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Takaaki Musha ; Mario.J.Pinheiro (Correspondence)

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Published at: http://www.ijsciences.com/pub/issue/2018-03/

DOI: 10.18483/ijSci.1562; Online ISSN: 2305-3925; Print ISSN: 2410-4477

General Relativistic Gravity Machine using

Electromagneto-Torsion Field

Takaaki Musha1, Mario J.Pinheiro2

1Advanced Sci.-Tech. Research Organization, Yokohama, Japan

2Dept. of Physics, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal

Abstract: Some field propulsion systems are based on the solution of General Relativity Theory and are related to

the connection between gravity and electromagnetic field. For example, Robert Forward proposed a gravity

machine working according to the Einstein’s General Relativity Theory, which requires ultra dense matter with the

density of a dwarf star to produce useful thrust, but the proposed theoretical scheme cannot be realized by

conventional technologies. The authors propose several concepts of a gravity machine utilizing an intense

electromagnetic field that produces sufficient thrust to propel the spaceship, in accordance with Einstein’s General

Relativity Theory.

1. Introduction

A breakthrough propulsion method has been required

for the purposes of interplanetary and interstellar

travel. Instead of conventional chemical propulsion

systems, field propulsion systems, which are based

on the General Relativity Theory, have been

proposed by many researchers. Some of them are

based on solutions of the General Relativity Theory

and are related to a connection between gravity and

electromagnetic field. The Unified Field Theory on

the connection between gravity and electromagnetic

field was obscure until the present time.

On the other hand, Robert L. Forward described the

theoretical generation of dipole gravitational fields by

accelerating a super-dense fluid through pipes wound

around a torus. Such techniques, though theoretically

sound, have been far beyond the reach of current

technology [1-8]. In his gravity machine, a mass flow

through a pipe wound around a torus produces a

co-gravitational field in a torus. If the mass flow is

accelerated, the co-gravitational field increases with

time and a dipole gravitational field is created. If the

pipe is filled with a massive liquid and this liquid is

moved back and forth in the pipe rapidly enough,

then an alternating push-pull gravity field will be

generated at the center of the ring. If the machine has

the appropriate scale, the liquid is dense enough and

moves fast enough, we have a gravity catapult that

could launch and retrieve spaceships by using its

gravity repulsion and attraction. An appropriate

configuration should have the form of a ring of

ultra-dense matter (the density of a dwarf star) and

using this a flying body could be expelled out the

other side of the hole with a greatly increased

velocity. But this system is far beyond the

conventional technologies and so the authors

proposed a system which generates a thrust by an

intense electromagnetic field inside a torus instead of

an ultra-dense material. This electromagnetic

method is in accordance with Einstein’s general

relativity theory.

2 Forward’s Gravity Machine

It is known that there is an analogical relation

between electromagnetic field and gravitational field

documented in research papers by Harris and

Braginsky [9,10] and shown as follows.

A particle mass

m

moving in a gravitational and

electromagnetic field follows its path according to the

equation of motion

where

e

is the charge of a mass m,

2/)(

gggg

are

Christoffel symbols of the second kind and

F

is

the electromagnetic field tensor. The Einstein’s field

equation of gravitation is given by

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From which, Harris obtain equations for the case

when the particle is slowly moving compared to the

speed of light and the gravitational field is

sufficiently weak so that nonlinear terms in Einstein’s

field equations can be neglected.Harris [9] obtained

the following set of magnetic-type gravity equations

where

G

is the gravitational constant,

g

is the

gravitational field,

K

is the co-gravitational field

(or gravito-magnetic field),

is the mass density,

and

is the scalar potential of electromagnetic

field. One of the most remarkable attribute of the

general theory of relativity is to predict the existence

of gravitational effects analogous to the magnetic

effects of electromagnetism.

By using the analogy to electromagnetism, the

so-called gravitomagnetic gravitational field, having

momentum of moving bodies as its source, Forward

has shown in his paper that it is possible to build a

machine to create a gravitational field using a system

of accelerated masses [6]. To bypass the complex

procedure of handling tensor algebra, lengthy and not

always leading to physically observable effects,

Forward proposed a set of analogues physical

quantities from where he obtained useful

connections. As it is well-known, a time varying

magnetic field creates a dipole field, and the value of

the electric field at the center of the torus is

where

R

is the radius of the torus,

r

is the radius

of one of the loops of wire wound around it and

N

is the total number of turns.

If we replace the wires with pipes carrying a massive

liquid, then the known analogy between the

electromagnetic and gravitational field can be

applied. Then the equivalent gravitational quantities

can be given by

where

g

is the gravitational field generated by the

total accelerated mass, as shown in Fig. 1.

Figure.1 Generator of a dipole gravitational field

Supposing that the gravitational permeability has the

value

26

1073.3

kgm/

, we have

ag 10

10

(

a

: amount of acceleration) at the

center of the torus, as shown in Fig.5. This is for

the case when the mass of the liquid through the

pipes has the density of a dwarf star, the pipes are as

wide as a football field and are wound around a torus

with kilometer dimensions, according to Forward,

which is far from present engineering capabilities.

Figure.2 Gravitational machine according to

Forward’s idea

By utilizing this gravitational machine, constant

upward gravitational field can be generated which

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17

can be used as a gravitational catapult capable of

pushing a body, as shown within the center of the

torus, in Fig.2.

Instead of this gravity machine, which cannot

actually be built, another gravity machine utilizing an

intense electromagnetic field can be considered.

3. Gravitational Machine by utilizing the

Electromagneto-Torsion Field

As early as 1951, P.A.M. Dirac published two papers

where he pointed out that we should take into account

quantum fluctuations in the flow of the aether

[12,13]. Inspired by the Dirac ideas, K.P. Sinha, C.

Sivaram and E.C.G. Sudarshan published in 1975 a

series of papers that suggested a new model for the

aether, in which it is a superfluid state of fermion and

anti-fermion pairs, describable by a macroscopic

wave function [14-16]. In their papers, they decided

to treat the superfluid as relativistic matter - by

putting it into the stress-energy tensor of the Einstein

field equations. This allows us to take an important

step – allowing us to describe relativistic gravity as

one of the small fluctuations of the superfluid

vacuum as well. Based on their ideas, we can

consider the possibility of a space propulsion

utilizing the co-gravitational field from the standpoint

of hydrodynamics. Such a term implies various fluid

dynamics which includes linear flow, separated flow

as well as a creation of vortices.

3.1 Theory of the Electromagneto-Toroidal

Structure

Among the various processes used in the natural

world, there is a common principle that relies on the

production of vortices by a material structure [17]

(e.g., wings, paddles, fins). Most probably this fact is

the realization of a general law of nature, to which is

associated we may call a local “twist” of the fluid,

firstly investigated by Viktor Schauberger and

Professor Von Karman with his experiments with the

flow for some distance behind a plate showing a

regular arrangement of vortex lines, the so called

“vortex street”, that remain behind the plate and

advancing at a more slow pace than the plate itself.

The observation of these facts make us to turn our

attention to the problem of the electrodynamic

acceleration of fluids by reaction against the physical

vacuum [18-23], or plasma medium, or any other

kind of fluid [17].

Our purpose in this section is to show that Magnus

and Abraham forces are a mathematical

representation of the same type of structure in the

fabric of space-time: a vortex capable of propelling

material bodies.

To make the idea of this underlying principle so

much simple, we may start to recall that, in the

framework of electrodynamics the ponderomotive

force acting on the material of an electromagnetic

propulsion device is provided by Abraham's force

density,

A

f

, a term which represents the force

communicated to a material structure (e.g., Refs.

[20,22-29]). It is also known that, in the framework

of hydrodynamics, the three-dimensional Magnus

force is given by [28]:

Mxy v vo z

f V V k

(10)

where

0v

V

is the velocity of the vortex center of

mass,

v

V

is the stream velocity,

is the fluid

density, and

z

k

is a vector oriented along the z

direction with magnitude equal to the circulation. We

may notice now that the “magnetic current force”

created by the magnetic charges that “flow” when a

magnetic field changes, is given by

00m

f E B H

(see discussion of the

concept in Ref. [27]). This is the “Abraham term”

appearing in the Abraham force density

A

f

, which

differs from the Minkowski force density by means

of the expression (see also Refs. [24,29] for further

clarification):

21

rr

AM

f f E H

tc

(11)

The last term of Eq.11 corresponds to the

vacuum-interactance, a concept introduced in Ref.

[30], and meaning a process of pushing material

bodies through interaction with the physical vacuum,

which is associated with the momentum as follows:

21

Vrr

g E H

c

(12)

Also, notice that the magnetic dipole at rest in an

external (and homogeneous) electric field

E

has

momentum given by

2

1

g M E

c

(13)

with

M

denoting the density of magnetic moment.

When the magnetism of the dipole changes, then the

density of force is given by the last term of Eq.(11).

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Surprisingly, it can be shown that the Magnus force

is analogous to the Abraham's force, as given by

Eq.11. This similarity between vast areas of the

physical theory, undoubtedly constitutes a successful

example of the unity of physics, and illuminates the

physical reality hidden inside the physical vacuum.

In fact, in a previous paper on “fluidic

electrodynamics” [22], we introduced a new

approach to the realm of the electromagnetic fields,

in terms of the potential functions (

,A

) and their

material derivative, as they emerge in quantum

mechanics as more fundamental quantities than the

(

,EB

) fields, predicting certain quantum

interference effects, like the Aharonov-Bohm (AB)

effect and the single-leg electron interferometer effect,

known as the Josephson effect.

The new methodology offered by the “fluidic

electrodynamics” approach is a helpful guide to

propulsion and energy engineering, avoiding more

complicated procedures. There is fundamental

reasons to attribute to the vector potential

A

the

property of the velocity of a “fluid” embedded in the

physical vacuum. To describe the inner nature of a so

pervasive and evasive medium, be it a mechanical

medium whose deformations correspond to the

electromagnetic fields, or a locally preferred state of

rest, is beyond our purpose now. Possibly this issue is

related to the Graham and Lahoz experimental

findings that “something in motion” is not duly took

into account in our present theories of the physical

universe. To describe the electromagnetic field it is

necessary to define the electric field

,E r t

, the

magnetic field

,B r t

; charge density

,rt

; and

the charge velocity

,v r t

. However, it is more

advantageous to associate the set of Maxwell's

equations with the electromagnetic potentials

,A r t

and

,rt

through the relationships:

,dA

E r t dt

, (14)

and as well

BA

.

Note that we introduced into Eq.14 the convective

derivative

d dt t v

, instead of the

Maxwell-Einstein operator

t

(see, Ref. [22] and

references therein).

Table 1 gives the correspondence of field variables in

electromagnetism and hydrodynamics. Notice, for

example, that

B

is the analogue to the angular

velocity instead of the vorticity.

Table 1. Correspondence of field variables in electromagnetism and hydrodynamics

ELECTROMAGNETISM

HUDRODYNAMICS

0

q

Kraftquelle-q

Permeability of the vacuum:

0

Mass density:

Electric potential:

Massic entalphy:

Scalar potential:

Potential velocity:

Vector potential:

A

Velocity (or hydrodynamic momentum):

u

Electric field:

E

Lamb vector:

l

Magnetic field:

B

Angular velocity:

2

,U r t

2

,

, , , ,

2

rt

p r t r t r t u r t

Electric current: I

Circulation:

Electromotiveforce:

A

E v B v A

t

Hydromotiveforce:

2

2

Hu p u

Eu

t

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Figure 3. An expanding toroidal disk.

The analogy suggests a new process of propulsion

using the Abraham's force to accelerate a plasma jet.

As already referred above, in the natural world, fishes

and birds propel themselves through a liquid medium

by using their limbs to transfer momentum to the

liquid via vortex structures. Their basic mechanism is

to form a vortex structure (e.g.: Ref. [21]). Hence,

next we will look at the mechanism that generates the

Magnus force. First of all, we may remark that it is

necessary to consume energy in order to

progressively enlarge the vortex with a characteristic

radial velocity (see Fig. 3). The toroidal structure is a

vortex ring formed by a closed vortex tube of a given

diameter (let us say

). As is well-known in fluid

dynamics, this structure is very stable. The duty

mechanism that provides this radial velocity (inward

or outward from the central axis) may have different

sources. One example is gas falling into stars, in the

case of polar jets; another is the sharp increase of

electric current generated by the growing magnetic

field of the plasma. With this kind of mechanism, we

can associate a given circulation

'

(due eventually to

an induced field

'

). The falling (or expelled) stream

of particles, most probably will acquire a curved

trajectory and angular momentum, all effects

concurring to the formation of the ring with

circulation

(and vorticity

). At the core of the

vortex structure, the resultant force is aligned along

the Z axis. Newton's third law predicts a mechanical

reaction force

mec

F

, which can propel a device (or a

magnetized fluid). Therefore, we must have (in

Figure 3, it represents the mechanical force pointing

downward). This is what must happens with a fluid.

But what could be the analogue in the physical

vacuum?

It can be shown that there is an electrodynamical

counterpart – the Abraham’s force - which plays an

analogous in the formation of what we will call the

“electromagnetoroid”. Let us now explore the

concept in more detail. Firstly, replace the

“hydrodynamic magnetization” term in Eq.13 with

the constitutive relationship

M

, where

represents a given property of the medium (a

dimensionless constant). The outlined mapping

shown in Table 1 gives us the analogous

hydrodynamic force (by unit of length):

2

H

m

dF l dv

ct

(15)

Here,

is the mass density and

dv

is the

differential volume element. Eq.(15) represents the

interaction of physical entities fed by different energy

sources: the circulation is associated with motion

around the vortex-ring, while the Lamb vector is

associated with the increasing vortex radius. The

axial vector

spirals about the azimuthal direction,

forming a closed circular loop around the main axis.

It is interesting to note that Eq.(15) points to the

existence of dual forces: one dependent on the fluid

angular acceleration (or time-dependent magnetic

force), the other dependent on the Lamb-vector time

dependency (or time-dependent electric field).

Let us use the cylindrical geometry, shown in Fig.7,

considering

u

and

rr

l l u

. Then, the total

force resulting from this geometry is given by the

following expression:

2'

Hr

mz

S

l

F u drdzrd

ct

(16)

We can arrange terms to obtain

'

'

H

mS

F dzrd dr

(17)

where we inserted the hydrodynamic form of

Ampère’s equation:

2'

lc

t

(18)

'

represents a different (axial) vector (than

). In

fact, it is the vorticity associated with the increasing

Lamb vector. The vorticity vector is oriented along

the radial axis and

c

is a characteristic speed of the

medium. Hence:

H

m

F dp dr

(19)

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However, we also have

''

r

dp v

. We

therefore obtain

''

H

m r r

F v dr v dr

(20)

The last integral of Eq.(34) is the circulation (by unit

of length). This result can be recast in the following

final form:

H

m

Fv

(21)

Eq.(21) shows that Abraham's force is the

electromagnetic analogue of Magnus's force in

hydrodynamics (by unit of length). Therefore, we

conclude that the Abraham's force represents a kind

of vortex structure formed in the physical vacuum.

The associated reaction force can propel a material

structure through space. From this general

mechanism (see, e.g., [28,29]), we can envisage the

engineering of novel mode of spaceship propulsion

based on generating electromagnetic vortices [30],

along with a new framework to develop high-current

accelerators and thermonuclear devices.

3.2 The Concept of Electromagneto-Toroidal

Gravity Machine

At first, we consider the gravitational theory for a

quasi-static field. Eq.(6) becomes

As the current of mass generated by the

electromagnetic field can be expressed as

BEcSJg 0

2

/

, where

S

is the

Poynting’s vector of electromagnetic field, we can

replace

g

J

by the electromagnetic momentum

BEJe 0

in Eq.(22). Then we have

From the equation

))/log(/( abrVE

, where

V

is the applied voltage, and

ba,

are the inner

and outer radii of the cylinder shown in Fig.4, we can

obtain[17]

if we suppose there is no field of co-gravitational

field.

Figure.4 Generation of

K

field by the

electromagnetic fields inside the tube structure

We consider the torus-shaped structure composed of

a co-axial condenser and coils curling around the

outer surface of the torus shown as follows:

Figure.5 Schematic diagram to generate an

impulsive electromagnetic field inside the Torus

A high intensity electromagnetic field can be

generated by the structure, as shown in Fig.5.

As shown in this figure, an impulsive strong

magnetic field is induced by an impulsive electric

current through the coils embedded in the dielectric

material under the intense electric field and a strong

co-gravitational field is generated.

Figure.6 Moving vortex ring in a fluid

As the co-gravitational field is similar in scope to a

vortex in fluid dynamics, as generated inside the

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torus shown in Fig.6, this torus-shaped bundle of

vortex lines can cause forward motion of the ring,

similar to the motion of a vortex within fluid

dynamics.

As the electrical toroidal device is a kind of fluid

accelerator, as shown in Ref. [18], acting on the

material device with a density of force given by

which is shown in Fig.7 with its resulting direction.

By corresponding electromagnetic and gravitational

symbols and a constant given by

gE

,

KB

and

G

4/1

0

, then it follows

Figure.7 The electromagnetic generated force,

analogous to the fluid dynamics

When we let

2

rg

(

r

; radius of the toroidal

structure,

: radial frequency of the spinning

structure), we have

If we assume to simplify a uniform magnetic

field,

constB

, we obtain the following order of

magnitude

where

v

is the speed of the rotating toroidal

structure. Therefore, from the above considerations,

we may conclude that there is the possibility to

generate a new gravitational field by applying

impulsive high electromagnetic field to the toroidal

device.

4. Numerical Calculation for the Rotating

Electromagneto- Toroidal Gravity Machine

If the considered gravity machine could be operating

with a velocity of the rotating toroidal structure to be

one percent of light speed, and considering the

parameters

mr 5

, B=100 Tesla,

1V

Giga volt,

and the duration of time for applying the impulsive

high voltage electric field be 1.0 pico second, we

have according to Eq.(29),

which is sufficiently large for thrusting a spacecraft.

Hence, it is considered possible to provide a design

that can allow the construction of an antigravity

machine as follows:

It is composed of a co-axial condenser whose surface

is overwound by the superconductor coil, which

generates a gravitational vortex around the

cylindrical body. Instead of Forward’s gravity

machine which utilizes the circulation of a

ultra-dense, superfluid through a spiral tubing array,

this system uses only a high intensity electromagnetic

field generated by the co-axial condenser and coils to

create a similar gravitational vortex.

Murad pointed out in his papers that Jefimenko’s

co-gravitational field is the elusive spin or torsion

field identified in Russian scientific literature [31,32].

This idea was first introduced by the French

mathematician Elie Cartan in 1913, then by Albert

Einstein aiming to a unified theory. Within the

framework of Cartan-Einstein theory, the existence of

these fields has been permitted. Scientists today are

recognizing that "spinning fields" really do exist. Just

as electromagnetic fields are caused by a charge and

gravitational fields are caused by weight, torsion

fields are created by any rotating objects (see also

[33,34]).

Figure.8 Rotating toroidal structure of the

propulsion system

Figure.8 shows the conceptual diagram of the gravity

machine designed to propel the spaceship. By pulsing

the electromagnetic field generated by the

superconducting coil, a strong co-gravitational field

can be generated inside the toroidal structure, as

illustrated in Fig.8. When this toroidal structure is

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rotating at very high speed around the vertical axis,

thrust can be generated to propel the spaceship.

5. CONCLUSION

In this work, some gravity machines, allowed within

Einstein’s general relativity theory, have been

presented. One design worked using ultra-dense fluid

matter, and another one utilizing an intense pulsing

electromagnetic field. Through numerical calculation

and quantitative discussion, the

electromagneto-toroidal propulsion system can

possibly produce sufficient thrust to propel a

spaceship, similar to Forward’s gravity machine.

However, from an engineering perspective, the

electromagneto-toroidal method seems to be far more

practical. With further research into such new

directions of space sciences, which are still nowadays

based on conventional physics, we may, in the future,

find a way to travel to the stars.

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