aquino - gravitational-electromagnetic field theory (1992)

• Unification of the Interactions • Interrelation between Gravitation and Electromagnetism • Incorporation of the Mach's Principle in the Gravitation Theory • Elimination of the Initial Singularity in the Friedmann Cosmological Model • Explanation for the White-Holes • Explanation for the Anomalies Verified in the Red-Shift of Stars and Galaxies • Explanation for the Quasars • Gravitation Control; Applications in Spacecraft • Explanation for Levitation; Applications Resulting from the Self-Control of the Gravitational Interaction • Gravitational Motor • Cold Nuclear Fusion and Transmutation of Chemical Elements by Gravitational Process • Superconductivity at Ambient Temperature by Cooper's Pairs Formation via Intensification of the Gravitational Forces

The Gravitational-Electromagnetic Field Theory, by author Fran de Aquino, describes in a consistent and rigorous way the unification of the four interactions: strong, weak, electromagnetic, and gravitational. It establishes still the interrelation between gravitation and electromagnetism, showing that it is possible to control the gravitational interaction by means of the action of electromagnetic fields. It is an extensive theory in which a great number of different things are interconnected. We can meet in it the incorporation of Mach's principle in the gravitation theory; the elimination of the initial singularity in Friedmann's cosmological model; explanation for anomalies verified in red shifts of stars and galaxies. It explains also the bases for the control of gravitation leading to some technological applications such as: gravitational propulsion, nuclear cold fusion, transmutation of chemical elements through gravitational process, superconductivity at ambient temperature by Cooper's pairs formation through intensification of the gravitational forces, and so on. In addition to these, we have to emphasize two other important aspects: It is possible to deduce directly from this theory the expression of the uncertainty principle that means the incorporation of quantum mechanics in Gravitational-Electromagnetic Field Theory. It is foreseen the existence of a fifth interaction, the psychic interaction, identified in the ascertainment of the apparent parity violation in beta decay reactions.

SUMMARY

Preface.................................................................................1

Introduction .........................................................................5

I. Theory ............................................................................21

II. Cosmological Applications...........................................63

III. Gravitational Spacecraft ............................................75

IV. Levitation...................................................................87

V. Energy Conversion ...................................................... 99

VI. Superconductivity ...................................................111

VII. Experimental............................................................ 119

"There are those who cross the forest and only see firewood"

Leon Tolstoi (1828/1910)

PREFACE

In this book we shall show that interactions may be described in a unified manner in a single classical theory, gathering in two large groups gravitational and electromagnetic interactions. Strong and weak nuclear interaction, as well as electrostatic, magnetostatic and electrodynamic interactions, make up the electromagnetic interactions group. The second group, of gravitational interactions, encompasses two types of interaction: gravitational interaction in the presence of electromagnetic fields, and pure electromagnetic interaction (absence of electromagnetic fields).

We use the General Theory of Relativity as the basis for our study, after having established the concept of gravitational-electromagnetic mass, herein introduced to complement the well-known concepts of gravitational and inertial mass.

The Unified Field Theory as stated herein establishes the interrelation between gravitation and electro-magnetism, showing that interaction described by the Newton-Einstein theory is a particular case of gravitational interaction that occurs in the absence of electromagnetic fields (pure gravitational interactions).

To conclude from the new equations obtained herein, gravitational interaction in the presence of electromagnetic fields may be attractive, null or repulsive, as opposed to pure gravitational interaction, which is known to be always attractive. In pratice, this means

2 GRAVITATIONAL - ELECTROMAGNETIC FIELD THEORY

precisely that the gravitational interaction may be controlled by the action of electromagnetic fields. From the theoretical viewpoint, these findings lend a wider significance to gravitational interaction, such as permitting the incorporation of Mach's principle in the theory of gravitation. According to that principle, local inertial forces are nothing but the gravitational influence of the other particles of the Universe. It may thus be possible to observe the disappearance of the inertial forces in a given particle, because the gravitational forces that act on it may be cancelled by the action of the external electromagnetic fields.

The Gravitational-Electromagnetic Field Theory furthermore makes it possible to explain cosmological phenomena of great interest, such as the final stage of the Universe's gravitational contraction process at each cycle, as well as the anomalies recorded in recent analysis of the red-shift in certain galaxies and stars. In addition to these cosmological applications, the theory makes it possible to identify a number of applications of a pratical nature, which should eventually yield important technological innovations. Among these are gravitational spacecraft and the gravitational motor, whose basic features are described in this book. Furthermore, the application of electromagnetic control to gravitational interaction in the nuclear fusion process deserves special mention.

In that application, it should be possible to make

FRAN DE AQUINO 3

the nuclei come close to each other and react, simply by raising the gravitational forces between them.

By the same process we can intensify the gravitational forces between electrons of atoms of a given substance to obtain the formation of pairs of electrons (Cooper's pairs) which is an essential requisite for the substance to get into the superconductor state.

I wish to express my thanks to all those who, directly or indirectly, contributed to this work, in particular to my friend and colleague Selisio Santiago Freire for his many valuable suggestions.

FRAN DE AQUINO

Sao Luis, (MA), Brasil

INTRODUCTION

In its desire to understand nature, mankind has sought

to discover universal laws that might explain in a unified

form the phenomena occurring in the Universe. Thus, the

unification of fundamental forces has been a constant theme

in physics, ever since Maxwell proved in the second half of

the 19th century that electrostatic and magnetostatic forces

were nothing but different manifestation of the same force.

With this unification, he triggered in the scientific

community of that time the ambition of unifying in one

single theory the two interactions then known, viz.

Electromagnetic and gravitational, described respectively by

the laws of Maxwell and Newton.

In 1916 Einstein proposed his General Theory of

Relativity which made it possible to describe gravitational

interaction with a precision by far exceeding that of

Newtonian Theory. Einstein's Theory rekindled hopes of

unifying the interactions.

In 1918, H. Weyl1 published a study on the subject.

Weyl proposed to modify the metrics connection used

1 Weyl, H. (1918). Sitzungsber. d. Preuss. Akad. d. Wiss, p. 465.


by Einstein in describing gravitation, by an equivalent

connection in which the electromagnetic field would be

contained in the tensor associated with the connection,

which distinguishes it from Christoffel's symbols.

Kaluza2 also tried, in 1921, to unify the two interac-

tions. While Weyl constructed a non-Riemannian geometry,

Kaluza increased the number of components of the metric

tensor, raising the number of dimensions: he believed that

in addition to the four dimensions (three spatial and one

temporal) there was a fifth, which did not have a direct

physical meaning.

Einstein himself, after relating gravitation to space-

time, was convinced that there also had to be some relation

between electromagnetism and gravitation. The Unified

Field Theory was the result of that conviction.

However, in spite of all the efforts - by Einstein as well

as his successors - these ended in failure. The attempts to

unify the two interactions proved fruitless.

2Kaluza, Th.(l92l). Sitzungsber. d. Preuss. Akad. d. Wiss, p. 966

FRAN DE AQUINO 9

In the thirties, two new forces were added to the known

fundamental forces of nature. They had been proposed in

order to explain several physical phenomena observed after

the discovery of radioactivity. The first force - proposed in

1934 by Fermi - would later (after the work of Feynmann

and Gell-Mann, starting in 1958) be called the weak

interaction, to which were attributed known radioactive

phenomena such as beta-decay. The second force, called the

strong interaction, was the result of the theory that nuclei

were made up of protons and neutrons, and that the nucleus'

stability derived from the existence of this new kind of

force. Thus there were known, by the end of the thirties, the

four types of fundamental interactions in nature, re-

spectively: strong, electromagnetic, weak, and gravitational,

whose relative intensities varied in the ratio of 1: 1/137:10-

12 : 10-39, respectively.

In the forties, while some workers were trying to unify

the electromagnetic and gravitational interactions, physicists

who were investigating elementary particles started to get

involved with another type of


unification - that of the strong, weak, and electromagnetic

forces.

With the advent of renormalizable quantum elec-

trodynamics it became possible to explain electromagnetic

interaction. This achievement encouraged physicists to

search for explanations for the other interactions. In 1954,

Yang and Mills generalized quantum electrodynamics,

introducing Gauge Symmetry and thus explaining

interactions communicated via quanta, charged or not, of

spin 1 (bosons), and not massive. Yang-Mills' theory

became known as Gauge Quantum Electrodynamics, and

would later supply the foundation for the Salam-Weinberg

theory that explains the origin of the weak interaction,

showing that it is of an electromagnetic nature.

According to the Salam-Weinberg theory, electro-

magnetic and weak interactions are communicated via the

exchange of four quanta: photons, in the case of

electromagnetic interaction; a pair of charged bosons, W+

and W-, in the case of weak interactions between leptons;

and finally, the neutral Z0 boson, responsible for weak

interactions with neutral lepton currents,

FRAN DE AQUINO 11

in which the scattering between neutral and charged leptons

occurs without the exchange of electric charge. In view of the

success of the Salam-Weinberg theory, physicists took a fresh

look at theories of the Yang-Mills-Salam-Weinberg type,

utilizing them in their efforts to explain the strong interaction.

Theories that explain the strong and weak interactions as

electromagnetical are known as Grand Unification Theories or

GUTs. In fact, this is an overly ambitious designation for theories

that do not even include gravitation, and that confine themselves

to explaining the origin of strong and weak interactions without

being able to describe them.

The fact that gravitational interaction can also be explained

by a quantum theory (involving the exchange of "virtual"

quanta3), and is described by a classical theory, makes it clear

that quantum theories are effective in explaining interactions,

even though they are unable to describe them. Classical theories,

on the other hand, though unable to explain interactions, can

describe them precisely. It is therefore to be

3As yet incompletely identified


expected that a unified theory of interactions, designed to

describe all interactions in a unified manner, would be a classical

theory.

In Chapter I we state the theory of the Gravitational-

Electromagnetic Field based on the ho-mogenization of the

quantities responsible for the interactions, such as: gravitational

mass mg; electric charge q; pole intensity p; etc. The new

quantity, which we call gravitational-electromagnetic mass,

allows a unified description of interactions, by means of

Einstein's equations from the General Theory of Relativity.

Gravitational-electromagnetic mass is nothing but the sum of

the particle's gravitational mass mg and electromagnetic mass me

(the latter defined so as to homogenize the quantities responsible

for electromagnetic interaction). So far as concerns the

gravitational mass of an elementary particle, we show that it is re-

lated to the inertial mass through the following factor:

FRAN DE AQUINO 13

which only differs significantly from unity under conditions

of extremely high electromagnetic energy density. In this

expression, W refers to the geometric media of volumetric

densities of external electromagnetic energy in the interior

of the particle, while refers to the volumetric density of

the particle's rest inertial energy.

The new equations for gravitational interaction that

result from the introduction of the said factor give a wider

meaning to gravitation and make it possible to explain a

number of physical phenomena of great interest.

From the new expressions for the gravitational forces in

a system of two isolated particles we conclude that the

gravitational forces that act on an elementary particle may

be not only reduced, but also inverted and intensified by the

action of electromagnetic fields.

In the case of macroscopic bodies, we find that

gravitational interaction may be controlled with lesser

volumetric densities of external electromagnetic energy.

What is more, we note that by means of a process we call

electromagnetic reversion it is possible to obtain


analogous effects with electromagnetic energy densities that

are much smaller yet.

Next, we check the effect of thermal radiation on the

gravitational mass of elementary particles and find that the

gravitational mass of these particles will be equal to their

inertial mass only when T = 0°K. At higher temperatures,

the gravitational mass will become smaller.

At room temperature, however, such variations are very

small and require very precise instruments for determination

(1 part in 1016). Fortunately, experiments at such a level of

precision are possible and have recently been carried out by

B. Holstein and J. Donoghue of the University of

Massachusetts, who found that electrons have about 10-14%

less gravitational mass at room temperature than at absolute

zero.

Another important agreement between the theory of the

gravitational-electromagnetic field and experience is to be

found in the gravitational interaction between atomic nuclei.

Here, we find that the relations

FRAN DE AQUINO 15

for their nucleons can reach magnitudes of the order of 10-2

as a consequence of the high densities of electromagnetic

energy, reciprocally determined in the interiors of the

nucleons by the intense electric and magnetic fields of these

particles. In accordance with the new equations obtained for

the intensities of the gravitational forces, this means that in

gravitational interactions at such levels there may occur

intensity variations of the order of 1%.

Recently, variations in the intensity of subatomic

gravitational forces, of the same order of magnitude, were

found experimentally - which led some authors to think of

the existence of a fifth interaction.

In Chapter II we present cosmological applications

derived from the Gravitational-Electromagnetic Field

Theory. At the outset we show, with respect to the final

stage of gravitational contraction of massive stars and

systems of greater mass, that at a certain stage of

gravitational contraction the neutrons' magnetic spin fields

may reduce the gravitational forces of attraction among

them to a point such that the gravitational pressure falls

below the thermal pressure,


causing the explosion of the system. Everything suggests

that the Universe itself must pass through this kind of stage

in the final moments of compression that culminate with the

Big Bang. Next, analysing the problem of the anomalies

found in the red-shift in the spectrum, we conclude that

such anomalies may be explained through the new

expression for the gravitational spectrum-shift, obtained in

this study. According to this expression, the shifts

calculated through Einsten's formula must be multiplied by

a dimensionless electromagnetic coefficient; the spectrum

differences should be interpreted as being the result of

intense volumetric energy densities in the observed bodies.

According to the same explanation, the huge red-shift of

quasars should not be interpreted as a Doppler shift - as is

normally done - but instead as a gravitational red-shift,

which should be calculated in accordance with the new

expression for gravitational spectral shifts.

Chapter III is devoted to a study of the control of

gravitational interaction in the specific case of utilization by

gravitational spacecrafts. We show how

FRAN DE AQUINO 17

spacecrafts may be endowed with unique performance

characteristics which, in the case of atmospheric travel,

allow them to move with various degrees of freedom and, in

the case of travel in outer space, allow them to reach

relativistic velocities, without the crew's undergoing any of

the inertial effects caused by the enormous rates of

acceleration required to reach velocities close to that of

light.

The study of control systems for gravitational in-

teraction, developed for spacecrafts, made us seriously

consider the possibility that the human body may possess

means of controlling gravitational interaction on itself. In

Chapter IV we show that the phenomenon of levitation may

be the result of a bioelectromagnetic process, involving the

nervous system's neurons and the body's water molecules.

On the basis of this process - in which water molecules

are subjected to a gravitational force that is repulsive in

relation to Earth, as a result of the fact that the ratios for such molecules may, under

certain circumstances, become greater than 1 - we find that

the performance of a gravitational spacecraft may


even be further improved. Among the gravitational effects

that can be produced we should mention the production of

artificial gravity inside the spacecraft, for the purpose of

atracting crew members to its floor (in cases of travel in

outer space). That could be done by intensifying the

attracting gravitational force between the water molecules

in the human body and those purposely placed in a reservoir

below the craft's floor.

In Chapter V, we study applications of electromagnetic

control to gravitational interaction for purposes of energy

conversion. We start by describing the Gravitational Motor

that essentially resembles a hydraulic turbine and whose

operating principle consists of causing to become repulsive

the gravitational force between Earth and the water

molecules on one side of the toroidal chamber of the

turbine. This makes for a rotary flow of water in the

chamber that impels the rotor. By coupling a conventional

electric generator to the gravitational motor, gravitational

energy may be converted in electrical energy. Still in this

chapter we shall focus on the gravitational process for

nuclear

FRAN DE AQUINO 19

fusion, a process which basically consists of using grav-

itational in lieu of thermal energy, in order to make nuclei

come close and react. Obviously, this is a process of cold

fusion, which may turn out to be very important for energy

production purposes.

Finally, in chapter VI we show that by the elec-

tromagnetic control of the gravitational interaction we also

can intensify the gravitational forces between the electrons

of atoms of a given substance and form the so called

Cooper's pairs, consequently allowing the substance to enter

the superconductor state at room temperature.

I. THEORY

In order to formulate a unified theory on interactions, we must at first homogenize the quantities in charge of interactions, such as: the gravitational mass mg, electric charge q, the pole intensity p, etc., so they can be united in a single expression.

Since the Einstein's equations have bigger chances to lead us to an unified theory than Maxwell's equations, since these latter are formulations corresponding to our experiences with very weak electromagnetic fields, let us unify all the quantities standing for the interactions into a single quantity, to be called gravitational-electromagnetic mass, mge, given by:

mge =mg + me (1-01)

where me is the electromagnetic mass which, in turn, is made up by the sum of the electric mass mq, magnetic mass mp, strong mass mF and the weak mass my. These latter two masses are respectively responsible for the strong and the weak interactions. Accordingly, we can write:

me = mq + mp + mF + mf (1.02)

and the electric and magnetic masses can be expressed as functions of q and p, respectively, i.e., we can write that mq =

and mp = where and are


coefficients of proportionalities. The expression for mF and mf

will be obtained later on.

The equation (1.02) presuppose the existence of magnetic

monopoles. Such monopoles foreseen by the first time 58 years

ago by P.A.M. Dirac1 only have had their masses evaluated in

1967 with the advent of the Salam-Weinberg Theory. It was

verified that inertial mass of the magnetic monopoles can be

some hundred times greater then the proton mass.2 In the

seventies, experiments carried out by Price, Shirk, Osborne e

Pinsky3 showed the possible existence of a magnetic monopole

with inertial mass about two hundred times greather than the

proton mass.

So far as concerns the gravitational mass mg, the experience

has not revealed any difference between mg and the inertial mass

m. By the way, Newton was the one to try to verify the existence

of a difference between said masses. He tried experiences with

simple pendulum, trying to verify variations in the m/mg ratio,

from the well-known expression

1 Dirac, P.A.M (1931), Proc. Roy. Soc., A 133, 60. 2 Hooft, G. (1974), Nucl. Phys. B 79, 276. 3 Price, P.B., Shirk, E.K., Osborne, W.Z., Pinsky, L.S. (1975) Phys. Rev. Lett., 35, 487.

FRAN DE AQUINO 25

for the simple pendulum period. Since no variation was found,

Newton inferred that the inertial and gravitational masses were

equivalent among each other.

In the late XIX Century, science had already at its

disposition very precise measuring instruments, and once again,

experiments were made towards finding a difference between m

and mg. It was the well-known experiment of Eotvos4 later on

repeated by P. Zeeman5 and Eotvos, Pekar and Fekete6 (with

precision better than 1 part per 109). Nevertheless, also in said

experiments, no difference could be found, between the inertial

mass and the gravitational mass.

More recently, the experiment was repeated with an even

better precision, by R. H. Dicke7 (variations of 1 part per 1011

could be detected). Subsequent repetitions of the Eotvos

experiment were further performed

4 Eotvos, R.V. (1890), Math. Naturwissen, Ber. Ungarn 8. 65 5 Zeeman, P. (1917), Proc. Ned. Akad. Wet, 20, 542 6 R. V. Eotvos, D. Pekar and E. Fekete (1922), Ann. Phys. 68, 11 7Dicke, R. H. (1963), Experimental Relativity in "Relativity, Groups and Topology" (Les Houches Lectures), p. 185


by Roppl, Krotkov and Dicke8 and by Braginskii and Panov9 the result was the same: no difference between the inertial mass and the gravitational mass could be found.

These experimental results express by no means the lack of existence of a connection between gravitational mass and inertial mass to the contrary, they just indicate that said relation is very difficult to be found experimentally, under the conditions the experiments were performed. We are to notice, then, that all said experiments were made under low external electromagnetic energy density conditions, and that is precisely the most important factor to be considered. A very important theoretical contribution for this question was obtained by J. Donoghue and B. Holstein10 that in 1986 showed, making use the formal methods of Quantum Mechanics, that the mass renormalization at T = 0 is expressed by mr = m+ with

(a is defined by the conventional Dirac Hamiltonian, H =

and, that the mass renormalization at T > 0 leads to the following expressions

8 P. G. Roppl, R. Krotkov and R. H. Dicke (1964) Ann. Phys. NY, 26, 442 9 V. B. Braginskii and V. I. Panov (1971), Zh. Eksp. Teor.

Fiz., 61, 873 10 Donoghue, J.F. and Holstein, B.R. (1986), European Journal of Physics, 8, 105

FRAN DE AQUINO 27

for inertial mass (m,) and gravitational (mg); mi = m + and mg = m + where is the temperature dependent mass shift given by

The expression of obtained by Donoghue and Holstein refers only to thermal energy. Then, we must obtain the generalized equation of for any type of electromagnetic energy. If we express the geometric media of volumetric densities of the external electromagnetic energy withing the particle by W, particularized in the thermal energy case by W = = , and the volumetric density of rest inertial energy of the particle by = pc2 = (m/V)c2, we verify that the expression

reduce to the form obtained by Donoghue and Holstein. We can still verify that

is generic

for the any type of electromagnetic energy. Then, comparing the inertial mass (mi) and gravitational mass (mg) equations, we have the following expression for mg : mg = mi — Consequently, the generalized equation of the gravitational mass for an elementary particle will be

The equation (1.04) says, therefore, that the grav-itational mass of a particle will be equal to its inertial


mass only in the absence of electromagnetic fields external to the particle (W = 0). On the other hand, as the value of is very high then, for small values of W the ratio becomes so small that detecting it experimentally is very difficult.

This fact, no doubt, led Newton's Eotvos' and other's experiments not to verify the difference between gravitational and inertial mass.

The gravitational mass of a given atom can be obtained by effecting the sum of gravitational masses of its elementary particles with the gravitational mass from the interaction energy of said particles. When the velocities of all particles of the atom are small in comparison with the light velocity, the gravitational masses of particles can be considered equal to their rest gravitational masses, in such a way that we can express the rest gravitational mass of an atom through the following expression

In this expression, Wi, Wj and Wk refer respectively to the geometric medias of the external electromagnetic

FRAN DE AQUINO 29

energy densities of each electron, proton and neutron of the atom; are the volumetric densities

of rest inertial energies of said particles, and m0e, m0p and m0n are their rest inertial masses.

Just as the interaction energy between electrons, protons and neutrons is distributed within the atom itself, we can say that the inertial mass m0x created by the interaction energy of its particles is also distributed in the atom's volume, Va, and will be a fraction of the atom's mass, i.e. m0x = k-1m0a, (k > 1). Thus, the gravitational mass from the interaction energy between the particle is equivalent to the gravitational mass of an elementary particle of inertial mass m0x and volume Vx = Va, i.e., according to the equation (1.04), given by:

mg0 (interaction) = (1.06)

In this expression, Wx is the geometric media of

volumetric densities of external electromagnetic energy

within the mass particle m0x, i.e., (Wx = Wa), and

= m0xc2/Va; Va is the middle volume of the atom. On the other hand, we can write that


where Thus, equation (1.06) can be

rewritten as follows:

mg0 (interactions) = m0x -

(1.08)

Considering now the equation (1.08) in (1.05), we have:

Within the elementary particles and so

that we can write

In turn, within the mass particle m0x (interior of the

atom) the values of and will depend on the type of atom. Thus,

(1.11)

FRAN DE AQUINO 31

where and It can be seen then

that, if the summation contained

in the equation (1.09) become neglectible in respect to

in a way that the equation (1.09) is

reduced to

In this expression, the index x of W was omitted in order to abbreviate the writing; , as already seen, is given by

where is the volumetric density of rest inertial mass of the atom's.

In regard to the gravitational rest mass of a macroscopic body made up of atoms of a same type, and with W equal in all of them, it is seen that, as said atom's velocity is small in comparison to the light velocity, the expression of mg0 (body) can have all its small parts in respect to the a mg0 (atom) neglected, i.e., we can write

Let us now make use of the Einstein's equations to

formulate the description of the unified interaction. As


we know, said equations, for mixed components, can be written as follows:

(1.15)

where the energy-momentum tensor for elementary particles, is given by:

(1.16)

In the General Theory of Relativity, the gravitational and inertial masses are considered equivalent, so that express indistictly the particle's mass density (the mass in the particle's "own volume" unit). One must make here a distinction between the particle's gravitational-electromagnetic mass density from the other mass densities. For such equation (1.16) will have changed for

and from now on, will be

used to assign the inertial mass density. Accordingly, the equations (1.15) will express the gravitational-electromagnetic field.

The theoretical complementations appearing as a result of the introduction of the new concept of gravitational-electromagnetic mass can be better seen in the non-relativistic case.

In the limit case of small velocities, the component g00 for the metric tensor is, as we know, related to the

FRAN DE AQUINO 33

non-relativistic potential (now for the gravitational-electromagnetic field), through the following expression

(1.17)

In addition, regarding the 4-velocity , we must disregard all the spatial components and just leave the temporal component i.e., we must write = 0, = = 1. Thus, out of all components of the

energy-momentum tensor we have just

(1.18)

The zero index of was omitted in order to abbreviate the writing. Therefore, from now on, refers to the density of rest gravitational-electromagnetic mass of the particle (rest gravitational-electromagnetic mass at the particle's "own volume" unit.)

It is further verified that the scalar T will be equal to the same quantity, i.e.,

T= = (1.19)

Taking then the equations (1.15) to = =0, and by substituting = T = in the obtained expression, it results

(1.20)


On the other hand, by making use of the general formula

(1.21)

we can demonstrate that

(1.22)

By comparing then the equations (1.20) and (1.22), it results

(1.23)

which is the expression of the unified field equation, in non-relativistic mechanics. We can observe that it has the Poisson's equations form. We can then write the general solutions of (1.23) by analogy to the Poisson's equation i.e.

(1.24)

Particularly in the case of a single particle of rest gravitational-electromagnetic mass mge creating the field, we will have

(1.25)

which is the non-relativistic potential of the gravitational electromagnetic field produced by the particle.

FRAN DE AQUINO 35

When me = 0 and W = 0 (absence of electromagnetic fields) the gravitational-electromagnetic mass of a particle is reduced in its rest inertial mass, m. In this case, the equation (1.25) is reduced to

(1.26)

which expresses the non-relativistic potential of the particle's pure gravitational field.

Pursuant to equation (1.02), the equation (1.25) can be further written as follows:

where mg, mq = mp = mF, mf refer to the

rest masses ( for v = 0). As verified, the

second member of such an expression is made up by the sum of potentials


which determine severally, in particles with masses

respectively, the following forces:

This equations just are applicable, obviously, up to the

limits of the respectives fields. In the case of (1.33), (1.34) and (1.35) they are valid for all r, seeing that this fields extend themselves indefinitly. But in the case of the strong and weak fields the reach is, as we know, on the order of 10-

15m, so this is also the limit of applicability of the equations (1.36) and (1.37).

Only quarks possess masses mF and mf. Thus, equations (1.36) and (1.37), respectively, are the expressions of the weak and strong forces between two

FRAN DE AQUINO 37

quarks. Only quarks suffer the effects of all interactions; elementary particles, as we know, are made up of quarks, so that the strong and weak nuclear interactions, commonly observed among them, are nothing but manifestations of more fundamental forces, those determined by the strong and weak masses.

Hadrons, as we know, are made up of three quarks; consequently, in the particular case in which only two hadrons interact isolatedly, we will have 6 quarks in interaction. Thus, it becomes obvious that resultants

and relative to the strong interactions between two hadrons, as well as resultants and relative to the weak interaction between them, will depend on the distribution of 6 quarks, which can obviously make the nuclear forces non-central, in agreement, as we know, with the experience. On the other hand, the distribution of quarks in the elementary particles11 must certainly depend on the rotational motions of the particles, since in this type of movement centrifugal forces will act upon the quarks by modifying their relative position. Thus, resultants

will also depend on the magnitudes and relative orientation of the angular momentums of spin and

11Hadrons, leptons, etc. Quarks will not considered here as elementary

particles, but as fundamental particles, in order to establish the appropriate

distinction.


orbital of the elementary particles. On the other

hand, although equation (1.36) is a function of r2, the intensities of and obviously, will not be simply

inversely proportional to the squared distance between the elementary particles.

The calculation of the strong and weak resultants is certainly very difficult, since we are dealing with simultaneous interactions between various particles and we know, we cannot solve them even for three in Newton's gravitational theory. However, in the specific case where only two quarks with masses mF and interact, this calculation is simple: the force between them is given by equation (1.36). We do not know the expression of the strong mass, but from the known expression of the fine structure constant, given by

(1.38)

we can write

(1.39)

Recalling now that the relative intensities of the strong and electrostatic forces respectively vary in a ratio of 1:1/137 and by comparing the first member of equation (1.39) with the second member of equation (1.36), we can write

(1.40)

FRAN DE AQUINO 39

where Z is an admensional coefficient. From the experience it is possible to conclude (measurements of strong nuclear forces) that Z 1.

As we can easily verify, the equation (1.40) is satisfied for

(1.41)

and

(1.42)

where KF = Z. In order to obtain the expression of the weak mass, we

will start from the expression of coupling constant Gw of weak interaction, given by:

(1.43)

We can rewrite this equation as follows

(1.44)

or else,

(1.45)

As we can observe, both members of this equation have the mass dimension. On the other hand, by comparing the second member of this equation with the expression


of the strong mass, we can by analogy conclude that it is the expression of the weak mass, i.e.,

(1.46)

where, for non-zero weak mass particles (quarks), Kf = K / 10-6. Recalling now equation (1.37) of the

weak interactions, we see that Ff . This

explain why the relative intensities of the strong and weak interactions are in the ratio of 1 : 10-12.

Experience shows that there are elementary particles (such as those with spin 0, 1, 2) which do not interact weakly. It also shows that there are particles (such as mesons K+ and K0) which do not interact strongly. In the former case, according to the above mentioned facts, the quarks of the particles must have zero weak mass (Kf = 0). In the latter case, they must have KF = 0. Since the quarks of these particles are structurally identical, but not the space-time geometry at the sites of the quarks, for it depends on the conditions of confinement of the quarks in the elementary particles, we conclude that coefficients Kf and KF for each quark must be interrelated with the local metrics of space-time. Thus, they may even become zero when subjected to certain confinement conditions, such as those which must occur in the previously mentioned elementary particles. Under different conditions (free

FRAN DE AQUINO 41

quarks or in a new group forming another particle), coefficients Kf and KF may take non-zero values, thus causing strong and weak forces to reappear.

The expressions of mF and mf are quantum equations and indicate the inclusion of the Quantum Theory in the Gravitational-Electromagnetic Field Theory. We can confirm this fact by verifing if the Uncertainty Principle can be directly deduced from Gravitational-Electromagnetic Field Theory. So, we will consider the equation (1.40) with both members divided by r and , rewritten in the following form:

(1.47)

As we can see, the term between parenthesis has the same dimensions of the linear momentum; exchanging it by p, and reminding that Z 1, the equation (1.47) is reduced to

(1.48)

Therefore, an uncertainty in the r co-ordinate

results in a uncertainty in the p momentum, according to the formula

(1.49)

This is the uncertainty principle relation for position and momentum. Therefore we can say that the uncertainty principle is incorporated in the Gravitational-Electromagnetic Field Theory. When we combine this


relation, directly obtained from theory, with the expression

derived from Fourier analysis and, according to single properties commons for all waves, we obtain the equations and E = that are the so called De Broglie-Einstein relations, that express the wave-particle duality. As we can verify, the uncertainty principle, in this new context, it is not only the basis for the Heisenberg-Bohr probabilistic affirmation, but it contain, in fundamental level, the own wave-particle dualism, seen that we can deduce from it the De Broglie-Einstein relations. It is than, the own substratum of quantum physics.

The weak interaction is, as we know, responsible for the ratioactive phenomena known as -decay. The simplest example of -decay is that of neutron instability

where Q = 0.78 MeV, and the half-life is of 12 min. The emission of natural radioactive substances are of this same class with general reaction of decay (Z, A) (Z + 1, A) + e- + + Q.

The violation of the parity conservation principle in reactions of -decay was one of the more surprising facts in Physics. Everything started, when in the middle of the fifthies the physicists Yang and Lee were particularly interested in the meson K decay. At that time they believed that in this process, two particles called and were involved. The strange fact was that such

FRAN DE AQUINO 43

particles showed exactly the same properties. They ad-mited then, that in fact, there was only one particle; as a consequence of this proposition, it resulted therefore, that in the course of weak interactions, parity conservation principle - that estipulate that brute matter must be unable to distinguish its right from its left - was violated.

A few months after the publication of Yang and Lee work, an experiment realised by C.S. Wu et al., indicated the non-conservation of parity in the -decay reactions. The experiment consisted of measuring the intensities of -particles emited (by Co Nuclei) perpendicularly towards a magnetic field and after repeat the measurement with the orientation of the magnetic field inverted. As the intensities differed in both cases, one can conclude that the parity was not conserved in the -decay reactions.

The non-conservation of parity implies that electrons be able to "choose" between their right and their left. Now, where choosing exist, isn't there by definition a psyche, as well ?

In physics, we want obstinately ignore the influence of psyche; isn't it precisely by the fact that we don't consider the possibility of such actions, in reactions of -decay that it results to an apparent violation of the parity conservations in weak interactions?


Let us consider the hypothesis that in reactions of -decay the particles emited carry, for some time, a certain quantity of psychic mass originated

from the transformation of equal quantity of nucleus inertial mass. Thus, brute matter acquires conscience and therefore do not conserve the parity anymore. Thus, there is no violation of the principle of parity conservation, in the course of the weak interactions. The parity non-conservation solely occurs after the decay, for the emited particles endowed with psychic mass. Consequently what the experiment of C. S. Wu verified was only that the -particle emited do not conserve the parity. And this is because of the fact they are bearers of psychic mass.

In the psychic mass, we have the source of psychic field responsible for the psychic interaction. If we add the psychic mass with the gravitational-electromagnetic mass given by (1.01) we will have the expression of the unified mass, This addition imply in a new potential in the equation (1.27) and, consequently, we will have for the intensities of the forces

and between two isolated psychic mass and the following equation:

If we admit, based on the energy conservation principle, the reversibility of the psychic mass, i.e., that

FRAN DE AQUINO 45

psychic mass can be originated not only from inertial mass but, also from any kind of mass and vice-versa, i.e.,

we will have as a consequence, that any type of mass, in a psychic field, can be increased by the transformation of the psychic field energy in the corresponding mass type and vice-versa. This, according to the equations (1.33), (1.34), (1.35), (1.36) and (1.37), means precisely the possibility of psychic control of the four interactions and explain how the psychic field act on brute matter.

A very great quantity of psychic mass can have been always present in the Universe and remains in it for an indeterminate time. In addition, the genesis of all masses of the Universe (strong, electromagnetic, weak and gravitational) can be the result of transformation of part of a gigantic initial psychic energy or Supreme Conscience and, this way, the Universe would be originated from the "will" of this Supreme Conscience.

Let us now the go back to equations (1.34) and (1.35), which are nothing but Coulomb's laws of electrostatic and magnetostatic, respectively. When we


proceed with the particularization of the gravitational-electromagnetic field equations for the non-relativistic case, and we consider mge in equation (1.24) as the gravitational-electromagnetic rest mass of the particle, we made, as a consequence of these particularization procedures, the electrodynamic force (Lorentz's force) disappear,

(1.50)

which is known to be a purely relativistic phenomenon. In spite of this fact, it is always possible to obtain it by means of a relativistic correction of equation (1.34) from the law of transformation for the electric field, given by12

(1.51)

where is the so-called Lorentz

factor. We thus obtain Coulomb's law in its generic form for free space, i.e.,

(1.52)

In which the motion of electrical charges is permitted. We see in this expression that the electrostatic force

12 See Silvester, P., (1971) Campos Eletromagneticos Modernos, Ed. Poligno,

Sao Paulo, p. 150-155.

FRAN DE AQUINO 47

is subjected to a relativistic correction (D varies with velocity), but we cannot make it disappear by selecting a suitable referential.

Maxwell equations, in turn, may be deducted by comparing equation (1.52) with that obtained by var-ing the action S for an electrical charge in an electromagnetic field13 (by means of Lagrange's equations), i.e.,

(1.53)

where is the potential vector and

is the potential scalar of the electromagnetic field. From the comparison between equations (1.52) and

(1.53) we obtain the following expressions for the electric field and magnetic flow density vectors:

These expressions, in turn, allow us to obtain the equations containing and in a simple way. We will then determine

(1.56)

13 See Landau, L. and Lifchitz, E. (1974), Teoria do Campo, Ed. Hemus, Sao Paulo, p. 65-66.


However, the rotational of a gradient is zero; therefore, equation (1.56) is reduced to

(1.57)

Taking the divergence of the two members of equation (1.55), we will have But since the

divergence of a rotational is zero, we then have

(1.58)

Equation (1.57) and (1.58) constitute the first pair of Maxwell's equations. In order to obtain the other pair, we must return to expression (1.53), which is the equation of the motion of a particle in a electromagnetic field. As mentioned earlier, it was obtained from Lagrange's equation written in a 3-dimensional form. From action S written in a 4-dimensional form, it is possible to obtain the motion equation in 4-dimensional formalism; we then obtain the so-called electromagnetic field tensor.14

On the other hand, by varing action S for an electromagnetic field which contains rather than point electrical charges a continuous density distribution we obtain four equations in 3-dimensional

14The reader may find the detailed calculations and results in Landau, L. and

Lifchitz, E., Teoria do Campo, Ed. Hemus, S. Paulo, p. 81-82.

FRAN DE AQUINO 49

form15 containing the components of the electromagnetic field tensor. By substituting the respective values for such componentes, we obtain equations which can been condensed into two vectorial equations, given by

(1.59) and

(1.60)

which constitute the second pair of Maxwell's equations. Let us return now to equation (1.33), which expresses the

intensity of the gravitacional force which acts on an elementary particle of rest gravitational mass placed in the gravitational field of particle with mass mg. By analogy the intensity of force which acts on mg due to is given by:

(1.61)

Thus, with equation (1.04) in mind, we may write that

or, in vectorial form,

15 Idem, p. 99-100.


where versor has the direction of the line connecting the centers of both particles, oriented from m towards m'.

As opposed to pure gravitational forces (W = W' = 0), which are only attractive ones, we see now that gravitational forces may be, besides attractive ones, repulsive or null. Assuming, for example, that but

we see that the force

between the particles will be a repulsive one, given by:

(1.64)

However, if we make and

the force becomes an attractive one, i.e.,

(1.65)

In the case of interaction between macroscopic bodies made up of one single type of atom, the gravitational forces between them may be calculated through the same expressions, since the expression of gravitational mass for this type of body (equation 1.14) has the same form of expression of the gravitational mass for elementary particles, simply changing and by and respectively. Under these conditions,

FRAN DE AQUINO 51

we observe that ratios and may be

rewritten in the following ways:

where

Considering the expression of given by equa-

tion (1.13), i.e., we see that most monoatomic solids present E0 and H0 given by

(V/m), (A/m), k> 1 . (1.72)

As one can observe, these are very high values, but which can be reduced by the following process: we know, from quantum electrodynamics, that may be increased by applying an oscillating electric field with a frequency equal to any of the frequencies of the electromagnetic spectrum of the substance. The


expression of without the dampening term (which makes the value of finite in the case of ) is

(1.73)

The influence of the dampening term in the value of varies for each value of frequency and it is quite likely that, for certain frequencies of the electromagnetic spectrum of the substance, the value of will considerably increase.

When increases, the electric forces of attraction between the electrons and the nuclei of the atoms decrease (F =

: ). Due to this, the eccentricities of the electrons orbits decrease, and so, the middles radii ri of this orbits increase, thus increasing the middles volumes of the atoms and also the value of since the magnetic (paramagnetic) susceptibility is, as we know, proportional to the squared permanent atomic magnetic momentum, which, in turn, is proportional to . Therefore, is directly proportional to The incresed middles volumes of the

atoms obviously determines a decrease in the value of Therefore, with the decrease of and the increase of and factors and will decrease and, according to equations (1.68) and (1.69), we see that the values of E0 and H0 may be significantly

FRAN DE AQUINO 53

reduced, thus enabling the control of gravitation by applying much less intense electric and magnetic fields (E

10l5V/m, H 1012 A/m). This process, which fundamentally results from the

action of oscillating fields, or more accurately, from the periodical inversion of electric and magnetic energy upon matter will be hereinafter called electromagnetic reversion process.

From the above we see that, by reducing the values of E0 and H0 by means of the electromagnetic reversion process, the possibility of controlling the gravitational interaction by applying ultra-intense magnetic fields (H > 106A/m) becomes quite promising, especially now that our technology already foresees the production of magnetic fields thousands of times more intense than the maximum produced in conventional inductors.

In practice, when it is possible to make H = H0, we will experimentally prove the truthfulness of Mach's Principle. That is, taking, for example, a particle of a subatomic substance with mass m', for which we have W'/ = 1 (by means of the electromagnetic reversion process and with the aid of superconductor inductors), we will see that the gravitational forces on the particle will cease, since they, according to equation


(1.62) herein, are expressed by

(1.74)

Under these circumstances, according to Mach's principle, the inertial properties of the particle must also cease. This principle, as we know, states that the local inertial forces are determined by the gravitational interaction of the local system with the distribution of cosmic masses. Consequently, when the intensities of the gravitational forces acting on the particle become zero ( = 0), the inertial properties of the particle must also disappear. As we can observe, the electromagnetic factor postulated in the beginning of this work, which relates gravitational mass to inertial mass, incorporates Mach's principle to the gravitational theory. A propos, such incorporation was greatly pursued by Einstein, who, as it is known, introduced the cos-mological term into his equations with this purpose.

We will now deal with the verification of the influence of thermal radiation on gravitational mass. According to the law of distribution of radiation energy of a black body, we know that thermal radiation contains photons of all frequencies. It is common to relate the energy of such photons to temperature by means of the expression < > kT. We can thus express the average amount of thermal energy in the

FRAN DE AQUINO 55

interior of a microscopic particle by kT, where is an absorption coefficient which depends on the particle. Consequently, the expression of W, due exclusively to the thermal radiation, may be written as W = kT/V where V is the particle's "own" volume. In the case of an electron, for example, considering equation (1.04), we have

(1.75)

From this expression we conclude that the gravitational mass of the electron will only be equal to its inertial mass when T = 0°K. At any higher temperature the gravitational mass becomes smaller.

As we have already seen, in the case of atoms, their rest gravitational mass can be expressed by

(1.76)

From equations (1.75) and (1.76), we can easily conclude that, at the same temperature T, the difference between inertial and gravitational mass is much larger than in the case of elementary particles.

The term ( kT/moec2)2 for room temperature (T 300° K) is smaller than 10-15. Thus, to experimentally ascertain variations in the gravitational mass of the electrons (due to thermal radiation), highly accurate instruments are necessary.


In a recent research work, B. Holstein and J. Donoghue, from the Massachusetts University, using instruments a hundred thousand times more accurate than those utilized by Dicke, observed that the gravitational mass of an elementary particle decreased with the increase of temperature, and that only at absolute zero were gravitational and inertial masse equivalent. In the case of electrons, it was possible to verify that they have 10-14% less gravitational mass at room temperature than at absolute zero. In the case of atoms the difference is even smaller.

The fact of thermal radiations containing photons of all frequencies means that they must contain radiations of the electromagnetic spectrum of the substances, and thus, the radiations of appropriate frequencies to significantly reduce the E0, H0 of the atoms (electromagnetic reversion process). However, since the densities of the power flows of such radiations are very weak (for T 300°K), we see that in a given body only a very small amount of atoms (as compared with the total) will be subjected to the action of said radiations. Therefore, only these atoms will have their E0, H0 decreased. Thus, in the case of our applying an ultra-intense magnetic field H to the body, making H > H0, these atoms will have their resulting gravi-tationals significantly altered. This, however, practi-

FRAN DE AQUINO 57

cally does not influence the resulting gravitational of the body if H is not much greater than H0.

In principle, we may significantly reduce the values of E0, H0 of an atom, both by means of suitable radiations of the elecromagnetic spectrum of the atom and by stationary electromagnetic fields of the same frequency. In practice, the disadvantage of radiation is high: besides the need of intense flows to attain the largest number of atoms, such kind of radiations have low matter penetration.

We will now consider the gravitational interaction at the subatomic level. Initially, it is necessary to evalutate the magnitudes of the volumetric densities of rest inertial energies of the elementary particles to be able to determine the rations W/ in the gravitational interactions of said particles.

The inertial rest masses of the elementary particles are well known16 They from the sum of all inertial masses arising from all the internal energies of the particle. Therefore, if is the volumetric density of the rest inertial mass of an elementary particle, we can

16The experiments used to determine the masses of the elementary particles

generally constitute inertial processes (in which forces intervene).

Therefore, what we measure is the inertial masses of the particles.


then express its volumetric density of rest inertial mass

by

However, the calculation of requires, besides the knowledge of the rest inertial mass of the particle, the knowledge of the "own volume" in which such mass is contained.

Very little is known about the geometric structure of the elementary particles. The hypothesis that such particles may actually be true micro-universes contained in our Universe is not new; it has been often proposed by several authors.

Such hypothesis contains, in its very essence, the idea of similarity - in the spatial sense - between the micro-universes of the elementary particles and our universe, which in our opinion constitutes a strong indication that similarly to the elementary particles, our universe is also closed. This possibility leads us to see a spatial correspondence between the micro-universes of the elementary particles, our own Universe and Einstein's model of the universe. That is, their volumes are finite, but under the clear understanding that space has no boundaries.

In view of the above, the volumes of the elementary particles may be calculated through the same equation that expresses the volume of Einstein's universe, which,

FRAN DE AQUINO 59

as a consequence of

(1.77) is

written as

(1.78)

In the case of elementary particles, R refers then to the respective curvature radii of these micro-universes; that is, in the case of protons, for example, R = 1.4 x 10-15m, so that for these particles the volumetric density of the rest inertial energy is given by

(1.79)

In the nuclei with high atomic mass the geometric media of the volumetric densities of external electro-magnetic energy, W, in each nucleon (reciprocally produced by electric and/or magnetic fields of the nucleons themselves) determines a marked reduction in the grav-itational mass of these particles, as we will see later on, which in turn reduces the intensity of the gravitational interaction between the atomic nuclei. We know that the magnetic field of the nucleons, due to their spin magnetic momentum, is given by

(1.80)


where is the spin magnetic momentum of the particle; is the so-called gyromagnetic factor, the value of which is 5.5851

for the proton and -3.8256 for the neutron. is the spin angular

momentum. In the case of protons, besides the spin magnetic

field, they present an electric field (due to their electric charge e)

with intensity

(1.81)

In the atomic nuclei, we may consider that the distance r

between nucleons is of the same order as the diameter of these

particles. Thus, taking equations (1.80) and (1.81), it is possible

to verify, in a first-approximation evaluation, that the ratios

W2/ for the nucleons may reach values in the order of 10-2!

Thus, according to equation (1.62), this means that in the

gravitational interactions between the atomic nuclei, there may

occur intensity variations in the order of 1%.

Variations of such magnitude have been experimentally

detected17 having even led some authors to

17 S.H. Aronson, G.L. Bock, H.Y. Cheng and E. Fischbach (1982), Phys. Rev. Lett. 48, 1306 and (1983) Phys. Rev. D28, 476, 495; E. Fischbach, H.Y. Cheng, S.H. Aronson and G.L. Bock (1982), Phys. Letters 116B, 73.

FRAN DE AQUINO 61

believe in the possible existence of a new type of interaction18 (hypercharge field).

The density W, within particle can be related with its rotation kinetics energy. It is the case, for example, of the protons, neutrons and electrons, when in orbital movement of radius R. The centripetal force

acting in these particles it places in a precession movement. This movement give origin a additional magnetic field that, by analogy with spin magnetic field (equation 1.80) can expressed by:

(1.82)

where is the precession gyromagnetic factor and the precession angular moment, given by =

= seen that rp rpartic; as we know, can be expressed by = r.Fc/S = R/S. The sign (+) in equation (1.82) indicates that the spin of the particle have the same orientation that its precession movement and, therefore, opposite orientation at its translation in the orbit of radius R. The sign (—) indicates the opposite.

In this last case, the field will have opposite ori-entation at , so that the density of electromagnetic energy within particle doesn't increase. So, W = 0. If however, the translation movement is opposite at

18 E. Fischbach, D. Sudarsky, A. Szafer, C. Talmadge, S.H. Aronson (1986), Phys. Rev. Lett. 56, 3.


the spin, will have the same orientation that and,

therefore, the density W within particle will be Wpartic = The atomics electrons spin in the same orientation of its

translation around the nucleus (s == +1/2), and so for these electrons is opposite to so that, in this case W = 0.

In macroscopic case, if a body turn in opposite orientation at the spin of its protons, neutrons and electrons, in each one of that particles will have a density Wpartic. The geometric media of that densities will expresses the value of W for the body.

Let us consider now a sphere with density that turn with angular velocity The gravitational forces between the sphere and the world, according to equation (1.63), for great values of will be repulsive, and given by:

(1.83)

As we see, if the sphere have very high rotation, the repulsive force can become very great than rest weight force of the sphere (P = msg).

We are therefore, in front of another possibility of gravitational contro. In this case, with the utilization of mechanical devices!

II. COSMOLOGICAL APPLICATIONS

The Gravitational-Electromagnetic Field Theory suggests explanations for interesting cosmological ques-tions, such as that of the final stage of gravitational contraction of massive stars (M ) as well as

of the Universe itself in each cycle and for the anomalies observed in recent analyses of the red-shift in galaxies and stars.

Initially we shall discuss the problem of the stars' gravitational contraction.

As is generally known, in a star's gravitational con-traction process its fate is directly linked to its mass. If the star's mass, at the moment of its birth, is less than 1.4 (the Schemberg-Chandrasekhar limit), its be-

comes a white dwarf. If, however, its mass exceeds that limit, the pressure generated by the degenerate state of matter no longer counterbalances the gravitational pressure, and the contraction proceeds. There then occur reactions between protons and electrons (capture of electrons), forming neutrons and anti-neutrinos. The collapse continues until the system regains stability (when the pressure generated by the neutrons is sufficient to stop the gravitational colapse). Such systems are the so-called neutron stars. There is also a critical mass for the stable configuration of neutron stars. This limit has not been fully defined as yet, but it is known that it is located between 1.8 and 2.4 Thus,


should the mass of the star exceed above-mentioned critical mass (massive stars), the collapse may continue.

The continuation of gravitational contraction also occurs in the remnants of neutron stars1. In that case, the process is slow, since such systems are generally endowed with great velocities of rotation around themselves (because of the conservation of the angular moment of rotation, during the contraction of the star), which rotation causes centrifugal forces that run counter to gravitational contraction. Nonetheless, the velocities of rotation diminishes progressively because the star emits electromagnetic radiation whose energy is taken precisely from its rotational energy. Therefore, however slowly, the contraction continues.

There thus exists a natural convergence of massive systems towards a state in which the neutrons are con-tinuosly compressed, causing a systematic reduction of the distances between their centers of mass. In that case, the Hn magnetic fields of the neutrons given by

(2.01)

1 This is the case with pulsar, for instance, which become neutron stars at the

end of their existence.

FRAN DE AQUINO 67

determine reciprocally, in their interiors, densities of magnetic energy WHn = 1/2 which increase in magnitude as the distances between neutrons decrease. Since WHn r-6 and the rest inertial energy density of the neutrons is proportional to , i.e. (where rn is the "radius" of the neutrons), the total density W in the interiors of the neutrons grows much more rapidly - with the decrease in the volumes of neutrons - than Consequently, the ratio W2/ for each neutron undergoes a progressive increase as the gravitational compression of the star proceeds. With that, the gravitational mass of the neutrons keeps on diminishing: as a result, the attracting gravitational forces between them also keep on progressively diminishing (equation 1.62). The phenomenon progresses up to a certain critical point, at which the gravitational pressure falls below the internal pressure produced by the neutrons. When this occurs, there starts an oscillatory catastrophic process that culminates in the star's explosion. This phenomenon has been noted in recent astronomical observations and clearly shows what -on a much greater scale - happened at the Big Bang. In other words, just as massive stars and systems of greater mass explode when they reach a critical point in the gravitational contraction process, the Universe too exploded due to an identical process in the final


instants of its contraction periods. The singularity in Friedmann's cosmological model is thus eliminated.2

The possibility that this process may occur, in the final stage of contraction of massive stars and greater-yet systems, as well as with the Universe itself in the final instants of its contraction periods, does not prevent the existence of black holes, as is predicted in the solution of Einstein's equation obtained by Schwarzchild3 which allows us to write

(2.02)

It will be seen that for

(2.03)

there occurs a singularity. That is the so-called Schwarzchild radius, which means that nothing, not even light, can escape from a body with mass mg if the latter is contained in a sphere whose radius is rs. Thus, any mass mg placed in a sphere of radius rs = 2G mg/c2 would be a black hole. However, if its matter became an ensemble of supercompressed neutrons - as occurs in the final stage of the gravitational compression process

2 PYiedmann, A. (1918). Z. Physik 10, 377. 3 Schwarzchild, K. (1916). Sitz. Preuss. Akad. Wiss., 189.

FRAN DE AQUINO 69

of massive stars - the black hole would explode for the same reason that they (massive stars) explode upon reaching the critical point.

For some time the existence of so-called white holes has been debated. Several authors have suggested that these may represent regions where matter is spurting in our Universe.

From all the preceding, we may infer that white holes represent either black holes that exploded, or massive stars of greater-yet systems that exploded because at a given moment their internal pressure overcame the gravitational pressure, following the process described above.

Let us now consider the problem of anomalies in the spectral red-shift of certain galaxies and stars. As we know, that phenomenon is generally explained as resulting from a combination of two effects - the Doppler-Fizeau and the Einstein (or gravitational) effects. The former is associated with the relative velocities of the source and of the observer, while the latter is caused by the difference in gravitational potential between source and observer.

If is the frequency of light at the moment of its emission, and if we assume that the red-shift resulted from the Doppler-Fizeau effect, the frequency that we will observe will be expressed by the following:


(2.04)

In this expression, v is the velocity of the source in relation to us which, according to Hubble's law, is given by

(2.05)

where is the so-called Hubble's constant and is the distance from the source in question. Recent determinations have assigned the value of 2.5 x 10-18 s-1 to Hubble's constant.

If we assume that the red-shift was caused by the Einstein effect, the relation between and is expressed by

(2.06)

where and are the gravitational field potentials at, respectively, the point of emission and the point of observation of the spectrum. If we observe on Earth a spectrum emitted by the Sun or stars, the according to equation (2.06), < 0, i.e., the shift occurs in the direction of lower frequencies (red-shift). Both the red-shift caused by the Doppler-Fizeau effect and that caused by the Einstein effect are generally accepted as having been experimentally confirmed.

FRAN DE AQUINO 71

Nonetheless, for some years a number of observers have been noting red-shift values that cannot be explained by either the Doppler-Fizeau or the Einstein effect.

That is, for instance, the case of the so-called Stefan quinted (made up of five galaxies discovered in 1877), whose galaxies are all located at approximately the same distance from Earth, according to very reliable and precise measuring methods. However, when measuring the velocity of each galaxy by the red-shift it produced, one finds that four of them move away at velocities much greater than that of the fifth.

Similar observations have been made on the Virgo constellation, where galaxies that belong to the same cluster feature great differences in their velocities of expansion, as deduced from their red-shifts.

It was furthermore found that galaxies of the spiral type feature a red-shift greater than that of galaxies located at the same distance.

The Sun, too, shows a red-shift that is greater than what would have been predicted by the Einstein effect.

All these anomalies in red-shifts are easily explained by the Gravitational-Electromagnetic Field Theory. They are the result of the fact that we disregarded the influence of electromagnetic energy in gravitational interaction. Thus, the expression for the grav-tiational spectrum shift supplied by Einstein's theory is


nothing but a special case of a more general expression, which now can be easily obtained on the basis of the explanations provided in Chapter I. Let us admit, for convenience's sake, that the emitting body (Body 1) is made up of atoms of the same kind with W1, being equal in all of them. In that case, in accordance with equations (1.14) and (1.28), the potential at point of emission will be given by

(2.07)

where refers to the volumetric density of the rest inertial energy of the atoms of body 1.

By analogy we may write for the observation point (body 2):

(2.08)

Transferring equations (2.07) and (2.08) to (2.06), we obtain:

FRAN DE AQUINO 73

If we assume that m1 m2, W1/ 1, and W2/ 1, the latter equations is reduced to

(2.10)

That means that the shifts computed by the Einstein effect in this case should be multiplied by the factor (W1/ )2. We may thus conclude that the anomalies found in above-mentioned cases should be interpreted as having been caused by the existence of an enormous density of electromagnetic energy in the observed bodies. Furthermore, the large red-shifts of quasars should not be interpreted as Dopper shifts - as is normally done - but as gravitational red-shifts calculated according to equation (2.09). This will eliminate the fantastic hypothesis (which would result from assuming a Doppler shift) to the effect that quasars are moving away from us at velocities close to the velocity of light and are therefore the located a fabulous distances from Earth. It will also eliminate the hyphotesis that, in order to appear as brilliantly as we see them, at such a distance, quasars must possess a very special kind of energy source. They are simply closer to us.

III. GRAVITATIONAL SPACECRAFT

In the electromagnetic reversion process, the oscillating

fields applied to a given substance may have a frequency equal to any of the frequencies of the electromagnetic

spectrum of the substance. However, the value of must

only suffer significant increases for certain frequencies of

said spectrum; among them, there will certainly be a critical

frequency for which the maximum value of will occur.

These critical frequencies must be the object of

experimental determination. On the other hand, as the low

levels of generally correspond to frequencies in the

infrared and microwave spectrum, we conclude that the

oscillating fields to be used in the electromagnetic reversion

process must be of extra high frequency.

In practice, the distribution of these fields depends on

the objectives to be attained with gravitation control. In a

spacecraft, for example, the objective of which is to use

gravitation to its full extent, we may position a source of

such fields in the center of the spacecraft and others

conveniently distributed on its outer surface (Fig. 3.1). With

such a distribution, we may attain, as we shall see later on,

an unheard-of performance for spacecrafts.


Fig. 3.1 - Gravitational Spacecraft

FRAN DE AQUINO 79

These sources may be able to produce oscillating fields in the various critical frequencies of the substances in which we intend to control gravitational interaction. One of these fields, produced by the central source, must have a suitable frequency to reduce the value of H0 of the nuclei of reactors R1 and R2 (gravitational reactors) in such a manner that, with an ultra-intense magnetic field HR, one is able to control the gravitational interaction on the nucleus of these reactors, thus permitting the spacecraft to rise, descend or incline as to its vertical axis.

To propel the spacecraft in the longitudinal direction, we may actuate the ultra-intense magnetic field He together with the sources of oscillating fields positioned in the front portion of the spacecraft (Fig. 3.2). If frequency of the electromagnetic fields produced by said sources equals frequency (critical frequency of the electromagnetic spectrum of nitrogen), the ratio He/HON to nitrogen in the region of actuation of the activated oscillating fields may become greater than 1. Consequently, according to equation (1.62), the gravitational force between the Earth and the nitrogen in this region becomes strongly repulsive, with nitrogen being subjected to an acceleration aN, given by

(3.01)


Thus, in the front region, the velocity of air (relative to the spacecraft surface) increases. Consequently, according to Bernoulli's equation, the atmospheric pressure in this region must decrease. A pressure gradient between the back and front part is thus established and, as a consequence, a force capable of propelling the spacecraft is created.

On the other hand, the continuity equation establishes that the increased velocity of the air in the front region of the spacecraft must cause the air density in this region to decrease. Thus, the higher the air velocity, the more rarefied it is. Consequently, the attrition between the front region of the spacecraft and the atmosphere will be reduced and, therefore, the thermal effects resulting from this attrition will also be reduced. In this manner, the spacecraft will be able to travel in the atmosphere at hypersonic velocities without undergoing excessive heat.

Another important fact to be observed is that the spacecraft can be braked in its displacement simply by inactivating the front sources of its oscillating fields and at the same time activating the sources distributed on the back part of the craft. Under these circumstances, the process is reversed; a force contrary to the displacement of the craft begins to act upon it, thus causing it to brake.

FRAN DE AQUINO 81

Fig. 3.2 - Propulsion in the Atmosphere


The spacecraft can be displaced to the left or to the right by the same process, that is, to displace it to the left we must activate sources distributed on the left surface of the craft, and those located on the right to displace it to the right. We can also have it rise by activating sources distributed on its top (Fig. 3.3-c).

When the spacecraft is parked on the surface of the Earth, we may generate a repulsive gravitational field around it by simply activating magnetic field Hi (Fig. 3.2) and making Hi/H0 1. Under these circumstances, the repulsive gravitational force between the spacecraft and any body close to it may become very intense, since it is expressed by:

(3.02)

Thus, in order to stop any individual from approaching the spacecraft, simply make Hi/H0 103.

Another gravitational effect likely to be obtained is that of controlling the inertial properties of the spacecraft. It is initially necessary to determine in the electromagnetic spectra of the substances which make up the spacecraft the frequencies for which it is possible to reduce the H0 of these substance to the same value. Thus, if the central source produces oscillating fields at these frequencies and field Hi is activated, making Hi/H0 = 1, we see that, according

FRAN DE AQUINO 83

to equation (1.62), the gravitational forces upon the spacecraft

cease and, as a consequence of Mach's principle, and so must its

inertial properties. This allows the crew not to suffer the inertial

effects derived from maneuvering the craft.

All these possibilities demonstrate that gravitational

spacecrafts are exceptionally advantageous in many instances.

They could be designed with the most varied forms and

according to the most varied objectives. Therefore, we will be

able to design spacecrafts not only for transportation in the

atmosphere (small and large distances) but also for interstellar

trips. Spacecrafts of this kind, when leaving the atmosphere of

the planet, must be positioned towards their destinations and

activate their gravitational reactors positioned on the rear part

(Fig. 3.4). The nucleus of the reactor is then subjected to a

gravitational acceleration due to the planet, given by

(3.03)

where HR is the magnetic field of the reactor. HOR the value of H0

for the nucleus of the reactor and M the mass of the planet.


Fig. 3.3 - Secondary Displacements

FRAN DE AQUINO 85

Fig. 3.4 - Propulsion in the Outer Space


Once propelled by the reactor, the spacecraft is subjected to an acceleration

(3.04)

where mR is the mass of the reactor nucleus and mn the spacecraft mass.

We then observe that, in this way, the spacecraft may be strongly accelerated (an g) for several hours.

We have already seen that, with the aid of magnetic field Hi we can make the gravitational interactions upon the spacecraft become zero and, therefore, offset the inertial forces upon it. This means that under these conditions we can impart the spacecraft with high accelerations without subjecting it or its crew to the inertial effects of such accelerations. In this manner, it is easy to see that gravitational spacecrafts, starting from rest, may be accelerated up to velocities close to that of light within a matter of a few minutes.

By travelling at such velocities, the distances in the Universe are significantly shortened for the crew members. This is what is known as Lorentz's contraction.

IV. LEVITATION

In this chapter, our purpose is to show that the human body has at its disposition some resources, towards controlling the gravitational interaction on itself.

First of all, however, let us say something about the neurons and the way they might give rise to extra-high frequency electromagnetic fields, necessary for the electromagnetic reversion process.

The main portion of a neuron is the so-called cell's body, and does not differ widely from that of the other cells. It is made up by the nucleus and cytoplasm. What renders the neuron different from the other cells are the ramifications (the so-called dentrites), which leave the cell body and get thinner, as they elongate.

In a given place within the cell body there is a particulary long extension, named axon, which might have over a meter of length and is branched only at its end.

A neuron contacts another by means of ramifications that are developed at its axon's end. When the nervous impulse reaches the axon's ramifications, something we name synaptic transmission of the impulse is performed. The synapsis is the functional contact between the membranes of two excited cells. The distance between the presynaptic and postsynaptic membranes, usually named synaptic cleft, is usually


from 15 to 20 nm. Said cleft is even larger in myoneural unions, ranging from 50 to 100 nm. There are also synapsis with presynaptic an postsynaptic membranes quite close to each other which, sometimes even touching themselves. In these cases, the direct electronic transmission of the impulse is renderred possible. Most of the times, however, when the cleft is large, the transmission of impulse is made through a chemical process, which starts with the synthetization, by the cell itself, of a chemical substance named acetylcholine,

which results from the reaction of acetic acid and choline, two componentes of the cells.

The acetylcholine is able to alter the sodium pump1 work by producing the cell membrane dispolar-ization.

The acetylcholine being formed in the cell, its existence is for a short length of time, otherwise no repolarization of the cell would exist, while acetylcholine remained within it. In fact, nervous cells have an enzyme

1A mechanism through which sodium ions are moved within the cells, giving rise to the membrane polarization.

FRAN DE AQUINO 91

named cholinesterase, which produces the decomposition of acetylcholine into acetic acid and choline, as in the beginning. With the decomposition process, the cell membrane alters once again, and then the repolarization proceeds. Thus, dispolarization and repolarization cycles suceed, the frequency of which depends on how fast the acetylcholine composition and decomposition take place.

Thus, the dentrites (or even the cell body) in the other neuron are affected by means of acetylcholine release, so starting a new electric impulse in the neighbour neuron. The impulse then runs up the second neuron, until the chemical effect comes into play again, at the axon's end, to overcome the following synapsis, and so on.

The electric charge densities at the axon ramifications' ends during said process give rise to reasonably intensive oscillating electric fields, the oscillation frequency of which may become very high, if also the cell's polarization and dispolarization rythm so becomes.

This possibility suggest us that the levitation might occur under special circumstances in which the polarization and dispolarization frequency for the nervous system's neurons becomes very high, reaching the critical frequency of the water's electromagnetic spectrum.


We know that nearly 45 to 75%2 of the human body is made up by water molecules. We also know that the H2O molecules are a part of the so-called polar group of molecules, which are featured by a permanent electric dipole. In case of a H2O molecule, the electrons tend to agglomerate around the oxygen atom which, because of that, becomes slightly negative in respect to the hydrogen atoms. Two electric dipoles are then established (with intensities of 5 x 10-30C.m) in the molecule and, consequently, with electric fields at the order of 109 V/m, through the water molecule. Accordingly, if the oscillation frequency of the electromagnetic fields produced by the neurons equals the frequency (the critical frequency of the water's electromagnetic spectrum), then the values of E0, H0 for the human body's water molecules might be reduced significantly, by renderring E4/ 1, which possibilitates the levitation. In order to evaluate the magnitude of we must at first observe that we can express the rest gravitational mass for a given molecule through the following expression:

2 Depends on the fat contents of an individual and his age. Younger and slimmer individuals have a higher water contents in their bodies.

FRAN DE AQUINO 93

(4.01)

Since the interaction energy between the atoms is distributed within the molecule itself, we can, also here, admit that the inertial mass moy created by the interaction energy of the atoms is distributed within the volume VM of the molecule and it will be a fraction of the molecule mass, i.e., moy = n-1m0M, (n > 1). Thus, the gravitational mass due to the interaction energy between the atoms is equivalent to the gravitational mass of an elementary particle with inertial mass moy and volume Vy = VM, i.e., according to the equation (1.04) given by:

(4.02)

In this expresion, Wy is the geometric media of volumetric densities of external electromagnetic energy within the mass particle moy, i.e., (Wy = WM) and = moyc2 / VM. On the other hand, we can write that


where The equation (4.02), thus, can

be rewritten as follows:

(4.03)

By taking this expression to equation (4.01), we obtain

(4.04)

and taking equation (1.12) into account, we can write

In case of light molecules, n is very large3 so results

and, therefore, we can write

(4.06)

3 Interatomic interaction energy in the molecule is very small in relation to the

molecule's rest inertial energy.

FRAN DE AQUINO 95

For water molecules, in the absence of magnetic fields (H = 0), we can then write:

(4.07) where

is given by

(4.08)

Thus, if is reduced (by means of the electromagnetic reversion process) to a given value lower than the electric field through of the water molecules (due to the electric dipole), resulting E4/ 1, said molecules will be subject to a gravitational force that is repulsive in relation to Earth, i.e., they will be subject to a gravitational acceleration

(4.09)

If all the water molecules of the human body are subject to such an acceleration, the repulsive gravitational force in the body would be very intense. However, this does not occur because the oscillating electric field produced by polarization and dispolarization of neurons is sufficiently intense only in the surroundings of the nervous system's ramification ends. Accordingly, only the water molecules close to said ends will have


their reduced by the electromagnetic reversion process. This way, only a small part of the H2O molecules in the human body will be subject to a repulsive acceleration and, consequently, the repulsive force on the human body should not be intense, but sufficient to make it levitate.

Based on the aforementioned in this chapter, the performace of a gravitational spacecraft can be improved even further. For example, we can conceive a "gravitational elevator" to hoist human bodies into a spacecraft. It would be the same principle as that of levitation. In this case, however, the oscillating electric field with the frequency would be produced in a given place of the spacecraft by means of a source specifically designed for such a purpose.

The production of artificial gravity within a spacecraft for the purpose of attracting the crew to be spacecraft's ground is another example of control on the gravitational forces acting on the human body's water molecules. This can be achieved by intensifying the gravitational attraction between the human body's water molecules and those intentionally placed into a reservoir beneath the spacecraft's ground. The central source of oscillating fields (fig. 3.1) must produce then an electromangetic field with a frequency so that E / 1 results, either for the water

FRAN DE AQUINO 97

molecules placed beneath the ground, or those contained in the crew members' bodies. So, according to equation (1.62), the gravitational forces between the water into the reservoir and that in the crew members' bodies will be attractive, the human bodies' water molecules, therefore, being subject to the following acceleration:

(4.10)

In order to obtain the desired gravity, the water mass within the reservoir, , must be previously estimated.

V. ENERGY CONVERSION

The gravitational energy can be directly converted into rotational kinetic energy, in a system we name gravitational motor. Quite similar to a water turbine, the gravitational motor is, therefore, entirely sealed, so that the water cannot escape from the rotor chamber (fig. 5.1). It has two sources, A and B, with electromagnetic fields with frequency to reduce the values of

for the water molecules. Thus, for example, when the source A is turned on and the value of for the water molecules to the left of the chamber become very lower than the electric fields through these latter (as a result of the permanent electric dipoles) the gravitational forces between the Earth and the water molecules at that place will become repulsive, as already seen. With this, the water mass in the left side of the motor tendes to move upwards. Simultaneously, the water mass to the right of the engine, under the effect of the attracting gravitational force, tends to displace downwards. A rotational water flow is then established, which moves the rotor of the motor, by providing it a given movement quantity.

In order to increase the motor power, an ultra-intense magnetic field, H, can be applied to the water chamber's left side, making H / > E / In addition, it is seen that the rotation direction of the rotor can be inverted, by turning off the source A


Fig. 5.1 - Gravitational Motor

FRAN DE AQUINO 103

and turning on the source B. In this case, the water molecules at the right of the motor will be repealed by the Earth, contrarily to those at the left side.

An important feature of the gravitational motor is the fact that the impact of its utilization on the environment will be virtually neglectible. Gravitational motors are not air-pollutant as the conventional combustion engines. They will be silent and demand no special installations for their operation. On the other hand, its relatively simple construction will allow this type of engine to be used for the most different purposes. In the conversion of gravitational energy into electric power, for instance, said engine - connected to an electric generator - will make up a gravelectric unit. In opposition to the hydroelectric plants, whose operation demand rivers, the graveletric units are able to run at whatever part of the Earth surface, since its operation will depend just on the control of gravitational forces acting on the water volume, at the rotor chamber. It is obvious that the intensities of gravitational forces acting on the water molecules will depend on the motor's relative position, i.e., its position in relation to the distribution of masses throughout the Universe. Consequently, and in order to achieve a better performance, the gravitational motors must be close to relatively massive celestial bodies, such as planets,


for instance. At Earth surface, a gravitational motor might have a considerable power available, able to supply our energetic needs.

Another important utilization of the gravitation electromagnetic control for the energy conversion, can be found in a nuclear fusion gravitational process.

Said process is a simple one, basically consisting in intensifying the gravitational forces acting between atomic nuclei, so that their intensities surpass the intensities of electrostatic repulsive force between them. The atomic nuclei, then, get close to each other, in a way to allow the action of strong forces, so causing the nuclear fusion.

Let us consider, for example, a given amount of hydrogen atoms, for which we reduce significantly the respective value of (by means of the electromagnetic reversion process). If, then, an extra-intense magnetic field H is applied to the system, so that the ratio H/ becomes very greater than 3.3 x 104, one verifies, according to equation (1.62), that the gravitational attracting forces between the hydrogen atoms nuclei (for E = E' = 0) are given by

(5.01)

FRAN DE AQUINO 105

By comparing the intensities of said forces with the intensities of electrostatic repulsive forces between said nucleus, as given by

(5.02)

it is seen that, under said circumstances, the hydrogen atoms will be subject to strong gravitational attraction, and such reactions as those of the type

are able to accur. In this process, where the gravitational energy is used to make the nuclei to unite and react, independently from the electrostatic respulsion, the need of thermal energy (high temperatures) is obviously eliminated, in order to have the reactions processed. It is, therefore, a process where cold fusion is achieved, which, in the practice, might become relevant for energy production.

It is also important to observe that the gravitational attracting forces between hydrogen atoms can be


intensified not only due to the action of magnetic fields, but because of electric fields as well. In this case, as easily verified, the attracting gravitational force expression (for H = H' = 0) is similar to equation (5.01), i.e.,

(5.07)

for E/ 3.3 x 104, the nuclear fusion is likewise

caused. We have seen in chapter I of this book that some atoms

of a given body could have their E0, H0 considerably reduced by the action of electromagnetic fields of the electromagnetic spectrum radiations of the substance, contained in the thermal radiation. This way, in a given volume of hydrogen, for instance, atoms with significantly reduced are able to occur. In order to evaluate the magnitude of for hydrogen atom, we must at first calculate the value of k = moa / m0x =

As we know,

(5.08) and

(5.09)

FRAN DE AQUINO 107

so that, in case of hydrogen atom, we have k = 3.5 x 107. Now, by means of the equation (1.68), the value of can be reached, i.e.,

(5.10)

Thus, if the value of E0 for these atoms is reduced to such a level that < 1010V/m (see chapter IV), as a result of the electromagnetic reversion process (herein determined through the thermal radiation), then it is easy to verify (equation 5.07) that the gravitational fusion of hydrogen atoms can occur, if they are within a region wherein the geometric media of volumetric densities of electromagnetic energy, W, is such that E > 1014V/m.

A favorable situation for this to occur is when two hydrogen atoms are so close to each other that the distance between them is similar to their electrons' radii orbits (fig. 5.2-a). Under these circumstances, the geometric media of the volumetric densities of external electromagnetic energy, as caused reciprocally within each atom by the electric fields of electrons, is such that E ~ 1015V/m.

Recent experimental results confirm our forecast that, under said situation, the fusion of nuclei might occur by the gravitational process of nuclear fusion. From early this year (1989), reactions of nuclear fusion


have been detected between deuterium nuclei placed within paladium. In this process, when an atom of deuterium displaces towards the octaedrical site of the other in the paladium crystalline structure (with all the octaedrical sites being occupied), a situation results, where the distance between the deuterium atoms is sufficiently small (fig. 5.2-b). It is then created, by the tensioning resulting from the presence of high deuterium contents locally concentrated within the paladium structure, a favourable situation for the gravitational fusion of the deuterium atoms. However, for occur the fusion it is also necessary that said atoms have been reached by critical frequency radiation from the deuterium electromagnetic spectrum, contained in the thermal radiation and therefore, being with their reduced to values of nearly 109 V/m. Finally, it is important to point out that, through the gravitational process of nuclear fusion, not only the transmutation of light chemical elements might be produced, but also that of high atomic mass elements. That is because, in case of high atomic mass (although the nuclear electrostatic repulsion is higher), the inertial masses of nuclei will be also higher and, therefore, the attracting gravitational forces between them will be higher. In addition, of course, it is always possible to increase the attracting gravitational force

FRAN DE AQUINO 109

Fig, 5.2 - (a) A favorable situation to gravitational fusion of hydrogen nuclei. (b) Cubic layout of paladium atoms (larger circles) and the localization of deuterium atoms (smaller circles), in a situation where these latter occupy all the octaedrical sites. If a deuterium atom displaces to the site of another one, a favorable situation for the gravitational fusion of nuclei occur.


by means of increasing the field Accordingly, in said process, either the transmutation of light elements or the heavy ones will have practically the same rate of difficulty.

VI. SUPERCONDUCTIVITY

The origin of superconductivity remained unknown for almost half a century after it had been discovered by Kamerlingh Onnes. Only in 1957, the physicists J. Bardeen, L. N. Cooper and T. Schrieffer, manage to formulate a theory for it. This theory which is called BCS, named after its authors is considered one of the most elegant theories of condensed matter physics; it explains all the effects observed so far and allows us to understand the origin of this phenomenon.

Besides explaining the origin of superconductivity in the traditional substances, BCS' theory shows the behavioral differences seen in the electrons of superconductors and on those of the common metals.

While in common metals the electrons form a gas (Quantum Gas) in the superconductor materials they join together in pairs (Cooper's pairs). However, the quantum character of the electrons make the superconductor state to become more than just a gas in pairs. The laws of quantum physics determines amazing con-sequences like, for instance; all Cooper's pairs must move at the same velocity, incurring, therefore, in the important conclusion that the superconductor state is a coherent one, in which all pairs travel at the same velocity.

In the metal conductors, the erratic trajectory of the electrons obey one restriction only and that is: the


Pauli's Exclusion Principle, which does not allow more than two electrons to share identical states.

In a superconductor with electrical current the pairs of electrons can occupy the same quantum state, being not subject, therefore, to the exclusion principle, which applies to single electrons. To detain the current, Cooper's pairs can be destroyed getting back, then, to the normal state.

As far as Cooper's pairs formation is concerned the BCS' theory shows that, in certain circumstances, attracting interaction between electrons may occur. This interaction is mediatted by the displacement of the ion crystalline structure when a electron passe through. Such forces are, however, very weak and a temperature of a few degrees can destroy the pairs.

In the case of ceramics superconductors it was verified, recently, that similar state to that proposed by BCS' theory occurs, except that the atracting interaction has a different origin, i.e., has been demonstrated that interaction of magnetic origin or those of transference of charge between ions could originate in these complex materials stronger attracting interactions than those caused by the displacement of the ions, in the crystalline structure.

From all the preceding and considering the Electromagnetic-Gravitational Field Theory it is easy

FRAN DE AQUINO 115

to see that we can utilize the electromagnetic control of the

gravitational interaction to intensify the gravitational forces

between the electrons, so that the intensities of these forces

surpass the intensities of the eletrostatic repulsion forces between

them, making it possible the Cooper's pairs formation.

If a substance has an atomic structure in such way that in

each of its atoms, the electron furthest from the nucleus is

suficiently near (r < 10-12m) of the most external electron of the

neighboring atom (fig. 6.1), the electric field of each one of these

electrons inside the other will have intensity E = >

1015V/m. In these if the value of Eoa is in the order of 1014 V/m,

as it occurs to most of the monoatomic solids (see equation 1.72)

and, if by the electromagnetic reversion process it is reduced to a

value in the order of 109 V/m then, the ratio E/Eoa will be, as a

result, greater than 105. On the other hand, according to the

equation (1.62) we can see that gravitational atraction forces

(atomics) between the two electrons (for H = H' = 0) will be

given by.

(6.01)

So, in order for the gravitational forces intensity be greater than

the electrostatic repulsion forces we must


have

(6.02)

Therefore we can conclude that in the conditions men-sioned here the electrons can be subject of gravitational atraction strong enough for them to bound together forming Cooper's pairs.

To stop the electric current we can destroy the Cooper's pairs by turning off the extra high frequency electromagnetic field used in the electromagnetic reversion process, to reduce Eoa. Once this is done, the value of Eoa returns to its normal value and the gravitational forces between the electrons will become very small.

Electromagnetic field of extra-high frequencies, necessaries in the electromagnetic reversion process, may be produced by Josephson Junctions that, as we know, consist in two superconductors separated by a dieletric. When a difference of potential V is applied to the superconductors, electrons tunneling through the dieletric establish a alternate supercurrent whose frequency is function of V and, may reach values in the order of 1012 Hz.

To produce the two superconductors of a Josephson Junction we may follow the tradictional way utilizing a superconductor material of low temperature such as a

FRAN DE AQUINO 117

Fig. 6.1 - Cubic disposition of atoms of a substance capable of becoming superconductor by the gravitational process of Cooper's pairs formation.


Niobio-Titanium alloy (which requires a liquid helium cooling system) or then, search for a type of material that would become superconductor in higher temperatures. As the supercondutivity gravitational process described in this chapter also requires electromagnetic fields with extra-high frequencies, as we have already seen, we verify that the utilization of the above mentioned process in the production of the superconductor for Josephson Junctions will be possible only if there would exist a specific substance (with atomic structure especificated in the fig. 6.1) that would become a superconductor under the effect of an electromagnetic field of smaller frequency, which may be produced from conventional electronic keying (up to 1010 Hz.).

In this case, it will be possible then, to produce, by means of superconductivity gravitational process the superconductors of the Josephson Junctions and then, produce oscillating fields with greater frequencies, and by this way making possible not only the gravitation control, by means of electromagnetic reversion process, but also make other substances superconductors.

VII. EXPERIMENTAL

In this chapter we will present the design of seven experimental set-ups which can be carried out in order to verify fundamental phenomena foreseen by the Gravitational Electromagnetic Field Theory.

When we devised such experimental set-ups, our intention was only to facilitate the work of the reader interested in the experimental verification of said phe-nomena. All experiments proposed herein are relatively simple and, in our opinion, will be sufficient for the experimental corroboration of the theory.

The necessary equipament and the experimental layouts for each experiment are generally quite traditional and known by all those familiar with Experimental Physics.

To build the experimental set-ups, the following equipament will be necessary:

- An ± 800V, lMHz/100GHz AC source. - A 1G/100 KG magnetometer. - A neutron and gamma ray detector. - A digital ohmmeter, sensitive to 1 - A 0/200V DC power supply. - An aerometer, 0-50 m/s. - A thermometer, 0-120°C. - A centrifugal water pump (1 1/2"). - Two dynamometers (as illustrated). - Two volumetric flasks (glass balloons).


- One glass tube ( = 38mm) sealed at one end.

Experiment 1 - Superconductivity Gravitational Process

In order to experimentally verify the superconductivity gravitational process explained in Chapter VI herein, it is necessary to discover a substance whose cubic arrangement of its atoms is analogous to that shown in Figure 6.1, Chapter VI.

A substance with this characteristic is germanium. Thus, this may be the first of the substances to be experimentally tested.

Method - A germanium rod must be subjected to an oscillating electric field with a frequency equal to the critical frequency of the electromagnetic spectrum of germanium, (Ge). Thus, by means of the electromagnetic reversion process, one is able to reduce the value of Eo for germanium, making it much smaller than the intensity of electric field E reciprocally determined in the interior of the outer electrons. One thus strongly intensifies the gravitational attraction between said electrons and they may join each other to form Cooper's pairs. When this takes place, germanium must become superconductive and then an ohm-meter connected to it (set-up 1) must indicate a null

FRAN DE AQUINO 123

SET-UP 1


resistance. Another form of ascertaining the supercon-ductive state is to place a magnet on the germanium rod and observe its flotation (Meissner's effect).

Set-up 1. - In this case the experimental set-up is extremely simple. The substance to be tested must be placed on an insulating base and the leads of the high-frequency voltage source must be positioned very close to the ends of the substance being tested.

Experiment 2 - Production of an ultra-intense magnetic field

Once the substance capable of becoming supercon-ductive through a superconductivity gravitational process is discovered, one may then build a ring with this substance and, from a conventional inductor, induce an electromotive force on the superconductive ring, thus giving rise to a supercurrent which, in turn, will produce an ultra-intense magnetic field.

Method - The ring must be positioned between the ends of the leads from the high-frequency voltage source, as shown in set-up 2. Thus, it becomes superconductive when the oscillating field is activated, returning to its normal state when the oscillating field is deactivated.

One must position the end of the magnetometer probe one meter away from the center of the ring

FRAN DE AQUINO 125

(vertical direction). The objective here is to measure intensity H of the magnetic field produced by the ring at that distance and, from this value, to calculate the magnitude of the field in the center of the ring (H0) through the known expression H = (r/d)3H0, where r is the ring radius and d the distance measured on the ring axis to the point being considered (in this case, d=l m).

Set-up 2 - The conventional inductor must be approximately 10 cm from the leads of the high-frequency voltage source to prevent the electric field lines of the oscillating field from deviating towards it, which would impair the concentration through the ring. On the other hand, as far as its location is concerned, it must have its center aligned with the superconductive ring. Another important aspect to be observed is the placement of the leads from the high-frequency voltage source inside a dielectric material conduit, to prevent the oscillating field lines (in the case of a metallic conduit) from dispersing away from the region where their concentration is necessary. Regarding the placement of the magnetometer probe, one must make sure that it does not contain ferromagnetic substances (which would be strongly attracted by the superfield). The probe must be fixed to a dieletric stand void of parts made of ferromagnetic material. Generally


SET-UP 2

FRAN DE AQUINO 127

speaking, one must remove from the experimental region any parts made of ferromagnetic material in order to avoid the action of the superfield on them.

Experiment 3 - Gravitational Interaction Control

The objective of this experiment is to verify the electromagnetic process of control the gravitational interaction by testing the theoretical assumptions.

Method - In this experiment, we will subject several substances (for which the critical frequencies of their electromagnetic spectra have already been determined) to oscillating fields with a frequency equal to the critical frequency of the substance, simultaneously subjecting them to an ultra-intense magnetic field. Thus, we will be able to verify the accuracy of the new expressions for the gravitational force deducted from Chapter I herein. We will also verify in this experiment the levitation principle proposed in Chapter IV. For this purpose, we must simply deactivate superfield H and subject a given volume of water to the action of an oscillating electric field whose frequency is equal to the critical frequency of water.


SET-UP 3

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Since most substances must certainly have a critical frequency above 100 GHz, we selected Josephson junctions to produce oscillating fields with higher frequencies. It is noteworthy observing that the superconductors of Josephson junctions may be produced by the superconductivity gravitational process.

Set-up 3 - The experimental set-up in this case is similar to the previous one, except for the addition of the device for the Josephson junctions and the device containing the test body and the dynamometer.

Experiment 4 - Nuclear Fusion Gravitational Process

In Chapter V herein we saw the nuclear fusion grav-itational process. The process is simple and basically consists in intensifying the gravitational forces acting between the atomic nuclei so that their intensities exceed the intensities of the electrostatic repulsive forces between them. The nuclei will then get sufficiently close and nuclear fusion can occur.

In the specific case of hydrogen atoms, as already shown, the necessary condition for the fusion to occur is that H/HOH > 3.3 x 104. That is, EOH must be reduced by the electromagnetic reversion process whereas the magnetic field H applied must be made sufficiently intense.


SET-UP 4

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Method - Considering the quantity of energy released in nuclear fusion reactions, we see that, in order for the total quantity of energy released during the unit of time (< 104J/s) not to be very large, which would make the experiment unfeasible, fusion must occur in very small volumes of hydrogen, something around 10-10m3/s. Thus, we have devised an experimental system where by very small hydrogen bubbles formed in a volume of water rise to a certain region where fusion will take place (fusion zone). Thus, besides controlling the volume of hydrogen, we may easily evaluate the rate of energy released by heating the water. On the other hand, we must also have a system to detect neutrons and gamma rays, for as we know, reactions of this kind are characterized not only by a high production of heat but also by the emission of neutrons and gamma rays.

Set-up 4 - Similar to the preceding one, except for the device containing the test body and the dynamometer, and the placement of a glass cylindrical container with water through the superconductive ring. The lower portion of this container is fitted with the hydrogen inlet. In the upper portion we conveniently position a thermometer and the gas outlet. The neutron and gamma ray detector must obviously be placed close to the fusion zone.


Experiment 5 - Principle of artificial gravity in spacecrafts

The production of artificial gravity inside a spacecraft in order to attract the crew members to the floor of the spacecraft is another important phenomenon of this theory. Said gravity is obtained by intensifying the gravitational attraction between the molecules of water in the human body and those purportedly placed in a water reservoir below the spacecraft floor. The phenomenon will be observed here by intensifying the gravitational attraction forces between the two volumes of water contained in two glass balloons fastened to dynamometers, as shown in set-up 5.

Method - A Josephson junction produces an oscillating electric field with a frequency equal to the critical frequency of water. The water molecules close to said junction have their Eo reduced, which then become much smaller than the electric field E ~ 109 V/m arising from the permanent electric dipole of the water molecules. When E4/ 1, the gravitational force between the water molecules is attractive (equation 1.63), with an intensity of F ~ (E/Eo)8Gmm'/r2.

Set-up 5 - Two glass balloons containing water are rigidly fastened to two dynamometers which, in turn, are fastened to the system's structure. A Josephson

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SET-UP 5


junction placed close to them is activated to produce the oscillating field with frequency

Experiment 6 - Control of gravity on atmospheric air (atmospheric propulsion principle)

According to Chapter III herein, if an ultra-intense magnetic field is activated in a certain region of the atmosphere and if we simultaneously apply to this region oscillating fields of frequencies equal to the critical frequencies of the gases which make up the air, we will see that relationships H/H0 for the air molecules in this region may become much greater than 1. Consequently, according to equation (1.63), the gravitational force between the Earth and the air in this region will become strongly repulsive.

Method - Two Josephson junctions simultaneously produce oscillating fields of frequencies respectively equal to the critical frequencies of nitrogen and oxygen (for, as we know, the average composition of air in the trophosphere is 78% nitrogen and 21% oxygen). When we activate the ultra-intense magnetic field H, the relationships H/H0 for the molecules of such gases will become much greater than 1, thus causing them to strongly accelerate inside the hard PVC tube placed through the superconductive ring. A suitably placed aerometer measures the velocity of air inside the tube.

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SET-UP 6


Set-up 6 - Similar to that of experiment 2, except for the addition of the Josephson junctions and the PVC tube with the aerometer.

Experiment 7 - Gravitational Motor Principle

When an oscillating field of frequency equal to the critical frequency of water makes smaller than E (because of the permanent electric dipoles), the gravitational forces between the Earth and the local molecules of water become repulsive, as seen above. If these molecules are in a sealed tubular circuit, a water flow is established in the piping, which can drive a turbine connected to the circuit.

Method - With the application of an oscillating field with frequency equal to the critical frequency of water, we will then have < E for the water contained in the piping, in the region where the oscillating field actuates. As a result, a water flow is established in the circuit, with a velocity which can be intensified by the action of an ultra-intense field H, when we make H/ E/ .

Set-up 7 - Also similar to that in experiment 2, except for the addition of a Josephson junction and a closed tubular circuit containing a centrifugal water pump to act as a turbine.

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SET-UP 7

aquino - gravitational-electromagnetic field theory (1992)

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