E-V_ov) / 4r_ov ћ k₁ = 10¹⁶ (E-V_ov)^½

            V_ov = 10¹⁷ GeV

            k₁= (2m_sp(E-V_ov)/ђ²) ^½ = (2mE(1- V_ov/E)/ђ²) ^½ = 10³¹(1-V_ov/E) ^½ 1/cm

            k_o = (2m_sp(E)/ ђ²) ^½ = 10³¹ 1/cm (for E mean ~10¹⁷ GeV)

 

Case 2 Barrier space E ~ V_ob

Classical force equation. The magnification ratio M of the super particle exceeds the return force after a single cycle.

            V_o  = V_ob / a² = return force per unit distance ~ 10^-61 dynes/cm²

            C_o = mT(E-V_ob)/ aћ k₁ = dissipation force per unit velocity in dynes/cm/sec

            E = total energy of the super particle

            T = transmission through the barrier ~ small if E<V_ov, and ~1 if E>V_ob.

            F_ocos ωt = electromagnetic driving force (gamma rays) in dynes.        

Quantum energy equation, Energy E of the super particle breaks through the barrier after absorbing a single resonant photon.

            Then the resonant frequency is:

            ω_r =  ν_r /2p = 1/2p [V_ob / r_ov² m]^½

                   = 1/2p x 10⁴² cy/sec

            λ_r = 10^-31 cm (see Appendix 1)

            Photon energy = hc/ λ_r ~10²⁷ ev = 10¹⁸ GeV (slightly under the Planck energy.)

            C_o /2m = T(E-V_ob) / 4r_ob ћ k₁

            V_ob = 10¹⁹ GeV

            k₁= (2m_sp(V_ob-E)/ђ²) ^½ = (2mV_ob(1-E/V_ob)/ђ²) ^½ = 10³³(1-E/V_ob) ^½ 1/cm

            k_o = (2m_sp(E)/ ђ²) ^½ = 10³³ 1/cm (for E mean ~10¹⁹ GeV)

Both cases are in the gamma ray range. Note that the resonant frequencies are such that a resonant gamma wave will fit neatly inside the vacuum shell (λ_r = 10^-11 cm) and the barrier walls (λ_r = 10^-31 cm) respectively as would be expected from quantum mechanics (compare with shell and wall size in reference 13, AP4.7A). Trying to put a quantum wave within potential energy boundaries alone would have predicted such resonant wavelengths. This agreement with expectations from quantum theory tends to support the acceptability of using classical equations along with quantum equations as proposed in this paper.

It is important to determine the time required to pump up the super particle energy to the barrier potential, in order to determine the size of the gamma generation zone required. Part of the particles in the thermal distribution in vacuum space will meet this requirement quickly, since the energy of some of the super particles in the vacuum Gaussian distribution are close to the barrier potential energy. However, if we take the worst case:

            E / E_m = 1 – Exp [-t(C_o /2m)] 

            Where:

            C_o /2m = T(E-V_ov) / 4r_ov ћ k₁ = 10¹⁶ (E-V_ov)^½ = 10¹⁵ sec, for E at its mean

            E_m = V_ob

Thus if enough forcing gammas are present, in ~10^-15 seconds, the envelope of the oscillations should have increased by a factor “e” driven by the gamma forcing function. hυ_r. In ~10^-13 seconds (dwell time), the envelope should have exceeded the shell potential, and the super particle should pass through

Now we must decide if we can generate gamma photons with the proper characteristics and at the correct rate. Ref 10 shows that generating gammas for Case 1 appears feasible using undulator or wiggler type synchrotron radiation generators. Gammas for Case 2 appear much harder, however, because of the extreme gamma energy. It may not be feasible to obtain enough photon energy to boost the super particle over the barrier potential with a single photon. A special type of gamma storage system may also be possible, however (see Appendix 1), although such a ring is highly speculative at present. Now we must determine the rate of gamma generation required, and the size of the gamma generation zone required.

There may be a problem in obtaining the above-mentioned dwell time. The dark matter is believed to rotate very slowly around the galactic center because it travels out from the central black hole rather than falling in from the outside under the influence of gravity as visible matter does. Now the visible matter is known to rotate around the galactic center at a speed of ~100 km/s at our radial distance from the center (Peebles, 47) (earth rotation speed around sun is ~ 30 km/sec, so galactic speed dominates). Thus there is a relative interaction speed between photons and particles of ~100 km/s (10⁵ cm/sec) In addition, the super particles passing out of the black hole have significant velocity heading toward the edge of the galaxy. They start just inside the event horizon at near light speed, but lose a significant portion of that speed in passing through the event horizon and escaping the black hole. We estimate they retain less than a tenth of that speed (<10⁹ cm/sec). This interaction speed might make it difficult to bathe one super particle passing through our gamma reactor in a beam of synchrotron generated gammas long enough to build up a resonance and increase the particle energy enough to cause the super particles to break through the barrier. In order to accomplish this goal, it will be necessary to shine the gamma ray beam down the evacuated rectangular tube (the reactor tube) in such a way that the gammas dwell on each volume of space in the tube for at least 10^-14 seconds. Now,

            t > L cm / 10⁹ cm/sec

            Where:

            L = tube length ~10 cm for convenience.

            Then,

            t > 10^-8 sec

Since this is much greater than the required dwell time (10^-14 seconds) of the gamma beam needed for a volume of the rectangular tube, the scan procedure in the tube will determine the dwell time needed to charge up the super particle energy E to V_ob. We will then continuously illuminate a tube with a beam H ~1cm high by ΔW ~10^-1 cm wide. We use these specifications because preliminary estimates indicate that they may be feasible with a Synchrotron radiation generator

After equilibrium has been established in the rate of passage of super particles through the barrier, the rate of appearance of super particles into particle space in a beam of gammas is determined by the rate of gamma input. Now each quantum of energy at the resonance frequency is 10⁶ ev. We assume that the polarization of the incoming gamma matches the direction of oscillation of the super particle. In order to exceed the barrier and push the super particle through it, we need to increase the kinetic energy by an amount

            ∆E = V_ob (1- E_m/V_ob) = 10¹⁹ (1- E_m/V_ob) GeV = 10²⁸ (1- E_m/V_ob) ev

            Where:

            E_m = ave starting energy of the super particle with the proper oscillation

                   =.10¹⁸ GeV 

            V_ob = 10¹⁹ GeV = 10²⁸ ev        

Thus, for each super particle passing through the barrier, the following number of photons coming in at the resonance frequency with energy 10⁶ ev must be absorbed

            ∆E / E_r ε = 10²⁸ (1- E_m/V_ob) / 10⁶ 10^-1.

                 = 0.9 x 10²³ gamma photons

Where:

            E_r = energy of the resonant gamma photons

                 = 10⁶ ev = 10⁶ x 10^-12 erg

            ε = efficiency of increase of super particle energy by the gamma photons.

               ~ 10^–

So in order to generate n_o super particles in each second, the power required is as follows.

            P = n_oV_ob (1- E_m/V_ob) E_r / E_r ε e

               =  n_o 0.9 x 10²³ x 10⁶ x 10^-10/ 10^-2 = n_o 0.9 x 10²¹ erg/sec

               =  n_o 0.9 x 10¹⁴ watts = n_o 0.9 x 10¹¹ KW

            Where:

            e = efficiency of conversion of electrical to gamma energy

               ~ 10^-2

In order to justify the efficiency numbers, we note the following. A generation rate of 10⁶ ev gammas in a fine beam with narrow polarization.is required to achieve the indicated rate of passage of super particles into particle space, and the efficiency of generation has three parts (1- E_m/V_ob), e, and ε. We start with the term (1- E_m/V_ob). In order to estimate this term_, we recall that the super particles are distributed in a Gaussian distribution that has a mean energy greater than ~10¹⁷ GeV, and a high-energy tail cutoff less than ~10¹⁹ GeV. Thus we estimate the average starting energy E_m to be ~10¹⁸ GeV, and (1- E_m/V_ob) = 0.9.

In order to estimate e_, we note that the generation of polarized synchrotron radiation is a relatively efficient process  (Ref 10). However, the direction of oscillation of the super particles is distributed uniformly in all directions, and interaction occurs only in the polarization direction.  But the beam will tend to align the nearly aligned super particles correctly, and many different super particles will pass through the reactor for the beam to select from. So we estimate the efficiency e to be ~10^-2.

Estimating the efficiency of increase of super particle energy by gammas ε is much more uncertain, as little is known about the details of this process., It is an electromagnetic process operating on the charge of an ionized super particle, so it can be quite efficient except for losses to internal states of the super particle. It should be noted that the internal states of the super particle are not known. Those states could absorb the applied energy of the gammas and keep that energy from producing the kinetic energy needed to force passage of the barrier. Thus it is not known if the above dwell time is enough time to cause the necessary buildup of energy needed to force a super particle over the barrier. If we measure gamma absorption bands, however, it may be possible to figure out where the energy is going. Then, we may be able to work out the procedures needed to increase the resulting kinetic energy.

 

Limitations to the Accuracy of the Results

As mentioned above, the applied gamma energy may not be converted efficiently into super particle kinetic energy because some of the energy may go into excitation of internal super particle states. Thus the super particles may not achieve the necessary energy to reach 10¹⁹ GeV and thus break over the barrier in a dwell time. We don’t understand the internal states well enough to determine the losses.

 

Summary and Conclusions

In this paper we have investigated the extraction of super particles through its spherical barrier. We found that the probability of transmission of super particles through the barrier may be increased by the excitation of the particles with a gamma ray pump. If it works correctly, a detectable number of super particles would result so they can be studied

It should be noted, however, that internal modes of the super particles may dissipate the gamma energy fast enough to lower the efficiency of the gamma ray pump, and stop the transmission. There may be a hint of the existence of super particles, however, if we measure the gamma energy absorbed. If we observe absorption lines, we could possibly determine the internal states absorbing the gammas. If this dissipation is severe enough, however, it may keep the particles from flowing over the barrier with the pump power currently achievable.

 

Appendix 1

Here we ask if it is possible to build a gamma storage ring. An undulater or wiggler type synchrotron radiation generator generates a very thin beam of photons. It may be possible to reflect such a beam against a sequence of dense metallic layers at a grazing incidence and form a ring. If the reflection coefficient were high enough, this ring would constitute a gamma storage ring, and it could then be used to pump up an intense, building, reinforcing gamma ring. This ring may be a much more efficient way to stimulate the super particles in our vicinity high enough to break over of their barrier.

 

References

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10.  https//en.wikipedia.org/Synchrotron_radiation#integrating
11.  P. J. E. Peebles, Principles of Physical Cosmology, Princeton, New Jersey, Princeton University Press, 1993.
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