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General Relativistic Gravity Machine using Electromagneto-Torsion Field

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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.
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Takaaki Musha ; Mario.J.Pinheiro (Correspondence)
takaaki.mushya@gmail.com : mpinheiro@ist.utl.pt
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Author(s) retain the copyright of this article. Publication rights with Alkhaer Publications.
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 Einsteins 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,
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
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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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
BEcSJg0
2
/
, where
S
is the
Poyntings vector of electromagnetic field, we can
replace
g
J
by the electromagnetic momentum
BEJe0
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
Einsteins 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 Forwards 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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