For updated version—see www.Aquater2050.com/2016/01/

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 building and moving bubble centered on a galaxy. The bubbles 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 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

This paper could be the culmination of all the prior work done on Model 1. This model describe 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, and spilling if the super particle kinetic energy exceeds the shell potential energy). Thus it might possibly be a source of energy for us in particle space if we can determine a convenient method to release it from behind the barrier. Such  a release procedure would provide an unlimited source of energy to convert into electrical energy if it is possible. It could also be a source of energy and reaction mass for stellar drives for space ships.

This energy 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 it 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 1, AP4.7.
• The process of creation and rotation of the galaxies (Dark matter)-see ref 2, AP4.7B.
• The UHECR (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.

Two variables cannot satisfy five equations without apriori connections in at least three of those equations. Not since the discovery of Planck’s constant have so many phenomena been explained by so few constants.

In order to determine how this extraction can be accomplished, consider the Schrödinger equation in the form (see ref 1, AP4.7):

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

Where:

            E = the energy of the particle.

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

And:

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

            w = the potential zone width.

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= (8p²m(V₀-E)/h²) ^1/2

            k_o = (8p²m(E)/h²) ^1/2

Clearly the transmission T is very low unless E is close to or greater than V₀. In this paper we will investigate how this transmission can be increased.

The Solution

First we must set up the rate of passage equations. 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 h/2p k_o n_sp / mr particles/sec

If:

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

            n_sp = N_u = number of particles in the observable universe, R will be rate of passage into the observable universe.

            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 /galaxy

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

            E ~ 10¹⁷ 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 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 particles and give up their phase change energy (10¹⁷ GeV/particle) into the particle space vacuum energy, or dark energy, which over 10¹⁰ years has made a dark energy of ~ 10^-4 GeV/cc. This is the same dark energy that causes the accelerated expansion of space that requires a potential energy of ~ 10^-4 GeV/cc.

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 of the zero rest mass of 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 be using equations from classical mechanics here, but with proper definition of terms from quantum mechanics, these equations appear to be applicable.

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:

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

There are two important cases that connect with the above cases.

Case 1 Vacuum space.

Here:

            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

            T = transmission through the barrier ~ 10^-50 if (E-V_ov) is large, and ~1 if small.

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

Then the resonant frequency if C_o is zero is:

ω_r /2p = 1/2p [V_ov / r_ov² m]^½

                       = 1/2p x 10²¹ cy/sec

And

            λ_r = 10^-11 cm

Photon energy = hc/ λ_r  = 10⁶ ev

Case 2 Barrier space

Here:

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

            C_o = mTV_ob / aћ k₁ = dissipation force per unit velocity in dynes/cm/sec

Then the resonant frequency is:

ω_r /2p = 1/2p [V_ov / r_ov² m]^½

              = 1/2p x 10⁴² cy/sec

And:

            λ_r = 10^-32 cm

            hν = 10²⁷ ev

Both cases are in the gamma ray range. Now we must decide if we can generate gamma rays accurately and in significant quantities. Ref 10 shows that generating gammas for Case 1 appears feasible using synchrotron radiation generators. Gammas for Case 2 appear much harder, however, because of the extreme gamma energy. They may not be feasible to generate.  

Now remember that the system must be under damped in order to obtain the magnification ratio needed to achieve barrier breakthrough, so:

            C_o²  – 4V_o /m < 0          

Thus,        

            [mTV_ov / r_ov ћ k₁]² – 4V_ov / r_ov² m < 0

This implies:

            (E – V_ov) > 10^-11/4

Most of the particles in the thermal distribution in vacuum space meet this requirement, since the mean energy of the super particles in vacuum space is greater than the vacuum space potential energy. Thus the super particles in vacuum space are mostly under damped.

Now we define critical damping as:

            C_oc = 2(V_o /m) ^½ 

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 (Wylie, 82):

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

Furthermore, note from above that the damping ratio C/C_oc approaches (but never reaches) zero for the super particles in the upper half of the thermal distribution, so the magnification ratio approaches (but never reaches) infinity for the high-energy particles. Thus, the magnification ratio becomes very high for the upper half of the thermal distribution.

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

Exp (t C_o /2m) 

 Where:

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

Thus in ~10^-15 seconds, the envelope of the oscillations has increased by a factor “e” driven by the gamma forcing function F_ocos ωt. Clearly the particle energy E is increasing very rapidly under the influence of the gamma beam.

There is a problem, however. The dark matter is believed to rotate very slowly around the galactic center because it diffuses 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. This interaction speed will make it difficult to focus our beam of synchrotron generated gammas on one set of super particles 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 focusing, it will be necessary to shine the gamma ray beam down an evacuated tube, and point the tube in the direction of the incoming flux of dark matter. The tube will have to be long enough to ensure that the beam will dwell on a single super particle long enough to cause resonance and thus force a super particle break out over the wall. We estimate this tube length as follows. Assuming the super particles move at 100 km/sec due to rotation around the galactic center, the time the super particles spend in the tube filled by gammas is:

 t = L cm / 10⁷ cm/sec

Where:

            L = tube length

We choose an L of 10² cm for convenience.

Then,

            t = 10^-5 sec

This is clearly much greater than the “e” rise time of 10^-15 seconds, so the super particle will be in the gamma beam the requisite time.

It should be noted that the internal states of the super particle that could dissipate the applied energy of the gammas are not known. Thus it is not known if 10^-5 seconds is enough time to force a super particle out over the barrier. However, 10^-5 seconds certainly means a large number of gammas passes through the tube. It seems likely, however, that the gammas must be coherent over the 10^-5 second duration of the interaction to insure that the gamma frequency remains matched to the resonant frequency during the interaction period. . With coherence, the number of cycles of interaction may be enough to ensure that the high-energy super particles can respond and achieve the magnification needed to push the particle close to 10¹⁹ GeV and thus force it beyond the barrier.

Reference 10 indicates that the frequency and polarization of the synchrotron gammas can be controlled within limits. If the pumping efficiency is high enough, and the polarization is stable, the application of these polarized, coherent gammas to the super particles will force the super particles through the barrier along a line parallel to the beam in both directions perpendicular to the beam and thus make a line source of super particles along both sides of the tube. If the tube is attached to a space ship and the super particles are absorbed by the ship on one side and released to space on the other, the tube becomes a thruster for the ship. In addition, the absorbed particles will heat the absorber, and the heat can be used to generate electricity for gamma production. Remember that the super particles exit vacuum space at ultra high energy, and so are traveling at a speed higher than normal light speed, so the drive efficiency (specific impulse) is very high.

Limitations to the Accuracy of the Results

As mentioned above, the applied gamma energy may not be absorbed efficiently enough or be given fast enough to insure that the super particles achieve the necessary magnification due to resonance to reach 10¹⁹ GeV and thus break over the barrier. This problem may occur because we do not understand the internal modes of the super particle well enough to be sure that the energy will not be dissipated too fast in internal modes to achieve this breakthrough.

Summary and Conclusions

In this paper we have investigated the transmission of super particles through and over its spherical barrier. We found that the transmission of super particles through the barrier may possibly be increased by the excitation of the particles with a gamma ray pump. We found also that the increased flow of super particles can be turned into a high efficiency drive for space ships if the efficiency of the gamma ray pump can be made high enough.

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.

References

1. L. H. Wald, “AP4.7B SHAPING THE DARK MATTER CLOUD” www.Aquater2050.com/2015/09/L. H. Wald, “AP4.7 DARK
2. MATTER AND ENERGY-FUNDAMENTAL PROBLEMS IN ASTROPHYSICS” www.Aquater2050.com/2015/09/

3. L. H. Wald, “AP4.7C DARK MATTER RATE EQUATIONS” www.Aquater2050.com/2015/09/
4. L. H. Wald, “AP4.7I THE SUPER PARTICLE AS A COSMIC RAY” www.Aquater2050.com/2015/10/
5. L. H. Wald, “AP4.7F GATHERING FOR THE BIG BANG” www.Aquater2050.com/2015/10/
6. L. H. Wald, “AP4.7G ORIGIN OF THE NEW REAL SCALAR FIELD” www.Aquater2050.com/2015/10/
7. L. H. Wald, “AP4.7J THE COMPLETENESS OF MODEL 1” www.Aquater2050.com/2015/11/
8. G. Kane, Modern Elementary Particle Physics, Ann Arbor, Michigan, Perseus Publishing.
9. C. R. Wylie, Jr., Advanced Engineering Mathematics, McGraw-Hill Book Company, Inc. 1951.
10.  https//en.wikipedia.org/Synchrotron_radiation#integrating
11.  P. J. E. Peebles, Principles of Physical Cosmology, Princeton, New Jersey, Princeton University Press.