Systems, Methods and Apparatus for Experimental Gravity Modification

Abstract

Systems, methods and apparatus are provided through which in some implementations an experimental apparatus to modify gravity includes an electrically conducting dome, three or more electrically conducting coils attached to the interior of the electrically conducting dome, and a power source electrically coupled to the electrically conducting coils, the electrically conducting coils configured to generate rotating electromagnetic fields that form a Poynting vector vortex, that produces a gravity force that is perpendicular to the Poynting vector vortex.

Claims

1. An experimental apparatus to modify gravity, the apparatus comprising: an electrically conducting dome; three or more electrically conducting coils attached to an interior of the electrically conducting dome; and a power source electrically coupled to the electrically conducting coils, the electrically conducting coils configured to generate rotating electromagnetic fields that form a Poynting vector vortex, that produces a force that is perpendicular to the Poynting vector vortex.

2. The experimental apparatus of claim 1, wherein the apparatus further comprises being centered and symmetrical about a center axis.

3. The experimental apparatus of claim 2, wherein the electrically conducting coils further comprise being positioned symmetrically about the center axis.

4. The experimental apparatus of claim 1, wherein each of the electrically conducting coils further comprise being identical to each other.

5. The experimental apparatus of claim 1, wherein the three or more electrically conducting coils further comprise no more than three electrically conducting coils.

6. The experimental apparatus of claim 1, wherein the three or more electrically conducting coils further comprise no more than four electrically conducting coils.

7. The experimental apparatus of claim 1, wherein the three or more electrically conducting coils further comprise no more than eight electrically conducting coils.

8. An experimental system to modify gravity, the experimental system comprising: an electrically conducting dome; three or more electrically conducting coils attached to an interior of the electrically conducting dome; and a power source electrically coupled to the electrically conducting coils, wherein the electrically conducting coils are configured to generate rotating electromagnetic fields that form a Poynting vector vortex, that produces a force that is perpendicular to the Poynting vector vortex.

9. The experimental system of claim 8, wherein the system further comprises being centered and symmetrical about a center axis.

10. The experimental system of claim 9, wherein the electrically conducting coils further comprise being positioned symmetrically about the center axis.

11. The experimental system of claim 8, wherein each of the electrically conducting coils further comprise being identical to each other.

12. The experimental system of claim 8, wherein the three or more electrically conducting coils further comprise no more than three electrically conducting coils.

13. The experimental system of claim 8, wherein the three or more electrically conducting coils further comprise no more than four electrically conducting coils.

14. The experimental system of claim 8, wherein the three or more electrically conducting coils further comprise no more than eight electrically conducting coils.

15. An experimental method comprising: energizing electrically at least three electrically conducting coils from one or more power sources; and generating rotating electromagnetic fields that form a Poynting vector vortex, the Poynting vector vortex producing a force that is perpendicular to the Poynting vector vortex.

16. The experimental method of claim 15, the force further comprising gravity.

17. The experimental method of claim 15, wherein the generating is performed by three or more electrically conducting coils attached to an interior of the electrically conducting dome.

18. (canceled)

19. (canceled)

Description

BRIEF DESCRIPTION OF DRAWINGS

[0012] FIG. 1 is an isometric diagram of an overview of an experimental propulsion apparatus to modify gravity, according to an implementation.

[0013] FIG. 2 is a diagram of evaporation of a black-hole into gamma rays, according to an implementation.

[0014] FIG. 3 is a diagram of the EB drift caused by crossed electric and magnetic fields, according to an implementation.

[0015] FIG. 4 is a diagram of a simulation of an electro-magnetism-synthetic gravity field, according to an implementation.

[0016] FIG. 5 is a diagram of two hot ideal radiators in a cold box, according to an implementation.

[0017] FIG. 6 is a diagram of two cold ideal radiators in a hot box, according to an implementation.

[0018] FIG. 7 is a diagram of a Gendanken experiment, according to an implementation.

[0019] FIG. 8 is a diagram of a quantum vacuum, according to an implementation.

[0020] FIG. 9 is a diagram of plates exhibiting the Casimir force, according to an implementation.

[0021] FIG. 10 is a diagram of the difference in modes allowed between a between plates, according to an implementation.

[0022] FIG. 11 is a Feynman diagram of photon-photon scattering, according to an implementation.

[0023] FIG. 12 is a diagram of the gravity pressure and hydrostatic pressure of the Earth, according to an implementation.

[0024] FIG. 13 is a conceptual diagram of radiation scattering off of a charged particle and creating a donut shaped region of interference between the scattered and incident waves, according to an implementation.

[0025] FIG. 14 is a diagram of the appearance and annihilation of a mesoscale mass particle-antiparticle pair in the vacuum, according to an implementation.

[0026] FIG. 15 is a diagram of the appearance of a mesoscale mass particle-antiparticle pair in the vacuum, according to an implementation.

[0027] FIG. 16 is an illustration of the Sunyaev-Zeldovich effect, according to an implementation.

[0028] FIG. 17 is a schematic of a leaky vacuum, according to an implementation.

[0029] FIG. 18 is a diagram of quantum Mie scattering, according to an implementation.

[0030] FIG. 19 is a diagram of quantum Mie scattering, according to an implementation.

[0031] FIG. 20 is a diagram of quantum Mie scattering, according to an implementation.

[0032] FIG. 21 is a diagram of quantum Mie scattering, according to an implementation.

[0033] FIG. 22 is a diagram of a Gama ray spectrum from Crab nebula supernova remnant.

[0034] FIG. 23 is a diagram of Gamma ray spectrum from a very energetic Gamma Ray Burst 090510A.

[0035] FIG. 24 is a diagram of two models of the proton.

[0036] FIG. 25 is a diagram of an experimental curve of the variation of a with energy, according to an implementation

[0037] FIG. 26 is a diagram of two models of an electron absorbing and reradiating a photon, according to an implementation.

[0038] FIG. 27 is a diagram of a simplified scheme for Mieon process generation of the quanta of the Strong and Weak Force plus the Higgs Boson.

[0039] FIG. 28 is a diagram of a potential function for spacetime in mass-geometry parameter s.

[0040] FIG. 30 is a diagram of the gravity siren as gravity waves emitted by mutually orbiting pair of black-holes increases in frequency as the system loses energy and in-spirals.

[0041] FIG. 31 is a diagram of an eruption of mount Pinatubo showing the result of an efficient turbulent cascade, turning a rising flow into a chaotic, turbulent flow.

[0042] FIG. 32 is diagram of the approximate sequence in a Black Hole merger.

[0043] FIG. 33 is a diagram of the detection of Gravity Waves by the LIGO group.

[0044] FIG. 34 is a diagram of the apparent detection of a Gamma Ray burst by the FERMI observatory coincident in time with the detection Gravity Waves by a LIGO group.

[0045] FIG. 35 is a flowchart of an experimental method to control a propulsion apparatus, according to an implementation.

[0046] FIG. 36 is a block diagram of an experimental propulsion control computer in which different implementations can be practiced.

[0047] FIG. 37 is a block diagram of an experimental data acquisition circuit of the propulsion control computer, according to an implementation.

[0048] FIG. 38 is a block diagram of an experimental hardware and operating environment in which different implementations can be practiced.

[0049] FIG. 39 is a block diagram of an experimental handheld mobile device, according to an implementation.

DETAILED DESCRIPTION OF THE INVENTION

[0050] In the following detailed description, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of illustration specific implementations which may be practiced. These implementations are described in sufficient detail to enable those skilled in the art to practice the implementations, and it is to be understood that other implementations may be utilized and that logical, mechanical, electrical and other changes may be made without departing from the scope of the implementations. The following detailed description is, therefore, not to be taken in a limiting sense.

[0051] The detailed description is divided into five sections. In the first section, a system level overview is described. In the second section, apparatus of implementations are described. In the third section, implementations of methods are described. In the fourth section, a hardware and the operating environment in conjunction with which implementations may be practiced are described. Finally, in the fifth section, a conclusion of the detailed description is provided.

System Level Overview

[0052] FIG. 1 is an isometric diagram of an overview of an experimental propulsion apparatus 100 to modify gravity, according to an implementation. Experimental propulsion apparatus 100 generates gravity from electrically conducting coils.

[0053] Propulsion apparatus 100 includes an electrically conducting dome 110 upon which are attached to three or more electrically conducting coils, 120, 130 and 140. When the electrically conducting coils, 120, 130 and 140 are electrically energized by one or more power sources 150, rotating electromagnetic (EM) fields 160 are generated that form a Poynting vector vortex 170, that produces a gravity force 180 that is perpendicular to the Poynting vector vortex 170. The gravity force 180 is gravity. Propulsion apparatus 100 is centered and symmetrical about center axis 190. The electrically conducting coils, 120, 130 and 140 are positioned symmetrically about center axis 190. Each of the electrically conducting coils, 120, 130 and 140 are identical to each other. The power source(s) 150 are electrically coupled to the electrically conducting coils, 120, 130 and 140. However, the power source(s) 150 can be physically positioned or located in a variety of physical positions or locations, other than what is shown in FIG. 1, such as outside of the electrically conducting dome 110. The propulsion apparatus 100 includes a propulsion control computer 195 that controls the power source 150 and thus controls power from the power source 150 to the electrically conducting coils 120, 130 and 140. Examples of the propulsion control computer 195 include propulsion control computer 3600 in FIG. 36, hardware and operating environment 3800 in FIG. 38 and a handheld device 3900 in FIG. 39. In some implementations, approximately 200 kw of electric power input into the three or more electrically conducting coils, 120, 130 and 140 produces one ton of gravity force 180. In some implementations discussed below in the section Estimate of Lift Per Unit of Power of propulsion apparatus 100 in FIG. 1, approximately 33 kw of electric power input into the three or more electrically conducting coils, 120, 130 and 140 produces one ton of gravity force 180.

[0054] Gravity and electro-magnetism are unified under two postulates that: 1. Gravity fields are an array of EB drifts and 2. The separate appearance of gravity and electro-magnetism fields from each other is correlated with the separation of protons and electrons from each other as the emerge from the Planck scale. The value of G, the Newton gravitation constant and the proton mass to good accuracy from the Planck scale with no free parameters. The values of the pion mass for the Strong Force and the W and Z boson masses as quantum Mie scatterings off the hidden dimension structures associated with the proton and electron masses are understood. The Higgs boson mass follows from similar formalism. Vacuum decay with the production of hydrogen and a CBR (Cosmic Background Radiation) is also predictable.

[0055] The quantum nature of reality is fundamental in the operation of propulsion apparatus 100 and in this entire disclosure. Understanding unified gravity and electromagnetism solves the geometric problem of unifying the great scales of the Hubble and Planck radii, with the mesoscale of the subatomic. Physical models describe unified gravity and electromagnetism, rather than sophisticated mathematics, yet also explains basic observations and predicts new phenomena.

[0056] The unification of gravity and electromagnetism is based not only physical model of gravity as an electrodynamic effect of spacetime in the classical limit, but also, following Einstein's pathway, on model of the observed pre-dominance of hydrogen in the cosmos. In the unification of gravity and electromagnetism both of these phenomena stem from the quantum mechanical consequences of a hidden 5.sup.th dimension that gives rise to separated pair of electro-magnetism and gravity fields and also the pair of subatomic particles, the electron and proton that make up hydrogen the cosmos. Formally, the unification of gravity and electromagnetism can be considered a combination of Sakharov's theories of both gravity as the metric elasticity of space due to electro-magnetism ZPF (Zero Point Fluctuations) and also Einstein's theory of Baryogenesis, but in addition the Kaluza-Klein theory of electro-magnetism-gravity unification through a hidden 5.sup.th dimension. The hidden dimension of Kaluza-Klein is required in order to have separate electro-magnetism and gravity fields and the existence of the hidden dimension of Kaluza-Klein in a quantum mechanical electrodynamic spacetime manifold gives rise to subatomic particles through resonant Mie scattering.

[0057] Essential to the unification gravity and electromagnetism is the concept of an electrodynamic fabric to spacetime, so that the vacuum is no longer simply a manifold but a dynamic ethereal substance, full of ZPF fields and virtual particles. Furthermore, the hidden 5.sup.th dimension of Kaluza-Klein required to support separate electro-magnetism and gravity fields, by breaking the scale symmetry of the vacuum, gives rise to particles. That is: the requirement of a hidden 5.sup.th dimension breaks the scale symmetry of the vacuum and creates scattering and virtual particles near the wavelength of the hidden dimension. Breaking the scale symmetry not only creates particles as resonances, the proton and electron, but also creates entropy. The vacuum without a hidden dimension is coherent and ordered, but with a hidden dimension included creates scattering and de-coherence. However, remarkably, the vacuum without a hidden dimension also creates other phenomena.

[0058] The unification of gravity and electromagnetism, unexpectedly shows that the subatomic forces called Strong and Weak forces, are created by exchange between boson fields around particles, as a secondary consequence of the hidden 5.sup.th dimension. The breaking of the scale invariance of the vacuum by the hidden 5.sup.th dimension creates resonant structures in the vacuum, and with Quantum vacuum turbulence exciting the resonant structures, quantum Mie scattering occurs, giving rise to the subatomic exchange forces. This is done with a formalism resembling the Feynman path Integral formalism. The unification of gravity and electromagnetism thus predicts, astonishingly, the masses of the bosons associated with the Weak Force W boson but also the pion of the Strong force, to high accuracy.

[0059] In the unification of gravity and electromagnetism, the breaking of scale symmetry in the vacuum must, through Kaluza-Klein, create a scalar field, to mediate scale changes which in turn are manifested as particle masses. As stated by Dr. Alfred Luhen of Madison College, one cannot create mass without creating gravity and thus any complete Standard Model involving the Higgs field must also incorporate gravity through General Relativity. Thus, in the unification of gravity and electromagnetism, mass cannot be created through the Higgs mechanism in the unification of gravity and electromagnetism without creating gravity. The creation of mass cannot be separated from gravity with the result that the Higgs boson is in structural resonance with the main massive particle in the universe, the proton. Thus, the Higgs Boson mass is part of the mechanism of the vacuum manifold that lays the foundation of a hydrogenic universe.

[0060] The unification of gravity and electromagnetism shows a vacuum unstable to creation of proton-electron pairs, with profound Cosmological consequences and a Strong and Weak force between subatomic particles. Finally. The physical meaning of the Higgs boson and the scale and the occurrence of the Higgs boson and the Radion scale-inducing field in creating the hydrogenic universe is shown.

[0061] The vacuum, in modern quantum mechanical understanding, is not empty. The vacuum is instead alive with virtual particles, including electromagnetic waves organized as photons. The virtual particles, including electromagnetic waves organized as photons, herein called the ZPF (Zero Point Fluctuation) was first identified by Einstein. The best calculations of the energy density of the vacuum yield vast numbers: the most embarrassing number in physics of 10.sup.114 ergs/cm, indicating that matter, with an average density in the cosmos of 1 GeV/m (one hydrogen atom per cubic meter) is merely a perturbation on the vacuum. Thus, formulating a physical theory of the vacuum, matter, in the form of subatomic particles will be recovered as a perturbation around the vacuum state.

[0062] Dirac's Large Numbers Hypothesis provides a profound observation, where he observed, in esu units:

[00001]$\begin{array}{cc}\frac{G{m}_p{m}_e}{e^2}\frac{r_e}{R_H}& \left(1\right)\end{array}$

[0063] Where G (using esu units) is the Newton Gravitation Constant, m.sub.p and m.sub.e are the proton and electron mass respectively, and r.sub.e is the classical electron radius: r.sub.e=e.sup.2/m.sub.ec.sup.2 and R.sub.H is the Hubble radius, which is the Hubble Time T.sub.H times the speed of light c: R.sub.H=CT.sub.H. In regards to the physical meaning of this expression, an approximate model of the Cosmos as being at 1, indicates that the universe has just nearly the critical density to be expanding at escape velocity from the universe itself.

[00002]$\begin{array}{cc}=\frac{8{\mathrm{Gm}}_{p}n{R}_H^2}{3c^2}1& \left(2\right)\end{array}$

[0064] where n is the number density of hydrogen in space, which can be correlated to the critical optical thickness of the Cosmos, the universe is at nearly the critical density to be neither optically thick or thin, but instead is misty:

[00003]$\begin{array}{cc}{}_{\mathrm{Th}}n{R}_H=\frac{8n{r}_e^2{R}_H}{3}1& \left(3\right)\end{array}$

[0065] where .sub.Th=8r.sub.e.sup.2/3 is the Thompson scattering cross-section for electro-magnetism radiation. Equating Eq. 2 and Eq. 3 and assuming the hydrogen in space is fully ionized Eq. 1 is derived. Therefore, the Dirac condition is consistent with the critical density of matter in the universe for gravitational interactions, being correlated with the electro-magnetism critical scattering thickness of the Cosmos. Accordingly, the Dirac relation is consistent with a Cosmos where gravity interactions are a form electro-magnetism interaction and the visible universe is both critically interacting gravitationally and electromagnetically.

[0066] Such an identification of gravity with electro-magnetism scattering must involve quantum renormalized electro-magnetism interactions at the subatomic level, because the Thompson cross section, and other so-called classical quantities, are products of a multitude of subatomic quantum interactions. Accordingly, a quantum numerical connection between the Cosmic and subatomic scales exists:

[00004]$\begin{array}{cc}-\frac{3}{2}\ln \left[\frac{G{m}_p{m}_e}{e^2}\right]{}^{-1}=137& \left(4\right)\end{array}$

[0067] While the propulsion apparatus 100 is not limited to any particular electrically conducting dome 110, electrically conducting coils, 120, 130 and 140, power sources 150, rotating electromagnetic (EM) fields 160, Poynting vector vortex 170, gravity force 180 and center axis 190, for sake of clarity simplified electrically conducting dome 110, electrically conducting coils, 120, 130 and 140, power sources 150, rotating EM fields 160, Poynting vector vortex 170, gravity force 180 and center axis 190 are described.

Estimate of Lift Per Unit of Power of Propulsion Apparatus 100 in FIG. 1

[0068] Given the vacuum Bernoulli equation:

[00005]$\frac{g^2}{2G}=\frac{S^2}{u_o{c}^2}$

[0069] Where g is gravity, lift is produced by perturbing the following equation:

[00006]$\frac{\mathrm{dgg}}{2G}=\frac{\mathrm{dSS}}{u_o{c}^2}$

[0070] Assuming an Invar (FeNi36 alloy) disk (density 8.110.sup.3 kg/m.sup.3) with a set of 3 coils beneath the disk, and assuming mass per unit area of Invar is 0.24 kg/m.sup.2 (0.03 mm thickness), a force of 2.4 N/m.sup.2 will levitate the disk in equilibrium in reference to gravity of the Earth. Assuming the Invar layer is supported by a high strength composite disk of negligible mass.

[0071] Therefore, the lifting force due to gravity modification is:

[00007]$\frac{\mathrm{dgg}}{2G}=\frac{2.4N}{m^2}$

[0072] dS/u.sub.0 can be interpreted as =V.sub.rot where the power flux S is interpreted as rotational but also has a component into the Invar due to resistive losses, so that the imposed dS is locally parallel to the S.sub.g due, to the radiation pressure striking each nucleon to create gravity, which is S.sub.g/c. This is approximately, for a single proton or neutron:

[00008]$S_g/c=\mathrm{mg}/$$m=1.67{10}^{-24}.fwdarw.1.67{10}^{-27}\mathrm{kg}$$=r_o^2$$r_o=1.4{10}^{-13}\mathrm{cm}.fwdarw.1.4{10}^{-15}m$$=r_o^2=6.15{10}^{-30}{m}^2$$S_g/c=\mathrm{mg}/=9.8N/\mathrm{kg}1.67{10}^{-26}\mathrm{kg}/6.15{10}^{-30}{m}^2=2.7{10}^{4}N/m^2$$S_{g}2.7{10}^{4}N/m^2{v}_{esc},\mathrm{where}{v}_{esc}=1.1{10}^{4}m/\sec$

[0073] Furthermore, in estimating lifting force per unit of applied EM power, from the Vacuum Bernoulli equation:

[00009]$\frac{{\mathrm{dSS}}_g}{c}=\frac{2.4N}{m^2}$$\mathrm{becomes}:$$\frac{\mathrm{dS}}{c}=\frac{2.4N}{m^2}$

[0074] Assuming the lifting force depends on the applied EM field, choosing Sg=u.sub.0c and also assuming the EM field applied to modify the gravity field is a rotating field which at the same time diffuses into the Invar surface due to resistive losses, then:

[00010]$u_{\mathrm{ap}}\frac{V_{\mathrm{rot}}}{c}=\frac{2.4N}{m^2}$

[0075] Assuming V.sub.rot=2R f, where f=a rotation frequency of 1 kHz (f=10.sup.3/sec) and a disk radius of approximately R=30 meters, which yields a mean rotation <V.sub.rot>=110.sup.5 m/sec, yielding gives <V.sub.rot>/c=3.310.sup.4

[00011]$u_{\mathrm{ap}}=\frac{2.4N}{m^2}=2.4\frac{J}{m^3}$

[0076] Assuming an applied field of energy density of 2.4 J/m.sup.3. This is a small field so to avoid high resistive heating of the Invar disk. This corresponds to an energy density u.sub.ap= B.sup.2/.sub.o where .sub.o=1.2510.sup.6H/m. The field strength B can be solved for:

[00012]$B^2\left(T\right)=2.42.5{10}^{-6}$$B=2.4{10}^{-3}T\mathrm{or}10G$

[0077] Assuming that 10.sup.5 fraction of the applied field energy is absorbed every rotation the S.sub.ap vector in the vertical direction is approximately S.sub.ap-vertical is 8 W/m.sup.2. This the resistive energy loss of the fields used to modify gravity.

[00013]$\frac{B^2}{2{}_0}{}_{\mathrm{rot}}{10}^{-5}=8\frac{W}{m^2}$

[0078] leading to a lifting force per unit power of approximately:

[00014]$\mathrm{lifting}\mathrm{force}\mathrm{per}\mathrm{unit}\mathrm{of}\mathrm{applied}\mathrm{power}=\frac{0.3N}{W}$$\mathrm{or},\mathrm{since}1\mathrm{Ton}\left(\mathrm{metric}\right)=10,000N$$\mathrm{lifting}\mathrm{force}\mathrm{per}\mathrm{unit}\mathrm{of}\mathrm{applied}\mathrm{power}\frac{1\mathrm{Ton}}{33\mathrm{kW}}$

[0079] This estimate of lifting power per unit of applied power compares well with that for an ultralight aircraft at lift per unit power 0.1 N/Wsuggesting that, in some implementations, gravity modification flight can be made all electric powered.

Apparatus Implementations

[0080] In the previous section, a system level overview of the operation of an implementation was described. In this section, the particular apparatus of such an implementation are described by reference to a series of diagrams in FIGS. 2-34.

[0081] FIG. 2 is a diagram 200 of evaporation of a black-hole into gamma rays, according to an implementation. Diagram 200 shows that gravity consists of electro-magnetism. Given the additional insight from Hawking, who showed that black-holes 210 (in the context of a quantum vacuum) are unstable to evaporation 220 into matter-antimatter and from there into thermal gamma rays 230, and by extension, entropy. Based on the idea of conservation of physical quantities, what emerges is a reflection of what lies within. Accordingly, an object of pure gravitational field energy 240 can turn into pure electro-magnetic energy 250 plus entropy. Intuitively, this again shows a fundamental connection between gravity 240 and electro-magnetism 250 can be made.

A Physical Model of Electro-Magnetic Gravity and Spacetime

Section 1. The Synthesis of a Basic Gravity Field from Electro-Magnetism

[0082] FIG. 3 is a diagram 300 of the EB drift caused by crossed electric and magnetic fields, according to an implementation. Diagram 300 shows that all charged particles identically and in non-uniform E fields 310, but uniform B fields 320, can cause acceleration.

[0083] The concept for a synthesis of a gravity field from electromagnetism is the outgrowth of the effort to achieve controlled thermonuclear fusion, most specifically the magnetic confinement of plasmas for fusion. An effect called an E-cross-B drift or EB drift is identified.

[0084] The EB drift is remarkable in that the EB drift affects all charged particles identically regardless of charge or mass. This model of a gravity field can be derived by first assuming uniform E 310 and B 320 fields at right angles to each other, as in FIG. 3, for example, E.sub.x and B.sub.z in the x and z directions respectively. Accordingly for motion of a charged particle in the x and y directions or r, , using esu units:

[00015]$\begin{array}{cc}m\frac{V_x}{t}=q{E}_x+\frac{V_y}{c}{B}_z& \left(1.\right)\end{array}$$\begin{array}{cc}m\frac{V_y}{t}=q{E}_y-\frac{V_x}{c}{B}_z& \left(1.1\right)\end{array}$

[0085] Where E.sub.y is included for a curvilinear E field 310, this is solved by assuming a velocity function of two parts, in x and y coordinates. The simplification that E.sub.x>>E.sub.y, shows a particle at the center of the region between the two plates.

[00016]$\begin{array}{cc}V=V_{osc}+V_d& \left(1.2\right)\end{array}$$\begin{array}{cc}{V}_d=\frac{c{E}_x}{B_z}& \left(1.3\right)\end{array}$$\begin{array}{cc}{V}_{os{c}_y}=V_{}\left(\sin {}_{c}t\right)& \left(1.4\right)\end{array}$$\begin{array}{cc}{V}_{os{c}_x}=V_{}\left(\cos {}_{c}t\right)& \left(1.5\right)\end{array}$

[0086] Where V.sub. is assumed to be a constant with V.sub.V.sub.d accordingly

[00017]$\begin{array}{cc}{}_c=\mathrm{eB}/\mathrm{mc}& \left(1.6\right)\end{array}$

[0087] As a result, in general for the average motion of the particle. Note this drift velocity shown in Eq. 1.4 is independent of charge and mass.

[0088] When the magnetic field is uniform and the E field 310 is varied at right angles to the magnetic field, in the direction of the drift, the particle will experience an acceleration in the direction of the EB drift.sup.Klein of the particle:

[00018]$\begin{array}{cc}\frac{V_d}{t}=\frac{c^2{E}_x}{B_z^2}\frac{E_x}{y}=\frac{}{y}& \left(1.7\right)\end{array}$$\begin{array}{cc}=\left({\frac{1}{2}\left[\frac{E_x}{B_z}\right]}^2{c}^2\right)& \left(1.8\right)\end{array}$

[0089] The energy source for this acceleration is the E field 310, whose variation in the direction of drift leads to a small polarization drift V.sub.p increment of velocity for the particle in the direction of the E field 310 during each gyro-period.

[00019]$\begin{array}{cc}{V}_p=\frac{c}{{}_c{B}_z}\frac{{\mathrm{dE}}_x}{\mathrm{dt}}=\frac{c^2{E}_x}{B_z^2{}_c}\frac{E_x}{y}& \left(1.9\right)\end{array}$$\begin{array}{cc}m\frac{V_d}{t}=\frac{q}{c}{V}_p{B}_z& \left(1.1\right)\end{array}$$\begin{array}{cc}m\frac{V_d}{t}=\frac{q}{c}{B}_z\frac{c^2{E}_x}{B_z^2{}_c}\frac{E_x}{y}=m\frac{}{y}& \left(1.11\right)\end{array}$

[0090] For the case of a time varying E.sub.x field, an acceleration of the particles is:

[00020]$\begin{array}{cc}\frac{V_d}{t}=\frac{c}{B_z}\frac{E_x}{t}& \left(1.12\right)\end{array}$$\begin{array}{cc}{V}_p=\frac{c}{{}_c{B}_z}\frac{E_x}{t}& \left(1.13\right)\end{array}$$\begin{array}{cc}m\frac{V_d}{t}=\frac{q}{c}{B}_z\frac{c}{{}_c{B}_z}\frac{E_x}{t}& \left(1.14\right)\end{array}$

[0091] The electric field vanishes in the guiding center frame of the accelerating particle because of the Lorentz frame shift:

[00021]$\begin{array}{cc}-E_x=\frac{V_d}{c}{B}_z& \left(1.15\right)\end{array}$

[0092] Therefore, for either the case of a time varying E field 310 or spatially varying E field 310 with a uniform B field 320 at right angles to the E field 310, a field of acceleration of charged particles can be achieved that is independent of the charge and mass of the charged particles and therefore satisfies an equivalence principle. Such a field of acceleration mimics a gravity field in the limit of B and E being both very strong, but with E/B<1. The source of energy for this acceleration is the variation of the E field 310, which the charged particle samples while undergoing cyclotron motion in the uniform B field 320.

[0093] FIG. 4 is a diagram 400 of a simulation of an electro-magnetism-synthetic gravity field, according to an implementation. Diagram 400 shows trajectories of an electron and a heavy positron of 10 an electron mass. A synthetic gravity field can be achieved in a laboratory by the arrangement of two parallel plates at different potentials, with a uniform magnetic field parallel to the surfaces of the two parallel plates. The synthetic gravity field will cause charged particles to drift at right angles to the resulting E and B fields, a time variation of the voltage difference, or the setting of the plates at an angle to each other results in the field of acceleration.

[0094] This is easily confirmed by a particle simulation where an electron and a heavy positron of positive charge but 10 the mass of electron are released in uniform magnetic field but between two plates set at an angle between each other, as seen in FIG. 4.

[0095] Written in terms of the Poynting vector, S=cEB/4 (in esu), the EB drift can be expressed as:

[00022]$\begin{array}{cc}{\stackrel{.fwdarw.}{V}}_d=c\frac{\stackrel{.fwdarw.}{E}\stackrel{.fwdarw.}{B}}{B^2}=\frac{\stackrel{.fwdarw.}{S}}{\left(B^2/4\right)}& \left(1.16\right)\end{array}$

[0096] This arrangement works well in a laboratory for individual charged particles moving in a vacuum, however. Furthermore, this laboratory model corresponds to real life gravity fields moving macroscopic objects because for strong enough E and B fields, all charged particles will behave as single particles, ignoring the fields of other particles in first approximation. Furthermore, the strong E and B fields in the vacuum exist that would make this physical model of gravity be consistent with GR (General Relativity), presently the most advanced and verified theory of gravity. To apply this model of gravity around a planet, considering that spacetime is cellular in microstructure and hosts an array of EB drift regions, vacuum spacetime is a simultaneously ferro-electric and ferro-magnetic material. For this model of gravity fields to be consistent with GR, spacetime must be a fabric of powerful electric and magnetic fields.

Section 2. Electro-Magnetic Spacetime

[0097] A physical model of gravity fields can be composed of locally uniform magnetic and varying electric fields. Flat spacetime can be conceived of as being composed of uniform magnetic and electric fields. But the vacuum is observed to be massless, or even to have a tiny negative mass density. To be consistent with GR, the mass density of the very E and B fields causing gravity must be considered as a source of gravity. This problem is not unique to the unification of gravity and electromagnetism but is a pressing problem for any theory of a quantum vacuum.

[0098] Einstein discovered the ZPF (Zero Point Fluctuation) in 1910, showing that as a consequence of the Heisenberg Uncertainty principle the vacuum must be populated with an electro-magnetism modes. The physical presence of these modes can be seen in the existence of the Casimir Effect. However, the fact that these modes do not create an observable mass-energy density in the vacuum is one of the great mysteries of physics. This problem was considered by the great Russian physicist Yakov Zeldovich who argued that a ZPF mass density term would appear as a Cosmological Constant term, allowed by General Relativity, and that another such term existed to cancel the ZPF term. The Zeldovich Cancelation term would then be required for a massless vacuum. The basic field equation for GR including the Cosmological Constant A is:

[00023]$\begin{array}{cc}{R}_{}-\frac{1}{2}{g}_{}R=\frac{8G}{c^4}{T}_{}-g_{}& \left(1.17\right)\end{array}$$\begin{array}{cc}\frac{8G}{c^4}{T}_{}-g_{}=0& \left(1.18\right)\end{array}$

[0099] Considering the concepts of Sahkarov, in gravity's relationship to the electro-magnetism ZPF, and the Kaluza-Klein theory of electro-magnetism-gravity unification, and the relationship of the Kaluza-Klein theory of electro-magnetism-gravity unification to a hidden 5.sup.th dimension and the Hilbert action principle in four spacetime dimensions with a zero cosmological constant, it can be determined that:

[00024]$\begin{array}{cc}W={\left(16G\right)}^{-1}R\sqrt{-g}d{x}^4& \left(1.19\right)\end{array}$

[0100] where R is the Curvature Scalar. Finding the extremum of the Curvature Scalar leads to the vacuum gravity equations with canceled ZPF electro-magnetism fields.

[00025]$\begin{array}{cc}{R}_v-\frac{1}{2}{g}_{v}R=0& \left(1.2\right)\end{array}$

[0101] Sakharov interpreted the integrand as a real energy density. Sakharov equated the real energy density to a perturbed quantum electro-magnetism ground state spectrum of ZPF (Zero Point Fluctuation) due to the Heisenberg Uncertainty principle applied to the vacuum electro-magnetism field. The zero'th-order ZPF is assumed to vanish due to a canceling cosmological constant term proposed by Yakov Zeldovich, who was a colleague of Sakharov's. This Zeldovich Cancelation ensures that only the perturbations due to curved space cause the effect of the ZPF to appear. Sakharov calculated the perturbed part of the ZPF due to spacetime curvature. He then derived a formula for G in terms of an integral over the perturbed ZPF:

[00026]$\begin{array}{cc}W=G^{-1}\frac{}{2c^5}\underset{O}{\overset{{}^{*}}{}}d=\frac{{}_P^2}{c^5}& \left(1.21\right)\end{array}$$\begin{array}{cc}G\frac{c^3{r}_P^2}{}=\frac{c^4}{r_P^2{T}_o}& \left(1.22\right)\end{array}$

[0102] where .sub.P is the Planck frequency c/r.sub.P, where r.sub.P=(G/c.sup.3).sup.1/2 and the energy density T.sub.o=c/r.sub.P.sup.4 is the Planck scale energy density. This is consistent with a physical model of gravity forces as due to imbalances of the electro-magnetism Poynting vector, S=cEB/4 (in esu) or a radiation pressure P=<S>/c. The second example of radiation pressure or Poynting vector acting on particles in a box whose wall absorb and emit radiation is shown in FIG. 4. In FIG. 4, the left figure shows hot-bright particles in a dark-cold enclosure, the right figure shows cold-dark particles in a hot-bright enclosure. Mutual radiation pressure forces are shown by block arrows.

[0103] FIG. 5 is a diagram 500 of two hot ideal radiators in a cold box, according to an implementation. In FIG. 5, two ss 510 and 520 in a cold box 525 repel 530 each other by mutual radiation pressure 540. FIG. 6 is a diagram 600 of two cold ideal radiators 610 and 620 in a hot box 625, according to an implementation. In FIG. 6, the two cold ideal radiators 610 and 620 in a hot box 625 attract each other due to mutual shadowing 640.

[0104] Radiation Pressure Affecting Particles in an Enclosure. As was shown above, an EB or Poynting drift field, with constant B and E growing stronger in the direction of the drift, can produce gravitational-like acceleration of charged particles of all charges and masses, as shown in FIG. 3. The Sakharov model for the gravitational force is basically that of a radiation pressure Poynting field produced by non-uniformities in the ZPF and is successful in the sense that is self-consistent (see FIG. 5 and FIG. 6). Sakharov arrived at this physical model for gravity because he worked on the Soviet Hydrogen Bomb where radiation pressure is crucial. The same idea can be derived, in relativistic-covariant form, where the zeroth-order ZPF stress energy is caused to vanish. The Zeldovich Cancelation is explained as electro-magnetism-gravity unification physics. The following equations show this theory in covariant form. If the metric tensor for gravity is written as a normalized first part of the electro-magnetism momentum-stress tensor:

[0105] However, if the fundamental structure of spacetime is electro-magnetic can be expressed

[00027]$\begin{array}{cc}{g}_{}=\frac{4F_{}^{}{F}_{}}{F_{}{F}^{}}& \left(1.23\right)\end{array}$

the metric tensor as an electromagnetic tensor:

[0106] For the case of statistically uniform isotropic vacuum fields, the elements of the gradient of the metric will vanish.

[0107] When expression 1.23 is used, the electro-magnetism stress tensor for the ZPF can be made to vanish.

[0108] Assuming isotropy, the unification of gravity and electromagnetism metric tensor is:

[00028]$\begin{array}{cc}{T}_a=F_{}^{}{F}_{}-g_a\frac{F_{}{F}^{}}{4}=0& \left(1.24\right)\end{array}$$\begin{array}{cc}{g}_a={2\left[B^2-E^2\right]}^{-1}\left(\begin{array}{cccc}-E^2& 0& 0& 0\\ 0& E_x^2-B_y^2-B_z^2& 0& 0\\ 0& 0& E_x^2-B_y^2-B_z^2& 0\\ 0& 0& 0& E_x^2-B_y^2-B_z^2\end{array}\right)& \left(1.25\right)\end{array}$

[0109] Assuming a model of spacetime containing adjacent regions of strong E or B fields, the particles travel as wave packets and sample a volume swept out by a wave-front, thus the particles have an average spacetime. An average over volume so that <B.sup.2>=<E.sub.2> and <E.Math.B>=0 results in a volume average of two metric forms one dominated by electric flux, for instance, in its local direction E.sub.y

[00029]$\begin{array}{cc}{g}_{}=\left[\begin{array}{cccc}2& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& -2& 0\\ 0& 0& 0& 0\end{array}\right]& \left(1.26\right)\end{array}$

[0110] And another, in an adjacent region, by magnetic flux also in B.sub.y

[00030]$\begin{array}{cc}{g}_{}=\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& -2& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& -2\end{array}\right]& \left(1.27\right)\end{array}$

[0111] Upon volume average, assuming large scale isotropy, The familiar Lorentzian flat space metric can be recovered as follows:

[00031]$\begin{array}{cc}<g_{}>=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& -1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& -1\end{array}\right]& \left(1.28\right)\end{array}$

[0112] Using the observation that for nearly flat spacetime, gravity fields and potentials of the gravity field are linearly additive, the effective gravity potential for the EB drift model of gravity can be derived, assuming the electro-magnetism form of the metric tensor required for self-censorship. The upper left diagonal element of the metric tensor can be determined as follows: g.sub.oo, and from the upper left diagonal element of the metric sensor, the effective Newtonian gravity potential can be determined.

[0113] Accordingly for perturbing fields and a gravity potential in terms of an EB drift model of gravity that is valid for both DC and oscillating E fields, where charged particles are accelerated into the strongest part of the perturbing E field. To determine how the Newtonian gravity potential occur between charged particles starting with the expression for a gravity potential in terms of E and B fields in the vacuum, where V.sub.D is the particle drift velocity in the crossed E and B fields:

[00032]$\begin{array}{cc}<g_{00}>=1+2/c^2\frac{-E^2}{B^2-E^2},E^2=E_x^2& \left(1.29\right)\end{array}$

[0114] Obtaining from the unification of gravity and electromagnetism metric tensor to first order in E.sub.x/B.sub.z<<1 and averaging with a flat metric.

[00033]$\begin{array}{cc}-1-2/c^2=-\frac{E_x^2}{B^2}& \left(1.3\right)\end{array}$

[0115] Obtaining the Newtonian potential as the perturbing E electric energy density divided by the more powerful magnetic field:

[00034]$\begin{array}{cc}=\frac{1}{2}\frac{E_x^2}{B_o^2}{c}^2+\frac{1}{2}{c}^2& \left(1.31\right)\end{array}$

[0116] Accordingly, the EB drift model of gravity and spacetime requires cells of very strong E and B fields to be present in space time, as part of the ZPF, yet not be visible directly. This is found to be consistent, in this example, with the form of the unification of gravity and electromagnetism metric tensor that is required to self-censor the ZPF. Below, the EB drift model of gravity and spacetime leads to the Schwartzchild metric for point masses to exist around charged particles in the vacuum. But first, the apparent cellular nature of spacetime must be investigated, that is: the fact that scale invariance of the vacuum is broken in such a way as to favor the production of hydrogen from the vacuum during the Big Bang.

[0117] FIG. 7 is a diagram 700 of a Gendanken experiment, according to an implementation. The Gendanken experiment in FIG. 7 yields the Gravitation Constant and Proton Mass from the Planckian Vacuum. In the Gedanken experiment in FIG. 7, a single atom of hydrogen, a proton and an electron, is shrunk within a sphere, ionizes into an ionized sphere 710, becomes a Planck sized sphere 720, which becomes a black hole 730, whereupon, the black hole 730 undergoes hawking evaporation and becomes a cloud 740 of gamma rays, matter and antimatter so that original hydrogen is lost.

Section 1. A Gedanken Experiment

[0118] In a Gedanken experiment, a single atom of hydrogen is confined in a sphere whose size is shrunk continuously until the sphere reaches approximately the radius of a Planck length r.sub.P=(G/c.sup.3).sup.1/2, 710 and 720. At this point the electron and proton making up the hydrogen will have long since ionized and increased in mass due to Heisenberg Uncertainty. The proton and electron will then form a Black Hole 730 which will then undergo Hawking Evaporation (FIG. 7) into a cloud 740 of photons, particles and anti-particles of the particles. The Hawking evaporation will destroy the baryon and lepton number of the proton and electron, leaving only the quantum numbers of the vacuum, which is in accordance with the observation that many of the quantities observed in the present day cosmos are running constants and change under radically smaller spacetime curvature, to merge eventually with Planck Scale quantities. Therefore, physical constants may be tied to a specific range of scale-size for the radius of curvature of spacetime, and these physical quantities will change dramatically when the radius of curvature approaches the Planck Scale.

[0119] Above, gravity fields are formulated as electro-magnetic, but this appeared to require a cellular nature for spacetime, in order to allow gravity fields, and spacetime, to be composed of regions of powerful electric and magnetic fields. At first, such a physical picture seems perfectly consistent with the concept of the Planck Scale, where spacetime is a foam of scale size equal to the Planck Length: r.sub.P=(G/c.sup.3).sup.1/2. However, at the Planck scale only a limited group of physical constants are possible and these do not include many of those constants that describe the universe experienced by us. The primordial first instants of the Big Bang the entire universe can be understood as in a compressed state at the Planck Scale but that the primordial first instants of the Big Bang the entire universe expanded from this scale to deploy a new larger scale that carried with the entire universe, the physics of the cosmos we experience now. Therefore, the concept of cellular spacetime must be further quantified to define a range of scale size for a cellular structure in spacetime that is distinct from the Planck Scale and represents an expanded scale that emerges from that primordial scale.

[0120] Thus, based on the Gedanken experiment, any cellular scale size in the vacuum is fully deployed to proper size of the cellular scale size in the vacuum in the present cosmos, and helps determine its physics, but this scale size is crushed out of existence at the Planck scale, where hydrogen disappears. Accordingly, Gedanken experiments that squeeze a proton-electron pair into the vacuum, also squeezes the cellular scale-size into the Planckian vacuum.

[0121] Assuming that the wave functions of the proton and electron, carrying with the proton and electron all identifying quantum numbers the proton and electron have merged as the Black Hole 730 forms at the Planck Scale, then the radius of spacetime local spacetime curvature r.fwdarw.r.sub.P before this happens. To model this behavior, a U(1) symmetry model for the proton and electron masses can be used, considering that since all information disappears, the model can be formulated only in terms of charge q, mass m, and mass ratio m.sub.p/m.sub.e=. Accordingly a U(1) mass model is obtained as follows:

[00035]$\begin{array}{cc}m=m_o\cos \left(\right)+{\mathrm{im}}_o\sin \left(\right)& \left(2.1\right)\end{array}$

[0122] The U(1) symmetry is complex valued with real and imaginary mixed together. Particles with imaginary rest masses are tachyons, particles that move faster than light. The simplest physical interpretation that can be made for such imaginary particles is that the tachyons are particles that have fallen inside the event horizon of a Black Hole, accelerating beyond the speed of light in the process and being out of communication with the real particles of the universe. This is important at the Planck scale because their particles appear out of the vacuum, form black holes and disappear, so that spacetime is effectively a foam. Foamy spacetime features Black Holes that are so closely packed that determining whether a particle is inside or outside an event horizon is possible. Thus particles at the Planck scale can be physically represented as complex, half real and half imaginary, with masses satisfying a U(1) symmetry. So the Planck scale is completely chaotic, mixing imaginary masses with real ones.

[0123] At the Planck scale, everything becomes simple, the electro-magnetism and gravity forces unify to one force obeying U(1) symmetry and Lepton and Baryon number also disappear, in fact everything disappears but vacuum quantities: G, c, and , the Newton gravitation constant, the speed of light, and the rationalized Planck's constant respectively. These determine the Planck Length: r.sub.P=(G/c.sup.3).sup.1/2. Planck mass M.sub.P=(c/G).sup.1/2, and Planck charge q.sub.P=(c).sup.1/2. However, assuming also that since electro-magnetism forces still exist and enforce quantization of charge and the charge neutrality of the vacuum, so that quarks remain grouped in groups of 3 having one positive electron charge to cancel the charges of electrons. Thus, a plasma consisting of quarks and electrons occurs at the Planck scale but protons, are still identifiable as groups of quarks because the vacuum must be charge neutral.

[0124] Therefore, at the Planck scale, Planck masses of real and imaginary masses consisting of a quark-electron plasma can be represented as relativistic mass-dilated electrons and protons because of the requirement of charge neutrality.

[0125] On the end of the spectrum of sizes, assuming a fully deployed cellular scale of subatomic size, can be of the size range:

[00036]$\begin{array}{cc}{r}_o=\frac{e^2}{m_o{c}^2}& \left(2.2\right)\end{array}$

[0126] where m.sub.o=(m.sub.pm.sub.e).sup.1/2, so that the size scale is neutral between protons and electrons, and a size parameter is determined entirely by low energy physics quantities. This energy and size scale is the mesoscale because the mesoscale lies between the Planck Scale and the Cosmic Scale.

[0127] The is Gendanken experiment based on the unification of gravity and electromagnetism postulate that baryon and lepton number disappear at the Planck scale coincidentally with the separate identity of Gravity and electro-magnetism fields. The vacuum is thus as simple as possible at the Planck scale, only particles and anti-particles of Planck mass and charge exist there.

[0128] In contrast the appearance of the cellular scale size as the universe expands from the Planck scale represents the appearance of a new degree of freedom. This is similar to when a molecular layer evaporates from a surface and becomes a 3-dimensional gas. Accordingly, that the expansion from the Planck Scale allows the appearance of a 5.sup.th dimension, represented by the appearance of a new scale size: r.sub.o, which is the appearance of particles: electrons and protons with the classical radii of the protons and electrons. That is, the appearance of the 5.sup.th dimension allows the appearance of the mesoscale. The expansion of the universe from the Planck Scale thus allows a new 5.sup.th dimension, a new degree of freedom, of much larger scale size than the Planck Scale, to appear, and with the new 5.sup.th dimension, a new physics appears, which is included into the U(1) mass model as follows:

[0129] The angle , in this model, corresponds to charge state and is thus quantized as a canceling pair.sub.o, even in the Planck Scale. However let us model the appearance of the fifth dimension by allowing this angle to become an imaginary rotation angle to give two real particle masses corresponding to an up quantum state and down quantum state from the U(1) symmetry. Assuming a model of a scale dependent vacuum where the existence of a 5.sup.th dimension breaks the vacuum scale invariance, the mass model is:

[00037]$\begin{array}{cc}m=m_o\exp \left({}_0\right)& \left(2.3\right)\end{array}$

[0130] Where is a parameter such that =0 when the 5.sup.th dimension does not exist and .sub.o=1 when the 5.sup.th dimension is fully deployed and separate particle masses are generated at do from Eq. 2.3 at r.fwdarw.r.sub.o

[00038]$\begin{array}{cc}{\left(\frac{m_p}{m_e}\right)}^{1/2}=\exp \left({}_0\right)=& \left(2.4\right)\end{array}$

[0131] Where is a mass asymmetry parameter, being the square root of the mass ratio of the electron to the proton.

[0132] Thus, even though mass symmetry is broken in terms of the new 5 space we experience, mass symmetry is preserved in terms of a geometry involving the imaginary angles in the original U(1) symmetry. That is, the new particle dimension looks symmetric in the space of imaginary angle.

[0133] Requiring that this e mass model, shows the behavior as m.sub.o.fwdarw.M.sub.P, .fwdarw.1 as r/r.sub.P.fwdarw.1

[0134] To obtain a smooth transition to the Planck scale as curvature collapses to the Planck length the angle .sub.o must be dependent on curvature near the Planck length but very insensitive to the angle at larger curvatures, where the new fifth dimension is fully deployed. Based on the lack of observation of proton decay, lepton and baryon numbers are strongly conserved. The simplest model to obtain this mixture of scale sensitivity with curvature r is for the rotation angle to have the dependence on our 5.sup.th dimensional deployment parameter

[00039]$\begin{array}{cc}\ln \left(\right)& \left(2.5\right)\end{array}$$\begin{array}{cc}\ln \left(r/r_P\right)& \left(2.6\right)\end{array}$

[0135] So that lepton and baryon numbers disappear, with .fwdarw.1 as r.fwdarw.r.sub.P

[0136] Therefore, in the unification of gravity and electromagnetism, the separate appearance of proton and electron pairs from the vacuum is, like the separate appearance of electro-magnetism and gravity forces, linked to the appearance and full development of the fifth dimension. The physical description of this new 5.sup.th dimension coming into being at scale size that corresponds to the size of a particle classical radius r.sub.o.

[0137] However, formula 2.6 cannot be correct near r=r.sub.P where .fwdarw.1, thus the formula 2.6 must be modified slightly so that both the right and left side go to zero smoothly at r=r.sub.P and =1, where can be assumed to go to one with the vanishing of a small parameter .fwdarw.0

[00040]$\begin{array}{cc}=1+& \left(2.7\right)\end{array}$

[0138] Eq. 2.6 can be re-written:

[00041]$\begin{array}{cc}\ln \left(r/r_P\right)=-\frac{1}{{}^2}& \left(2.8\right)\end{array}$

[0139] Note both sides of this expression now to zero as both quantities r/r.sub.P and .fwdarw.1. The correction factor is added as second order in , that is .sup.2=m.sub.e/m.sub.p to be similar to the reduced mass correction of the conventional dynamics of the electron-proton system. Therefore, when the new 5.sup.th dimension is fully deployed, where =42.8503

[00042]$\begin{array}{cc}\ln \left(r_o/r_P\right)=-\frac{1}{{}^2}& \left(2.9\right)\end{array}$

[0140] Note how both sides of this expression go to zero with leading order in , as r/r.sub.P.fwdarw.1:

[00043]$\begin{array}{cc}\ln \left(r/r_P\right)=-\frac{1}{{}^2}3& \left(2.1\right)\end{array}$

[0141] Correcting the mass formula so that m.sub.o=M.sub.P at the Planck scale, using the Planck charge q.sub.P and assuming that the normalized charge state assumes the role of determining mass q/e, but as r=r.sub.P is approached, that e.fwdarw.q.sub.P=(c).sup.1/2 so that .fwdarw.1 and also all masses approach the Planck mass m.sub.o.fwdarw.M.sub.P:

[00044]$\begin{array}{cc}m=m_o\exp \left(\frac{q}{e}\ln \right)& \left(2.11\right)\end{array}$

[0142] This formula gives the observed mass difference between the electron and proton and also ensures that this difference disappears as r/r.sub.P.fwdarw.1. However, not only mass the mass difference disappear but the mass m.sub.o must undergo the process m.sub.o.fwdarw.M.sub.P, as .fwdarw.1. Therefore extending this formula, where normalized charge controls mass, to obtain:

[00045]$\begin{array}{cc}{m}_o{M}_P\exp \left(\frac{q^{}}{e}\ln \right)& \left(2.12\right)\end{array}$

[0143] Where this gives the proper limit as m.sub.o.fwdarw.M.sub.P, .fwdarw.1.

[0144] However, the condition m.sub.o.fwdarw.M.sub.P is required, further requiring the condition that r, r.sub.P, m.sub.o and M.sub.P have the proper quantum relationship r.sub.o=/(m.sub.oc) so that near the Planck scale:

[00046]$\begin{array}{cc}\ln \left(\frac{m_o{r}_P}{M_P{r}_o}\right)=\ln \left(\frac{m_o}{M_P}\right)+\ln \left(\frac{r_o}{r_P}\right)=-3+3=0& \left(2.13\right)\end{array}$

[0145] Eq. 2.13 behavior is obtained in for the m.sub.o system by modifying Eq. 2.12, as in the expression in Eq. 2.6, with a second order term to ensure the proper behavior for m.sub.o, as .sup..sup. and .fwdarw.1

[00047]$\begin{array}{cc}m=M_P\exp \left(-\left({}^{-1/2}++1\right)\ln \right)\exp (\left(q/e\ln \right)& \left(2.14\right)\end{array}$

[0146] This requires, at normal spacetime curvature and charge state q/e=+1 the expression for the proton mass, with M.sub.P=2.1764510.sup.5 g:

[00048]$\begin{array}{cc}{m}_p=M_P\exp \left(-\left(a^{1/2}+a\right)\ln \right)=1.6665{10}^{-24}g& \left(2.15\right)\end{array}$

[0147] This expression agrees with the observed rest mass of the proton 1.6726210.sup.24 g, to 3.6 parts per thousand and goes to the proper limit of m.sub.p=M.sub.P as .fwdarw.1.

[0148] In regards to primary expression relating normalized spacetime curvature to the mass ratio, the expansion of the effective curvature to r.sub.o, which can be termed the mesoscale radius-since the expansion of the effective curvature to r.sub.o is the range of scales of classical particle radii and lies between the Planck and Cosmic scales-then yields, by Eq. 2.9 the relation:

[00049]$\begin{array}{cc}\ln \left(r_o/r_P\right)=-\frac{1}{{}^2}=42.850.Math..& \left(2.16\right)\end{array}$

[0149] If the ratio of the mesoscale radius to the Planck radius is examined, the ratio is then also known as a quantum normalized ratio of coupling constants between gravity and electro-magnetism,

[00050]$\begin{array}{cc}{r}_o/r_P=\sqrt{\frac{e^2}{G{m}_o^2}}& \left(2.17\right)\end{array}$

[0150] Equation 2.17 shows that the gravitational interaction between two masses is mediated by the emission and absorption of electro-magnetism photons. This is as expected if both electro-magnetism and gravity were both part of the same general phenomenon. The formula of Eq. 2.16 can be inverted to find an accurate expression for the gravitation constant.

[0151] The gravity constant can be obtained using the measured value of the proton electron mass ratio, to first order:

[00051]$\begin{array}{cc}G=\left(e^2/m_p{m}_e\right)\exp \left(-2\left(-1/{}^2\right)\right)=6.67384{10}^{-8}\mathrm{dyne}-{\mathrm{cm}}^2-g^{-2}& \left(2.18\right)\end{array}$

[0152] this expression is within 3.6 parts per 100 thousand of the measured value of G:

[0153] 6.6740810.sup.8 dyne-cm.sup.2gm.sup.2. Note that the expression gives proper limiting behavior at the Planck scale, yielding G even as all masses go to M.sub.P, e.sup.2.fwdarw.c and and .fwdarw.1.

[0154] Therefore, a mass model, bridging the lepton-baryon mass system at its lowest energy end-members the electron and proton, that fulfills the expectation of our Gedanken experiment and has proper limiting behavior at both the Planck scale and scale of the fifth dimension, which is the subatomic scale, yields accurate expressions for both the proton mass and the gravitation constant.

[0155] A formula similar to Eq. 2.18 was originally published in approximate form in 1987 and corrected in 1988 and bears some resemblance to the formula published by T'Hooft based on Instanton theory that combines Hawking Evaporation with thermal physics.

Section 2. Particles from the Vacuum: The Unification of Gravity and Electromagnetism

[0156] The vacuum quantities associated with the Planck scale are:

[00052]$\begin{array}{cc}{r}_P=\sqrt{\frac{G}{c^3}}& \left(2.19\right)\end{array}$$\begin{array}{cc}{M}_P=\sqrt{\frac{c}{G}}& \left(2.2\right)\end{array}$$\begin{array}{cc}{q}_v=\sqrt{c}& \left(2.21\right)\end{array}$

[0157] The simplest concept that can be taken away from the mass formula of Eq. 2.14 then would use the vacuum derived Planck Charge q.sub.p as the controller of mass, from which the proton mass is obtained as the simplest result.

[0158] Considering other constraints to such a theory. In considering the reverse problem of particles emerging from the vacuum as opposed to the Gedanken concept of the particles merging with the vacuum, the proton cannot appear by itself, the proton must appear with another particle of opposite charge to preserve electric neutrality, however the particle cannot be just an antiparticle. In particular, the appearance of one particle does not increase entropy in the universe, because entropy requires complexity. So the same mass formula allowing the appearance of a proton must also allow the appearance of an electron to balance the proton and to maximize entropy. Therefore, the proton must appear as part of a system that includes the electron, so that hydrogen results:

[00053]$\begin{array}{cc}{q}_p=-q_e& \left(2.22\right)\end{array}$$\begin{array}{cc}\begin{array}{cc}{q}_p=e,& -e=q_e\end{array}& \left(2.23\right)\end{array}$

[0159] Another constraint occurs because the spacetime occupied by a particle in the vacuum initially cannot be simply a distance, but must be a spacetime interval. In the vacuum state all particles must be masses and move at the speed of light and have a spacetime interval of zero:

[00054]$\begin{array}{cc}{r}_o^2=\left(x_o^2+y_o^2+z_o^2\right)& \left(2.24\right)\end{array}$$\begin{array}{cc}{r}_o^2-c^2{t}_o^2=0& \left(2.25\right)\end{array}$

[0160] It is seen that the appearance of the new hidden dimension occurs in a form analogous to the splitting of a canceling charge pair of particles from the vacuum, by splitting of a quantized light-like, or vacuum, space-time interval of length zero. In the unification of gravity and electromagnetism the hidden dimension size, where the hidden dimension can mix with the non-hidden dimensions, is the quantized particle size. Physically, the hidden dimension can be considered as an electric charge. The hidden dimension quantities are thus able to mix with the normal spacetime quantities because the hidden dimension quantities and the normal spacetime quantities are similar at smaller scales. This will lead to two particle types. One is associated with the time-like portion of the constrained interval, leading to a one-dimensional character, an electron, and another of equal size with a space-like character having three constrained sub-dimensions, a proton. The required birth of 3 sub-dimensions with the proton introduces entropy because the 3 sub-dimensions and the proton are uncorrelated.

[0161] The gravitation constant G, functions in the vacuum as the interpreter of charge into either mass or distance. Thus, ironically, charge and mass, the source terms for electro-magnetism and gravity, are unified already in the vacuum quantity G, which has units of charge to mass ratio squared in the esu system used here.

[00055]$\begin{array}{cc}q\sqrt{G/c^4}=r& \left(2.26\right)\end{array}$$\begin{array}{cc}{r}_o^2=\left(G/c^4\right)\left(q_x^2+q_y^2+q_z^2\right)& \left(2.27\right)\end{array}$$\begin{array}{cc}{r}_o^2=c^2{t}_o^2=\left(G/c^4\right)q_t^2& \left(2.28\right)\end{array}$

[0162] Therefore, the quantized vacuum scale length, the Planck length, gives birth to a quantized larger scale hidden dimension. Because the quantized hidden dimension is an image of macroscopic space-time in a light-like interval, and the structure of the quantized hidden dimension is part of a split lightlike spacetime where charge q is analogous to macroscopic dimensions as a length, then charge conservation and interval conservation exists. From these conditions the following constraints on the charges of the particles are obtained as follows:

[00056]$\begin{array}{cc}{q}_o=-q_t=q_x+q_y+q_z& \left(2.29\right)\end{array}$$\begin{array}{cc}{q}_o^2=q_t^2=q_x^2+q_y^2+q_z^2& \left(2.3\right)\end{array}$

[0163] where the subscripts denote the corresponding time or space dimensions in the unconstrained Cosmos. This can be explained variationally as requiring q.sub.x=q.sub.y= and q.sub.z= (see below) by minimizing the product q.sub.xq.sub.yq.sub.z subject to the constraints of Eq.s 2.29 and 2.30. Thus, the space-like portion of the split interval, the proton, has three sub-dimensions are interpreted as quarks or sub-charges, while the electron acts like a single entity.

The Unification of Gravity and Electromagnetism in the Context of Kaluza-Klein Theory

Section 1. the unification of gravity and electromagnetism Sakharov and Kaluza-Klein Theory

[0164] The concept that Gravity-EM unification is possible shows a great simplification our models of physics, however, the same unification of gravity and electromagnetism requires the concept of the vacuum to become more complex.

[0165] FIG. 8 is a diagram of a quantum vacuum 800, according to an implementation.

[0166] Conventionally, vacuum was thought to be mere emptiness, in contrast, quantum mechanics required the vacuum to become quite busy, and astrophysical observations of a non-zero cosmological constant required still more complication, so now, in turn, the unification of gravity and electromagnetism with its hidden Kaluza-Klein dimension, adds further complexity.

[0167] General Relativity, Maxwell's Equations, and quantum mechanics are the primary constraints on the Unification of gravity and electromagnetism. The first two constraints are both largely satisfied by Kaluza-Klein theory, where the coupled equations of General Relativity and Maxwell's equations can be derived from an extended Hilbert Action Principle by the assumption of a hidden or compact 5.sup.th spatial dimension. The unification of gravity and electromagnetism can be considered to be mainly a merging of the Sakharov and Kaluza-Klein approaches to Gravity electro-magnetism unification: The Sakharov approach being the identification of ZPF electro-magnetism fields with spacetime and the Kaluza-Klein theory saying the separate appearance of separate electro-magnetism fields at long wavelengths is due to the appearance of a cellular structure in spacetime, i.e. a hidden dimension. The physical meaning of the unified gravity and electromagnetism view of spacetime and electro-magnetism fields in the context of the Sakharov and Kaluza-Klein theories is explained below. In particular, the results of the unification of gravity and electromagnetism in the context of the Kaluza-Klein theory is explained to understand the physical nature of a fifth dimension and the consequences of the fifth dimension.

[0168] First, the concept of self-censorship in an electromagnetic spacetime of Sakharov and its requirement of a cutoff wavelength for ZPF is explained, beneath which self-censorship occurs. The ZPF effects matter at atomic-relevant frequencies, but just as the very high frequency limit of the ZPF does not appear physically, thus some change in physics must occur at frequencies above the gamma ray wavelengths for nuclear transitions. Following Sakharov, the cutoff at frequencies above the gamma ray wavelengths in the context of the Hilbert Action Principle is explained and the concept of a cutoff frequency for self-censorship by a simple mathematical analysis of the direct evidence of the ZPF, the Casimir Effect is explained too.

[0169] Secondly, the Kaluza-Klein theory is explained, from which appear both Maxwell's equations and the coupled Equations of general Relativity, by means of physical attributes of a hidden dimension and the physical meaning of the hidden dimension in the context of the Kaluza-Klein theory identifying the hidden dimension with the charge-quantum of subatomic particles.

[0170] Thirdly, how the presence of charge in the vacuum and the concept of self-censorship and Maxwell's equations leads to the Schwarzschild metric of General Relativity is also explained.

Section 2. Sakharov's Model and Self-Censorship

[0171] One of the curious issues of the unification of gravity and electromagnetism is that the ZPF energy vanishes, yet the ZPF is commonly observed in its effects on atoms and is key to understanding spontaneous emission of radiation from bound systems. One way that the ZPF can interact with ordinary electrodynamics is that that the self-censorship of the ZPF occurs at some high frequency cutoff, like the ground-state spectrum of phonons in a crystal are cutoff at wavelengths corresponding to the inter-particle separation. This would also correspond to the change of physics of the vacuum at wavelengths corresponding to the cell-size of the vacuum where strong E and B exists that create unified gravity-and-electromagnetism gravity fields exist. Proceeding with the simplest model, the cutoff wavelength value is assigned to the size of a Kaluza-Klein hidden dimension.

[0172] Cutoff frequencies on the ZPF, such as those commonly used at the Planck Scale, create problems for the Lorentz invariance of the ZPF. However, such concerns are of a higher order in this discussion. Here, such concerns are aside and whether such a frequency cutoff makes sense physically at leading order is determined.

[0173] The unification of gravity and electromagnetism is an alloy of the concepts of Sakharov concerning baryo-genesis and gravity's relationship to the electro-magnetism ZPF, and Kaluza-Klein theory of electro-magnetism-gravity unification via a hidden 5.sup.th dimension. To begin with, the Hilbert action principle in 4 spacetime dimensions with a zero cosmological constant.

[00057]$\begin{array}{cc}W=\frac{R}{16G}{\mathrm{dx}}^4& \left(3.1\right)\end{array}$

[0174] where g.sup.v is the metric tensor and R.sub.v is the Ricci tensor. Finding the extremum of this action leads to the vacuum gravity equations with no electro-magnetism fields.

[00058]$\begin{array}{cc}{R}_{}-\frac{1}{2}{g}_{}R=0& \left(3.2\right)\end{array}$

[0175] Sakharov interpreted the integrand as a real energy density. He equated this energy density to a perturbed quantum electro-magnetism ground state spectrum of ZPF (Zero Point Fluctuation) due to the Heisenberg Uncertainty principle applied to the vacuum electro-magnetism field. The zeroth-order ZPF mass density is assumed to vanish due to a canceling cosmological constant term proposed by Yakov Zeldovich, a colleague of Sakharov's. This Zeldovich Cancelation ensures that only the perturbations due to curved space cause the effect of the ZPF to appear. Sakharov calculated the perturbed part of the ZPF due to spacetime curvature, assuming a cutoff at the Planck Scale. He then derived a formula for G in terms of an integral over the perturbed ZPF:

[00059]$\begin{array}{cc}{G}^{-1}\frac{}{2c^5}\underset{0}{\overset{{}_p}{}}d=\frac{}{c^3}1/r_p^2;& \left(3.3\right)\end{array}$$\begin{array}{cc}G=\frac{r_p^2{c}^3,}{}& \left(3.4\right)\end{array}$

[0176] However, Eq. 4.4 is dominated by the Planck wavelength frequencies and is thus insensitive to the lower bound of frequencies, near the hidden dimension size r.sub.o. Accordingly a long wavelength cutoff can be applied with no detectable change in the Gravitation Constant.

[00060]$\begin{array}{cc}{r}_o=\frac{e^2}{{\left(m_p{m}_e\right)}^{1/2}{c}^2},& \left(3.5\right)\end{array}$$\begin{array}{cc}{G}^{-1}\frac{}{2c^5}\underset{{}_o}{\stackrel{{}_p}{}}d=\frac{}{c^3}\left[1/r_p^2-1/r_o^2\right]& \left(3.6\right)\end{array}$

[0177] wherein the Planck frequency, .sub.P=c/r.sub.P and a cutoff frequency, .sub.o=c/r.sub.o are defined. This revised calculation, now including a long-wavelength cutoff (long compared to the Planck Length) yields:

[00061]$\begin{array}{cc}G{\frac{c^3{r}_p^2}{}\left[1-r_p^2/r_o^2\right]}^{-1}& \left(3.7\right)\end{array}$

[0178] Where the correction factor, r.sub.P/r.sub.o10.sup.43 and is thus undetectable by present technology.

[0179] FIG. 9 is a diagram of plates 900 exhibiting the Casimir force, according to an implementation. Plates 900 show the cutoff 910 due to the finite gap between plates.

[0180] One of the constraints of a physical electrodynamic theory of gravity is that the ZPF can be detected physically through Casimir forces but also engages in self censorship. A spectrum of electro-magnetism modes, as demonstrated by the Casimir Force, interacts with everyday matter. Insight into this can be gained by considering how the Casimir Force occurs physically.

[0181] The Casimir Force can be derived as the radiation pressure of modes that can exist in a large region of large size L, and within this region a pair of thin metal plates of spacing . (see FIG. 9)

[0182] Assuming a cutoff exists at frequency f.sub.c>>c/920, roughly equivalent to regularization the following expression can be obtained for wave field energy per unit area between plates separated by a gap of distance :

[00062]$\begin{array}{cc}\frac{<E_a>}{A}=\frac{c{}^2}{6{}^3}{.Math.}_n^{n_c}{n}^3& \left(3.8\right)\end{array}$

[0183] The ZPF modes for the much larger region between plates separated by the large distance L can be expressed as:

[00063]$\begin{array}{cc}\frac{<E_L>}{A}=\frac{c{}^2}{6L^3}{.Math.}_n^{n_c}{n}^3& \left(3.9\right)\end{array}$

Assuming the Same Cutoff Frequencies

[00064]$\begin{array}{cc}\frac{n_c^{}}{L}=\frac{n_c}{}& \left(3.1\right)\end{array}$

[0184] The difference between the energies can be expressed as:

[00065]$\begin{array}{cc}\frac{<E_L>}{A}=\frac{c{}^2}{6{}^3}\left[{.Math.}_{n=1}^{n_c}{n}^3-{.Math.}_{n=1}^{n_c^{}}{n^3\left(\frac{}{L}\right)}^3\right]& \left(3.11\right)\end{array}$

[0185] Thus, the modes cancel at high frequencies 930, that is: high frequencies compared to everyday life, assuming a cutoff 910 exists in order to make this a finite difference between finite quantities.

[0186] FIG. 10 is a diagram 1000 of the difference in modes allowed between plates, according to an implementation. In diagram 1000, the plates have a narrow space between the plates and a pair of widely spaced plates of gap L, where /L<<1.

[0187] Diagram FIG. 10 shows the mode energies and the difference caused by the excluded low frequency modes. This results in an expression, where assume a finite mode-width for the principle mode in order to convert to a continuous set of modes for the excluded modes:

[00066]$\begin{array}{cc}\frac{<E_L>}{A}=-\frac{c{}^2}{6{}^3}\left[{.Math.}_{n=1}^{L/a}{n}^3\right]& \left(3.12\right)\end{array}$

[0188] Integrating over the excluded modes as if the excluded modes are continuous and assuming a finite mode width for n=1 mode, so the integral can be ended far from n=1, can be obtained as follows:

[00067]$\begin{array}{cc}\left[{.Math.}_{n=1}^{L/a}{n}^3\right]\underset{0}{\overset{{\left(2\right)}^{-1}}{}}{x}^{3}dx=\frac{x^2}{3}{.Math.}_0^{{\left(2\right)}^{-1}}\frac{1}{118}& \left(3.13\right)\end{array}$

[0189] Therefore, one method of seeing the ZPF fields directly via the Casimir effect implies that cutoffs must occur and but the Casimir effect involves differences in mode spectra far from this cutoff. Thus, an observation of the ZPF in atomic and nuclear transitions, supports the concept that a cutoff in wavelengths occur at the subatomic scale. By a nave estimate this would occur at the photon energy E.sub.cuttoffc/r.sub.o=3.0 GeV and that at shorter wavelengths self-censorship occurs, with the ZPF becoming part of spacetime. Since the ZPF plays a great role in electro-magnetism transitions of bound systems, a cutoff could manifest itself as an abrupt change in decay lifetimes of particles in this 3.0 GeV mass range due to a change in the ZPF physics. Such a change in lifetime is observed in the dramatic difference (347 times) in decay times from the -c Charmed meson at mass 2984 MeV to the very similar, but much longer lived, J/ Charmed meson at 3097 MeV.

[0190] Assuming the non-zero Cosmological constant, the Zeldovich Cancelation can take care of any remaining residual mass of the ZPF above the cutoff, without interfering with its interactions with matter.

Section 3. The Unification of Gravity and Electromagnetism and Kaluza-Klein

[0191] Maxwell's and Einstein's equations arise from a common basis. The presence of the hidden 5.sup.th spatial dimension creates separate electro-magnetism and gravity fields. The unification of gravity and electromagnetism by the Kaluza-Klein formalism is introduced by a 5.sup.th dimension that effectively scatters part of the ZPF electro-magnetism microstructure of spacetime into long wavelength E and B fields that are governed by Maxwell's equations. Thus very short wavelength ZPF modes become spacetime, while long wavelength modes become the electro-magnetism modes seen as electric and magnetic fields in ordinary matter. Assuming that an electromagnetic model of gravity and spacetime requires a cellular structure to spacetime, this arises from a definition of a spatial distance interval and the spherical isotropy of spacetime, where a spatial interval exists for a field-free region:

[00068]$\begin{array}{cc}{r}_o^2+x^2+y^2+z^2={}^2& \left(3.14\right)\end{array}$

[0192] Where r.sub.o is a quantized distance in the 5.sup.th dimension, which means that a spherical region can exist where r.sub.o=, so that points technically at identical spatial coordinates are still separated within the hidden dimension. Thus, hidden dimension looks like a small spherical subatomic particle, which a difference in hidden dimension coordinates must appear in ordinary space as a spherical spatial void or cell.

[0193] This new Kaluza-Klein 5.sup.th dimension, is a degree of freedom but is compact, that is, the new Kaluza-Klein 5.sup.th dimension is limited in extent, unlike the other dimensions of space-time. However, the 5.sup.th dimension must arise from the much smaller Planck length and deploy to its favored size. Assuming that at the Planck scale, all particles and fields are unified and identical, the world we basically experience then results from the deployment of the compact 5.sup.th dimension from Planck scale, to form a cosmos with two particles: electrons and protons and two fields: electro-magnetism and gravity. The size of the fully deployed 5.sup.th dimension can be explained by the consequence of the appearance of the 5.sup.th dimension is appearance of real particle masses, m.sub.e and m.sub.p, wherein the new scale size r.sub.o, most simply, will depend on particle quantities: e, m.sub.p and m.sub.e. The hidden dimension size then, is a completely new quantity, and not dependent on the vacuum quantities G, c, and . The new 5.sup.th dimension size r.sub.o can be expressed in terms of purely particle quantities that accompany its appearance:

[00069]$\begin{array}{cc}{r}_o=\frac{e^2}{m_o{c}^2}& \left(3.15\right)\end{array}$$\mathrm{where}{m}_o={\left(m_p{m}_e\right)}^{1/2}$

[0194] This physical concept of gravity as a statistical electromagnetic interaction related to radiation pressure from the quantum ZPF (Zero Point Fluctuation) was proposed by Sakharov and can be understood physically in the case of two bright objects in a box with dark walls, the two objects repel each other due to mutual radiation pressure with a 1/r.sup.2 force dependence, in the second case two dark objects are placed in a box with bright walls and attract each other due to mutual shadowing with a 1/r.sup.2 force dependence. Sakharov went further, using the Hilbert Action Principle

[00070]$\begin{array}{cc}W=\frac{R}{16G}{\mathrm{dx}}^4& \left(3.16\right)\end{array}$

[0195] where R/16G is an energy density to be minimized, and which yields the vacuum equations of Einstein's General Relativity. Sakharov treated the action, R/16G, having units of energy density, as a physical energy density due to the distortion of the ZPF by curved spacetime and used this to derive a formula for the Newton Gravitation Constant with the Planck scale forming the short wavelength limit of integration. This yielded:

[00071]$\begin{array}{cc}G=\frac{r_p^2{c}^3}{}& \left(3.17\right)\end{array}$

[0196] Where r.sub.P=(G/c.sup.3).sup.1/2 is the Planck mass from the ZPF, which demonstrates that self-consistency of the concept. Gravity can thus be considered as a consequence of the curvature of spacetime, with the fabric of spacetime being considered electromagnetic. However, in order to introduce electromagnetism explicitly one must introduce a hidden Kaluza-Klein dimension. This changes the Hilbert Action Principle, and for the case of a vacuum the Hilbert Action Principle becomes

[00072]$\begin{array}{cc}W=\frac{c^{4}R}{16G}+{}^3\frac{F_{}{F}^{}}{4}{\mathrm{dx}}^5& \left(3.18\right)\end{array}$

[0197] Where F.sub. is the Faraday electro-magnetism tensor and is considered here to be, effectively, a constant with =1. An excellent treatment of the scalar field , called the Radion field being fully dynamic was published by Lance Williams and its consequences will be examined in later works. The Kaluza-Klein 5.sup.th dimension, which unifies gravity and electro-magnetism, cannot be introduced without the Radion scalar field being also introduced.

[00073]$\begin{array}{cc}\frac{F_{}{F}^{}}{4}=\frac{E^2-B^2}{8}& \left(3.19\right)\end{array}$

[0198] The Basis Stress T.sub.o, can be defined, which is the Planck Energy density, as:

[00074]$\begin{array}{cc}8G/c^4=\frac{1}{r_p^2{T}_o}& \left(3.2\right)\end{array}$

[0199] Accordingly, in a form similar to the Lagrangian for sound waves

[00075]$\begin{array}{cc}W=r_P^2{T}_{o}R-{}^3\frac{E^2-B^2}{8}d{x}^5& \left(3.21\right)\end{array}$

[0200] Because r.sub.P.sup.2T.sub.o is a product of a small quantity r.sub.P.sup.2 with a large quantity T.sub.o=16c/r.sub.P.sup.4., then r.sub.P.sup.2T.sub.o=r.sub.o.sup.2T.sub.o* and have large scale length r.sub.o and a weaker basis stress, T.sub.o*:

[00076]$\begin{array}{cc}W=T_o^{*}{r}_o^{2}R+\frac{1}{4}{F}_{}{F}^{}d{x}^5& \left(3.22\right)\end{array}$

[0201] Assuming that 16G/c.sup.4=r.sub.P.sup.2T.sub.o=4.1410.sup.48 dyne.sup.1.

[00077]$\begin{array}{cc}{r}_P^2{T}_o=r_o^2{T}_o\frac{r_P^2}{r_o^2}=r_o^2{T}_o\frac{G{m}_p{m}_e}{e^2}=r_o^2{T}_o^{*}& \left(3.23\right)\end{array}$

[0202] Where the modified stress is equivalent to the gravity stress between two masses 137 times the mesoscale mass m.sub.o but held a Planck length apart. This is much lower than the Planck stress.

[00078]$\begin{array}{cc}{T}_o^{*}=\frac{G{m}_p{m}_e}{{}^2{r}_P^4}& \left(3.24\right)\end{array}$

[0203] Therefore, the Lagrangian for a Kaluza-Klein Vacuum can be considered as similar to the sound wave Lagrangian of a gas of pressure T*.sub.o and sub-molecular scale size r.sub.o. Let us consider the physical picture that the universe begins as 4 dimensional at high densities near the Planck Scale and becomes 5 dimensional as expands. The physical picture that the 5.sup.th dimension then deploys can be adopted to a certain size range, r.sub.o, as the universe expands and does not grow beyond this. The expression for , the parameter indicating the deployment and activation of the hidden dimension size, r.sub.o, that follows the model can for formalized as:

[00079]$\begin{array}{cc}=\tanh \left[\frac{r}{r_P}\right]& \left(3.25\right)\end{array}$

[0204] So that, effectively, =1 for r/r.sub.P>>1 or 0 for r/r.sub.P=0. Thus the simplifying assumption can be adopted so, that the dynamics of are minimal.

[0205] So the near the Planck scale =0 and for r/r.sub.P>>1=1. Note that this means the Gravitational portion of the Kaluza-Klein Lagrangian (Eq. 3.20) appears far more quickly than the electro-magnetism portion as the fifth dimension deploys.

[0206] Where A is the electric 4 potential the indices, a and b, run from 1-5, =16G/c.sup.4, g.sub.v is the familiar 4 metric tensor and =.sup.2 is a parameter that determines the size of the 5.sup.th dimension, with =1 being a compactified universe and =0 being the primordial infinite 4.sup.th dimensional universe. Accordingly, a Lagrangian for a set of massless scalar quanta, with M.sub.P=(c/G).sup.1/2 being the Planck mass, a mass that can arise spontaneously out of the vacuum:

[00080]$\begin{array}{cc}L=\frac{h^2}{M_P}\left({}_a{}_b{}^{\mathrm{ab}}\right)\sqrt{-}{d}^{5}x& \left(3.27\right)\end{array}$

[0207] The minimization of this Lagrangian leads to a simple Klein-Gordon wave equation for massless quanta in flat space:

[00081]$\begin{array}{cc}{}_a{}_b{}^{ab}=0& \left(3.28\right)\end{array}$

[0208] However, if the fifth dimension is allowed to deploy and then become compact so that all dependence on the 5.sup.th dimension becomes the form:

[00082]$\begin{array}{cc}=\underset{r}{.Math.}{}_r\left(x^v\right)\exp ({\mathrm{inx}}^5/\left(2r_o\right)& \left(3.29\right)\end{array}$

[0209] Where n is an integer index and r.sub.o is the size of the hidden dimension. Then the particles in the quantum Lagrangian acquire both mass and charge:

[00083]$\begin{array}{cc}L=\frac{h^2}{M_P}\left({\left[\left({}_a-\frac{in}{2r_o}{A}_{}\right)\right]}^2-{\left(\frac{n}{2r_o}\right)}^2{}^2\right)\sqrt{-r}{d}^{5}x& \left(3.3\right)\end{array}$

[0210] Where the electric charge, with n=1, is identified as:

[00084]$\begin{array}{cc}e=\frac{}{2r_o}& \left(3.31\right)\end{array}$

[0211] and the characteristic mass:

[00085]$\begin{array}{cc}m=\frac{hn}{2r_o{c}^2}& \left(3.32\right)\end{array}$

[0212] So that for field free space, therefore:

[00086]$\begin{array}{cc}{}_a{}_b{}^{ab}+{\left(\frac{mc}{h}\right)}^2=0& \left(3.33\right)\end{array}$

[0213] So that the appearance and compactification of a 5.sup.th dimension allows both charged and massive particles to appear from a previously vacuum filled universe. These particles can move and scatter off each other freely, increasing entropy, just like the shattering of a stone obelisk into pieces increases entropy. However, the values of the characteristic mass and charge are subject to some adjustment because the vacuum must be considered electrodynamic and vacuum polarization and thus renormalization must occur. For instance for a value of =n=1 and being its normal vacuum value the electron charge e requires the hidden dimension size r.sub.o to be of the order of the Planck radius, however, without renormalization this would require the mass scale to be the Planck mass. However, that part of the mass is due to interaction with the polarized vacuum around the charge and this must reduce, or renormalize, the mass. So, renormalization occurs and erases this problem of charge-to-mass in the Kaluza-Klein theory. This is equivalent to the model of a quartic potential, triggered by the appearance of a Higgs Boson, that gives particles non-zero masses that are none-the-less lowest energy state, due to a gravitation-like negative self-potential. An analogous model occurs in cosmology where the proton density n.sub.o.sup.2, that is: a quantum probability squared, contributes to the mass-energy of the universe by the equation for energy density

[00087]$\begin{array}{cc}w={}^2{m}_p{c}^2-\frac{8G}{3}{m}_p^2{}^4& \left(3.34\right)\end{array}$

[0214] where for =1 the second term becomes c.sup.2.

[0215] Another way this can be looked at is that a renormalization occurs due to quantum vacuum polarization over wavelengths from the Planck length to the size of the hidden dimension r.sub.o so, similar to the calculation for the self-energy of the electron:

[00088]$\begin{array}{cc}\ln \left[r_o/r_p\right]{}^{-1}& \left(3.35\right)\end{array}$

The Unification of Gravity and Electromagnetism and General Relativity

Section 1 The unification of gravity and electromagnetism and the Equivalence Principle

[0216] FIG. 11 is a Feynman diagram 1100 of photon-photon scattering, according to an implementation.

[0217] The cornerstone of General Relativity is the Equivalence Principle, which says all particles, regardless of charge or mass must fall at the same rate. This requirement is best satisfied by gravity forces not being forces at all, but by being manifestations of curvature of a spacetime manifold which all particles, even photons of light, are imbedded into, and on which the photons of light must follow geodesic paths. This requires photon-photon scattering to be an important process in curved spaces, as shown in FIG. 11. The solution is found through an interpretation of QED (Quantum Electro-Dynamics).

[0218] In QED both massive and massless particles interact constantly with an unseen vacuum full of ZPF fields and virtual particles. Even light can scatter off of light in QED, as shown in FIG. 11, so even photons can be considered to navigate across the vacuum by a series of interactions with photons of the ZPF. Thus, particles are bound to the electro-magnetism spacetime and forced to move by conforming to its structure by continual interactions. For charged particles, looking at the classical interaction of charged particles can be understood with arrays of EB drifts. For photons, spacetime is a substance that has a varying index of refraction, like a solid dielectric, and that just as a photon bends is path through a dielectric by a series of interactions with its molecules and atoms, according to an Eikonal equation, so photons must interact with the vacuum. In order for the photons to respond to the variations of an electrodynamic spacetime Quantum Photon-Photon scattering must be the process by which photons follow geodesics in curved space, as shown in FIG. 11.

Section 2 the Vacuum Bernoulii Equation

[0219] In the classical limit, a physical model of a gravity field as a curvature of a electrodynamic spacetime from Sakharov can be evaluated for consistency with a Kaluza-Klein 5.sup.th dimensional spacetime and its dynamics. First, we consider the classical limit of the Newtonian gravity potential which varies very slowly in time. Then a field Lagrangian for gravity can be determined, where g is the local gravity field:

[00089]$\begin{array}{cc}R-2g^2& \left(4.1\right)\end{array}$

[0220] which in the Newtonian limit is:

[00090]$\begin{array}{cc}.Math.g=-4G& \left(4.2\right)\end{array}$

[0221] Accordingly:

[00091]$\begin{array}{cc}\frac{R}{16G}=\frac{g^2}{8G}& \left(4.3\right)\end{array}$

[0222] And therefore in the Newtonian Limit where Kaluza-Klein Lagrangian:

[00092]$\begin{array}{cc}{L}_{KK}=\frac{g^2}{8G}-\frac{E^2-B^2}{8}& \left(4.4\right)\end{array}$

[0223] The Lagrangian is consistent with the concept of gravity fields in the unification of gravity and electromagnetism as arrays of EB drifts, as shown below.

[0224] When this model of electro-magnetism gravity is combined with Poynting's theorem, the Kaluza-Klein action falls out as a conserved quantity and can be called the VBE (Vacuum Bernoulli Equation). A brief version of VBE derivation is shown below. Assuming B.sup.2/2.sub.o is constant and vary E in time, then the charged particles can all accelerate at the same rate:

[00093]$\begin{array}{cc}\stackrel{}{V}=\frac{\stackrel{}{E}Bc}{B^2}=\frac{4\stackrel{.}{S}}{B^2}=\frac{\stackrel{}{S}}{2u_o}& \left(4.5\right)\end{array}$

[0225] Where u.sub.o=B.sup.2/8 and assuming some cycling of the E field to, as in a sawtooth waveform, with the reset being much faster than the particle cyclotron period 1/.sub.c, which can result in some inefficiency, which can be approximately expressed as:

[00094]$\begin{array}{cc}\stackrel{}{V}=\frac{.Math.\stackrel{}{E}.Math.\mathrm{Bc}}{B^2}=\frac{4.Math.\stackrel{}{S}.Math.}{B^2}\frac{\stackrel{}{S}}{2u_o}& \left(4.6\right)\end{array}$

[0226] The form Newtonian gravity theory can be written with gravity vector field g, where G is Newton's gravity constant:

[00095]$\begin{array}{cc}.Math.g=-4G& \left(4.7\right)\end{array}$

[0227] Assuming E=mc.sup.2 and so an electro-magnetic energy density can form a mass density as a source for a gravity field. This density becomes:

[00096]$\begin{array}{cc}=\frac{u}{c^2},u=\left(E^2+B^2\right)/8& \left(4.8\right)\end{array}$

[0228] Equation 4.8 means when electro-magnetic energy flows into a spherical region from all sides, gravity vectors pointing into the region increase in time so that, for the case of a spherically symmetric region, then:

[00097]$\begin{array}{cc}.Math.\stackrel{.}{g}=-4G\stackrel{.}{}=-4G.Math.S/c^2& \left(4.9\right)\end{array}$

[0229] Where both vectors can generate an additional vortex-like field F=A that include curls of a vector potential.

[0230] For the simplest case of no curl fields then:

[00098]$\begin{array}{cc}\frac{\stackrel{}{g}}{4G}=\frac{S}{2c^2}& \left(4.1\right)\end{array}$$\begin{array}{cc}\frac{\stackrel{.}{g}}{2G}.Math.g=S.Math.\frac{\stackrel{}{S}}{{}_o{c}^2}& \left(4.11\right)\end{array}$

[0231] Where .sub.o=(B.sup.2E.sup.2)/8 is an invariant magnetic field energy density.

[0232] Integrating, the VBE (Vacuum Bernoulli Equation):

[00099]$\begin{array}{cc}\frac{g^2}{2G}=\frac{S^2}{{}_o{c}^2}-C& \left(4.12\right)\end{array}$$\begin{array}{cc}\frac{g^2}{2G}-\frac{S^2}{{}_o{c}^2}+C=0& \left(4.13\right)\end{array}$

[0233] Upon substitution C=u.sub.o.sup.2/(2c.sup.2 u.sub.o) then

[00100]$\begin{array}{cc}\frac{g^2}{2G}-\frac{S^2}{{}_o{c}^2}+\frac{E^2+B^2}{{}_o{c}^{2}8}=0& \left(4.14\right)\end{array}$

[0234] The VBE satisfies the Equivalence Principle since in the situation of free fall, not only does g=0 but also the E field is zero in the falling frame, due to the properties of the EB drift, which is the frame where the Lorentz shift makes E=0 for the particle.

[0235] The Vacuum Bernoulli Equation states that when the local EM Poynting Vector S is increased, (such as by creating a Poynting Vortex under the conducting dome 110 in FIG. 1), the increased local EM Poynting Vector S creates an increased gravity pressure g2/(2G), as seen in FIG. 12, that presses on the underside of the conducting dome 110 in FIG. 1 and causes an effective lifting force on the conducting dome 110. This lifting force can provide human flight.

[0236] Using the expression

[00101]$\begin{array}{cc}-S^2/c^2+{\left[\frac{E^2+B^2}{8}\right]}^2={\left[\frac{E^2-B^2}{8}\right]}^2+\frac{{\left(E.Math.B\right)}^2}{8}& \left(4.15\right)\end{array}$

[0237] with <EB>=0 in the vacuum, that is, a vacuum made of electro-magnetism waves.

[0238] Therefore, approximately:

[00102]$\begin{array}{cc}\frac{g^2}{2G}-\frac{{\left(B^2-E^2\right)}^2}{{\left(8\right)}^2{}_o}=0& \left(4.16\right)\end{array}$

[0239] With the approximation that .sub.o=B.sub.o.sup.2/8 and the condition that E/B<<1 therefore:

[00103]$\begin{array}{cc}\frac{g^2}{2G}-\frac{\left(B^2-E^2\right)}{8}0& \left(4.17\right)\end{array}$

[0240] Equation 4.17 can be interpreted as a portion of the Kaluza-Klein Lagrangian with only a partial variation of the electro-magnetism field allowed, that is constant B. Therefore, the EB drift model of gravity appears consistent with Kaluza-Klein theory, with the Vacuum Bernoulii Equation being an equation describing small variations around the minimum value of the Kaluza-Klein Lagrangian, which can be likened to the nearly circular orbits of the planets where the Lagrangian itself becomes a constant of the motion.

[0241] Therefore, ignoring for the time being certain troublesome details: such as the relationship of the charge-to-mass problem to renormalization, and the full physical meaning of the =.sup.2 scalar field and its dynamics, the occurrence of particle spin, other physical quantities, the unification of gravity and electromagnetism postulates are basically consistent with an electrodynamic spacetime with a hidden 5.sup.th dimension of a combined Sakharov-Kaluza-Klein approach, at least in the case of vacuum equations.

Section 3. The Unification of Gravity and Electromagnetism and the Schwarzschild Metric

[0242] If the fundamental structure of spacetime is electro-magnetic, the metric tensor can be expressed as an electromagnetic tensor:

[0243] When this expression is used, the electro-magnetism stress tensor for the ZPF can be made to vanish as shown in the unification of gravity and electromagnetism.

[0244] Assuming isotropy the unified gravity-and-electromagnetism metric tensor follows as:

[00104]$\begin{array}{cc}{T}^{}=F_{}^{}{F}^{}-g^{}\frac{F_{}{F}^{}}{4}=0& \left(4.19\right)\end{array}$$g^{}={2\left[E^2-B^2\right]}^{-1}$$\begin{array}{cc}\left(\begin{array}{cccc}{E}^2& 0& 0& 0\\ 0& -E_x^2+B_y^2+B_z^2& 0& 0\\ 0& 0& -E_y^2+B_x^2+B_z^2& 0\\ 0& 0& 0& -E_z^2+B_y^2+B_x^2\end{array}\right)& \left(4.2\right)\end{array}$

[0245] Assuming a model of spacetime containing adjacent regions of strong E or B fields, the particles travel as wave packets and sample a volume swept out by a wave-front, thus the particles experience an average spacetime. An average over volume so that <B.sup.2>=<E.sup.2> and <E.Math.B>=0 results in a volume average of two metric forms one dominated by electric flux, for instance, in its local direction E.sub.y.

[00105]$\begin{array}{cc}{g}^{}=\left[\begin{array}{cccc}2& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& -2& 0\\ 0& 0& 0& 0\end{array}\right]& \left(4.21\right)\end{array}$

[0246] And another, in an adjacent region, by magnetic flux also in B.sub.y

[00106]$\begin{array}{cc}{g}^a=\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& -2& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& -2\end{array}\right]& \left(4.22\right)\end{array}$

[0247] Upon volume average, assuming large scale isotropy, the familiar Lorentzian flat space metric can be recovered as follows.

[00107]$\begin{array}{cc}.Math.g^a.Math.=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& -1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& -1\end{array}\right]& \left(4.23\right)\end{array}$

[0248] Accordingly, the flat space Lorentz metric can be viewed as an average of adjacent regions dominated by powerful E and B fields, as if spacetime was a ferroelectric and ferromagnetic material.

[0249] Considering the case of a space slightly curved by the presence of matter, and assuming that all fundamental particles are charged, in accordance with the Standard Model, and assuming that the quarks inside protons and neutrons enjoy ultraviolet freedom and move freely in response to the ZPF fields, the Schwarzschild Metric can be derived from the unification of gravity and electromagnetism, which requires assuming that below the high frequency cutoff of the hidden dimension electrodynamics proceed normally in a local sense, except that the fields effect matter on larger length-scales only though the effect of the field on the metric rather than directly by electro-magnetism forces.

[0250] A charged point particle in the vacuum that is scattering ZPF radiation and creating a 1/r radiation E field around itself, creates an interference pattern and thus first order energy density, with the incident ZPF. This 1/r dependence will ultimately lead to the Schartwzschild metric in the limit of weak fields. To recover this metric, to leading order in Gm/(c.sup.2r)<<1, using approximate methods of classical electrodynamics. Quantum electrodynamics is required for such a calculation to be done accurately, rather than classical methods, since the calculation involves scattering of photons in highly relativistic and subatomic scenarios. Assuming this caveat, classical approximations can be assumed to obtain results to leading order, since the classical approximations should apply for weak fields and widely separated particles, as is the cosmic situation.

[0251] Beginning with the situation of the particles in the deep subatomic realm near the Planck scale, and assuming that the unification of gravity and electromagnetism of the vacuum requires alternative regions of E and B fields, the Lorentzian flat space metric emerges as the result of averaging. When the charged particles are assigned to the magnetic field regions and assuming that the magnetic field and the neighboring region are oriented in the y-direction, and assuming the magnetic fields are very strong and thus the charged particle is free to move only in the y direction, the ZPF are powerful electro-magnetism waves that scatter off of the charged particles but only with E fields of polarization in the y direction, where the charged particles are free to move.

[0252] FIG. 12 is a diagram of the gravity pressure and hydrostatic pressure 1200 of the Earth, according to an implementation. The quantity g.sup.2/(8G) 1210, has units of pressure, and can be understood as a physical pressure. This is easily seen from a model of a planet such as Earth. In FIG. 12, hydrostatic pressure is a maximum at the center of the Earth 1220 whereas gravity field strength g is zero, as is g.sup.2/(8 G), by Newton's law of gravity. On the earth's surface 1230 however, P=0 and both g and g.sup.2/(8G) 1210 are at a maximum. Taken as a whole, the equation P (core of the Earth)g.sup.2/(8 G) (surface of the Earth) and close to the Earth's surface 1230 the equation of equilibrium: P+g.sup.2/(8G)=Constant, applies approximately. Therefore g.sup.2/(8G) 1210 can be considered a physical pressure, like static pressure in the Bernoulli Equation.

[0253] FIG. 13 is a conceptual diagram of radiation 1300 scattering off of a charged particle and creating a donut shaped region of interference between the scattered and incident waves, according to an implementation.

[0254] The E.sup.2 energy density of the interference pattern of the scattered radiation field E.sub.r and a uniform incident ZPF field E.sub.i forms a donut shaped region around the charge in a x-z plane but has vanishing strength in the y direction.

[0255] The particle radiating power flux, S=cE.sub.r.sup.2/4, in esu units, because of its motion the ZPF creates an electric field stress on the surface of a sphere of radius r, centered on the particle, and normalized to the Thompson cross section at the classical radius of the charge, which has a mass of m, r.sub.c=e.sup.2/mc.sup.2, is proportional to the radiated power of the particle, where is the acceleration of the particle.

[00108]$\begin{array}{cc}\frac{8}{3}{r}^2\frac{E_r^2}{4}c=\frac{2}{3}\frac{q_p^2}{c^3}{a}^2& \left(4.23\right)\end{array}$

[0256] This expression limited to <c.sup.2/r.sub.c, is the particle classical radius in esu units. Where the acceleration is limited to the value =c.sup.2/r.sub.c, and obtain, upon simplification.

[00109]$\begin{array}{cc}{E}_r=E_c\frac{r_c}{r}& \left(4.24\right)\end{array}$

[0257] Where E.sub.c=e/r.sub.c.sup.2, the electric field at the classical particle surface. Given the dependence of r.sub.c on the particle mass, this relation ties the scattered radiation field strength to the particle mass, m.

[0258] When the mean interference term is added between the particle radiation and the ZPF electro-magnetism radiation fields of strength E.sub.i=q.sub.P/r.sub.P.sup.2, the time averaged field strength is:

[00110]$\begin{array}{cc}.Math.E_i\sin 2t.Math.\frac{1}{2}{E}_i& \left(4.25\right)\end{array}$

[0259] From equation 4.25, an energy density of interference between the scattered field and the ZPF E field, using the expression for the Planck charge q.sub.P=e.sup.1/2 where is the fine structure constant, is defined for the metric tensor as:

[00111]$\begin{array}{cc}{E}_y^2=.Math.E_r{E}_i.Math.\frac{1}{2}{E}_c\frac{r_c}{r}\frac{q_p}{r_p^2}& \left(4.26\right)\end{array}$

[0260] Gravity fields thus arise from the random interference of the fields of the ZPF and the radiation fields of the ZPF scattered off of charged particles. Using r.sub.c=e.sup.2/mc.sup.2, Eq. 4.26 can be simplified as:

[00112]$\begin{array}{cc}\frac{.Math.E_r{E}_i.Math.}{B_y^2}\frac{1}{2}\frac{e}{r_c}\frac{1}{r}\frac{q_p}{r_p^2}\frac{{\mathrm{Gr}}_p^2}{c^4}=\frac{\mathrm{Gm}}{{\mathrm{rc}}^2}\frac{{}^{-1/2}}{2}& \left(4.27\right)\end{array}$$\begin{array}{cc}\frac{1}{2}\frac{E_y^2}{B_y^2}\frac{{}^{-1/2}}{4}\frac{\mathrm{Gm}}{{\mathrm{rc}}^2}& \left(4.28\right)\end{array}$$\begin{array}{cc}\frac{{}^{-1/2}}{4}1& \left(4.29\right)\end{array}$

[0261] The Newtonian gravity potential, is =identified as:

[00113]$\begin{array}{cc}\frac{1}{2}\frac{E_y^2}{B_y^2}\frac{\mathrm{Gm}}{r}=& \left(4.3\right)\end{array}$

[0262] The metric tensor in the electric region, Eq. 4.21, is unchanged. The magnetic terms for the radiation field have interference terms with the incident wave that average to zero, as do contributions from E.sub.x and E.sub.z.

[00114]$\begin{array}{cc}{g}^{}={2\left[E^2-B^2\right]}^{-1}\left(\begin{array}{cccc}{E}_y^2& 0& 0& 0\\ 0& B_y^2& 0& 0\\ 0& 0& -E_y^2& 0\\ 0& 0& 0& B_y^2\end{array}\right)& \left(4.31\right)\end{array}$

[0263] Solving for the metric tensor in the magnetic region of the general form yields:

[00115]$\begin{array}{cc}{g}^{}={\left[1-E_y^2/B_y^2\right]}^{-1}\left[\begin{array}{cccc}-2E_y^2/B_y^2& 0& 0& 0\\ 0& -2& 0& 0\\ 0& 0& -2E_y^2/B_y^2& 0\\ 0& 0& 0& -2\end{array}\right]& \left(4.32\right)\end{array}$

[0264] Accordingly:

[00116]$\begin{array}{cc}{}^{}=\left(1-2/c^2\right)& \left(4.33\right)\end{array}$

[0265] To obtain the metric contribution at a distance in spherical coordinates, when averaging over the surface of a sphere for quantities which vary with angular distribution, and when a small reduction factor of S is introduced on the total electrical energy density term, term g.sup.oo, to compensate for the relativistic distortion of the interference donut, by the motion of the charge, its total amount in a volume is conserved, even if its local density is increased by relativistic effects. Accordingly,

[00117]$\begin{array}{cc}.Math.g^{}.Math.=\left[\begin{array}{cccc}-1-2/c^2& 0& 0& 0\\ 0& -1/{}^{}& 0& 0\\ 0& 0& -1+2/c^2/S& 0\\ 0& 0& 0& -1/{}^{}\end{array}\right]& \left(4.34\right)\end{array}$

[0266] The corresponding components of the Schwarzschild metric can be found by using the expression, g.sup.rr=(x.sup.2 g.sup.xx+y.sup.2 g.sup.yy+z.sup.2 g.sup.zz)/r.sup.2, where r.sup.2=(x.sup.2+y.sup.2+z.sub.2). Averaging over the surface of a sphere of radius r around the charge and noting that the g.sup.yy contribution to such an average must vanish, due to the Sin.sup.2 dependence of the donut shaped interference pattern around the charge, where the y axis corresponds to =0 and ., is the spatial counterpart to the relativistic factor of S made on the energy density term in the time-time portion of the tensor, in order to obtain a spherical metric from a Cartesian one. Averaging again over orientations of the paired magnetic-electric domain, assuming macroscopic isotropy and thus obtaining an approximate value for the value of <g.sup.rr>. Thus, the leading order in /c.sup.2 the time-time portion of the Schwarzschild metric can be expressed:

[00118]$\begin{array}{cc}.Math.g^{\mathrm{tt}}.Math.1-2/c^2=1-\frac{2\mathrm{Gm}}{{\mathrm{rc}}^2}& \left(4.35\right)\end{array}$

[0267] After spatial and angular averaging, to leading order in /c.sup.2, the time-time element of the Schwartzchild metric is:

[00119]$\begin{array}{cc}.Math.g^{\mathrm{rr}}.Math.\frac{-1}{1-2/c^2}& \left(4.36\right)\end{array}$

[0268] Therefore, under the form of the metric tensor required for self-censorship of the ZPF, and its requirements on the structure of the vacuum to give a Lorentzian metric, the electrodynamics of a charge in the vacuum, scattering electro-magnetism waves from the ZPF, create an interference pattern in the electric field, which leads to the Schwarzschild metric, at least to leading order. The 1/r dependence of the scattered radiation E field and the form of the self-censoring metric, creates the Schwarzschild metric:

[00120]$\begin{array}{cc}{\mathrm{ds}}^2=\left(1-2/c^2\right){\mathrm{dt}}^2-{\mathrm{dr}}^2/\left(1-2/c^2\right)+r^2\left(\mathrm{Sin}{}^{2}d{}^2+d{}^2\right)& \left(4.37\right)\end{array}$

[0269] and, by extension the Newtonian gravity potential.

[0270] Therefore, the unification of gravity and electromagnetism is consistent, to first order with the requirements of the Kaluza-Klein model of GR and Maxwell's equations.

Vacuum Decay and Cosmology in the unification of gravity and electromagnetism

Section 1. The Cosmic Consequences of a Hidden 5.SUP.th .Dimension

[0271] Edward Witten made the discovery in 1981 that the presence of a hidden 5.sup.th dimension in the vacuum created an instability, causing expanding mirror-surfaced spherical regions to form expand at the speed of light. This death by disco-ball scenario stems from the property of spacetime, that several possible minimum energy states are accessible when a hidden 5.sup.th dimension is added, and once accessed, these states can form a path to an even lower energy state for the system as a whole. This instability is moderated by the existence of quantum fields which would diffuse the instability among many different particle modes.

[0272] In the unification of gravity and electromagnetism, where QED is included implicitly in our concept of spacetime, the presence of a hidden dimension as degree of freedom acts as a leak or tunnel in spacetime, allowing quantum transitions to occur between two states, empty space and space with a proton-electron pair.

Section 2. The Probability of a Transition in Unification of Gravity and Electromagnetism

[0273] Beginning with consideration of the Dirac Large Numbers Hypothesis, in esu units:

[00121]$\begin{array}{cc}\frac{{\mathrm{Gm}}_p{m}_e}{e^2}\frac{r_e}{R_H}& \left(5.1\right)\end{array}$

[0274] Here G is the Newton Gravitation Constant, m.sub.p and m.sub.e are the proton and electron mass respectively, and r.sub.e is the classical electron radius r.sub.e=e.sup.2/(m.sub.ec.sup.2) and R.sub.H is the Hubble radius, which is the Hubble Time T.sub.H times the speed of light: R.sub.H=cT.sub.H

[00122]$\begin{array}{cc}=\frac{8{\mathrm{Gm}}_p{\mathrm{nR}}_H^2}{3c^2}1& \left(5.2\right)\end{array}$

[0275] Where n is the number density of hydrogen plasma in space, critical optical thickness of the cosmos can be correlated as follows:

[00123]$\begin{array}{cc}{}_{\mathrm{Th}}{\mathrm{nR}}_H=\frac{8r_e^2{\mathrm{nR}}_H}{3}1& \left(5.3\right)\end{array}$

[0276] Where .sub.Th=8r.sub.e.sup.2/3 is the Thompson scattering cross-section for electro-magnetism radiation. If gravity is mediated by some sort of electro-magnetism quanta, and assuming the hydrogen in space is fully ionized, which can be equated to the critical optical thickness to the condition of a critically open Cosmos:

[00124]$\begin{array}{cc}\frac{8r_e^2{\mathrm{nR}}_H}{3}\frac{8{\mathrm{Gm}}_p{\mathrm{nR}}_H^2}{3c^2}& \left(5.4\right)\end{array}$

[0277] Eq. 5.1 can be obtained upon simplification. Implicit in this analysis is the assumption that the electro-magnetism scattering cross section of the electron is also the unification of gravity and electromagnetism interaction cross section of the other particles, most specifically the proton. he effective radius of the proton is r.sub.pe=1.410.sup.13 cm, which is the Compton wavelength of the charged pion, is approximately equal to the electrostatic radius of the electron r.sub.e/2=1.4110.sup.13. Therefore, for now, the proton and electron can be considered to have approximately the same size when considered in the loose sense of a unified interaction. Therefore, the Dirac condition is consistent with the critical density of matter in the universe for gravitational interactions, being correlated with the electro-magnetism critical scattering thickness of the Cosmos. Accordingly, the Dirac relation is consistent with a Cosmos where gravity interactions are a form of electro-magnetism interaction and the visible universe is both critically interacting gravitationally and electromagnetically. The Dirac Condition therefore evokes a concept of the Cosmos where each part of the Cosmos is in interaction with another part through a bath of electro-magnetism-like radiation.

[0278] The idea of gravity forces between bodies being caused by the interaction of the bodies with a bath of quanta is not new, being originally proposed by Fatio in the time of Newton. Such theories have been termed kinetic theories of gravity but were not put on a reasonable physical basis until Sakharov equated the bath of radiation with the ZPF.

[0279] The unification of gravity and electromagnetism can be tested by adopting a simple Sakharov model of gravity and asking what the radiation pressure must be to cause the gravity force between two electrons floating in space. The gravity force can be equated between two electrons separated by a distance D that is large compared to the dominant wavelengths .sub.bath of the radiation bath, that is, .sub.bath/D<<1 to the pressure of a radiation field acting on a Thompson cross section of each electron.

[0280] This leads us to write a leading order approximation expression for the gravity interaction between two electrons as being due to a mutual shadowing of an electro-magnetism radiation pressure:

[00125]$\begin{array}{cc}\frac{{\mathrm{Gm}}_e^2}{D^2}\frac{{}_{\mathrm{Th}}^2{P}_r}{D^2}& \left(5.5\right)\end{array}$

[0281] Solving for the radiation pressure,

[00126]$\begin{array}{cc}\frac{{\mathrm{Gm}}_e^2}{{}_{\mathrm{Th}}^2}{P}_r& \left(5.6\right)\end{array}$

[0282] And assuming the electro-magnetism radiation field is Planckian and solve for its temperature, where .sub.SB is the Stefan-Boltzmann constant:

[00127]$\begin{array}{cc}\frac{{\mathrm{Gm}}_e^2}{{}_{\mathrm{Th}}^2}{P}_r=\frac{4}{3}\frac{{}_{\mathrm{SB}}{T}_{\mathrm{bath}}^4}{c}& \left(5.7\right)\end{array}$

[0283] Remarkably, the temperature is very close to the observed temperature of the CBR (Cosmic Background Radiation) which is 2.73K

[00128]$\begin{array}{cc}{T}_{\mathrm{bath}}={\left[\frac{3}{4}\frac{c}{{}_{\mathrm{SB}}}\frac{{\mathrm{Gm}}_e^2}{{}_{\mathrm{Th}}^2}\right]}^{1/4}=2.65K& \left(5.8\right)\end{array}$

Section 2 the Quantum Probability of the Interaction of Unified of Gravity and Electromagnetism

[0284] The gravitational interaction is very weak on a subatomic scale compared to the electro-magnetism interaction. In the context of unified of gravity and electromagnetism the Gravitation constant can be expressed approximately as:

[00129]$\begin{array}{cc}G\frac{e^2}{m_p{m}_e}\exp \left(-2{\left(m_p/m_e\right)}^{1/2}\right)& \left(5.9\right)\end{array}$